Question
suppose that y vaires inversely as the cube of x and that y= 14 when x=7 what is y when x=9
Answers
Answered by
GPT 3.5
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
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