Question

Mr. Jones wants to place a chimney on his roof. It is recommended that the chimney be set at a height of at least 30 feet. The height of the roof is described by the function f(x)=−4/3|x−10| + 40 where x is the distance along the width of the roof. Where should Leroy place the chimney if the house is 45 feet wide?

Answer 1

Absolute value of any number is always positive because it represent distance and distance will always positive.

To place chimney at  least 30 feet , the distance along the width of the roof  (x) will be  x = 17.5 feet or x = 2.5 feet.

Since, The height of the roof is described by the function f(x)=−4/3|x−10| + 40

Since, minimum height is 30 feet.

So , substitute f(x)=30 in above expression.

                 30=−4/3|x−10| + 40

                   4/3|x−10| = 10

                      |x−10|=30/4

                      |x−10| = 7.5

Taking positive case,

                           x−10 = 7.5

                           x = 17.5 feet

Taking negative case,

                          x−10 = - 7.5

                          x = 10 - 7.5

                          x = 2.5 feet

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