Name
Algebra" Pre AP
Worksheet 8.1
Worksheet
11.1
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Vrite an equation for each statement.
1.
3.
Then solve the equation.
Find y when x = 8, if x varies directly as y and y = 9,
when x = 6.
2.
Find y when x = 15, ify varies inversely as x and
x = 10 when y = 12.
4.
Find x when y
=
9, if Y varies directly as x and x
=
15
when y = 6.
Find x when y = 27, if Y varies inversely as x and x = 9
when y = 45.
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5.
Find y when x = 5, and z = 3, if Y varies jointly as x = 3
and z = 2 when y = 18.
6.
Find y when x = 6 and z = 8, if Y varies jointly as x = 4
and z = 2 when y = 6.
7.
Find y when x = 76, if Y varies inversely as x and
y = 100, when x = 35.
8.
If Y varies inversely as x and V = 3 when x = 6, find x
when V = 18.
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9.
11.
13.
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10.
If z is jointly proportional to x and V, and z = 18 when
x=: 0.4 and V = 3, find z when x = 1.2 and V = 2.
12.
If w is jointly proportional to u and v, and w = 24
when u = 0.8 and v = 5, for what value of u will
w = 18 when v = 27
14.
If
varies inversely as x and V = 4 when x
when x 11.
If Y varies directly as X2 and y
=7
when x
y when x = 7.
=
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I
Suppose that w varies directly as Z2 and inversely as
Suppose that r varies directlv as p and inversely as
the square of q, and that r = 27 when p = 3 and
q = 2. Find r when p = 2 and q = 3.
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t
=
9, then find
=
=
=
xy, and that w 10 when x 15, Y 2,
and z = 5. Find z when w = 2, x = 8, andv
l
=
=
27.
= 2, fino
y
15.
The weight M of an object on the moon varies directly as its weight E on earth. A person who weighs 95 kg on
Earth weights 15.2 kg on the moon.
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16.
The number of kilograms
=rof
kg contains 64 kg of water.
17.
The volume V o~~a~ties
of 32
18.
kg/ern'. What will be
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How much would a 105 kg person weigh on the moon?
water W in a human body varies directly as the total weight.
A person weighing 96
How many kilograms of water are in a person weighing 75 kg?
3
inversely as the pressure P upon it. The volume of a gas is 200 m under a pressure
its volume under a pressure of 40 kg/ern"?
In a closed room, the number of hours of safe oxygen level varies inversely as the number of people in the room.
If there are 2 hours of safe oxygen level when there are 100 people, how many hours of safe oxygen level are
there for 600 people?
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19.
A load of 12 kg stretches a spring to a total length of 15 ern, and a load of 30 kg stretches it to a length of 18 cm.
Find the natural (unstretched) length of the spring.
20.
Hooke's law states that the distance d a spring is stretched by a hang object varies directly as the weight wof
the object. If the distance is 40 cm when the weight is 3 kg, what is the distance when the weight is 5 kg?
21.
The time to drive a certain distance varies inversely according to the rate of speed. Mary drives 47 mph for
4 hours. How long would it take her to make the same trip at 55 mph?
22.
The distance an object falls from rest varies directly as the square of the time it has fallen.
during the first half second, how far did it fall during the next two seconds?
23.
The intensity of light, measured in lux, is inversely proportional to the square of the distance between the light
source and the object illuminated. A light meter 7.5 m from alight source registers 24 lux. What intensity
would it register 15 m from the light source?
24.
To determine the number of deer in a forest, a conservationist catches 612 deer, tags them, and releases them.
Later, 244 deer are caught, and it is found that 72 of them are tagged. Estimate how many deer are in the
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If the object fell 4 ft
forest.
25.
The stretch in a wire under a given tension varies directly as the length of the wire and inversely as the square of
its diameter. A wire having length 2 m and diameter 1.5 mm stretches 1.2 mm. If a second wire of the same
material (and under the same tension) has length 3 m and diameter 2.0 mm, find the amount of stretch.
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26.
A beam 3 em wide and 5 cm deep can support a load of 630 kg. What load can it support when turned on its
side? The load is jointly proportional to the width and square of depth.
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27.
The number N of aluminum cans used each year varies directly as the number of people using the cans. If 250
people use 60,000 cans in one year, how many cans are used each year in a city with population 850,0007
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28.
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The frequency of a radio signal varies inversely as the wave length. A signal of frequency 1200 kilohertz (kHz),
which might be the frequency of an AM radio station, has wave length 250 m. What frequency has a signal of
wave length 400 m?
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k.f{z