Solution_pdf - han(kh23638 – Assignment1 – luecke –(57510 1 This print-out should have 14 questions Multiple-choice questions may continue on

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: han (kh23638) – 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 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....
View Full Document

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.

Page1 / 8

Solution_pdf - han(kh23638 – Assignment1 – luecke –(57510 1 This print-out should have 14 questions Multiple-choice questions may continue on

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online