Pre-Calc Homework Solutions 40

Pre-Calc Homework Solutions 40 - 40 Chapter 1 Review x 2 y...

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50. For simplicity, we assume that x and y are linear functions of t and that the point ( x , y ) passes through ( 2 3, 2 2) for t 5 0 and (4, 2 1) for t 5 1. Then x 5 f ( t ), where f (0) 5 2 3 and f (1) 5 4. Since slope = } D D x t } 5 } 4 1 2 2 ( 2 0 3) } 5 7, x 5 f ( t ) 5 7 t 2 3 5 2 3 1 7 t . Also, y 5 g ( t ), where g (0) 5 2 2 and g (1) 5 2 1. Since slope 5 } D D y t } 5 } 2 1 1 2 2 ( 2 0 2) } 5 1 y 5 g ( t ) 5 t 2 2 5 2 2 1 t . One possible parametrization is: x 5 2 3 1 7 t , y 5 2 2 1 t , 2‘ , t , ‘ . 51. For simplicity, we assume that x and y are linear functions of t and that the point ( x , y ) starts at (2, 5) for t 5 0 and passes through ( 2 1, 0) for t 5 1. Then x 5 f ( t ), where f (0) 5 2 and f (1) 5 2 1. Since slope 5 } D D x t } 5 } 2 1 1 2 2 0 2 } 5 2 3, x 5 f ( t ) 5 2 3 t 1 2 5 2 2 3 t . Also, y 5 g ( t ), where g (0) 5 5 and g (1) 5 0. Since slope 5 } D D y t } 5 } 0 1 2 2 5 0 } 5 2 5, y 5 g ( t ) 5 2 5 t 1 5 5 5 2 5 t . One possible parametrization is: x 5 2 2 3 t , y 5 5 2 5 t , t $ 0. 52. One possible parametrization is: x 5 t , y 5 t ( t 2 4), t # 2.
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