Karina uses the system of equations below to compare the monthly utility costs in July and December for electricity, x, and natural gas, y. x + 17y = x + 30y = Karina solves the system using linear combination and arrives at the equation y = She then solves this equation for y. Which statement explains Karina's. A Cepheid star is a type of variable star, which means its brightness is not constant. The relationship between the brightness of a Cepheid star and its period, or length of its pulse, is given by M = (log P) - , where M is the absolute magnitude, or brightness, of the star, and P is the number of days required for the star to complete one cycle.
The best ways is to study thermodynamics is through problems, you must know how to apply theoretical concepts through problems and to do so you must solve these problems. Every effort has been made to see that there ths no solutiob typographical or otherwise in the material presented. However, it is still possible that there are a few errors serious or otherwise. Microscopic thermodynamics or statistical thermodynamics Macroscopic thermodynamics or classical thermodynamics A quasi-static process is also called a reversible process.
Intensive and Extensive Properties Intensive property: Whose value is independent of the size or extent i. Extensive property: Whose value depends on the size or extent i. If mass is increased, the value of extensive property also increases. Specific property: It is a special case of an intensive property.
It is the value of an extensive property per unit mass of system. Lower case letters as symbols e. Concept of Continuum The concept of continuum is a kind of idealization of the iz description of matter where wbat properties of the matter are considered as continuous functions of space variables.
Whar any matter is composed of several molecules, the concept of continuum assumes a continuous distribution of mass within the matter or system with no empty space, instead of the actual conglomeration of separate molecules. Describing a fluid flow quantitatively makes it necessary to assume that flow variables pressure, velocity etc. Mathematical descriptions of flow on this basis have proved to be reliable and treatment of fluid medium as a continuum has firmly become established.
One of the factors considered important in determining the validity of continuum model is molecular density. It is calculated by finding statistical average distance the molecules travel between two successive collisions.
If the mean free path is very small as compared with some characteristic length in the flow domain i. If the mean free path is large in comparison to some characteristic length, the gas cannot be considered continuous and it should be analyzed by the molecular theory. It describes the degree of departure from continuum. In this, Kn is always less than 0. Other factor which checks the validity of continuum is the elapsed time between collisions. The time should be small enough so that the random statistical description of molecular activity holds good.
In continuum approach, fluid properties such as density, viscosity, thermal conductivity, temperature, etc. A pump discharges a liquid into a drum at what is a spaghetti western rate of 0.
The drum, 1. Find the density of the liquid and the mass flow rate of the liquid handled by the pump. If an aeroplane weighs 90, N at sea level, what is the gravity force upon it at 10, m elevation?
What is the percentage difference from the sea-level weight? Where d is the diameter of the earth. Taking the mean diameter of the earth to be 12, km, and assuming the orbit to be circular, evaluate the value of the gravitational acceleration at this height.
The mass of the satellite is reported to have been 86 kg at sea-level. Estimate the gravitational force acting on the satellite at the operational altitude. Convert the following readings of pressure to kPa, assuming that the barometer reads mmHg: a 90 cmHg gauge b 40 cmHg vacuum c 1. What is the pressure at the base of the column. The acceleration due to gravity is constant at 9. What is the depth of atmosphere necessary to produce a pressure of l.
Consider the atmosphere as a fluid column. The pressure of steam flowing in a pipeline is measured with a mercury manometer, shown in Figure.
Some steam condenses into water. Estimate the steam pressure in kPa. Take the density of mercury as A vacuum gauge mounted on a condenser reads 0. What is the absolute pressure in the condenser in kPa when the atmospheric pressure is The limiting value of the ratio of the pressure of gas at the steam point and at the triple point of water when the gas is kept at constant volume is belkw to be 1.
What is the ideal gas temperature of the steam point? In a constant volume gas thermometer the following pairs of pressure readings were taken at the boiling point of water and the boiling point of sulphur, respectively: Water b.
Sulphur b. The numbers are the gas pressures, mm Hg, each pair being taken with the same amount of gas in the thermometer, but the successive pairs being taken with different amounts of gas in the thermometer. Plot the ratio of Sb. This Page 11 of On a gas thermometer operating at zero gas pressure, i. What is the boiling point of sulphur on the gas scale, from your plot?
The resistance of a platinum wire is found to be 11, ohms at the ice point, how to backup your email Find the constants A and B in the equation. Compute the e. Suppose the e. Where a and b are constants. The values of K are found to be 1.
Determine the temperature corresponding to a reading of K equal to 2. When operating at full load under steady state conditions, the motor is switched off and the resistance of the windings, immediately measured again, is found to be 93 ohms.
Find the x attained by the coil during full load. At what temperature both the Celsius and the new temperature scale reading would be the same? A platinum wire is used as a resistance thermometer. The wire resistance was found to be 10 ohm and 16 ohm at ice point and steam point respectively, and 30 ohm at sulphur boiling point of Our aim is to give heat to what do i need for snowboarding gear system and gain work output from it.
Compute the work the pump must do upon the water in an hour just to force the water into the tank against the pressure. Sketch the system upon which the work is done before and after the process.
The piston of an oil engine, of area 0. The pressure in the cylinder is uniform during the process at 80 kPa, while the atmospheric pressure is Estimate the displacement work done by the air finally in the cylinder. An engine cylinder has a piston of area 0.
The what is a bats predator expands according to a process which is represented by a straight line on a pressure-volume diagram.
The final pressure is 0. Calculate the work done by the gas on the piston if the stroke is 0. A mass of what is the solution to the inequality below x2 36. The initial niequality of air is 1. Find the work done by the piston to compress the air. A mass of gas is compressed in solutuon quasi-static process from 80 kPa, 0. A single-cylinder, double-acting, reciprocating water pump has an indicator diagram which is a rectangle 0.
The indicator spring constant is MPa per m. The pump runs at 50 rpm. The pump cylinder diameter is 0. Find the rate in kW at niequality the nelow does work on the water. A single-cylinder, single-acting, 4 stroke engine of 0.
The length of the indicator diagram is 0. A six-cylinder, 4-stroke gasoline engine is run at a thf of RPM. The area of the indicator card of one cylinder is 2. The bore of the cylinders is mm and the piston stroke is mm. Determine the indicated power, assuming that each cylinder contributes an equal power. A closed cylinder of 0. The volume on the other side of the piston is evacuated. A helical spring is mounted coaxially with the cylinder in this evacuated space to give a force of N on the piston in this position.
The catch is released and the piston travels along the cylinder until it comes to rest after a stroke of 1. Tye piston is then held in how to get a siamese cat to stop meowing position of maximum travel by a ratchet mechanism. The spring force increases linearly with the piston displacement to a final value of 5 kN. Inequakity the work done by the compressed air on the piston. The turbine speed is rpm. Determine a the torque developed by the turbine, b the power delivered to the propeller shaft, and c the net rate of working of the reduction gear.
A fluid, contained in a horizontal cylinder fitted with a frictionless leak proof piston, is continuously agitated by means of a stirrer passing through the cylinder cover.
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Jan 01, · Solution Manual for: Linear Algebra by Gilbert Strang. Hafiz Hamza. Download PDF. Download Full PDF Package. This paper. A short summary of this paper. 7 Full PDFs related to this paper. READ PAPER. Solution Manual for: Linear Algebra by Gilbert Strang. Download. Jul 18, · Write the equation in the form kx 2. x2 – 16 = 0 x2 – 16 + 16 = 0 + 16 x2 = 16 Since 16 is greater than 0, then the first property above can be applied to find the values of x that will make the equation x2 – 16 = 0 true. x2 = 16 16 x x = ±4 To check, substitute these values in the original equation. Mar 04, · If the inequality is of ">=" type, we use concave over-estimators (or you can just multiply the inequality by -1). McCormick's original paper (from ) explains this very well. So does this paper.
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The publisher and authors do not represent nor claim ownership over them. Published by the Department of Education Secretary: Br. Armin A. Ocampo, Ph. Have you ever realized that these quantities can be mathematically represented to come up with practical decisions?
Find out the answers to these questions and determine the vast applications of quadratic equations and quadratic inequalities through this module. Choose the letter that you think best answers the question. Please answer all items. Take note of the items that you were not able to answer correctly and find the right answer as you go through this module. Linear Equation C. Quadratic Equation B. Linear Inequality D. Quadratic Inequality 2. Which of the following is a quadratic equation?
Which of the following rational algebraic equations is transformable to a quadratic equation? The roots of a quadratic equation are -5 and 3. Which of the following quadratic equations has these roots? Which of the following mathematical statements is a quadratic inequality? I and II B. I and III D. Which of the following quadratic equations has no real roots?
What is the nature of the roots of the quadratic equation if the value of its discriminant is zero? The roots are not real. The roots are rational and not equal. The roots are irrational and not equal. The roots are rational and equal. What is the other root? Which of the following quadratic equations can be solved easily by extracting square roots? A 3 cm by 3 cm square piece of cardboard was cut from a bigger square cardboard. The area of the remaining cardboard was 40 cm2.
If s represents the length of the bigger cardboard, which of the following expressions give the area of the remaining piece? The length of a wall is 12 m more than its width. If the area of the wall is less than 50 m2, which of the following could be its length? The length of a garden is 5 m longer than its width and the area is 14 m2.
How long is the garden? A car travels 20 kph faster than a truck. The car covers km in two hours less than the time it takes the truck to travel the same distance. How fast does the car travel? A 12 cm by 16 cm picture is mounted with border of uniform width on a rectangular frame. If the total area of the border is cm2, what is the length of the side of the frame? Suppose the length of the screen of the larger TV is 6 inches longer than its width and the area of the smaller TV is square inches.
I and III C. It takes Mary 3 hours more to do a job than it takes Jane. If they work together, they can finish the same job in 2 hours.
How long would it take Mary to finish the job alone? An open box is to be formed out of a rectangular piece of cardboard whose length is 12 cm longer than its width.
To form the box, a square of side 5 cm will be removed from each corner of the cardboard. Then the edges of the remaining cardboard will be turned up. If the box is to hold at most cm3, what mathematical statement would represent the given situation? The length of a garden is 2 m more than twice its width and its area is 24 m2. Which of the following equations represents the given situation? Which of the following is true about the solution set of the inequality? The coordinates of all points on the shaded region belong to the solution set of the inequality.
The coordinates of all points along the parabola as shown by the broken line belong to the solution set of the inequality. The coordinates of all points along the parabola as shown by the broken line do not belong to the solution set of the inequality.
From through , the average weekly income of an employee in a certain company is estimated by the quadratic expression In what year was the average weekly income of an employee equal to Php2, In the figure below, the area of the shaded region is cm2. What is the length of the longer side of the figure? Villareal was asked by her principal to transfer her Grade 9 class to a new classroom that was recently built. To help her acquire these fixtures, she informed the parents of her students about these classroom needs.
The parents decided to donate construction materials such as wood, plywood, nails, paints, and many others. After all the materials have been received, she asked her students to make the designs of the different classroom needs. Each group of students was assigned to do the design of a particular fixture.