The opening of a tunnel that travels through a mountainside can be modeled by , where x and y are measured in feet. The x-axis represents the ground. a. Find the width of the tunnel at ground level.
b. How tall is the tunnel?

(a) 30 feet

(b) 30 feet.

Step-by-step explanation:

Given that the opening of a tunnel that travels through a mountainside can be modeled by

, where x and y are measured in feet.

(a) At the ground level,

So, the width of the tunnel at ground level is distance between the extreme point of the tunnel on the grount.

For, , the extreme points of the tunnel.

So, the extreme points of the tunnel are, and .

Hence, the width of the tunnel at the ground level

feet.

(b) The maximum height of the tunnel can be determiment by determining the maxima of the given function.

First determining the value of x for which the slope of the graph is zero.

From equation (i),

-2x=0

And  

which is always negative, so at x=0 the value of y is maximum.

Again, put x=0 in equation (i), we have

feet.

Hence, the tunnel is 30 feet tall.

are you an artist's daughter? cuz dang you a fine piece of art, girl.