Posted by **Anonymous** on Tuesday, December 13, 2011 at 9:43pm.

A carpenter is cutting a 3ft by 4ft elliptical sign from a 3ft by 4ft piece of plywood. The ellipse will be drawn using a string attached to the board at the foci of the ellipse.

A)How far from the ends of the board should the string be attached?

B)How long should the string be?

- College Algebra -
**drwls**, Wednesday, December 14, 2011 at 1:52am
The semimajor axis is a = 2 ft.

The semiminor axis is b = 1.5 ft.

The equation of the ellipse is

x^2/a^2 + y^2/b^2 = 1

I have assumed (0,0) is the center of the rectangle.

The foci are at y = 0 and x = +/- c, where

c = sqrt[a^2 - b^2] = sqrt1.75

= 1.323 ft

The distance of the foci from the closest end of the board is 4 - 1.323 = 2.677 ft

String length = 2c = 2*s

- analytic geometry -
**drwls**, Wednesday, December 14, 2011 at 1:55am
Ignore the final '=2s '

The answer got sent before I could finish.

2c = 2.646 ft is the string length

- College Algebra -
**Anonymous**, Wednesday, December 14, 2011 at 11:52am
the sum of one half a number, one third a number and one twelfth of a number is 33. find the original number

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