SOLUTION: An arch in the form of a semiellipse is 64 ft wide at the base and has a height of 30 ft. How high is the arch at a width of 20 ft from the center of the base? Round your answer

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: An arch in the form of a semiellipse is 64 ft wide at the base and has a height of 30 ft. How high is the arch at a width of 20 ft from the center of the base? Round your answer       Log On


   

Question 632284: An arch in the form of a semiellipse is 64 ft wide at the base and has a height of 30 ft.
How high is the arch at a width of 20 ft from the center of the base? Round your answer
to the nearest tenth.
10
Answer by lwsshak3(11628) About Me  (Show Source):
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An arch in the form of a semiellipse is 64 ft wide at the base and has a height of 30 ft.
How high is the arch at a width of 20 ft from the center of the base? Round your answer
to the nearest tenth.
**
Given problem is finding the equation of an ellipse with horizontal major axis and center at (0,0), then plugging in given x to find y.
Its standard form: x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2%2B1, a>b
a=32 ft (horizontal distance from center to vertex)
a^2=32^2=1024
b=30 ft (vertical distance from center to top of the arch)
b^2=900
equation: x%5E2%2F1024%2By%5E2%2F900=1
solve for y when x=20 ft from center
..
20%5E2%2F1024%2By%5E2%2F900=1
y^2/900=1-20^2/1024=1-400/1024=1-.391=0.609
y^2=.609*900=548.44
y=√548.44
y≈23.4
Height of the arch at a width of 20 ft from the center of the base≈23.4 ft