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When the price is set at $20, the rate of change in sales volume is -0.086. The number of units sold will fall by 86.

Volume is defined as the space occupied by an item inside the confines of three-dimensional space. It is also known as the object's capacity. Volume is a measurement of an object's capacity. For example, the capacity of a cup is 100 ml if it can carry 100 ml of water up to the brim. Volume is also the amount of space filled by a three-dimensional object. Volume and mass are the two fundamental qualities of matter. Volume is simply the amount of space occupied by a thing. There are several methods for measuring volume depending on the physical condition of an item.

Here,

dy/dp = -174/5 [3p + 1]^-7/5

Substitute p = 20 in the above equation, we get

dy/dp = -0.086

(b) The sales volume will decrease by 86 units.

The rate of change in sales volume when the price is $20 is -0.086. The sales volume will decrease by 86 units.

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The Debye length is calculated as λD = (1/1.00 * 10^-5 mol/l * 298 K)^(1/2) = 28.6 Å.

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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For elastic collision: conserve the total kinetic energy of the system and  conserve the total momenta of the system.

option B and C.

This is a type of collision in which the two objects move with a different velocities after the collision.

In elastic collision both momentum and kinetic energy is conserved unlike the inelastic collision where only momentum is conserved and the kinetic energy of the system is not conserved.

Thus, we can conclude that in an isolated system during elastic or inelastic collision the sum of the initial momentum of the system is equal to the sum of the final momentum of the system.

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It is not a proper scale to measure which intensifies 10 times over as it increases by value. The scale which have a short and regular intervals are more accurate.

There are various kinds of measuring gadgets which can be used in appropriate occasions. For example in a chemical lab, there are graduated beakers, measuring vessels, electronic balances, burettes, pipettes etc.

Each type of measuring vessels are used in different situations. In all cases, measuring devices with small regular interval of scale is very easy to use and helps for an accurate measurement especially in the case small volume samples.

Therefore, it is not a proper scale which intensifies 10 times over as it increase by a value. We can't take the intermediate values properly with this scale.

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Use Coulomb's law: F = k q₁ q₂ / r² F = (9×10⁹) (6.0×10⁻¹⁰) (2.3×10⁻¹⁵) / (0.02 m)². F = 3.1×10⁻¹¹

The Coulomb's inverse-square law, sometimes known as Coulomb's law, is an experimental physical principle that measures the force exerted between two electrically charged particles that are stationary.

 The rule was known earlier, but Charles-Augustin de Coulomb, a French physicist, published it for the first time in 1785, giving it its name. Because it made it possible to debate the amount of electric charge in a meaningful way, Coulomb's law was crucial to the development of the theory of electromagnetic, perhaps even its beginning point.

According to the rule, the electrostatic attraction or repulsion between two point charges has a magnitude that is directly proportional to the product of the charges'.

Therefore, Use Coulomb's law: F = k q₁ q₂ / r² F = (9×10⁹) (6.0×10⁻¹⁰) (2.3×10⁻¹⁵) / (0.02 m)². F = 3.1×10⁻¹¹.

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The electrostatic force between these two charges can be determined using Coulomb's law. The electric force acting here is

According to Coulomb's law of force, the electrostatic force between two charges separated by a distance of r is given as follows:

Fc = Ke q1 q2 /r²

where Ke = 8.9 × 10⁹ Nm²/C²

Given the charge of  grain  =  3.0 × 10⁻¹⁵ C

charge of another grain piece  = 3.5 × 10⁻¹⁵ C

distance r = 4 cm = 0.04 m

Then Fc =  8.9 × 10⁹ Nm²/C²  ( 3.0 × 10⁻¹⁵ C ) ( 3.5 × 10⁻¹⁵ C)/(0.04 m)² = 5.8 × 10⁻¹⁷N

Therefore, the net electric force acting between the charged grains is  5.8 ×  10⁻¹⁷N.

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Answer:

0.5

Explanation:

The coefficient of static friction (μs) can be calculated using the formula:Friction Force = μs x Normal ForceWhere Normal force is the weight of the object = 86 NThe force required to move the box is 44 N, which is the Friction forceSo,44 N = μs x 86 NTherefore, the coefficient of static friction (μs) = 44 N / 86 N = 0.5The coefficient of static friction between the box and the surface is 0.5.

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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The distance which the sled which is weighing 32 kg and has a speed of 5.5 m/s will travel before stopping is 15.1 meters.

Friction is the force which resists the sliding or rolling of one solid object over the another object. Frictional forces, such as the one traction needed to walk without slipping, may be beneficial, however they also present a great measure of opposition to the motion of object.

In this problem, we are to utilize the kinematic equation in the form;

Vf² = Vi² + 2aD

where, Vi is the initial velocity, Vf is the final velocity, a is the acceleration and D is the distance traveled.

Given,

Mass of boy and sled (m) = 32 kg

Speed of boy and sled (Vi) = 5.5 m/s

Average force (F) = 32 N

Using the equation for Newton's Second Law of Motion with the friction force opposing the motion:

Fs = ma

a = Fs/ m

a = -32/ 32

a = -1m/s²

Plugging the values in the obtained acceleration into the kinematic equation, we get:

(0)² = (5.5)² + 2(-1)D

D = (5.5)²/ 2

D = 30.25/ 2

D = 15.1 meters

The distance which the sled will travel before stopping is 15.1 meters.

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The gravitational force of an object is describes as amount of force of attraction of the massive object due to another massive object.

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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Answer:A: Acceleration

Explanation: I hope this helps!

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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An object can encounter some resistance when moving through the fluid medium of air.

The drag force is the oppositional force applied by the air to a moving object. The size of the cross section A of the front face of the item, the density of the air, and the square of the object's velocity v all contribute to the drag force.

With motion exclusively in the vertical direction and letting

downward be positive, we have that

dv/dt = g - pv, where g = 32 ft/, and so

dv/dt + pv = g. The integrating factor is , so

d/dt( × v) = g× ----->

v = (g/p)× + C ----->

v(t) = (g/p) + C×

Now v(0) = (g/p) + C = 0, and so C = -g/p, giving us

v(t) = (g/p)×(1 - ).

Now we are given that lim(t->infinity)(v(t)) = 99 mi/h = 145.2 ft/s,

so since -> 0 as t -> infinity we have g/p = 145.2 ft/s ------>

p = 32 ft/s^2 / (145.2 ft/s) = 0.2204 s^-1 .

Next, since we have defined downward as positive, the expression

we have for v(t) will equal dy/dt where y(0) = 0 and y increases as

the paratrooper falls. So

dy/dt = v(t) = (g/p)×(1 - )), so

y(t) = (g/p)×(t + (1/p)×) + K.

Now y(0) = (g/p)×(0 + (1/p)) + K = 0 ----->

K = -(g/p^2) = 32 / 0.2204^2 = -658.76 ft, so

y(t) = (145.2)×(t + (4.5372)×e^(-0.2204×t)) - 658.76.

Next, y(6) =  (145.2)×(6 + (4.5372)×e^(-0.2204×6)) - 658.76 = 444.84 feet.

The computed drag coefficient is substantially higher than anticipated.

The free fall distance is the longest distance an individual can travel in a predetermined amount of time. However, the distance covered in the time frame indicated in the news report is significantly greater than the greatest distance that could be covered. Consequently, the news story is exaggerated.

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It depends on the data. If the data matches what is expected based on the known properties of absorbance and transmittance using a spectrophotometer, then the graphs will show the expected trends.

If the data does not match what is expected, then the graphs may not show the expected trends.

A diagram or pictorial representation that organises the depiction of data or values is known as a graph. The relationships between two or more items are frequently represented by the points on a graph.

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Answer:

4.57 m/s

Explanation:

mass of baseball (m1) = 0.15kg

velocity of baseball (v1) = 35 m/s

mass of milt and hand (m2) = 10kg

velocity of mitt and hand (v2) = 0 m/s

final velocity of mitt, hand, and ball = vf

Conservation of momentum since they are colliding and sticking together after collision:

Pb = Pa

m1v1 + m2v2 = (m1+m2)vf

plug in:

(0.15kg)(35m/s) + (10kg)(0m/s) = (0.15kg + 10kg)vf

5.25 = 1.15vf

vf = 4.57 m/s

The student can use a meterstick and stopwatch to measure the centripetal acceleration.

Acceleration of an object on a circular orbit. Velocity is a vector quantity (that is, it has both magnitude, velocity, and direction), so as an object moves along a circular path, its direction changes constantly, and so does its velocity, causing acceleration. increase. Centripetal acceleration is defined as the property of motion of a body through a circular orbit. An object that moves in a circle and has an acceleration vector pointing to the center of the circle is called centripetal acceleration. Spinning a ball on an overhead string causes it to experience centripetal acceleration.

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As the curved path is confined to the XY plane the component of magnitude.

Find the direction of the force on a proton ?

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Answer: Stars turn hydrogen into heavier elements through a process called nuclear fusion. This occurs when the nuclei of hydrogen atoms come together under intense heat and pressure, releasing a large amount of energy in the form of light and heat. This process is triggered by the intense gravity at the core of a star and continues until the star runs out of fuel and eventually dies.

Explanation:

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.

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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Due to the refraction of light when we look the coin embedded in a glass cube it appears to be closer at the top of the cube.

Refraction is the bending of a light ray when it goes from an optically rare medium to an optically denser medium. It is determined by the refractive index. Refractive index of a substance is the ratio the speed of light in a vacuum to the speed of light in the substance.

So refractive index 1.5 tells that the speed of light in the glass will be 1.5 times slower than the speed of light in vacuum. That's why it will gets bent towards the normal when it will pass through the glass. So the coin will appear closer to the top surface of the cube.

Hence the option C is correct.

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From insulating threads, two thin metal spheres are suspended close to one another. One sphere has a net charge while the other sphere has no net charge. The spheres will exert no net electrostatic force on each other. The correct option is A.

The uncharged balloon in an experiment advances toward the charged rod. The net charge from the charged sphere distributes onto both evenly, so they are each charged with same sign. The positive and negative charges neutralise, any residual charge is spread evenly. So, both spheres are charged with same sign. If there is no residual charge, both remain neutral.

Suppose the sphere is positively charged, the neutrally charged sphere becomes is negatively charged. The other sphere is polarised by the positively charged one, with a negative charge on the side that is nearest to the first sphere. Now the second sphere moves towards the first sphere.

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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]

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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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.

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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Answer:It will shoot back up

Explanation:It is not going to change from positive to negative because you pushed it! It will stay positive and repel away from the positive.

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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When an excited electron from a higher energy level returns to a lower energy level by releasing energy in the form of light, a bright-line spectrum of sodium is created.

In physics, energy is the quantitative quality that is imparted to a body or a physical system and is visible in the form of heat and light. The law of conservation of energy holds that energy can be transformed in form but cannot be generated or destroyed. Energy is defined by scientists as the ability to do tasks. People have learnt how to convert energy from one form to another and then utilize it to conduct labor, which makes modern civilization feasible. Energy is the ability to do tasks. It can take the form of a potential, kinetic, thermal, electrical, chemical, nuclear, or other energy.

Here,

The sodium bright-line spectrum is formed when an excited electron from a higher energy level returns to the lower energy level by releasing energy in the form of light, resulting in a sodium bright-light spectrum.

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Mass of woman: 60 kg , Mass of elevator and scale: 815 kg and Starting from rest means Vo = 0 m/s Force applied is 9410 Newtons in the positive y direction (making up positive y and down negative y) g = -9.8 m/s^2.

Fy = m*a

Solution:  Two forces acting on the elevator: Force of gravity against the force of the tension in the cable.  Therefore: Sigma Fy = m*a Force of cable on the elevator + Force of gravity = (mass of the woman + mass of the elevator + mass of the scale)*Acceleration of the elevator.

9410 N + (mass of elevator + mass of woman + mass of scale)*(-9.8 m/s^2) = (mass of elevator + mass of woman + mass of scale) * a 9410 N + (815 kg + 60 kg)* (-9.8 m/s^2) = (815 kg + 60 kg)*a 9410 N + (-8575 N) = 875*a 835 N = 875 kg*a 835 N / 875 kg = a a = 0.95 m/s^2.

Therefore, Mass of woman: 60 kg , Mass of elevator and scale: 815 kg and Starting from rest means Vo = 0 m/s Force applied is 9410 Newtons in the positive y direction (making up positive y and down negative y) g = -9.8 m/s^2.

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In order to expand future biopower production, states would need to acquire large quantities of biomass materials such as wood and agricultural crops like corn, switchgrass, and other grasses.

These materials are used in the production of biofuels, which is a type of renewable energy generated from organic matter. Biomass materials are typically converted into liquid fuels such as ethanol or biodiesel for use in vehicles, or burned for electricity generation. Additionally, states may need to acquire large quantities of organic waste materials like animal manure and food scraps for use in anaerobic digestion systems that generate biogas. Biogas is a type of renewable energy that can be used to produce electricity or heat.

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If the bar has mass m , find the distance d that the bar must move along the rails from rest to attain speed v is v²m/2ILB

According to the velocity meaning, it can be defined as the rate of change of the object’s position with respect to a frame of reference and time. It might sound complicated, but velocity is basically speeding in a specific direction. It is a vector quantity, which means we need both magnitude (speed) and direction to define velocity. The SI unit of it is metre per second (ms-1). If there is a change in magnitude or the direction of the velocity of a body, then it is said to be accelerating.

Initial velocity describes how fast an object travels when gravity first applies force on the object. On the other hand, the final velocity is a vector quantity that measures the speed and direction of a moving body after it has reached its maximum acceleration.

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