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If y varies inversely as x and y = 8 when x = 4, find y when x = 16?

Answer 1

Genesis Allen

#y=2#

The statement is expressed as #yprop1/x#

#"inverse means " 1/"variable"#

To convert to an equation introduce k, the constant of variation.

#y=kxx1/x#

#rArry=k/x#

To find k use the given condition that y = 8 when x = 4

#8=k/4rArrk=4xx8=32#

#rArr" equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=32/x)color(white)(2/2)|)))#

#x=16toy=32/16#

#rArry=2" when " x=16#

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Answer 2

Hazel Anglin

To find y when x = 16, we can use the inverse variation formula: y = k/x.

First, we need to find the value of k, which is the constant of variation.

Given that y = 8 when x = 4, we can substitute these values into the formula: 8 = k/4.

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

Now that we have the value of k, we can substitute it back into the formula: y = 32/x.

To find y when x = 16, we substitute x = 16 into the formula: y = 32/16.

Simplifying this expression, we find that y = 2.

Therefore, when x = 16, y = 2.

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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.