Composed functions are useful for evaluating complex systems, but it is important to understand the range and domain of both functions to ensure that the composed form is valid.
Understanding how composed functions operate within a system is essential to understanding mathematics. Composed functions are essentially a combination of two functions, usually denoted as f(g(x)) or g(f(x)).
The domain of a composed function is the set of all possible input values from the first function, which can either be the same as the domain of the first function or a subset of it.
Similarly, the range of a composed function is the set of all possible output values from the second function, which can either be the same as the range of the second function or a subset of it.
For two functions to be composed, they must be compatible in the sense that the range of the first function is the same as the domain of the second function.
Otherwise, the composed form of the two functions would not make sense mathematically. In addition, some pairs of functions can be composed only for certain values of x, meaning that a composed function may not be valid for all possible input values.
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a small, 300 g cart is moving at 1.20 m/s on a frictionless track when it collides with a larger, 4.00 kg cart at rest. after the collision, the small cart recoils at 0.870 m/s . What is the speed of the large cart after the collision? Express your answer to three significant figures and include the appropriate units.
Answer:
The speed of the large cart after the collision is 0.0248 m/s.
Explanation:
In this example we will use the Conservation of Momentum.
The Conservation of Momentum states that the momentum of a system is remains the same if no external forces are acting on the system.
Our question is an example of a partially elastic collision.
In a partially elastic collision momentum is conserved and the 2 objects move at different speeds. Kinetic energy is not conserved.
We can come up with an equation for this situation
[tex]m_1V_{i1} +m_2V_{i2}=m_1V_{f1} +m_2V_{f2}[/tex]
Let the small cart be object 1 and let the large cart be object 2.
Convert 300 grams to kilograms.
1 kg = 1000 g
0.3 kg = 300 g
We are given
[tex]m_1=[/tex] 0.3 kg
[tex]V_{i1} =[/tex] 1.20 m/s
[tex]m_2=[/tex] 4.00 kg
[tex]V_{i2} =[/tex] 0 m/s
[tex]V_{f1} =[/tex] 0.870 m/s
Inserting our values into the equation gives us
[tex](0.3*1.2)+(4*0)=(0.3*0.870)+(4*V_{f2})[/tex]
Lets simplify and evaluate [tex]V_{f2}[/tex].
Anything multiplied by 0 is equal to 0
[tex](0.3*1.2)=(0.3*0.870)+(4*V_{f2})[/tex]
Evaluate each set of parenthesis.
[tex]0.36=0.261+4V_{f2}[/tex]
Subtract [tex]0.261[/tex] from both sides of the equation.
[tex]0.099=4V_{f2}[/tex]
Divide each side of the equation by 4.
[tex]0.02475=V_{f2}[/tex]
Round to 3 significant figures.
[tex]V_{f2} =0.0248[/tex]
The graph represents the velocity as a function of time for an object in one- dimensional motion. Identify which statement below correctly describes the motion at t = 3 S. A. The object is speeding up and the acceleration is positive. B. The object is speeding up and the acceleration is negative.
C. The object is slowing down and the acceleration is positive.
D. The object is slowing down and the acceleration is negative.
The graph shows that the velocity of the object decreases from t = 2 s to t = 3 s, indicating that the object is slowing down. D. The object is slowing down and the acceleration is negative.
The rate of change of velocity is negative, so the acceleration is also negative.
The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar quantity. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.
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using the method of joints, determine fab , fbc , and fbd , the magnitude of the force in each of the members connected to joint b. assume for your calculations that each member is in tension, and include in your response the sign of each force that you obtain by applying this assumption.
We may utilise the force equilibrium equations at joint B to find the magnitudes of fab, fbc, and fbd by assuming that each member is in tension. Since the forces are thought to be under tension, the indicators of the forces will be favourable.
First, we must count the number of unknown forces and equilibrium equations at the joint. In this instance, there are three equilibrium equations and three unknown forces (FAB, FBC, and FBD).
The following equations of equilibrium can be used, assuming that each component is under tension:
ABA - FBC = 0 (sum of forces in the x-direction)
FABsin(theta) - FBCos(theta) equals zero (sum of forces in the y-direction)
FABcos(theta), FBCsin(theta), and FBD add up to 0 (sum of moments)
Theta is the angle between AB and BC, where. The magnitude of the force in each of the members linked to joint B may be calculated by solving these equations.
There will be a positive FAB, a positive FBC, and a negative FBD.
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During the lecture, we calculated the Debye length at physiological salt concentrations and temperature, i.e. at an ionic strength of 150 mM (i.e. 0.150 mol/l) and a temperature of T=310 K. We predicted that electrostatic interactions are effectively screened beyond distances of 8.1 Å in solutions with a physiological salt concentration.1)What is the Debye length in a sample of distilled water with an ionic strength of 10.0 µM (i.e. 1.00 * 10^-5 mol/l)? Assume room temperature, i.e. T= 298 K, and provide your answer as a numerical expression with 3 significant figures in Å (1 Å = 10^-10 m).
The Debye length is calculated as λD = (1/1.00 * 10^-5 mol/l * 298 K)^(1/2) = 28.6 Å.
What is length?Length is a measure of distance between two points, usually denoted by the unit of measurement being used. It can be measured in a variety of ways, including in meters, miles, centimeters, or inches. Length can also be used to measure the size or dimensions of an object, such as the width of a table or the height of a building. Length can also be used to measure time, such as in seconds or minutes.
The Debye length in a sample of distilled water with an ionic strength of 10.0 µM is approximately 28.6 Å (2.86 * 10^-9 m). This value is calculated using the Debye-Hückel approximation, which states that the Debye length λD is equal to the square root of the inverse of the ionic strength I multiplied by the temperature T, i.e. λD = (1/I*T)^(1/2). Therefore, the Debye length is calculated as λD = (1/1.00 * 10^-5 mol/l * 298 K)^(1/2) = 28.6 Å.
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Which statement regarding correct laboratory attire is NOT correct?
A. If you have long hair, it should be pulled back and secured for lab work.
B. You should avoid loose or dangling clothing or jewelry during lab work.
C. There is no need to wash your clothes after completing lab work.
D. You should wear clothing that covers your midriff and upper legs.
E. You should wear shoes that fully cover your feet.
Following lab work, there is no need to wash your clothes. When it comes to lab attire, this statement is false.
Dress in long pants or skirts, closed-toed shoes, and long hair tied back. Wearing shorts, short skirts, sandals, baggy apparel, or jewelry that hangs loose is prohibited. 2. Lab coat: Put on an arm-covering lab coat.
When working in a lab, it's crucial to dress appropriately. To protect yourself against spilled chemical, biological, or radioactive substances, falling items, and other lab risks, dress according to the below-listed rules.
The clothing's primary function is obviously to shield us from the elements. It helps prevent wind damage and provides protection from sunburn. In the winter, it offers thermal insulation.
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air at 30,000 feet is at a temperature of -35.0 c. a sample of air was collected and the mixture is 75.56% nitrogen, 23.15% oxygen and 1.29% argon (percentages are by mass). if .594 moles of air are captured in a 45.0 l container from a plane flying at 30000 feet:
0.594 moles of air were collected from the plane flying at an altitude of 30,000 feet and is at a temperature of -35.0 C.
What is temperature?Temperature is the measure of the average kinetic energy of the particles in a substance. It can be measured in degrees Celsius (°C), Fahrenheit (°F), or Kelvin (K). Temperature is an important physical property of matter, as it can affect the state of a substance.
The total moles of air in the container is 45.0 L * (1.00 mol/22.4 L) = 2.01 mol.
Since the sample is 75.56% nitrogen, 23.15% oxygen, and 1.29% argon, the moles of each are:
Nitrogen = 0.7556 * 2.01 mol = 1.52 mol
Oxygen = 0.2315 * 2.01 mol = 0.46 mol
Argon = 0.0129 * 2.01 mol = 0.03 mol
The 0.594 moles of air collected from the plane is the difference between the total moles and the moles of nitrogen, oxygen, and argon:
Air = 2.01 mol - 1.52 mol - 0.46 mol - 0.03 mol = 0.594 mol
Therefore, 0.594 moles of air were collected from the plane flying at an altitude of 30,000 feet and is at a temperature of -35.0 C.
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how high can a man weighing 86.5 k jump on pluto?
It is not possible for a human to jump on Pluto as the planet is not capable of supporting human life.
The atmospheric pressure on Pluto is less than one hundred-thousandth of Earth's and the temperature is around -230 degrees Celsius. Additionally, there is no solid surface for a person to stand on and jump from.
What is pluto?Generally, Pluto is a dwarf planet in the Solar System that was discovered in 1930 by Clyde Tombaugh.
It is located in the Kuiper Belt, a region of the Solar System beyond Neptune that is populated by small, icy bodies. Pluto is the largest known object in the Kuiper Belt, and it has five known moons: Charon, Styx, Nix, Kerberos, and Hydra. In 2006, the International Astronomical Union (IAU) reclassified Pluto as a "dwarf planet," which means that it is not a full-fledged planet like Earth or Mars.
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What statement best describes the gravitational force of an object?
The gravitational force of an object is describes as amount of force of attraction of the massive object due to another massive object.
What is gravitational force?
Regardless of whether two objects have equivalent masses or not, the gravitational force will pull them together. Newton's Universal Law of Gravitation also states that everything in the universe, including you, pulls everything else. Newtons, abbreviated N, are the standard unit of gravitational force.
Mathematically, gravitational force between two objects of mass m₁ and m₂ separated by a distance r is given by:
F = Gm₁m₂/r²
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