# If y varies directly with x, if y=4 when x=16, how do you find y when x=6?

A direct variation is always of the form

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To find ( y ) when ( x = 6 ), given that ( y ) varies directly with ( x ) and ( y = 4 ) when ( x = 16 ), you can use the direct variation formula.

The direct variation formula states: ( y = kx ), where ( k ) is the constant of variation.

First, find the constant of variation (( k )) using the given values: ( y = 4 ) when ( x = 16 ).

[ 4 = k \times 16 ]

[ k = \frac{4}{16} = \frac{1}{4} ]

Now that you have the value of ( k ), you can use it to find ( y ) when ( x = 6 ):

[ y = \frac{1}{4} \times 6 = \frac{6}{4} = 1.5 ]

So, when ( x = 6 ), ( y = 1.5 ).

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To find the value of y when x equals 6 in a direct variation, you can use the direct variation formula. First, determine the constant of variation (k) by dividing y by x when they are given values. Then, use this constant to find y when x equals 6.

In this case, when y equals 4 and x equals 16, you can find the constant of variation (k) by dividing 4 by 16, which equals 0.25.

Then, using the constant of variation, you can find y when x equals 6 by multiplying 0.25 by 6, which equals 1.5.

Therefore, when x equals 6, y equals 1.5.

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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.

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