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?
1 Explanation
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Diego Scharifker
I find this answer given by the OG to be wrong, but I must be missing out on something.
I tried with t=9 and got that N(t)=180 which obviously is a positive, not a negative as the explanation states.
Any ideas?
When t = 5, the value of 20(t 5)2 + 500 is 500. For all values of t between 0 and 10, inclusive, except t = 5, the value of 20(t 5)2 is negative and 20(t 5)2 + 500 < 500. Therefore, the tank reaches its maximum depth 5 hours after 2:00 in the morning, which is 7:00 in the morning.
1 Explanation