If y varies inversely as #x^2# and y = 10 when x=2 , find y when x = 0.5?
Write it as an inverse proportion first
Change into an equation by multiplying by a constant.
Find the value of the constant
Use the constant in the equation
Solve for y when x = 0.5
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To find y when x = 0.5, we can use the inverse variation equation.
The inverse variation equation is y = k/x^2, where k is the constant of variation.
To find the value of k, we can substitute the given values of y and x into the equation.
When y = 10 and x = 2, we have 10 = k/2^2.
Simplifying this equation, we get 10 = k/4.
To solve for k, we can multiply both sides of the equation by 4, giving us 40 = k.
Now that we have the value of k, we can substitute it back into the inverse variation equation to find y when x = 0.5.
Using y = k/x^2 and substituting k = 40 and x = 0.5, we get y = 40/(0.5)^2.
Simplifying this equation, we have y = 40/0.25.
Therefore, y = 160 when x = 0.5.
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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.
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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