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anonymous
 one year ago
Two towns, A and B, are 13.0 miles apart and located 8.0 and 3.0 miles east, respectively, of a long, straight highway. A construction company has a contract to build a road from town A to the highway and then to town B. Determine the length (to the nearest tenth of a mile) of the shortest road that meets these requirements.
anonymous
 one year ago
Two towns, A and B, are 13.0 miles apart and located 8.0 and 3.0 miles east, respectively, of a long, straight highway. A construction company has a contract to build a road from town A to the highway and then to town B. Determine the length (to the nearest tenth of a mile) of the shortest road that meets these requirements.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@ganeshie8 can you draw it picture,so that i can solve?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0dw:1436781239171:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0dw:1436782203008:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0I think we need to find the minimum length of that road

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0did they told us that the road should meet at the same point to highway?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@ManhattanProject do you have any idea about answer?

dumbcow
 one year ago
Best ResponseYou've already chosen the best response.2dw:1437272681909:dw now express distance of 2 roads as function of x \[f(x) = \sqrt{x^2 +8^2} + \sqrt{(12x)^2 +3^2}\] minimize function by taking derivative and setting equal to 0 (use chain rule) \[f'(x) = \frac{x}{\sqrt{x^2+64}}  \frac{12x}{\sqrt{(12x)^2 + 9}} = 0\] Solve for x first square both sides \[\frac{x^2}{x^2+64} = \frac{(12x)^2}{(12x)^2 +9}\] \[x^2 (x^2 24x +153) = (x^2 +64)(x^2 24x+144)\] \[57x^2 (64)(24)x +(64)(144) = 0\] \[19x^2  512x+3072 = 0\] At this point just plug it into quadratic formula (remember x < 12) \[x = 9.02\] Now plug this value into f(x) to get length of shortest road
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