Shore Line
A woman is in a boat 5 miles from the coast. She wants to get to a point six miles on the shore line. Whe?
4. A woman is in a boat 5 miles coast. She wants to reach a point 6 miles on the shore line. Where should it come down, if it can Row 2 km / h and walk 4 km / h?
Okay, let's assume there is no update and that you want to do is minimize the time. If it tries to reach the point 6 land, it will come ashore at the point x. It must row to the hypotenuse of a right triangle with one leg 5 (the distance from the coast) and the other leg x (distance along the coast), so it is a hypotenuse of length sqrt (25 ^ 2 + x) by the theorem of Pythagoras. And then she must walk a distance of 6 - x. In terms of time, given the speeds above, it takes t = sqrt (25 + x ^ 2) / 2 + (6 - x) / 4:00 to reach point. You need to minimize T. You can reduce t in putting this function in a graphing calculator if you have the right. If not for the calculation then you're probably supposed to calculate it yourself, and for that you are using the differentiation, the minimum occurs when t dt / dx = 0. The derivative of the above function is dt / dx = 2x / (4 * sqrt (25 + x ^ 2) - 1 / 4. Setting equal to zero gives 2x / (4 * sqrt (25 + x ^ 2) - 1 / 4 = 0 ==> 2x / (4 * sqrt (25 + x ^ 2) = 1 / 4 ==> 8x = 4 * sqrt (25 + x ^ 2) ==> 64x ^ 2 = 16 (25 + x ^ 2) ==> 64x ^ 2 = 400 + 16x ^ 2 ==> 48x ^ 2 = 400 ==> x ^ 2 = 8333 ==> x = 2.89 miles downshore its current position. Note that -2.89 is also a solution and it is significant in this problem because the woman could certainly upshore online destination, but the rules of logic, without checking it mathematically.
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