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dtan5457
 one year ago
pre calc question
dtan5457
 one year ago
pre calc question

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You want to minimize the TOTAL TIME. Split that into two parts: Tw = walking time. Tr = rowing time. Now make a diagram. He is at M, and wants to reach Q. So he aims the boat at P:  + Q(3,1)    P(x,0) ++*++ Coast  1 2 3    M(0,2) MP = sqrt(x^2 + 4) PQ = sqrt((x3)^2 + 1) Row MP in Tr = MP/2 = sqrt(x^2 + 4)/2 Walk PQ in Tw = PQ/4 = sqrt((x3)^2 + 1)/4 Total time is the sum of those; T = sqrt(x^2 + 4)/2 + sqrt((x3)^2 + 1)/4 Now do the usual stuff: 2x 2(x  3) dT/dx =  +  4 sqrt(x^2 + 4) 8 sqrt((x3)^2 + 1) x (x  3) dT/dx =  +  2 sqrt(x^2 + 4) 4 sqrt((x3)^2 + 1) Set that equal to zero: x (x  3) 0 =  +  2 sqrt(x^2 + 4) 4 sqrt((x3)^2 + 1) 2x sqrt((x3)^2 + 1) + (x  3)sqrt(x^2 + 4) 0 = ... 4 sqrt(x^2 + 4) sqrt((x3)^2 + 1) Set the top to zero: 2x sqrt((x3)^2 + 1) + (x  3)sqrt(x^2 + 4) = 0 2x sqrt((x3)^2 + 1) = (3  x)sqrt(x^2 + 4) Square both sides: 4x^2((x  3)^2 + 1) = (9  6x + x^2)(x^2 + 4) 4x^2(x^2  6x + 9 + 1) = (9  6x + x^2)(x^2 + 4) 4x^4  24x^3 + 40x^2 = 9x^2  6x^3 + x^4 + 36  24x + 4x^2 3x^4  18x^3 + 27x^2 = + 36  24x 3x^4  18x^3 + 27x^2 + 24x  36 = 0 x^4  6x^3 + 9x^2 + 8x  12 = 0 x = 1 is an obvious solution: 1  6 9 8  12 (1) 1 5 4 12  1  5 4 12 zero x^3  5x^2 + 4x + 12 = 0 is the reduced equation. A quickanddirty graph of x^3  5x^2 + 4x + 12 shows only a root for a negative number. So x = 1 is the solution

Here_to_Help15
 one year ago
Best ResponseYou've already chosen the best response.0https://answers.yahoo.com/question/index?qid=20130403135357AAHZFha
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