Here is what what written about this Lean-To:
A lean-to has a wooden floor, a 10 feet high open front, wooden side and back walls, and a wooden roof that tilts down at an angle of 45 degrees. What are the dimensions of the lean-to with the largest possible floor area that can be constructed...
Okay. I am figuring this out slowly but I am. So now I have for P= 2h+2r+(pi)r and for A=2rh+1/2(pi)r^2. I solved for h and got h=(a-1/2(pi)r^2)/(2r). After filling that back into the perimeter formula I got P=((2a-(pi)r^2)/(2r))+2r+(pi)r. For the derivative, which is where I am having trouble...
Thank you for your help. I have been working on this problem and I am still having trouble. I will do the best to type out the work I have done so far.
P=4r+2h
A=2rh+((pi)(r^2)/2)
I then solved the area formula for h and came up with:
h=(A-(pi)(r^2)/4r)
And then plugged this in for h in...
Homework Statement
This is from the book Calculus Single Variable, 4th edition:
The cross-section of a tunnel is a rectangle of height h surmounted by a semicircular roof section of radius <i>r</i>. If the cross-sectional area is A, determine the dimensions of the cross section which...