contestada

. 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

The standard equation of the ellipse centered at origin behind the shape of arch is presented below:

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

#SPJ1

Otras preguntas