The quantity q varies inversely with the square of m and directly with the product of r and x. When q is 2.5, m is 4 and the product of r and x is 8. What is the constant of variation?
K=5
q = k(1/m^2)(rx)
plug in the given values
2.5 = k(1/16)(8)
solve for k
Let's break down the problem step by step:
Step 1: Write down the inverse variation equation.
The inverse variation equation can be expressed as:
q = k / (m^2)
Step 2: Write down the direct variation equation.
The direct variation equation can be expressed as:
q = k * (r * x)
Step 3: Use the given information to solve for the constant of variation, k.
From the information given, we know that when q is 2.5, m is 4 and the product of r and x is 8. Let's substitute these values into the equations.
For the inverse variation equation:
2.5 = k / (4^2)
2.5 = k / 16
To solve for k, we can cross-multiply:
2.5 * 16 = k
40 = k
For the direct variation equation:
2.5 = 40 * (r * x)
2.5 = 40 * 8
2.5 = 320
Step 4: Answer the question.
The constant of variation, k, is 40.
To find the constant of variation, we need to set up the equation using the given information.
We know that q varies inversely with the square of m, so we can write:
q = k/m^2
where k is the constant of variation.
We also know that q varies directly with the product of r and x, so we can write:
q = k * (r * x)
Now we can solve for the constant of variation, k.
We are given that when q is 2.5, m is 4 and the product of r and x is 8. Plugging these values into the equation, we get:
2.5 = k/4^2
Simplifying, we have:
2.5 = k/16
To solve for k, we can cross multiply:
2.5 * 16 = k
40 = k
Therefore, the constant of variation is k = 40.