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math151au09es.border.17.Hmwk5

# math151au09es.border.17.Hmwk5 - Andrew Robert Border...

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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 Stewart’s 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) 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 cross-sections which look like: 6 10 6 8 h 5 5 If the pool is being filled at a rate of 0.8 cubic feet per minute, how fast is the water level rising when the depth of water is 4 feet?

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math151au09es.border.17.Hmwk5 - Andrew Robert Border...

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