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.

y varies inversely with x, and x = 7 when y = 35. Find the inverse variation equation and use it to find the value of x when y = 50.