If *a*,*b*, *c* are positive and, then *b* is called the mean proportional or the geometric mean.

Work out the geometric mean between each pair of numbers.

4 and 9

If *a*,*b*, *c* are positive and, then *b* is called the mean proportional or the geometric mean.

Work out the geometric mean between each pair of numbers.

10 and 8

Use the given values to write an equation relating *x* and *y*, where *x*
and *y* vary inversely. Then find *y* when *x* = 3.

*x* = 7, *y* = –3

Use the given values to write an equation relating *x* and *y*, where *x*
and *y* vary inversely. Then find *y* when *x* = 3.

*x* = 5, *y* = 1

*x* and *y*, where *x*
and *y* vary inversely. Then find *y* when *x* = 3.

The variable *z* varies jointly with the product of *x* and *y*.

Find an equation that relates the variables *x*, *y*, and *z*.

The given values are

Use the given values to write an equation relating *x*, *y* and *z*, where *z* varies jointly with *x* and *y*. Then find *z*
when *x* = –3 and *y* = 5.

*x*
= 3/4, *y* = (2/9), *z* = 6

If *c*
varies jointly with *m* and *n*, and *n* varies directly with *s*, show that *c* varies jointly with *m* and *s*.

Suppose *t*
varies jointly with *a* and *b*, and *t* = 90 when *a* = 5 and *b* = 6. Find *t* when *a* = 6 and *b* = 5.

A paycheck varies directly with the number of hours worked.

Suppose the pay for 20 hours of work is $238.25.

What is the pay for 500 hours of work?

A pump empties a swimming pool in 60 minutes at the rate of 1500 L/min.

If the rate of pumping is 2500 L/min, how long does it take to empty the swimming pool?

The curved surface area of a cylinder varies jointly with the radius of its base and its height. Find the constant of variation.

The work *W* (in joules) done when lifting an object varies jointly with the mass *m *(in kg) of the object and the height *h*(in meters) that the object is lifted. The work done when a 140 kg object is lifted 1.6 meters is 2060.8 joules. Write an equation that relates *W*, *m* and *h*. How much work is done when lifting a 100 kg object 1.5 meters?