SECTION 7.8 Variation 481Find each power. See Sections 1.2 and 5.1.
Find the value of for the given values of a and b. See Section 1.3.
49.a=5,b= 12 50.a=7,b= 24
a^2 +b^282 1 - 322 - 122 3.5^2PREVIEW EXERCISES
27 ft18 ft10 ft
?35.Over a specified distance, rate varies
inversely with time. If a Nissan 370Z on
a test track goes a certain distance in
one-half minute at 160 mph, what rate is
needed to go the same distance in three-
fourths minute?
36.For a constant area, the length of a rec-
tangle varies inversely as the width. The
length of a rectangle is 27 ft when the
width is 10 ft. Find the width of a rec-
tangle with the same area if the length is
18 ft.37.The current in a simple electrical circuit varies inversely as the resistance. If the cur-
rent is 20 amps when the resistance is 5 ohms, find the current when the resistance is
8 ohms.
38.If the temperature is constant, the pressure of a gas in a container varies inversely as the
volume of the container. If the pressure is 10 lb per in a container with volume 3 ,
what is the pressure in a container with volume 1.5?
39.The force required to compress a spring varies directly as
the change in the length of the spring. If a force of 12 lb is
required to compress a certain spring 3 in., how much force
is required to compress the spring 5 in.?
40.In the inversion of raw sugar, the rate of change of the amount of raw sugar varies directly
as the amount of raw sugar remaining. The rate is 200 kg per hr when there are 800 kg
left. What is the rate of change per hour when only 100 kg are left?
41.The area of a circle varies directly as the square of its radius. A circle with radius 3 in.
has area 28.278. What is the area of a circle with radius 4.1 in. (to the nearest
thousandth)?
42.For a body falling freely from rest (disregarding air resistance), the distance the body falls
varies directly as the square of the time. If an object is dropped from the top of a tower
400 ft high and hits the ground in 5 sec, how far did it fall in the first 3 sec?
43.The amount of light (measured in footcandles) produced by a light source varies in-
versely as the square of the distance from the source. If the amount of light produced 4 ft
from a light source is 75 footcandles, find the amount of light produced 9 ft from the
same source.
44.The force with which Earth attracts an object above Earth’s surface varies inversely as the
square of the object’s distance from the center of Earth. If an object 4000 mi from the cen-
ter of Earth is attracted with a force of 160 lb, find the force of attraction on an object
6000 mi from the center of Earth.
in.^2ft^3ft^2 ft^3Length
Length3 in.