If y varies inversely as the cube root of x, and y = 12 when x = 8, find y when x = 1.
y = k x^(-1/3)
12 = k (1/2)
k = 24
y = 24 x^(-1/3)
if x = 1
y = 24 (1/1) = 24
24
How do u find k
To solve this problem, we need to use the inverse variation relationship and the given values to find the constant of variation. Once we have the constant, we can substitute the given value of x to find the corresponding value of y.
The inverse variation relationship can be represented mathematically as: y = k/x^(1/3), where k is the constant of variation.
First, substitute the given values of x and y into the equation and solve for k:
12 = k/(8)^(1/3)
To simplify, cube root of 8 is 2, so we have:
12 = k/2
Solve for k:
k = 12 * 2 = 24
Now we have the constant of variation k = 24.
To find y when x = 1, substitute the value into the equation:
y = 24/(1)^(1/3)
Since any number raised to the power of 1/3 is itself, we have:
y = 24/(1)
y = 24
Therefore, when x = 1, y = 24.