A construction crew has to dig ditches for a set of pipes that must carry water...

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A construction crew has to dig ditches for a set of pipes that must carry water from point A to both of points B and C (see figure). Points B and C are 2 km apart and point A is 2 km from the midpoint of B and C. They want to dig as little as possible and they believe the best way to do that is to dig from point A to some point D along the midline a distance h from the midpoint of B and C. They know that they should choose h satisfying 0 h 2 but they are not sure exactly what value of h to use. 2 km 2 km B D h= C A a) Formulate an expression L(h) for the total length of ditch. h L(h) = (2 points.) b) Now calculate the value of h which minimizes the amount of ditch to be dug. If there is more than one such value give your answer as a comma separated list. (3 points.) A construction crew has to dig ditches for a set of pipes that must carry water from point A to both of points B and C (see figure). Points B and C are 2 km apart and point A is 2 km from the midpoint of B and C. They want to dig as little as possible and they believe the best way to do that is to dig from point A to some point D along the midline a distance h from the midpoint of B and C. They know that they should choose h satisfying 0 h 2 but they are not sure exactly what value of h to use. 2 km 2 km B D h= C A a) Formulate an expression L(h) for the total length of ditch. h L(h) = (2 points.) b) Now calculate the value of h which minimizes the amount of ditch to be dug. If there is more than one such value give your answer as a comma separated list. (3 points.)