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The concentration of a certain chemical in a full water tank

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The concentration of a certain chemical in a full water tank [#permalink] New post 23 Jun 2009, 04:01
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81% (02:45) correct 19% (04:18) wrong based on 50 sessions
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. To the nearest 0.1 foot, at what depth is the concentration equal to 6 parts per million?

(A) 2.4 ft
(B) 2.5 ft
(C) 2.8 ft
(D) 3.0 ft
(E) 3.2 ft

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-concentration-of-a-certain-chemical-in-a-full-water-tank-23165.html
[Reveal] Spoiler: OA
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Re: concentration of certain chemical [#permalink] New post 23 Jun 2009, 04:06
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(3 + (4/sq root (5-x)))=6
(4/sq root (5-x))=3
sq root (5-x)=4/3
x=5-(16/9)
x=3.2
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Re: concentration of certain chemical [#permalink] New post 23 Jun 2009, 06:18
Yes, thats the answer thanks.
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Re: concentration of certain chemical [#permalink] New post 10 Apr 2014, 20:07
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Re: The concentration of a certain chemical in a full water tank [#permalink] New post 11 Apr 2014, 03:03
Expert's post
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. To the nearest 0.1 foot, at what depth is the concentration equal to 6 parts per million?

(A) 2.4 ft
(B) 2.5 ft
(C) 2.8 ft
(D) 3.0 ft
(E) 3.2 ft

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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-concentration-of-a-certain-chemical-in-a-full-water-tank-23165.html
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Re: The concentration of a certain chemical in a full water tank   [#permalink] 11 Apr 2014, 03:03
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