A variable 'm' varies directly as 'a' and inversely as 'b'. If m=6 when a=7 and b=4, what is 'm' when a=9 and b=12?
M= constant*a/b
Find the constant from the first set of data, then, using that, find m in the second set.
m directly to a and inversely to b
m=ka m=k1dividedb
6=k7
6divided by 7=0.857
To find the constant of variation, we can rearrange the formula:
m = constant * (a / b)
Using the given values m = 6, a = 7, and b = 4:
6 = constant * (7 / 4)
Now, let's solve for the constant:
6 = constant * (7 / 4)
6 = (7/4) * constant
6 * (4/7) = constant
24/7 = constant
So, the constant of variation is 24/7 (or approximately 3.43).
Now we can use this constant to find m when a = 9 and b = 12:
m = constant * (a / b)
m = (24/7) * (9 / 12)
Simplifying:
m = (24/7) * (3/4)
m = (24 * 3) / (7 * 4)
m = 72 / 28
m ≈ 2.57
Therefore, when a = 9 and b = 12, the value of m is approximately 2.57.
To find the constant in the direct and inverse variation equation, we can use the first set of data, where m = 6, a = 7, and b = 4. We can plug these values into the equation:
6 = k * (7/4)
To solve for k, we can rearrange the equation to isolate k:
k = 6 * (4/7)
k = 24/7
Now that we have the value of the constant k, we can use it to find m when a = 9 and b = 12. Plugging these values into the equation:
m = (24/7) * (9/12)
Simplifying the expression:
m = (3/1) * (3/1)
m = 9
Therefore, when a = 9 and b = 12, m = 9.