Answer:
the truck should not be higher than 12.934 ft
Step-by-step explanation:
if the bridge underpass is half of an ellipse , then the arch function will be B(x,y) such that
x²/a² + y²/b² = 1 , for x≥0 and y≥0 and y=0 for x≤0
where x= width , y= height
for
a= length of the bridge underpass = 40 ft
b= height of the bridge underpass = 13 ft
x²/(40 ft)² + y²/(13 ft)² = 1
that represents all the points of the arch
the maximum height is reached when the truck touches the arch, then
for a point x= 4 ft wide , since 8 foot wide represents 4 foot to the left (x=-4) and 4 foot to the right (x=4)
then
(4 ft)²/(40 ft)² + y²/(13 ft)² = 1
1/100 - y²/(13 ft)² = 1
y/13 ft = √(1-1/100) = 3/10*√11
y= 3/10*√11 * 13 ft = 12.934 ft
y= 12.934 ft
then the truck should not be higher than 12.934 ft
