suppose that y vaires inversely as the cube of x and that y= 14 when x=7 what is y when x=9
If y varies inversely as the cube of x, we can write the equation:
y = k/x^3
Where k is the constant of variation.
To find the value of k, we can use the given information that when x = 7, y = 14:
14 = k/7^3
14 = k/343
k = 14 * 343
k = 4802
Now we can substitute the value of k into the equation and solve for y when x = 9:
y = 4802/9^3
y = 4802/729
y ≈ 6.59
To find the value of y when x = 9, we can use the inverse variation equation: y = k/x^3, where k is the constant of variation.
First, let's substitute the given values of y and x into the equation to solve for k:
14 = k/7^3
Simplifying the equation:
14 = k/343
To solve for k, we can multiply both sides by 343:
k = 14 * 343
k = 4802
Now that we know the value of k, we can substitute it into the inverse variation equation to find y when x = 9:
y = 4802/9^3
Calculating the expression:
y = 4802/729
y ≈ 6.59
Therefore, when x = 9, y is approximately equal to 6.59.