Practice: Direct, Inverse and Joint Variation
1. Write and graph a direct variation equation that contains the point
2. X and y vary directly. Write an equation that relates
, when x =
18 and y = 4.
Find y when x = 12.
3. X and y vary directly. Write an equation that relates
, when x =
12 and y = 84.
Find x when y =
Tell whether the data in the table show direct variation. If so, write an equation relating x and y.
6. The time it takes a diver
to ascend safely to the surface varies directly with the depth. It takes a minimum of 0.75
minutes for a safe ascent from a depth of 45 feet. Write an equation that relates time and depth, then predict the
minimum time for a safe ascent f
rom a depth of 100 feet.
Tell whether x an y show a direct variation, inverse variation or neither.
4 2( 2)
The variables x and y vary inversely. Use the given values to write an equation relating x and y. Find y when x = 0.5.
variable z varies
with x and y
. Use the given values to write an equation relating x, y and z
. Find z when
x = 4 and y=7.
x y z
x y z
x y z
20. Boyle’s Law states that for a constant temperature, the pressure of p of a gas varies inversely with its volume. A
sample of oxygen gas has a volume of 50.25 cubic milliliters at a pressure of 20.6 atmospheres.
Find the constant of varia
Write an equation that relates p and V.
Find the volume of the oxygen gas if the pressure changes
to 15.2 atmospheres.
Write an equation for the given relationship. (question s 21
21. x varies directly with y and inversely with z
22. y varies jointly with x and the square of z.
23. w varies inversely with y and jointly with x and z.
Write a function for the given statement. Use k as the constant of variation.
24. h varies directly as W, and inversely as
the square of r.
25. L varies jointly as A and H, and inversely as T.
26. The mass
of a concrete block varies jointly as the length
of the block.
of an automobile varies jointly as the mass
and the square of the speed
28. The intensity of a sound
varies directly as the amplitude
of a sound source, and inversely as the square of
from the source.
29. For a
horizontal beam supported at both ends, the maximum safe load
, varies directly as the width
square of the thickness
, and inversely as the distance d between supports.