1. **State the problem:** We have an arched bridge 30 m wide and 40 m tall at the highest point. We want to check if a sailboat with a 25 m tall sail can fit under the bridge 6 m away from the center. 2. **Model the bridge arch:** Assume the arch is a parabola symmetric about the center. The width is 30 m, so the arch spans from $x=-15$ to $x=15$ with the highest point at $x=0$, $y=40$. 3. **Find the parabola equation:** Let the parabola be $y = a x^2 + b x + c$. Since it's symmetric, $b=0$. The vertex is at $(0,40)$, so $c=40$. 4. **Use boundary conditions:** At $x=\pm 15$, the height is 0 (ground level), so: $$0 = a (15)^2 + 40 \implies 0 = 225 a + 40$$ 5. **Solve for $a$:** $$225 a = -40 \implies a = -\frac{40}{225} = -\frac{8}{45}$$ 6. **Parabola equation:** $$y = -\frac{8}{45} x^2 + 40$$ 7. **Find height at $x=6$ m from center:** $$y = -\frac{8}{45} (6)^2 + 40 = -\frac{8}{45} \times 36 + 40 = -\frac{288}{45} + 40 = -\frac{64}{10} + 40 = -6.4 + 40 = 33.6$$ 8. **Compare sail height:** The sail is 25 m tall, and the bridge height at 6 m from center is 33.6 m. 9. **Conclusion:** Since $33.6 > 25$, the sailboat can fit under the bridge at 6 m from the center. **Final answer:** Yes, the sailboat with a 25 m tall sail can fit under the bridge 6 m away from the center.