I need help with verifying this problem. Sorry for the poor quality of the image. It was provided with low quality.
Write the equation of the parabola to find the height of a cable above the ground at a distance of 250 m from the base of the mooring tower. The cable resists a load of equal weight at equal horizontal distances.
This is what I did:
$$y=ax^2$$ $$100=a(500)^2$$ $$100=a(250,000)$$ $$\frac{100}{250,000}=\frac{a(250,000)}{250,000}$$ $$\frac{1}{2,500}=a$$
Then, the equation is
$$y=ax^2$$ $$y=\frac{1}{2,500}x^2$$
I would appreciate knowing if it's right or wrong. If wrong, what's wrong? Thanks.
You are correct. Now you need to substitute $x = 250$ metres to find the height of the cable there, which is just:
$$y = \frac{1}{2500}(250)^2 = 25$$
This answer makes sense as it is in between $0$ and $100$, which are the heights of the parabola at $x = 0$ and $x = 500$ respectively.