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. An arch has the shape of a semi-ellipse. The arch
has a height of 12 feet and a span of 40 feet. Find
an equation for the ellipse, and use that to find the
distance from the center to a point at which the
height is 6 feet. Round to the nearest hundredth.

Respuesta :

The height of the arch at a distance of 5 feet from the center is approximately 10. 93 feet

Equation of an eclipse

It is important to note that the standard equation of an eclipse centered at origin behind the shape of arch is given as;

[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2}[/tex]

Where;

  • x - Horizontal distance, in feet
  • y - Vertical distance, in feet
  • a - Horizontal semi - axis length (half-width), in feet
  • b  - Vertical semi - axis length (height), in feet

If we know that x = 6feet , a = 20 feet and b = 12feet, then the height of the arch at this location is;

[tex]y = b . \sqrt{1 + \frac{x^2}{a^2} }[/tex]

[tex]y = 12. \sqrt{1 - \frac{6^2}{20^2} }[/tex]

[tex]y = 10. 92[/tex] feet

Thus, the height of the arch at a distance of 5 feet from the center is approximately 10. 93 feet

Learn more about eclipses here:

https://brainly.com/question/16904744

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