Variation

Inverse

100

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,

200

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

300

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: 10,15,20

Y=112/X; 11.2, 7.47, 5.6

400

Y varies inversely as X. Write the inverse-variation equation, and find Y for the given values of X. Y=1000 when X=0.2; X-values: 10^2,10^3,10^4

Y=200/X; 2,0.2,0.02

500

Y varies inversely as X. Write the inverse-variation equation, and find Y for the given values of X. Y=13.5 when X= 4.5 X-values: 0.5,1,1.5,2, and 2.5

Y=60.75/X; 121.5,60.75,40.5,30.375,24.3

Joint

100

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

200

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

300

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

400

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

500

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

100

Z varies jointly as X and Y, and inversely as W. write the combined-variation equation, and find Z 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; -15.75

200

Z varies jointly as X and Y, and inversely as W. write the combined-variation equation, and find Z 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

300

Z varies jointly as X and Y, and inversely as W. write the combined-variation equation, and find Z 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

400

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

500

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

100

Define Inverse variation

Answer will Vary

200

Define joint variation

Answers will vary

300

Define Combined variation

Answers will vary

400

What letter symbolizes the constant of variation?

K

500

This variable is only present in Combined Variations.

Z

State the relationship

100

Y=K/X

Inverse Variation

200

Y=(K/X)ZY

Combined variation

300

Y=KXZ

Joint Variation

400

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

Joint variation

500

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