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 |
Mathematics, Surveying and Transportation Engineering
MSTE - Mathematics, Surveying and Transportation Engineering
Common name: Math
Algebra, Trigonometry, Statistics, Geometry, Calculus, Differential Equations, Engineering Mechanics, Engineering Economy, Surveying, Transportation Engineering
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 |
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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