# If y varies inversely as the square of x and y = 8 when x = 2, then what is the value of y when x = -1?

To find the value of y when x = -1, we can use the inverse variation formula.

The inverse variation formula states that if y varies inversely as the square of x, then y = k/x^2, where k is a constant.

To find the value of k, we can substitute the given values of y and x into the formula.

When y = 8 and x = 2, we have 8 = k/2^2.

Simplifying this equation, we get 8 = k/4.

To solve for k, we can multiply both sides of the equation by 4, giving us 32 = k.

Now that we have the value of k, we can substitute it back into the inverse variation formula to find the value of y when x = -1.

Using y = k/x^2 and substituting k = 32 and x = -1, we get y = 32/(-1)^2.

Simplifying this equation, we have y = 32/1, which means y = 32.

Therefore, when x = -1, the value of y is 32.

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The answer is

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So our formula is:

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If (y) varies inversely as the square of (x), we can express this relationship using the formula:

[y = \frac{k}{x^2}]

Where (k) is a constant of proportionality.

Given that (y = 8) when (x = 2), we can substitute these values into the equation to find the value of (k):

[8 = \frac{k}{2^2}]

[8 = \frac{k}{4}]

[k = 8 \times 4 = 32]

Now that we know (k = 32), we can find (y) when (x = -1) by substituting this value into the equation:

[y = \frac{32}{(-1)^2}]

[y = \frac{32}{1}]

[y = 32]

So, when (x = -1), (y) has a value of (32).

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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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