April 2017

Problem
Compute the value of b if A and B are orthogonal.
$${\bf A} = 2{\bf i} + b{\bf j} + {\bf k}$$

$${\bf B} = 4{\bf i} - 2{\bf j} - 2{\bf k}$$

A.   6 C.   4
B.   5 D.   3

 

Problem
The sum of the first n terms of a series is 3^(2n - 1) + b. What is the quotient of the 9th and the 7th term?

A.   81 C.   83
B.   82 D.   84

 

Problems
A compound curve has the following characteristics:

I1 = 24° D1 = 6°
I2 = 36° D2 = 4°
Stationing of P.C. = km 10 + 420

Compute the stationing of P.C.C.

A.   km 10 + 560 C.   km 10 + 520
B.   km 10 + 540 D.   km 10 + 500

Fluid mechanics

Submitted by marzx3198 on April 3, 2017 - 4:15pm

A hollow sphere 6 in inside diameter is rotated on a cable at 100 rpm. If the cable is 6 ft long and makes an angle of 30 degrees with the horizontal, what is the pressure in the center of the sphere if it is full of water? what is the equivalent specific weight at that point?

Problem
Given the position function x(t) = t4 - 8t2, find the distance that the particle travels at t = 0 to t = 4.

A.   160 C.   140
B.   150 D.   130

 

Understanding Motion Curves by Example: Particle with Variable Acceleration

Problem
A tensile load of 8000 kg elongates a 1-m long square rod by 1 mm. Steel modulus of elasticity is 2 × 106 kg/cm2. What is the dimension of a side of the rod?

A.   5 cm C.   2 cm
B.   1 cm D.   4 cm

 

Problem
A grade of -5% is followed by a grade of 1%, the grades intersecting at the vertex (Sta. 10 + 060). The change of grade is restricted to 0.4% in 20 m. Compute the length of the vertical parabolic sag curve in meters.

A.   360 m C.   300 m
B.   320 m D.   340 m

 

Stuck finding out the manual solution for finding x in this logarithmic equation

Submitted by Je Gonzaga on April 9, 2017 - 5:59pm

Good day,

I got stuck finding the manual solution for this problem without relying to the solve function of Casio calculator

The original equation was

[(1+x)40] -1 = (181205.95/3000)x

Then I tried using properties of logarithm and I simplified it to this equation:

[ln(181205.95/3000)]/40 = ln(1+x) - (1/40)[ln(x+3000/181205.95)]

0.102526 = ln(x+1) - 0.025ln(x+0.0165557)

Answer: x = 0.02

Jhun Vert's picture

What number x is greater than x^n?

Submitted by Jhun Vert on April 13, 2017 - 11:36am

What number x > xn?
Where n = positive integer greater than 1.

Problem 911 | Combined Axial and Bending

Problem 911
A concrete dam has the profile shown in Figure P-911. If the density of concrete is 2400 kg/m3 and that of water is 1000 kg/m3, determine the maximum compressive stress at section m-n if the depth of the water behind the dam is h = 15 m.
 

911-gravity-dam.gif

 

Problem 912 | Combined Axial and Bending

Problem 912
Compute the stresses at A and B on the link loaded as shown in Figure P-912 if P = 9000 lb and F = 3000 lb.
 

912-rectangular-link.gif

 

Inner Circle Reading of the Double Vernier of a Transit

Problem
Figure P-SF01 is a double vernier of a transit and the dashed line indicate the two sets of coincident lines. What is the reading of the inner circle?
 

01-008-vernier-circle-reading.gif

 

A.   175° 42' C.   184° 18'
B.   193° 8' D.   181° 3'

 

Problem 914 | Combined Axial and Bending

Problem 914
The structure shown in Figure P-914 is hinged to fixed is hinged to fixed supports at A and C. Assume that the pin connections at A, B, and C are frictionless. The bars are each 4 in. by 4 in. in section. Compute the maximum compressive stress developed in bar AD.
 

914-two-bar-structure.gif

 

Problem 915 | Combined Axial and Bending

Problem 915
For the structure in Problem 914, compute the maximum tensile stress developed in bar CB.
 

914-two-bar-structure.gif

 

esmilitar's picture

Angle of Elevation

Submitted by esmilitar on April 17, 2017 - 11:00pm

Please help to solve this problem:
The angle of elevation of a point C from a point B is 29042'; the angle of elevation of C from another point A 31.2 m directly below B is 59023'. How high is C from the horizontal line through A?

Problem 916 | Combined Axial and Bending

Problem 916
For the structure shown in Figure P-916 is hinged to fixed supports at A and E. Compute the maximum compressive stress developed in bar BDE if its cross section is 200 mm square. Neglect the weights of the members.
 

916-given-structural-assembly.gif

 

Jhun Vert's picture

Solve for $x$: $\dfrac{1}{x} + \dfrac{1}{x + 2} = 1$

Submitted by Jhun Vert on April 19, 2017 - 7:01am

Determine the value of x from the following equation:
$\dfrac{1}{x} + \dfrac{1}{x + 2} = 1$

Jhun Vert's picture

In tossing a coin, what is the probability of getting three consecutive heads or tails

Submitted by Jhun Vert on April 19, 2017 - 7:26am

If Benjie throws a coin until a series of three consecutive heads or three consecutive tails appears, what is the probability that the game will end on the fourth throw?

Jhun Vert's picture

Calculate $0.5 + 0.5^2 + 0.5^3 + \ldots + 0.5^{20}$

Submitted by Jhun Vert on April 19, 2017 - 7:37am

Using your calculator, find the value of
$0.5 + 0.5^2 + 0.5^3 + \, ... \, + 0.5^{20}$

Problem 917 | Combined Axial and Bending

Problem 917
For the structure in Problem 916, calculate the maximum compressive stress in bar ABC if its cross section is 200 mm square.
 

916-fbd-member-abc.gif

 

Jhun Vert's picture

Minimum amount of money that must be spent before three gumballs of the same color are dispense

Submitted by Jhun Vert on April 19, 2017 - 9:42pm

A vending machine dispenses gumballs in a regular repeating cycle of ten different colors. If a quarter buys 3 gumballs, what is the minimum amount of money that must be spent before three gumballs of the same color are dispense?

Jhun Vert's picture

Round off 314.587321 into four significant figures

Submitted by Jhun Vert on April 21, 2017 - 8:54am

Round off 314.587321 into four significant figures

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