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