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
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) (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(52855) (Show Source): You can put this solution on YOUR website! .
The algebra solution is THIS :
Complete the square
4t^2 - 36t + 95 = - + 95 = + 95 - 81 = + 14.
The term is always non-negative, and with positive addend of 14 it never becomes less than 14 kilometers.
Answer. The minimum distance is 14 kilometers.