POLAR COORDINATES

POLAR  COORDINATES 

Polar points are plotted using the polar coordinate plane with the line OX as initial line or polar axis, point 0 as the pole or origin and the distance of the point from O as the radius vector.
                           
The position of any point P in the plane is determined if the length of the line OP together with the angle that this line makes with OX are known, both the length and the angle being measured in a definite sense.





From the figure :
     r  = radius vector,  + if measured along the terminal side of Ө, 
                                  –  if measured in the opposite direction along the terminal side of Ө 
     Ө = polar angle
     OX = initial line or polar axis
     O = pole or origin

Polar Coordinate paper – it is where the polar points are plotted.
              ( to be illustrated on the board during lecture )

Plot the following points :

1.    ( 2, 30º )                6.  ( 3,  60º )  
2.    ( 4, 225º )              7.  ( 4,  – 315º )  
3.    ( – 6, –120º )         8.  ( – 3, –240º )
4.    ( – 4,  330º )          9.  ( 4, – 330º )
5.    ( 6, – 150º )          10. (– 6, 150º )  

Distance between two points in Polar Coordinates : by Cosine law

Conversion
A.    Polar to rectangular coordinates
         1)  x = r cos Ө
         2)  y = r sine Ө


B.    Rectangular to Polar coordinates
         1)  r = sqrt( x² + y² )
         2)  Ө = Arctan ( y/x )

Exercises :  Numbers colored red is an assignment to be passed on January 6 or 7, 2010.

1.    The point ( r , Ө ) is equidistant from ( 2 , 90º ) and (– 2 , 150º ). Express the statement into an algebraic expression.

2.    Show that the given points ( 2 , 45º ), ( sqrt( 2 ), 90º ) and ( – 2 , 135º ) are vertices of a right triangle and find its area.

3.    Convert to rectangular coordinate.
a)    ( 3 , 240º )
b)    ( 4 , 150º )
c)    (– 5 , 150º )
4.    Convert to polar coordinate
a)    ( 2 , –2 )
b)    ( – 1 , – sqrt ( 3 ) )
c)    ( – 3 , 3 ) 
5.    Find the distance between the following points.
a)    ( 3 , 240º )  and (– 5 , 150º )
b)    ( 4 , 150º ) and ( 2 , 45º )
c)    ( 2 , 90º ) and  ( – 2 , 135º )

PHYSICS E 101 Assignment ( Motion )

Physics E 101  Uniform  Motion  Assignment

1. Roy normally drives on a freeway from a city C to city A at an average speed of 90 km/hr and his trip took him 2 hours and 30 minutes. One day with heavy traffic, he slows down and drive the same distance at an average speed of 75 km/hr. How much longer does the trip take for Roy?

2. Two cyclists travel simultaneously towards each other from points 40 km apart. Cyclist A has a speed of 12 km/hr while cyclist B travels 4 km/hr slower than cyclist A. How many hours will they meet each other ? How far apart are they after 75 minutes?

3. A car is moving with an average speed of 72 km/hr. Determine (a) the total distance traveled by the car in 50 minutes, (b)the time needed to travel 90 000 m.

4. It is now 1:00 PM. At what time before 2:00 o’clock with the minute hand overtake the hour hand? At what time before 2:00 o’clock will the minute hand and the hour hand become perpendicular for the first time? At what time before 2:00 o’clock will the minute hand and the hour hand become perpendicular for the second time ?

5. Calculate your average speed in m/s and km/hr if you jog at 2.5 m/s for 10 minutes and then walk at 600 m for 400 seconds.

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HINTS for ANALYTIC GEOMETRY TRINAL EXAM

HINTS FOR TRINALS

1. Locate the point which is at a distance 4 from (7, 4) and  at a distance of sqrt(26) from (2, -1).

            Ans. (3, 4) ,  (7, 0)

2. Locate the point which is equidistant from (3, 8), (5, 2) and (-3, -4).

            Ans. (-2, 3)

3. Locate the point which is equidistant from (3, 1) and (-2, 2); also equidistant from (1, 2) and (3, 0).

            Ans.  (0, -1)

4. Show that the points (-2, 4), (3, -1) and (-1, -3) are the vertices of an isosceles triangle and find the area.

            Ans.  A = 15 sq u

5. A circle has center at (1, 2) and passes through (8, 3). Does this circle pass through (-4, -3)? Through (5, 8)? Through (0, 9)?

7. Show in two ways that the quadrilateral with vertices (0, -1), (1, 2), (-4, 7) and (-5, 4) is a parallelogram.

8. Show that the points (-1, -2), (5, 4) and (-3, 0) are vertices of a right triangle and find its area.

            Ans. 12 sq u

9. Locate the point which is equidistant from (-3, 0) and (1, 4 and at a distance 5 from (-1, 7).

            Ans. (-1, 2), (-6, 7)

10. Determine the angle from L1 along (4, 3),(6, -2) and L2 along (9, 5),(6, -2). 

            Ans. 135 degrees

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Language 102 Nihongo

  New words :
   1. kago – basket       10. donata  no – whose
   2. hako – box            11. okii – large, big
   3. mado – window     12. chisaii – small, tiny
   4. mizu – water          13. omoi – heavy
   5. kutsu – shoes        14. nimots’(nimotsu) – baggage, luggage
   6. ki – tree                15. kaban – bag, brief case, traveling bag 
   7. heya – room     16. ts’tsumi (tsutsumi)–a package,a bundle 
   8. ringo – apple     17. shobai – business, trade, profession
   9. mikan – orange    18. karui – light ( in weight ) 
                     
                          
  Lesson 3 :    PERSONAL PRONOUNS

   Singular form        Plural form
   1. watashi – I      watakushidomo/watashi tachi – we
   2. anata – you     anata tachi/anata gata – you
   3. kare – he      karera – they
      kanojo – she        kanojo tachi – they


   Possessive pronouns: Use no to show possession after the personal
                        pronouns

   watashi no – my     watashi tachi no – our
   anata no – your     anata tachi no/ anata gata no – your
   kare no – his     karera no – their
   kanojo no – her     kanojo tachi no – their

  Notes:

   1. “tachi” or “ra” means plural in number.
   2. “karera” is used when referring to a group composed
       of males and females. “karera” being the plural male
       form of “he” ( they ) naturally dominate and encompasses
       “kanojo” ( they for females ).


 Vocabulary words 

   hoteru – hotel               shumi – hobby      
   sekken – soap              zasshi – magazine      
   byooin – hospital              tomodachi – friend      
   kaisha – company, office      eiga – movie      
   tokei – watch              saifu – wallet      
   doa – door                  kuuraa – air conditioner  
   kuruma – car                  shimbun – newspaper 
   kabe – wall                   hankachi – handkerchief
   kaaten – curtain


  Examples :  “no”  used as possessive adjective

 1. Kore wa anata no sekken desu.     This is your soap.
 2. Are wa watashi no ie desu.         That is my house.
 3. Kore wa kare no kuruma desu.     This is his car.
 4. Kore wa Tanaka san no kaban desu.     This is Mr. Tanaka’s bag.
 5. Anata no shumi wa nan desu ka.     What is your hobby?


  “no”  used as descriptive adjective

 6. Kore wa Nihon no kuruma desu.     This is a Japanese car.
 7. Tani san wa eigo no sensei desu.     Mr. Tani is an English teacher.
 8. Are wa Amerika no eiga desu ka.     Is that an American movie ?

   
 Note :  The particle “no” placed between two nouns usually makes
         the first noun the modifier of the second noun. Thus,
         “watashi no tomodachi” means my friend. This no usually
         corresponds to “of” or ‘s.

   Anata no tomodachi – your friend.       
   Sato-san no kuruma – Mr. sato’s car
   Watashi tachi no shimbun – our newspaper
   watashi no tokei – my watch
   

 Common occupations

  kaikei-gakari – accountant      ginkoo-in – bank employee            
  ten-in – sales clerk               shachoo – company president
  eiyooshi – nutritionist           kaisha-in – company employee      
  gaikookan – diplomat                isha – doctor              
  gishi – engineer                ha-isha – dentist
  kangofu – nurse           taishikan-in – embassy employee   
  jaanarisuto – journalist       untenshu – driver              
  shufu – housewife               bengoshi – lawyer              
  iyayu – actress           ongakuka – musician
  danyu – actor           jimu-in – office worker/ clerk     
  kookanshu –operator(telephone)  gaka – painter          
  keikan – policeman           koomu-in – public servant
  bijinesuman – businessman       scholar – gakusha              
  gakusei – student               sakka – writer          
  hisho – secretary           kankoo gaido – tour guide
  gaadoman – security guard       uketsukegakari – receptionist    
  sensei / kyoshi – teacher       sojiin – cleaner (janitor)     
  keeji – detective           yosaichi – dressmaker
  sejyusi – pilot           syomin – merchant            
  jitsugyoka – businessman        roodoosha – worker/laborer    
  hooka – farmer           taiku – carpenter
  bobi – waiter           kasyu – singer            
  jugjoin – employee              gyohu – fisherman          
  romusya – laborer           bengoshi – lawyer
  syosetsuka – novelist       shimbunkisya – journalist        
  daijin – minister
  kikaiko – mechanic


Languages: 

  Go – means language. It  is used as a suffix in one’s country
       denoting his / her native language.

  Examples :
 
   Chuugokugo – Chinese language     Nihongo – Japanese language
   Firipingo – Filipino language          Eigo – English language
   Kankokugo – Korean language         Supeingo – Spanish language
   Doitsugo – German language         Indogo – Indian language
   Taigo – Thai language         Gaikokugo – Foreign language


   Expression to tell how one looks like :

    1. mitai desu – look (s)like  
    2. ni miemasen – do(es) not look a like


   Examples:
    1. Anata wa Nihonjin mitai desu.    You look like a Japanese.
    2. Anata wa Doitsujin ni miemasen.     You don’t look like a German.


 Basic grammar : 
    1. Anata wa Kato san desu ka.  Are you Mr. Kato ?
    2. Hai, soo desu.            Yes, I am.
    3. Kore wa saifu desu ka.       Is this a wallet ?
    4. Iie, chigaimasu.           No, it isn’t.
    5. Are wa sekken desu ka.        Is that a soap ?
    6. Hai, soo desu.           Yes, it is.
    7. Kore wa nan desu ka.        What is this ?
    8. Kore wa hon desu ka.       Is this a book 
    9. Iie, chigaimasu.           No, it isn’t.
   10. Kore isu desu ka.        Is this a chair ?
   11. Hai, soo desu.           Yes, it is.
   12. Are wa isu desu ka.        Is that a chair ?
   13. Iie, chigaimasu.        No, it isn’t.
   14. Kore wa mado desu ka.        Is this a window ?
   15. Iie, sore wa doa desu.       No, that is a door.


  Note :

   “Hai soo desu”, is use to affirm a statement said by
       the other party. This is used in reply only to a
       “be – verb”. For instance, an American is ask
       “Amerikajin desu ka.”  The American can affirm by
       answering “Hai, soo desu” or “Iie, chigaimasu” to
       deny the truth of a statement said by another
       person. Literally, “Iie, chigaimasu” means
       “No, its different”.


  Daily Expressions :
  1. Shitsurei shimasu./Sumimasen   Excuse me.
  2. Gomen nasai./Sumimasen deshita. I’m sorry.
  3. Ojama itaashimasu.         Sorry to disturb you.
  4. Ojama itashimashita.         Sorry to have disturbed you.
  5. Doozo ohaire kudasai.            Please come in. 
  6. Doozo okake kudasai.            Please sit down. 
  7. Arigatoo gozaimasu.           Thank you.
  8. Doo itashimashite. .           Don’t mention it.
  9. Chotto matte kudasai.         Wait a moment please.
  10. Koko de matte ite kudasai.   Wait here till I get back.
  11. Omatase itashimashita.         I am sorry to have kept you waiting.
  12. Sonomama omachi kudasai.     Hold your line please.
  13. Hanashichuu desu.          Line is busy.
  14. Sayoonara.                Good bye.  
  15. Oyasumi nasai.             Goodnight
  16. Itte mairimasu.             I’m going out  or  I’m leaving.
  17. Itte rasshai.            Good bye, have a nice time.
  18. Tadaima.                I am back.
  19. Okaeri nasai.            Welcome back.    

 NOTES :
 1. Shitsurei shimasu./Sumimasen – Excuse me.
            This is use to express an apology when you interrupt
        someone in a conversation. Also, when you want to excuse
        yourself from a gathering, you say this to the people who
        will stay behind as an apology for leaving ahead of them.
 
 2. Gomen nasai. / Sumimasen deshita – I’m sorry.
             This is use to express an apology when you ask for
        someone’s pardon for breaking his property or for stepping
        on his foot.  “Gomen nasai” is mostly used by children and
        women than “sumimasen deshita”.

 3. Ojama itaashimasu. – Sorry to disturb you.

 4.  Ojama itashimashita.    –   Sorry to have disturbed you.
            These two expressions are used when one is about
       to disturbed somebody upon entering his house. Before
       leaving another’s place, one says “ojama itashimashita” 
       which means  “I’m sorry to have disturbed you”. The
       difference between Excuse me ( shitsurei shimasu or
       sumimasen ) and I’m sorry ( Gomen nasai or sumimasen
       deshita):

     The difference between these two is that Excuse me
       ( shitsurei shimasu or sumimasen ) is normally said before
       the act or deed is done while I’m sorry ( Gomen nasai or
       sumimasen deshita ) is said after the act or deed has been
       accomplished.

   Excuse me is said when you cause the inconvenience or disturbance
       to another. For example you want to :  

        a. pass through between two people engaged in conversation.

     b. interrupt the conversation of someone else.
   
        c. get off the elevator and someone’s blocking the way out.

    d.  catch the attention of another.

    e.  reach for the dish across the table.

  I’m sorry is said when :
        a. you’ve done something wrong.
     b. you want to ask for pardon or express apology.

 5. Doozo ohaire kudasai. –  Please come in. 
              This is said when you greet a visitor at the entrance 
        of your house and you want to let him/ her in.

 6. Doozo okake kudasai.  – Please sit down. 
              You say this as a sign of courtesy when you invite
        another to sit down.

 7. Arigatoo gozaimasu.  – Thank you.
              This one of the most common expression of thanks.
        When speaking to equals, subordinates and intimate friends,
        “gozaimasu” is often omitted.      
       
 8. Doo itashimashite. – Don’t mention it.
               Literally means “why or how come”. The idea of the
         sentence is why you say such a thing ? ( when there no
         reason to say so). It corresponds to “Don’t mention it,
         Not at all, You are welcome, That’s alright , etc.”  
   
 9. Chotto matte kudasai. – Wait a moment please.
               This is said when you want someone to wait for you.
         This a more polite way of saying “shooshoo omachi kudasai.”

10. Koko de matte ite kudasai. –  Wait here till I get back.
               Literally, it means “please wait and stay here”. 
         This is said when you want to tell somebody to wait
         for you at a certain place while you go elsewhere.

11. Omatase itashimashita. – I am sorry to have kept you waiting.
                You will say this when you have made somebody wait 
          for you ( by being late or otherwise.)

12. Sonomama omachi kudasai. – Hold your line please.
                This used when talking on the telephone to tell
         the other party to wait for a while.

13. Hanashichuu desu.  – Line is busy.
                This also another telephone expression.

14. Sayoonara.  – Good bye.          

15.  Oyasumi nasai. –  Goodnight.
                This can be use when you say farewell to somebody
         who is about to leave.  As a daily expression, it can
         be use in the office, or in school when you leave that
         place and won’t meet one another until the next day. But
         if you leave from one place late in the evening, you’d
         better say “oyasumi nasai”. Sometimes the two expressions
         are used together as “Sayoonara,oyasumi nasai”.

16. Itte mairimasu. – I’m going out or I’m leaving. 

17. Itte rasshai. – Good bye, have a nice time.
                  This is addressed to someone left in the house,
          office, etc. The literal meaning is “ I’ll go out and
          come back here.”  The way to respond to this expression
          is to say “Itte rasshai.”  The literal meaning is “Go for
          a nice day (or business) and come back safely.

18. Tadaima. – I am back.               

19.  Okaeri nasai.  –  Welcome back.
            When you return from work or after having met some
        appointment, you say “Tadaima.  To those who were left
        behind. The response from them should be “okaeri nasai”
        whose literal meaning is “Welcome back”. 


           BASIC GRAMMAR :  Kono,  Sono  &  Ano

   Kono, Sono and Ano are pronouns which always stand immediately
       before nouns. They are never used alone.

   Kore, Sore and Are are usually followed by the particle “wa” 
       when use in a sentence while Kono, Sono and Ano are never
       followed by the particle “wa” when use in a sentence. 
       They are always followed by a noun.

   Examples ( Reibun ) :
       Kono kaban – this bag         Sono zasshi – that magazine
       Ano  hito – that person         Ano hoteru – that hotel


     Sentences ( Bunshoo ) :
      1. Kono pen wa watashi no desu.      This pen is mine.        
          Kore wa pen desu.          This is a pen.

      2. Sono saifu wa watashi no desu.    That wallet is mine.
          Sore wa saifu desu.         That is a wallet

     Use the words given in the parenthesis to make a sentence.
      1. Kore wa watashi no hon desu.     This is my book.
                         ( your, his, her, ours, theirs )
      2. Kono hon wa watashi no desu.    This book is mine.
                         ( yours, his, hers, ours, theirs )
      3. Ano uchi wa Takasi san no desu. That house is Mr. Takasi’s.
           ( Mr. Doyo’s, Miss Sato’s, Miss Suzuki’s, Mrs. Yataki’s)


   Useful expressions :

    1. Wakarimasu ka.         Do you understand ?
    2. Wakarimasu.          I understand.    
    3. Wakarimasen.          I don’t understand.
    4. Wakarimashita ka.     Did you understand ? 
    5. Wakarimashita.          I understood.       
    6. Wakarimasen deshita.  I didn’t  understand.
    7. Shitte imasu ka.      Do you know ?
    8. Shirimasen.          I don’t know.
    9. Shitte imasu.          I know.
   10. Doo desu ka.          How is it ?
   11. Doo deshita ka.          How was it ?

     
  “mo” is a particle which adds the sense of also, too.
 Unlike the English word too, “mo” is not added but takes
 the place of  “wa”  as in the following sentences :
     
   1. Kono hito wa gakusei  desu.  This person is a student.
      Kono hito mo gakusei desu.   This person is also a student. 

   2. Ogawa san wa Nihongo no sensei desu.  
           Mr. Ogawa is a Japanese language teacher.

      Yataki-san mo  Nihongo no sensei desu.
           Mr. Yataki is also a Japanese language teacher.


  “mo” is also used in a negative sentence as in the following
      sentences :

   1. Kore wa jibiki dewa arimasen.   
             This is not a dictionary.

      Sore mo jibiki dewa arimasen.   
             That is not a dictionary either.

   2. Yamada san wa koomuin dewa arimasen.   
           Miss Yamada is not a government employee.

      Ikeda san mo koomuin dewa arimasen.    
           Miss Ikeda is not a government  employee either.

    New words ( Adjectives )
      wakai – young          oishii – delicious        
      omoshiroi – interesting   yasashii – easy; kind        
      muzukashii – difficult     ookii – big
      chiisai – small             atarashii – new 


    New Vocabulary ( atarashii tango )

       kyookai – church         terebi – television    
       shiken – examination         sakki – a while ago
       bangumi – program ( t v )    kawa – river        
       doko emo – (not) anywhere    doko nimo – nowhere    
       yuubinkyoku – post office    depaato – department store


  Examples :
  1. Kanojo wa wakai desu.         She is young.
  2. Watashi no uchi wa chiisai desu.     My house is small.
  3. Ano hoteru wa atarashii desu.     That hotel is new.
  4. Kono eiga wa omoshiroi desu.    This movie is interesting.


    PURE ADJECTIVES :

  atsui – hot / thick           tsuyoi – strong            
  yowai – weak               usui – thin                
  yoi – good               katai – hard                    
  mazui – unsavory; unskillful       yawarakai – soft             
  takai – tall / expensive       tanoshii – pleasant            
  sabishii – lonely           yasui – cheap                
  nagai – long               isogashii – busy            
  ooi – many               sei ga takai – tall ( person )    
  omoi – heavy               sei ga hikui – short ( person )   
  amai – sweet               karui – light                
  hiroi – wide               suzushii – cool            
  atatakai – warm           akai – red                 
  shiroi – white           tooi – far                
  kuroi – black           hayai – early / fast            
  osoi – late / slow           akarui – bright            
  aoi – blue               asai – shallow           
  samui – cold ( weather )        tsumetai – cold ( object )    
  warui – bad                     hazukashii – ashamed 
  hikui – low                     subarashii – wonderful
  mijikai – short                 sukunai – few 
  nigai – bitter                  suppai – sour
  semai – narrow                  chikai – near
  kiiroi – yellow                 kurai – dark
  fukai – deep                    kawaii – cute 



  BASIC GRAMMAR
   1. Kono hon wa omoshirokunai desu.    
                 This book is not interesting.
   2. Watashi no tokei wa yasukatta desu.       My watch is cheap.
   3. Anata no uchi (ie) wa chikai desu ka.    Is your house near ?


  In Japanese grammar, a pure adjective is conjugated as follows :

     Present     Present negative        Past        Past negative
  affirmative                         affirmative

  omoshiroi     omoshirokunai       omoshirokatta   omoshirokunakatta
  yasui       yasukunai          yasukatta          yasukunakatta
  chikai      chikakunai          chikakatta      chikakunakatta
  yawarakai      yawarakakunai          yawarakakatta   yawarakakunakatta

    Note : All pure adjectives end in letter “i” ;however they are
           conjugated in cases where they are used as complements in
           a be–verb sentence. For example, in the sentence “ subject,
           wa omoshiroi desu” “omoshiroi” is used as a complement.
           In such a case as this, depending on the verb tense and
           whether its negative or positive, pure adjective should be
           conjugated by dropping the final “i”  and replacing it with
           “kunai”, “katta”, and “kunakatta”.


Type A  ( Affirmative and Negative Sentences )
   1. Kare wa sei ga takai desu.      He is tall.    
             (present affirmative, sei ga takai )
   2. Kanojo wa isogashikunai desu.        She is not busy. 
             ( Present negative,  isogashikunai)
   3. Shiken wa muzukashikatta desu.    The examination was difficult.
          ( past affirmative, muzukashikatta )
   4. Ano eiga wa omoshiro kunakatta desu.    
              That movie was not interesting.
               ( past negative,  omoshiro kunakatta )


 Type  B ( Interrogative sentences )
    1. Shiken wa muzukashikatta desu ka. Was the test difficult ?
                   ( past affirmative, muzukashikatta )
    2. Shiken wa muzukashikunakatta desu ka.    Wasn’t  the test difficult ?
               ( past negative, muzukashikunakatta )
    3. Kare wa sei ga takai desu ka.      Is he tall ? 
                    ( present affirmative, sei ga takai )
    4. Kare wa sei ga takakunai desu ka.   Isn’t he tall ?
                    ( present negative, sei ga takakunai )
    5. Yamada-san wa isogashi desu ka.      Is Mr. Yamada busy ? 
                    (present affirmative, ishogashii )
    6. Kanojo wa isogashikatta desu ka.     Was she busy ?
                    ( past affirmative, isogashikatta )


 BASIC GRAMMAR : 
       Verb “to go” together with its propositions “e” or “ni”
  
       “e” or “ni” is a particle to indicate the destination and
          the direction. You can always use this particle after places,
          such as Midsayap e ( to Midsayap ), Nihon e ( to Japan ),
          Pikit e ( to Pikit ), etc.
  
  

MATH N 223 INCLINATION and SLOPE

INCLINATION and SLOPE  

Definition of terms:
1.    Angle of inclination – is the least counterclockwise
         angle from the positive x-axis to the line.

  2. Slope(m) – is the tangent of the angle of inclination.

     m = tan α
        m =(y₂ – y₁) / (x₂ - x₁)
         where x₂ is not = x₁)
 

Notes :
  a) A line sloping upward to the right has a positive
       slope.
  b) A line sloping downward to the right has a negative
       slope.
  c) The slope of a line parallel to the x-axis is zero.
  d) The slope of a line parallel to the y-axis is
       undefined.

PARALLEL AND PERPENDICULAR LINES

Theorem 1: Two lines are parallel if and only if their
            slopes are equal.

          m₁ = m₂
         
          where :
         m₁ = is the slope of the line L₁
         m₂ = is the slope of the line L₂

Theorem 2: Two lines are perpendicular if and only if their
         slopes are negative reciprocals.

         m₁ = -1/m₂

        or (m₁)(m₂) = -1

MATH N 223 Take home Quiz

 MATH N 223 TAKE HOME QUIZ # 1
   (to be submitted on November 30, 2010)

 Solve all problems in a yellow pad.

 1. The center of a circle is at (2, -5) and one point on the circle is
    (-4, 2). Determine the other end of the diameter through (-4, 2).

 2. The three vertices of a parallelogram are (1, -3), (-3, -1) and
    (3, 5). Determine the fourth vertex.

 3. The segment from (-1, 4) to (2, -2) is extended three times its
    own length. Determine the terminal point.

 4. The segment from (-2, -3) and (6, 1) is extended each way a distance
     equal to one-fourth its own length. Determine the terminal points.
 
 5. Show that the points (4, 0), (2, 1) and (-1, -5) are vertices of a
     right triangle and find its area.

 6. The segment joining (2, -4) and (9, 3) is divided into two segments,
     One of which is three-fourths as long as the other. Determine the
     Points of division.
 
 7. Find the radius of a circle with center at (-2, 1), if a chord of
     length 10 is bisected at (-3, 0).

 8. Locate the point which is equidistant from (-3, 0) and (1, 4)
     and at a distance 5 from (-1, 7).

 9. Determine the midpoint of the segment joining (5, 6) and
      (7, -12).

10. The segment joining (20, 16) and (-20, -16) is to be divided
       into four equal parts. Determine the points of division.
       

F Elect 3 (Analytic ) Take home Exam

This are the additional problems to the first 3 problems given during
our lecture. Solve all problems and submit your solutions on
November 22, 2010 during our lecture.

4. Show that the points (-1, -2), (5, 4) and (-3, 0) are vertices of
a right triangle and find its area.

5. The center of a circle is at (-3, -2) and its radius is 7 units.
Determine the length of of the chord which is bisected at (3, 1).

6. The segment from (-1, 4) to (2, -2) is extended three times its
own length. Determine the terminal point.

7. Show that the points (1, 4), (7, 0), (5, -3) and (-1, 1) are vertices
of a rectangle, and find the area.

8. The center of a circle is at (2, -5) and one point on the circle is
(-4, 2). Determine the other end of the diameter through (-4, 2).

9. The three vertices of a parallelogram are (1, -3), (-3, -1) and
     (3, 5). Determine the fourth vertex.

10. The segment joining (5, 11) and (-3, -1) is to be divided into four equal parts. Determine the points of division.

LANG 102 Tape Lesson 2

1 :  DESU

  Lesson
 1.Kore wa hon desu.                         This is a book.
 2.Sore wa hon desu ka.                     Is that a book ?
   Hai, sõ desu                                    Yes, it is.
   Iie, sõ dewa arimasen.                      No, it isn’t.
 3.Kore wa hon dewa arimasen.          This isn’t a book.
 4.Kore wa hon dewa arimasen ka.     Isn’t  this a book ?
 5.Are mo hon desu ka.                      Is that also a book ?
 6.Kore wa nan desu ka.                    What is this ?
   ( Sore wa ) Nõto desu.                   (That is) a notebook.
 7.Kore wa hon desu ka, nõto desu ka.   Is this a book or a notebook ?
   ( Sore wa ) hon desu.                          (That is) a book.
 8.Kore wa watashi no hon desu.            This is my book.
 9.Sore wa anata no nõto desu ka.          Is that your notebook?
10.Kore wa dare no nõto desu ka.          Whose notebook is this ?
   (Sore wa) Tanaka san no ( nõto ) desu. (That is) Mr. Tanaka’s ( notebook )
11.Dore ga watashi no ( nõto ) desu.         Which is mine ? ( my notebook )
12.Kore wa hon de sore wa jisho desu.     This is a book, and that is a dictionary.
13.Kyõ wa getsuyõbi de ashita wa kayõbi desu. Today is Monday, and tomorrow is Tuesday.
14.Kyõ wa shogoto de ashita wa yasumi desu.   Today is working day, and tomorrow is a holiday.

Physics E 101 Lesson 1

Physics : INTRODUCTION
Physics is a major science, dealing with the systematic study of the basic properties of the universe, the forces they exert on one another, and the results produced by these forces. Physics is closely related to the other natural sciences and, in a sense, encompasses them. Chemistry, for example deals with the interaction of atoms to form molecules. Much of modern geology is largely a study of the physics of the earth and is known as geophysics. Astronomy deals with the physics of the stars and outer space. Even living systems are made up of fundamental particles and, as studied in biophysics and biochemistry, they follow the same type of laws as the simpler particles traditionally studied by a physicist.
The emphasis on the interaction between particles in modern physics, known as the microscopic approach, must often be supplemented by a macroscopic approach that deals with larger elements or systems of particles. This macroscopic approach is indispensable to the application of physics to much of modern technology. Thermodynamics, a branch of physics developed in the 19th century, deals with the elucidation and measurement of properties of a system as a whole and remains useful in other fields of physics; it also forms the basis of much of chemical and mechanical engineering. Such properties as the temperature, pressure and volume of a gas have no meaning for an individual atom or molecule; these thermodynamic concepts can only be applied directly to a very large system of such particles. A bridge exists, however, between the microscopic and macroscopic approach; another branch of physics; known as statistical mechanics, indicates how pressure and temperature can be related to the motion of atoms and molecules on a statistical basis.
Physics emerged as a separate science only in the early 19th century, until that time a physicist was often also a mathematician, philosopher, chemist, biologist, engineer, or even primarily a political leader or an artist. Today, the field has grown to such an extent that with few exceptions modern physicists have to limit their attention to one or two branches of the science. Once the fundamental aspects of a new field are discovered and understood, they become the domain of engineers and other applied scientist. The 19th century discoveries in electricity and magnetism, for example, are now the concentrations of electrical and communication engineers; the properties of matter discovered at the beginning of the 20th century have been applied in electronics; and the discoveries of nuclear physics, have passed into the hands of nuclear engineers for applications to peaceful or military uses.

MATHEMATICS as a language of science
Mathematics is the language of physics; that is when ideas in science are expressed in mathematical terms:
1. They are unambiguous.
2. They do not have double meanings, that so often confuse the discussion of ideas expressed in
common language.
3. They are easier to verify or disprove by experiment.
4. The methods of mathematics and experimentation led to enormous success in science.
5. The abstract mathematics developed by mathematicians is often years later found to be the
exact language by which nature can be described.
Mathematics is the language of physics does not mean that mathematics is physics or physics is mathematics.

THE SCIENTIFIC METHOD – is a method that is extremely effective in gaining, organizing, and applying new knowledge. The steps are :
1. Recognize a problem.
2. Make an educated guess --- a hypothesis. Hypothesis is an educate guess that is only considered factual after it has been demonstrated by experiments. If a hypothesis has been tested over and over again and has not been contradicted it may become known as a law or principle.
3. Predict the consequences of the hypothesis
4. Perform experiments to test predictions.
5. Formulate the simplest general rule that organizes the three main ingredients --- hypothesis, prediction, and experimental outcome --- into a theory.
The success of science has more to do with an attitude common to scientists than with a particular method. This attitude is one of inquiry, observation, experimentation and humility.

THE DOMAIN OF PHYSICS

A. According to size of objects studied
1. Quantum domain – the domain of small objects. Objects are considered small if their sizes are
comparable to or smaller than the size of an atom.
2. Non-quantum domain – the domain of large objects. Objects are considered large if they are larger than the size of an atom.

B. According to speed of objects studied
1. Relativistic domain – the domain at high speed, that is if the speed of the moving object is comparable to
the speed of light.
2. Non-relativistic domain – the domain at low speed, that is the speed of the moving object is less than the
speed of light.

C. Newtonian domain – a combination of the division according to size and speed. It is the domain of large
objects at low speeds, the one we deal in our daily lives. (In honor of Sir Isaac Newton, the 17th century
physicist who played the key role in developing the physics of large objects moving at low speed).

D. Mechanics – is the study of the relation between the force and the resulting motion. It seeks to account
quantitatively for the motion of objects having given properties in terms of the force acting on them.

1. Newtonian mechanics – is the mechanics of the Newtonian domain. It deals with systems containing
objects which are large and which move at low speed.

2. Relativistic mechanics – is the mechanics of the relativistic domain. In 1905, Einstein showed that a
different approach was necessary for the study of objects moving at speeds so high as to be comparable
to the speed of light.

3. Quantum mechanics – is the mechanics of the quantum domain. It was developed about the same time
with relativistic mechanics by Max Planck, Louis de Broglie, Erwin Schrodinger and others. They found
out that the Newtonian mechanics could not explain the motion of objects whose size is in the atomic
scale or smaller.

E. Electromagnetism – is the study of the properties and consequences of the electromagnetic force, which is
one of the fundamental forces in nature. The fundamental forces are gravitational force, electromagnetic
force, strong nuclear force and weak nuclear force.

F. Solid-state physics is a branch of physics that deals with the properties of solids. A particular problem in
solid – state physics, for instance the properties of materials use in transistors, is solve by employing the
mechanics of whichever domain is most appropriate.

G. Heat and Thermodynamics


THE FUNDAMENTAL MEASURABLE QUANTITIES IN PHYSICS
1. Length 3. Time 5. Luminous intensity 7. Molecular quantity
2. Mass 4. Temperature 6. Electric charge ( current )

THE FUNDAMENTAL MEASURABLE QUNATITIES IN MECHANICS
1. Length 2. Mass 3. Time



Measurement is a scientific comparison between an unknown quantity to a fixed known quantity called standard.

Systems of Measurement
1. English system (British Engineering system) – originated in England
2. Metric system – originated in France

Systeme International d’Unites ( SI ) adopted by the International Bureau of Weights and Measures in 1960.
The units of the MKS is adopted as the base units of the SI system.


Base Units of each System of measurement

Measurable Quantities in Mechanics Metric System English System
CGS MKS FPS
Length Centimeter ( cm ) Meter ( m ) Foot ( ft )
Mass Gram ( g ) Kilogram (kg ) Slug ( lbm )
Time Second ( s ) Second ( s ) Second ( s )

Reasons for adopting the Metric system:
1. It is scientifically planned.
2. It is a decimal system.
3. It is universally accepted.

DISADVANTAGES OF THE ENGLISH SYSTEM
1 yard = ( King Henry I ) distance from the tip of his nose to the end of his thumb
1 inch ( 1324 ) = length of three grains of barleycorns laid end to end
1 mile = 1000 double step of an average soldier
1 foot = length of the foot of the king

THE CONCEPT OF THE METER
To be discuss in class with demonstrations



THIS IS AN INTERNET STORE...

Irregular Verbs (Spanish)

1. Venir – to come

Present indicative (presente del indicativo):
yo vengo, tú vienes, usted/él/ella viene
nosotros/as venimos, vosotros/as venís, ustedes/ellos/ellas vienen

Preterite (pretérito): yo vine, tú viniste, usted/él/ella vino
nosotros/as vinimos, vosotros/as vinisteis, ustedes/ellos/ellas vinieron

Imperfect indicative (imperfecto del indicativo): yo venía, tú venías, usted/él/ella venía
nosotros/as veníamos, vosotros/as veníais, ustedes/ellos/ellas venían

Future (futuro): yo vendré, tú vendrás, usted/él/ella vendrá
nosotros/as vendremos, vosotros/as vendréis, ustedes/ellos/ellas vendrán


2. infinitive (infinitivo): empezar - to start , to begin
Gerund (gerundio): empezando

Present indicative (presente del indicativo):
yo empiezo, tú empiezas, usted/él/ella empieza
nosotros/as empezamos, vosotros/as empezáis, ustedes/ellos/ellas empiezan

Preterite (pretérito): yo empecé, tu empezaste, usted/él/ella empezó
nosotros/as empezamos, vosotros/as empezasteis, ustedes/ellos/ellas empezaron

Imperfect indicative (imperfecto del indicativo):
yo empezaba, tú empezabas, usted/él/ella empezaba
nosotros/as empezábamos, vosotros/as empezabais, ustedes/ellos/ellas empezaban

Future (futuro): yo empezaré, tú empezarás, usted/él/ella empezará
nosotros/as empezaremos, vosotros/as empezaréis, ustedes/ellos/ellas empezarán


3. Infinitive (infinitivo): traer – to bring
Gerund (gerundio): trayendo
Participle (participio): traído

Present indicative (presente del indicativo):
yo traigo, tú traes, usted/él/ella trae
nosotros/as traemos, vosotros/as traéis, ustedes/ellos/ellas traen

Preterite (pretérito): yo traje, tu trajiste, usted/él/ella trajo
nosotros/as trajimos, vosotros/as trajisteis, ustedes/ellos/ellas trajeron

Imperfect indicative (imperfecto del indicativo):
yo traía, tú traías, usted/él/ella traía
nosotros/as traíamos, vosotros/as traíais, ustedes/ellos/ellas traían

Future (futuro): yo traeré, tú traerás, usted/él/ella traerá
nosotros/as traeremos, vosotros/as traeréis, ustedes/ellos/ellas traerán


4. Infinitive (infinitivo): querer - to want
Gerund (gerundio): queriendo (wanting)
Participle (participio): querido (wanted)

Present indicative (presente del indicativo):
yo quiero, tú quieres, usted/él/ella quiere
nosotros/as queremos, vosotros/as queréis, ustedes/ellos/ellas quieren
(I want, you want, etc.)

Preterite (pretérito): yo quise, tu quisiste, usted/él/ella quiso
nosotros/as quisimos, vosotros/as quisisteis, ustedes/ellos/ellas quisieron
(I wanted, you wanted, etc.)

Imperfect indicative (imperfecto del indicativo):
yo quería, tú querías, usted/él/ella quería
nosotros/as queríamos, vosotros/as queríais, ustedes/ellos/ellas querían
(I used to want, you used to want, etc.)
Future (futuro): yo querré, tú querrás, usted/él/ella querrá
nosotros/as querremos, vosotros/as querréis, ustedes/ellos/ellas querrán
(I will want, you will want, etc.)


5. Infinitive (infinitivo): ver (to see)
Gerund (gerundio): viendo (seeing)
Participle (participio): visto (seen)

Present indicative (presente del indicativo):
yo veo, tú ves, usted/él/ella ve
nosotros/as vemos, vosotros/as véis, ustedes/ellos/ellas ven
(I see, you see, etc.)

Preterite (pretérito): yo vi, tu viste, usted/él/ella vio
nosotros/as vimos, vosotros/as visteis, ustedes/ellos/ellas vieron
(I saw, you saw, etc.)

Imperfect indicativo (imperfecto del indicativo):
yo veía, tú veías, usted/él/ella veía
nosotros/as veíamos, vosotros/as veíais, ustedes/ellos/ellas veían
(I used to see, you used to see, etc.)

Future (futuro): yo veré, tú verás, usted/él/ella verá
nosotros/as veremos, vosotros/as veréis, ustedes/ellos/ellas verán
(I will see, you will see, etc.)


6. Infinitive (infinitivo) to go: ir
Following are the conjugations for the verb ir, which typically means "to go." Irregular forms are indicated in boldface. Other translations other than those given are possible.

Gerund (gerundio) going: yendo
Participle (participio)gone: ido

Present indicative (presente del indicativo) I go, you go, etc.:
yo voy, tú vas, usted/él/ella va
nosotros/as vamos, vosotros/as vais, ustedes/ellos/ellas van

Preterite (pretérito) I went, you went, etc.: yo fui, tu fuiste, usted/él/ella fue
nosotros/as fuimos, vosotros/as fuisteis, ustedes/ellos/ellas fueron

Imperfect indicative (imperfecto del indicativo) I used to go, you used to go, etc.: yo iba, tú ibas, usted/él/ella iba
nosotros/as íbamos, vosotros/as ibais, ustedes/ellos/ellas iban

Future (futuro) I will go, you will go, etc.:
yo iré, tú irás, usted/él/ella irá
nosotros/as iremos, vosotros/as iréis, ustedes/ellos/ellas irán

Note: The preterite conjugation is the same as that of the verb ser. The context typically will indicate which verb is being conjugated.


7. Infinitive (infinitivo) haber – to have
Haber is not used in the imperative mood.
Note: Haber is used most frequently as an auxiliary verb to form the perfect tenses. It also has two other uses: In the third-person present indicative form of hay, it can mean "there is" or "there are." It is also used in the phrase hay que, meaning "it is necessary." With those meanings, haber also can be used in the other third-person tenses.

Gerund (gerundio) habiendo
Past participle (participio) habido

Present indicative (presente del indicativo)
yo he, tú has, usted/él/ella ha (hay)
nosotros/as hemos, vosotros/as habéis, ustedes/ellos/ellas han (hay)

Preterite (pretérito)
yo hube, tu hubiste, usted/él/ella hubo
nosotros/as hubimos, vosotros/as hubisteis, ustedes/ellos/ellas hubieron

Imperfect indicativo (imperfecto del indicativo)
yo había, tú habías, usted/él/ella había
nosotros/as habíamos, vosotros/as habíais, ustedes/ellos/ellas habían
Future (futuro): yo habré, tú habrás, usted/él/ella habrá
nosotros/as habremos, vosotros/as habréis, ustedes/ellos/ellas habrán


8. Poder – to be able

Gerund (gerundio): pudiendo
Participle (participio): podido

Present indicative:
yo puedo, tú puedes, usted/él/ella puede
nosotros/as podemos, vosotros/as podéis, ustedes/ellos/ellas pueden

Preterite (pretérito):
yo pude, tu pudiste, usted/él/ella pudo
nosotros/as pudimos, vosotros/as pudisteis, ustedes/ellos/ellas pudieron

Imperfect indicativo (imperfecto del indicativo):
yo podía, tú podías, usted/él/ella podía
nosotros/as podíamos, vosotros/as podíais, ustedes/ellos/ellas podían

Future (futuro):
yo podré, tú podrás, usted/él/ella podrá
nosotros/as podremos, vosotros/as podréis, ustedes/ellos/ellas podrán


9. Conjugation of almorzar – to eat lunch

Infinitive (infinitivo) Almorzar
Gerund (gerundio) Almorzando
Participle (participio) Almorzado

Present indicative(presente del inidicativo)
yo almuerzo, tú almuerzas, usted/él/ella almuerza
nosotros/as almorzamos, vosotros/as almorzáis, ustedes/ellos/ellas almuerzan

Preterite (pretérito)yo almorcé, tu almorzaste, usted/él/ella almorzó
nosotros/as almorzamos, vosotros/as almorzasteis, ustedes/ellos/ellas almorzaron

Imperfect indicativo
(imperfecto del indicativo) yo almorzaba, tú almorzabas, usted/él/ella almorzaba nosotros/as almorzábamos, vosotros/as almorzabais, ustedes/ellos/ellas almorzaban

Future (futuro) yo almorzaré, tú almorzarás, usted/él/ella almorzará
nosotros/as almorzaremos, vosotros/as almorzaréis, ustedes/ellos/ellas almorzarán


10. Conjugation of andar – to walk
Infinitivo - andar
Gerund (gerundio)- andando
Participle (participio) - andado
Present indicative (presente del inidicativo)
yo ando, tú andas, usted/él/ella anda
nosotros/as andamos, vosotros/as andáis, ustedes/ellos/ellas andan

Preterite (pretérito) yo anduve, tu anduviste, usted/él/ella anduvo, nosotros/as anduvimos, vosotros/as anduvisteis, ustedes/ellos/ellas anduvieron
Imperfect indicativo (imperfecto del indicativo)
yo andaba, tú andabas, usted/él/ella andaba
nosotros/as andábamos, vosotros/as andabais, ustedes/ellos/ellas andaban

Future (futuro) yo andaré, tú andarás, usted/él/ella andará
nosotros/as andaremos, vosotros/as andaréis, ustedes/ellos/ellas andarán


11. Conjugation of argüir - to deduce, prove, argue
Infinitive (infinitivo) argüir
Gerund (gerundio) arguyendo
Participle (participio) argüido

Presente yo arguyo, tú arguyes, usted/él/ella arguye
nosotros/as argüimos, vosotros/as argüís, ustedes/ellos/ellas arguyeren

Preterite (pretérito)yo argüí, tu argüiste, usted/él/ella arguyó
nosotros/as argüimos, vosotros/as argüisteis, ustedes/ellos/ellas argüieron

Imperfect indicative
(imperfecto del indicativo) yo arguya, tú arguyas, usted/él/ella arguya
nosotros/as arguyamos, vosotros/as arguyais, ustedes/ellos/ellas arguyan

Future (futuro) yo argüiré, tú argüirás, usted/él/ella argüirá
nosotros/as argüiremos, vosotros/as argüiréis, ustedes/ellos/ellas argüirán


12. Conjugation of averiguar – verify, to find out
Note: The irregularities are in the uses of the umlaut or dieresis over the u when it is followed by an e; the pronunciation is regular.

Infinitive(infinitivo) averiguar
Gerund (gerundio) averiguando
Participle (participio) averiguado

Present indicative (presente del inidicativo)
yo averiguo, tú averiguas, usted/él/ella averigua
nosotros/as averiguamos, vosotros/as averiguáis, ustedes/ellos/ellas averiguan

Preterite (pretérito) yo averigüé, tu averiguaste, usted/él/ella averiguó
nosotros/as averiguamos, vosotros/as averiguasteis, ustedes/ellos/ellas averiguaron

Imperfect indicativo
(imperfecto del indicativo)
yo averiguaba, tú averiguabas, usted/él/ella averiguaba
nosotros/as averiguábamos, vosotros/as averiguabais,
ustedes/ellos/ellas averiguaban

Future (futuro) yo averiguaré, tú averiguarás, usted/él/ella averiguará
nosotros/as averiguaremos, vosotros/as averiguaréis, ustedes/ellos/ellas averiguarán


13. Conjugation of bendecir – to bless, to consecrate
Note: Also following this pattern is maldecir.

Infinitive (infinitivo) bendecir
Gerund (gerundio) bendiciendo
Participle (participio) bendecido

Present inbendicative(presente del inbendicativo)
yo bendigo, tú bendices, usted/él/ella bendice
nosotros/as bendecimos, vosotros/as bendecís, ustedes/ellos/ellas bendicen

Preterite (pretérito) yo bendije, tu bendijiste, usted/él/ella bendijo nosotros/as bendijimos, vosotros/as bendijisteis, ustedes/ellos/ellas bendijeron

Imperfect inbendicative (imperfecto del inbendicativo)
yo bendecía, tú bendecías, usted/él/ella bendecía
nosotros/as bendecíamos, vosotros/as bendecíais, ustedes/ellos/ellas bendecían

Future (futuro) yo bendeciré, tú bendecirás, usted/él/ella bendecirá
nosotros/as bendeciremos, vosotros/as bendeciréis, ustedes/ellos/ellas bendecirán


14. Conjugation of buscar – to look for
The following conjugation pattern is used by many verbs that end in -car. The irregularity is in spelling only, not in pronunciation.
Note: Other verbs following this pattern include acercar, aparcar, aplicar, arrancar, atacar, colocar, comunicar, criticar, chocar, edificar, equivocar, explicar, indicar, marcar, perjudicar, pescar, practicar, provocar, publicar, sacar, secar, suplicar, tocar, and volcar. The irregular forms are in spelling only; the pronunciation follows the regular pattern.

Infinitive (infinitivo) buscar
Gerund (gerundio) buscando
Participle (participio) buscado
Present indicative (presente del inidicativo)
yo busco, tú buscas, usted/él/ella busca
nosotros/as buscamos, vosotros/as buscáis, ustedes/ellos/ellas buscan

Preterite (pretérito) yo busqué, tu buscaste, usted/él/ella buscó
nosotros/as buscamos, vosotros/as buscasteis, ustedes/ellos/ellas buscaron

Imperfect indicativo
(imperfecto del indicativo) yo buscaba, tú buscabas, usted/él/ella buscaba nosotros/as buscábamos, vosotros/as buscabais, ustedes/ellos/ellas buscaban

Future (futuro) yo buscaré, tú buscarás, usted/él/ella buscará
nosotros/as buscaremos, vosotros/as buscaréis, ustedes/ellos/ellas buscarán


15. Conjugation of avergonzar – to feel ashame, to be ashame
Infinitivo - avergonzar
Gerund (gerundio) - avergonzando
Participle (participio) - avergonzado
Present indicative (presente del inidicativo)
yo avergüenzo, tú avergüenzas, usted/él/ella avergüenza
nosotros/as avergonzamos, vosotros/as avergonzáis, ustedes/ellos/ellas avergüenzan

Preterite (pretérito) yo avergoncé, tu avergonzaste, usted/él/ella avergonzó
nosotros/as avergonzamos, vosotros/as avergonzasteis,
ustedes/ellos/ellas avergonzaron

Imperfect indicativo (imperfecto del indicativo)
yo avergonzaba, tú avergonzabas, usted/él/ella avergonzaba
nosotros/as avergonzábamos, vosotros/as avergonzabais,
ustedes/ellos/ellas avergonzaban

Future (futuro) yo avergonzaré, tú avergonzarás, usted/él/ella avergonzará, nosotros/as avergonzaremos, vosotros/as avergonzaréis,
ustedes/ellos/ellas avergonzarán


16. Conjugation of caber – to fit, to be capable
Infinitive (infinitivo) caber
Gerund (gerundio) cabiendo
Participle (participio) cabido
Present indicative (presente del indicativo)
yo quepo, tú cabes, usted/él/ella cabe
nosotros/as cabemos, vosotros/as cabéis, ustedes/ellos/ellas caben

Preterite (pretérito) yo cupe, tu cupiste, usted/él/ella cupo
nosotros/as cupimos, vosotros/as cupisteis, ustedes/ellos/ellas cupieron

Imperfect indicativo
(imperfecto del indicativo)yo cabía, tú cabías, usted/él/ella cabía
nosotros/as cabíamos, vosotros/as cabíais, ustedes/ellos/ellas cabían

Future (futuro) yo cabré, tú cabrás, usted/él/ella cabrá
nosotros/as cabremos, vosotros/as cabréis, ustedes/ellos/ellas cabrán


17. Caer – to fall
Infinitive(infinitivo) Caer
Gerund (gerundio) cayendo
Participle (participio) caído
Presente yo caigo, tú caes, usted/él/ella cae
nosotros/as caemos, vosotros/as caéis, ustedes/ellos/ellas caen

Preterite (pretérito) yo caí, tu caíste, usted/él/ella cayó
nosotros/as caímos, vosotros/as caísteis, ustedes/ellos/ellas cayeron

Imperfect indicativo (imperfecto del indicativo)
yo caía, tú caías, usted/él/ella caía
nosotros/as caíamos, vosotros/as caíais, ustedes/ellos/ellas caían

Future (futuro) yo caeré, tú caerás, usted/él/ella caerá
nosotros/as caeremos, vosotros/as caeréis, ustedes/ellos/ellas caerán


18. Conjugation of cocer – to cook, to boil, to bake
Note: Torcer also follows this pattern.

Infinitive (infinitivo) cocer
Gerund (gerundio) cociendo
Participle (participio) cocido
Present indicative (presente del indicativo)
yo cuezo, tú cueces, usted/él/ella cuece
nosotros/as cocemos, vosotros/as cocéis, ustedes/ellos/ellas cuecen

Preterite (pretérito) yo cocí, tu cociste, usted/él/ella coció
nosotros/as cocimos, vosotros/as cocisteis, ustedes/ellos/ellas cocieron

Imperfect indicativo (imperfecto del indicativo)
yo cocía, tú cocías, usted/él/ella cocía
nosotros/as cocíamos, vosotros/as cocíais, ustedes/ellos/ellas cocían

Future (futuro) yo coceré, tú cocerás, usted/él/ella cocerá
nosotros/as coceremos, vosotros/as coceréis, ustedes/ellos/ellas cocerán


19. Conjugation of coger – to pick, to take hold, to catch
Note: Other verbs following this pattern include encoger, escoger, proteger, and recoger. The differences from the regular conjugation are in spelling only, not pronunciation.

Infinitive (infinitivo) coger
Gerund (gerundio) cogiendo
Participle (participio) cogido

Present indicative (presente del indicativo)
yo cojo, tú coges, usted/él/ella coge
nosotros/as cogemos, vosotros/as cogéis, ustedes/ellos/ellas cogen

Preterite (pretérito) yo cogí, tu cogiste, usted/él/ella cogió
nosotros/as cogimos, vosotros/as cogisteis, ustedes/ellos/ellas cogieron

Imperfect indicativo
(imperfecto del indicativo) yo cogía, tú cogías, usted/él/ella cogía nosotros/as cogíamos, vosotros/as cogíais, ustedes/ellos/ellas cogían

Future (futuro) yo cogeré, tú cogerás, usted/él/ella cogerá
nosotros/as cogeremos, vosotros/as cogeréis, ustedes/ellos/ellas cogerán


20. Conjugation of comenzar – to begin, to commence
Note: Other verbs following this pattern include empezar and tropezar.

Infinitive (infinitivo) comenzar
Gerund (gerundio) comenzando
Participle (participio) comenzado
Present indicative (presente del inidicativo)
yo comienzo, tú comienzas, usted/él/ella comienza
nosotros/as comenzamos, vosotros/as comenzáis, ustedes/ellos/ellas comienzan

Preterite (pretérito) yo comencé, tu comenzaste, usted/él/ella comenzó nosotros/as comenzamos, vosotros/as comenzasteis, ustedes/ellos/ellas comenzaron

Imperfect indicativo (imperfecto del indicativo)
yo comenzaba, tú comenzabas, usted/él/ella comenzaba
nosotros/as comenzábamos, vosotros/as comenzabais, ustedes/ellos/ellas comenzaban

Future (futuro) yo comenzaré, tú comenzarás, usted/él/ella comenzará
nosotros/as comenzaremos, vosotros/as comenzaréis, ustedes/ellos/ellas comenzarán


21. Conjugation of conducer – to drive, to lead
Note: Other verbs following this pattern include introducir, producir, reducir, reproducir, seducir, and traducir.

Infinitive(infinitivo) conducir
Gerund (gerundio) conduciendo
Participle (participio) conducido

Present indicative (presente del indicativo)
yo conduzco, tú conduces, usted/él/ella conduce
nosotros/as conducimos, vosotros/as conducís, ustedes/ellos/ellas conducen

Preterite (pretérito) yo conduje, tu condujiste, usted/él/ella condujo
nosotros/as condujimos, vosotros/as condujisteis, ustedes/ellos/ellas condujeron

Imperfect indicative (imperfecto del indicativo)
yo conducía, tú conducías, usted/él/ella conducía
nosotros/as conducíamos, vosotros/as conducíais, ustedes/ellos/ellas conducían

Future (futuro) yo conduciré, tú conducirás, usted/él/ella conducirá
nosotros/as conduciremos, vosotros/as conduciréis, ustedes/ellos/ellas conducirán


22. Conjugation of conocer – to know, to meet
This conjugation pattern also is used by many other verbs that end in -cer.

Note: Other verbs following this pattern include agradecer, complacer, crecer, desconocer, desobedecer, florecer, merecer, nacer, obedecer, ofrecer, perecer, pertenecer, and reconocer.
Infinitive (infinitivo) conocer
Gerund (gerundio) conociendo
Participle (participio) conocido

Present indicative (presente del indicativo)
yo conozco, tú conoces, usted/él/ella conoce
nosotros/as conocemos, vosotros/as conocéis, ustedes/ellos/ellas conocen

Preterite (pretérito) yo conocí, tu conociste, usted/él/ella conoció
nosotros/as conocimos, vosotros/as conocisteis, ustedes/ellos/ellas conocieron

Imperfect indicativo
(imperfecto del indicative) yo conocía, tú conocías, usted/él/ella conocía nosotros/as conocíamos, vosotros/as conocíais, ustedes/ellos/ellas conocían

Future (futuro) yo conoceré, tú conocerás, usted/él/ella conocerá
nosotros/as conoceremos, vosotros/as conoceréis, ustedes/ellos/ellas conocerán


23. Conjugation of contar – to tell, to count
Note: Other verbs following tghis pattern include acordar, acostar, apostar, comprobar, consolar, costar, demostrar, encontrar, mostrar, probar, recordar, soltar, sonar, soñar, and volar.

Infinitive(infinitivo) contar
Gerund (gerundio) contando
Participle (participio) contado
Present indicative (presente del inidicativo)
yo cuento, tú cuentas, usted/él/ella cuenta
nosotros/as contamos, vosotros/as contáis, ustedes/ellos/ellas cuentan

Preterite (pretérito) yo conté, tu contaste, usted/él/ella contó
nosotros/as contamos, vosotros/as contasteis, ustedes/ellos/ellas contaron

Imperfect indicativo
(imperfecto del indicative) yo contaba, tú contabas, usted/él/ella contaba nosotros/as contábamos, vosotros/as contabais, ustedes/ellos/ellas contaban

Future (futuro) yo contaré, tú contarás, usted/él/ella contará
nosotros/as contaremos, vosotros/as contaréis, ustedes/ellos/ellas contarán


24. Conjugation of continuar - to continue
Note: Also matching this pattern is actuar.

Infinitive(infinitivo) continuar
Gerund (gerundio) continuando
Participle (participio) continuado
Present indicative (presente del inidicativo)
yo continúo, tú continúas, usted/él/ella continúa
nosotros/as continuamos, vosotros/as continuáis, ustedes/ellos/ellas continúan

Preterite (pretérito) yo continué, tu continuaste, usted/él/ella continuó nosotros/as continuamos, vosotros/as continuasteis, ustedes/ellos/ellas continuaron

Imperfect indicativo (imperfecto del indicativo)
yo continuaba, tú continuabas, usted/él/ella continuaba
nosotros/as continuábamos, vosotros/as continuabais,
ustedes/ellos/ellas continuaban

Future (futuro) yo continuaré, tú continuarás, usted/él/ella continuará
nosotros/as continuaremos, vosotros/as continuaréis, ustedes/ellos/ellas continuarán


25. Conjugation of convertir – to convert
This conjugation pattern is also used for several other verbs.

Note: Other verbs following this pattern include adherir, advertir, arrepentir, convertir, digerir, divertir, herir, hervir, invertir, and referir.

Infinitive(infinitivo) convertir
Gerund (gerundio) convertiendo
Participle (participio) convertido
Present indicative (presente del indicativo)
yo convierto, tú conviertes, usted/él/ella convierte
nosotros/as convertimos, vosotros/as convertís, ustedes/ellos/ellas convierten

Preterite (pretérito) yo convertí, tu convertiste, usted/él/ella convertió
nosotros/as convertimos, vosotros/as convertisteis, ustedes/ellos/ellas convirtieron

Imperfect indicative (imperfecto del indicativo)
yo convertía, tú convertías, usted/él/ella convertía
nosotros/as convertíamos, vosotros/as convertíais, ustedes/ellos/ellas convertían

Future (futuro) yo convertiré, tú convertirás, usted/él/ella convertirá
nosotros/as convertiremos, vosotros/as convertiréis, ustedes/ellos/ellas convertirán


26. Conjugation of creer – to believe
This conjugation pattern is also used by verbs such as creer and poseer.

Note: The irregularity of creer is a matter of spelling, not pronunciation. Other verbs following this pattern are leer and poseer.

Infinitive (infinitivo) creer
Gerund (gerundio) creyendo
Participle (participio) creído
Present indicative (presente del indicativo)
yo creo, tú crees, usted/él/ella cree
nosotros/as creemos, vosotros/as creéis, ustedes/ellos/ellas creen

Preterite (pretérito) yo creí, tu creíste, usted/él/ella creyó
nosotros/as creímos, vosotros/as creísteis, ustedes/ellos/ellas creyeron

Imperfect indicativo
(imperfecto del indicativo) yo creía, tú creías, usted/él/ella creía
nosotros/as creíamos, vosotros/as creíais, ustedes/ellos/ellas creían

Future (futuro) yo creeré, tú creerás, usted/él/ella creerá
nosotros/as creeremos, vosotros/as creeréis, ustedes/ellos/ellas creerán


27. Conjugation of dar – to give
Infinitive(infinitivo) dar
Gerund (gerundio) dando
Participle (participio) dado
Present indicative (presente del inidicativo)
yo doy, tú das, usted/él/ella da
nosotros/as damos, vosotros/as daís, ustedes/ellos/ellas dan
Preterite (pretérito) yo di, tu diste, usted/él/ella dio
nosotros/as dimos, vosotros/as disteis, ustedes/ellos/ellas dieron

Imperfect indicativo
(imperfecto del indicativo) yo daba, tú dabas, usted/él/ella daba
nosotros/as dábamos, vosotros/as dabais, ustedes/ellos/ellas daban

Future (futuro) yo daré, tú darás, usted/él/ella dará
nosotros/as daremos, vosotros/as daréis, ustedes/ellos/ellas darán


28. Conjugation of delinquir - to commit a crime
Note: This verb is regular in its pronunciation but irregular in its spelling.

Infinitive (infinitivo) delinquir
Gerund (gerundio) delinquiendo
Participle (participio) delinquido
Present indicative (presente del indicativo)
yo delinco, tú delinques, usted/él/ella delinque
nosotros/as delinquimos, vosotros/as delinquís, ustedes/ellos/ellas delinquen

Preterite (pretérito) yo delinquí, tu delinquiste, usted/él/ella delinquió nosotros/as delinquimos, vosotros/as delinquisteis, ustedes/ellos/ellas delinquieron

Imperfect indicative (imperfecto del indicativo)
yo delinquía, tú delinquías, usted/él/ella delinquía
nosotros/as delinquíamos, vosotros/as delinquíais, ustedes/ellos/ellas delinquían

Future (futuro) yo delinquiré, tú delinquirás, usted/él/ella delinquirá
nosotros/as delinquiremos, vosotros/as delinquiréis, ustedes/ellos/ellas delinquirán


29. Conjugation of Decir – to say , to tell
Forms of decir that are in boldface are irregular. Verbs that are conjugated following the same pattern are condecir, contradecir, desdecir, intradecir and predecir.
Infinitive (infinitivo) - decir
Gerund (gerundio) - diciendo
Participle (participio) - dicho
Present indicative (presente del indicativo)
yo digo, tú dices, usted/él/ella dice
nosotros/as decimos, vosotros/as decís, ustedes/ellos/ellas dicen

Preterite (pretérito)
yo dije, tu dijiste, usted/él/ella dijo
nosotros/as dijimos, vosotros/as dijisteis, ustedes/ellos/ellas dijeron

Imperfect indicative (imperfecto del indicativo)
yo decía, tú decías, usted/él/ella decía, nosotros/as decíamos, vosotros/as decíais, ustedes/ellos/ellas decían

Future (futuro)
yo diré, tú dirás, usted/él/ella dirá, nosotros/as diremos, vosotros/as diréis, ustedes/ellos/ellas dirán


30. Conjugation of dormir - to sleep
Infinitive (infinitivo) dormir
Gerund (gerundio) durmiendo
Participle (participio) dormido
Present indicative (presente del indicativo)
yo duermo, tú duermes, usted/él/ella duerme
nosotros/as dormimos, vosotros/as dormís, ustedes/ellos/ellas duermen

Preterite (pretérito) yo dormí, tu dormiste, usted/él/ella durmió
nosotros/as dormimos, vosotros/as dormisteis, ustedes/ellos/ellas durmieron

Imperfect indicative
(imperfecto del indicativo) yo dormía, tú dormías, usted/él/ella dormía
nosotros/as dormíamos, vosotros/as dormíais, ustedes/ellos/ellas dormían

Future (futuro) yo dormiré, tú dormirás, usted/él/ella dormirá, nosotros/as dormiremos, vosotros/as dormiréis, ustedes/ellos/ellas dormirán


31. Conjugation of dirigir – to direct
Note: Other verbs following this pattern include exigir and surgir. The verb is regular in pronunciation but not in spelling.

Infinitive (infinitivo) dirigir
Gerund (gerundio) dirigiendo
Participle (participio) dirigido

Present indicative (presente del indicativo)
yo dirijo, tú diriges, usted/él/ella dirige
nosotros/as dirigimos, vosotros/as dirigís, ustedes/ellos/ellas dirigen

Preterite (pretérito) yo dirigí, tu dirigiste, usted/él/ella dirigió, nosotros/as dirigimos, vosotros/as dirigisteis, ustedes/ellos/ellas dirigieron
Imperfect indicative (imperfecto del indicativo)
yo dirigía, tú dirigías, usted/él/ella dirigía
nosotros/as dirigíamos, vosotros/as dirigíais, ustedes/ellos/ellas dirigían

Future (futuro) yo dirigiré, tú dirigirás, usted/él/ella dirigirá, nosotros/as dirigiremos, vosotros/as dirigiréis, ustedes/ellos/ellas dirigirán


32. Conjugation of esparcir – to scatter, to spread
Note: This verb is regular in pronunciation but not in spelling.

Infinitive(infinitivo) esparcir
Gerund (gerundio) esparciendo
Participle (participio) esparcido
Present indicative (presente del indicativo)
yo esparzo, tú esparces, usted/él/ella esparce
nosotros/as esparcimos, vosotros/as esparcís, ustedes/ellos/ellas esparcen

Preterite (pretérito) yo esparcí, tu esparciste, usted/él/ella esparció, nosotros/as esparcimos, vosotros/as esparcisteis, ustedes/ellos/ellas esparcieron

Imperfect indicative
(imperfecto del indicativo) yo esparcía, tú esparcías, usted/él/ella esparcía nosotros/as esparcíamos, vosotros/as esparcíais, ustedes/ellos/ellas esparcían

Future (futuro) yo esparciré, tú esparcirás, usted/él/ella esparcirá
nosotros/as esparciremos, vosotros/as esparciréis, ustedes/ellos/ellas esparcirán


33. Conjugation of distinguir – to distinguish
Note: This verb is regular in pronunciation but not in spelling..

Infinitive(infinitivo) distinguir
Gerund (gerundio) distinguiendo
Participle (participio) distinguido
Present indicative (presente del indicativo)

yo distingo, tú distingues, usted/él/ella distingue
nosotros/as distinguimos, vosotros/as distinguís, ustedes/ellos/ellas distinguen

Preterite (pretérito) yo distinguí, tu distinguiste, usted/él/ella distinguió
nosotros/as distinguimos, vosotros/as distinguisteis,
ustedes/ellos/ellas distinguieron

Imperfect indicative (imperfecto del indicativo)
yo distinguía, tú distinguías, usted/él/ella distinguía
nosotros/as distinguíamos, vosotros/as distinguíais,
ustedes/ellos/ellas distinguían
Future (futuro) yo distinguiré, tú distinguirás, usted/él/ella distinguirá
nosotros/as distinguiremos, vosotros/as distinguiréis, ustedes/ellos/ellas distinguirán


34. Conjugation of enviar - to send
Note: Other verbs following this pattern include desviar, fiar, and guiar.

Infinitive(infinitivo) enviar
Gerund (gerundio) enviando
Participle (participio) enviado
Present indicative (presente del inidicativo)
yo envío, tú envías, usted/él/ella envía
nosotros/as enviamos, vosotros/as enviáis, ustedes/ellos/ellas envían

Preterite (pretérito) yo envié, tu enviaste, usted/él/ella envió
nosotros/as enviamos, vosotros/as enviasteis, ustedes/ellos/ellas enviaron

Imperfect indicativo (imperfecto del indicativo)
yo enviaba, tú enviabas, usted/él/ella enviaba
nosotros/as enviábamos, vosotros/as enviabais, ustedes/ellos/ellas enviaban

Future (futuro) yo enviaré, tú enviarás, usted/él/ella enviará
nosotros/as enviaremos, vosotros/as enviaréis, ustedes/ellos/ellas enviarán


35. Conjugation of elegir - to choose
Note: Other verbs following this pattern include corregir, fingir and regir.

Infinitive(infinitivo) elegir
Gerund (gerundio) eligiendo
Participle (participio) elegido

Present indicative (presente del indicativo) yo elijo, tú eliges, usted/él/ella elige, nosotros/as elegimos, vosotros/as elegís, ustedes/ellos/ellas eligen
Preterite (pretérito) yo elegí, tu elegiste, usted/él/ella elegió, nosotros/as elegimos, vosotros/as elegisteis, ustedes/ellos/ellas eligieron

Imperfect indicative (imperfecto del indicativo)
yo elegía, tú elegías, usted/él/ella elegía
nosotros/as elegíamos, vosotros/as elegíais, ustedes/ellos/ellas elegían

Future (futuro) yo elegiré, tú elegirás, usted/él/ella elegirá
nosotros/as elegiremos, vosotros/as elegiréis, ustedes/ellos/ellas elegirán


36. Conjugation of entender – to understand
Note: Other verbs following this pattern include ascender, atender, defender, descender, and perder.

Infinitive(infinitivo) entender
Gerund (gerundio) entendiendo
Participle (participio) entendido

Present indicative (presente del indicativo)
yo entiendo, tú entiendes, usted/él/ella entiende
nosotros/as entendemos, vosotros/as entendéis, ustedes/ellos/ellas entienden

Preterite (pretérito) yo entendí, tu entendiste, usted/él/ella entendió nosotros/as entendimos, vosotros/as entendisteis, ustedes/ellos/ellas entendieron

Imperfect indicativo (imperfecto del indicativo)
yo entendía, tú entendías, usted/él/ella entendía
nosotros/as entendíamos, vosotros/as entendíais, ustedes/ellos/ellas entendían

Future (futuro) yo entenderé, tú entenderás, usted/él/ella entenderá
nosotros/as entenderemos, vosotros/as entenderéis, ustedes/ellos/ellas entenderán

37. Conjugation of errar -
Infinitive(infinitivo) errar
Gerund (gerundio) errando
Participle (participio) errado

Present indicative (presente del inidicativo)
yo yerro, tú yerras, usted/él/ella yerra
nosotros/as erramos, vosotros/as erráis, ustedes/ellos/ellas yerran

Preterite (pretérito) yo erré, tu erraste, usted/él/ella erró
nosotros/as erramos, vosotros/as errasteis, ustedes/ellos/ellas erraron

Imperfect indicativo (imperfecto del indicativo)
yo erraba, tú errabas, usted/él/ella erraba
nosotros/as errábamos, vosotros/as errabais, ustedes/ellos/ellas erraban

Future (futuro) yo erraré, tú errarás, usted/él/ella errará
nosotros/as erraremos, vosotros/as erraréis, ustedes/ellos/ellas errarán


38. Conjugation of gozar - to enjoy
Note: Other verbs following this pattern include abrazar, adelgazar, amenazar, aplazar, aterrizar, avanzar, bostezar, cazar, cristalizar, cruzar, descalzar, deslizar, destrozar, disfrazar, economizar, embarazar, encabezar, endulzar, garantizar, izar, lanzar, organizar, realizar, rezar, rechazar, trazar and utulilzar. These verbs are regular in pronunciation. However, the z changes to a c when it comes before an e.

Infinitive (infinitivo) gozar
Gerund (gerundio) gozando
Participle (participio) gozado

Present indicative (presente del inidicativo)
yo gozo, tú gozas, usted/él/ella goza
nosotros/as gozamos, vosotros/as gozáis, ustedes/ellos/ellas gozan

Preterite (pretérito) yo gocé, tu gozaste, usted/él/ella gozó
nosotros/as gozamos, vosotros/as gozasteis, ustedes/ellos/ellas gozaron

Imperfect indicativo
(imperfecto del indicativo) yo gozaba, tú gozabas, usted/él/ella gozaba
nosotros/as gozábamos, vosotros/as gozabais, ustedes/ellos/ellas gozaban

Future (futuro) yo gozaré, tú gozarás, usted/él/ella gozará
nosotros/as gozaremos, vosotros/as gozaréis, ustedes/ellos/ellas gozarán


39. Conjugation of hacer – to make, to do
Note: Other verbs following this pattern are deshacer and satisfacer.
Infinitive(infinitivo) Hacer
Gerund (gerundio) Hacienda
Participle (participio) Hecho

Present indicative (presente del indicativo)
yo hago, tú haces, usted/él/ella hace
nosotros/as hacemos, vosotros/as hacéis, ustedes/ellos/ellas hacen

Preterite (pretérito) yo hice, tu hiciste, usted/él/ella hizo
nosotros/as hicimos, vosotros/as hicisteis, ustedes/ellos/ellas hicieron

Imperfect indicativo (imperfecto del indicativo)
yo hacía, tú hacías, usted/él/ella hacía
nosotros/as hacíamos, vosotros/as hacíais, ustedes/ellos/ellas hacían

Future (futuro) yo haré, tú harás, usted/él/ella hará
nosotros/as haremos, vosotros/as hacéis, ustedes/ellos/ellas harán


40. Conjugation of huir – to flee
Note: Other verbs following this pattern include concluir, construir, contribuir, destruir, influir, and other verbs ending in -uir.

Infinitive (infinitivo) Huir
Gerund (gerundio) Huyendo
Participle (participio) Huido

Present indicative (presente del indicativo)
yo huyo, tú huyes, usted/él/ella huye
nosotros/as huimos, vosotros/as huís, ustedes/ellos/ellas huyen

Preterite (pretérito) yo huí, tu huiste, usted/él/ella huyó
nosotros/as huimos, vosotros/as huisteis, ustedes/ellos/ellas huyeron

Imperfect indicative (imperfecto del indicativo)
yo huía, tú huías, usted/él/ella huía
nosotros/as huíamos, vosotros/as huíais, ustedes/ellos/ellas huían

Future (futuro) yo huiré, tú huirás, usted/él/ella huirá
nosotros/as huiremos, vosotros/as huiréis, ustedes/ellos/ellas huirán

41. Conjugation of oir - to hear

Infinitive (infinitivo) oír
Gerund (gerundio) oyendo
Participle (participio) oído
Present indicative
(presente del indicativo) yo oigo, tú oyes, usted/él/ella oye
nosotros/as oímos, vosotros/as oís, ustedes/ellos/ellas oyen

Preterite (pretérito) yo oí, tu oíste, usted/él/ella oyó
nosotros/as oímos, vosotros/as oísteis, ustedes/ellos/ellas oyeron

Imperfect indicative
(imperfecto del indicativo) yo oía, tú oías, usted/él/ella oía
nosotros/as oíamos, vosotros/as oíais, ustedes/ellos/ellas oían

Future (futuro) yo oiré, tú oirás, usted/él/ella oirá
nosotros/as oiremos, vosotros/as oiréis, ustedes/ellos/ellas oirán


42. Conjugation of teñir - to dye
Infinitive (infinitivo) teñir
Gerund (gerundio) tiñendo
Participle (participio) teñido o tinto

Present indicative (presente del indicativo)
yo tiño, tú tiñes, usted/él/ella tiñe
nosotros/as teñimos, vosotros/as teñís, ustedes/ellos/ellas tiñen

Preterite (pretérito) yo teñí, tu teñiste, usted/él/ella tiñó
nosotros/as teñimos, vosotros/as teñisteis, ustedes/ellos/ellas tiñeron

Imperfect indicative
(imperfecto del indicativo) yo teñía, tú teñías, usted/él/ella teñía nosotros/as teñíamos, vosotros/as teñíais, ustedes/ellos/ellas teñían

Future (futuro) yo tiñiré, tú teñirás, usted/él/ella teñirá
nosotros/as teñiremos, vosotros/as teñiréis, ustedes/ellos/ellas teñirán



43. Conjugation of volver – to return
Note: Other verbs following this pattern are absolver, devolver, disolver, desenvolver, resolver, and revolver.

Infinitive (infinitivo) volver
(to turn, return, go back)
Gerund (gerundio) Volviendo
Participle (participio) Vuelto

Present indicative presente del indicativo)
yo vuelvo, tú vuelves, usted/él/ella vuelve
nosotros/as volvemos, vosotros/as volvéis, ustedes/ellos/ellas vuelven

Preterite (pretérito) yo volví, tu volviste, usted/él/ella volvió
nosotros/as volvimos, vosotros/as volvisteis, ustedes/ellos/ellas volvieron

Imperfect indicativo
(imperfecto del indicativo) yo volvía, tú volvías, usted/él/ella volvía nosotros/as volvíamos, vosotros/as volvíais, ustedes/ellos/ellas volvían

Future (futuro) yo volveré, tú volverás, usted/él/ella volverá
nosotros/as volveremos, vosotros/as volveréis, ustedes/ellos/ellas volverán

44. Conjugation of vestir - to dress
Note: Other verbs conjugated in this pattern include competir, despedir, impedir, medir, pedir and repetir and servir.

Infinitive(infinitivo) vestir
Gerund (gerundio) vistiendo
Participle (participio) vestido

Present indicative (presente del indicativo)
yo visto, tú vistes, usted/él/ella viste
nosotros/as vestimos, vosotros/as vestís, ustedes/ellos/ellas visten

Preterite (pretérito) yo vestí, tu vestiste, usted/él/ella vistió
nosotros/as vestimos, vosotros/as vestisteis, ustedes/ellos/ellas vistieron

Imperfect indicative (imperfecto del indicativo)
yo vestía, tú vestías, usted/él/ella vestía
nosotros/as vestíamos, vosotros/as vestíais, ustedes/ellos/ellas vestían

Future (futuro) yo vestiré, tú vestirás, usted/él/ella vestirá
nosotros/as vestiremos, vosotros/as vestiréis, ustedes/ellos/ellas vestirán

45. Conjugation of valer – to be worth
Infinitive(infinitivo) valer
Gerund (gerundio) valiendo
Participle (participio) valido
Present indicative (presente del indicativo)
yo valgo, tú vales, usted/él/ella vale
nosotros/as valemos, vosotros/as valéis, ustedes/ellos/ellas valen

Preterite (pretérito) yo valí, tu valiste, usted/él/ella valió
nosotros/as valimos, vosotros/as valisteis, ustedes/ellos/ellas valieron

Imperfect indicativo (imperfecto del indicativo)
yo valía, tú valías, usted/él/ella valía
nosotros/as valíamos, vosotros/as valíais, ustedes/ellos/ellas valían

Future (futuro) yo valdré, tú valdrás, usted/él/ella valdrá
nosotros/as valdremos, vosotros/as valdréis, ustedes/ellos/ellas valdrán


46. Conjugation of vencer - to conquer
Note: Also following this pattern are mecer and convencer. This pattern is regular in pronunciation but not in spelling.

Infinitive(infinitivo) vencer
Gerund (gerundio) venciendo
Participle (participio) vencido

Present indicative (presente del indicativo)
yo venzo, tú vences, usted/él/ella vence
nosotros/as vencemos, vosotros/as vencéis, ustedes/ellos/ellas vencen

Preterite (pretérito) yo vencí, tu venciste, usted/él/ella venció
nosotros/as vencimos, vosotros/as vencisteis, ustedes/ellos/ellas vencieron

Imperfect indicativo (imperfecto del indicativo)
yo vencía, tú vencías, usted/él/ella vencía
nosotros/as vencíamos, vosotros/as vencíais, ustedes/ellos/ellas vencían

Future (futuro) yo venceré, tú vencerás, usted/él/ella vencerá
nosotros/as venceremos, vosotros/as venceréis, ustedes/ellos/ellas vencerán



47. Conjugation of romper - to break
Infinitive(infinitivo) romper
Gerund (gerundio) rompiendo
Participle (participio) roto

Present indicative (presente del indicativo)
yo rompo, tú rompes, usted/él/ella rompe
nosotros/as rompemos, vosotros/as rompéis, ustedes/ellos/ellas rompen

Preterite (pretérito) yo rompí, tu rompiste, usted/él/ella rompió
nosotros/as rompimos, vosotros/as rompisteis, ustedes/ellos/ellas rompieron

Imperfect indicativo (imperfecto del indicativo)
yo rompía, tú rompías, usted/él/ella rompía
nosotros/as rompíamos, vosotros/as rompíais, ustedes/ellos/ellas rompían

Future (futuro) yo romperé, tú romperás, usted/él/ella romperá
nosotros/as romperemos, vosotros/as romperéis, ustedes/ellos/ellas romperán