32. A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the angle between the string and the horizontal decreasing when 200 ft of string has been let out?

Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter65: Achievement Review—section Six
Section: Chapter Questions
Problem 58AR: Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places...
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Question
3.9-Number 32, please. Using related rates and drawn up diagrams of triangles, solve the story problem below.
3:15
ponit. A cross-section is shown in the figure. If the pool is being filled at a rate of 0.8 t/min, now
fast is the water level rising when the depth at the deepest point is 5 ft?
6
X
12
31. The sides of an equilateral triangle are increasing at a rate of 10 cm/min. At what rate is the area of
the triangle increasing when the sides are 30 cm long?
32. A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the angle
between the string and the horizontal decreasing when 200 ft of string has been let out?
33. A car is traveling north on a straight road at 20 m/s and a drone is flying east at 6m/s at an
elevation of 25 m. At one instant the drone passes directly over the car. How fast is the distance.
between the drone and the car changing 5 seconds later?
Answer
34. If the minute hand of a clock has length r (in centimeters), find the rate at which it sweeps out area
as a function of r.
Transcribed Image Text:3:15 ponit. A cross-section is shown in the figure. If the pool is being filled at a rate of 0.8 t/min, now fast is the water level rising when the depth at the deepest point is 5 ft? 6 X 12 31. The sides of an equilateral triangle are increasing at a rate of 10 cm/min. At what rate is the area of the triangle increasing when the sides are 30 cm long? 32. A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the angle between the string and the horizontal decreasing when 200 ft of string has been let out? 33. A car is traveling north on a straight road at 20 m/s and a drone is flying east at 6m/s at an elevation of 25 m. At one instant the drone passes directly over the car. How fast is the distance. between the drone and the car changing 5 seconds later? Answer 34. If the minute hand of a clock has length r (in centimeters), find the rate at which it sweeps out area as a function of r.
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