Question

Which are possible values for z? The value of z varies inversely with the value of w . The constant of variation is (4)(w) . Check all that apply.

a) z = (4)(w) , w = 1

b) z = 2 , w = 3

c) z = 8 , w = 2

d) z = (1)(w) , w = 4

Answer 1

Option (a) is the correct answer as it is the only one where z varies inversely with w and maintains the constant of variation of (4)(w).

Step-by-step explanation:

The student's question involves an inverse variation where the variable z varies inversely as w. The constant of variation is given as (4)(w). We can express this relationship with the equation zw=k, where k is the constant of variation. To identify the correct values for z, we can plug in the provided values for w into the inverse variation formula and see which options maintain a constant value of k.

• For option (a), if z=(4)(w) when w=1, then k would equal 4 which agrees with the constant of variation.
• Option (b) would be correct if k equals 6 when z=2 and w=3.
• Option (c) has z=8 when w=2, which would give k=16, not matching the given constant.
• Option (d) suggests z=w when w=4, leading to k=16, which again is incorrect.

By evaluating each option against the inverse variation formula, we can determine that option (a) is the only one that maintains the constant of variation as (4)(w).