SOLUTION: A tunnel has the shape of a semi-ellipse that is 15 ft. high at the center and 36 ft. across at the base. At most how high should a passing truck be, if it is 12 ft. wide for it to

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A tunnel has the shape of a semi-ellipse that is 15 ft. high at the center and 36 ft. across at the base. At most how high should a passing truck be, if it is 12 ft. wide for it to      Log On


   

Question 1043507: A tunnel has the shape of a semi-ellipse that is 15 ft. high at the center and 36 ft. across at the base. At most how high should a passing truck be, if it is 12 ft. wide for it to be able to fit to the tunnel? Round off your answer to two decimal places.
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Center of the rode is like the origin on a cartesian coordinate plane.
x%5E2%2F18%5E2%2By%5E2%2F15%5E2=1
Solve for y and use the upper branch.

Decide how you want the truck to be positioned; middle over the center line of the rode, or none of the truck crossing the center line. How tall is the truck? Width is only part of the problem to solve.

Imagine the truck will drive in the middle of the rode to try to pass under the tunnel. This leaves 6 feet on either side of the center of the rode. Now, what must y be? Is the truck too tall for this?