Thursday

October 23, 2014

October 23, 2014

Posted by **Anonymous** on Thursday, April 4, 2013 at 12:52am.

- calc -
**Reiny**, Thursday, April 4, 2013 at 8:27amLet the width of the rectangle be 2x , making the radius of the semicircle = x

let the height of the rectangle be y

then 2x + 2y + 2πx = 24

x + y + πx = 12

y = 12-x-πx

Assume that the amount of light (L) is a function of the area

L= area of rectangle + (1/2) area of semicircle

= 2xy + (1/2)(1/2)π x^2

= 2x(12-x-πx) + (1/4)π x^2 = 24x - 2x^2 - 2πx^2 + (1/4)π x^2

dL/dx = 24 - 4x - 4πx + (1/2)πx

= 0 for a max of L

times 2

48 - 8x - 8πx + πx = 0

48 = x(8 + 8π - π)

x = 48/(8+7π) = appr1.6

then r = 5.37

State the conclusion

(check my arithmetic, I should have written it out on paper)

**Answer this Question**

**Related Questions**

Calc - A Norman window consists of a rectangle capped by a semi-circular ...

calculus - A Norman window has the shape of a rectangle surmounted by a ...

calculus - Construct a window in the shape of a semi-circle over a rectangle.If ...

Pre calculus - A window is made up of a circle embedded in a rectangle so that ...

Calculus 2 - Calculus. Mary designed a new viewing window consisting of a ...

math - A Norman window has the shape of a rectangle surmounted by a semicircle...

Calculus - A Norman window has the shape of a rectangle surmounted by a ...

Math - A norman window is constructed by adjoining a semicircle to the top of an...

Geometry - I have a picture of a window showing a square in the center with ...

Calculus - A Norman window has the shape of a rectangle surmounted by a ...