Math 125 Find an equation of variation if the following conditions ...

Math 125 Fall 11

Chapter 7 Variations

Find an equation of variation if the following conditions exist.

1) Suppose that y varies directly as z and y = 42 when z = 378 .

A)

y

=

-

1 2

z

B)

y=

1 9

z

C) y = -2z

D) y = 9 z

2) Suppose m varies directly as p and m = 15 when p = 3 .

A) m = 5p

B)

m

=

1 5

p

C) m = 12 p

D) m = 18 p

3) Suppose y varies directly as x and y = 0.5 when x = 0.1 .

A) y = 0.6 x

B)

y

=

1 5

x

C) y = 5x

D) y = 0.4 x

Solve.

4) According to Ohm's law, the electric current I, in amperes, in a circuit varies directly as the voltage V. When 7 volts are applied, the current is 3 amperes. What is the current when 9 volts are applied?

A) 21 amperes

B) 2.33 amperes

C) 3.86 amperes

D) 19 amperes

5) The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container 4 cm on a side is 192 g, find the weight of the liquid in a cubical container 3 cm on a side.

A) 27 g

B) 81 g

C) 15 g

D) 9 g

Find an equation of variation in which y varies inversely as x and the following is true.

6) y = 24, when x = 3

A)

y

=

8 x

B)

y

=

27 x

C)

y

=

72 x

D) y = 8x

7) y = 0.125, when x = 24

A)

y

=

4 x

B) y = 3x

C)

y

=

3 x

D)

y

=

6 x

8) y = 0.2, when x = 0.1

A)

y

=

0.3 x

B) y = 2x

C)

y

=

2 x

D)

y

=

0.02 x

Solve.

9) The weight that a horizontal beam can support varies inversely as the length of the beam. Suppose that a 5-m beam can support 140 kg. How many kilograms can a 2-m beam support?

A) 0.0714 kg

B) 14 kg

C) 0.0029 kg

D) 350 kg

1

10) It takes 12 hours for 5 people to paint a house. How long will it take 2 people to do the job?

A) 4.8 hr

B) 33 hr

C) 30 hr

D) 5 hr

Find an equation of variation in which the following are true.

11) x varies inversely as the square of y, and x = 12 when y = 17.

A)

x

=

1 -5y2

B)

x

=

1 3468y2

C)

x

=

3468 y2

D) x = 3468y2

12) y varies jointly as x and the square of z, and y = 3 when x = 2 and z = 6

A)

y

=

1 12

xz2

B)

y

=

1 24xz2

C)

y

=

1 4

xz

D)

y

=

1 24

xz2

13)

y

varies

jointly

as

x

and

z

and

inversely

as

the

product

of

w

and

p,

and

y

=

27 175

when

x

=

3,

z

=

9,

w

=

7,

and

p = 5.

A)

y

=

wp 5xz

B)

y

=

5wp xz

C)

y

=

xz 5wp

D)

y

=

5xz wp

Solve.

14) The cost of stainless steel tubing varies jointly as the length and the diameter of the tubing. If a 5 foot length with diameter 2 inches costs $48.00 , how much will a 10 foot length with diameter 3 inches cost?

A) $149.57

B) $144.00

C) $149.30

D) $141.60

Solve the problem.

15) The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 2.25 lb when the masses are 4 ft apart, what is the attraction when the masses are 6 ft apart?

A) 4 lb

B) 2 lb

C) 3 lb

D) 1 lb

2

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