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Find dy/dx if y = 2t1/3 – 3t1/2 + 1 and t = cos (x – π/6) when x = π/2.
Find the second derivative of y = (2x-1)2 + x3 .
Find the point of inflection of the curve y = x3 – 3x2 + 8.
Determine the maximum perimeter of a right triangle whose hypotenuse is 6 m long.
Find the approximate increase in surface area of the sphere using differentials, if the radius increases from 2 to 2.05.
Find the length of arc of the curve y = ln cos x from x = 0 to x = π/6.
Find the volume generated by revolving an ellipse whose equation is 4x2 + 9y2 = 36 about the line 3x + 4y = 30.
The integral of (3)4x dx is ____.
Find the area of the region bounded by the line x = y; x = 2; and y = 1/x2 .
The base of a solid is a circle whose radius is 4 and every plane section perpendicular to the diameter is a square. Find the volume of the solid.
Which is not part of the group?
How many ways can 4 boys and 4 girls be seated alternatively in the row of eight chairs?
How many 4-digit numbers can be formed from the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 if repetition is not allowed?
Two red books and 4 blue books are placed at random on a shelf. What is the probability that the blue books will not be together?
If 10 coins are tossed, what is the probability that it will show at most 2 “Heads”?
Three cards are drawn from a deck of 52 cards. Find the probability that all cards are of one suit.
How many committees of 3 men and 4 women can be formed from 8 men and 6 women if a particular man must not be selected?
The arithmetic mean and harmonic mean of two numbers are 5 and 3.2 respectively. Determine the geometric mean.
If the probability of a defective bolt is 0.1. Determine the standard error for a distribution of defective bolts in a total of 400.
If the probability of a defective bolt is 0.1. For a confidence level of 95%, determine the margin of error for a distribution of defective bolts in a total of 400
A 5 H coil whose resistance is 10 Ω is connected in series with a 30 Ω resistor and to a 120 V battery and a switch. The switch is closed at t = 0 second. Determine the voltage drop across the 30 Ω at t = 0.2 second
Solve for (D3 + 4D) y = 0
A 40 Ω resistance and a 250 μF capacitor are connected in series and to a 120 V battery and a switch. The switch is closed at t = 0 second. Determine the voltage across the resistor at t = 0.015 second.
Find the differential equation whose general solution is y = c1e-3x + c2 x e-3x
A ship weighing 30,000,000 kg starts from rest. Assuming that the resistance in kg to motion is 1000v, where v is the speed in m/s, and the thrust of the ship by the propeller is 15,000 kg, determine the limiting speed.
Determine the differential equation for the orthogonal trajectories of the family of curve x2 + y2 = C2
Find the differential equation of the family of parabolas having their vertices at the origin and their foci on the x-axis
Determine the Laplace transform of the function f(t) = 1- te-t .
A 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 At what rate did people contract the disease after three weeks in people per week?
A nuclear power plant meltdown that initiated from the routine maintenance of a reactor.
An employee obtained a loan of P 10,000 at the rate of 6 % compounded annually in order to repair a house. How much must he pay monthly to amortize the loan within a period of 10 years?
Ralph wishes to have P35,000 when he retires 15 years from now. If he can expect to receive 4% annual interest, how much he set aside in each of 15 equal annual beginning of year deposits?
Calculate the present value of series of twenty-five equal annual payments of Php 5,000.00 starting five years from today. Assume an effective interest rate of 6%.
Given that the discount rate is 15%, what is the equivalent uniform annual cash flow of the following stream of cash flows?
Year 0 ——–P100,000
Year 1 ——–P200,000
Year 2 ——–P50,000
Year 3 ——–P75,000
A man inherit a regular endowment of P100,000 every end of 3 months for X years. However he may choose to get a single lump of P3,702,969.8 at the end of 4 years. If the rate of interest was 14% compounded quarterly, what is the value of X
A machine costs P 8,000.00 and an estimated life of 10 years with salvage value of P500.00. What is its book value after 8 years using straight- line method?
What is the book value of an equipment purchased three years ago for P 15,000 if it is Depreciated using the sum of the years digit method? The expected life is 5 years.
A machine costing P45,000 is estimated to have a salvage value of P4,350 when retired at the end of 6 yrs. Depreciation cost is computed using a constant percentage of the declining book value. What is the annual rate of depreciation in %?
A copying machine has a useful life of 3 years and a salvage value of P 20,000 was brought for P 135,000. If the owner decides to sell after using it for 2 years, how much should the selling price be so that he will not lose or gain, if the gain of the interest is 5%. (Hint: Apply the Sinking Fund method).
Karbate is
Which of the following unit processes is essential in the manufacture of commercial explosives and military high explosives?
A 20% aqueous solution of Na2CO3 and 25% aqueous solution of Ca(OH)2 were reacted to produce caustic soda solution. The precipitate which formed was analyzed to contain 5% H2O, 1% NaOH, 94% CaCO3. The concentration of NaOH solution produced is _________.
The carbonating tower used in Solvay Process of soda ash manufacture is made of
When phosphorus trichloride PCl3(l) reacts with water, the products are
Aluminum does not corrode as does iron, because
What is the purpose of a converter in steel production?
Phosphoric acid is the most important of the phosphorus oxoacids. Industrially, phosphoric acid is prepared by
Why is either pure oxygen or oxygen diluted with argon used in a converter instead of air?
Which of the following statements is false?
Stalagmometer is used for the measurement of ___________.
Shell and tube pass heat exchanger is an example of _________ parameter system
Dilatometer is used to measure
Starting temperature of optical radiation pyrometer.
Heat input in case of a water heater is __________ variable
The level of a liquid under pressure can be determined using
Laplace transform of a ramp input of slope K is
The time difference by which the output of a P-D controller leads the input when the input changes linearly with time.
Mode used for transmitting signal for one kilometer distance
Continuous measurement of moisture content of paper in paper industry is done by measuring
PRC stands for
The new intellectual property code is
RA 8293 is
The new IP code follows the
A trademark can be registered if it consists of the flag or coat of arms or other insignia of the Philippines or any of its political subdivisions or of any foreign nation.
The reproduction of one back up copy of a computer program is permitted without the authorization of the owner of copyright, by the lawful owner of the computer program
Why should we support the code of ethics?
National Pollution Control Commission (NPCC) has been abolished and were replaced by Environmental Management Bureau under
Republic Act No. 8749 as known as Clean Air Act of 1999 banned the use of leaded gasoline which contain toxic component called
The person who uses the invention for profit without permission from the inventor is called
Determine the max shearing stress in a helical spring with 20mm diameter wire and mean radius of 8 cm if it supports 2kN of load.
The maximum stress to which a material maybe subjected without the occurrence of permanent strain remaining upon the complete release to stress.
A golf leaves the golf club at an angle of 60°above the horizontal reference with a velocity of 25 m/s. How high does it go?
What is the highest ordinate of the stress-strain diagram?
This type of landfill uses the natural contour of the land.
Two cylinders having weight of 200 kN and 100 kN with radius of 100 mm and 200 mm respectively are placed with the heavier weight above the lighter weight and both of them are placed in a container having a width of 400 mm. Assuming that the lengths of the container and the cylinders to be the same, what is the reaction between the cylinders.
The reciprocal of bulk modulus of any fluid is called _____.
A car starts from rest and has a constant acceleration of ft/s². Find the average velocity during the first 10 seconds of motion.
The diagram of an isolated body with the representation of all external forces acting on it.
A car tire is 30 inches in diameter. How fast in rpm does the wheel turn on the axle when the automobile maintains a speed of 30 mph?
The siren of a fire engine has a frequency of 500 Hz. If the fire engine approaches a stationary car at 20 m/s, what frequency does a person in a car hear?
A 600-N block rests on a 30° plane. If the coefficient of static friction is 0.30, what is the magnitude of a force applied horizontally to the block just to prevent the block from sliding down the plane?
A man standing 3360 ft from a high cliff hits a tree stump with an axe, and hears the faint echo 6.4 s later. What is the velocity of sound in the air that day?
A body of mass 10 kg slides down a frictionless plane inclined at 37° with the horizontal. Find its acceleration.
Which of the following does NOT contain a unit of length?
A mild steel column is hollow and circular in cross section with an external diameter of 350 mm and internal diameter of 300 mm. It carries a compressive axial load of 2000 kN. What is the corresponding strain of the column? Modulus of elasticity = 200 GPa.
It is the highest ordinate on the stress-strain curve.
This equation establishes a mathematical relationship among the moments at any three consecutive supports of a continuous beam.
Compute the nominal shear stress at the surface in MPa for a 40-mm diameter shaft that transmits 750 kW at 1500 rpm. Axial and bending loads are assumed negligible.
The maximum stress to which a material maybe subjected without the occurrence of permanent strain remaining upon the complete release to stress
A baseball diamond is a square whose sides are 90 ft long. If a batter hits a ball and runs to the first base at the rate of 20 ft/s. How fast is his distance from the second base changing at the instant when he has run 50 ft?
It is a charge neutralization step in water treatment that involves the conditioning of the suspended, colloidal, and dissolved matter.
If your company bought supplies on credit, the transaction made can be classified based on its effect on the accounting equation as:
For the production of bath soaps, the cost of the packaging material of the bath soaps can be classify as:
The systems theory views a situation in which an accident might occur as a system comprised of components in which of the following?
Controlling hazards through better product design or process improvement is which of the Three Es of Safety?
Manager discusses the current gaps of a particular team in the business review meeting.
This chemical is used to remove carbonate hardness.