SOLUTION: The opening of a cave 20 feet wide is in the shape of a semi ellipse. If the height of the opening is 15 feet at the center, how high is the opening 5 feet from the center? Pls

Question 970979: The opening of a cave 20 feet wide is in the shape of a semi ellipse. If the height of the opening is 15 feet at the center, how high is the opening 5 feet from the center?
Pls Help me.
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!
The opening of a cave 20 feet wide is in the shape of a semi ellipse.
If the height of the opening is 15 feet at the center, how high is the opening 5 feet from the center?

Given:
A semi-ellipse opening 20' wide and 15' high at the centre.
Find height of opening at 5' from centre.

Solution:
We have an ellipse centred at origin, with
a = semi-x-axis = = 10'
b = semi-y-xaxis = 15'

The standard equation of an ellipse is

Substituting a and b,

At 5' from centre, x=5:

Solve for y:

' approximately

Answer:
The height of the cave opening at 5' from the centre is approximately 12.99'
RELATED QUESTIONS
The opening of the a cave 20 feet wide is in the shape of semi ellipse. If the height of... (answered by robertb)

1.) A tent opening is triangular in shape. The area of the opening is 12 square feet and... (answered by chitra)

A tunnel through a mountain for a four lane highway is to have a semi- elliptical... (answered by Edwin McCravy)

A bridge is to be built across a waterway which is 50 feet wide and is frequented by... (answered by ankor@dixie-net.com)

A tunnel throught mountain is for a four-lane highway is to have semi-ellitical opening.... (answered by greenestamps)

A tunnel through a mountain takes the shape of a semi-ellipse. The tunnel is 100 feet... (answered by lwsshak3)

A large fireplace in a hotel has a rectangular opening with a height of 5 feet and a... (answered by nerdybill)

A family is finishing a room in their basement. The room is 20 feet long and 14 feet... (answered by math_tutor2020)

To accommodate the road beneath, the arch is 100 feet wide at its base, 20 feet high in... (answered by scott8148)