2016 May

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

 

Slope of a Curve with 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

 

Distance From a Point to a Plane

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

 

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

 

Amount of Sales Needed to Receive a Specified 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

 

Absolute Pressure at 200 mm Below the Surface of Liquid Mercury

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

A.   126 kPa C.   128 kPa
B.   130 kPa D.   132 kPa

 

Truss With Tension-Only Diagonals

Situation
Diagonals BG, CF, CH, and DG of the truss shown can resist tension only.
 

2016-may-truss-tension-diagonals.gif

 

If W = 3 kN and P = 0, find the following:
1.   the force in member CF.

A.   4.76 kN C.   4.67 kN
B.   4.32 kN D.   4.23 kN

2.   the force in member BF.

A.   3.2 kN C.   3.4 kN
B.   3.3 kN D.   3.5 kN

3.   the force in member DH.

A.   2.8 kN A.   2.5 kN
B.   2.8 kN D.   2.7 kN

 

Fundamental Frequency of Fourier Equation in Cosine Form

Problem
Given the Fourier equation:

f(t) = 5 cos (20πt) + 2 cos (40πt) + cos (80πt)

What is the fundamental frequency?

A.   10 C.   40
B.   20 D.   30

 

Truss With Flexible Cable Diagonals

Situation
Flexible cables BE and CD are used to brace the truss shown below.
 

2016-may-counter-doagonals.gif

 

1.   Determine the load W to cause a compression force of 8.9 kN to member BD.

A.   7.80 kN C.   26.70 kN
B.   35.64 kN D.   13.35 kN

2.   Which cable is in tension and what is the tensile reaction?

A.   BE = 12.58 kN C.   BE = 6.29 kN
B.   CD = 6.29 kN D.   CD = 12.58 kN

3.   If W = 20 kN, what will be the tensile reaction of member CE?

A.   6.67 kN C.   0
B.   13.33 kN D.   10 kN

 

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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