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The longevity of a certain metal construction is determined by the fol

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The longevity of a certain metal construction is determined by the fol  [#permalink]

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New post 03 Nov 2014, 09:01
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A
B
C
D
E

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Question Stats:

87% (01:21) correct 13% (01:55) wrong based on 79 sessions

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Tough and Tricky questions: Word Problems.



The longevity of a certain metal construction is determined by the following formula: \(l = (7.5 - x)^4 + 8.97^c\), where l is the longevity of the construction, in years, x is the density of the underlying material, in g/cm^3, and c is a positive constant equal to 1.05 for this type of metal constructions. For what value of density, x, expressed in g/cm^3, will the metal construction have minimal longevity?

A. -7.5
B. 0
C. 7.5
D. 15
E. 75

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Re: The longevity of a certain metal construction is determined by the fol  [#permalink]

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New post 03 Nov 2014, 10:08
1
Bunuel wrote:

Tough and Tricky questions: Word Problems.



The longevity of a certain metal construction is determined by the following formula: \(l = (7.5 - x)^4 + 8.97^c\), where l is the longevity of the construction, in years, x is the density of the underlying material, in g/cm^3, and c is a positive constant equal to 1.05 for this type of metal constructions. For what value of density, x, expressed in g/cm^3, will the metal construction have minimal longevity?

A. -7.5
B. 0
C. 7.5
D. 15
E. 75

Kudos for a correct solution.


My Solution:

Is the answer C?
Acc to the equation 8.97^ C is constant. So The value of L will be minimal when (7.5 - x)^4 =0.
Solving: x= 7.5
Plugging the value: (7.5 - 7.5)^4 = 0
Checking: (7.5 - (-7.5))^4 =(15)^4 (too big)
Since the power is even, the result will be positive. So B, D, E give bigger values.

The question is tricky so I think I am missing some key info. Am I?
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Re: The longevity of a certain metal construction is determined by the fol  [#permalink]

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New post 03 Nov 2014, 10:56
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1
IMO the answer is C.

To minimize this we need to min \((7.5-x)^4\).

The min value of which is 0 when x = 7.5

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Re: The longevity of a certain metal construction is determined by the fol  [#permalink]

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New post 03 Nov 2014, 22:07
1
Answer = C

For minimum longevity, equate

\((7.5-x)^4 = 0\)

x = 7.5
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Re: The longevity of a certain metal construction is determined by the fol  [#permalink]

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New post 01 Apr 2018, 02:39
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Re: The longevity of a certain metal construction is determined by the fol &nbs [#permalink] 01 Apr 2018, 02:39
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