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Unformatted text preview: Andrew Robert Border Homework 5 due Fri, Nov 13 at 11:59 pm Course: math151au09es This problem set covers Sections 3.9  4.1 of the text. Recitation Call#: . Carefully read all instructions for entering answers into WeBWorK. Set: Hmwk5 1. (2 pts) Suppose xy = 1 and dy dt = 2. Find dx dt when x = 4. dx dt = 2. (2 pts) A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.3 cm/min. At what rate is the volume** of the snowball decreasing when the diameter is 17 cm? (Note the answer is a positive number). Rate = cm 3 min **) Look up the formula for the volume of a sphere in the front reference pages of Stewarts book. 3. (2 pts) The height of a triangle is increasing at a rate of 1 cm min while the area of the triangle is increasing at a rate of 2 cm 2 min . At what rate is the base of the triangle changing when the height is 10 cm and the area is 95 cm 2 ? Rate = cm min 4. (3 pts) A street light is at the top of a 20 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 5 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 35 ft from the base of the pole? Rate = ft sec 5. (3 pts) A A A A A A A A A A A j u x 4200 A lighthouse is situated on a small island 4200 feet from a straight shoreline. If the beacon on the lighthouse makes 5 rev olutions per minute, how fast is the light beam moving along the shoreline when it is pointing 4000 feet away from the near est point on the shoreline to the lighthouse? To solve this problem, we first need to express the distance x along the shoreline between the light beam and the nearest point to the lighthouse, in terms of the angle u shown in the above picture. We find that x = (Your answer should be an expression in u .) We have that du dt = radians per minute and that dx dt = feet per minute. 6. (3 pts) A swimming pool is 17 feet wide and has transverse crosssections which look like: @ @ @ @ 6 10 6 8 6 ?...
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This note was uploaded on 11/17/2009 for the course MATH 151 taught by Professor Any during the Fall '08 term at Ohio State.
 Fall '08
 Any
 Math

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