Math

A fireplace arch is to be constructed in the form of a semi ellipse. The opening is to have a height of 3 feet at the center and a width of 8 feet along the base. The contractor cuts a string of a certain length and nails each end of the string along the base in order to sketch the outline of the semi ellipse.
a.) What is the total length of the string?
b.)How far from the center should the string be nailed into the base?

  1. 👍 0
  2. 👎 0
  3. 👁 1,537
  1. He must nail the ends of the string at the focal points of the ellipse
    For this ellipse:
    c^2 + 3^2 = 4^2
    c^2 = 7
    c = √7

    so one of the focal points is (√7, 0) , clear √7 units form the centre
    using the definition of ellipse properties, the length of the string is 8 units

    1. 👍 0
    2. 👎 0
    👨‍🏫
    Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    A fireplace arch is to be constructed in form of a semiellipse. The opening is to have a height of 2 feet at the center and a width of 6 feet along the base. The contractor cuts a string of a certain length and nails each end of

  2. math

    An arch in the form of a semi ellipse has a span of 10 meters and a central height of 4 m. Find the heights of the arch at a point of 3 meters from the semi minor axis.

  3. Trigonometry

    An elliptical arch is constructed which is 6 feet wide at the base and 9 feet tall in the middle. Find the height of the arch exactly 1 foot in from the base of the arch. looking for direction with what ellipse equation is and how

  4. Trig

    A railroad tunnel is shaped like semi-ellipse. The height of the tunnel at the center is 69 ft and the vertical clearance must be 23 ft at a point 16ft from the center. Find an equation for the ellipse.

  1. Algebra

    The arch of the bridge below is half an ellipse, a "semi-ellipse". The arch is 148m long and has a height of 48m at the center. The height of the arch is 10m at point p. What is the distance from p to the center?

  2. algebra

    You live near a bridge that goes over a river. The underside of the bridge is an arch that can be modeled with the function y=-0.000475x^2+0.851x, where x and y are in feet. How high above the river is the bridge(the top of the

  3. English

    In An Inconvenient Truth, the author uses which of the following to emphasize how humans can improve the atmosphere? a. the opening of "A Silent Alarm" b. the opening of "What exactly are greenhouse gases" c. the opening of

  4. Math Help!

    Sometimes scale drawings are shown on graph paper. Each square on this graph paper is 1/4 inch, Use the scale drawing of the living room to answer each question. What is the lenth of the fireplace in inches? The fireplace has 5

  1. Math

    The rainbow bridge of Utah is a natural arch that is approximately parabolic in shape. The arch is about 88m high. It is 84m across the base. Determine a quadratic relation, in standard form, that models the shape of the arch My

  2. Math math

    the arch of a concrete bridge is a semi ellipse having a span of 60 ft and a central height of 20 ft. if the roadway is 25 ft above the base. find at 10 ft intervals the distance from the arch to the roadway. ( im completely lost

  3. Math

    Question: A tunnel with a parabolic arch is 12 m wide. If the height of the arch 4 m from the left edge is 6 m, can a truck that is 5 m tall and 3.5 m wide pass through the tunnel? Justify your decision. I drew the graph of the

  4. math

    McDougal's Restaurant has a play area for children under and around their giant arch ( in the shape of parabola with negative orientation). They plan to set up a new activity that allows children to bungee jump from the arch. The

You can view more similar questions or ask a new question.