Postclass 10.1-solutions

Postclass 10.1-solutions - im(gi768 Postclass 10.1...

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im (gi768) – Postclass 10.1 – sadun – (53088) 1 This print-out should have 9 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points Determine A so that the curve y = 6 x + 26 can be written in parametric form as x ( t ) = t - 5 , y ( t ) = At - 4 . 1. A = 5 2. A = - 4 3. A = - 5 4. A = - 6 5. A = 6 correct 6. A = 4 Explanation: We have to eliminate t from the parametric equations for x and y . Now from the equation for x it follows that t = x + 5. Thus y = 6 x + 26 = A ( x + 5) - 4 . Consequently A = 6 . 002 10.0points Find a Cartesian equation for the curve given in parametric form by x ( t ) = 1 2 t 2 , y ( t ) = 1 8 t 3 . 1. x = y 4 / 3 2. x = y 3 / 2 3. x = y 2 / 3 4. x = 2 y 4 / 3 5. x = 2 y 3 / 2 6. x = 2 y 2 / 3 correct Explanation: We have to eliminate the parameter t from the equations for x and y . But from the equation for y , it follows that t = 2 y 1 / 3 , in which case x = 1 2 parenleftBig 2 y 1 / 3 parenrightBig 2 = 2 y 2 / 3 . 003 10.0points Determine a Cartesian equation for the curve given in parametric form by x ( t ) = 4 ln(4 t ) , y ( t ) = t . 1. y = 1 2 e x/ 8 correct 2. y = 1 4 e x/ 2 3. y = 1 2 e x/ 4 4. y = 1 2 e 8 /x 5. y = 1 4 e x/ 4 6. y = 1 4 e 4 /x Explanation: We have to eliminate the parameter t from the equations for x and y . Now from the equation for x it follows that t = 1 4 e x/ 4 .
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im (gi768) – Postclass 10.1 – sadun – (53088) 2 But then y = parenleftBig 1 4 e x/ 4 parenrightBig 1 / 2 = 1 2 e x/ 8 . 004 10.0points Describe the motion of a particle with posi- tion P ( x, y ) when x = 2 sin t , y = 3 cos t as t varies in the interval 0 t 2 π . 1. Moves once clockwise along the ellipse (2 x ) 2 + (3 y ) 2 = 1 , starting and ending at (0 , 3). 2. Moves along the line x 2 + y 3 = 1 , starting at (2 , 0) and ending at (0 , 3). 3. Moves once clockwise along the ellipse x 2 4 + y 2 9 = 1 , starting and ending at (0 , 3). correct 4. Moves along the line x 2 + y 3 = 1 , starting at (0 , 3) and ending at (2 , 0). 5. Moves once counterclockwise along the ellipse (2 x ) 2 + (3 y ) 2 = 1 , starting and ending at (0 , 3).
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  • Fall '07
  • Sadler
  • René Descartes, Parametric equation

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