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

Question

Dennis Huerta

Physics

12 April, 12:31

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

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Answers (1)

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Madison · Answer 1

b) 7.00

Explanation:

N (t) = - 20 (t - 5) ²

dN / dt = - 20 x 2 (t - 5)

For maximum N (depth)

dN/dt = 0

- 40 (t - 5) = 0

t = 5

So at 2 + 5 = 7.00 am depth of water reaches its maximum.