SOLUTION: As you know my brother Jim is an avid fisherman. He varies the depth at which he fishes according to the following function: D(t) = -t2 + 10t where t is measured in hours. Estim

Algebra ->  Systems-of-equations -> SOLUTION: As you know my brother Jim is an avid fisherman. He varies the depth at which he fishes according to the following function: D(t) = -t2 + 10t where t is measured in hours. Estim      Log On


   



Question 319362: As you know my brother Jim is an avid fisherman. He varies the depth at which he fishes according to the following function: D(t) = -t2 + 10t where t is measured in hours. Estimate the time when he fishes at the greatest depth and tell me that depth.
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
+D%28t%29+=+-t%5E2+%2B+10t+
.
Is a "quadratic" -- a parabola that opens upwards (because the coefficient associated with the t^2 term is negative). Therefore, the vertex is at the lowest point.
.
Axis of symmetry = -b/(2a) = -10/(-2) = 5 hours
.
+D%28t%29+=+-t%5E2+%2B+10t+
+D%285%29+=+-5%5E2+%2B+10%285%29+
+D%285%29+=+-25+%2B+50+
+D%285%29+=+25+
.
That's the depth -- problem doesn't say what the units are.