Homework 6 MATH 2413 Calculus I Complete all work neatly on your own paper and not on this assignment sheet itself. All steps should be shown and your work must be easily readable. Problems without work or explanation will receive no credit. You will be turning in all homework online through 02L. Related Rates dx d 1. A particle moves along the curve y = y'xz +1 in such a way that y = 4. Find dy when x = 3. t t 2. A ladder 15 feet tall leans against a vertical wall ofa house. If the bottom of the ladder is pulled away horizontally from the house at 4 ft/sec, how fast is the top ofthe ladder sliding down the wall when the bottom of the ladder is 9 feet from the wall? 3. Two automobiles start from a point A at the same time. One travels west at 72 miles per hour; the other travels north at 54 miles per hour. How fast is the distance between them increasing 3 hours after they start? 4. An observer stands 25 feet from the base of a flagpole and watches a flag being lowered at a rate of 5 ft/sec. Determine the rate at which the angle of elevation from the observer to the flag is changing at the instant that the flag is 25 feet above eyeslevel. 5. At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 10 cubic ft per minute. The diameter of the base ofthe cone is approximately three times the altitude. At what rate is the height of the pile 1 changing when the pile is 15 ft high? (The volume of a cone is V = 331311.) 6. A snowball is in the shape ofa sphere. Its volume is increasing at a constant rate of 10 cubic inches per minute. 4 How fast is the radius increasing when the volume of the sphere is 362rin3 ? (The volume of a sphere is V = E1173 .) 7. The base of a triangle is shrinking at a rate of 1 cm/min and the height of the triangle is increasing at a rate of 5 cm/min. Find the rate at which the area of the triangle changes when the height is 22 cm and the base is 10 cm. 3 8. A trough has ends shaped like isosceles triangles. with width 3 m and height 4 m. and the trough is 10 m long. Water is being pumped into the trough at a rate of 4 cubic meters per minute. At what rate does the height of the water change when the water is T / 1 m deep? l /10 9. A circle is inscribed in a square. as shown in the figure. The circumference ofthe circle is increasing at a constant rate of 6 in/sec. As the circle expands, the square expands to maintain the condition of tangency