April 2021

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:

There are five harmonic means between 4/3 and 4/11. What is the fourth term?

How far apart are the foci of the curve $9x^2 + 25y^2 - 18x + 100y - 116 = 0$.

The map shows 5 cm representing 450 km. What actual distance is represented by a map distance of 2.8 cm?

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?

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...

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.

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?

Find the volume of the tetrahedron bounded by the coordinate planes and the plane $8x + 12y + 4z - 48 = 0$.