# Hotmath

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

Use the given values to write an equation relating
*
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?