Suppose that y varies inversely with the square root of x and y=50 when x=4, how do you find y when x=5?

Answer 1
If #y# varies inversely with #sqrt(x)# then #y*sqrt(x) = c# for some constant #c#
Given #(x,y)=(4,50)# is a solution to this inverse variation then #50*sqrt(4) = c# #rarr c = 100 color(white)("xxxxxxxxxx")# (see note below) and the inverse variation equation is #y*sqrt(x) = 100#
When #x = 5# this becomes #y*sqrt(5) = 100#
#sqrt(5) = 100/y#
#5 = 10^4/y^2#
#y = sqrt(5000) = 50sqrt(2)#
Note: I have interpreted "y varies inversely with the square root of x" to mean the positive square root of x (i.e. #sqrt(x)#) which also implies that y is positive. If this is not the intended case, the negative version of y would also need to be allowed.
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Answer 2

To find y when x=5, we can use the inverse variation equation. First, we need to find the constant of variation (k) by substituting the given values into the equation.

y = k / √x

Substituting y=50 and x=4 into the equation:

50 = k / √4

Simplifying:

50 = k / 2

Multiplying both sides by 2:

100 = k

Now that we have the constant of variation (k), we can find y when x=5 by substituting the values into the equation:

y = k / √x

Substituting k=100 and x=5:

y = 100 / √5

Simplifying:

y = 100 / √5

Therefore, when x=5, y is approximately equal to 44.72.

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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.

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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