The concentration of a certain chemical in a full water tank

OCDianaOC - This question's wording is not easy. I rephrased it.

Given: a chemical concentration of 6
Given: a formula that will tell how deep the water is at a particular concentration, IF we have the concentration (we do)
Formula: \(3 + \frac{4}{\sqrt{5-x}}\)

Set the formula equal to concentration. The concentration of 6, in tandem with the formula, will yield depth.

\(3 + \frac{4}{\sqrt{5-x}} =\\
6\)
Subtract 3 from both sides:

\(\frac{4}{\sqrt{5-x}} = 3\)
Square both sides:

\((\frac{4^2}{(\sqrt{5-x})^2}) = 3^2\)

\((\frac{16}{(5-x)}) = 9\)
Multiply both sides by denominator and solve:

\(16 = 9(5 - x)\)
\(16 = 45 - 9x\)
\(9x = 29\)

\(x = \frac{29}{9} = 3.2\) feet

Answer E

Hope that helps.

**The language "where 0 < x < 4," is mostly irrelevant. It's to keep the denominator in the formula positive. (Can't divide by zero, can't take the square root of a negative number.)
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Given: at a depth that is x feet below the top of the tank, the concentration is \(3 + \frac{4}{\sqrt{5-x}}\) parts per million.

Question: at what depth, for which x, is the concentration equal to 6 parts per million? So, for which x, is \(3 + \frac{4}{\sqrt{5-x}}\) equal to 6?

\(3 + \frac{4}{\sqrt{5-x}}=6\) --> \(x\approx{3.2}\).

Answer: E.

Hope it's clear.
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3 + 4/sqrt(5-x) = 6

4/sqrt(5-x) = 3

16/(5-x) = 9

9x = 29 -> x = 3.2

I was going to go with 3.0...but then the question says witin 0.1 feet...and with 3.0..we get within 0.2 feet...so I would have just picked 3.2 at that point....

anyway

4/sqrt(5-x)=3

16/(5-x)=9

16=45-9x

solve for X...

3 + 4/sqrt(5-x) = 6

solve for x, x = 29/9 = 3.2 ft

E

You are tired. Go to bed

not yet...its raining here...and I want to go to the gym

to go or not to go to gym is the question...what would GSR do?hmm

Thumbs up! for a 'go' to gym!

gym it is...see you in an hr...

My brain is cloudy, going to gym to clear it up....but how did you guys know to set the equation equal to 6? Once we get to the equation the math is easy but I did not know where to begin. Can someone explain?
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I've been trying to wrap my head around how to set up that equation, but am not able to. Could someone please help me out with why I should be equating 6ppm with the concentration at x feet?

Can you show me step-by-step how to solve this one? I'm missing something...

YAAAAY! Your explanation is perfect. I finally understand how to solve this now!

Thank you!

Given: The concentration of a certain chemical in a full water tank depends on the depth of the water. At a depth that is x feet below the top of the tank, the concentration is \(3 + \frac{4}{\sqrt{5-x}}\) parts per million, where 0 < x < 4.

Asked: To the nearest 0.1 foot, at what depth is the concentration equal to 6 parts per million?

6 = \(3 + \frac{4}{\sqrt{5-x}}\)
\(\sqrt{4}{\sqrt{5-x}} = 3\)
5-x = 16/9 = 1.8 to the nearest .1 foot
x = 5 -1.8 = 3.2 to the nearest .1 foot

IMO E

Shouldn't the answer be total -x = depth of water.
The water depth is given as x feet below the top of the tank.

When we equate the equation with 6 and derive at an answer, then the value gives the depth from the top of the tank. inorder to dervice at water depth, we will have to do total depth - top of the depth

Please correct my understanding.

The depth of the water is measured from the top of the tank to the bottom. Hence, those are the same.
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