If m varies directly as v^2, and m=2 when v=3, calculate the value of m when v=6
Use direct proportions.
Given
m : v²
and
2 : 3²
X : 6²
Cross multiply to get X
X = 2*6²/3²
= 2*36/9
= 8
To calculate the value of m when v=6, we can use the variation equation m = kv^2, where k is the constant of variation.
Using the given information, we can solve for k.
m = kv^2
2 = k(3^2)
2 = 9k
Divide both sides of the equation by 9:
2/9 = k
Now that we have determined the value of k, we can substitute it back into the variation equation to calculate m when v=6.
m = (2/9)(6^2)
m = (2/9)(36)
m = 8
Therefore, when v=6, m is equal to 8.
To solve this problem, we need to use the concept of direct variation and set up a proportion.
The equation "m varies directly as v^2" can be written as:
m = k * v^2
where k is the constant of variation.
To find the value of k, we can use the given information where m = 2 when v = 3. Substituting these values into our equation, we get:
2 = k * 3^2
2 = k * 9
k = 2/9
Now that we know the value of k, we can find the value of m when v = 6 by substituting it into our equation:
m = (2/9) * 6^2
m = (2/9) * 36
m = 8
Therefore, when v = 6, m is equal to 8.