SOLUTION: Jim is a fisherman. He varies the depth at which he fishes according to the following function: D(t)= -t^2+10t where t is measured in hours. Estimate the time when he fishes at the

Question 65295: Jim is a fisherman. He varies the depth at which he fishes according to the following function: D(t)= -t^2+10t where t is measured in hours. Estimate the time when he fishes at the greatest depth and tell me that depth.
Found 2 solutions by josmiceli, Earlsdon:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
D(t)= -t^2+10t
If this is put in the form
, the the maximum is at (,)
b = +10
a = -1
-b/(2a) = -10/-2
-10/-2 = 5
D(5) = -(5)^2 + 10*5
D(5) = -25 + 50
D(5) = 25
so, the maximum is at (5,25)
He fishes at a depth of 25 in 5 hours. Is D in units of feet?
Problem didn't say.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Since the equation for the depth as a function of time is a parabola that opens downward (), the vertex of the parabola occurs at the maximum value of the independent variable, t.
The t-coordinate of the vertex can be found by: where: b = 10 and a = -1.

The maximum depth, D, occurs at t = 5 or 5 hours.
To find the value of D at this time, substitute t=5 into the original equation and solve for D.

The maximum depth is 25 feet(?).
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