Assignment 1

Assignment 1 - patino(mp25752 – Assignment1 – luecke...

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Unformatted text preview: patino (mp25752) – Assignment1 – luecke – (57510) 1 This print-out should have 14 questions. Multiple-choice 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 Ct, C 2 8 t 2 parenrightBig , ≤ t ≤ 4 , is the arc of the parabola 8 y = x 2 from (0 , 0) to (4 , 2), find the coordinates of the point P on this arc corresponding to t = 2. 1. P = parenleftBig 2 , 1 2 parenrightBig correct 2. P = parenleftBig 1 8 , 1 parenrightBig 3. P = parenleftBig 1 2 , 2 parenrightBig 4. P = parenleftBig 1 , 1 2 parenrightBig 5. P = parenleftBig 1 , 1 8 parenrightBig 6. P = parenleftBig 1 8 , 2 parenrightBig Explanation: The point P has coordinates parenleftBig Ct vextendsingle vextendsingle vextendsingle t =2 , C 2 8 t 2 vextendsingle vextendsingle vextendsingle t =2 parenrightBig = parenleftBig 2 C, C 2 2 parenrightBig , so we need to find C . But we are told that the graph of parenleftBig Ct, C 2 8 t 2 parenrightBig passes through (4 , 2) when t = 4. Thus 4 C = 4 , i . e ., C = 1 . Consequently, P = parenleftBig 2 C, C 2 2 parenrightBig = parenleftBig 2 , 1 2 parenrightBig . keywords: parametric curve, parabola 002 10.0 points Determine A so that the curve y = 3 x + 1 can be written in parametric form as x ( t ) = t- 1 , y ( t ) = At- 2 . 1. A =- 1 2. A = 1 3. A = 3 correct 4. A =- 3 5. A = 2 6. A =- 2 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 + 1. Thus y = 3 x + 1 = A ( x + 1)- 2 . Consequently A = 3 . 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 . 1. y = 1 2 x 3 / 2 patino (mp25752) – Assignment1 – luecke – (57510) 2 2. y = 1 2 x 2 / 3 correct 3. y = 1 4 x 2 / 3 4. y = 1 4 x 4 / 3 5. y = 1 2 x 4 / 3 6. y = 1 4 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 8 parenleftBig 2 x 1 / 3 parenrightBig 2 = 1 2 x 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 ) = 3 sin 2 4 t . 1. x 5- y 3 = 1 15 2. 3 x- 5 y = 15 3. 3 x + 5 y = 15 correct 4. 5 x + 3 y = 15 5....
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This note was uploaded on 10/21/2009 for the course M 53215 taught by Professor Lueke during the Spring '09 term at University of Texas.

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Assignment 1 - patino(mp25752 – Assignment1 – luecke...

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