if f varies jointly as q^2 and h, and if f = 72 when q = 3 and h = 4, find h when f = 48 and q = 2
f = khq^2 , where k is a constant
given: f = 72 , q=3 , h=4
72 = k(4)(9)
k = 2
so f = 2hq^2
when f=48 , and q=2
48 = 2h(4)
h = 6
is fbs jointly as q 2 and h and f = 24 when q = 2 and h = 2 find x when q = 3 and h = 4
To find the value of h when f = 48 and q = 2, we need to use the joint variation equation that states f varies directly with the product of q^2 and h.
Step 1: Set up the joint variation equation:
f = k * q^2 * h
Step 2: Use the given values to find the constant of variation, k.
Using the first set of values where f = 72, q = 3, and h = 4:
72 = k * 3^2 * 4
72 = k * 9 * 4
72 = k * 36
k = 72/36
k = 2
So the constant of variation is 2.
Step 3: Substitute the new values of f and q into the equation to find h.
Using the second set of values where f = 48 and q = 2:
48 = 2 * 2^2 * h
48 = 2 * 4 * h
48 = 8h
h = 48/8
h = 6
Therefore, when f = 48 and q = 2, h is equal to 6.
To find the value of h when f = 48 and q = 2, we need to use the given information that f varies jointly as q^2 and h.
When two variables vary jointly, it means they are directly proportional to each other. In this case, f varies jointly as q^2 and h can be written as:
f = k * q^2 * h
Where k is the constant of variation.
To find the value of k, we need to use the given information that when q = 3 and h = 4, f = 72. Substituting these values into the equation, we get:
72 = k * 3^2 * 4
72 = 36k
Dividing both sides by 36, we find k = 2.
Now that we have the value of k, we can substitute it back into the equation with the new values of f and q to find h when f = 48 and q = 2:
48 = 2 * 2^2 * h
48 = 8h
Dividing both sides by 8, we find that h = 6.
Therefore, when f = 48 and q = 2, h = 6.