March 2021

For a spherical triangle: A = 63° 19.6'; b = 124° 17.8'; and c = 83° 16.6', find a.

Find the area reflected by the triangle ABC on the xy-plane with A(1, 10, 10), B(6, 2, 4) and C(12, 6, 1).

P3000 quarterly for ten years accumulates to P181,205.95, find the nominal rate of interest compounded quarterly.

Find the radius of the circumscribing circle of the regular octagon having an area of 320 cm².

Two men starting at the same point walk in opposite direction for 4 meters turn left and walk another 3 meters. What is the distance between them?

What is the number that is one half of one quarter of one tenth of 400?

Find the area of the spherical lune of radius 2.5 m and a central angle of 15°.

Through a given cone of altitude h and base A, two planes are passed parallel to the base, cutting the altitude $\frac{1}{3}h$ and $\frac{2}{3}h$ units from the base. Find the ratio of the volumes of the two frustums thus formed.

A man invested P100,000 at an interest rate of 10% compounded annually. What will be the final amount of his investment, in terms of today’s peso, after 5 years, if inflation remains the same at the rate of 8% per year?

Determine the volume of a regular tetrahedron of edge 2 ft.