SOLUTION: The distance D km between two ships A and B at time t hours is given by the formula D = 4t^2 - 36t +95. Find the minimum distance between the ships

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The distance D km between two ships A and B at time t hours is given by the formula D = 4t^2 - 36t +95. Find the minimum distance between the ships       Log On


   

Question 1122435: The distance D km between two ships A and B at time t hours is given by the formula D = 4t^2 - 36t +95. Find the minimum distance between the ships
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The distance D km between two ships A and B at time t hours is given by the formula D = 4t^2 - 36t +95. Find the minimum distance between the ships
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1st derivative = 8t - 36
8t-36 = 0
t = 4.5 hours
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D = 4*4.5^2 - 36*4.5 + 95
D = 14 km
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Without calculus:
The closest point is the vertex of the parabola, at t = -b/2a = 36/8 = 4.5
D = 14 kms

Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
.
The algebra solution is  THIS : 

Complete the square


4t^2 - 36t + 95 = %282t-9%29%5E2 - 9%5E2 + 95 = %282t-9%29%5E2 + 95 - 81 = %282t-9%29%5E2 + 14.


The term   %282t-9%29%5E2  is always non-negative, and with positive addend of 14 it never becomes less than 14 kilometers.


Answer.  The minimum distance is 14 kilometers.