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Unformatted text preview: han (kh23638) – Assignment1 – luecke – (57510) 1 This printout should have 14 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 10.0 points If the constant C is chosen so that the curve given parametrically by parenleftBig C 2 12 t 2 , Ct parenrightBig , ≤ t ≤ 5 , is the arc of the parabola y 2 = 12 x from (0 , 0) to (3 , 6), find the coordinates of the point P on this arc corresponding to t = 2. 1. P = parenleftBig 12 5 , 12 25 parenrightBig 2. P = parenleftBig 6 5 , 3 25 parenrightBig 3. P = parenleftBig 3 25 , 6 5 parenrightBig 4. P = parenleftBig 12 25 , 12 5 parenrightBig correct 5. P = parenleftBig 3 25 , 12 5 parenrightBig 6. P = parenleftBig 6 5 , 12 25 parenrightBig Explanation: The point P has coordinates parenleftBig C 2 12 t 2 vextendsingle vextendsingle vextendsingle t =2 , Ct vextendsingle vextendsingle vextendsingle t =2 parenrightBig = parenleftBig C 2 3 , 2 C parenrightBig , so we need to find C . But we are told that the graph of parenleftBig C 2 12 t 2 , Ct parenrightBig passes through (3 , 6) when t = 5. Thus 5 C = 6 , i . e ., C = 6 5 . Consequently, P = parenleftBig C 2 3 , 2 C parenrightBig = parenleftBig 12 25 , 12 5 parenrightBig . keywords: parametric curve, parabola 002 10.0 points Determine A so that the curve y = 4 x + 3 can be written in parametric form as x ( t ) = t 2 , y ( t ) = At 5 . 1. A = 3 2. A = 3 3. A = 4 4. A = 4 correct 5. A = 5 6. A = 5 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 + 2. Thus y = 4 x + 3 = A ( x + 2) 5 . Consequently A = 4 . 003 10.0 points Find a Cartesian equation for the curve given in parametric form by x ( t ) = 4 t 2 , y ( t ) = 8 t 3 . 1. x = y 2 / 3 correct 2. x = y 4 / 3 han (kh23638) – Assignment1 – luecke – (57510) 2 3. x = 2 y 2 / 3 4. x = 2 y 3 / 2 5. x = y 3 / 2 6. x = 2 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 parenleftbigg 1 2 y 1 / 3 parenrightbigg 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 4 t , y ( t ) = 2 sin 2 4 t . 1. 2 x + 5 y = 10 correct 2....
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This note was uploaded on 10/05/2009 for the course MATH M408M taught by Professor Luecke during the Spring '09 term at École Normale Supérieure.
 Spring '09
 Luecke
 Math

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