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: Valencia (drv252) 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 = x 2 8 from (0 , 0) to (4 , 2) is given parametrically by ( Ct , y ( t ) ) , t 3 , find the coordinates of the point P on this arc corresponding to t = 2. 1. P = parenleftBig 2 9 , 8 3 parenrightBig 2. P = parenleftBig 8 3 , 8 9 parenrightBig correct 3. P = parenleftBig 8 9 , 8 3 parenrightBig 4. P = parenleftBig 4 3 , 2 9 parenrightBig 5. P = parenleftBig 2 9 , 4 3 parenrightBig 6. P = parenleftBig 4 3 , 8 9 parenrightBig 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 ) = parenleftBig 4 3 parenrightBig 2 t 2 . Consequently, when t = 2, P = (2 C, y (2)) = parenleftBig 8 3 , 8 9 parenrightBig . 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 Find a Cartesian equation for the curve given in parametric form by x ( t ) = 4 t 2 , y ( t ) = 8 t 3 . 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 parenleftbigg 1 2 y 1 / 3 parenrightbigg 2 = y 2 / 3 ....
View
Full
Document
This note was uploaded on 03/26/2009 for the course CH 302 taught by Professor Holcombe during the Spring '07 term at University of Texas at Austin.
 Spring '07
 Holcombe
 Chemistry

Click to edit the document details