This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: patino (mp25752) 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 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....
View Full
Document
 Spring '09
 Lueke

Click to edit the document details