39.The weight of an object on Earth is directly proportional to the weight of that same object on
the moon. A 200-lb astronaut would weigh 32 lb on the moon. How much would a 50-lb dog
weigh on the moon?
40.The pressure exerted by a certain liquid at a given point is directly proportional to the
depth of the point beneath the surface of the liquid. The pressure at 30 m is 80 newtons.
What pressure is exerted at 50 m?
414 CHAPTER 7 Rational Expressions and Functions
41.The volume of a can of tomatoes is di-
rectly proportional to the height of the
can. If the volume of the can is 300
when its height is 10.62 cm, find the
volume of a can with height 15.92 cm.
42.The force required to compress a spring
is directly proportional to the change
in length of the spring. If a force of
20 newtons is required to compress a
certain spring 2 cm, how much force is
required to compress the spring from
20 cm to 8 cm?
cm^3
10.62 cm
20 cm 18 cm
20
newtons
?
8 cm
43.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 576 ft high and
hits the ground in 6 sec, how far did it fall in the
first 4 sec?
44.The amount of water emptied by a pipe varies directly as the square of the diameter of the
pipe. For a certain constant water flow, a pipe emptying into a canal will allow 200 gal of
water to escape in an hour. The diameter of the pipe is 6 in. How much water would a
12-in. pipe empty into the canal in an hour, assuming the same water flow?
45.Over a specified distance, rate varies inversely with time. If a Dodge Viper 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?
46.For a constant area, the length of a rectangle varies inversely as the width. The length of a
rectangle is 27 ft when the width is 10 ft. Find the width of a rectangle with the same area
if the length is 18 ft.
47.The frequency of a vibrating string varies inversely as its length. That is, a longer string
vibrates fewer times in a second than a shorter string. Suppose a piano string 2 ft long
vibrates 250 cycles per sec. What frequency would a string 5 ft long have?
48.The current in a simple electrical circuit varies inversely as the resistance. If the current is
20 amps when the resistance is 5 ohms, find the current when the resistance is 7.5 ohms.
49.The amount of light (measured in foot-candles) produced
by a light source varies inversely as the square of the dis-
tance from the source. If the illumination produced 1 m
from a light source is 768 foot-candles, find the illumina-
tion produced 6 m from the same source.
50.The force with which Earth attracts an object above Earth’s surface varies inversely as the
square of the distance of the object from the center of Earth. If an object 4000 mi from the
center of Earth is attracted with a force of 160 lb, find the force of attraction if the object
were 6000 mi from the center of Earth.
51.For a given interest rate, simple interest varies jointly as principal and time. If $2000 left
in an account for 4 yr earned interest of $280, how much interest would be earned in 6 yr?
576
ft
1 m
