I have been stuck on this problem for over a week and I don't even know how to start the problem.
Parabola equation y= 4(100 - x^2/2500)
x and y are measured in feet
A. Find the length of the road across the bridge
B. find the height of the parabolic arch at the center of the span
C. Find the lengths of the vertical girders at intervals of 100 feet from the center of the bridge
( graph of upside down parabola)
problem is on photobucket
username: piggerockalbum
album: math problems
I can't log into your photobucket, (needs password)
so I will "guess" at a diagram
expanding and simplifying your equation I got
y = (-1/625)x^ + 400
b) at the centre, x = 0
so y = 400
the bridge is 400 ft high
width of bridge, let y = 0 (on the x-axis)
0 = (-1/625)x^2 + 400
x^2 = (625)(400)
x = ±25(20) = ±500
So the bridge is 1000 ft wide
for vertical girders
let x = 100, 200, 300 , 400
x = 100
y = (-1/625)(100)^2 + 400 = 384
x = 200
y = (-1/625)(200)^2 + 400 = 336
etc.
I apologize, but as an AI text-based bot, I am unable to access or view external websites or images. However, I can help guide you through the problem by explaining the steps to solve it.
To find the length of the road across the bridge (part A), you need to determine the horizontal distance between the two points where the parabola intersects the x-axis. Since the equation given is in terms of x and y, we can set y to 0 and solve for x.
1. Set y = 0 in the equation:
0 = 4(100 - x^2/2500)
2. Simplify the equation:
0 = 400 - x^2/62.5
3. Multiply both sides by 62.5 to eliminate the fraction:
0 = 400 * 62.5 - x^2
4. Rearrange the equation:
x^2 = 400 * 62.5
5. Take the square root of both sides:
x = sqrt(400 * 62.5)
The value of x will be the horizontal distance of the road across the bridge.
To find the height of the parabolic arch at the center of the span (part B), substitute x = 0 into the equation and solve for y.
1. Set x = 0 in the equation:
y = 4(100 - 0^2/2500)
2. Simplify the equation:
y = 4(100 - 0)
3. Calculate the value of y:
y = 400
The value of y will be the height of the parabolic arch at the center of the span.
To find the lengths of the vertical girders at intervals of 100 feet from the center of the bridge (part C), you need to find the corresponding y-values for the given x-coordinates.
1. Choose x-values at intervals of 100 feet from the center of the bridge. For example, you can take x = -100, 0, 100.
2. Substitute each x-value into the equation and solve for y:
- When x = -100:
y = 4(100 - (-100)^2/2500)
- When x = 0:
y = 4(100 - 0^2/2500)
- When x = 100:
y = 4(100 - 100^2/2500)
By substituting each x-value, you will obtain the corresponding y-values, which will give you the lengths of the vertical girders at those intervals of 100 feet from the center of the bridge.
I hope this explanation helps you with your problem-solving! Let me know if you have any further questions.