December 2017

Water is flowing into a conical cistern at the rate of 5 m³/min. The height of the cone is 10 m and the radius of the upper base 5 m. How fast in m/min is the radius of water changing when there is 6 m deep of water in the cone?

Find the length of the latus rectum of the following ellipse: 25x² + 9y² - 300x - 144y + 1251 = 0.

What time after 3:00 o’clock would the hour-hand and the minute-hand of a continuously driven clock subtends an angle of 45° for the second time?

A right spherical triangle ABC of a sphere of radius 50 cm has angle C = 90°, A = 56° and side b = 47°. Find the area of the triangle in square centimeter.

The total surface area of a closed cylindrical tank is 153.94 square meter. If the volume is to be maximum, what is its height in meters.

Find the area bounded by the y-axis and the lines y = 6x - 1 and y = x/4 + 3.

A time deposits of P110,000 for 31 days earns P890.39 on maturity date after deducting the 20% withholding tax on interest income. Find the rate of interest per annum.

A trough has an open top 0.30 m by 6 m and closed vertical ends which are equilateral triangles 30 cm on each side. It is filled with water to half its depth. Find the volume of water in cubic meters.

Find the angle subtended by the line segment through (0, 0, 0) and (3, 8, 5) from the xy-plane.