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Question 688106: An arch is in the form of a semiellipse. It's 50 metres wide at the base and has a height of 20 metres. How wide is the arch at the height of 10 metres above the base? This is my question please help on the solution, i tried it so many times but i can't gate the clue yet. Help me .
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! An arch is in the form of a semiellipse. It's 50 metres wide at the base and has a height of 20 metres. How wide is the arch at the height of 10 metres above the base?
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Use standard form of equation for an ellipse wit horizontal major axis:
(x-h)^2/a^2+(y-k)^2/b^2=1, a>b, (h,k)=(x,y) coordinates of center.
For given problem:
place center at (0,0)
a=25
a^2=625
b=20
b^2=400
Equation: x^2/625+y^2/400=1
at a height of 20 metres, the coordinates are (x,20)
plug in these coordinates and solve for x
x^2/625+y^2/400=1
x^2/625+10^2/400=1
x^2/625+100/400=1
x^2/625=1-1/4=3/4=.75
x^2=.75*625=468.75
x=√468.75
x≈21.65
2x≈43.3
At the height of 10 metres above the base, the arch is 43.3 metres wide.
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