If a right circular cone has a base radius of 35 cm and an 45 cm, solve for the total surface altitude of volume in cmPp raised to (3PP), of area in cmPP raised to (2PP) and the cone.

Determine the outside diameter of a hollow steel tube that will carry tensile load of 500 KN at a seress of to be one-tenth of the outside diamete 140 Mpa. Assume the wall thickness 1/10 of the outside diameter.

*A house can be constructed in as many days as there are men in the group of construction personnel.if the number of men is reduced by 4, the project is delayed by 5 days. Determine the original number of construction personnel.

A river is 580 ft wide. The bridge construction across the river is banked 1/7 of its length in the east and 1/6 of the length in the west. What is the length of the bridge?

A and B together weight 242 pounds. They balance when A is seated 5 feet from the fulcrum on one side of a lever and B is seated 6 feet from the fulcrum on the other side. Find the weight of A.

A group of students rented a convention hall for P240.00. If there were 4 students less, the share of each would have been P2.00 more. How many students were in the group?

A train running at 60 kph decelerated at 2 m/min? for 14 minutes. Find the distance travelled, in km within this period

The radius of the earth is 3960 mi. The gravitational acceleration of the earth's surface is 32.16 fps?. What is the velocity of escape from the earth in is?

A car travelling on a horizontal unbanked circular track of radius and the track is 0.30. Determine the cars velocity while travelling at a radius of 34 m, without skidding.

Trailer travels at 85 mi/hr around a banked highway curve with a radius of 1000 ft. What banking angle is necessary such that friction f = 0.3 to resist the centrifugal force?

A body weighing 180 ib starts from rest and slides down a plane at an angle of 30° with the horizontal for which the coefficient of friction f = 0.3. How far will it move when t = 4 sec

In a small factory with a capacity of 500,000 units per year with a 75% efficiency, the annual income is P500,000 and fixed cost of P180,000 and variable cost of P0.52 per unit. What is the break-even point?

Two planes fly toward each other from points 2500 km apart, at the rates of 600 kph and 400 kph. When will they meet if they start at the same instant?

An object moves along a straight line such that, after t minutes, its distance from its starting point is S = 20t + 5/t + 1) meters. At what speed, in mimin will it be moving at the end of 4 minutes?

Find the area bounded by the curve y? = 1 - x and the line y = 1 + X

A painting of height 3 ft hangs on a wall with bottom of the painting & ft above the floor. How far from the wall should Lindsay, whose eyes are 5 ft from the floor stand in order to get the best view of the painting. (The best view occurs when the angle of vision from the bottom to the top of the painting is maximized)?

A man at point A on the shores of a circular lake of radius 1 mile wants to reach point B on the shore diametrically opposite A. If he can row a boat 3 mile/hr and jog 6 mihr, at what angle & with the diameter should he row in örder to reach B in the shortest possible time?

According to Newton's law of cooling the temperature of an object changes at a rate proportional to the difference in temperature between the object and the outside medium. If an object whose temperature is 70° is placed in a medium whose temperature is 20ºF and 40°F after 3 minutes, what will its temperature be after 6 minutes?

public health report states that t weeks after the outbreak of a new strain of flu, the number of people in thousands who will contract the disease is Q(t) = 10/1 + 100e^-1.5t. At what rate did people contract the disease after two weeks?

A police car is 20 ft away from a long straight wall, Its bacon, rotating 1 revolution per second, shines a beam of light on the wall. How fast is the beam moving when it is closest to the police car?

A rectangle is to be inscribed in the ellipse x^2/200 + y^2/50 = 1.

An open box is to be constructed from a 12 12 inches piece of cardboard by cutting away squares of equal size from the four comers and folding up the sides. Determine the size of the cut out that maximizes the volume of the box?

A factory operator bought a diesel generator set P10,000 and agreed to pay the dealer uniform sum at the end of each year for 5 years at 8% compounded semi-annually, that the final payment will cancel the debt for principal and interest. What is the annual payment?

A ski resort installs two new ski lif at a cost of P1,600,000. The resort expects annual gross revenue to increase P500,000 while it incurs an annual expense of P50,000 for lift operations and maintenance. What is the payback period?

The probability that a married man watches a certain television show is 0.4 and the probability that a married woman watches the show is 0.5. The probability that a man watches the show given that his wife does is 0.70. Find the probability that at least 1 person of married couple will watch the show.

invested Php 50,000. Part of it he put in an oil stock from which he hoped to received a 20% retum per year. The rest he invested in a bank stock which was paying 6% per year. If he receiver Php 400 more the first year from the bank stock that from the oil stock, how much did he investi the oil stock?

The dimensions of a rectangle are continuously changing. The width increases at the rate of 3 in/2 while the length decreases at the rate of 2 in/s. Af one instant the rectangle is a 20-in square. How fast is this area changing 3 seconds later?

Water is being pumped into the conical tank at the rate of 100 f*/min. The height of the tank is 20 ft and its radius is 5 ft, how fast the water level rising when the water height is 10 f?

Change the equation y = x from rectangular to polar coordinates.

A runner and his trainer are standing together on a circular track of radius 100 meters. When the trainer gives a signal, the runner starts to run around the track at a speed of 10 m/s. How fast is the distance between the runner and the trainer increasing when the runner has run ¼ of the way around the track?

A man makes a business trip from his house to Batangas in 2 hours. One hour later, he retums home in traffic at a rate of 20 kph less that his going rate. If he is gone a total of 8 hours. How fast did he travel going back home?

A right circular tank of depth 12 feet and radius of 4 feet is half full of oil weighing 60 pounds per cubic foot. Find the work done in pumping the oil to a height 6 feet above the tank.

The UN forces in Iraq uses a type of missile that hits its target with a probability of 0.3. How many missiles should be fired that there is at least an 80% probability of hitting the target?

A real estate firms owns the Parklane Garden Apartment units. At $250 per month every apartment can be rented. However, for each $10/month increase there will be two vacancies with no possibility of filling them. The firm wants to receive $17,980 per month from rent. What rent should be charged for each apartment?

A compensating balance refers to that practice wherein a bank requires a borrower to maintain on deposit a certain portion of a loan during the term of the loan. To meet the expenses of the retooling, the Victor Company finds it must borrow P95,000. The Metrobank, with whom they have had no prior association, requires a compensating balance of 15%. To the nearest thousand, what must be the amount of the loan to obtain the needed funds?

A manufacturer of metal ware found that his profit varies as the product of the amount spent for promotion and the square of the amount of production. How much of the capital spent for production?

A man bought 23 chickens for P29.00. The cocks cost P3.00 each, the hens P1.50 each, and the chicks at 0.50 each. How many cocks, hens and chicks did he buy?

A horizontal platform with a diameter of 6 m revolves about its center at 20 rpm. Find the tangential speed, in mis of a point at the edge of the flatform.

A coin is baised so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, what is the probability of getting 2 tails and 1 head?

The probability that a doctor correctly diagnosis a particular illness is 0.70. Given that the doctor makes and incorrect diagnosis, the probability that the doctor makes an incorrect diagnosis and the patient sues

A man finds the angle of elevation of the top of the tower to be 30°. He walks 85 m nearer the tower and finds angle of elevation to be 60 deg. What is the height of the tower?

What is the area bounded by y = 0, y = ex, x = 0, x= 2.

Abasalthe fatt of 20 a square whose sides are 90 R. long. If a bater hits the bail and runs to frst 50 ft?base at the rate of 20 f/sec, how fast is his distance from the second base changing when he runs

The dimensions of a rectangle are continuously changing. The width increases at the rate of 3 in2 while the length decreases at the rate of 2 in/s. At one instant the rectangle is a 20-in square. How fast is this area changing 3 seconds later?

through filled with water is 2 m long and has a cross section in the shape of an isosceles trapezoid 30 cm wide at the bottom, 60 cm wide at the top, and height of 50 cm. If the trough leaks water at the rate of 2000 cm^3/min; how fast is the water level falling when the water is 20 cm deep?

A father, Max is 24 years older than his son Joey. In 8 years he will be twice as old as his son Joey. what the present age?

During a stress-strain testconducted in the laboratory, the unit deformation at a stress of 35 MPa was observed to ba 167 x 10 raised to -6 m/m if the proportional limit was 200 MPu: what Is the modulus of elasticity. What is the strain corresponding to t Htress of 80 MPa?

The mass flow rate of Refrigerant Freon 12 through a heat exchanger is Ibs/min. Enthalpy of Refrigerant Freon entry is Refrigerant Freon exit is 26. 102 BTU/16 BTU/lb. Water coolant is allowed and of to rise 10 deg F. The water flow fate in liters. perminute is

A bullet weighing 4 grams was fired from a gun with the barrel measuring 12cm long. if the bullet was fired with a speed of 380 m/s solve the energy of the bullet in joules

A pipe lining material of silicon carbide used in the conveyance of pulverized coal to fuel a boiler, has thickness of 2 cm and inside diameter of 10 cm. Find the volume of the material of a pipe length of 6 meter in liters.