# Video Discussion: MSTE-00 Preboard 1

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## Preboard 1 - Part 1

Video Solution Problem
Find the area enclosed by the curve $r^2 = 64 \cos 2\theta$.
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?
A circle of radius 15 cm is revolved about a line tangent to it. What is the surface area of the resulting solid?
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.
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?

## Preboard 1 - Part 2

Problem Video Solution
The area under the curve y = x2 between the values x = 1 and x = 7 is closest to:
A 3-degree simple curve has an external distance of 23 m. What is the length of the long chord?
Find the radius of curvature of the curve $y = x^3 - 2x^2 + 5x - 3$ at $x = 5$.
A gang of pipe layers working under the supervision of foreman A can finish a pipe-laying job in 20 days...

In how many days will the original gang of pipe layers, under the supervision of foreman B, finish the original pipe-laying job?

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.
Corner Bearing from P Distance from P
A N 47° 32' W 36.25 m
B N 68° 52' E 58.32 m
C Due South 65.25 m

Determine the area of the lot in square meter.

## Preboard 1 - Part 3

Video Solution Problem
Find the volume of the tetrahedron bounded by the coordinate planes and the plane $8x + 12y + 4z - 48 = 0$.
At 6:00 A.M., a fighter plane took off at 410 kph from an aircraft carrier, maintaining the direction of N 50° E. The carrier kept on moving due south at 28 kph. At 7:30 A.M., the communication between the plane and the carrier was lost. What was the communication range in km?
Line AB has point A(4, 5) and point B(-3, -2). Find point C along line AB if distance BC is three times the distance AC.
A dog is tied with a chord 3 m long to the edge of a circular tank 8 m in diameter. The point where the cord is attached to the tank is at the same elevation as the dog’s collar. Determine the total area about which the dog can move, in square meter.
A company invests P10,000 today to be repaid in five years in one lump sum at 12% compounded annually. If the rate of inflation is 3% compounded annually, how much profit in present day pesos is realized over five years?

## Preboard 1 - Part 4

Problem Video Solution
The map shows 5 cm representing 450 km. What actual distance is represented by a map distance of 2.8 cm?
How far apart are the foci of the curve $9x^2 + 25y^2 - 18x + 100y - 116 = 0$.
There are five harmonic means between 4/3 and 4/11. What is the fourth term?
Find $y'$ if $x = 2 \arccos (2t)$ and $y = 4 \arcsin (2t)$.
A contractor bought a concrete mixer at P120,000.00 if paid in cash. The mixer may also be purchased by installment to be paid within 5 years. If money is worth 8%, the amount of each annual payment, if all payments are made at the beginning of each year, is:

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