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HW1solution_pdf

HW1solution_pdf - Valencia(drv252 assignment 1 luecke(58600...

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Valencia (drv252) – assignment 1 – luecke – (58600) 1 This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. HINTS. CalC11b16b: sin/cos = tan; CalC11b29s: The slope oF a line is the slope oF the tangent at any point on the line; CalC11b40a: What is the convention about the square root sign? 001 10.0 points IF the constant C is chosen so that the parabolic arc y = x 2 8 From (0 , 0) to (4 , 2) is given parametrically by ( Ct , y ( t ) ) , 0 t 3 , fnd the coordinates oF the point P on this arc corresponding to t = 2. 1. P = p 2 9 , 8 3 P 2. P = p 8 3 , 8 9 P correct 3. P = p 8 9 , 8 3 P 4. P = p 4 3 , 2 9 P 5. P = p 2 9 , 4 3 P 6. P = p 4 3 , 8 9 P Explanation: We have to determine y ( t ) and C so that 8 y ( t ) = C 2 t 2 , while x (0) = 0 , y (3) = 2 , 3 C = 4 . Thus C = 4 3 , 8 y ( t ) = p 4 3 P 2 t 2 . Consequently, when t = 2, P = (2 C, y (2)) = p 8 3 , 8 9 P . keywords: parametric curve, parabola 002 10.0 points Determine A so that the curve y = 9 x + 42 can be written in parametric Form as x ( t ) = t - 5 , y ( t ) = At - 3 . 1. A = - 11 2. A = 10 3. A = - 9 4. A = 9 correct 5. A = - 10 6. A = 11 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 = 9 x + 42 = A ( x + 5) - 3 . Consequently A = 9 . 003 10.0 points ±ind a Cartesian equation For the curve given in parametric Form by x ( t ) = 4 t 2 , y ( t ) = 8 t 3 .
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Valencia (drv252) – assignment 1 – luecke – (58600) 2 1. x = 2 y 4 / 3 2. x = y 2 / 3 correct 3. x = y 3 / 2 4. x = 2 y 2 / 3 5. x = 2 y 3 / 2 6. x = y 4 / 3 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 = 1 2 y 1 / 3 , in which case x = 4 p 1 2 y 1 / 3 P 2 = y 2 / 3 . 004 10.0 points Find a Cartesian equation for the curve given in parametric form by x ( t ) = 5 cos 2 2 t , y ( t ) = 3 sin 2 2 t . 1. 3 x - 5 y = 15 2.
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HW1solution_pdf - Valencia(drv252 assignment 1 luecke(58600...

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