. A bridge over a river is built in the shape of a parabolic arch. The bridge has a span of 100 feet. The height of the arch is 10 feet at a point 40 feet from the center. Find the height of the arch at its center.

The height of the arch at its center is 250/9 or about 27.78 feet.

Step-by-step explanation:

We can write an equation to model the parabolic arch.

Let the left-most point of the arch be the origin (0, 0).

Since the bridge has a span of 100 feet, the right-most point must be (0, 100).

We can use the factored form of a quadratic:

Where p and q are the x-intercepts.

Our x-intercepts are x = 0 and x = 100. Hence:

At a point 40 feet from the center, the height of the arch is 10 feet.

The center is x = 50. So, a point 40 feet from the center can be either x = 10 or x = 90.

So, for instance, when x = 10, y = 10. Substitute and solve for a:

So:

The same value will result if we let x = 90 and y = 10.

Hence, our equation is:

The height of the arch at its center will be when x = 50. Hence:

spinning a 1, 2, or 3. option d.

step-by-step explanation: when spinning a number graph up to 4, and aiming for any number less than 3, that automatically eliminates the number 4. now you have two numbers to spin on that are less than 3, but the number 3 is included in this question because it's no greater of an number than itself. i hope this you : )

{3 + i, 3 - i, 3, -1}

step-by-step explanation: