Civil and Environmental Engineering Answers

1.Find the centroid of the region bounded by the curve 𝑦 = 𝑥3 and 𝑦 = 4𝑥 in the first quadrant. 

2. Find the centroid of the solid of revolution generated by revolving the region bounded by 𝑦 = 4𝑥 − 𝑥2 and the x-axis about the y-axis.

A conical vessel full of water is 16 feet across the top and 12 feet deep. Find the work required to pump all the water to a point 2 feet above the top of the vessel.

A spring has a natural length of 0.2 meters. If a 25-N force is required to keep it stretched to a length of 0.3 meters. How much work is done in stretching it from 0.2 m to 0.25 m?

A conical vessel 12 cm deep and with a radius of 6 cm at the top, is being filled with water. If the rate at which the water rises is 2 cm/sec, how fast is the volume increasing when the water is 4 cm deep?

Evaluate the integral cos⁷3x dx with the limits from 0 to π/6.

what is the area bounded by the curves y=8-x^2.

Find the area bounded by the x-axis, the line x=4, and the parabola y²=4x.

A water tank has an orifice of 8.0 cm2 in it's vertical side, 3. M below the level surface of the water. What is the rate of discharge assuming there is no energy wasted, in m/s?

A water tank has an orifice 8 cm² in its vertical side 3 m below the level surface of water. What is the rate of discharge assuming there is no energy wasted, in m/s?

explain various obstacles in chaining and ranging?