“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

Let x and y denote two quantities. Then y varies directly with x if there is a nonzero constant k such that Direct Variation 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?

Let x and y denote two quantities. Then y varies inversely with x if there is a nonzero constant k such that Inverse Variation 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.

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 m 1 and m 2 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.”

Homework #7: pg.210 #63, 65, 71, b: Inverse and Joint Variation