# Unknown X in rectangle

1. Oct 18, 2013

### meshac A

Last edited: Oct 18, 2013
2. Oct 18, 2013

### adjacent

I haven't studied parabolas but that's a parabola with a depth of 3m and arc length of 6m.So maybe you can then find the apparent length.Then you can find x.

Last edited: Oct 18, 2013
3. Oct 18, 2013

### meshac A

i've been on it for a while now,.i'll like to see your attempt

4. Oct 18, 2013

### adjacent

I don't know anything about parabolas yet.Maybe you can use some equation relating arc length,depth and apparent lenght

5. Oct 18, 2013

### Staff: Mentor

I'm assuming that what you drew is a parabola. Is that a reasonable assumption?

If so, the equation of your parabola is y = cx2, assuming that the vertex is at (0, 0). From the drawing, the points (b, 3) and (-b, 3) are on the parabola.

The arc length shown in the drawing is the length along the curve between (-b, 3) and (b, 3). Due to symmetry, we can work with half this length, or 3 units.

Since y = cx2, then y' = 2cx, which I will use in the formula for arc length. Also, since (b, 3) is a point on the curve, then 3 = c*b2.

This equation equates the arc length integral with the known length:
$$\int_0^b \sqrt{1 + (2cx)^2}dx = 3$$

This gives you two equations in the unknowns b and c, so it should be possible to determine b and c.

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