8-1) Find a mathematical model for the verbal statement. (Usekfor the constant of proportionality.)

For a constant temperature, the pressurePof a gas is inversely proportional to the volumeVof the gas.

2) Find a mathematical model that represents the statement. (Determine the constant of proportionality.)

yvaries inversely asx.(y=4whenx=24.)

3) Find a mathematical model that represents the statement. (Determine the constant of proportionality.)

yis inversely proportional tox³.(y=3whenx= 2.)

4) Find a mathematical model that represents the statement. (Determine the constant of proportionality.)

zvaries jointly asxandy.(z=80whenx=4andy=5.)

5) Find a mathematical model that represents the statement. (Determine the constant of proportionality.)

Pvaries directly asxand inversely as the square ofy.

(P=28/3whenx=84andy=9)

6) Use Hooke's Law, which states that the distance a spring stretches (or compresses) from its natural, or equilibrium, length varies directly as the applied force on the spring.

A force of 220 newtons stretches a spring 0.12 meter. What force stretches the spring0.16meter? (Round your answer to two decimal places.)

answer_______ N

Question 7-The workWrequired to lift an object varies jointly with the object's massmand the heighththat the object is lifted. The work required to lift a120-kilogramobject1.8 metersis2116.8 joules.Find the amount of work required to lift a150-kilogramobject1.8meters.

Answer : W=_______ J

Question -8 Use the fact that the resistance of a wire carrying an electrical current is directly proportional to its length and inversely proportional to its cross-sectional area.

If #28 copper wire (which has a diameter of 0.0126 inch) has a resistance of 66.17 ohms per thousand feet, what length of #28 copper wire will produce a resistance of33.2ohms? (Round your answer to the nearest foot.)

Answer _______ ft