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by tracyyahoo » Tue Oct 04, 2011 5:35 pm
Acoording to a certain estimate, the depth N(t), in centimeters, of the water in a certain tank at t hours past 2:00 in the morning is given by N(t)= -20(t-5)+500 for 0=t=10. According to this estimate, at what time in the morning does the depth of the water in the tank reach its maximum???

a) 5:30 b) 7:00 c) 7:30 d) 8:00 e)9:00

Could someone explain in details , tahnk you.

OA is B not A not C ok~~~~ I chose C I have my reasons, pls explain why A???
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by sanju09 » Wed Oct 05, 2011 1:12 am
tracyyahoo wrote:Acoording to a certain estimate, the depth N(t), in centimeters, of the water in a certain tank at t hours past 2:00 in the morning is given by N(t)= -20(t-5)+500 for 0=t=10. According to this estimate, at what time in the morning does the depth of the water in the tank reach its maximum???

a) 5:30 b) 7:00 c) 7:30 d) 8:00 e)9:00

Could someone explain in details , tahnk you.

OA is B not A not C ok~~~~ I chose C I have my reasons, pls explain why A???
Please recheck your question, because the depth function N (t) = -20(t - 5) + 500 for 0 ≤ t ≤ 10 suggests that N (t) will be maximum when the expression -20(t - 5) will attain its maximum value within the interval 0 ≤ t ≤ 10, and that happens at t = 0 or at 2:00 in the morning, which is none of the choices.
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by tracyyahoo » Wed Oct 05, 2011 6:17 am
Sorry, sorry, my bad...

N(t)= -20(t-5)^2+500
sanju09 wrote:
tracyyahoo wrote:Acoording to a certain estimate, the depth N(t), in centimeters, of the water in a certain tank at t hours past 2:00 in the morning is given by N(t)= -20(t-5)+500 for 0=t=10. According to this estimate, at what time in the morning does the depth of the water in the tank reach its maximum???

a) 5:30 b) 7:00 c) 7:30 d) 8:00 e)9:00

Could someone explain in details , tahnk you.

OA is B not A not C ok~~~~ I chose C I have my reasons, pls explain why A???
Please recheck your question, because the depth function N (t) = -20(t - 5) + 500 for 0 ≤ t ≤ 10 suggests that N (t) will be maximum when the expression -20(t - 5) will attain its maximum value within the interval 0 ≤ t ≤ 10, and that happens at t = 0 or at 2:00 in the morning, which is none of the choices.
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by GMATGuruNY » Wed Oct 05, 2011 6:38 am
tracyyahoo wrote:According to a certain estimate, the depth N(t), in centimeters, of the water in a certain tank at t hours past 2:00 in the morning is given by N(t)= -20(t-5)²+500 for 0≤t≤10. According to this estimate, at what time in the morning does the depth of the water in the tank reach its maximum?

a) 5:30 b) 7:00 c) 7:30 d) 8:00 e)9:00
Depth = -20(t-5)²+500.

-20(t-5)² ≤ 0.
Thus, the maximum depth will occur when -20(t-5)² = 0.
-20(t-5)² = 0 when t=5.

2am + 5 hours = 7am.

The correct answer is B.
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by seema19 » Wed Oct 05, 2011 7:39 am
GMATGuruNY wrote:
tracyyahoo wrote:According to a certain estimate, the depth N(t), in centimeters, of the water in a certain tank at t hours past 2:00 in the morning is given by N(t)= -20(t-5)²+500 for 0≤t≤10. According to this estimate, at what time in the morning does the depth of the water in the tank reach its maximum?

a) 5:30 b) 7:00 c) 7:30 d) 8:00 e)9:00
Depth = -20(t-5)²+500.

-20(t-5)² ≤ 0.
Thus, the maximum depth will occur when -20(t-5)² = 0.
-20(t-5)² = 0 when t=5.

2am + 5 hours = 7am.

The correct answer is B.
@GMATGuruNY - why should -20(t-5)² <= 0 ???
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by GMATGuruNY » Wed Oct 05, 2011 7:54 am
seema19 wrote:
@GMATGuruNY - why should -20(t-5)² <= 0 ???
The square of a number cannot be negative.
Thus, (t-5)²≥ 0.

If (t-5)²> 0:
-20(t-5)² = negative*positive = negative, in which case -20(t-5)²<0.

If (t-5)²= 0:
-20(t-5)² = negative*0 = 0, in which case -20(t-5)²=0.

Thus, -20(t-5)²≤ 0.
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