Algebra II Honors Direct and Inverse Variations - SchoolNotes

Algebra II Honors Direct and Inverse Variations

For each of the following, write an expression for the bolded variable, then solve for the variable

in the scenario given.

1. y varies directly as x. If y = 3 when x = 6, what is y when x = 8?

2. y varies directly as x2. If y = 3 when x = 6, what is y when x = 8?

3. y varies inversely as x. If y = 3 when x = 6, what is y when x = 9?

4. y varies inversely as x2. If y = 3 when x = 6, what is y when x = 9?

5. z varies jointly as x and y. If z = 12 when x = 9 and y = 4, what is z when x = 7 and y = 2?

6. z varies directly as x and inversely as y. If z = 6 when x = 4 and y = 5, what is z when x = 8

and y = 3?

7. Once the brake is applied, the distance, d, it takes to stop a car is directly proportional to the

square of the velocity of the car, v. If a car traveling at 20mph can be stopped after 16 feet, how

far does it take to stop a car traveling at 70mph?

8. The volume of a gas, V, varies directly with the temperature in Kelvin, T, and inversely with

the pressure, P. If a certain gas has a volume of 340m3 at a temperature of 300¡ãK under a

pressure of 200kPa (kilopascals, a unit of pressure), what will be the volume of the same gas at a

temperature of 330¡ãK under a pressure of 400kPa?

9. The slope, m, at which a curve should be banked varies inversely with the radius of the curve,

r, and directly with the square of the maximum speed of cars, v, that will use it. If a curve of

radius 4000 feet carrying cars traveling at a maximum speed of 50mph has a slope of 0.05. What

slope should the road have on a curve of radius 2000 feet if the maximum speed is 25mph?

10. The power, P, produced by an electric circuit varies directly as the square of the voltage, V,

and inversely as the resistance, R. If a voltage of 120V on a circuit with a resistance of 20?

produces 720W, what voltage applied to a circuit with a resistance of 30? will produce 120W?

(Note: ? is a measure of resistance, W is a measure of power)

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