Problem 5: Evaluate $\displaystyle \int \dfrac{(6z - 1) \, dz}{\sqrt{(2z + 1)^3}}$ by Algebraic Substitution
Problem
Evaluate $\displaystyle \int \dfrac{(6z - 1) \, dz}{\sqrt{(2z + 1)^3}}$
Problem 4: Evaluate $\displaystyle \int \dfrac{y \, dy}{\sqrt[4]{1 + 2y}}$ by Algebraic Substitution
Problem
Evaluate $\displaystyle \int \dfrac{y \, dy}{\sqrt[4]{1 + 2y}}$
Problem 3: Evaluate $\displaystyle \int \dfrac{x^3 \, dx}{(x^2 + 1)^3}$ by Algebraic Substitution
Problem
Evaluate $\displaystyle \int \dfrac{x^3 \, dx}{(x^2 + 1)^3}$
Problem 2: Evaluate $\displaystyle \int y^3\sqrt{2y^2 + 1} \,\, dy$ by Algebraic Substitution
Problem
Evaluate $\displaystyle \int y^3\sqrt{2y^2 + 1} \,\, dy$
Problem
If the first derivative of the equation of a curve is a constant, the curve is:
| A. circle | C. hyperbola |
| B. straight line | D. parabola |
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Problem
A triangular shaped channel is to be designed to carry 700 L/s on a slope of 0.0001. Determine what vertex angle and depth of water over the vertex will be necessary to give a section with minimum perimeter, assuming the channel is made of timber, n = 0.012. Use Manning’s formula.
| A. θ = 45°, h = 1.425 m | C. θ = 45°, h = 2.125 m |
| B. θ = 90°, h = 2.215 m | D. θ = 90°, h = 1.215 m |
Problem
A vertical circular gate in a tunnel 8 m in diameter has oil (sp. gr. 0.80) on one side and air on the other side as shown in Figure HD-73. If oil is 12 m above the invert and the air pressure is 40 kPa, where will a single support be located to hold the gate in position (above the invert of the gate)?
| A. 1.36 m | C. 3.24 m |
| B. 1.84 m | D. 2.62 m |
Problem
A vertical rectangular plate is submerged half in oil (s = 0.8) and half in water such that its top edge is flushed with the oil surface. What is the ratio of the force exerted by water on the lower half to that by oil acting on the upper half?
| A. 1.53 | C. 4.33 |
| B. 2.55 | D. 3.25 |
Problem
Assuming specific weight of air to be constant at 12 N/m3, what is the approximate height of Mt. Banahaw if a mercury barometer at the base of the mountain reads 654 mm and at the same time another mercury barometer at the top of the mountain reads 480 mm.
| A. 1642.3 m | C. 3051.4 m |
| B. 1934.5 m | D. 1735.2 m |
Problem
What is the equivalent pressure head in cm of water to a pressure of 150 kPa?
| A. 1340 | C. 1630 |
| B. 1140 | D. 1530 |
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