SOLUTION: a tunnel has a shape od semi ellipse that 15ft hight at the center,and 36ft across at the base. a most how high should padsing truck be, if it is 12ft wide, for it to be able to fi

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


   

Question 1087820: a tunnel has a shape od semi ellipse that 15ft hight at the center,and 36ft across at the base. a most how high should padsing truck be, if it is 12ft wide, for it to be able to fit through the tunnel? Round off your answer to the decimal places.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
NOTE: I am going to round the answer to 2 decimal places, because the rounding required was not clearly stated.

Here is a cross-section of that tunnel
(with conveniently placed x- and y-axes):
. The ellipse equation is x%5E2%2F18%5E2%2By%5E2%2F15%5E2=1
Here is the tallest 12-foot wide truck places exactly in the middle of that tunnel:
.
For that ruck to fit inside the tunnel h must be
at most the ellipse value for y when x=6 .
6%5E2%2F18%5E2%2By%5E2%2F15%5E2=1
%286%2F18%29%5E2%2By%5E2%2F15%5E2=1
%281%2F3%29%5E2%2By%5E2%2F15%5E2=1
1%2F9%2By%5E2%2F15%5E2=1
y%5E2%2F15%5E2=1-1%2F9
y%5E2%2F15%5E2=8%2F9
y%5E2=15%5E2%2A8%2F3%5E2
y%5E2=3%5E2%2A5%5E2%2A2%5E2%2A2%2F3%5E2
y%5E2=5%5E2%2A2%5E2%2A2
y%5E2=%285%2A2%29%5E2%2A2
y%5E2=10%5E2%2A2
y=10sqrt%282%29=about+14.14 .
So, if a truck is 12ft wide, for it to be able to fit through the tunnel,
the top of the truck must be at most highlight%2814.14ft%29 high.