If b varies directly as the square root of w and b equals a negative 24 when w equals 36, what is w when b is equal to 1/8?
" b varies directly as the square root of w" --> b = k√w, where k is a constant
given: b = -24 , w = 36
-24 = k√36
k = -24/6 = -4
b = -4√w
1/8 = -4√w
√w = -1/32
by definition √w will be a positive number , so there is no solution.
Are you sure b wasn't -1/8 ?
yes this is off a take home test
To find the value of w when b is equal to 1/8, we can use the direct variation equation that relates b and w.
The direct variation equation states that when two variables are directly proportional, they can be represented by the equation b = k * √w, where k is the constant of variation.
First, we need to find the value of k using the given information. We know that when w equals 36, b equals -24. Plugging these values into the equation, we have:
-24 = k * √36
Now, let's solve for k:
-24 = k * 6 (since √36 = 6)
-24 / 6 = k
-4 = k
So, we have determined that the constant of variation, k, is -4.
Now, we can use this value of k to find the value of w when b equals 1/8.
1/8 = -4 * √w
Let's solve for √w:
√w = (1/8) / -4
√w = 1/(-8 * -4)
√w = 1/32
Now, let's square both sides of the equation to isolate w:
w = (1/32)^2
w = 1/1024
Therefore, when b is equal to 1/8, w is equal to 1/1024.