A circular cone having an altitude of 9 m is divided into 2 segments having the same vertex. If the smaller altitude is 6 m, find the ratio of the volume of the small cone to the big cone.

The central angle of a spherical wedge is 1 radian. Find its volume if its radius is 1 unit.

A regular triangular pyramid has an altitude of 9 m and a volume of 187.06 cu. m. What is the base edge in meters?

4x² - y² = 16 is the equation of a/an

Find the 6th term of the sequence 55, 40, 28, 19, 13,....

Each angle of a regular dodecagon is equal to

Factor the expression 3x³ - 3x² -18x

JJ is three times as old as Jan-Jan. Three years ago, JJ was four times as old as Jan-Jan. The sum of their ages is

Six years ago, Nilda was five times as old as Riza. In five years, Nilda will be three times as old as Riza. What is the present age of Riza?

If p - q = 5 and pq = k/2, then p² + q² equals

Find the value of w in the following equations: 3x - 2y + w = 11 x + 5y -2w = -9 2x + y - 3w = -6

Given: log₃(x² - 8x) = 2, Find x.

The arc of sector is 9 units and its radius is 3 units. What is the area of the sector in square units?

Find the area (in cm²) of a regular octagon inscribed in a circle of radius 10 cm?

Given a triangle, C = 100° , a = 15 m, b = 20 m. Find c.

What is the acceleration of a body that increases in velocity from 20 m/s to 40 m/s in 3 seconds?

A ball is dropped from a building 100 m high. If the mass of the ball is 10 gm after what time will the ball strike the earth?

A projectile leaves a velocity of 50 m/s at an angle of 30° with the horizontal. Find the maximum height that it could reach.

Find the polar equation of the circle of radius 3 units and center at (3,0).

What is the area enclosed by the curve 9x² + 25y² - 225 = 0?

Find the equation of the directrix of the parabola y² = 16x.

What is the spherical excess of a spherical triangle whose angles are all right angles?

A goldsmith has two alloys of gold, the first being 70% pure and the second being 60% pure. How many ounces of the 60% pure gold must be used to make 100 ounces of an alloy which will be 66% gold?

Ten liters of 25 % salt solution and 15 liters of 35 % salt solution are poured into a drum originally containing 30 liters of 10 % salt solution. What is the per cent concentration of salt in the mixture?

Ten less that four times a certain number is 14. Determine the number.

Find the product of two numbers such that twice the first added to the second equals 19 and three times the first is 21 more than the second.

If eight is added to the product of nine and the numerical number, the sum is seventy one. Find the unknown number.

Multiply the following: ( 2x + 5y ) ( 5x - 2y )

If f(x) = 2x² + 2x + 4, what is f(2)?

One degree on the equator of the earth is equivalent to _____ in time.