Problem
A germ population has a growth curve $Ae^{0.4t}$. At what value of $t$ does its original value doubled?
| A. t = 7.13 | C. t = 1.73 |
| B. t = 1.37 | D. t = 3.71 |
Problem
The sum and product of three distinct positive integers are 15 and 45, respectively. What is the smallest integer?
| A. 1 | C. 5 |
| B. 9 | D. 3 |
Problem
A contractor can buy a dump trucks for P800,000 each (surplus) or rent them for P1,189 per truck per day. The truck has salvage value of P100,000 at the end of its useful life of 5 years. Annual cost of maintenance is P20,000. If money is worth 14% per annum, determine the number of days per year that a truck must be used to warrant the purchase of the truck.
| A. 200 | C. 198 |
| B. 199 | D. 197 |
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Problem
Mar wants to make a box with no lid from a rectangular sheet of cardboard that is 18 inches by 24 inches. The box is to be made by cutting a square of side x from each corner of the sheet and folding up the sides. Find the value of x that maximizes the volume of the box.
| A. 4.3 inches | C. 10.6 inches |
| B. 5.2 inches | D. 3.4 inches |
Situation
An investment of P250,000 is made at the end of each year with interest of 2.5% compounded annually.
- Determine the equal-payment-series compound-amount factor after 10 years.
A. 11.203 C. 9.632 B. 10.578 D. 8.736 - Determine the total amount of the investment after 10 years.
A. P2,800,000.00 C. P2,400,000.00 B. P2,600,000.00 D. P2,200,000.00 - How long (in years) will it take for the investment to amount to P10,000,000.00?
A. 25 C. 15 B. 18 D. 28
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Problem
A train is moving at the rate of 8 mi/h along a piece of circular track of radius 2500 ft. Through what angle does it turn in 1 min?
| A. 15.18° | C. 13.18° |
| B. 13.16° | D. 16.13° |
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Problem
Find the Cartesian equation of the curve represented by $x = 4t + 3$ and $y = 16t^2 - 9$, -∞ < t < +∞.
| A. $y = x^2 + 6x$ | C. $y = x^2 + 4x$ |
| B. $y = x^2 - 6x$ | D. $y = x^2 - 4x$ |
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Problem
Find the equation of a sphere of radius 3 and tangent to all three coordinate planes if the center is on the first octant.
| A. $x^2 + y^2 + z^2 - 9 = 0$ |
| B. $x^2 + y^2 + z^2 - 6x - 6y - 6z + 18 = 0$ |
| C. $x^2 + y^2 + z^2 - 4x - 4y - 4z + 12 = 0$ |
| D. $x^2 + y^2 + z^2 - 8x - 8y - 8z + 14 = 0$ |
Situation
Given:
Effective Depth, d = 380 mm
Compressive Strength, fc' = 30 MPa
Steel Strength, fy = 415 MPa
- The beam is simply supported on a span of 5 m, and carries the following loads:
- Superimposed Dead Load = 16 kN/m
Live Load = 14 kN/mWhat is the maximum moment, Mu (kN·m), at ultimate condition? $U = 1.4D + 1.7L$
A. 144 C. 104 B. 158 D. 195 - Superimposed Dead Load = 16 kN/m
- Find the number of 16 mm diameter bars required if the design moment at ultimate loads is 200 kN·m.
A. 2 C. 6 B. 4 D. 8 - If the beam carries an ultimate concentrated load of 50 kN at midspan, what is the number of 16 mm diameter bars required?
A. 2 C. 4 B. 3 D. 5
Situation
The total length of the beam shown below is 10 m and the uniform load $w_o$ is equal to 15 kN/m.
1. What is the moment at midspan if x = 2 m?
| A. 37.5 kN·m | C. -187.5 kN·m |
| B. -37.5 kN·m | D. 187.5 kN·m |
2. Find the length of overhang x, so that the moment at midspan is zero.
| A. 2.5 m | C. 2.4 m |
| B. 2.6 m | D. 2.7 m |
3. Find the span L so that the maximum moment in the beam is the least possible value.
| A. 5.90 m | C. 5.92 m |
| B. 5.88 m | D. 5.86 m |
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