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: Granillo, Yvette – Homework 8 – Due: Oct 20 2005, 3:00 am – Inst: Edward Odell 1 This printout should have 20 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points A rock is thrown into a still pond and causes a circular ripple. If the radius of the ripple is increasing at a rate of 6 ft/sec, at what speed is the area of the ripple increasing when its radius is 2 feet? 1. speed = 22 π sq. ft/sec 2. speed = 22 sq. ft/sec 3. speed = 24 π sq. ft/sec correct 4. speed = 20 sq. ft/sec 5. speed = 23 sq. ft/sec 6. speed = 24 sq. ft/sec 7. speed = 20 π sq. ft/sec 8. speed = 21 π sq. ft/sec Explanation: The area, A , of a circle having radius r is given by A = πr 2 . Differentiating implicitly with respect to t we thus see that dA dt = 2 πr dr dt . When r = 2 , dr dt = 6 , therefore, the speed at which the area of the ripple is increasing is given by speed = 24 π sq. ft/sec . keywords: Stewart5e, 002 (part 1 of 1) 10 points A point is moving on the graph of xy = 3. When the point is at (2 , 3 2 ), its xcoordinate is increasing at a rate of 6 units per second. What is the speed of the ycoordinate at that moment and in which direction is it moving? 1. speed = 9 2 units/sec, decreasing y correct 2. speed = 11 2 units/sec, increasing y 3. speed = 13 2 units/sec, increasing y 4. speed = 11 2 units/sec, decreasing y 5. speed = 9 2 units/sec, decreasing y Explanation: Provided x,y 6 = 0, the equation xy = 3 can be written as y = 3 /x . Differentiating implicitly with respect to t we thus see that dy dt = 3 x 2 dx dt . whenever x 6 = 0. When x = 2 , dx dt = 6 , therefore, the corresponding rate of change of the ycoordinate is given by dy dt fl fl fl x =2 = 6 ‡ 3 x 2 ·fl fl fl x =2 = 9 2 . Consequently, the speed of the ycoordintate is 9 2 units per second and the negative sign indicates that the point is moving in the di rection of decreasing y . keywords: Stewart5e, 003 (part 1 of 1) 10 points Granillo, Yvette – Homework 8 – Due: Oct 20 2005, 3:00 am – Inst: Edward Odell 2 A street light is on top of a 10 foot pole. A person who is 4 feet tall walks away from the pole at a rate of 3 feet per second. At what speed is the tip of the person’s shadow moving when he is 10 feet from the pole? 1. tip speed = 31 6 ft/sec 2. tip speed = 29 6 ft/sec 3. tip speed = 5 ft/sec correct 4. tip speed = 14 3 ft/sec 5. tip speed = 16 3 ft/sec Explanation: If x denotes the distance of the tip of the person’s shadow from the pole and y denotes the distance of the person from the pole, then the shadow and the lightpole are related in the following diagram (0 , 10) (10 , 4) y x By similar triangles, 4 x y = 10 x , so (10 4) x = 10 y . Thus, after implicit differentiation with respect to t , (10 4) dx dt = 10 dy dt ....
View
Full
Document
This test prep was uploaded on 04/16/2008 for the course M 408k taught by Professor Schultz during the Spring '08 term at University of Texas.
 Spring '08
 schultz

Click to edit the document details