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Mackenzie L. Akbar Handbook of structural steel connection design and details E-book 1 Musy. Arthur Design of concrete structures S. Water and wastewater engineering: Open channel hydraulics. Reinforced concrete design E-book 1 Davis.

David Earthquake science and society 1 Kett. Peter Building surveys. Failed bridges: Irving Engineered concrete: Author Title Year Andre Hydrology: Kraig Construction management fundamentals. Mike Introduction to engineering ethics.

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Mark Jr. Transportation infrastructure engineering: Kumares Labi. International student ed. Jack C. P9, b. P6, c. P7, d. P10, How many machines will minimize the total cost? What market price will the expenditure be the greatest?

After how many hours will the hourly number of units be maximized? An inferior product with large advertising budget sells well when it is introduced, but sales fall as people discontinue use of the product. After how many weeks will the sales be maximized? After how many months is the proportional maximized? How many cars should be produced for a minimum cost?

After how many hours will the hourly number of units be maximized and what would be the maximum hourly output? What is the maximum productivity expected? The sum of two numbers is equal to S. Find the maximum cost from year to Find the marginal profit for a production of 50 units.

A viaduct is traversed by a truck running at 15mph at the same time that another truck traveling at a speed of 30mph on the street 22ft below and at right angle to the viaduct, approached the point directly below the viaduct from a distance of 55ft. Find the nearest distance between the trucks. What is the largest volume for the cone?

Four squares are cut out of a rectangular cardboard 50cm by 80 cm. What is the largest possible volume for such a box? An isosceles triangle with equal sides of 20cm has these sides at a variable equal angle with the base. Determine the max area of the triangle. Formerly, for a package to go by parcel post, the sum of its length and girth could not exceed cm.

Find the dimensions of the rectangular package of greatest volume that could be sent. The cross-section of a trough is an isosceles trapezoid. If the trough is made by bending up the sides of s strip of metal 12cm wide, what would be the angle of inclination of the sides and the width across the bottom if the cross-sectional area is to be a maximum?

Find the minimum amount of thin sheet that can be made into a closed cylinder having a volume of cu inches in square inches. The cost of electric energy consumed by a train per hour is directly proportional to the cube of its speed and is P per hour at 50kph. Other expenses such as salaries, depreciation, overhead, etc. Find the most economical speed of the train in kph. A businessman found out that his profit varies as the product of the amount spent for production and the square root of the amount spent for advertisement.

If his total budget for these expenses is P1. A steel girder 16m long is moved on rollers along a passageway 8m wide and into a corridor at right angles with the passageway. Neglecting the width of thr girder, how wide must the corridor be? A can manufacturer receives an order for milk cans having a capacity of cu cm. Each can is made from a rectangular sheet of metal by rolling the sheet into a cylinder; the lids are stamped out from another rectangular sheet.

What are the most economical proportions of the can? A triangle has a variable sides x, y and z subject to the constraint that the perimeter P is fixed to 18cm. What is the maximum possible area for the triangle? Postal regulations require that a parcel post package shall be not greater than cm in the sum of its length and girth perimeter of the cross-section. What is the volume in cu cm of the largest package allowed by the postal regulations if the package is to be rectangular in cu cm?

Divide 60 into 3 parts so that the product of the three parts will be a maximum, find the product. Find the radius of the circle inscribe in a triangle having a max area of The area of a circle inscribe in a triangle is equal to Find the max area of the triangle.

Find the perimeter of a triangle having a max area that is circumscribing a circle of radius 8cm. If the production of the commodity this year is units and the production is increasing at the rate and the production is increasing at the rate of units per year, what is the current rate at which the labor force should be increased? Sugar juice is filtering through a conical funnel 20cm, deep and 12cm across top, into a cylindrical container whose diameter is 10cm.

When the depth of the juice in the funnel is 10cm, determine the rate at which its level in the cylinder is rising. An airplane, flying horizontally at an altitude of 1km, passes directly over an observer. If the constant speed of the plane is kph, how fast is its distance from the observer increasing 30seconds later?

A metal disk expands during heating. If its radius increases at the rate of 20 mm per second, how fast is the area of one of its faces increasing when its radius is 8. The structural steel work of a new office building is finished. Across the street 20m from the ground floor of the freight elevator shaft in the building, a spectator is standing and watching the freight elevator ascend at a constant rate of 5 meters per second.

How far is the distance between the boy and the automobile changing when the boy is 6m, past the point directly over the path of the automobile and the automobile is 8m past the point directly under the path of the boy? How fast is the abscissa changing when the ordinate is 4? An air traffic controller spots two planes at the same altitude converging on a point as they fly at right angles to one another.

One plane is miles from the point and is moving at mph. The other plane is miles from the point and has the speed of mph. How much time does the traffic controller have to get one of the planes on a different flight path? Find the rate of the LRT train and the car are separating one second later. A street light is 8m from a wall and 4m from a point along the path leading to the shadow of the man 1.

The man walks towards the wall at the rate of 0. A mercury light hangs 12 ft above the island at the center of Ayala Avenue whish is 24 ft wide. A cigarette vendor 5ft tall walks along the curb of the street at a speed of fpm. How fast is the tip of the shadow of the cigarette vendor moving at the same instant? Water is the flowing into a conical vessel 15cm deep and having a radius of 3. Two sides of a triangle are 5 and 8 units respectively.

If the included angle is changing at the rate of one radian pr second, at what rate is the third side changing when the included angle is 60 degrees?

The two adjacent sides of a triangle are 5 and 8 meters respectively. A triangular trough is 12m long, 2m wide at the top and 2m deep. If water flows in at the rate of 12 cu m per min, find how fast the surface is rising when the water is 1m deep.

An observer is stationed at a point on the track directly opposite the starting point and collinear with the center of the circular track. A plane ft from the earth is flying east at the rate of mph. It passes directly over a car also going east at 60mph. How fast are they separating when the distance between them is ft? A horseman gallops along the straight shore of a sea at the rate of 30mph.

A battleship anchored 3 miles offshore keeps searchlight trained on him as he moved along. Find the rate of rotation of the light when the horseman is 2 miles down the beach? The water surface is rising at the rate of 0. What is the diameter of the tank? Find the rate of change of the surface area when the radius is 6cm. How fast is the volume changing when each edge is 10cm long? How fast is the radius of the balloon changing at the instant the radius is 2cm? Find the rate of change of its volume when the radius is 4cm and its altitude is 6cm.

Find the rate of change of its diagonal when each edge is 10cm long. Determine the rate of change of the circumference when the radius is 6cm. When a squares of side x are cut from the corners of a 12cm square piece of cardboard, an open top box can be formed by folding up the sides. As x increases uniformly at the rate of 0. A trough 10m long has as it ends isosceles trapezoids, altitude 2m, lower base, 2m upper base 3m. An object is dropped freely from a bldg.

An observer at a horizontal distance of 30m from a bldg is observing the object is it was dropped. Determine the rate at which the distance between the object and the observer is changing after 2sec.

Car A moves due east at 30kph at the same instant car B is moving S 30deg E. The distance from A to B is 30km. Find how fast is the speed between them are separating after one hour. The upper radius of the frustum of a cone is 1. If the water rises at the rate of 0. Water is flowing into a conical vessel 18 cm deep and 10 cm across the top. If the rate at which the water surface is rising is The base of the cone is approximately twice the altitude.

Find the height of the pile if the height of he pile is changing at the rate of 0. A company is increasing its production of a certain product at the rate of units per month. Find the rate of change of the revenue with respect to time in months when the monthly production is A machine is rolling a metal cylinder under pressure.

The radius of the cylinder is decreasing at the rate of 0. At what rate is the length h changing when the radius is 2. Two sides of a triangle are 15cm and 20cm long respectively. Two sides of a triangle are 30cm and 40cm respectively. Find the vertical component of the velocity at the point 1,2. The acceleration of the vehicle at any point of the trajectory is a vector having magnitude and direction.

The search light of a lighthouse which is positioned 2km from the shoreline is tracking a car which is traveling at a constant speed along the shore. If the searchlight is rotating at the rate of 0. A light is at the top of a pole 80 ft high.

A ball is dropped at the same height from a point 20 ft from the light. An airplane is flying at a constant speed at an altitude of ft on a line that will take it directly over an observer on the ground.

Find the speed of the airplane. A horizontal trough is 16 m long and its ends are isosceles trapezoids with an altitude of 4m lower base of 4m and an upper base of 6m. What is the length of the sides if the area is increasing at the rate of The two adjacent sides of a triangle are 6m and 8m respectively. Water is pouring into a swimming pool. What is the angular velocity of the wheel?

At what extreme rates in fps is P moving along the curve? At the instant the bomb was dropped, the angle of depression of the target is 45 degrees and is increasing at the rate of 0. Determine the value of h. Glycerine is flowing into a conical vessel 18cm deep and 10 cm across the top at the rate of 4 cu cm per min.

The deep of glyerine is h cm. If the rate which the surface is rising is 0. When the water is h cm deep, the water level is rising at the rate of 0. What is the value of h? A train, starting noon, travels north at 40 mph. Another train starting from the same pint at 2pm travels east at 50mph. How fast are the two trains separating at 3pm? An automobile is traveling at 30 fps towards north is approaching an intersection. When the automobile is ft from the intersection, a truck traveling at 40fps towards east is 60ft from the same intersection.

The automobile and the truck are on the roads that are at right angles to each other. How fast are they separating after 6 sec? Another train starting from the same point at 2pm travels east at 50 mph. How fast are the trains separating after a long time? At noon a car drives from A towards the east at 60mph. Another car starts from B towards A at 30 mph. B has a direction and distance of N 30 degrees east and 42m respectively from A. Find the time when the cars will be nearest each other.

A ferris wheel 15 m in diameter makes 1 rev every 2 min. If the center of the wheel is 9m above the ground, how many fast is a passenger in the wheel moving vertically when he is A bomber plane, flying horizontally 3. When the angle is 30 degrees, what is the speed of the plane in mph? Two railroad tracks are perpendicular to each other. At 12pm there is a train at each track was approaching the crossing at 50kph, one being km the other km away from the crossing.

How fast in kph is the distance between the two trains changing at 4pm? Find the maximum height to which the ball will rise if S is expressed in meters and t in seconds.

Find the equation of the curve whose slope is 4x-5 and passing through 3,1. The point 3,2 is on a curve and at any point x,y on the curve the tangent line has a slope equal to 2x A rectangular lot has an area of sq m.

Find the least amount of fence that could be used to enclose the area. A student club on a college campus charges annual membership due of P10, less 5 centavos for each member over How many members would give the club the most revenue from annual dues? A company estimates that it can sell units per weak if it sets the unit price at P3. Find the number of units sold each week and its unit price per max revenue. Determine the production level that will produce the max profit and what would this profit be?

ABC company manufactures computer spare parts. With its present machines, it has an output of units annually. With the addition of the new machines the company could boosts its yearly production to units. What production level maximizes total yearly profit?

The fixed monthly cost for operating a manufacturing plant that makes transformers is P and there are direct costs of P for each unit produced. The manufacturer estimates that units per month can be sold if the unit price is P and that sales will in crease by 20 units for each P10 decrease in price.

Compute the number of units that must be sold per month to maximize the profit. Compute the unit price. For what number x is the average cost a minimum? Find the shortest ladder that can reach the bldg with one end resting on the ground outside the wall. If the hypotenuse of a right triangle is known, what is the relation of the base and the altitude of the right triangle when its area is maximum? The hypotenuse of a right triangle is 20cm. What is the max possible area of the triangle in sq cm?

A rectangular field has an area of 10, sq m. What is the least amount of fencing meters to enclose it? A monthly overhead of a manufacturer of a certain commodity is P and the cost of material is P1. If not more than units are manufactured per month, labor cost is P0. The manufacturer can sell units per month at P7. Find the number of units that should be produced each month for maximum profit.

Find two numbers whose product is m and whose sum is minimum. Find two numbers whose sum is 36 if the product of one by the square of the other is a maximum. Find the minimum amount of thin sheet that can be made into a closed cylinder having a volume of cu in.

A downloader is to take a plot of land fronting street, the plot is to be rectangular and three times its frontage added to twice its depth is to be 96 meters. What is the greatest number of sq m be may take? If the fixed cost is pesos, what is the cost of producing 15 units? A pig weighing lb gains 8 pounds per day and cost 6 pesos per day to maintain. The market price for the pig is seven pesos and fifty centavos per pound but is decreasing 10 centavos per day.

When should the pig be sold? It costs a bus company P to run a bus on a certain tour, plus P15 per passenger. The capacity of the bus is 20 persons and the company charges P35 per ticket if the bus is full. For each empty seat, however, the company increases the ticket price by P2.

For maximum profit how many empty seats would the company like to see?

A book publisher prints the pages of a certain book with 0. Find the dimensions of the page that will maximize the printed area of the page if the area of the entire page is 96 sq inches. The cost of manufacturing an engine parts is P and the number which can be sold varies inversely as the fourth power of the selling price. Find the selling price which will yield the greatest total net profit.

The price of the product in a competitive market is P An entrepreneur starts new companies and sells them when their growth is maximized. If the entrepreneur wants to sell the company before profit begins to decline, after how many years would the company be sold? How many items will produce a maximum profit?

The following statistics of a manufacturing company shows the corresponding values for manufacturing x units. What maximum daily profit that the company can expect of this product? A certain unit produced by the company can be sold for What would be the corresponding price per unit in order to have a max revenue?

Find the maximum cost from the year to P9, b. P6, c. P7, d. P10, How many machines will minimize the total cost? What market price will the expenditure be the greatest? After how many hours will the hourly number of units be maximized? An inferior product with large advertising budget sells well when it is introduced, but sales fall as people discontinue use of the product. After how many weeks will the sales be maximized? After how many months is the proportional maximized?

How many cars should be produced for a minimum cost? After how many hours will the hourly number of units be maximized and what would be the maximum hourly output?

What is the maximum productivity expected? The sum of two numbers is equal to S. Find the maximum cost from year to Find the marginal profit for a production of 50 units. A viaduct is traversed by a truck running at 15mph at the same time that another truck traveling at a speed of 30mph on the street 22ft below and at right angle to the viaduct, approached the point directly below the viaduct from a distance of 55ft.

Find the nearest distance between the trucks. What is the largest volume for the cone? Four squares are cut out of a rectangular cardboard 50cm by 80 cm. What is the largest possible volume for such a box? An isosceles triangle with equal sides of 20cm has these sides at a variable equal angle with the base.

Determine the max area of the triangle. Formerly, for a package to go by parcel post, the sum of its length and girth could not exceed cm. Find the dimensions of the rectangular package of greatest volume that could be sent.

The cross-section of a trough is an isosceles trapezoid. If the trough is made by bending up the sides of s strip of metal 12cm wide, what would be the angle of inclination of the sides and the width across the bottom if the cross-sectional area is to be a maximum?

Find the minimum amount of thin sheet that can be made into a closed cylinder having a volume of cu inches in square inches. The cost of electric energy consumed by a train per hour is directly proportional to the cube of its speed and is P per hour at 50kph. Other expenses such as salaries, depreciation, overhead, etc. Find the most economical speed of the train in kph.

A businessman found out that his profit varies as the product of the amount spent for production and the square root of the amount spent for advertisement. If his total budget for these expenses is P1. A steel girder 16m long is moved on rollers along a passageway 8m wide and into a corridor at right angles with the passageway. Neglecting the width of thr girder, how wide must the corridor be? A can manufacturer receives an order for milk cans having a capacity of cu cm.

Each can is made from a rectangular sheet of metal by rolling the sheet into a cylinder; the lids are stamped out from another rectangular sheet. What are the most economical proportions of the can? A triangle has a variable sides x, y and z subject to the constraint that the perimeter P is fixed to 18cm.

What is the maximum possible area for the triangle? Postal regulations require that a parcel post package shall be not greater than cm in the sum of its length and girth perimeter of the cross-section.

What is the volume in cu cm of the largest package allowed by the postal regulations if the package is to be rectangular in cu cm? Divide 60 into 3 parts so that the product of the three parts will be a maximum, find the product. Find the radius of the circle inscribe in a triangle having a max area of The area of a circle inscribe in a triangle is equal to Find the max area of the triangle. Find the perimeter of a triangle having a max area that is circumscribing a circle of radius 8cm.

If the production of the commodity this year is units and the production is increasing at the rate and the production is increasing at the rate of units per year, what is the current rate at which the labor force should be increased?

Sugar juice is filtering through a conical funnel 20cm, deep and 12cm across top, into a cylindrical container whose diameter is 10cm.

When the depth of the juice in the funnel is 10cm, determine the rate at which its level in the cylinder is rising. An airplane, flying horizontally at an altitude of 1km, passes directly over an observer. If the constant speed of the plane is kph, how fast is its distance from the observer increasing 30seconds later? A metal disk expands during heating.

If its radius increases at the rate of 20 mm per second, how fast is the area of one of its faces increasing when its radius is 8. The structural steel work of a new office building is finished. Across the street 20m from the ground floor of the freight elevator shaft in the building, a spectator is standing and watching the freight elevator ascend at a constant rate of 5 meters per second.

How far is the distance between the boy and the automobile changing when the boy is 6m, past the point directly over the path of the automobile and the automobile is 8m past the point directly under the path of the boy?

How fast is the abscissa changing when the ordinate is 4? An air traffic controller spots two planes at the same altitude converging on a point as they fly at right angles to one another. One plane is miles from the point and is moving at mph.

The other plane is miles from the point and has the speed of mph. How much time does the traffic controller have to get one of the planes on a different flight path? Find the rate of the LRT train and the car are separating one second later. A street light is 8m from a wall and 4m from a point along the path leading to the shadow of the man 1. The man walks towards the wall at the rate of 0. A mercury light hangs 12 ft above the island at the center of Ayala Avenue whish is 24 ft wide.

A cigarette vendor 5ft tall walks along the curb of the street at a speed of fpm. How fast is the tip of the shadow of the cigarette vendor moving at the same instant?

Water is the flowing into a conical vessel 15cm deep and having a radius of 3. Two sides of a triangle are 5 and 8 units respectively. If the included angle is changing at the rate of one radian pr second, at what rate is the third side changing when the included angle is 60 degrees?

The two adjacent sides of a triangle are 5 and 8 meters respectively. A triangular trough is 12m long, 2m wide at the top and 2m deep. If water flows in at the rate of 12 cu m per min, find how fast the surface is rising when the water is 1m deep.

An observer is stationed at a point on the track directly opposite the starting point and collinear with the center of the circular track. A plane ft from the earth is flying east at the rate of mph. It passes directly over a car also going east at 60mph.

How fast are they separating when the distance between them is ft? A horseman gallops along the straight shore of a sea at the rate of 30mph. A battleship anchored 3 miles offshore keeps searchlight trained on him as he moved along. Find the rate of rotation of the light when the horseman is 2 miles down the beach?

The water surface is rising at the rate of 0. What is the diameter of the tank? Find the rate of change of the surface area when the radius is 6cm. How fast is the volume changing when each edge is 10cm long? How fast is the radius of the balloon changing at the instant the radius is 2cm?

Find the rate of change of its volume when the radius is 4cm and its altitude is 6cm. Find the rate of change of its diagonal when each edge is 10cm long.

Determine the rate of change of the circumference when the radius is 6cm. When a squares of side x are cut from the corners of a 12cm square piece of cardboard, an open top box can be formed by folding up the sides. As x increases uniformly at the rate of 0. A trough 10m long has as it ends isosceles trapezoids, altitude 2m, lower base, 2m upper base 3m.

An object is dropped freely from a bldg. An observer at a horizontal distance of 30m from a bldg is observing the object is it was dropped. Determine the rate at which the distance between the object and the observer is changing after 2sec. Car A moves due east at 30kph at the same instant car B is moving S 30deg E.

The distance from A to B is 30km. Find how fast is the speed between them are separating after one hour. The upper radius of the frustum of a cone is 1. If the water rises at the rate of 0. Water is flowing into a conical vessel 18 cm deep and 10 cm across the top.

If the rate at which the water surface is rising is The base of the cone is approximately twice the altitude.