## Fundamental Frequency of Fourier Equation in Cosine Form

**Problem**

Given the Fourier equation:

*f*(

*t*) = 5 cos (20π

*t*) + 2 cos (40π

*t*) + cos (80π

*t*)

What is the fundamental frequency?

A. 10 | C. 40 |

B. 20 | D. 30 |

## Amount of Sales Needed to Receive a Specified Monthly Income

**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.

A. P150,000 | C. P450,000 |

B. P350,000 | D. P250,000 |

## Area Bounded by Intersecting Chords in a Circle

**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*.

A. 61.04 cm^{2} |
C. 39.84 cm^{2} |

B. 52.05 cm^{2} |
D. 48.62 cm^{2} |

## Slope of a Curve of Given Parametric Equations

**Problem**

A point moves in the plane according to equations *x* = *t*^{2} + 2*t* and *y* = 2*t*^{3} - 6*t*. Find *dy*/*dx* when *t* = 0, 2, 5.

A. -3, -3, -12 | C. 3, 3, 12 |

B. 3, -3, 12 | D. -3, 3, 12 |

## A solid spherical ball remolded into a hollow spherical ball

**Problem**

A 523.6 cm^{3} 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.

A. 1.3 cm | C. 1.2 cm |

B. 1.5 cm | D. 1.6 cm |

## Partially Filled Cylindrical Tank Rotated at 90 rpm

**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.

A. 1.26 m | C. 2.46 m |

B. 1.91 m | D. 1.35 m |

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

A. 140 L | C. 341 L |

B. 152 L | D. 146 L |

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

A. 2.87 m | C. 3.15 m |

B. 2.55 m | D. 2.36 m |

## Distance From a Point to a Plane in 3D-Space

**Problem**

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

A. 1/2 | C. 2/3 |

B. 2 | D. 1.5 |

## Find the Integral of dx / sqrt(1 + sqrt(x))

**Problem**

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

A. 4.667 | C. 5.333 |

B. 3.227 | D. 6.333 |

## Influence Lines for Beams

A downward concentrated load of magnitude 1 unit moves across the simply supported beam *AB* from *A* to *B*. We wish to determine the following functions:

- reaction at
*A* - reaction at
*B* - shear at
*C*and - moment at
*C*

when the unit load is at a distance *x* from support *A*. Since the value of the above functions will vary according to the location of the unit load, the best way to represent these functions is by influence diagram.