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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 18 Sep 2006, 12:44
The concentration of a certain chemical in a full water tank depends on the depth of the water. At a depth that is x feer below the top of the tank, the concentration is 3+(4/sq rt of 5-x) parts per million, where 0<x<4. To the nearest 0.1 ft, at what depth is the concentration equal to 6 parts per million?

Is substituting the answer choices the best way to solve this?

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

Is this considered a difficult question?
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Re: Word Problem [#permalink] New post 18 Sep 2006, 14:52
rfrcuhetr1 wrote:
The concentration of a certain chemical in a full water tank depends on the depth of the water. At a depth that is x feer below the top of the tank, the concentration is 3+(4/sq rt of 5-x) parts per million, where 0<x<4. To the nearest 0.1 ft, at what depth is the concentration equal to 6 parts per million?

Is substituting the answer choices the best way to solve this?

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

Is this considered a difficult question?


I don't understand the red part of the problem
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Re: Word Problem [#permalink] New post 18 Sep 2006, 17:03
Iawfy wrote:

I don't understand the red part of the problem


3 + 4/sqrt(5-x) I'm guessing
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Re: Word Problem [#permalink] New post 18 Sep 2006, 17:50
rfrcuhetr1 wrote:
The concentration of a certain chemical in a full water tank depends on the depth of the water. At a depth that is x feer below the top of the tank, the concentration is 3+(4/sq rt of 5-x) parts per million, where 0<x<4. To the nearest 0.1 ft, at what depth is the concentration equal to 6 parts per million?

Is substituting the answer choices the best way to solve this?

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

Is this considered a difficult question?


this is quite simple.

3+(4/sqrt(5-x) = 6
4/sqrt(5-x)=3
sqrt(5-x)=4/3
5-x=9/16
x=3.2

So E
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Last edited by cicerone on 24 Sep 2008, 23:59, edited 1 time in total.
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 [#permalink] New post 18 Sep 2006, 21:21
rfrcuhetr1, you could also plug in and get to an answer relatively fast. of all the answers which one is the easiest to plug in into the equation? it's D, 3.0. so,

3 + (4/sqrt(5-3)) = 3 + 4/sqrt(2) = 3 + 2*sqrt(2) = 3 + sqrt(8).

since sqrt(9) is 3, sqrt (8) has to be < 3, so 3 +sqrt(8) is less than 6.

so that eliminates A through D and you are left with E.
  [#permalink] 18 Sep 2006, 21:21
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