Variation

Inverse

1

Y varies inversely as X. Write the inverse-variation equation, and find Y for the given values of X. Y=36 when X=9; X-values: 3,4,5,6

Y= 324/X; 108, 81, 64.8,54,

2

Y varies inversely as X. Write the inverse-variation equation, and find Y for the given values of X. Y=0.5 when X=8; X-values: 5,4,3,2,1

Y=4/X; 0.8,1,1,3,2,4

3

Y varies inversely as X. Write the inverse-variation equation, and find Y for the given values of X. Y=14 when X=8; X-values: 4

Y=112/X; 28

4

BONUS

Y=200/X; 2,0.2,0.02

5

Y varies inversely as X. Write the inverse-variation equation, and find Y for the given value of X. Y=13 when X= 4. X=2

Y=52/X;  Y=26

Joint

1

Y varies Jointly as X and Z Write the Joint-Variation equation, and find Y for the given values of X and Z. Y=-108 when X=-4 and Z=3; X=6 and Z=-2

Y=9XZ; -108

2

Y varies Jointly as X and Z Write the Joint-Variation equation, and find Y for the given values of X and Z. Y=15 when X=9 and Z=1.5; X=18 and Z=3

Y=10/9XZ; 60

3

Y varies Jointly as X and Z Write the Joint-Variation equation, and find Y for the given values of X and Z. Y=120 when X=8 and Z=20; X=54 and Z=7

Y=3/4XZ; 283.5

4

Y varies Jointly as X and Z Write the Joint-Variation equation, and find Y for the given values of X and Z. Y=10^4 when X=10^2 and Z=10^1; X=10^5 and Z=10^2

Y=10XZ; 10^8

5

A prism has a height of eight inches, a length of X and a Width of Z. Write an equation for the volume of the prism, and find the volume of the prison when the length is 4 inches and the width is 2 inches

V=8XZ; 64 cubic inches

Combined

1

Z varies jointly as X and Y, and inversely as W. write the combined-variation equation, and find X for the given values of X,Y, and W. Z=3 when X=4, y=-2 and W=-4; X=6,Y=7,W=-4

Z=2XY/W; -21

2

Z varies jointly as X and Y, and inversely as W. write the combined-variation equation, and find X for the given values of X,Y, and W. Z=36 when X=9, Y=10 and W=15; X=10,Y=18,W=5

Z=6XY/W; 216

3

Z varies jointly as X and Y, and inversely as W. write the combined-variation equation, and find X for the given values of X,Y, and W. Z=100 when X=100, Y=7 and W=2; X=3.5,Y=24,W=27

Z=2XY/7W; 8/9

4

DAILY DOUBLE!!! A bicycle's pedal gear has 53 teeth and is rotating at 65 revolutions per minute. A chain links the pedal gear to a rear-wheel gear that has 18 teeth and is attached to a 26-inch wheel. At what speed, in miles per hour, is the bicycle traveling?

14.5 miles per hour

5

The electrical resistance of a wire varies directly as its length and inversely as the square of its diameter. A wire with a length of 200 inches and a diameter of one-quarter of an inch has a resistance of 20 ohms. Find the electrical resistance in a 500 inch wire with the same diameter.

50 Ohms

Definitions

1

Define Inverse variation

Answer will Vary

2

Define joint variation

Answers will vary

3

Define Combined variation

Answers will vary

4

What letter symbolizes the constant of variation?

K

5

BONUS

W

State the relationship

1

Y=K/X

Inverse Variation

2

Y=(K/X)ZY

Combined variation

3

Y=KXZ

Joint Variation

4

y=-108 when X=-4 and Z=3

Joint variation

5

The number of minutes needed to solve an exercise set of variation problems varies directly as the number of problems and inversely as the number of people working on the solutions. It takes 4 people 36 minutes to solve 18 problems. How many minutes will it take 6 people to solve 42 problems?

Combined variation