SOLUTION: A 7 - foot tall, 9-foot wide truck is approaching a tunnel on a one-way road. The arch at the tunnel's entrance forms the upper half of an ellipse with a height of 12 feet at the c

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A 7 - foot tall, 9-foot wide truck is approaching a tunnel on a one-way road. The arch at the tunnel's entrance forms the upper half of an ellipse with a height of 12 feet at the c      Log On


   

Question 1184384: A 7 - foot tall, 9-foot wide truck is approaching a tunnel on a one-way road. The arch at the tunnel's entrance forms the upper half of an ellipse with a height of 12 feet at the center and a base of 10 feet wide. Will the truck be able to fit through the arch?​
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!


The green rectangle 9'x7' rectangle represents the truck.  From the picture
it looks like it won't fit.

The equation of the (whole) ellipse is

x%5E2%2F5%5E2%2By%5E2%2F12%5E2=1

The red curve is the top half of the ellipse.

Solving for x and taking the positive square root, we get

x+=++%285sqrt%28144+-+y%5E2%29%29%2F12

We see if substituting 7 for y allows the truck's width.

x+=++%285sqrt%28144+-+7%5E2%29%29%2F12
x+=+4.06116431

So the truck would have to be no wider than twice that for a
height of 7 feet. Twice that is 8.122328621.
 
The truck is 9 foot wide, so it's too wide to go in the
tunnel.

[Note: you could have solved for y instead of x and seen that
it was too tall for a width of 9 feet.]

Edwin