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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 3 km apart and point A is 3 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 are not sure exactly what value of h to use. B 3 km C Ꭰ 3 km h A (a) Formulate an expression L(h) for the total length of ditch. L(h) = 3-h+2sqrt(2(25)+h^2) (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. h = 1.5 km Note: You do not need a calculator to solve this problem.

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 3 km apart and point A is 3 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 are not sure exactly what value of h to use. B 3 km C Ꭰ 3 km h A (a) Formulate an expression L(h) for the total length of ditch. L(h) = 3-h+2sqrt(2(25)+h^2) (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. h = 1.5 km Note: You do not need a calculator to solve this problem.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter5: Similar Triangles
Section5.CR: Review Exercises
Problem 41CR
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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 3 km apart and point A is 3 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 are not sure exactly what value of h to use. B 3 km C Ꭰ 3 km h A (a) Formulate an expression L(h) for the total length of ditch. L(h) = 3-h+2sqrt(2(25)+h^2) (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. h = 1.5 km Note: You do not need a calculator to solve this problem.
Transcribed Image Text: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 3 km apart and point A is 3 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 are not sure exactly what value of h to use. B 3 km C Ꭰ 3 km h A (a) Formulate an expression L(h) for the total length of ditch. L(h) = 3-h+2sqrt(2(25)+h^2) (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. h = 1.5 km Note: You do not need a calculator to solve this problem.
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