Evaulate

Find the 2000th digit in the decimal equivalent to 1785/9999 starting from decimal point.

The orange bulbs of a light flash every 12 seconds, the red bulbs flash every 10 seconds and the green bulbs flash every 15 seconds. If they all start flashing together, in every how many seconds will they flash simultaneously together again?

what is the value of k

What is the term free of x of the expansion

The sum of Jay’s & Carl’s ages is 24. In 3 years, Jay will be twice as old as Carl. How old is Carl now?

Mary is 30 years old. Mary was twice as old as Ann was when Mary was old as Ann is now. How old is Ann?

If an alloy containing 30% silver is mixed with a 70 % silver alloy to get 800 pounds of 40% silver alloy, how much of the 30 % silver alloy must be used?

Fifteen men can finish a job in 16 days. Five men were working together at the start and after 8 days 3 men were added. How many days will it take to finish the job?

solve for x

How many minutes after 4 o’ clock will the hands of the clock be together?

In a class of 40 students, 28 like calculus and 23 like chemistry. How many like both calculus and chemistry?

If the supplement of an angle is 7/2 of its complement, find the value of the angle.

If log of 2 to the base 2 plus log of x to the base 2 is equal 4, then the value of x is

At certain point, the angle of elevation of the top of a flagpole, which stands on level ground is 40 deg. Seventy-five feet nearer the pole, the angle of elevation is 50 deg. How high is the pole?

A PLDT tower and a monument stand on level plane. The angles of depression of the top and bottom of the monument viewed from the top of the PLDT tower are 20 and 35 degree, respectively. The height of the tower is 50 m. Find the height of the monument.

If sin A = 3/5 and A is in the second quadrant while cos B = 7/25 and B is in the first quadrant, find sin(A-B).

Given the triangle ABC in which A = 50 degree, b = 100 m and c = 200 m. Find the length of the side a.

An engineer left a point walking at 6.5 kph in a direction E20 degree A cyclist leaves the same point at the same time in a direction E50 degree S traveling at a constant speed. Find the average speed of the cyclist if the engineer and the cyclist are 80 km apart after 5 hours.

An oblique isosceles triangle inscribed in a circle. If one side of the triangle has a length of 10 cm and the angle subtended by the side is 15 deg, determine the area of the circle.

Find the distance between (4, -3) and (2, 5)

If the point (x,4) is equidistance from (5, -2) and (3,6), find x.

The segment (-1,4) to (2, -2) is extended two times its own length. Find the terminal point.

The line segment connecting (x, 6) and (9, y) is bisected by the point (10,3). Find the values of x and y.

Determine k such that the line 3x-2y-7 = 0 is parallel to the line 6x-ky+2 = 0.

Determine the area of the triangle bounded by the straight lines x + 2y = 7, 3x - 4y = 1, and 2x - y= -6.

The coordinates of a polygon are (2, 0), (0, 8), (5, 4), and (-3, 4). What is the area?

Given the circle x2+y2-10x +4y+4 =0. Find the coordinates of the center.

A regular pentagon has sides of 20 cm. An inner pentagon with sides of 12 cm is inside and concentric to the larger pentagon. Determine the area inside and concentric to the larger pentagon but outside of the smaller pentagon.

Find the area of a regular octagon inscribed in a circle of radius 12 cm.

A goat is tied to a corner of a 30 ft by 35 ft building. If the rope is 40 ft long, what is the maximum area the goat can cover.

A cubical container that measures 3 in on a side is tightly packed with 8 marbles and is filled with water. All the 8 marbles are in contact with the walls of the container and adjacent marbles. All the marbles are the same in size. What is the volume of the water in the container?

A pyramid with square base has an altitude of 15 cm. If the edge of the base is 10 cm. Calculate the volume of the pyramid.

A frustum of a regular pyramid has an upper base of 8 m by 80 m and a lower base of 10 m by 100 m and an altitude of 12 m. Find its volume.

A factory building has four entrance doors. In how many ways can a person enter and leave by different doors.

In how many ways can a set of 8 distinct books be arranged in a bookshelf?

In how many different ways can 3 persons be seated in consecutive seats in a row of 8 seats?

In how many ways can 3 marines and 5 armies be seated on a bench if the armies must be seated together?

In how many ways can 6 single engineers and 4 beautiful nurses be arranged in a round table if the nurses insisted to be seated side by side?

A bag contains 4 white and 5 black balls. If the two balls are drawn in succession without replacement, what is the probability that both balls are black?

A fair coin is tossed 5 times. What is the probability of getting exactly 2 heads?

Two students are working independently on a problem. Their respective probabilities of solving a problem are 1/4 and 3/4. What is the probability that at least one of them will solve the problem?

Find the probability that a couple having 4 children will have at least one girl.

Solve for the mean: 10 30 26 40 8 30 16 28 31 17.

Solve for the sample standard deviation: 5 7 9 10 12 15

Evaluate the limit of (1-cosX)/X^2 as X approaches 0.

What is the derivative of 2xe^x?

Determine the slope of the curve y = x^2+3x-25 at x = 2.

Find the radius of curvature of x^2-2x+y^2-2y=2 at any point.

What is the minimum point of y = x^3/3 – 9x^2/2 +18x

What is the point of inflection of y = x^3/3 – 9x^2/2 +18x

A closed cylindrical container has a capacity of 120 m3. Determine the minimum surface area.

A rectangular storage area is to be constructed along the side of a tall building. A security fence is required along the remaining 3 sides of the area. What is the maximum area that can be enclosed with 800 m of fencing?

What is the area of the largest rectangle that can be inscribed in a semi-circle of radius 2 m?

Water is flowing into a vertical cylindrical tank at the rate of 24 ft3/min. If the radius of the tank is 4 ft, how fast is the surface rising?

Evaluate the integral of x^3+3x+10 with respect to x, from 0 to 2.

What is the area bounded by the curve y^2 = x and the line x = 9?

Find the area bounded by the curves x^2 + y^2 = 9 and 4x^2 + 9y^2 = 36 on the 1st and 2nd

Determine the generated volume of the region bounded by y = x^2 - 4x + 5, x = 1, x = 4, and the x-axis if it is revolved at the x-axis.

Determine the generated volume of the region bounded by y = x^2 and the x-axis from x = 1 to x = 3 if it is revolved at the y-axis.

Determine the arc length of y = ln(secx) from x = 0 to x = pi/4

The rate of population growth of country is proportional to the number of inhabitants. If the population of a country now is 40 million and 50 million in 10 years’ time, what will be its population 35 years from now?

A thermometer reading is 18F is brought into a room where the temperature is 70F; a minute later, the thermometer reading is 31F. Determine the temperature reading 8 minutes after the thermometer is first brought into the room.A thermometer reading is 18F is brought into a room where the temperature is 70F; a minute later, the thermometer reading is 31F. Determine the temperature reading 8 minutes after the thermometer is first brought into the room.

Determine the general equation of

Determine the general equation of

Simplify i^2 + 3i - 5

Simplify (5 + 2i)^3

Simplify i^1000+i^375-i^200

Determine the determinant of

Determine the determinant of

Determine the Inverse Laplace transform of

Assume the three forces intersect at a single point. What is the magnitude of the resultant? F1= i + 3j - 4k F2 = 2i - 7j + k F3 = i - 4j + 2k

Find the resultant of the following forces: F1 = 600 N at 20 deg at the first quadrant, F2 = 800 N at 30 deg at the second quadrant and F3 = 200 N at 60 deg in the fourth quadrant.

A 200 N block is initially at rest on a flat surface that is inclined at 30 degrees. If the coefficient of friction is 0.3, find the force in N required to start the block moving up the plane.

A smooth 3.5 kg collar on the top portion of a rod is attached to a spring whose initial position is horizontal. The spring has a stiffness of 3 N/m and an unstretched length of 0.75 m. If the collar is released from rest, determine the acceleration of the collar in m/s2 at the instant it went down at 1 m below its initial position.

A car moves in a straight line such that for a short time its velocity is defined by v = 3t^2 + 2t ft/s, where t is in seconds. Determine the position in ft when t = 5 s. When t = 0, the position is on the reference point.

The track for a racing event was designed so that riders jump off the slope at 30 deg, from a height of 1 m. During a race, it was observed that the rider remained in mid air for 2 second. Determine the maximum height he attained in reference to the ground in m.

A car is at rest on a sloping driveway. By accident, a small child releases the brake of the car. How fast will the car be moving in m/s when it reaches the street? The street is 1.5 m below the original position of the car.

A rope is stretched between two rigid poles 40 ft apart. A load of 300 lbs was placed at the midpoint of the rope that caused it to sag 5 ft. What is the approximate tension in the rope in lbs?

A 2 m long cantilever beam has a 10 kN/m distributed load. What is the moment in kN-m at the built-in end?

A homogeneous ladder 18 ft long and weighing 120 lbs rests against a smooth wall. The angle between it and the floor is 70 deg. The coefficient of friction between the floor and the ladder is 0.20. How far up the ladder can a 180 lb man walk before the ladder slips?

Four turns of rope around a horizontal post will hold a 1000 lb weight with a pull of 20 lbs. Find the coefficient of friction between the rope and the post.

A square with 4 cm side is placed inside a rectangle whose base and height are 10 cm and 8 cm, respectively. If the square is located at the left most part and 2 cm above the base of the rectangle, determine the abcissa of the centroid for the area outside the square but inside the rectangle. The reference is at the lower left edge.

An automobile moving at a constant velocity of 15 m/s passes a gasoline station. Two seconds later, another automobile leaves the gasoline station and accelerated at a constant rate of 1.5 m/s^2. How soon will the second automobile overtake the first in seconds?

The position of a particle moving along the x-axis is given by x = t^2 - t + 8, where x is in units of m and t is in seconds. Find the velocity of the particle when t = 10 s.

A stream flows at 6 km/h. At what angle upstream should a boat traveling at 12 km/h be launched in order to react the shore directly opposite to the launch point?

A block with a mass of 150 kg slides down a frictionless wedge with a slope of 40 deg. The wedge is moving horizontally in the opposite direction at a constant velocity of 6 m/s. What is most nearly the absolute speed of the block 2 s after it is released from rest?

A bank charges 12 % simple interest on a 500 pesos loan. How much will be repaid if the loan is paid back in one lump sump after 3 years?

A bank charges 15 % simple interest on a 1500 pesos loan. How much is the interest after 3 years?

A merchant puts his 4000 pesos to a small business for a period of 6 years. With a given interest rate on the investment of 15 % per year, compounded annually, how much will he collect at the end of the 6th year?

By the condition of a will, the sum of 20000 pesos is left to a girl to be held in trust fund by her guardian until it amounts to 40000. When will the girl received the money if the fund is to be invested at 8 % compounded quarterly.

What will be the annuity for an indefinite period of time if the interest is 6 % and the present worth is 1500 pesos?

A parent on the day the child is born wishes to determine what lumpsum would have to be paid into an account bearing interest at 5 % compounded annually, in order to withdraw 35000 each on the child’s 18th, 19th, 20th, and 21st birthdays.

A house and lot can be acquired a down payment of 200000 pesos and a yearly payment of 100000 at the end of each year for a period of 10 years, starting at the end of 5 years from the date of purchase. If the money is worth 12 % compounded annually, what is the cash price of the property?

The annual maintenance cost of a machine is 8848 pesos. If the cost of making a forging is 56 pesos per unit and its selling price is 135 pesos per forged unit, find the number of units to be forged to break-even.

A trapezoid has two equal slanting sides, a 6 cm base and a 3 cm top parallel to and 6 cm above the base. Determine the moment of inertia of the trapezoid area relative to the top side, in cm4.

A bullet of mass 25 grams is fired and strikes a 2 kg block resting on a frictionless surface with a velocity of 600 m/s. If the block is attached to a spring (k=20kN/m). How long will the spring be compressed in cm until the block and the bullet are brought to a stop?

What uniform annual amount should be deposited each year in order to accumulate P100,000 at the end of the 5th annual deposit if money earns 10% interests?

In five years, P18,000 will be needed to pay for a building renovation. In order to generate this sum, a sinking fund consisting of three annual payments is established now. For tax purposes, no further payments will be made after three years. What payments will be made after three years. What payments are necessary if money is worth 15% per annum?