Answer:
The length of the bridge is 126.492 feet.
Step-by-step explanation:
Let , where is the position from the middle of the bridge, measured in feet, and is the height of the bridge at a location of x feet, measured in feet. In this case, the length of the bridge is represented by the distance between the x-intercepts of the parabola, which we now find by factorization:
(Eq. 1)
Given that the parabola is symmetrical with respect to y-axis, then the length is two times the magnitude of the value found above, that is:
The length of the bridge is 126.492 feet.
1. Arrange all the terms containing y on the left side and all other terms on the right hand side.
-y = -x^2 + 6x - 8
2. Complete the square on the right side of the equation.
(x-3)^2 - 1
3. Reorder the right side of the equation to match the vertex form of a parabola.
4. Use the vertex form, y = a(x - y)^2 + k, to determine the values of a, h, and k.
a = 1, h = 3, k = -1
5. Find the vertex (h, k).
(3, -1)
Answer:
Step-by-step explanation:
Let the distance from the tie in point to the point at the level of Tutu's neck be x.
Then the length of the rope is the hypotenuse of the right triangle formed by this line and height of the tree at which rope is tied in.
<u>We can find x as:</u>
- cos 68 deg = x/13
- x = 13 cos 68 deg
- x = 4.9 feet (rounded)
<u>Required distance is:</u>