# HW 6 - wolz(cmw2833 – HW 6 – ODELL –(54615 1 This...

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Unformatted text preview: wolz (cmw2833) – HW 6 – ODELL – (54615) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Determine A so that the curve y = 4 x + 15 can be written in parametric form as x ( t ) = t- 4 , y ( t ) = At- 1 . 1. A =- 3 2. A = 5 3. A = 4 correct 4. A =- 5 5. A =- 4 6. A = 3 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 + 4. Thus y = 4 x + 15 = A ( x + 4)- 1 . Consequently A = 4 . 002 10.0 points Find a Cartesian equation for the curve given in parametric form by y ( t ) = 1 2 t 2 , x ( t ) = 1 8 t 3 . 1. y = 2 x 4 / 3 2. y = 2 x 2 / 3 correct 3. y = 2 x 3 / 2 4. y = x 4 / 3 5. y = x 2 / 3 6. y = x 3 / 2 Explanation: We have to eliminate the parameter t from the equations for x and y . But from the equation for x , it follows that t = 2 x 1 / 3 , in which case y = 1 2 parenleftBig 2 x 1 / 3 parenrightBig 2 = 2 x 2 / 3 . 003 10.0 points Find a Cartesian equation for the curve given in parametric form by x ( t ) = 4 cos 2 2 t, y ( t ) = 5 sin 2 2 t. 1. x 5 + y 4 = 1 20 2. 5 x- 4 y = 20 3. x 4- y 5 = 1 20 4. 4 x + 5 y = 20 5. x 5- y 4 = 1 20 6. 5 x + 4 y = 20 correct Explanation: We have to eliminate the parameter t from the equations for x and y . Now cos 2 θ + sin 2 θ = 1 . Thus x 4 + y 5 = 1 . But then after simplification, the curve has Cartesian form 5 x + 4 y = 20 . wolz (cmw2833) – HW 6 – ODELL – (54615) 2 004 10.0 points Determine a Cartesian equation for the curve given in parametric form by x ( t ) = 3 ln(4 t ) , y ( t ) = √ t. 1. y = 1 2 e 6 /x 2. y = 1 2 e x/ 6 correct 3. y = 1 3 e 4 /x 4. y = 1 3 e x/ 2 5. y = 1 2 e x/ 3 6. y = 1 3 e x/ 4 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/ 3 . But then y = parenleftBig 1 4 e x/ 3 parenrightBig 1 / 2 = 1 2 e x/ 6 . 005 10.0 points 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 counterclockwise along the ellipse x 2 4 + y 2 9 = 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). 6. Moves once clockwise along the ellipse (2 x ) 2 + (3 y ) 2 = 1 , starting and ending at (0 , 3)....
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HW 6 - wolz(cmw2833 – HW 6 – ODELL –(54615 1 This...

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