Okay, don’t freak out. It’s more simple than it seems.
To find the area of this rectangle you use length x length
Let’s look for the length first
Use the bottom left and right points
(-2.25,-1) and (2.25,-1)
The length is a horizontal line so we use the x-coordinates. The distance from -2.25 to 2.25 is 4.5
Now let’s find the height. Let’s use the top left and bottom left coordinates.
(-2.25,4) and (-2.25,-1)
The height is a vertical line. The y-coordinates. Their difference is 5.
So 4.5 x 5 = 22.5

3 0

3 years ago

A tunnel is built in form of a parabola. The width at the base of tunnel is 7 m. On

uysha [10]

Given:

The width at the base of parabolic tunnel is 7 m.

The ceiling 3 m from each end of the base there are light fixtures.

The height to light fixtures is 4 m.

To find:

Whether it is possible a trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel.

Solution:

The width at the base of tunnel is 7 m.

Let the graph of the parabola intersect the x-axis at x=0 and x=7. It means x and (x-7) are the factors of the height function.

The function of height is:

$h(x)=ax(x-7)$ ...(i)

Where, a is a constant.

The ceiling 3 m from each end of the base there are light fixtures and the height to light fixtures is 4 m. It means the graph of height function passes through the point (3,4).

Putting x=3 and h(x)=4 in (i), we get

$4=a(3)((3)-7)$

$4=a(3)(-4)$

$\dfrac{4}{(3)(-4)}=a$

$-\dfrac{1}{3}=a$

Putting $a=-\dfrac{1}{3}$ , we get

$h(x)=-\dfrac{1}{3}x(x-7)$ ...(ii)

The center of the parabola is the midpoint of 0 and 7, i.e., 3.

The width of the truck is 4 m. If is passes through the center then the truck must m 2 m on the left side of the center and 2 m on the right side of the center.

2 m on the left side of the center is x=1.5.

A trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel is possible if h(1.5) is greater than 2.8.

Putting x=1.5 in (ii), we get

$h(1.5)=-\dfrac{1}{3}(1.5)(1.5-7)$