Pre-Calc Homework Solutions 97

# Pre-Calc Homework Solutions 97 - Section 3.6 dx dt dy dt dy...

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45. } d d x t } 5 } d d t } t 5 1 } d d y t } 5 } d d t } ˇ t w 5 } 2 ˇ 1 t w } } d d y x } 5 5 } 1/(2 1 ˇ t w ) } 5 } 2 ˇ 1 t w } The line passes through 1 } 1 4 } , ! } 1 4 } § 2 5 1 } 1 4 } , } 1 2 } 2 and has slope 5 1. Its equation is y 5 1 1 x 2 } 1 4 } 2 1 } 1 2 } , or y 5 x 1 } 1 4 } . 46. } d d x t } 5 } d d t } (2 t 2 1 3) 5 4 t } d d y t } 5 } d d t } ( t 4 ) 5 4 t 3 } d d y x } 5 5 } 4 4 t t 3 } 5 t 2 The line passes through (2( 2 1) 2 1 3, ( 2 1) 4 ) 5 (5, 1) and has slope ( 2 1) 2 = 1. Its equation is y 5 1( x 2 5) 1 1, or y 5 x 2 4. 47. } d d x t } 5 } d d t } ( t 2 sin t ) 5 1 2 cos t } d d y t } 5 } d d t } (1 2 cos t ) 5 sin t } d d y x } 5 5 } 1 2 sin co t s t } The line passes through 1 } p 3 } 2 sin } p 3 } , 1 2 cos } p 3 } 2 5 1 } p 3 } 2 } ˇ 2 3 w } , } 1 2 } 2 and has slope 5 ˇ 3 w . Its equation is y 5 ˇ 3 w 1 x 2 } p 3 } 1 } ˇ 2 3 w } 2 1 } 1 2 } , or y 5 ˇ 3 w x 1 2 2 } ˇ p 3 w } . 48. } d d x t } 5 } d d t } cos t 5 2 sin t } d d y t } 5 } d d t } (1 1 sin t ) 5 cos t } d d y x } 5 5 } 2 co si s n t t } 5 2 cot t The line passes through 1 cos } p 2 } , 1 1 sin } p 2 } 2 5 (0, 2) and has slope 2 cot 1 } p 2 } 2 5 0. Its equation is y 5 2.
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