Name__________________________________ Practice: Direct ...

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Nov 26, 2013 (3 years and 22 days ago)

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Name__________________________________





Practice: Direct, Inverse and Joint Variation











SOL: A2.T10


1. Write and graph a direct variation equation that contains the point
(4,10)
.










Equation:
_____________





2. X and y vary directly. Write an equation that relates
x
and
y
, when x =
-
18 and y = 4.


Find y when x = 12.


3. X and y vary directly. Write an equation that relates
x
and
y
, when x =
-
12 and y = 84.


Find x when y =
-
4.


Tell whether the data in the table show direct variation. If so, write an equation relating x and y.

4.









5.





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.

7.
2 3
y x
 



8.
3
x
y




9.
1
2
x
y




10.
4 2( 2)
y x
  



11.






12.







13.










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.

14.
4,6
x y
 




15.
1
48,
12
x y
 




16.
2.4,3.6
x y
 




The
variable z varies
jointly

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.

17.
3.5,30
x y z
  



18.
1
6,,24
2
x y z
  



19.
3
,18,9
2
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.

a.

Find the constant of varia
tion.





b.

Write an equation that relates p and V.

c.

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


23)


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.

(questions 24
-
29)


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

M

of a concrete block varies jointly as the length
l
, width
w

and thickness
t

of the block.



27. The
collision impact
I

of an automobile varies jointly as the mass
m

and the square of the speed
v
.



28. The intensity of a sound
S

varies directly as the amplitude
A

of a sound source, and inversely as the square of


the distance
d

from the source.



29. For a
horizontal beam supported at both ends, the maximum safe load

L
, varies directly as the width
w

and the


square of the thickness
t
, and inversely as the distance d between supports.