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The cube root of x varies inversely as the square of y. If x=27 when y=4 how do you find the value of x when y=6?

Answer 1

To find the value of x when y=6, we can use the inverse variation formula. The cube root of x varies inversely as the square of y can be expressed as:

∛x = k/y^2

where k is the constant of variation.

To solve for k, we can substitute the given values x=27 and y=4 into the equation:

∛27 = k/4^2

Simplifying, we have:

3 = k/16

Multiplying both sides by 16, we get:

k = 48

Now, we can use this value of k to find x when y=6:

∛x = 48/6^2

Simplifying, we have:

∛x = 48/36

Cubing both sides, we get:

x = (48/36)^3

Evaluating this expression, we find:

x ≈ 2.37

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Answer 2

Abigail Allen

#x=64/27#

#root(3)x prop 1/y^2 or root(3)x = k* 1/y^2 ;x=27 ,y=4 :. root(3) 27 = k/4^2 or 3 =k/16 or k=48 #. So the equation is #root(3)x = 48* 1/y^2 ; y=6 ; x= ? root(3)x = 48* 1/6^2= 4/3 :. x =(4/3)^3=64/27 #[Ans]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.