Please check my work, the answer I am suppose to get is 17.5, but instead I got 2.5.
Solve the problem.
66. y varies jointly as a and b inversely as the square root of c, y=24 when a=6,b=4, and c=49. Find y when a=2, b=5, and c=16.
-I got: y=kab/ sqrt of c, y=2*5/ sqrt of 16, y=10/4, which reduces to y=2.5
to find k:
24 = k(6)(4)/√49
which gave me k=7
then y = 7ab/√c
and for the second data values:
y = 7(2)(5)/51√16
= 70/4
=17.5
To solve the problem, we need to use the given information and the appropriate formula.
The given equation is: y varies jointly as a and b inversely as the square root of c, written as y = k * (a * b) / sqrt(c).
First, let's find the value of the constant k using the initial conditions: y = 24, a = 6, b = 4, and c = 49.
Plugging these values into the equation, we get: 24 = k * (6 * 4) / √49.
Next, we need to solve for k.
Multiply both sides by √49 to get rid of the square root:
24 * √49 = k * (6 * 4).
24 * 7 = k * 24.
Now, divide both sides by 24:
24 * 7 / 24 = k.
7 = k.
So, k = 7.
Now that we have the value of k, we can find y when a = 2, b = 5, and c = 16.
Plugging these values into the equation, we get: y = 7 * (2 * 5) / √16.
Simplifying this expression gives us: y = 70 / 4.
Dividing 70 by 4, we get: y = 17.5.
Therefore, the correct answer is y = 17.5, not 2.5.