March 2021

The geometric mean and arithmetic mean of two numbers are respectively 8 and 17. Find the harmonic mean.

Given $f(x) = (x - 4)(x + 3) + 4$. When $f(x)$ is divided by $(x - k)$, the remainder is k, find the value of k.

Find the equation of the radical axis of the two circles having equations of $x^2 + y^2 + 4x + 6y - 3 = 0$ and $x^2 + y^2 + 12x + 14y + 60 = 0$.

What is the length of the line with slope 4/3 from point (6, 4) to the y-axis?

Determine the distance from point (2, 1) to the line 4x - 3y + 5 = 0.

An airplane flew from Davao whose latitude is 14° N and longitude of 121° 30' E on a course of S 30° W and maintaining uniform altitude. At what longitude will the plane cross the equator?

A pole cast a shadow 15 m long when the angle of elevation of the sun is 61°. If the pole has lean 15° from the vertical directly towards the sun, what is the length of the pole?

A sphere is circumscribing a cubical box having a volume of 8000 cm³. Compute the volume of the space between the cubical box and the sphere.

Find the volume of a circular cone having a base radius of 20 cm and axis 30 cm, if the axis makes an angle of 60° from the base.

Compute the cost of lumber necessary to resurface a foot-bridge 16 feet wide and 150 feet long with 2-inches planks, if lumber is P48.00 per board foot.