Asked by Regine
A gutter with trapezoidal cross-section is to be made from a long sheet of stainless steel that is 30 cm wide by turning up one-fourth of the width on each side. What width across the top will give the maximum cross sectional area?
Answers
Answered by
Steve
So, the sloping sides are 7.5 each, and the bottom is 15cm wide. Thus, if the top has width 2x+15, we have a cross-section area
a = (2x+15 +15)/2 √((15/2)^2-x^2)
= (x+15)/2 √(225-x^2)
da/dx = -(8x^2+60x-225) / (2√225-x^2))
da/dx=0 when x=2.7452
So, the width for maxim area is 20.49cm
a = (2x+15 +15)/2 √((15/2)^2-x^2)
= (x+15)/2 √(225-x^2)
da/dx = -(8x^2+60x-225) / (2√225-x^2))
da/dx=0 when x=2.7452
So, the width for maxim area is 20.49cm
Answered by
Anonymous
The shape of a patio is triangular with a height of 8 ft and base of 17 ft. What is the cost of outdoor carpeting to cover the patio if the carpeting costs $6.50 per ft2?