“There's two kinds of people in this world, there's
winners and there's losers. Okay, you know what the
difference is? Winners don't give up.”
3.4b: Inverse and Joint Variation
Direct Variation
Let x and y denote two quantities. Then y varies directly
with x if there is a nonzero constant k such that
y  kx
1) Suppose y varies directly with x. If y = 3 when x = 9…
a) Find a general formula relating x and y.

b) What is y when x = 21?
Direct Variation
2) The number of gallons of water W used when taking a
shower varies directly with the time t in minutes. A shower
lasting 5 minutes uses 30 gallons of water. How much
water is used in a shower lasting 11 minutes?
Inverse Variation
Let x and y denote two quantities. Then y varies inversely
with x if there is a nonzero constant k such that
k
y
x
3) Suppose y varies inversely with x. If y = 12 when x = 5…
a) Find a general formula relating x and y.

b) What is y when x = 2?
Inverse Variation
4) The maximum weight W that can be safely supported by
a 2-inch by 4-inch piece of pine varies inversely with its
length l. Experiments indicate that the maximum weight
that a 10-foot-long pine 2-by-4 can support is 500 pounds.
Find the maximum weight that can be safely supported by
a length of 25 feet.
Joint/Combined Variation
When a variable quantity Q varies directly with the product
of two or more other variables, we say that Q varies jointly
with these quantities.
Combinations of direct and/or inverse variation may occur.
This is usually referred to as combined variation.
Joint/Combined Variation
5) Newton’s Formula states that the force of gravitation F
between two bodies varies jointly as the product of their
masses m1 and m2 and inversely as the square of the
distance between them d. If we use G as the gravitational
constant (of proportionality), write the equation for
Newton’s formula.
Joint/Combined Variation
6) The force F of the wind on a flat surface positioned at a right
angle to the direction of the wind varies jointly with the area A
of the surface and the square of the speed v of the wind. A wind
of 30 miles per hour blowing on a window measuring 4 feet by 5
feet has a force of 150 pounds. What is the force on a window
measuring 3 feet by 4 feet caused by a wind of 50 miles per
hour?
Joint/Combined Variation
7) The loss of heat L through a wall varies jointly
with the area A of the wall and the temperature
difference T between the inside and outside and
varies inversely with the thickness d of the wall. If
the temperature difference is 20° F, a wall with an
area of 100 square feet and thickness 0.8 feet has a heat loss of
210 Btu/hr. Find the heat loss for a wall of the same area having
a thickness of 6 inches and a temperature difference of 40° F.
“I'm getting pulled over. Everyone, just... pretend to
be normal.”
3.4b: Inverse and Joint Variation
Homework #7:
pg.210 #63, 65,
71, 75