Can someone please help with this word problem?

An arch in the shape of a semi-ellipse at its bottom extremity is to support a walkway crossing over a highway. Construct a coordinate system with the positive y-axis projecting vertically upward from the center of the highway and the x-axis crossing perpendicular to the highway at ground level, positive axis to the right. The highway itself is 80 feet wide. The ends of the arches are 100 feet apart. The clearance at the edges of the highway must be 14 feet from the highway vertically to the bottom of the arch structure. If the equation of the ellipse that will meet these specifications is written in the form

x2/(a2) + y2/(b2) = 1, y > 0, then correct to the nearest tenth of a unit, b =

A) 9.6

B) 10.4

C) 12.0

D) 13.2

E) 14.5

F) 20.0

G) 23.3

H) 25.0

I) none of these

1 Answer

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  • JOHN
    Lv 7
    8 years ago

    G) 23.3 [I had some difficulty interpreting your info. Anyway the main features of my solution are (1) a=50 and (2) the point (40,14) lies on x^2/50^2 +y^2/b^2 = 1, which enabled me to find b].

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