|
Question 624119: a single-lane highway must pass under a serious of bridges. it is proposed that the bridges be shaped as semi-ellipses with the height equal to the width. the builder feels he must allow room for a 6foot wide, 12foot high truck to pass under it. what is the lowest bridge that can be built to serve this purpose?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! a single-lane highway must pass under a serious of bridges. it is proposed that the bridges be shaped as semi-ellipses with the height equal to the width. the builder feels he must allow room for a 6foot wide, 12foot high truck to pass under it. what is the lowest bridge that can be built to serve this purpose?
**
use equation of ellipse with vertical major axis and center at (0,0): x^2/b^2+y^2/a^2=1
a=height of bridge
b=1/2 of width=a/2
point of ellipse: (6,12) (allow for truck to pass)
..
Equation: x^2/b^2+y^2/a^2=1
6^2/b2+12^2/a^2=1
36/(a/2)^2+144/a^2=1
36/(a^2/4)+144/a^2=1
4*36/a^2+144/a^2=1
144/a^2+144/a^2=1
288/a^2=1
a^2=288
a=√288
a=16.97
the lowest bridge that can be built=16.97 ft in height
|
|
|
| |
