Suppose that y varies inversely as t he cube of x. If y is 1/2 when x is 2 , find the constant of variation and variation equation
y = k / x^3
.5 = k / 8
k = 4
y = 4 / x^3
To find the constant of variation and the variation equation, we will use the formula for inverse variation:
y = k/x³.
Given that y is 1/2 when x is 2, we can substitute these values into the equation to find the constant of variation, k.
1/2 = k/2³.
To solve for k, we can cross-multiply and simplify:
1/2 * 2³ = k,
1/2 * 8 = k,
k = 4.
The constant of variation is k = 4. Now, we can form the variation equation using this value:
y = 4/x³.
Therefore, the variation equation for y varying inversely as the cube of x is y = 4/x³.