Pre-Calc Homework Solutions 109

# Pre-Calc Homework Solutions 109 - Section 3.7 d(4 dt 109 44...

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44. v ( t ) 5 s 9 ( t ) 5 } d d t } (4 1 6 t ) 3/2 5 } 3 2 } (4 1 6 t ) 1/2 (6) 5 9(4 1 6 t ) 1/2 a ( t ) 5 v 9 ( t ) 5 } d d t } [9(4 1 6 t ) 1/2 ] 5 } 9 2 } (4 1 6 t ) 2 1/2 (6) 5 27(4 1 6 t ) 2 1/2 At t 5 2, the velocity is v (2) 5 36 m/sec and the acceleration is a (2) 5 } 2 4 7 } m/sec 2 . 45. Acceleration 5 } d d v t } 5 } d d t } [8( s 2 t ) 1/2 1 1] 5 4( s 2 t ) 2 1/2 1 } d d s t } 2 1 2 5 4( s 2 t ) 2 1/2 ( v 2 1) 5 4( s 2 t ) 2 1/2 [(8( s 2 t ) 1/2 1 1) 2 1] 5 32( s 2 t ) 2 1/2 ( s 2 t ) 1/2 5 32 ft/sec 2 46. y 4 2 4 y 2 5 x 4 2 9 x 2 } d d x } ( y 4 ) 2 } d d x } (4 y 2 ) 5 } d d x } ( x 4 ) 2 } d d x } (9 x 2 ) 4 y 3 } d d y x } 2 8 y } d d y x } 5 4 x 3 2 18 x } d d y x } 5 } 4 4 x y 3 3 2 2 1 8 8 y x } 5 } 2 2 x y 3 3 2 2 9 4 x y } Slope at (3, 2): } 2 2 ( ( 3 2 ) ) 3 3 2 2 9 4 ( ( 3 2 ) ) } 5 } 2 8 7 } Slope at ( 2 3, 2): } 2( 2 2( 3 2 ) ) 3 3 2 2 9 4 ( ( 2 2) 3) } 5 2 } 2 8 7 } Slope at ( 2 3, 2 2): } 2 2 ( ( 2 2 3 2 ) ) 3 3 2 2 9 4 ( ( 2 2 3 2 ) ) } 5 } 2 8 7 } Slope at (3, 2 2): } 2( 2 2 (3 2 ) ) 3 3 2 2 9 4 ( ( 3 2 ) 2) } 5 2 } 2 8 7 } 47. (a) x 3 1 y 3 2 9 xy 5 0 } d d x } ( x 3 ) 1 } d d x } ( y 3 ) 2 9 } d d x } ( xy ) 5 } d d x } (0) 3 x 2 1 3 y 2 } d d y x } 2 9 x } d d y x } 2 9( y )(1) 5 0 (3 y 2 2 9 x ) } d d y x } 5 9 y 2 3 x 2 } d d y x } 5 } 9 3 y y 2 2 2 3 9 x x 2 } 5 } 3 y 2 y 2 2 3 x x 2 }
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