College Algebra

posted by .

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 -

    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 -

    Ignore the final '=2s '
    The answer got sent before I could finish.
    2c = 2.646 ft is the string length

  • College Algebra -

    the sum of one half a number, one third a number and one twelfth of a number is 33. find the original number

  • College Algebra -

    Slight mistake in the first answer...The total distance the foci are apart from each other is 2.6457 ft. BUT the distance of the foci from the closest end of the board is 2 - 1.32288 = .67712 ft. Since c^2= a^2 - b^2, and 2a=4, and a=2, therefore a-c is equal to 2-1.32288 which is only .67712 ft. Also, string length is equal to 2c + 2(a-c)=2c + 2a - 2c which is only equal to 2a. So, the string length is 4 ft.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. pre-cal

    a rectangular board is 2 by 12 units. How far from the short sides of the board will the foci be located to determine the largest elliptical tabletop?
  2. Math Word Problem

    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 …
  3. Math

    find the surface area and volume of a similar figure that is larger by scale factor of 25 using 3.14//// 5ft, 4ft, 3ft
  4. Calc

    Oscar Corporation is planning to construct an elliptical gate at its headquarters. The width of the ellipse will be 5 feet across and its maximum height along the center will be 3 feet. The company wants to place two bright spots at …
  5. Geometry

    What is the area semi-circle piece of glass for Norman glass when the width is 3ft. and the length is 4ft?
  6. physics

    The angular momentum of a planet is conserved if taken with respect to: a)The center of the ellipse b) The focus of the ellipse at the sun c)The focus of the ellipse opposite the sun d)Both foci of the ellipse
  7. math help

    please explain your answer and how you got it.. Samantha had a board that was 6ft. 8in.long.she cut off a piece that was 2 ft.10in.long.how much board does she have left?
  8. math m,

    A sheet of cardboard 3ft by 4ft will be made into a box by cutting equal sized square
  9. math

    What is the are of 18ft 18ft 4ft 3ft 3ft
  10. math

    A 4ft piece of pipe needs to be divided into pieces that are 2/3ft long. How many pieces are made?

More Similar Questions