Question
Construct a window in the shape of a semi-circle over a rectangle.If the distance around the outside of the window is 12 feet.What dimensions will result in the rectangle having the largest possible area?
We need to find Amax
I know the circmfrence is 12
12=w+2L+a/2(pie)
I'm not sure about the equation above.
Thank you!
We need to find Amax
I know the circmfrence is 12
12=w+2L+a/2(pie)
I'm not sure about the equation above.
Thank you!
Answers
bobpursley
in the equation above, I hope a=w/2
so the length around the top semicircle is PI*a=PI*w/2
12= w+2L+PI w/2
12=w(1+PI/2)+2L
area= wL+1/2 PI (w/2)^2
so solve for L in the perimeter equation, and then put that in for L in the area equation.
Take the derivative of area wrespect to w, set to zero, and solve for w.
Then go back and solve for L.
so the length around the top semicircle is PI*a=PI*w/2
12= w+2L+PI w/2
12=w(1+PI/2)+2L
area= wL+1/2 PI (w/2)^2
so solve for L in the perimeter equation, and then put that in for L in the area equation.
Take the derivative of area wrespect to w, set to zero, and solve for w.
Then go back and solve for L.
thanks!!
Related Questions
A window is made up of a circle embedded in a rectangle so that the diameter of the circle is a side...
Calculus. Mary designed a new viewing window consisting of a rectangle and a semi circle for a fresh...
Given that a window entails a rectangle capped by a semi-circle, given that the semi-circle’s diamet...
Hey Jiskha,
came across this problem in my maths homework and I can't seem to solve it.
Can some...