Page 1
1.
Given that y is inversely proportional to x, and y = 4 when x = 21. Find a general
formula to describe the relationship.
2.
Given that y is inversely proportional to x, and y = 10 when x = 15. Find y when x is
25.
3.
Given that y is inversely proportional to the square of x and
6y=
when
512x=
, find
a general formula to describe the relationship.
Write your answer with positive exponents.
4.
Given that y is inversely proportional to the cube root of x and
8y=
when
4x=
, the
formula
p
k
yx
=
describes this relationship.
Find A) p and B) k.
5.
Given that y is inversely proportional to the square of x and
6y=
when
49x=
, the
formula
p
k
yx
=
describes this relationship.
Find p and k.
A)
p is 54 and k is 2
B)
p is 6 and k is 3
C)
p is 2 and k is 54
D)
p is 3 and k is 6
6.
Given that y is inversely proportional to the square root of x and
3y=
when
4x=
,
find y when
5x=
.
Round your answer to 2 decimal places, if necessary.
7.
Given that y is inversely proportional to the cube root of x and
5y=
when
512x=
,
A) find a general formula to describe the relationship (write your answer with positive
exponents) and,
B) use the formula to find y when
5x=
. Round your answer to 2 decimal places, if
necessary.
Page 2
8.
The percentage of sunlight, s, that filters through water is inversely proportional to the
depth of the water, d. If 10 meters below the surface only 25% of sunlight is visible,
find what percent of sunlight will be visible 30 meters below the surface.
Round your answer to 2 decimal places, if necessary.
9.
Given that w is directly proportional to x and inversely proportional to y, and
16.6w=
when
16x=
and
25y=
, find a formula to describe this relationship.
Use only positive exponents and use fractional exponents rather than radicals, if
necessary. Round values to 2 decimal places, if necessary.
10.
Given that w is directly proportional to the square root of x and inversely proportional to
y, and
0.33w=
when
1x=
and
3y=
, find w when
9x=
and
7y=
. Round your
answer to 2 decimal places, if necessary.
11.
Given that w is directly proportional to the cube of x and inversely proportional to the
square root of y and,
390.72w=
when
216x=
and
64y=
,
A) find a formula to describe the relationship (use only positive exponents and
fractional exponents rather than radicals, if necessary) and,
B) use the formula to find w when
8x=
and
3y=
. Round your answer to 2
decimal places, if necessary.
12.
The amount of time needed to paint the interior of an office building is directly
proportional to the square footage of the building and inversely proportional to the
number of painters on the job. If 6 painters needed 77 hours to paint a 44,000 square
foot office building, find how many hours would it take for 7 painters to paint a 34,000
square foot office building?
Round your answer to 2 decimal places, if necessary.
13.
The gravitational force between two heavenly bodies is inversely proportional to the
square of the distance between the two bodies. If two planets that are 3,400 Gm apart
share a gravitational attraction of 0.004343 N, what would the force between two
planets of similar size that are 8400 Gm apart? Round the answer to 6 decimal places if
necessary.
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Answer Key