BESAVILLA ENGINEERING MATHEMATICS PDF

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besavilla engineering mathematics | Get Read & Download Ebook besavilla engineering mathematics as PDF for free at The Biggest ebook library in the world. BESAVILLA ENGINEERING MATHEMATICS GMG9PC PDF - Welcome to our library, Are you looking for BESAVILLA ENGINEERING MATHEMATICS. Engineering Mathematics by Gillesania - Ebook download as PDF File .pdf) or view presentation slides online. Besavilla - Mathematics (Algebra).


Besavilla Engineering Mathematics Pdf

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Besavilla - Mathematics (Algebra) - Download as PDF File .pdf), Text File . txt) or view presentation slides online. Civil Engineering Board Examination. Download Engineering Mathematics by Gillesania. View Test Prep - Multiple Choice Questions in ENGINEERING MATHEMATICS By Venancio I. Besavilla, Jr. norinkgibipen.cf from E-MATH at University of Cebu.

If a population of a country now is 40 million and 50 million in 10 years time, what will be its population 20years from now? The Bureau of Census record in shows that the population in the country doubles compared to that of In what year will the population trebles assuming that the rate of increase in the population is proportional to the population?

A tank contains liters of fresh water. Find the amount of salt in the tank after 30 min. In a tank are liters of brine containing 50 kg total of dissolved salt.

Pure water is allowed to run into the tank at the rate of 3 liters per minute. Brine runs out of the tank at rate of 2 liters per minute. The instantaneous concentration in the tank is kept uniform by stirring. How much salt is in the tank at the end of 1 hour? The laplace transform of cos wt is: A thin heavy uniform iron rod 16m long is bent at the 10 m mark forming a right angle L — shaped piece 6m by 10m of bend.

What angle does the 10m side make with the vertical when the system is in equilibrium? Three men carry a uniform timber. One takes hold at one end and the other two carry by means of a crossbar placed underneath. At what point of timber must the bar be placed so that each man may carry one third of the weight of the weight of the timber?

The timber has a length of 12 m. A painters scaffold 30m long and a mass of kg, is supported in a horizontal position by a vertical ropes attached at equal distances from the ends of the scaffold. Find the greatest distance from the ends that the ropes may be attached so as to permit a kg man to stand safely at one end of scaffold.

A cylindrical tank having a diameter of 16 cm weighing kN is resting on a horizontal floor. A block having a height of 4 cm is placed on the side of the cylindrical tank to prevent it from rolling.

What horizontal force must be applied at the top of the cylindrical tank so that it will start to roll over the block? Assume the block will not slide and is firmly attached to the horizontal floor. Two identical sphere weighing kN are each place in a container such that the lower sphere will be resting on a vertical wall and a horizontal wall and the other sphere will be resting on the lower sphere and a wall making an angle of 60 degrees with the horizontal.

The line connecting the two centers of the spheres makes an angle of 30 degrees with the horizontal surface. Determine the reaction between the contact of the two spheres. Assume the walls to be frictionless. The 5 m uniform steel beam has a mass of kg and is to be lifted from the ring B with two chains, AB of length 3m, and CB of length 4m.

Determine the tension T in chain AB when the beam is clear of the platform. Two men are just to lift a kg weight of crowbar when the fulcrum for this lever is 0. If the men interchange positions, they can raise a kg weight.

What force does each man exert? A man exert a maximum pull of N but wishes to lift a new stone door for his cave weighing 20 N. It carries a concentrated load of 20 kN at the left end and 40 kN at 2m from the right end of the beam. If it is supported at 2m from the left end and the right end, compute the reaction at the right end of the beam. When one boy is sitting 1.

However, when the first boy carries an additional weight of 14 kg and sit 1. AC is 4. AC is horizontal while B is supported by roller acting on the wall AB. An airtight closed box of weight P is suspended from a spring balance. If the bird flies without accelerating.

What is the balance reading? A tripod whose legs are each 4 meters long supports a load of kg. Determine the load of each leg. Determine the share of load in percent carried by supports at A, E and F.

The square steel plate has a mass of kg with mass at its center G. Calculate the tension at each of the three cables with which the plate is lifted while remaining horizontal. A horizontal Circular platform of radius R is supported at three points A, B and C on its circumference. A and B are 90 degrees apart and C is degrees from A. The platform carries a vertical load of kN at its center and kN at a point d on the circumference diametrically opposite A.

Compute the reaction at C. A ladder 4m long having a mass of 15kg is resting against a floor and an wall for which the coefficients of static friction are 0. The block has a weight of 20 kN. If the coefficient of friction between the block and the inclined plane is 0. The 8cm side is perpendicular to the inclined plane. A uniform ladder on a wall at A and at the floor at B.

Point A is 3. Determine the minimum coefficient of friction at B required for a mass weighing 65 kg to use the ladder assuming that there is no friction at A. A block having a mass of kg is placed on top of an inclined plane having a slope of 3 vertical to 4 horizontal. When a man weighing N reaches a point 2.

Determine the coefficient of friction between the ladder and the floor if the coefficient of friction between the ladder and the wall is 0. A dockworker adjusts a spring line rope which keeps the ship from drifting along side a wharf. The coefficient of friction between the rope and the cast-steel mooring bit is 0. The top of the 15 kg ladder has a small roller, and the ground coefficient of static friction is 0. The uniform pole of length 4m and mass kg is leaned against a vertical wall.

If the coefficient of static friction between the supporting surfaces and the ends of the poles is 0.

A horizontal force P acts on the top of a 30 kg block having a width of 25 cm, and a height of 50cm. If the coefficient of static friction is 0. Solve for the force P to obtain equilibrium. A kg crate impends to slide down a ramp inclined at an angle of What is the frictional resistance?

If the coefficient of friction is 0. Coefficient of friction is 0. The block is subjected to a force 87N parallel to the inclined plane which causes an impending motion down the plane. If the coefficient of motion is 0.

A rectangular block having a width of 8cm and height of 20 cm, is reating on a horizontal plane. If the coefficient of friction between he horizontal plane and the block is 0.

A ladder is resting on a horizontal plane and a vertical wall. If the coefficient of friction between the ladder, the horizontal plane and the vertical wall is 0. Three identical blocks A, B and C are placed on top of each other are place on a horizontal plane with block B on top of A and C on top of B.

The coefficient of friction between all surfaces is 0. Each block has a mass of 50kg. The distance from the front wheel to the rear wheel is cm and its centroid is located at 50 cm from the surface of the plane. Determine the value of W is a force N applied parallel to the inclined plane to cause an impending motion upward. The block is subjected to a force 87 N parallel to the inclined plane which causes an impending motion down the plane. Compute the coefficient of friction between the block and the inclined plane.

The coefficient of friction between the 60 kN block is to remain in equilibrium, what is the maximum allowable magnitude for the force P?

Find the value of P acting to the left that is required to pull the wedge out under the kg block. Determine the horizontal thrust P in adjusting screw necessary to raise the mounting if the wedge supports one fourth of the total engine weight of 20 N.

The total coefficient of friction for all surfaces is 0. Two blocks connected by a horizontal link AB are supported on two rough planes as shown. The coefficient of friction for block A on the horizontal plane is 0.

What is the smallest weight of block A for which equilibrium of the system can exists? Is the system in equilibrium? If not, find the force P so that the system will be in equilibrium.

A 12 kg block of steel is at rest on a horizontal cable. The coefficient of static friction between the block a table is 0. The pull required to overcome the rolling resistance of a wheel is 90 N acting at the c enter of the wheels. If the weight of the wheel is 18 N and the diameter of the wheel is mm, determine the coefficient of rolling resistance. A kN weight is to be moved by using 50 mm diameter rollers. If the coefficient of the rolling resistance for the rollers and floor is 0.

The ball strikes at the sidewalk at ground level 4 sec later. Determine the velocity with which the ball hits the ground. A train starts from rest at station P and stops from station Q which is 10km from station P.

A car starting from rest picks up at a uniform rate and passes three electric post in succession. The posts are spaced m apart along a straight road. The car takes 10sec to travel from first post to sec post and takes 6 sec to go from the second to the third post. Determine the distance from the starting point to the first post. A stone is dropped from the deck of Mactan Bridge. The sound of the splash reaches the deck 3 seconds later. At a uniform rate of 4 drops per second, water is dripping from a faucet.

Assuming the acceleration of each drop to be 9. What is its average velocity during the first 5 seconds of motion? What is its min. Determine the velocity after 3 seconds. Compute the total distance the car has traveled from the start after 8 sec. A train passing at point A at a speed of 72 khp accelerates at 0. How far from point a will be 2min after passing point A.

Compute the distance the car has traveled after 12 sec from the start. Determine the total distance traveled. A train starting at initial velocity of 30 kph travels a distance 21 km in 8 min. How far in meters will it travel in 45 sec? An object experiences the velocity as shown in the diagram. How far will it move in 6 seconds?

How far does it travel in 15 seconds? Answer in SI. A shell is fired vertically upward with an initial velocity of fps. It is timed to burst in 7 sec.

Four seconds after firing the first shell, a second shell is fired with the same velocity. This shell is time to burst in 5 sec. An observer stationed in a captive balloon near the line of fire hears both burst. At the same instance what is the elevation or height of the balloon. Assume velocity of sound to be fps. A ball is dropped from a balloon at a height of m. Find the highest point reached by the ball and the time of flight.

Engineering Mathematics by Besavilla.pdf

Determine the velocity with which the ball hits the ground and the height of the window above the ground level. A ball is dropped freely from a balloon at a height m. If the balloon is rising Find the highest point reached by the ball and the velocity of the ball as it strikes the ground. How far does the automobile move while its speed increases uniformly from 15 kph to 45 kph in 20 sec? An automobile is moving at 20 kph and accelerates at 0. Compute the distance traveled by the car at the end of 45 sec.

How long will it take for the ball to hit the ground? The ball strikes the ground 4 sec later. Determine the height of the window above the ground. A stone was dropped freely from a balloon at a height of m above the ground. Determine the velocity of the stone at it hits the ground.

Find the velocity and the position of the ball above the ground after 5 seconds. Determine the velocity and the time that it strikes the ground. Find the velocity of the ball at a height of 40 m above the ground. Determine the height of the ball after 2 seconds. What would be the velocity of the ball after 8 seconds? How long will it take for the projectile to hit the ground surface?

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A solid homogenous circular cylinder and a solid homogenous sphere are placed at equal distances from the end of an inclined plane.

Assuming that no slipping occurs as the two bodies roll down the plane, which of them will reach the end of the plane first? Assume that they have the same weight and radius. Determine the minimum value of the coefficient of friction which will prevent slipping.

A common swing 7. Two boys each weighing N are swinging on it. How much many degrees on each side of the vertical can they swing without exceeding the designed load? A wooden block weighing 20N rests on a turn table having a radius of 2m at a distance on 1m from the center.

The coefficient of friction between the block and the turn table is 0. A ball at the end of a cord cm long is swinging with a complete vertical circle just enough velocity to keep it in the top. If the ball is released from the cord where it is at the top point of its path, where will it strike the ground cm below the center of the circle. A wooden block having a weight of 50 N is placed at a distance 1. Determine the minimum coefficient of friction of the blocks so that it will not slide.

Radius of circular platform is 3m. A 2N weight is swing in a vertical circle of 1m radius and the end of the cable will break if the tension exceeds N. Which of the following most nearly gives the angular velocity of the weight when the cable breaks? A weight is attached to a chord and forms a conical pendulum when it is rotated about the vertical axis.

If the period of rotation is 0. A ball having a weight of 4N is attached to a cord 1. Determine the rpm. A wheel is rotating at rpm. Find the maximum acceleration of a mass at the end of a 2m long string. A turbine started from rest to rpm in 6 min at a constant acceleration.

Find the number of revolution that it makes within the elapsed time. Traffic travels at 65 mph around banked highway curved with a radius of feet.

What banking angle is necessary such that friction will not be required to resist the centrifugal force? The rated speed of a highway curve of 60m radius of 50 kph. If the coefficient of friction between the tires and the road is 0. What is the rotational kinetic energy? An automobile travels on a perfectly horizontal, unbanked circular track of radius R. The coefficient of friction between the tires and the track is 0.

At what speed will skidding impend if the coefficient of friction is 0. A child places a picnic basket on the outer rim of merry go round that has a radius of 4.

How large must the coefficient of static friction be for the basket to stay on the merry go round? The car travels and additional 21 m before coming to rest. What coefficient of friction is assumed in this calculation? A point on the rim of a rotating flywheel changes its speed its speed from 1. The angular speed of a rotating flywheel a radius of 0. Compute the value of its normal acceleration and the tangential speed.

Compute the normal acceleration. What force of friction is required to keep the car on its circular path? A rotating wheel has a radius of 2 feet and 6 inches. A point on the rim of the wheel moves 30ft in 2sec. Find the angular velocity of the wheel. A prismatic AB bar 6m long has a weight of N. It is pin connected at one end at A.

A prismatic bar weighing 25 kg is rotated horizontally about one of its ends at a speed of 2. Determine the thickness of the plank that can be penetrated by the bullet. A balikbayan box is placed on top on a flooring of a delivery truck with a coefficient of friction between the floor and the box equal to 0. If the truck moves at 60 kph, determine the distance that the truck will move before the box will stop slipping. The box weighs N. Assume resisting force of friction, to be 0. At the foot of the ramp, the motor is turned off.

How far does the car travel up the inclined before it stops? A car is running up a grade of 1 in at a speed of Neglecting friction, how far will the car have gone after 3 minutes from the point where the engine conk out?

A 70 kg man stands on a spring scale on an elevator.

During the first 2 seconds starting from rest, the scale reads 80 kg. Find the velocity of the elevator at the end of 2 seconds and the tension T in the supporting cable fro the during the acceleration period.

The total weight of the elevator, man and scale is N. A cylinder having a mass of 40 kg with a radius of 0.

Determine the magnitude and location of the horizontal force P if the coefficient of friction is 0. After it was released for 3sec, find the distance that the block has traveled assuming that there is no friction between the block and the plane. Compute also the velocity after 3 sec. If the block is initially at rest and the coefficient of friction between the inclined plane and the block is 0.

The slight melting of ice renders the surfaces frictionless; calculate the velocity of the foot of the incline. Find the apparent weight of N man standing inside the elevator during its ascent and calculate the tension in the supporting cable.

How far will it move during the third second? What force is necessary to accelerate a lbs railway electric car at the rate of 1. A freight car having a mass of 15 Mg is towed along the horizontal track. Neglect friction and the mass of the wheels. An elevator weighing lb attains an upward velocity of 16 fps in 4 sec with uniform acceleration. A block weighing N rests on a plane inclined upward to the right at slope 4 vertical to 3 horizontal.

The block is connected by a cable initially parallel to the plane passing through a pulley which is connected to another block weighing N moving vertically. The coefficient of kinetic friction between the N block and the inclined plane is 0. What is the shortest time that the truck can be bought to a stop such that the boxes do not shift? Two barges are weighing 40 kN and the other 80 kN are connected by a cable in quiet water.

Initially the barges are m apart. If friction is negligible calculate the distance moved by the 80 kN barge. Two blocks A and B weighs N and N respectively is supported by a flexible cord which passes through a frictionless pulley which is supported by a rod attached to a ceiling.

Neglecting the mass and friction of the pulley, compute the acceleration on the blocks and the tension on the rod supporting the frictionless pulley. Two 15 N weights A and B are connected by a massless string hanging over a smooth frictionless peg. If a third weight of 15N is added to A and the system is released, by how much is the force on the peg increased?

Find the force exerted by B and C by pushing to the right with an acceleration of 1. Three blocks A, B and C are placed on a horizontal frictionless surface and are connected by chords between A, B and C.

A weight 9 kN is initially suspended on a m long cable. The cable weighs 0. If the weight is then raised m how much work is done in Joules. What is the kinetic energy of lb automobile which is moving at 44 fps? After reaching the bottom of the plane, the box move at horizontal floor at distance 2m before coming to rest.

If the coefficient of friction between the box and the plane and the box and the floor is 0. Compute the coefficient of friction between the floor and the block. A car weighing 40 tons is switched to a 2 percent of upgrade with a velocity of 30 mph. A car weighing 10 kN is towed along a horizontal surface at a uniform velocity of 80 kph. The towing cable is parallel with the road surface.

When the car is at foot of an incline as shown having an elevation of 30m, the towing cable was suddenly cut. At what elevation in the inclined road will the car stop in its upward motion?

The block shown starting from rest and moves towards the right. What is the velocity of block B as it touches the ground? How far will block A travel if the coefficient of friction between block A and the surface is 0. Assume pulley to be frictionless. A 10 kg block is raised vertically 3 meters.

What is the change in potential energy? Answer in SI units closest to: If the car is allowed to run back what velocity will it have at the foot of the grade? A ton train is accelerated from rest to a velocity of 30 miles per hour on a level track. How much useful work was done? A drop hammer weighing 40 kN is dropped freely and drives a concrete pile mm into the ground.

What is the average resistance of the soil in kN? The block is pushed 2 feet horizontally. What is the work done by this force?

Engineering Mathematics Vol. 1 by Gillesania_1

A small rocket propelled test vehicle with a total mass of kg starts from rest at A and moves with negligible friction along the track in the vertical plane as shown. If the propelling rocket exerts a constant thrust T of 1. The loss of mass due to the expulsion of gases by the rocket is small and may be neglected. If the maximum compression of the spring is mm, what is the value of W? Disregard the mass of spring. A N weight falls from rest from a height of mm and strikes a spring which compresses by mm.

Compute the value of the spring constant, neglecting the mass of the spring. Compute the value of h is meter. A block weighing N is dropped from a height of 1. What velocity will the block have at the instant the spring is deformed mm? Find the maximum deflection of the spring.

Compute the store energy of the spring in N-m. As the crate slides 3. Determine the horse power developed by the train. An elevator has an empty weight of N. It is designed to carry a maximum load of 20 passengers from the ground floor to the 25 th floor of the building in a time of 18 seconds. Assuming the average weight of the passenger to be N.

An engine hoist 1. If concrete weighs A train weighs 15 kN. An engine having a 40 hp rating is used as an engine hoist to lift a certain weight of height 8 m. Determine the maximum weight it could lift in a period of 20 sec.

Compute the coefficient of restitution. If the coefficient of restitution is 0. How high above the ground will the ball strike if the coefficient of restitution is 0. They collide and are coupled during impact. Neglecting friction due to skidding, determine their final common velocity and the gain or loss in kinetic energy after impact. If the boat weighs kg, what is the velocity of the boat when the man comes to rest relative to the boat?

Compute the value of coefficient of restitution. The weight of car A is 14 tons and of car B is 10 tons. Determine the velocities of the car after impact assuming that the bumpers got locked after impact. Both cars are moving in the same direction to the right. Two cars A and B have weights equal to 12 tons and 8 tons respectively are moving in opposite directions. Two cars bumped each other. Determine the velocity of the cars after impact assuming the bumpers get locked.

A N drop hammer falling freely trough a height of 0. Assuming the hammer and the pile to cling together after the impact, determine the average resistance to penetration of the pile. Two identical balls collide as shown. They collide head on and stick together. Their velocity after collision is: A bullet weighing 0.

To what angle from the vertical will the block and embedded bullet swing? If the block is moved a distance mm along the surface, what was the velocity of the bullet before striking? A 60 ton rail car moving at 1 mile per hour is instantaneously coupled to a stationary 40 to rail car. What is the speed of the coupled cars? What momentum does a 40 lbm projectile posses if the projectile is moving mph? A kg block is in contact with a level of coefficient of kinetic friction is 0.

If the 50 kg is then removed, hos much longer will the block continue to move? Determine the mass of the body if coefficient of restitution is 0. A wood block weighing Assume that the bullet remains inside the block. The system is used to determine experimentally the coefficient of restitution.

Weight of A is N while that of b is N. The ball A and B are attached to stiff rods of negligible weight. Ball A is released from rest and allowed to strike B. If the impact lasts for 0. Mass of A is 15kg and that of B is 10kg. A N block is in contact with a level plane whose coefficient of kinetic friction is 0. If the block is acted upon a horizontal force of N, at what time will elapse before the block reaches a velocity of How much longer will the block continue to move?

For how long will the body moves before it stops? A N block is resting on an incline plane whose slope is 3 vertical to 4 horizontal. Coefficient of friction between the block and the plane is 0.

The 9kg block is moving to the right with a velocity of 0. A 50kg block initially at rest is acted upon by a force P which varies as shown. Knowing the coefficient of kinetic friction between the block and the horizontal surface is 0. The motion of the block starting from rest is governed by the a-t curve shown. Determine the velocity and distance traveled after 9 sec.

Neglecting friction. From the V-t curve shown compute the distance traveled by a car starting form rest after 6 sec. A bullet weighing 50g is fired into a block of wood weighing 20 lbs on a top of a horizontal table. The block moves 45 cm. What is the speed of the bullet in kph before hitting the block?

Assume that the bullet is embedded of the block. Compute the velocity of the block 2 s after it has started from rest. Find the rate of interest. It is the practice of almost all banks in the Philippines that when they grant a loan, the interest the interest for one year is automatically deducted from the principal amount upon release of money to a borrower.

Since you have to pay the amount of P80 in one year after, what then will be the effective interest rate? He received from the bank P1 and promised to pay P1 at the end of 9 months.

A man borrowed from a bank with a promissory note that he signed in the amount of P for a period of one year. He received only the amount of P21, after the bank collected the interest and additional amount of P85 00 for notarial and inspection fees. What was the rate of interest that the bank collected in advance? The corporation will accept a promissory note for P20 non-interest for days.

If discounted at once, find the proceeds on the note. P18 b. P19 c. P18 d. P18 How much wil be due at the end of 75 days? Almagro made a money market of P1 for 30 days at 7. P3 b. P4 c. P6 d. P5 What is the highest rate, simple interest at which the downloader can afford to borrow money in order to take advantage of the discount? In downloading a computer disk, the downloader was offered the options of paying P cash at the end of 30 days or P at the end of days. At what rate is the downloader paying simple interest if he agree to pay at the end of days.

On March 1, Mr. Almagro obtains a loan of P from Mr. On March 15, , Mr. What does he receive? P 2 P1 A deposit of P was made for 31 days. Find the rate of return annually.

P46 b. P44 c. P46 d. P45 A man borrowed P from a bank and promises to pay the amount for one year. He received only the amount of P after the bank collected an advance interest of P What was the rate of discount and the rate of interest that the bank collected in advance. The amount of P12 in 4yrs.

P 14 P 15 P 16 He signs a promissory note promising to pay P per month at the end of 4th, 6th, and 7th months respectively.

Determine the amount of money that he received from the bank. What is the accumulated amount of P10 after 10 years? P13 By the condition of a will, the sum of P is left to a girl to be held in thrust fund by her guardian until it amounts to P50 A man expects to receive P25 in 8 years. Compute the compounded interest after 4 years and 9 months.

P was deposited for a period of 4 years and 6 months and bears on interest of P85 What is the rate of interest if it is compounded quarterly? If the sum now is P A man wishes to have P40 in a certain fund at the end of 8years. P24 P36 P28 P30 What is the nominal rate of interest compounded continuously for 10 years if the compounded amount factor is equal to 1. American Express Corp. Compute the effective rate of interest. What is the nominal rate of interest compounded continuously for 8 years if the pre4sent worth factor is equal to 0.

What is the difference of the amount 3 yrs. P50 If a sum of money triples in a certain period of time at a given rate of interest, compute the value of the single payment present worth factor. If the single payment amount factor for a period of 5 years is 1. What is the nearest value of the interest rate? If the single payment present worth factor for a period of 8 years is 0. Which of these gives the lowest effective rate of interest?

It takes Find the value of x. Compute the value of x. If it takes the money up to quadruple in Fifteen years ago P was deposited in a bank account an today it is worth P The bank pays semi-annually.

Engineering Mathematics Vol. 1 by Gillesania_1

What was the interest rate paid on this account? You borrow P for one year from a friend at an interest rate of 1. Compare how much money you will save or lose on the transaction. You will pay P more than if you borrowed from the bank b. You will save P55 by borrowing from your friend c. Find the angular velocity of a flywheel whose radius is 20 ft. Find the area of parabolic segment whose base is 10 and height of 9 meters.

A line which a curve approach infinity but will never intersect. An organization that aims to block the entry of a new comer. They differ by 4. Find the number. Assuming the earth to be a sphere of radius 6. Compute the mass of the earth. A material has a modulus of elasticity of GPa. Find the minimum cross sectional area of the said material so as not to elongate by more than 5mm for every 2m length when subjected to 10 kN tensile force.With the addition of the new machines the company could boosts its yearly production to units.

What is its min.

What is the allowable error in measuring the edge of a cube that is intended to hold a cu m, if the error in the computed volume is not to exceed 0.

P1 Find the derivative of 4 arc tan 2x. P6 d. The coefficient of friction between the rope and the cast-steel mooring bit is 0. P45 If the coefficient of static friction between the supporting surfaces and the ends of the poles is 0. Formerly, for a package to go by parcel post, the sum of its length and girth could not exceed cm.

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