A plank of length L=2.200 m and mass M=4.00 kg is suspended horizontally by a thin cable at one end and to a pivot on a wall at the other end as shown. The cable is attached at a height H=1.70 m above the pivot and the plank's CM is located a distance d=0.700 m from the pivot.
Calculate the tension in the cable.

The final area of the plate is 4.0000352 [tex]m^2[/tex] if the temperature raised to 100 °C and the coefficient of linear expansion of iron is 1.1 x 10-7.

Expecting that the plate of iron is rectangular, we can involve the recipe for warm extension of solids to compute the last region of the plate. The equation for direct warm development is given by ΔL = αLΔT, where ΔL is the adjustment of length, α is the coefficient of straight extension, L is the first length, and ΔT is the adjustment of temperature.

Since the region of the plate is given by A = L*W, where L is the length and W is the width, we can involve the equation for straight warm extension to compute the adjustment of length of the plate and afterward use it to compute the last region.

ΔL = αLΔT = [tex](1.1 x 10^-7 m/oC)(2 m)(80 oC) = 1.76 x 10^-5 m[/tex]

The last length of the plate is L + ΔL = 2 m + 1.76 x [tex]10^-5[/tex] m = 2.0000176 m (approx.)

The last width of the plate is thought to be unaltered as it isn't impacted by the adjustment of temperature.

Thusly, the last region of the plate is A = L*W = (2.0000176 m)(2 m) = 4.0000352 [tex]m^2[/tex] (approx.)

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The formula you mentioned is known as the dot product formula or the scalar product formula. It is used to find the angle between two vectors u and v.

Let's start by defining the vectors u and v. Suppose we have two vectors u and v in a two-dimensional space.

u = (u1, u2)

v = (v1, v2)

The dot product of these vectors is defined as:

u . v = |u| |v| cos(β)

where |u| and |v| are the magnitudes of the vectors u and v respectively, and β is the angle between the vectors u and v.

Now, let's derive this formula. The dot product of two vectors u and v is given by:

u . v = (u1 × v1) + (u2 × v2)

The magnitude of a vector is given by:

|u| = sqrt(u1² + u2²)

|v| = sqrt(v1² + v2²)

We can use the dot product and magnitude equations to obtain:

cos(β) = (u . v) / (|u| × |v|)

Multiplying both sides by |u| × |v| gives us:

|u| × |v| × cos(β) = u . v

Therefore, we have derived the dot product formula:

u . v = |u| × |v| × cos(β)

This formula can be used to find the angle between two vectors u and v in any two-dimensional or three-dimensional space.

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The complete question is-

Write the proof of the formula

u.v=|u||v|cosβ

A Stone Is Dropped Into a Deep Water Well. The Sound of The Stone Hitting The Water Is Heard After 3.4 Seconds. then The Depth of The Water Well is 56.6 m.

In terms of physics, sound is a vibration that travels through a transmission medium like a gas, liquid, or solid as an acoustic wave. Sound is the receipt of these waves and the brain's perception of them in terms of human physiology and psychology. Only acoustic waves with frequencies between about 20 Hz and 20 kHz, or the audio frequency range, may cause a human to have an auditory sensation. These correspond to sound waves in air with an atmospheric pressure of 17 metres (56 ft) to 1.7 centimetres (0.67 in) in wavelength. Ultrasounds are sound waves with a frequency higher than 20 kHz that are inaudible to humans. Infrasound refers to sound frequencies below 20 Hz. Animals of different species have different hearing ranges. Acceleration of the stone is 9.8 m/s²

according to kinematics,

s = ut + 1/2 at²

s =  1/2 ×9.8×3.4²

s = 56.6 m

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The time taken by the cars to meet is 5.4 x 10³ s.

Speed of car A, v₁ = 45 km/h = 12.5 m/s

Speed of car B, v₂ = 55 km/h = 15.27 m/s

Distance between the cars, d = 150 km = 15 x 10⁴m

The expression for the time taken by the cars to meet can be given as,

Time = Distance/Average speed

t = d/(v₁ + v₂)

Applying the values of d, v₁ and v₂.

t = 15 x 10⁴/(12.5 + 15.27)

t = 15 x 10⁴/27.77

t = 5.4 x 10³ s

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Answer: In this scenario, we have two carts colliding with each other. One cart weighs 250 kg and is moving at a speed of 8 m/s, while the other cart weighs 100 kg and is initially at rest.

After the collision, the 250 kg cart continues moving forward, but at a slower speed of 3 m/s. We want to find out the speed at which the 100 kg cart moves after the collision.

To solve this, we use the principle that the total "push" or momentum before the collision should be the same as the total momentum after the collision.

Since the 100 kg cart is initially at rest, its momentum is zero. The momentum of the 250 kg cart before the collision is 250 kg * 8 m/s = 2000 kg·m/s.

After the collision, the momentum of the 250 kg cart becomes 250 kg * 3 m/s = 750 kg·m/s.

To find the momentum of the 100 kg cart after the collision, we subtract the momentum of the 250 kg cart after the collision from the total momentum before the collision: 2000 kg·m/s - 750 kg·m/s = 1250 kg·m/s.

Now, we divide this momentum by the mass of the 100 kg cart to find its velocity: 1250 kg·m/s / 100 kg = 12.5 m/s.

Therefore, the 100 kg cart moves at a velocity of 12.5 m/s after the collision, in the opposite direction of the 250 kg cart's motion.

The order of increasing mass is:

An electron < An atomic nucleus < a DNA molecule < a cell.

     An electron is a fundamental particle with a negative charge and has a very small mass of order [tex]10^{-31}\ kg[/tex]. Which makes it the lightest in the group.

     An atomic nucleus consists of protons and neutrons which both individually have larger mass than an electron. The order of magnitude of the nucleus's mass is [tex]10^{-27}\ kg[/tex] or higher.

     A DNA molecule is a polymer chain of nucleotides and it carries genetic information. It contains many atoms, therefore it makes sense that it should have more mass than an atomic nucleus. Each human cell has about DNA of mass of order [tex]10^{15}\ kg[/tex].

     Lastly, A cell has the most mass in the given list since it encompasses everything else in the list.

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The amount of heat required to change the ice cube of mass 720 g from ice at a temperature of -10 ˚C to water at temperature of 15 ˚C is 300963.6 J

First, we shall obtain the heat required to change the ice from -10 ˚C to 0 °C. Details below:

H₁ = MCΔT

H₁ = 0.72 × 2220 × 10

H₁ = 15984 J

Next, we shall obtain the heat needed to melt the ice. Details below:

H₂ = m × ΔHf

H₂ = 0.72 × 333000

H₂ = 239760 J

Next, we shall determine the heat required to change the water from 0 °C to 15 °C. Details below:

H₃ = MCΔT

H₃ = 0.72 × 4187 × 15

H₃ = 45219.6 J

Finally, we shall determine the heat required to change the ice from -10 ˚C to water at temperature of 15 ˚C Details below:

Q = H₁ + H₂ + H₃

Q = 15984 + 239760 + 45219.6

Q = 300963.6 J

From the above calculations, we can conclude that the heat required to change the ice from -10 ˚C to water at 15 ˚C is 300963.6 J

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Magnetic particle separation is a powerful tool for separating particles based on their velocities in a magnetic field, and it has significant practical applications in various scientific and technological fields.

To separate particles of different velocities moving in a magnetic field, one can utilize a technique called magnetic field separation or magnetic particle separation.

This method takes advantage of the fact that charged particles moving in a magnetic field experience a force called the Lorentz force, which acts perpendicular to both the velocity vector and the magnetic field.

The basic principle behind magnetic particle separation is to apply a magnetic field perpendicular to the motion of the particles. The Lorentz force will then cause the particles to curve in different directions based on their velocities and charges.

By carefully controlling the strength and direction of the magnetic field, particles with different velocities can be steered onto different paths and separated.

One common approach to achieve magnetic particle separation is to use a device called a magnetic separator. This device typically consists of a strong magnet or a series of magnets arranged to create a uniform magnetic field.

The particles to be separated are injected into a chamber or a flow system where the magnetic field is applied. As the particles move through the magnetic field, they experience the Lorentz force and deviate from their original trajectory. The degree of deviation depends on their velocity and charge.

By carefully adjusting the magnetic field strength, particle size, and other parameters, it is possible to optimize the separation process and achieve effective separation of particles with different velocities. This technique has various applications in fields such as biomedical research, environmental monitoring, and materials science.

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The time will take a skateboard and dog with force 9N to stop the skateboard and dog is 8 seconds.

The force is defined as the push or pull of an object. The force equals the mass and acceleration of the object obtained from Newton's second law. Acceleration defines the change in velocity by the time taken. The force is defined as the rate of change of momentum and time. Momentum is defined as the product of mass and velocity and the unit of momentum is Kg.m/s.

From the given,

mass of dog (m) = 24 kg

The initial speed of dog (u) = 3 m/s

mass of skateboard and dog = 3 + 24 = 27 kg.

The final speed of dog (v) = 0 m/s

Force = 9N

time =?

F = dp/dt, rate of change of momentum and time.

F(dt) = dp

dt = (dp)/F

    =(Pf - Pi)/F

Pf is the final momentum and Pi is the initial momentum.

Pi = m×v = 24×3 = 72 kg.m/s²

Pf = m×v = 27×0 =0 kg.m/s²

dt = (0-72)/9

   = 8s

Thus, the time taken to stop the skateboard and dog is 8s.

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The resistance values from the givens are having a consistent value ranging from 27 to 33 ohms depending upon the supply of voltage and current.

Ohm's law gives the relation between the voltage, current, and resistance. Ohm's law states that the applied voltage is directly proportional to the current flow in the conductor. Thus, V∝I, V is the voltage and I is the current.

Ohm's law can also be written as, V = IR, where R is the resistance and the unit of resistance is ohm. The resistance is the factor that resists or opposes the current flow in the curcuit. When resistance increases, current flow in the circuit decreases and vice-versa.

From the given values, the resistance values changes when there is a change in voltage and current. The current and voltage have linear relationship, and these calculations make the idealsitic assumptions and can not hold true in practical applicaitons, when woeking with non-ohmic or non-linear components.

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The charge R is positive and the charge L is negative hence, the correct option is option D.

The electric charges are of two types and they are positive and negative charge. There is an attractive force between the two charges. The electric field is formed around the charges and the electric field is denoted by using field lines around it.

The field lines are emerging from positive charge and end up in a negative charge. The field lines never intersect with each other. Hence, from the given, the field lines emerging from the positive charge(R) and end up in the negative charge(L).

Hence, the ideal solution is option D.

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The electrical conductivity of copper at 300 K is 6.03 x 10⁷ Ω⁻¹m⁻¹.

Thermal conductivity is a property of a substance that describes its ability to conduct heat. Electrical conductivity is the ability of a material to conduct electricity. The two are related because both involve the movement of electrons in the material.

To calculate the electrical conductivity of copper at 300 K, we need to use the Wiedemann-Franz law, which states that the ratio of the thermal conductivity (κ) to the electrical conductivity (σ) is proportional to the temperature (T) of the material.

The Wiedemann-Franz law is given by:

L = κ/σT

Where L is the Lorenz number, which is a constant equal to 2.45 x 10⁻⁸ W Ω/K².

Rearranging this equation to solve for σ, we get:

σ = κ/(LT)

Plugging in the values for κ, L, and T, we get:

σ = 470.4 W/m K / (2.45 x 10⁻⁸ W Ω/K² x 300 K)
σ = 6.03 x 10⁷ Ω⁻¹m⁻¹

Therefore, the electrical conductivity of copper at 300 K is 6.03 x 10⁷ Ω⁻¹m⁻¹.

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The magnitude of the resultant vector is obtained by finding the sum of two horizontal vectors and the sum of two vertical vectors. Thus, option C is correct.

The resultant vector is the single vector that has the same effect in the number of vectors collectively produced. The resultant vector in the horizontal and vertical direction is obtained by drawing a diagonal and hence by using the Pythagoras theorem.

To find resultant vector is obtained by finding the sum of two horizontal vectors and vertical vectors and then using the Pythagoras theorem.

Thus, the ideal solution is option C.

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The point on the image that is the source of the sound / sound waves travelling would be B. 2.

When a sound is produced, such as a musical note or spoken word, it initiates a disturbance at the source, which sets the surrounding particles in motion. As these particles oscillate back and forth, they generate regions of compression and rarefaction, resulting in the formation of longitudinal waves.

The propagation of sound waves emanates from a central source, radiating outward in a spherical pattern, thereby creating an expanding wavefront. This fundamental principle of wave behavior stems from the point-source nature of sound waves, wherein they originate from a central locus and disperse in all directions.

This central source in the image is 2.

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The image distance is the distance of the image formed to the lens.

option C.

The distance between the point of incidence of a lens and the point where the image is formed is called image distance.

The image distance, that is the distance of the image formed by a lens for a given object distance (u) and the focal length (f) of the lens, is given by the following lens formula;

1/f = 1/v  + 1/u

where;

Thus, based on the formula and explanation given above, we can conclude that object distance is the distance of the object to the lens and image distance is the distance of the image formed to the lens.

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The medium in which electromagnetic waves and mechanical waves travel is one of their primary distinctions. Light and other electromagnetic waves, including radio waves, can move through void space without the aid of a physical medium.

They may move through vacuum, air, or other materials and are made up of oscillating electric and magnetic fields. The propagation of mechanical waves, such as sound or water waves, on the other hand, depends on a physical medium.

To transport energy, they rely on particle interactions and displacements in the medium. Since mechanical waves need a physical medium to carry their energy, they cannot move through a vacuum.

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Answer:

To solve this problem, we can use the formula:

Work = Force x Distance x cos(theta)

where Work is the amount of work done on the pizza, Distance is the distance the pizza is lifted, theta is the angle between the force and the displacement, and cos(theta) is the cosine of the angle between the force and displacement.

We are given that the work done on the pizza is 116 kJ, the distance the pizza is lifted is 3.85 cm (which is 0.0385 m), and the angle between the force and the displacement is 0 degrees (since the force is applied in the same direction as the displacement).

Plugging in these values, we get:

116 kJ = Force x 0.0385 m x cos(0)

Simplifying and converting the units of work to joules, we get:

116,000 J = Force x 0.0385 m

Solving for Force, we get:

Force = 116,000 J / 0.0385 m

Force = 3,012,987.01 N

Therefore, the delivery man exerts a force of approximately 3,012,987.01 Newtons on the pizza to lift it 3.85 cm higher.

Every action have equal and opposite reaction. for example when we fire bullet from a gun, the gun will recoil back and bullet moves forward. In case of rocket, rocket is fired, thrust is reaction of force applied by the gas on the floor.

A push or a pull that an object experiences as a result of interacting with another item is known as a force. Interactions result in forces! As was covered in Lesson 2, certain forces are the result of contact interactions (reaction, frictional, tensional, and applied forces are examples of contact forces), whilst other forces (gravitational, electrical, and magnetic forces) are the consequence of action-at-a-distance interactions. Newton postulated that whenever objects A and B interact, they exert forces on one another. You put a downward force on the chair when you sit on it, and the chair responds by exerting an upward force on your body. This contact creates two forces: one force on the chair and one force on your body.

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The distance of the screen from the mirror should be 60 cm in order to get a sharp image of the object.

To find the distance of the screen from the mirror, we can use the mirror formula:

1/f = 1/v + 1/u

where f is the focal length of the mirror, u is the distance of the object from the mirror, and v is the distance of the image from the mirror.

In this case, the focal length is given as -20 cm (negative sign indicates that the mirror is a concave mirror), and the object is placed at a distance of 30 cm from the mirror. Therefore, we have:

1/-20 = 1/v + 1/30

Solving for v, we get:

v = -60 cm

The negative sign of the image distance indicates that the image is formed behind the mirror, which means it is a virtual image.

Now, to find the distance of the screen from the mirror, we can use the magnification formula:

m = -v/u

where m is the magnification of the image, which is given as -1 in this case (since the image is virtual and inverted), and u is the distance of the object from the mirror.

Substituting the values, we get:

-1 = -60/u

Solving for u, we get:

u = 60 cm

Therefore, the distance of the screen from the mirror should be 60 cm in order to get a sharp image of the object. It's important to note that this solution assumes that the mirror and screen are both perpendicular to the optical axis of the mirror, and that the object is small compared to the size of the mirror. If these assumptions are not true, the solution may be more complex.

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Answer:

Carbon dioxide and water vapour

Explanation:

So the products of a combustion reaction are primarily:

carbon dioxide + water vapour, however other gases such as nitrogen, methane, and sulphur dioxide are also produced in smaller concentrations.

Carbon dioxide and water vapour are the main byproducts

Answer:

Carbon dioxide

Explanation:

The major byproduct of fossil fuel combustion is carbon dioxide. When fossil fuels such as coal, oil, and natural gas are burned, they release carbon dioxide into the atmosphere. This is because fossil fuels are made up of hydrocarbons, which are compounds made up of carbon and hydrogen. When these compounds are burned, they react with oxygen in the air to produce carbon dioxide [tex]\rm (CO_2)[/tex] and water vapor [tex]\rm (H_2O)[/tex].

Methane is also produced during fossil fuel combustion, but in smaller amounts compared to carbon dioxide. Sulfuric acid is not a byproduct of fossil fuel combustion, but rather a product of the reaction between sulfur dioxide [tex]\rm (SO_2)[/tex] and water vapor in the atmosphere. While water vapor is also produced during fossil fuel combustion, it is not considered a major byproduct, as it is a natural component of the air and atmosphere.

When the given wave pulse meets, then the diagram C represents the superposition of the pulses. Therefore, option C is correct.

The superposition of wave pulses refers to the phenomenon that occurs when two or more wave pulses are present in the same medium simultaneously. When these pulses overlap, their displacements combine to create a resultant wave.

The principle of superposition states that when waves meet, their displacements add algebraically at each point of overlap. This means that at any given point in space and time, the displacements of the individual waves are added together to determine the net displacement at that point.

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It takes 2.04 seconds for the object to accelerate from -10.0 m/s to -30.0 m/s.

Velocity is a measure of an object's speed in a specific direction. It is calculated by dividing the distance traveled by the time taken and specifying the direction of the motion.

We can use the following formula to find the time taken for an object to change velocity under constant acceleration:

Δv = a × Δt

where Δv is the change in velocity, a is the acceleration, and Δt is the time taken.

In this case, the initial velocity is -10.0 m/s, and the final velocity is -30.0 m/s. So, the change in velocity is:

Δv = (-30.0 m/s) - (-10.0 m/s) = -20.0 m/s

The acceleration of the falling object is -9.80 m/s² (negative because the object is falling downward).

Now, we can rearrange the formula to solve for Δt:

Δt = Δv / a

Substituting the values we have:

Δt = (-20.0 m/s) / (-9.80 m/s²) = 2.04 seconds

Therefore, The object accelerates from -10.0 m/s to -30.0 m/s in 2.04 seconds.

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The voltage drop across R3 is 34.5 volts.

Voltage, also known as electric potential difference, is a measure of the difference in electric potential energy between two points in an electrical circuit, and it is measured in volts. It is the driving force that moves electric charges through a circuit, from a higher potential to a lower potential.

To determine the voltage drop across R3 in this circuit, we need to first find the equivalent resistance of R2, R3, and R4, since they are connected in parallel. We can then find the total resistance of the circuit by adding the equivalent resistance in series with R1, and finally use Ohm's Law to calculate the voltage drop across R3.

The equivalent resistance of R2, R3, and R4 in parallel can be calculated as:

1/R_parallel = 1/R2 + 1/R3 + 1/R4

1/R_parallel = 1/20 + 1/25 + 1/10

1/R_parallel = 0.15

R_parallel = 1/0.15

R_parallel = 6.67 ohm

The total resistance of the circuit can be found by adding R1 and the equivalent resistance in series:

R_total = R1 + R_parallel

R_total = 15 + 6.67

R_total = 21.67 ohm

Now we can use Ohm's Law to calculate the current flowing through the circuit:

I = ET / R_total

I = 30 / 21.67

I = 1.38 A

Finally, we can use Ohm's Law again to calculate the voltage drop across R3:

V_R3 = I * R3

V_R3 = 1.38 * 25

V_R3 = 34.5 V

Therefore, the voltage drop across R3 is 34.5 volts.

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The intrepid hero has done 2.332 x Joules of work in pushing the crate.

To ascertain the work done by the traveler, we first need to find the power he applied on the case. As per Newton's subsequent regulation, force is equivalent to mass times speed increase, so the power applied by the traveler on the container is:

Force = mass x speed increase = 220 kg x 2  = 440 N

Then, we really want to work out the distance the case was moved. The pilgrim pushed the box a distance of 5.3 km, or 5,300 m.

At long last, we can compute the work done by the pioneer utilizing the equation:

Work = force x distance = 440 N x 5,300 m = 2.332 x 10^6 Joules

Thusly, the valiant legend has done 2.332 x  Joules of work in pushing the case.

The space pilgrim takes care of business on the case by applying a power that makes it speed up. The work done is equivalent to the power duplicated by the distance over which the power is applied. Involving the recipe for force, F=ma, and the given qualities for mass and speed increase, we can ascertain the power applied. Then, at that point, involving the recipe for work, W=Fd, and the given distance, we can ascertain the work done. The work done by the adventurer is 2.332 x  J.

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Answer:

C. does not change the velocity of an object.

Explanation:

Centripetal force is the force that acts on an object moving in a circular path and is directed towards the center of the circle. It is responsible for changing the direction of the object's velocity towards the center of the circle, but it does not change the magnitude of the velocity, which means that it does not affect the speed of the object. Therefore, option B and D are incorrect. The direction of the velocity is constantly changing due to the centripetal force, but the magnitude of the velocity, or speed, remains constant. Option A is also incorrect because centripetal force is not responsible for increasing the speed of the object, but rather for changing the direction of its velocity.

The density of the solid is (4.10 ± 0.78) × 10^3 kg/m^3.

To calculate the density of the cube below formula can be used:

ρ = m/V

where ρ is density, m is mass, and V is volume. For a cube, the volume is given by:

V = (side)^3

Therefore, the uncertainty in density can be calculated using the formula:

δρ/ρ = sqrt[(δm/m)^2 + 3(δs/s)^2]

where δρ is the uncertainty in density, δm is the uncertainty in mass, δs is the uncertainty in side, and s is the value of the side.

Now, putting in the given values:

s = (1.00 ± 0.06) cm = 0.01 ± 0.0006 m

m = (41.0 ± 0.4) g = 0.0410 ± 0.0004 kg

Volume, V = (0.01 m)^3

                  = 1.0 × 10^-6 m^3

Therefore, the density is:

ρ = m/V

  = 0.0410 kg/1.0 × 10^-6 m^3

  = 4.10 × 10^4 kg/m^3

Now substituting the values and calculating the uncertainty in density:

δρ/ρ = sqrt[(δm/m)^2 + 3(δs/s)^2]

δρ/ρ = sqrt[(0.0004/0.0410)^2 + 3(0.0006/0.01)^2]

δρ/ρ = 0.019

Therefore, the uncertainty in density is:

δρ = (0.019)(4.10 × 10^4 kg/m^3)

     = 779 kg/m^3

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Chemical change involves the rearrangement of atoms or molecules in a substance, resulting in the formation of new substances with different properties than the original substance.

A chemical change in a chemical reaction is a process where one or more substances undergo a chemical transformation, resulting in the formation of new substances with different chemical and physical properties than the original substances. During a chemical change, the atoms or molecules of the reacting substances are rearranged through chemical reactions, leading to the breaking and forming of chemical bonds and the release or absorption of energy.

Chemical changes occur when a material's chemical makeup is changed, creating one or more new compounds with qualities that are distinct from those of the original substance. Chemical reactions that result in the breaking and building of chemical bonds occur when the atoms or molecules of the substances involved are reorganized during a chemical shift. The release or absorption of energy in the form of heat, light, or sound is typically accompanied by this process.

Therefore, Rearranging atoms or molecules in a substance causes chemical change, which creates new compounds with differing properties from the original one.

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An example of a physical change of matter is (c) Melting ice.

Explanation: Melting ice is an example of a physical change of matter. When ice melts, it undergoes a change in state from a solid to a liquid, but its chemical composition remains the same. The water molecules in ice rearrange themselves to form liquid water, but no new substances are formed. This change can be reversed by cooling the liquid water to below its freezing point, causing it to solidify back into ice. Physical changes do not involve a change in the chemical identity of the substance, only a change in its physical properties, such as shape, size, or state.

In contrast, options a) Burning wood, b) Digesting food, and d) Rusting iron involve chemical changes. Burning wood involves a chemical reaction where wood reacts with oxygen to produce carbon dioxide, water vapor, and ash. Digesting food involves the breakdown of complex molecules into simpler ones through chemical reactions in the body. Rusting iron is a chemical reaction where iron reacts with oxygen and moisture in the air to form iron oxide.

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Note: The complete question is:

Which of the following is an example of a physical change of matter?

a) Burning wood

b) Digesting food

c) Melting ice

d) Rusting iron

Segment a, which is drawn from the center of the polygon perpendicular to one of its sides, is called the apothem.

The typical hexagon has a surface area of around 874.6 square meters.

To find the area of a regular polygon, use the formula:

Area = (1/2) x Perimeter x Apothem

Find the perimeter of the polygon. Since the polygon has n sides, use the formula:

Perimeter = n x s

where s = length of one side.

Since s = 18m, find n by using the formula:

n = 360° / (180° - (360° / n))

where n = number of sides.

Plugging in the values:

n = 360° / (180° - (360° / n))

n = 360° / (180° - (360° / 6))

n = 6

So the polygon has 6 sides, which makes it a hexagon.

Now find the perimeter:

Perimeter = n x s

Perimeter = 6 x 18

Perimeter = 108m

Next, find the apothem, use the formula:

Apothem = s / (2 x tan(π/n))

Plugging in the values:

Apothem = 18 / (2 x tan(π/6))

Apothem = 9√3 m

Now use the formula for the area:

Area = (1/2) x Perimeter x Apothem

Area = (1/2) x 108 x 9√3

Area ≈ 874.6 m²

Therefore, the area of the regular hexagon is approximately 874.6 square meters.

Find out more on hexagon here: https://brainly.com/question/28821314

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