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

yis inversely proportional tox³.(y=5whenx= 2.)

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

yvaries inversely asx.(y=7whenx=25.)

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

zvaries jointly asxandy.(z=24whenx=2andy=4.)

4)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 spring0.19meter? (Round your answer to two decimal places.)

5)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-kilogramobject1.9meters.

6)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 of33.5ohms? (Round your answer to the nearest foot.)