If f varies jointly as q2 and h, and f=24 when q=2 and h=2, find f when q=3 and h=5
f = k * q^2 * h ... 24 = k * 2^2 * 2 ... k = 3
f = 3 * 3^2 * 5
To solve this problem, let's set up the equation based on the given information.
We are given that f varies jointly with q^2 and h. This can be expressed as:
f = k * q^2 * h
where k is the constant of variation.
Next, we can use the initial condition to find the value of k. We are given that when q = 2 and h = 2, f = 24. Substituting these values into the equation, we have:
24 = k * 2^2 * 2
Simplifying this equation, we get:
24 = k * 4 * 2
24 = 8k
Dividing both sides by 8, we find:
k = 3
Now that we know the value of k, we can substitute it back into the equation:
f = 3 * q^2 * h
Finally, we can find the value of f when q = 3 and h = 5 by substituting these values into the equation:
f = 3 * 3^2 * 5
f = 3 * 9 * 5
f = 135
Therefore, when q = 3 and h = 5, f is equal to 135.
To solve this problem, we need to determine the constant of variation in the joint variation equation. Then, we can substitute the given values of q and h into the equation to find the value of f.
The joint variation equation is expressed as:
f = k * q^2 * h
To find the constant of variation, we can use the given values of f, q, and h when they are all equal to 24, 2, and 2 respectively:
24 = k * (2^2) * 2
24 = 4k * 2
24 = 8k
k = 24/8
k = 3
Now that we have determined the constant of variation (k = 3), we can use it to find the value of f when q = 3 and h = 5:
f = 3 * (3^2) * 5
f = 3 * 9 * 5
f = 135
Therefore, when q = 3 and h = 5, f is equal to 135.