Solve variation problem
if m varies jointly as z and p, and m=10 when z=2 and p=7.5, find m when z=5 and p=7
By "jointly as" assume you mean "proportional to". If so,
m = 10*(5/2)*(7/7.5) = 23.333
To solve this variation problem, we need to use the formula for joint variation:
m = k * z * p
where:
- m is the variable that varies jointly
- z and p are the other two variables that are directly proportional to m
- k is the constant of variation
To find the value of k, we can rearrange the formula and substitute the given values:
m = k * z * p
10 = k * 2 * 7.5
10 = 15k
k = 10/15
k = 2/3
Now that we have determined the value of k, we can use the formula to find the value of m when z = 5 and p = 7:
m = k * z * p
m = (2/3) * 5 * 7
m = 70/3
m ≈ 23.33
Therefore, when z = 5 and p = 7, the value of m is approximately 23.33.