Problem
Determine the absolute pressure in a vessel of mercury at a point 200 mm below its surface.

Problem
Given the Fourier equation:
 

$$f(t) = 5 \cos (20\pi t) + 2 \cos (40\pi t + \cos (80\pi t)$$
 

What is the fundamental frequency?

Problem
A salesperson earns P60,000 per month plus a commission of 20% of sales. Find the minimum amount of sales needed to receive a total income of at least P150,000 per month.

Problem
Chords AB and CD intersect each other at E inside the circle. AE = 8 cm, CE = 12 cm, and DE = 20 cm. If AB is the diameter of the circle, compute the area of AEC.

Problem
A point moves in the plane according to equations x = t² + 2t and y = 2t³ - 6t. Find dy/dx when t = 0, 2, 5.

Problem
A 523.6 cm³ solid spherical steel ball was melted and remolded into a hollow steel ball so that the hollow diameter is equal to the diameter of the original steel ball. Find the thickness of the hollow steel ball.

Situation
An open cylindrical vessel 1.3 m in diameter and 2.1 m high is 2/3 full of water. If rotated about the vertical axis at a constant angular speed of 90 rpm,
1.   Determine how high is the paraboloid formed of the water surface.

2.   Determine the amount of water that will be spilled out.

3.   What should have been the least height of the vessel so that no water is spilled out?

Problem
Find the distance from the point A(1, 5, -3) to the plane 4x + y + 8z + 33 = 0.

Problem
Evaluate $\displaystyle \int_0^9 \dfrac{1}{\sqrt{1 + \sqrt{x}}}$