Question

The value of z varies inversely with the value of w. The constant of variation is 1/2. Which are possible values forz and w? Check all that apply.

A) z=2,w=3
B) z=1,w=2
C) z=4,w=15
D) z=6,w=8

Answer 1

The possible values for z and w, given an inverse variation with a constant of variation of 1/2, are z=1, w=2 and z=6, w=8.

Step-by-step explanation:

The value of z varies inversely with the value of w. The constant of variation is 1/2. This means that as z increases, w decreases, and vice versa. To determine which values for z and w are possible, we can use the equation for inverse variation: z = k/w, where k is the constant of variation.

From the given options, we can check if the value of z equals 1/2 times the value of w for each option. Let's check:

1. A) z=2, w=3: z = 2, w = 3; z = (1/2) * w (not equal)
2. B) z=1, w=2: z = 1, w = 2; z = (1/2) * w (equal)
3. C) z=4, w=15: z = 4, w = 15; z = (1/2) * w (not equal)
4. D) z=6, w=8: z = 6, w = 8; z = (1/2) * w (equal)

From the above calculations, the possible values for z and w are: B) z=1, w=2 and D) z=6, w=8.