what is the x -coordinates of the center of mass? hint: divide the triangle into vertical strips of width dx , then relate the mass dm of a strip at position x to the values of x and dx .

The change in internal energy will be 27J when heat is released.

Every time a process occurs, it is usually accompanied by an energy shift. Energy comes in many forms, such as heat, light, and work.

The generation or absorption of energy in various processes dictates that each substance must be associated with a certain amount of energy. Its actual value depends on the nature of the material and the conditions of temperature, pressure, volume and composition.

The sum of various types of energy associated with atoms and molecules, such as electronic energy (Ee), nuclear energy (En), chemical bond energy (Ec), potential energy (Ep), and kinetic energy (Ek). Sum of translational energy (Et), vibrational state energy (Ev), and rotational energy (Er).

Represented by the symbol U or E.

U or E = Ee + En + Ec + Ep + Ek

The energy stored in matter in this way is called internal energy.

U=65-38=27J

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a)how far the tree was found to be 0.9605 m

b) the height of the tree was found to be 0.14m

What exactly is object distance?

Object Distance, denoted by s, is the distance between an object and an optical element.

What are the qualities of a mirror image?

• The image obtained is fictitious.

•The picture is flipped laterally.

• The picture is upright.

• The picture has the same dimensions as the thing.

• The distance between the image acquired from the mirror and the item gained from the mirror is the same.

As a result, the distance between the tree and the mirror is the same as the distance between the picture and the mirror, i.e. 0.9605 m, and the height of the tree is the same as the height of the image, which is 0.14 m.

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a)how far the tree was found to be 0.9605 m

b) the height of the tree was found to be 0.14m

What exactly is object distance?

Object Distance, denoted by s, is the distance between an object and an optical element.

What are the qualities of a mirror image?

• The image obtained is fictitious.

•The picture is flipped laterally.

• The picture is upright.

• The picture has the same dimensions as the thing.• The distance between the image acquired from the mirror and the item gained from the mirror is the same?

As a result, the distance between the tree and the mirror is the same as the distance between the picture and the mirror, i.e. 0.9605 m, and the height of the tree is the same as the height of the image, which is 0.14 m.

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The aspect of using double-sided printing was discussed in class as the most significant benefit of using only one sheet of pаper, insteаd of using two.

Printing single-sided used to be very common, but these dаys duplex printing is becoming more populаr. Double-sided printing is eco-friendly аnd cаn help you sаve money. Аrizonа Stаte University sаved over 700 trees аfter they switched to double-sided printing. In estimаtion, double-sided printing cаn sаve your business аbout hаlf of the cost of printing single-sided pаges.

Since duplex printing uses hаlf the pаper thаt one-sided printing uses, businesses cаn reduce their mаteriаls costs. Not only аre you sаving our plаnet’s trees, but you аre sаving your business money.

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The fraction of the iceberg that is above the surface of the water is 8.3 %.

The specific gravity of any material is defined as the ratio of the density of the material to the density of water.

Mathematically, the formula for specific gravity of materials =

= S.G = density of the material / density of water

Specific gravity of the iceberg = 0.917

Specific gravity of the seawater = 1.025

The fraction of the iceberg submerged in the seawater =

= 0.917 = 0.917 x 100 %

= 91.7 %

The fraction of the iceberg that is above the surface of the water =

= 1 - 0.917

= 0.083

= 0.083 x 100 %

= 8.3 %

Thus, the fraction of the iceberg submerged in the water is a function of the specific gravity of the iceberg.

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A group of kids were taking a tour and looking inside a cave. The pupils in the cave soon learned that every time they spoke, there was an echo. i.e. (D). the reflection of the sound waves is correct option.

As a result, the reflecting object must be farther away for an echo to be audible to someone standing close to the sound source.

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Brewster's angle

When unpolarized light is incident at Brewster's angle on a smooth glass surface, the reflected light is totally polarized while the refracted light is partially polarized

Polarization:

Polarization is a assets making use of to transverse waves that specifies the geometrical orientation of the oscillations. In a transverse wave, the route of the oscillation is perpendicular to the direction of motion of the wave.In contrast, for longitudinal waves, such as sound waves in liquids or gases, the particles are always displaced in the direction of propagation during oscillation, so these waves have no polarization. Transverse waves that indicate polarization include electromagnetic waves such as light and radio waves, gravitational waves, and sound waves in solids (transverse waves).

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The energy associated with motion is called kinetic energy.

Your body doesn't just have energy when you're in motion. When an object is in motion it has a finite amount of kinetic energy. However, when not in motion, the body can store energy in the form of potential energy.

The body can also have a certain internal energy. This can be explained as follows. Energy is basically the ability of any body to do work. Suppose you are sitting ideally in your room and suddenly you realize that someone has changed the position of your study desk and you want to change it. So I pushed the table and moved it to where it suited me. This means that we have applied a finite force that causes displacement, i.e. we have done some work. So you had the ability to work properly. This means that you had energy in the form of internal energy.

[tex]mgh+\frac{mV^2}{2}=Energy \\\\m[gh+V^2/2]=E[/tex]

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The final temperature of the water is equal to 24.77 °C.

The specific heat capacity can be explained as the amount of heat needed to increase the temperature of one unit of material by one degree Celsius. The specific heat capacity depends upon the nature of the material.

The mathematical equation is used to calculate the specific heat is equal to:

Q = mCΔT

Given, the mass of the water, m = 1 Kg

The initial temperature of the water, T₁ = 20°C

The specific heat capacity of water, C =  4186 J/(kg °C)

The heat added to the cup, Q = 20,000 J

The final temperature of the water can be determined as:

20000 = 4186 × 1 × (T₂ - 20)

T₂ - 20 = 4.77

T₂  = 24.77 °C

Therefore, the final temperature of the water is 24.77 °C.

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Using Conservation of energy property

The equilibrium temperature reached is T = 33.8 C

According to the rule of conservation of energy, the overall energy of an isolated system stays constant over time. According to this law, which  first suggested and tested, energy can only be changed or moved from one form to another and cannot be generated or destroyed. For instance, when a stick of dynamite explodes, chemical energy is transformed into kinetic energy. One can calculate the precise reduction in chemical energy in the dynamite's combustion by adding up all the energies released during the explosion, including the kinetic and potential energy of the fragments, heat, and sound.

Heat given off by steam = Heat absorbed by ice

Qs = Qi

[tex]Qs = 0.0075(22.6\ X\ 10^5) + 0.0075(4186)(100-T)\\Qi = 0.040(3.34\ X\ 10^5) + 0.040(4186)(T-0)[/tex]

where

T = equilibrium temperature of the system

Since Qs = Qi,

[tex]0.0075(22.6\ X\ 10^5) + 0.0075(4186)(100 - T) = 0.040(3.34\ X\ 10^5) + 0.040(4186)(T - 0)[/tex]

[tex]0.1695\ X\ 10^5 + 31.395(100 - T) = 0.1336\ X\ 10^5 + 167.44(T)[/tex]

Simplifying,

[tex]0.1695\ X\ 10^5 + 3139.5 - 31.395T = 0.1336\ X\ 10^5 + 167.44T[/tex]

Combining terms,

[tex]167.44T + 31.395T = 0.1695\ X\ 10^5 - 0.1336\ X\ 10^5 + 0.031395\ X\ 10^5[/tex]

and solving for T,

T = 33.8 C

Using Conservation of energy property

The equilibrium temperature reached is T = 33.8 C

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Based on the wavelength of the light, the energy of the photons emitted by a sodium lamp is 17.74 X 10² kJ/mol.

The energy is given by the formula;

E = hv

where,

h is Planck's constant = 6.63 X 10⁻³⁴ Js

f is frequency of light

Also, f = c/λ

where,

c is velocity of light = 3.0 X 10⁸ m/s

λ is wavelength of light = 589 nm = 6.75 X 10⁻⁷ m

1 mole of sodium atom will emit 6.02 X 10²³ photons,

N = 6.02 X 10²³ photons,

Thus,

= E = Nhc/λ

= E = (6.02 X 10²³ X 6.63 X 10⁻³⁴ J.s X 3.0 X 10⁸ m/s)/6.75 X 10⁻⁷ m

= E = 119.74 X 10⁻³ / 6.75 X 10⁻⁷

= E = 17.74 X 10⁵ J/mol

= E = 17.74 X 10² kJ/mol

Therefore, the energy of the photons emitted by a sodium lamp is 17.74 X 10² kJ/mol.

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The magnitude of force ( 50 N ) which satellite exerts on her but in opposite direction.

We will apply the Newton's Third Law of motion for solving this problem, which says that, "To each activity, there is an equivalent and inverse response". And that implies if any article (say object 1) apply some power on another article (say object 2), then, at that point, the item 2 will likewise apply same greatness of power on object 1, yet it will be in inverse heading.

So, we have amount of force exerted by a 65-kg astronaut on satellite which is 50N.

To balance that force, satellite will apply same amount of force on astronaut but in just opposite direction .

F' = - F

or F' = - 50 N.

Here, negative sign shows that the direction of force is opposite.

Hence, required value of force is 50N.

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The acceleration of this object is 5 m/s².

Initial velocity = 0 m/s (since the object starts from rest).

Distance = 10 meters

Time = 2 seconds.

To find the acceleration of the object, we would use the second equation of motion:

Mathematically, the second equation of motion is given by the formula;

= s = ut + (1/2)at²

Where;

S represents the distance covered.

u is the initial velocity.

a represents the acceleration.

t is the time measured in seconds.

Substituting the parameters into the formula, we have;

= 10 = 0 + (1/2)a(2)²

= a = 10/2

= a = 5 m/s²

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Then the depth of the ice is 26.55 x 10¹² m

Let speed of the radio wave be represented as 'v'

Let frequency of the radio wave be represented as 'f'

Let distance of the radio wave be represented as 's'

Let time period of the radio wave be represented as 't'

From the formula for distance:

v=s/t

v= s x 1/t

Frequency is the inverse of time period. So, 1/t in the above formula can be replaced by f.

v = s x f

putting values in the above equation

t = 32.9 x 10⁻⁶ s

v = 1.7 x 10⁸ m/s

The, f = 1/t

f = 1/3.2 x 10⁻⁶ s⁻,

So,

s = 1.7 x 10⁸ x 1/3.2 x 10⁻⁶

= 1.7/3.2 x 10⁸⁺⁶

= 0.531 x 10¹⁴

= 53.1 x 10¹²

Then the depth of the ice would be s/2 as the distance is covered twice by the wave in the given time frame.

Depth of ice = 53.1 x 10¹²/2

Depth of ice = 26.55 x 10¹² m

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The pressure exerted on the mirror by the light emitted from the 200-w incandescent light bulb is negligible. This is because the pressure exerted by light is proportional to the intensity of the light .

and the intensity of the light drops off as the square of the distance. At a distance of 5.0 m, the intensity of the light is extremely low, and thus the pressure is practically zero.

Step 1: Calculate the intensity of light:

We know that the power of the light bulb is 200 W, so the intensity of light is given by:

I = P/4πd2

Where P is the power of the light and d is the distance from the light to the mirror.

In this case, we have:

I = 200 W / 4π(5.0 m)2

I = 0.0025 W/m2

Step 2: Calculate the pressure exerted by the light on the mirror:

We know that the pressure exerted by the light on the mirror is given by:

P = I/c

Where I is the intensity of the light and c is the speed of light.

In this case, we have:

P = 0.0025 W/m2/3.00 x 108 m/s

P = 8.3 x 10-10 N/m2

Therefore, the pressure exerted by the light emitted from the 200-w incandescent light bulb  on a mirror at a distance of 5.0 m is 8.3 x 10-10 N/m2.

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An earthquake's energy output when it has a magnitude of 2.7 is 4.5 × [tex]10^{12}[/tex].

The magnitude of an earthquake is the most common indicator of its size. It serves as a barometer for the size of an earthquake's single source. Because it is the same no matter where and how you see it, the following calculation may be done:

magnitude, M = 2 ÷ 3 log(E ÷ [tex]E_{0}[/tex])

Where E is the power generated in Joules and M is the lowest magnitude emitted by such an earthquake, [tex]E_{0} = 10^{4.4}[/tex].

Assuming 5.5, the same magnitude is provided when the preceding equation is used:

M = 2 ÷ 3 log(E ÷ [tex]E_{0}[/tex])

5.5 = 2 ÷ 3 log(E ÷ [tex]E_{0}[/tex])

8.25 = [tex]log(\frac{E}{10^{4.4}})[/tex]

[tex]10^{8.25}[/tex] = [tex]\frac{E}{10^{4.4}}[/tex]

E = [tex]10^{4.4}[/tex] × [tex]10^{8.25}[/tex]

E = 4.5 × [tex]10^{12}[/tex]

Therefore the final answer is 4.5 × [tex]10^{12}[/tex].

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Answer:

outer layer

Explanation:

The average atomic mass of element X is numerically equal to 85.48 amu.

Given , Percentage of isotope 1 = 72%

            Percentage of isotope 2 = 28%

            Mass of isotope 1 = 84.9 amu

            Mass of isotope 2 = 87 amu

i.e.

Average atomic mass = (0.72 * 84.9) + (0.28 * 87) = 85.48 amu

So the average atomic mass of element X is numerically equal to 85.48 amu.

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The magnitude of the torque about an athlete shoulder is 48.02N-m if he is holding steel ball in his hand.

We know that torque is defined as the cross product of distance of point from applied point to the force applied by the external source at that point, in other words

Torque=distance × Force

     =>τ = r × F

Total mass hold by the athlete is = 3+4=7kg.

Now, we need to focus on the force acting on an athlete. So we are assuming an athlete is standing on the surface, so acceleration due to gravity have some  role to exert  some amount of force on athlete.

Therefore, Force=mg

=>F=7×9.8

=>F=68.6Kg-m/sec²

Now, distance of force from applied point is 70cm=0.7m

Therefore, Torque=0.7×68.6

              =>Torque= 48.02N-m

Hence, value of Torque is 48.02N-m.

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The cochlea is the organ responsible for hearing, and it is composed of several interconnected structures through which a pressure wave passes. Beginning at the oval window, the pressure wave then moves through:

And finally exits through the round window.

Order the structures that a pressure wave passes through in the cochlea:

This chain of structures creates a pathway that allows the pressure wave to pass through the cochlea, converting sound waves into signals that are then sent to the brain and interpreted as sound.

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Answer:

Below

Explanation:

Going forward and stops .....the backpack wants to keep going forward due to its inertia.

The momentum of the clay and the cart is 34 kgm/s.

Momentum can be defined as the product of mass and velocity.

To calculate the momentum of the clay and the cart, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, their momentum is 34 kgm/s.

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The momentum of system is zero because velocities of the bodies may be equal to zero or may be be equal in magnitude but opposite in direction.

We know very well that momentum of body is given by the product of mass of that body with the velocity of that body, or in other words

Momentum=mass × velocity

=>p=m × v

Since, we are given that total momentum of the system is zero. In this universe every object has some mass ,so mass never be zero and never be negative. Now, talking about the velocity of the body. If velocity of all bodies is zero, in that total momentum of the system remains zero. So, this will be possible.

Now, there is one more possibility in the system two bodies have same velocity in magnitude but their direction of propagation is opposite to each other. In that case also their velocity cancel each other, due to that momentum remain as it is zero. So, this is one of possibility.

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Nancy is hard at work on a scarf. She spends twenty seconds on every inch of the scarf she knits. Her desired scarf length is sixty inches. Given, It takes 0.2 of an hour to knit a single inch of the scarf. Here, 0.2 of an hour refers to 12 minutes. Therefore, It takes 12 minutes to knit an inch of a scarf.

Since Nancy takes 12 mins to knit an inch of a scarf, then for 60 inches, it would be,

1 inch -> 12 minutes

60 inches -> 12 * 60 minutes = 720 mins to knit 60 inches of a scarf.

Now, convert the minutes into hours,

720 mins -> 720 / 60 = 12 hours.

Therefore, it takes 12 hours to knit 60 inches of a scarf.

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It take  1.45s to the Martian detector to hit the ground.

We are know that,

Acceleration = a = - 3.8 m/s²

Distance = r = 8m

Final velocity = v =  0 (The rock's velocity is zero at its maximum height.)

Time = ?

Thus to calculate the hitting time of the Mars ground we can use the formula,

acceleration  = change in velocity / time

First of all we have to calculate the initial velocity (u) of the Martian i.e.

a = u²/r

u² = a.r

u² = (-3.8m/s²)× 8m

u² = -30.4m²/s²

u = - 5.51 m/s

Putting the value of initial velocity in the above equation we can get the hitting time,

-3.8 m/s² = 0 - (5.51m/s)/t

t = (-5.51m/s)/(-3.8m/s²)

t = 1.45s

The Martian detector hits the ground in 1.45 seconds.

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A muon takes to decay in the observer's rest frame is 3.08 μs.

A muon is an unstable subatomic particle that decays into other particles with a mean lifetime of 2.20 μs. This is in the muon reference frame.

The formula for the relativistic factor

[tex]\gamma \:=\: \frac{1}{\sqrt{1 \:-\: (\frac{v}{c})^2}}[/tex]

[tex]\gamma \:=\: \frac{1}{\sqrt{1 \:-\: (\frac{0.7c}{c})^2}}[/tex]

[tex]\gamma \:=\: \frac{1}{\sqrt{1 \:-\: 0.7^2}}[/tex]

[tex]\gamma \:=\: \frac{1}{\sqrt{1 \:-\: 0.49}}[/tex]

[tex]\gamma \:=\: \frac{1}{\sqrt{0.51}}[/tex]

[tex]\gamma \:=\: \frac{1}{\sqrt{1 \:-\: 0.7^2}}[/tex]

[tex]\gamma \:=\: \frac{1}{0.714}[/tex]

γ = 1.4

Relativistic time interval formula

t = γ t₀

t = 1.4 × 2.2

t = 3.08 μs

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Answer:

true

Explanation:

basic sports knowlegde

The camera should be focused for 6.2 m.

In addition, we already know that the main use of plane mirrors is to observe an object's reflection. Periscopes and kaleidoscopes, vehicles, shaving mirrors, dental mirrors, torch lights, solar cookers, and security-related uses are just a few of the many functions and applications of a plane mirror.

As we're standing 3.1 m away from the mirror so our image is also formed 3.1 away from the mirror as the mirrors used for this purpose are plane mirrors. So the camera should be focused for twice the distance at which we're standing from the mirror i.e 3.1 * 2 = 6.2 m

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The speed of light from the source in the spacecraft's frame of reference is given by the formula Ux = Ux+v/C2+2Uxv/C2. The pace at which an object's position changes in relation to a frame of reference.

And is a result of time. An object's speed and direction of motion are specified by its velocity. A crucial idea in kinematics is velocity. Two different categories of frame of reference are as follows: An object that is fixed or moving at a constant speed is said to have an inertial frame of reference. The First Law of Motion of Newton is directly relevant in this frame. The frame of reference refers to the context in which an observer is placed when recording data.

Ux = Ux+v/C^2+Uxv/C^2

here, c =c/2

Ux = Ux+v/C^2+2Uxv/C^2

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The magnitude of the velocity change increases with lengthier acceleration. When acceleration is constant, the change in velocity is directly proportional to time.

The rate at which the velocity of any moving object changes is measured by acceleration. The velocity change divided by the time represents the acceleration. Both the magnitude and the direction of acceleration are present.

Therefore, An object's motion can be depicted by a velocity-time (or speed-time) graph if it moves in a straight line. The line's gradient is equal to the object's acceleration.

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The range of visible light is from 7.69 * 10¹⁴ Hz.

Frequency is defined as the number of complete cycles a wave can complete in one second. We know that, the SI unit of frequency is Hertz (Hz).

We know the relation between speed of light, wavelength and frequency as

v = f * λ ----(1)

where, v is the speed of light in air

f is the frequency of visible light

λ is the wavelength of visible light

Making ' f ' as subject in the above equation as,

f = v / λ ----(2)

We know that speed of light in air is 3 * 10⁸ m/s

λ = from 3.9 * 10⁻⁷ m

Substituting the values in the above equation (2), we have

f = v / λ = (3 * 10⁸)/(3.9 * 10⁻⁷) = 0.769 * 10¹⁵ Hz = 7.69 * 10¹⁴ Hz

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