A parabolic arch sculpture is on top of a city bank. A model of the arch is y = −0.005x^2 + 0.3x where x and y are in feet. The image is of a rectangle which represents the building of a Bank and its height is 30 feet. On top of it a semi circle is placed whose diameter is equal to the width of the rectangle. a. What is the distance from the highest point of the arch to the ground? b. What is the width of the bank?

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Answerprofit;

The answer is    (d) 7/2======we have    we also  have an integral      notice how function f splits up at x = 0. there's a left piece and a right pieceso we'll need to do the same thing with our integral: split it at x = 0we use a property of integrals that allows us to split up and sum:     notice that for the piecewise function f, the function has the equationf(x) = x when x  ≤ 0. so for the integral  , f(x) = x so it changes into      for the piecewise function f, the function has the equationf(x) = x+1  when x  > 0. for the integral  , we have    therefore, back to our splitted integral: