If w varies directly as z and w = 9 when z = -6, find w when z = 3.
a) 0
b) -4.5
c) -2
d) 4.5
w = kz
so, w/z = k, a constant. So, you want w such that
w/3 = 9/-6
To find the value of w when z = 3, we can use the direct variation formula:
w = k * z
where k is the constant of variation. To determine the value of k, we can use the given information that w = 9 when z = -6:
9 = k * (-6)
To solve for k, divide both sides of the equation by -6:
k = 9 / -6
k = -1.5
Now that we have the value of k, we can substitute it into the direct variation formula to find w when z = 3:
w = -1.5 * 3
w = -4.5
Therefore, the answer is:
b) -4.5