To determine the area of a triangular lot ABC, a surveyor set-up a transit at point P inside the lot and recorded the following bearing and distances of each corners of the lot from P.
April 2021
A gang of pipe layers working under the supervision of foreman A can finish a pipe-laying job in 20 days. The same gang of pipe layers working without the supervision of a foreman can finish the same pipe-laying job in 25 days. The project engineer, desiring to finish the job in 20 days, employed the gang of pipe layers under the supervision of foreman A. However, at the end of the fifth working day, foreman A quit the job.
Find the radius of curvature of the curve $y = x^3 - 2x^2 + 5x - 3$ at $x = 5$.
A 3-degree simple curve has an external distance of 23 m. What is the length of the long chord?
The area under the curve $y = x^2$ between the values $x = 1$ and $x = 7$ is closest to:
Company A has a fixed expense of P1.5M monthly and each unit is produced at P20. Company B has a fixed expense of P500,000 per month and can produce the same unit at P60. At what number of units of monthly production will company A have the same overall cost as company B?
A vertical summit curve has tangent grades of +2.6% and -1.5%. Using h1 = 1.37 m and h2 = 0.1 m, calculate the minimum length of curve if the required sight distance is 137 m.
A circle of radius 15 cm is revolved about a line tangent to it. What is the surface area of the resulting solid?
A car travels with an initial velocity of 10 m/s or 36 km/hr. If it is decelerating at a rate of 3 m/sec-sec, how far, in meters, does it travel before stopping?
Find the area enclosed by the curve $r^2 = 64 \cos 2\theta$.