A piece of paper is 0.05 inch thick. Each time the paper is folded into half, the thickness is doubled. If the paper was folded 12 times, how thick in feet would the folded paper be?

Find the sum of the first five terms of the G.P. if the third term is 144 and the sixth term is 486

Spheres of the same radius are piled to form a pyramid with a square base until there is one sphere at the top layer. If there are 4 spheres on each side of the square, find the total number of spheres in the pile.

A laboratory keeps two acid solutions on hand. One is 20% acid and the other is 35% acid. How many liters of distilled water should be added to a liter of 35% acid solution in order to dilute it to a 20% acid solution?

After the price of petroleum oil went up by 10%, a consumer reduced his oil consumption by the same percent. By what percent would his petroleum bill be changed?

A speedboat can travel 10 miles downstream in the same amount of time as it goes 6 miles upstream. If the velocity of the river current is 3 mph, find the speed of the boat in still water.

John's rate of doing work is 3 times as fast as Bill. On a given day John and Bill work together for 4hrs then Bill was called away and John finishes the rest of the job in 2hrs. How long would it take Bill to do the complete job alone?

In a pile of logs, each layer contains one more log than the layer above and the top contains just one log. If there are 105 logs in the pile, how many layers are there?

The sum of the ages of Peter and Paul is 21. Peter will be twice as old as Paul 3yrs from now. What is the present age of Peter?

A code is composed of 2 letters, the first being a vowel and a three digits. In how many ways can it be made without repetition?

In how many ways can 5 men and 5 women be seated in a round table if each woman is to be seated between two men?

Find the sum of all odd integers between 100 and 1000

How many 4-digit even numbers can be formed from the digits 0 to 9 if each digit is to be used only once in each number?

A political analyst asked a group of people how they felt about two political policy statements. Each person was to respond A(agree), N(neutral) and D(disagree) to each NN, ND, AN,..., DD. Assuming each response combination is equally likely, what is the probability that the person being interviewed agrees with exactly one of the two political policy statements?

Three randomly chosen senoir high school students were administered a drug test. Each was evaluated as positive to the test (P) or negative to the test (N). Assume the positive combinations of the to the drug test was PPP, PPN, PNP, NPP, PNN, NPN, NNP, NNN. Assuming each possible combinations are equally likely, what is the probablity that atleast one student gets a negative result.

A bag contains 3 white balls and 5 red balls. If two balls are drawn in succession without returning the first ball drawn, what is the probability that the balls drawn are both red?

Donations were made by alumni for a school to fund a new computer room. Data shows that 80% of alumni give at least P50. If the school administration contacts 20 alumni, what is the probability that 15 of them will give at least P50

Studies have shown a particular TV commercial is understood by 25% of preschool pupils and 80% of grade school pupils. If a TV advertising agency randomly selected one preshooler and one grade-schooler, what is the probability that neither child would understand the commercial, assuming the children reactions are independent?

The mean duration of television commercials on a given network is 75 seconds, with standard deviation of 20 seconds. Assume that duration times are normally distributed, what is the probability that a commercial will last less than 35 seconds?

If sin A = 4/5, A in quadrant II, sin B = 7/25, B in quadrant I, Find sin (A+B)

If cos 2x = 2, find cos 3x

Simplify 1/(csc x + cot x) + 1/(csc - cot x)

Given y = 4cos2x, determine the amplitude

If xcosθ + ysinθ = 1 and xsinθ - ycosθ = 3, find the relationship between x and y

A tower cast a shadow of 15m long when the angle of elevation of the sun is 61^o. If the tower has leaned 15^o from the vertical towards the sun, what is the length of the tower?

Points A and B, 1000m apart are plotted on a straight highway running east and west. From A, the bearing of the tower C is 32^o W of N and from B, the bearing of C is 26^o N of E. Approximate the shortest distance of tower C to the highway.

Two towers are 60m apart. From the top of the shorter tower, the angle of elevation of the top of the taller tower is 40^o. How high is the taller tower if the height of the smaller tower is 40m?

Find the length of chord of a circle of radius 20 cm subtended by a central angle of 150^o

Two stones are 1 mile apart and are of the same level as the foot of the hill. The angles of depression of the two stones viewed from the top of the hill are 5degrees and 15degrees respectively. Find the height of the ill.

Two circles of different radii are concentric. If the length of the chord of the bigger circle that is tangent to the smaller circle is 50 cm, calculate the are bounded by the two circles

Find the area in sq.cm of the equilateral triangle inscribed in a circle of radius 20 cm

Find the are in cm² of the circle circumscribing an isosceles right triangle having an area of 162 cm²

The sides of a triangular lot are 130m, 180m and 190m. The lot is to be divided by a line bisecting the longest side and drawn from the opposite vertex. Find the length of this dividing line in meter.

Find the are of a regular 6 pointed star of David inscribed in a circle of radius 5cm.

How many sides have a polygon if the sum of its interior angles equals twice the sum of its exterior angles?

A solid consist of a cone and a hemisphere sharing bases of radius r. If the height of the cone is 10cm and the volume of conical hemispherical portions of the solid thus formed are equal, find the total volume of the solid in cu.cm

A right circular cone whose vertex angle is 90^o has a diameter of sphere as its axis and has its vertex on the sphere. Determine the ratio of the volume of the cone to that of sphere.

Find the volume of the solid common between intersecting cylinders with radius of 3ft.

A tetrahedron is a solid which is a member of the polyhedrons. It has 4 faces which are all equilateral triangles. Find its volume if edge is 12 cm long.

If the straight lines ax + by + c = 0 and bx + cy + a = 0 are parallel, then which of the following is correct?

Find the radius of the circle 2x^2 + 2y^2 - 3x - 4y -1 = 0

An arc in the form of a parabolic curve is 40m across the bottom. A flat horizontal beam 26m long is placed 12m above the base. Find the height of the arc.

Find the perimeter of the ellipse 9x^2 + 18x + 25y^2 - 100y = 116

The line 6x + y - k = 0 is tangent to the parabola x^2 = -y + 16. Find the value of k.

The major axis of the elliptical path in which the earth moves around the sun is approximately 186000000 miles and the eccentricity of the ellipse is 1/60. Determine the apogee of the earth in miles.

Find the value of k for which the length of the tangent from point (5,4) to the circle x^2 + y^2 + 2ky = 0 is 1

Find the angle between the planes 3x - y + z - 5 = 0 and x + 2y + 2z + 2 = 0

Find the volume of the pyramid formed in the first octant by the plane 6x + 10y + 5y - 30 = 0 and the coordinate planes

Find the volume of a cube having its two faces laid in the planes 2x - y + 2z - 3 = 0 and 6x - 3y + 6z + 8 = 0

Find the equation of the tangent line to the curve x^3 + y^3 = 9 at the point (1,2)

Find the point of inflection of the curve x^3 - 3x^2 - x + 7.

Determine the curvature of the curve y^2 = 16x at the point (4,8)

The volume of sphere is increasing at the rate of 6cc/hr. At what rate is the surface area increasing in sq.cm/hr when the radius is 50cm?

Sand falls onto a conical pile at the rate of 10 cu. in/s. The radius of the base of the pile is always 1/2 of the altitude. How fast is the altitude of the pile increasing when it is 5 inches deep?

One end of a 32mm ladder resting on a horizontal plane leans on the wall. Assume the foot of the ladder to be pushed towards the wall at the rate of 2m/min. How far from the wall is the foot of the ladder when the top of the ladder is rising at the rate of 3m/min?

Find the radius of the largest right circular cylinder inscribed in a sphere of radius 5.

A statue 3m high is standing on a base of 4m high. If an observer's eye is 1.5m above the ground, how far in meter should he stand from the base in order that the angle subtended by the statue is a maximum?

A cylindrical steam boiler is to be constructed having a capacity of 30cu.m. The material for the side costs P25/m^2 and for the ends P40/m^2. Find the radius for least cost.

A steel girder 8m long is moved on rollers along the passageway 4m wide and into a corridor at right angles to the passageway. Neglecting the width of the girder, how wide must the corridor be?

Find the area bounded by one arch of the companion to the cycloid x = aθ, y = a(1 - cosθ) and the x-axis

Find the area enclosed by the cardioid r = a(1 + sinθ)

Find the area enclosed by the loop of y = 4x^2 (1 - x)

The area under the portion of the curve y = cosx from x = 0 to x = π/2 is revolved about the x-axis. Find the volume of the solid generated.

Evaluate the integral of (4x / (x^2 + 4))dx from x = 1 to x = 7 by Simpson's Rule with n = 6

Find the volume generated by revolving the ellipse x^2/a^2 + y^2/b^2 = 1 about the tangent x = a.

Find the I_o for the area of the curve r^2 = a^2cosθ

Evaluate the integral of x y z dz dy dx from z = 0 to z = 3, y = 0 to y = 2 and x = 0 to x = 1

Find the mass of lamina in a given region and density function D(x,y), 0 ≤ x ≤ pi/2, 0 ≤ y ≤ cosx and p = 7x

Find the are bounded by the parabolas y = 5x - x^2 and y = x^2 - 2x

The differential equation of the line passing through the origin is

What is the solution to the first order difference equation y(k + 1) = y(k) + 5

According to Newton's law of cooling the rate at which the substance cools in the air is proportional to the difference between the temperature of the substance and that of air. If the temperature of the air is 30C and the substance cools from 100C to 70C in 15min, how long will it take to cool 100C to 50C

A certain radioactive substance has a half-life of 38hrs. Find how long it takes in hours for 90% of the radioactivity to be dissipated?

Solve the differential equation (D^2 + 1)y = cot x

Evaluate the Laplace transform of sintcost

Evaluate the inverse Laplace 20/s(s + 10)

Find log (3 + j4)

Evaluate the limit of (z^2 + 1)/(z^6 + 1) as z approaches i.

What is the principal cube root of the complex number (8,60deg)?

What is the coefficient of x^3 in the Taylor's series equivalent of the polynomial 1/(2 + x) about x = 0

Given vectors are A = 8i + 2j +2k, B = 4i + 2j + 4k and C = 6i + 8j + 10k. What is the value of (A + B)dot(B + C)

What is the volume of the parallelepiped with sides represented by zero - based vectors A = 2i - 2j + k, B = 4i + 2j + 2k and C = i + 5j + 4k?

What is the angle between the 2 vectors A = 4i + 12j + 6k and B = 24i - 8j + 6k?

The equation /z - 3/ + /z + 3/ = 10 represents which of the following curve?

It is a conic section with B² - 4AC - 0

Find the Eigen values of the 2x2 matrix with elements at row 1 of 3 and 2 and at row 2 of 5 and 0.

Find the Wronskian of the following functions; e^x, cos x and sin x.

It is a conic section with B² - 4AC less than zero and eccentricity less than one is,

It is a locus of point with difference of distances from two fixed points is a constant

Evaluate the limit of x sin (pi/x) as x approaches infinity.

At what quadrant where sinx and cosx are both increasing

A certain money P draws interest compounded continuously. If at a certain time there is Po pesos in the account, determine the time in years when the principal attains the value 2Po pesos, if the annual interest rate is 2%

Two circles with different radius but with the same center is called ________ circle

Evaluate i^247

Evaluate (3 + j4) raised to (3 + j4)

The three points (1, -2, -3), (2, 0, -1) and (a, b, 3) lie on straight line, find the values of a and b

In polar coordinates system, the distance from a point to the pole is known as;

The axis of the hyperbola passing through its foci is called

Evaluate sinh(i pi/6)