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Unformatted text preview: miller (zdm77) assignment 1 luecke (58600) 1 This printout should have 13 questions. Multiplechoice questions may continue on the next column or page find 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 2 = 16 x from (0 , 0) to (4 , 8) is given parametrically by ( x ( t ) , Ct ) , t 5 , find the coordinates of the point P on this arc corresponding to t = 2. 1. P = parenleftBig 16 25 , 16 5 parenrightBig correct 2. P = parenleftBig 8 5 , 16 25 parenrightBig 3. P = parenleftBig 8 5 , 4 25 parenrightBig 4. P = parenleftBig 4 25 , 8 5 parenrightBig 5. P = parenleftBig 16 5 , 16 25 parenrightBig 6. P = parenleftBig 4 25 , 16 5 parenrightBig Explanation: We have to determine x ( t ) and C so that 16 x ( t ) = C 2 t 2 , while x (0) = 0 , x (5) = 4 , 5 C = 8 . Thus C = 8 5 , 16 x ( t ) = parenleftBig 8 5 parenrightBig 2 t 2 . Consequently, when t = 2, P = ( x (2) , 2 C ) = parenleftBig 16 25 , 16 5 parenrightBig . keywords: parametric curve, parabola 002 10.0 points Determine A so that the curve y = 8 x + 20 can be written in parametric form as x ( t ) = t 3 , y ( t ) = At 4 . 1. A = 8 2. A = 8 correct 3. A = 9 4. A = 7 5. A = 7 6. A = 9 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 + 3. Thus y = 8 x + 20 = A ( x + 3) 4 . Consequently A = 8 . 003 10.0 points Find a Cartesian equation for the curve given in parametric form by y ( t ) = 1 8 t 2 , x ( t ) = 1 8 t 3 . miller (zdm77) assignment 1 luecke (58600) 2 1. y = 1 4 x 4 / 3 2. y = 1 2 x 4 / 3 3. y = 1 2 x 3 / 2 4. y = 1 4 x 3 / 2 5. y = 1 4 x 2 / 3 6. y = 1 2 x 2 / 3 correct 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 8 parenleftBig 2 x 1 / 3 parenrightBig 2 = 1 2 x 2 / 3 ....
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 Fall '07
 Gilbert
 Slope

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