The document provides examples of direct and inverse variations and instructions on how to translate statements of direct and inverse variation into mathematical equations using a constant of variation k. It also gives problems to solve for the indicated variable in various scenarios involving direct and inverse variation.

2. Translate each of the following into
mathematical equation. Use k as the
constant of variation.
1. The height (h) of a circular cylinder of a
given volume is inversely proportional to the
square of the radius (r).
2. To balance a seesaw, the weight (w) is
inversely proportional to the distance (d)
from the fulcrum.

3. Translate each of the following into
mathematical equation. Use k as the
constant of variation.
3. The weight (w) of a body varies inversely
as the square of the distance (d) from the
center of the Earth.
4. At a constant temperature, the volume (V)
of a gas varies inversely as the pressure (P)
upon it.

4. Identify whether the given is Inverse or
Direct Variation. Find k and the equation of
Variation.
x 10 15 6 5 3
y 3 2 5 6 10
x 4 5 6 8 12
y 28 35 42 56 84
x 30 40 50 60 80
y 4 3 2.4 2 1.5

6. Find the constant of variation and the
equation:
1.y varies inversely as x and y = 6 when
x = 18.
2.y varies inversely as x and y = 15 when
x = 2/5.
3.y varies inversely as x and y = - 12
when x = - 3

7. SOLVE FOR THE INDICATED VARIABLE IN
EACH OF THE FOLLOWING
1.If y varies inversely as x and y = 10
when x = 2, find y when x = 10.
2.Suppose a varies inversely with b.
When b = 4 and a = ½, find a when b =
18.

8. SOLVE FOR THE INDICATED VARIABLE IN
EACH OF THE FOLLOWING
3. The number of hours t required to finish
a certain job varies inversely as the
number of persons n on the job. If 16
persons require 18 hours to finish the job,
how long would it take 64 persons to
finish the job?