# Suppose that y varies directly as the square root of x...?

Suppose that y varies directly as the square root of x, and that y=36 when x=225. what is y when x=205? (round to 2 decimal places)

I have learned inverse variation well but I cannot seem to grasp direct. My class is online and every time I try and think I have the right answer it shows up as wrong. Can you please help me? I would appreciate if you show the work so I do not have to ask another problem like this.

I have learned inverse variation well but I cannot seem to grasp direct. My class is online and every time I try and think I have the right answer it shows up as wrong. Can you please help me? I would appreciate if you show the work so I do not have to ask another problem like this.

## 2 Answers

- Let, y = okay.√x, where, okay is steady, and For, x=256, y = 21, SO, 21 = ok.√256 = 16k, ===> k = 21/sixteen, hence, y = (21/16)√x, NOW, for, x = 207, ===> y = (21/sixteen)√(207), OR, y = 18.884 >================================< reply00
- For y to vary directly as the square root of x, the equation would be as follows.

y = K * sqrt(x) where K is a constant of proportionality, and sqrt(x) is the square root of x.

The reason that K is in there will be obvious in a moment.

if x = 225, then the square root of x = 15

So, the equation y = sqrt(x) doesnt work, because we know from the problem statement that for x = 225, y = 36, and not 15.

So, we have to add a scale factor.

Let K = 36/15

So the equation becomes

Y = K * sqrt(x)

y = (36/15) * sqrt(x)

Now, substitute for x = 225

y = (36/15) * sqrt(225)

y = (36/15) * 15

y = 36 <== the desired result

So, the value of K was picked by setting the numerator equal to the result you want (36) and the denominator equal to the result that you don't want (15), so that it cancels out the value of sqrt(225)

So the final equation is

y = (36/15) * sqrt(x)

Now, y still varies directly with sqrt(x). If you were to plot the y vs. sqrt(x), you would get a straight line, running through the origin, with a slope of K.

For the second part of the problem, let y = 205.

Then,

y = (36/15) * sqrt(205) = 34.36

Hope this helps,

-Guru00

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