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bcddd214

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The perimeter of a Norman window is 20 meters. Find the dimensions of the window that admits most light.

A norman window is the half circle window on top of a typical residential door.

C/2=2?r/2=?r
2x+2y+?x=20
2y=20-2x-?x
2y/2=(20-2x-?x)/2
2y/2=20/2-2x/2 (-?x)/2
y=(20-2x-?x)/2
y=10-x- ?x/2
A=1/2 ?x^2+2x*(20-2x-?x)/2
 
The perimeter of a Norman window is 20 meters. Find the dimensions of the window that admits most light.

A norman window is the half circle window on top of a typical residential door.

C/2=2?r/2=?r
2x+2y+?x=20
2y=20-2x-?x
2y/2=(20-2x-?x)/2
2y/2=20/2-2x/2 (-?x)/2
y=(20-2x-?x)/2
y=10-x- ?x/2
A=1/2 ?x^2+2x*(20-2x-?x)/2
Click to expand...

Good. Now 1) distribute; 2) simplify; 3) find the derivative, dA/dx; 4) set dA/dx = 0 and solve for x to find maxima/minima.
 
wjm11 said:
The perimeter of a Norman window is 20 meters. Find the dimensions of the window that admits most light.

A norman window is the half circle window on top of a typical residential door.

C/2=2?r/2=?r
2x+2y+?x=20
2y=20-2x-?x
2y/2=(20-2x-?x)/2
2y/2=20/2-2x/2 (-?x)/2
y=(20-2x-?x)/2
y=10-x- ?x/2
A=1/2 ?x^2+2x*(20-2x-?x)/2
Click to expand...

Good. Now 1) distribute; 2) simplify; 3) find the derivative, dA/dx; 4) set dA/dx = 0 and solve for x to find maxima/minima.
Click to expand...

By distribute, do you mean this?
A=1/2 ?x^2+2x(10)-2x(x)+2 (?x/2)
 
By distribute, do you mean this?
A=1/2 ?x^2+2x(10)-2x(x)+2 (?x/2)
Click to expand...

Yes, except be careful: "A=1/2 ?x^2+2x(10)-2x(x)+2 (?x/2)" should be "A = (1/2) ?x^2 + 2x(10) - 2x(x) - 2x (?x/2)".
 
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