Fundamental Frequency of Fourier Equation in Cosine Form
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?
| 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 cm2 | C. 39.84 cm2 |
| B. 52.05 cm2 | D. 48.62 cm2 |
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Slope of a Curve of Given Parametric Equations
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.
| A. -3, -3, -12 | C. 3, 3, 12 |
| B. 3, -3, 12 | D. -3, 3, 12 |
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A solid spherical ball remolded into a hollow spherical ball
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.
| 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 |
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Distance From a Point to a Plane in 3D-Space
Problem
Find the distance from the point A(1, 5, -3) to the plane 4x + y + 8z + 33 = 0.
| A. 1/2 | C. 2/3 |
| B. 2 | D. 1.5 |
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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 |
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Influence Lines for Trusses
Example
For the Pratt truss shown below, draw the influence diagram for members JK, DK, and DE.
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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.
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