1
If x \propto \dfrac1y, and x = 4 when y = 100, find x when y = 10.
Chapter 28 · Variation
Chapter challenge
Ten problems drawn from every lesson in the chapter. Get each one right on your first try for a perfect score. A new set is drawn each time.
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0of 10 done
From Inverse and Joint Variation, exercise 5
From Problems in Variation, exercise 23
2
Find the length of a pendulum which vibrates once in 2 seconds. (Use the facts of Exercise 22.)
From Constants, Variables, and Direct Variation, exercise 3
Problems in variation:
3
If x \propto y, and x = h when y = k, find y when x = m.
From Problems in Variation, exercise 24
4
The pressure of wind on a flat (plane) surface varies jointly as the area of the surface and the square of the wind's velocity. The pressure on one square foot is .9 pounds when the wind is moving at the rate of 15 miles per hour. Find the velocity of the wind when the pressure on one square yard is 18 pounds.
From Inverse and Joint Variation, exercise 4
5
If x varies inversely as y, and x = 6 when y = 7, find x when y = 21.
From Problems in Variation, exercise 13
6
If a wagon wheel 4 feet 8 inches in diameter makes 360 revolutions in going a certain distance, how many revolutions will a wheel 5 feet in diameter make in going the same distance?
From Constants, Variables, and Direct Variation, exercise 2
Problems in variation:
7
If x \propto y, and x = 6 when y = 10, find y when x = 15.
From Inverse and Joint Variation, exercise 10
8
If d varies directly as t^2, and d = 64 when t = 2, find d when t = 4.
From Problems in Variation, exercise 12
9
The weight of any object below the surface of the earth varies directly as its distance from the center of the earth. An object weighs 100 pounds at the surface of the earth. What would be its weight (a) 1000 miles below the surface (radius of the earth = 4000 miles)? (b) 2000 miles below the surface? (c) at the center of the earth?
From Problems in Variation, exercise 21
10
The weight of a sphere of given material varies directly as the cube of its radius. Two spheres of the same material have radii 2 inches and 6 inches respectively. The first weighs 6 pounds. Find the weight of the second.