# If y varies inversely as the cube root of x, and y = 12 when x = 8, how do you find y when x = 1?

To find y when x = 1, we can use the inverse variation equation.

First, we need to determine the constant of variation, which is denoted as k.

Using the given information, when y = 12 and x = 8, we can set up the equation:

y = k / ∛x

Substituting the values, we have:

12 = k / ∛8

To solve for k, we can multiply both sides of the equation by ∛8:

12 * ∛8 = k

Now, we can find the value of k:

k ≈ 12 * 2 ≈ 24

Now that we have the value of k, we can use it to find y when x = 1.

Plugging in the values into the inverse variation equation:

y = k / ∛x

y = 24 / ∛1

Since the cube root of 1 is 1, we have:

y = 24 / 1

Therefore, y = 24 when x = 1.

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Change the variation to an equation by multiplying by a constant.

Now we can calculate y for any given x.

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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.

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.

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.

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