Question

Determine whether the equation represents direct, joint, or inverse variation. Then identify the constant.

t = 100/s
y/5 = x
p/qr = 4
C = 2πr
V = 1/3πr^2h
xy = 2/5

Answer 1

The equation t = 100/s represents inverse variation with a constant of variation of 100.

Step-by-step explanation:

The equations can be classified as direct, joint, or inverse variation based on their forms:

1. t = 100/s represents inverse variation because t and s are inversely related. The constant of variation is 100.
2. y/5 = x represents direct variation because y and x are directly related. The constant of variation is 5.
3. p/qr = 4 represents joint variation because the variables p, q, and r are combined in a way that represents direct variation. The constant of variation is 4.
4. C = 2πr represents direct variation because the circumference C and the radius r are directly related. The constant of variation is 2π.
5. V = 1/3πr^2h represents direct variation because the volume V and the product of the radius r and height h are directly related. The constant of variation is 1/3π.
6. xy = 2/5 represents direct variation because x and y are directly related. The constant of variation is 2/5.