For light of wavelength 589 nm, calculate the critical angles for the following substances when surrounded by air.
polystyrene

flint glass

1.3391 is the specific-heat ratio\gamma .

What is adiabatic process ?

An adiabatic process is one in which no heat is gained or lost by the system. Thefirst law of thermodynamics with Q=0 shows that all the change in internal energyis in the form of work done. This puts a constraint on the heat engine process leading to the adiabatic condition shown below. This condition can be used to derive the expression for the work done during an adiabatic process.

The ratio of the specific heats ? = CP/CV is a factor in determining the speed of sound in a gas and other adiabatic processes as well as this application to heat engines. This ratio ? = 1.66 for an ideal monoatomic gas and ? = 1.4 for air, which is predominantly a diatomic gas.

IN THE ABOVE PROBLEM,

P_iV_i^\gamma =P_fV_f^\gamma=2.53P_iV_f^\gamma

=> from this, we get : (Vi/Vf)^gamma = 2.53

and Vf= 1/2 Vi => Vi/Vf =2

thus, 2^gamma = 2.53

=>  gamma ln(2) = ln (2.53)

=> gamma = ln(2.53) / ln(2) =1.3391

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Relativistic kinetic energy can be expressed as Ek=mc2√1−(v/c)2)−mc2 where mm is rest mass, v is velocity, and c is the speed of light.

If the velocity of a body is bisected, its kinetic energy becomes one-fourth as kinetic energy is directly proportional to the speed quad. This formula examines the total rest mass energy and kinetic energy of motion.

This equation discloses that the kinetic energy of an object is directly proportional to the square of its speed. That means that for a binal increase in speed, the kinetic energy will increase by a factor of four. For a threefold growth in speed, the kinetic energy will increase by a factor of nine.

So we can conclude that An object at rest has no kinetic energy. But turn on its position, it will have a form of potential energy.

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The current (I₃) flowing through the triple resistor is 1.55 Amperes.

The amount of electric current (I) flowing through a conductor or conductor will be directly opposite the potential difference/voltage (V) applied to it and inversely with the resistor (R).

From that sound, Ohm's law can be formulated mathematically into the following equation:

V = I x R

I = V/R

R = V/I

Information:

V = Voltage or difference or voltage, unit volts (V)

I = Current, the unit is amperes (A)

R = Resistance, the unit is ohms (W)

In the problem R₃ = 31.00 Ohm and V₃ = 20.00 V. So the current flowing from resistor three is

I₃ = V₃/R₃

I₃ = 31.00/20.00

I₃ = 1.55 Amperes

The current (I₃) flowing through the triple resistor is 1.55 Amperes.

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The car is moving at 21 m/s after the 6 seconds.

This is because:

Initial velocity + (Acceleration x Time) = Final velocity

15 m/s + (2 m/s/s x 6 seconds) = 21 m/s.

The car is moving at 21 m/s after the 6 seconds.

This is because acceleration is the rate of change of velocity, so the velocity of the car increases by 2 m/s for every second it accelerates, which results in a total increase of 12 m/s in 6 seconds. Adding the initial velocity of 15 m/s, the car's final velocity is 21 m/s.

Acceleration is a fundamental concept in physics and it refers to the rate at which velocity changes over time. It can be expressed mathematically as the derivative of velocity with respect to time.

In the given scenario, the car's acceleration is 2 m/s/s which means that the velocity of the car increases by 2 m/s for every second that it accelerates. Therefore, in 6 seconds, the velocity of the car increases by:

The initial velocity of the car was 15 m/s and after 6 seconds of acceleration, the final velocity is:

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The minimum uncertainty in the energy of the state of an atom in a excited state is 3.28 x 10^(-8)eV.

The formal uncertainty principle basically states that if the uncertainty in the energy (E) times the uncertainty in the time (t) is more than or equal to b, then the uncertainty in the momentum (p) times the uncertainty in the position (x) is greater or equal to b. The Planck constant (6.63 x 10-34 J s) is represented by the letter h, or h/2 = 1.05 x 10-34 J s.

The excited state of an atom (Δt)= 10^-8 s.

Maximum uncertainty in time => Minimum uncertainty in the energy state

h= 6.6 x 10^ (-34) j/s

ΔE = h/4πΔt = 6.6 x 10^ (-34) j/s / 4π x 10^-8

                                 => 5.25 x 10^(-27) J

Converting to eV

ΔE   => 5.25 x 10^(-27) J x 1eV/1.6 x 10^(-19)

       => 3.28 x 10^(-8)eV.

They lack a fixed energy, according to the time-energy uncertainty principle, and each time they decay, the energy they release varies somewhat. The theoretical energy of the state is where the average energy of the departing photon peaks, although the distribution has a finite width known as the natural linewidth.

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The change in enthalpy (delta H) for formation of HBr from the single, isolated H and Br atoms is -103 KJ/mol.

The amount of energy needed to break one mole of bonds between the atoms in gaseous molecules is known as bond energy. The bond energy of a diatomic molecule is therefore referred to as the enthalpy of atomization since in the gaseous state, molecules totally disintegrate into atoms.

H2 + Br2 => 2HBr

ΔH = Change in enthalpy of reaction ={ Bond enthalpy of reactants -

                                                                    Bond enthalpy of products}

ΔH => { H-H + Br-Br - 2 x(H-Br)}

 => { 436+193-2x(366)}

=> -103 KJ/mol.

The amount of energy needed to break one mole of bonds that are present between the atoms in gaseous molecules is known as bond energy. The bond energy of a diatomic molecule is therefore referred to as the enthalpy of atomization since in the gaseous state, molecules totally disintegrate into atoms.

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The magnitude of the force and the impulse applied to the car are  85714 N and  30000 N-s respectively.

The definition of force in physics is: The push or pull on a massed object changes its velocity. An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.

The magnitude of the force applied to the car = change in momentum/time interval

= (1200 kg × 25 m/s - 1200 kg×0)/0.35 second

= 85714 N.

The impulse applied to the car = change in momentum

= (1200 kg × 25 m/s - 1200 kg×0)

= 30000 N-s.

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Their end velocities might be similar or the same if object an is going in the same direction as object b, which is due north, while object b is moving in the opposite direction, due south.

They clash directly with one another. The beginning and final velocities would both be zero because of the momentum conservation law. In physics, an elastic collision is a collision between two bodies in which the total kinetic energy remains constant. In an ideal, elastic collision, there is no net conversion of kinetic energy into heat, noise, or potential energy. There is no kinetic energy lost after an exact elastic collision between two objects.

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The horizontal range (R) of a projectile is defined as the horizontal distance it travels while in flight. It is equal to the product of the initial velocity (V) of the projectile, the sine of the angle of projection (θ), and the time of flight (T). R = V * T * sinθ

The maximum height (H) of a projectile is reached at the peak of its trajectory and is equal to the product of half of the gravitational acceleration (g), and the square of the time of flight (T) . H = (1/2) * g * T^2

Given that the horizontal range is equal to three times the maximum height, we can set up the following equation:

R = 3H

We know that R= V * T * sinθ and H = (1/2) * g * T^2

Substituting these equations into the first equation we get:

V* T * sinθ = 3(1/2) * g * T^2

Dividing both sides by T and simplifying, we get:

sinθ = (3/2) * sqrt(g/V)

If we know the value of g (gravitational acceleration) and the initial velocity of the projectile we can calculate the angle of projection. However, in general this is an inverse trigonometric function and the angle of projection is not a exact value, but it is defined in the range of values for the inverse trigonometric functions.

It's important to note that this equation assumes a level ground, no air resistance and constant acceleration due to gravity.

Roll a skateboard on sand, then roll it on gravel. - this experiment could answer this question. Hence, option (B) is correct.

An experiment is a technique used to confirm or deny a hypothesis, as well as assess the likelihood or effectiveness of something that has never been tried before. Experiments show what happens when a specific factor is modified, which sheds light on cause-and-effect relationships.

The purpose and scope of experiments vary widely, but they all rely on a repeatable process and a logical examination of the outcomes. Natural experimental experiments are also a thing.

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The surface area of the disk is AD is 70.5 cm2. and the area of the square is As 56.25 cm2.

Surface area is the total area of the exposed surfaces of a three-dimensional object. It is the sum of the areas of all the faces of the object. Surface area is a measure of how much exposed area a 3D object has, and is used in many fields such as engineering, architecture, and geometry. Surface area is important in many applications, such as calculating the amount of paint needed to cover a wall or the amount of material needed to make a product.

For the disk, the surface area is calculated using the formula AD = πr2, where r is the radius of the disk. Since the circumference of the disk is given as 30cm, we can calculate the radius as r = 30/2π = 4.7124 cm. Therefore, the surface area of the disk is AD = π(4.7124)2 = 70.5 cm2.
For the square, the area is calculated using the formula As = s2, where s is the length of one side of the square. Since the perimeter of the square is given as 30cm, we can calculate the length of one side as s = 30/4 = 7.5 cm. Therefore, the area of the square is As = (7.5)2 = 56.25 cm2.

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The current in the circuit 10 us after the switch is moved from a to b is 0 A.

What is circuit?
A circuit is an interconnection of electronic components, such as resistors, capacitors, and transistors, which are connected by conductive pathways to create a closed loop. The components are arranged in such a way that an electrical current is able to flow through them, allowing electricity to be used to power machines and devices. Circuits can be used to transmit signals, store and process information, and generate and control power. They are an essential part of modern electronics and are used in everything from computers and mobile phones to cars and home appliances. Circuit design is an important field of engineering and requires a high level of technical expertise to create reliable and efficient circuits.

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The distance between the two charged particles is 0.082 m.

The distance between the two charges is calculated by applying Coulomb's law of electrostatic force as shown below.

Mathematically, the formula for the force of attraction or repulsion between two charged particles is given as;

F = ( kq₁q₂ ) / ( r² )

where;

r² = ( kq₁q₂ ) / ( F )

r = √ [ ( kq₁q₂ ) / ( F ) ]

The distance between the two charged particles is calculated as;

r = √ [ (  9 x 10⁹ x 500 x 10⁻⁹ x 1 x 10⁻⁶ ) / ( 670 x 10⁻³ ) ]

r = 0.082 m

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Answer: Constant Variable

Explanation: Constant variable is what stays the same during the experiment. In an experiment the dependent variable changes when changes are made to the independent variable. But in any experiment, the Constant variable stays the same.

Work is the movement of an object against an opposing force.

What is work?

It is a measure of energy transfer that occurs when an object is moved over a distance by an external force at least part of which is applied in the direction of the displacement.

What is the work unit?

The SI unit of work is the joule (J). Joule is the work done by the force of one newton causing a displacement of one meter. Sometimes, a newton-meter (N-m) is also used for measuring work.

What is the formula of work?

Work done (W) is the dot product of force (f) and displacement (ds). The formula is W = F · d s.

How is work related to energy?

Energy should be transferred to an object to move it. Transferring energy can be in the form of force. This amount of energy transferred by the force to move an object is called work or work done.

Thus, the correct answer is work.

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The ratio of the magnitude of 2 to the magnitude of 1 is 1.

To solve this problem, we can use the concept of electric field and kinematics.

We know that the force acting on a proton due to an electric field is given by the equation F = qE, where q is the charge of the proton and E is the electric field.

Since the proton is released from rest, we can assume that the initial velocity of the proton is zero.

Using kinematic equations, we can find the final velocity of the proton after it has been in electric field 1 for 29.8 seconds.

v = at = Eq/m * t = Eq* t / m

where a is the acceleration of the proton due to the electric field, t is the time it spends in the field, m is the mass of the proton,

Now we can use the final velocity to calculate the distance traveled by the proton in field 1.

s = vit + 0.5at^2 = Eq* t^2 / 2m

Once the proton is in field 2, it will have a velocity in the opposite direction, and it will be acted upon by the new electric field 2, which will cause it to decelerate and eventually come to rest again.

vf = vi + at = -Eq* t / m

Now we can calculate the time it takes for the proton to come to rest again

s = vit + 0.5at^2 = Eq* t^2 / 2m

where s is the distance traveled by proton in field 2, vf is the final velocity of the proton, and vi is the initial velocity of the proton.

Now we can equate the distance traveled in field 1 and field 2 to the distance traveled in 7.65 sec.

Eq1* t^2 / 2m = Eq2* t^2 / 2m

Eq1/Eq2 = 1

So the ratio of the magnitude of 2 to the magnitude of 1 is 1

The force is reduced by a factor of 4.

In physics, the idea of impulse is crucial, especially when examining collisions and impacts. The impulse of a force causes a change in an object's momentum when it acts on it for a predetermined amount of time. The shift in momentum is greater the stronger the stimulus.

Using the formula to determine force -

I = FΔt

The Δt for the impulse increased from 0.005s to 0.0020s.

Thus,

= 0.0020 / 0.005

= 4

Therefore,

F = I/4Δt

This means that the force is reduced by a factor of four.

Complete Question

A safety helmet extends the time of impact from 0.005 s to 0.020 s. By what factor is the average force that causes the impact reduced?

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The position of its image(measured from the center of the ornament)? in cm 18.05 cm; b)the height of its image 7.90 mm.

Diameter is a straight line passing through the centre of a cricle or other shape,or the length of such as milimeter, centimetres, Inches,and feet.
The position of the object's image is 18.05 cm from the center of the ornament, which is calculated by subtracting the object's distance from the center of the ornament (24.50 cm) from the diameter of the ornament (6.45 cm). The height of the image can be determined by multiplying the height of the object (3.95 mm) by the ratio of the object's distance from the center of the ornament (24.50 cm) to the radius of the ornament (3.225 cm). This gives 7.90 mm.
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You would need to survive the thermosphere: difficult temperatures, solar radiations, low air pressures and low air density with difficulty in breathing.

A layer of gases known as the atmosphere envelops the planet Earth. The gravitational pull of the planet's neighbor, Earth, keeps it close to the surface. The three primary elements of the atmosphere are nitrogen, oxygen, and argon.

The thermosphere, which is located above the mesosphere, is a zone where the temperature rises as you ascend. The sun's powerful UV and X-ray radiation is what is responsible for the temperature rise. The upper thermosphere can reach temperatures of up to 2,000 degrees Celsius.

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The maximum speed of the oscillating object in the figure is 3.93x10^-2 m/s.

What is oscillating object?
Oscillating objects are items that move back and forth in a regular pattern. This type of motion is known as oscillation, and it is the basis of many everyday activities. Examples of oscillating objects include pendulums, tuning forks, fans, and clocks. Oscillation occurs when a force is applied to an object and it moves in one direction until a certain point is reached, then it reverses direction and moves back to its starting point. This cycle continues until the force is removed. Oscillation is also used in technology, such as in the production of sound waves, and in the operation of motors, turbines, and other machines. It is also found in nature, for example in ocean waves, the movement of stars and planets, and in the behavior of animals.

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The magnitude of the force is 1.39 * 10^-4 N.

We have to note that the force that is acting between any two charges could be the force of attraction or it would be a force of repulsion. In the case of the forces that we have here, we would be talking about a force of attraction since we are dealing with opposite charges.

We have;

F = Kq1q2/r^2

q1 and q2 = charges

K = electric constant

r = distance of separation

F = force

Then we have;

F = 9 * 10^9 * 5 * 10^-9 * (-10 * 10^-10)/(0.018)^2

F = -4.5 * 10^-8/3.24 * 10^-4

F = -1.39 * 10^-4 N

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In order to find the magnitude of the electric field, we can use the equation

E = V / d

where E is the electric field, V is the potential difference, and d is the distance between the two points.

In this case, the potential difference between the ends of the 2-meter stick is 400 V and the distance between the two points is 2 meters. So we can plug in these values into the equation:

E = 400 V / 2 m = 200 V/m

So the magnitude of the electric field is 200 V/m.

The potential difference between its ends of a 2-meter stick that is parallel to a uniform electric field is 400 V. The magnitude of the electric field is  200V/m.

A charged particle placed in a specific location within an electric field experiences an electric force that is measured as the electric field magnitude (E). In terms of volts per meter (V/m), it is the force per unit positive charge (q) at that location.

[tex]E = \frac{V}{d}[/tex]

E = electric field magnitude in volts per meter (V/m),

V = potential difference in volts (V),

d = distance in meters (m)

V=400 V

d=2 m

[tex]E = \frac{400}{2}[/tex]

E =  200 V/m.

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An iron block in a furnace is heated and consequently expands, which means that its density is less.

Density -

Definition of density: A material's density is determined by how closely it is packed. As the mass per unit volume, it has that definition. Symbol for density: D or Formula for Density: Where is the density, m is the object's mass, and V is its volume, the equation is: = m/V.

The amount of matter that makes up a thing is referred to as its mass. Density refers to how closely together atoms are packed, or how close together they are in a substance. The concept of mass is used to quantify inertia. Contrarily, the degree of compactness is defined by density.

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The ball has 2.0 Joules of kinetic energy after hitting the wall.

The energy that is moving or doing work is known as an object's kinetic energy. It can be stated using the following formula:

K.E = [tex]\frac{1}{2} mv^2[/tex]

where m is the ball's mass and v is its final velocity following impact.

The rubber ball has a mass of 1.0 kg.

Before the collision, the rubber ball was moving at a speed of 2.0 m/s.

After the collision, the rubber ball's final speed was 2.0 m/s slower.

Following the contact and after it bounces off the wall, the ball's kinetic energy is calculated as follows

K.E = [tex]\frac{1}{2} mv^2[/tex]

K.E = [tex]\frac{1}{2} \times 1 \times (2)^2[/tex]

K.E = 4/2

K.E =2.0 Joules

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The kinetic energy of the ball after it bounces off the wall is 2.0 Joules.

The kinetic energy of an object is the energy that is in motion or performing work. It can be expressed by using the formula:

[tex]K.E=\frac{1}{2} mv^2[/tex]

The Kinetic energy of the ball after the collision and when it bounces off the wall is computed as:

[tex]K.E. =\frac{1}{2} *1.0*(2.0)^2[/tex]

K.E. = 2.0 Joules

In physics, the kinetic strength of an item is the energy that it possesses because of its motion. it's far described as the work needed to boost up a frame of a given mass from rest to its said speed. Having gained this power during its acceleration, the frame continues this kinetic power except for its pace adjustments. An equal quantity of labor is carried out by means of the body when decelerating from its current speed to a country of relaxation. officially, kinetic power is any time period in a gadget's Lagrangian which incorporates a spinoff with respect to time.

Kinetic electricity is the power an object has due to its motion. If we need to boost up an item, then we must observe a force. applying pressure calls for us to do paintings. After paintings have been done, strength has been transferred to the item, and the object may be moving with a brand new constant speed.

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A pitcher throws a ball at 90 mph and the catcher stops it in her glove, the possible for both positive and negative work.

What is work ?

Work is force that is applied over a distance. Driving a car up a hill, drawing down a captive helium balloon, and raising something against Earth's gravitation are some examples of work. Energy takes the form of work in the mechanical world. The joule, which is equal to one newton metre (N m), is the accepted unit of labour.

What is positive work ?

The same work performed on an item is referred to as positive work whenever force and displacement are both moving in a substantially comparable direction. An illustration of this is how a body travelling forward on a horizontal surface interacts with force and displacement.

a.) the work done on the ball by the pitcher is always be positive.

because when the pitcher throws the ball with force F and the ball also moves in the direction of force so the work done will be positive.

B.) The work done on the ball by the catcher will be negative.

because the fielder has to stop the motion of the ball to catch. this means the direction of force is applied against the motion of the ball so the work done will be negative in this case.

Therefore, A pitcher throws a ball at 90 mph and the catcher stops it in her glove, the possible for both positive and negative work.

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1. The rank of the vector combinations on the basis of their magnitude is -  a+b = a +d > a+c > f +c = d > a + e

A physical quantity that has both directions and magnitude is referred to as a vector quantity. A lowercase letter with a "hat" circumflex, such as "û," is used to denote a vector with a magnitude equal to one. This type of vector is known as a unit vector.

Position, force, torque, velocity, and displacement are a few examples of vector quantities.

1. a + c

⇒ 2+1 unit

⇒ 3 unit  

2. a + b

⇒ 2√2 unit

3. a + e

⇒ 2 -1

⇒ 1 unit

4. a +d

⇒ 2√2 unit

5. f+ c

⇒ 2 unit

6. a+d

⇒ 2√2 unit

7. f+c

⇒ 2 unit

8. a+b

⇒ 2√2 unit

9. a+e

⇒ 1 unit

10. a+c

⇒ 3 unit

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Complete Question -

Six vectors (a through f ) have the magnitudes and directions indicated in the figure. (Figure 1)

1.Rank the vector combinations on the basis of their magnitude.

Rank from largest to smallest. To rank items as equivalent, overlap them.

a+c

f+c

d

a+b

a+e

a+d

7.802% fraction of the alpha's kinetic energy is transferred to the gold .

What is momentum ?

Momentum, the product of a particle's mass and its velocity. Momentum is a vector quantity. It has both magnitude and direction. Isaac Newton's second law of motion states that the rate of change of momentum over time is equal to the force acting on a particle. See Newton's Laws of Motion.

From Newton's second law,  if a particle is subject to a constant force over a period of time, the product of that force and the time interval (momentum) equals the change in momentum. Conversely, the momentum of a particle is a measure of the time it takes for a constant force to come to rest.

let,

mass of the alpa particle, m1=4u

initial speed is u1 and final speed is v1

and mass of the gold nucleus, m2=197u

initial speed is u2 and final speed is v2

in head on collission,

V2=2*m1*u1/(m1+m2)

v2=(2*4u)*u1/(4u+197u)

v2=(8/201)*u1

now, K2/K1=(1/2*m2*v2^2)/(1/2*m1*u1^2)

=(m2/m1)*(v2/u1)^2

=(197/4)*((8/201)*u1/*u1)^2

=(197/4)*(8/201)^2

=0.07802

=7.802% ------is answer

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It will take approximately 63.5 years to reduce a 25 mg sample of cesium-137 to 8.7 mg.

Beta decay is a type of radioactive decay in which a beta particle (an electron or a positron) is emitted from the nucleus of an atom. Cesium-137 is a radioactive isotope of cesium that undergoes beta decay and has a half-life of 30 years.

The half-life of a radioactive material is the amount of time it takes for half of the initial amount of the material to decay. In other words, if you start with a certain amount of radioactive material, after 30 years, half of that initial amount will have decayed. After another 30 years, half of the remaining material will have decayed, and so on.

We can use the formula: N(t) = N0 * (1/2)^(t/T1/2) where

We know that N0 = 25 mg, T1/2 = 30 years, and we want to find t when N(t) = 8.7 mg.

So we can set up the equation:

8.7 mg = 25 mg * (1/2)^(t/30 years)

Solving for t, we find:

t = (30 years) * log2(8.7mg/25mg)

t = approximately 63.5 years

It will take approximately 63.5 years to reduce a 25 mg sample of cesium-137 to 8.7 mg.

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The three characteristics of an object which are represented by a motion map are the position, acceleration, velocity and is therefore denoted as option D.

This is a term which is referred to as a one-dimensional plots built off of a position line and is denoted by a horizontal axis which makes it possible to mark the position of a body or a vehicle at any point in time.

It contains arrows which are specifically used to record its velocity and acceleration and is therefore the reason why option D was chosen as the most appropriate choice.

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Answer: option D.

Explanation:

If the thickness of a uniform wall is doubled, the rate of heat transfer through the wall is halved.

What is heat transfer?

Heat transfer is the movement of heat from one substance or material to another. Heat transfer takes place through three principal mechanisms: conduction, radiation, and convection.

What are the 3 types of heat transfer?

How does thickness affect heat transfer?

The thicker the material, the more time it takes to transfer the same amount of heat.

What will happen to the heat transfer rate if you double the thickness of the insulation?

The higher the R-value, the greater the resistance to heat transfer. When you double the thickness of a material, the R-value also doubles but the thermal conductivity through the new total thickness is cut by half.

Thus, option c) halved is the correct answer.

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