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The mass of the other skater who is pushed is 51.4 kilograms.

According to the law of conservation of momentum,

The total linear momentum is always conserved in a system if no external force is applied.

So. we can write,

Initial momentum = final momentum

Initial momentum is zero as both the skater are at rest.

So, Final momentum should be 0,

Final momentum = 0

M₁V₁ + M₂V₂ = 0

M₁ is the mass of first skater,

V₁ is the final speed of the first skater,

M₂ is the mass of the second skater,

V₂ is the final speed of the second skater, V₂ will taken as negative because the second skater is pushed into opposite direction,

Putting all the values,

61(0.75) = -M₂(-0.89)

M₂ = 51.4 Kg.

So, the mass of the skater is 51.4 kg.

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The coefficients of the variables in each equation can be arranged in a row to create the coefficient matrix. A constant term should always be written on the right in standard form for each equation.

A coefficient matrix, a variable matrix, and a constant matrix can all be used to describe a system of linear equations in matrix form.

Think about the system,

2x+3y=8

5x−y=−2

X and Y are the variables that we have. As a result, the variable matrix can be written as [xy].

The constant terms from the equations, 8 and 2, are on the right side of the equivalence. The first and second rows of the constant matrix are occupied by the two integers in that order since they are the ones that correspond to the first and second equations. The matrix then takes the form [82].

The system is now represented by the equation [2531] [xy] = [82].

Now, the system is denoted as [2531] [xy]=[82].

You can see that the matrix representation is identical to the system of equations using matrix multiplication.

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A ball is released from a certain height of 20m then the time taken by the ball to fall is 2 sec and the velocity is 20m/s

Here: s (height) = h =20

a=g=±10m/s

a=10m/s (since it is dropped)

[tex]v^{2} -u^{2} =2as\\v^{2} =2*10*10\\v^{2}= 200[/tex]

(u=0; it is dropped not thrown)

v=20m/s

for calculating time we know,

v=u+at

20= 0+ 10xt

t=20/10

t=2seconds

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Answer:

1. If the knot is in equilibrium - no net force acts on the knot.

2. F1x = 0                 F1y = -F1

   F2x = -F2 cos θ1        F2y = F2 sin θ1

    F3x = F3 cos θ2        F3 = sin θ2

3.    Fx net = 0        

       Fy net = 0          for equilibrium to occur

4. F2 cos θ1 = F3 cos θ2

   F1 = M g = 2.1 * 9.8 = 20.6 N

    F2 sin 30 + F3 sin 60 = 20.6      balancing forces in y-direction

or   .5 F2 + .866 F3 = 20.6       (use this equation below )   (I)

    F2 cos 30 = F3 cos 60       as stated above

    .866 F2 = .5 F3        or F3 = 1.732 F2        substituting for θ

    .5 F2 + .866 (1.732 F2) = 20.6       using (I) above

   2.0 F2 = 20.6       and

     F2 = 10.3 N

    F3 = 1.732 * 10.3 = 17.8 N

Check:

    10.3 * .866 = .5 * 17.8        using values above

     8.92 = 8.9       forces balance

Also    .5 * 10.3 + .866 (1.732 * 10.3) = 20.6

option c A gun is fired horizontally from a tower with a muzzle velocity of 100 m/s. The bullet will arrive 100m away and arrive 1 second late if air resistance is ignored.

That is not to argue that there isn't a velocity increase. It absolutely depends on the specific firearm, cartridge, and loading in question. The reason for an increase in velocity is that the pressures are slightly higher, which causes the bullet to move less before engaging the rifling.

However, a significant improvement in accuracy is what many handloads will discover. A smaller distance to the rifling reduces the possibility of any bullet tipping and the variation in breech pressures that exists between different rounds. From round to round, slightly variable pressures can and will be produced even with equal powder loads, down to less than 1/10th of a grain. It's a simple reality.

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The magnitude of the magnetic torque on the coil is 9.435 Nm.

A magnetic field exerts a torque that tries to align the normal vector of a loop of current with the magnetic subject. the size of the torque on a loop

The magnetic torque, τ, skilled by using a unmarried particle of quantity V and domain magnetization Md whose moment is oriented at attitude θ to carried out induction B is given by means of τ=mHsinθ where m=MdV is the magnetic second of the particle.

This is the torque on a modern-wearing loop in a uniform magnetic field. This equation can be proven to be valid for a loop of any form. The loop includes a modern I, has N turns, every of area A and the perpendicular to the loop makes an angle θ with the field B.

Calculation:-

τ = μ×B

 = I A B sin90°

 = 4.38 × 3.14×(0.77)²×  1.157

 = 9.435 N m.

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To travel at 230 m/s at an altitude where the air density is 1.0 kg/m3, the jet's engines must deliver 111kN of thrust.

Air Density is defined as the mass of an object, including air, divided by its volume.

Scientists measure density in terms of kilogrammes per cubic metre when using the metric system.

The density of the air is influenced by its temperature, pressure, and water vapour content. We'll discuss dry air initially, so just temperature and pressure will be a concern.

In addition to a fundamental explanation of air density, we will go into how humans are affected by decreased air density, such as that experienced at high altitudes, how humidity influences air density in unexpected ways, and how air density affects things like aircraft, baseballs, and even racing automobiles.

The density of the air in a free environment drops as temperature increases.

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A Car is travelling at a speed of 60 km/h and then  accelerates to the velocity 85 km/h than acceleration in 5 sec is given by 18000 km/h² .

Acceleration of body is defined as rate of change of the velocity with respect to the time. Acceleration is a vector quantity it have magnitude as well as direction.

Acceleration =  (final velocity - initial velocity )/ time

Acceleration =  change in velocity / change in time

Given that in the question that the velocity changes from 60 km/h to 85 km/h in 5 sec =( 0.00138 h ) then the acceleration of the car is given as,

Acceleration of the car  = (60 - 85)/0.00138

Acceleration of the car  = 18000 km/h²

Acceleration of the car travelling with the velocity 60 km/h to final the velocity 85 km/h in time 5 sec is given by 18000 km/h².

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Acceleration of the sled is 0.62m/s^2

Acceleration of the child is 0.13m/s^2

They met at 2.6m from the child's initial position

The question is incomplete, the complete question is given below:

a 40.0-kg child and an 8.40-kg sled are on the surface of an icy lake 15.0 meters apart. the child exerts a 5.20 n force on the sled towards them via a rope they’ve attached.(a) What is the acceleration of the sled? m/s2(b) What is the acceleration of the child? m/s2(c) How far from the child's initial position do they meet? m

Part a

Acceleration of the sled:

Mass of sled=8.40kg

Force=5.20N

Acceleration=F/m

                     =5.2/8.4

                      =0.62m/s^2

Part b

Acceleration of the child

Mass of the child=40kg

Force=5.20N

Acceleration=F/m

                    =5.2/40

                    =0.13m/s^2

Part c

Distance from the child's initial position they met

They accelerate towards each other at =0.62+0.13

                                                                 =0.75m/s^2

The time to meet is given by:

We use kinematic equation to find this,

s=ut+1/2at^2

u=0m/s^2

a=0.75m/s^2

s=15m

t=?

15 =0*t+ (1/2) (0.75) t^2

15=(1/2)*0.75t^2

t=6.32 sec

The child moves:

s=ut+1/2at^2, u=0, a=0.13, t=6.32

 =(1/2) (0.13) 6.32^2

 =2.6m

Hence they met at 2.6m from the child's original position

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The environmental impact of the changes in the amount of energy resources is reduction in air pollution.

Energy resources are the materials that can act as sources of energy which is grouped into two namely:

From the given figures,

In 2014 renewable energy = 19%; while in 2015 it is = 25%

In 2014 non renewable energy when added = 79%; while in 2015 it is = 73%

This shows that there was reduction in the use of non renewable energy from 2014 to 2015 by 6%.

This would affect the environment positively as there would be reduction in air pollution caused by non renewable energy resources.

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With low-frequency stimulation, the muscle relaxes fully between contractions, resulting in identical twitches twitches per stimulus.

Alpha motor neurons are the motor neurons that innervate the fibers of the skeletal muscle. A number of branches, each innervating a different muscle fiber, are formed as the alpha motor neuron enters the muscle. A motor unit is made up of one alpha motor neuron and all of the muscle fibers it innervates. Small motor units with 3-5 muscle fibers per motor neuron are found in muscles that are involved in delicate, coordinated control. Our hand and eye muscles, as well as those that control eye movement, have very small motor units.

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150 Watts is the power of 600 J of work completed in 4 seconds.

The rate at which work is completed is referred to as power. It has the following mathematical expression:

[tex]Power = work/time[/tex]

The power can be obtained using the above formula.

From the mentioned query, the following information was observed:

Work = 600 J

Time = 4 s

Power =?

[tex]Power = Work/Time \\Power = 600/4[/tex]

power = 150 watts

Thus, 150 Watts are generated by 600 J of work completed in 4 seconds.

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A system of diatomic ideal gas contracts from a volume of 4.1 m3 to a final volume of 1.3 m3. if the process proceeds at constant pressure of 148 kpa. The energy transferred by heat, where positive is energy transferred into the system, and negative is energy transferred out of the system is(Q)=  1450.4 KJ

Energy is a physical term that means if a force is applied on a object and the object move some distance that means there is some energy is generate in that object. It is a vector quantity. It can be measured in Joule.

To calculate the energy we using the formula,

Q = nCp AT

Or, Q = nCp(T₂-T₁)

Or, Q = nCp[P(V₂ - V₁) /nR] ....eq(1)

Here we are given,

V₁ =Initial volume = 4.1 m³

V₂= final volume = 1.3 m³

Process is isobaric so,

p= Constant pressure= 148 kP = 148 x 10³ P

n = Number of moles = 1

Cp= specific heat at constant pressure.

For diatomic molecule Cp = 7R/2

we know, AT = T₂-T₁

From ideal gas equation

PV = nRT

T = PV/ nR

T₁= PV₁/nR

And T₂ = PV₂/nR

Now to calculate energy = Q in KJ transferred by heat at constant pressure.

Substitute all these values in eq (1)

Q = n(7R/2) [P(V₂ - V₁) /nR]

Or, Q = 7P(V₂ - V₁)/2

Or, Q = 3.5(148 × 10³ P) (4.1- 1.3) m³

Or, Q = 1450.4 x 10³ J ........(P.m3 = J)

Or, Q = 1450.4 KJ

From the calculation we can say that, The energy transferred by heat, where positive is energy transferred into the system, and negative is energy transferred out of the system is(Q)=  1450.4 KJ

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The current in each branch of the circuit is 9.5 A and 0 A.

Point B, according to Kirchoff's junction law equation is

i = i₁ + i₂                                                            ......equation 1

Now, according to Kirchoff's Loop law,

Loop 2 is anticlockwise, calculates the current i₂ equation is

21.4 - 50i₂ - 6 - i - 100i₂ = 0

150i₂ + i = 15.4                                                            ......equation 2

Loop 1 is clockwise, calculates the current i₁ equation is

20.5 - 30i₁ - 6 - i - 40i₁ - i₁ = 0

80i₁ + i = 14.5                                                            ........equation 3

substitute equation 1 in equation 3 for the value of i,

81i - 80i₂ = 14.5                                                  .....equation 3

Upon, subtracting equation 3 from equation 2, we get i₂ = 9.5 A

substituting the value of i₂ in equation 3, we get i = 9.5A

Hence on substituting value for i₁, in equation 1 , we get i₁ = 0 A

Hence, the current in each branch of the circuit is 9.5A, 9.5A, 0A

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The cycling of matter in Earth’s atmosphere is related to the movement of dust from the Sahara desert to the Amazon because the biosphere is a major ecosystem that connects all ecosystems around the world.

The ecosystems are specific geographic regions in which biotic factors (life) and abiotic factors (e.g. dust) interrelate to shape the environmental condition of the area, while the term biosphere makes reference to a major ecosystem that connects all these region in the world.

Therefore, we can conclude that ecosystems are interconnected to shape the biosphere, thereby the phenomena that occur in Sahara desert are able to modify the conditions in a Forest like Amazon.

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a. The magnitude of the force exerted on the electron F = 3.64*10^-18N

b. The force F is 4.08*10^11 times the weight of the electron

a. In order to calculate the magnitude of the force exerted on the electron you first calculate the acceleration of the electron, by using the following formula:

v: final speed of the electron = 7.00*10^5 m/s

vo: initial speed of the electron = 3.00*10^5 m/s

a: acceleration of the electron = ?

x: distance traveled by the electron with certain speed= 5.0cm = 0.05m

you solve the equation (2) for a and replace the values of the parameters:

[tex]a=v^{2} - V^{2} /2x[/tex]

a=4×10^12 m/s²

to calculate the force we now use the second Newton law :

F=ma

m: mass of the electron = 9.11*10^-31kg

F=3.64*10^-18N

The magnitude of the force exerted on the electron is 3.64*10^-18N

b. given weight of  electron is :

Fg=mg

Fg = 8.92*10^-30N

The Division between the force electron and the weight of the electron F is:

F/Fg=4.08*10^11

The force F is 4.08*10^11 times the weight of the electron

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Any bridge is subject to three different types of forces: the dead load, the live load, and the dynamic load. The weight of the bridge itself is discussed in the first of these words.

Any of the four fundamental forces in physics—gravitational, electromagnetic, strong, and weak—that control how objects or particles interact as well as how some particles decay—is referred to as a fundamental force, also known as a fundamental interaction.

Compression and tension are the two main forces that are ever-present on a bridge. A force that compresses or shortens the object it is acting on is known as a compressive force. A force known as tension or tensile force works to stretch or expand the object it is acting on.

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The power dissipated by the resistor is 3000W.

Electrical power, or (P), in a circuit is a unit of measurement for the rate at which energy is consumed or produced inside a circuit. The energy produced or delivered by an energy source, such as a voltage, is absorbed by the associated load.

In physics, power is referred to as the rate of energy conversion or transfer over time. The unit of power in the SI system, often known as the International System of Units, is the Watt (W). A single joule per second is one watt. Power was formerly referred to as activity in some research. A scalar quantity is power.

The resistor's power dissipation can be computed as P = I²R

here ,

I = 2 A

R =  750

Therefore P= 2² x 750 W

= 3000W

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The magnitude of the total velocity of the package at the moment it is thrown as seen by an observer on the ground is D = 193m/s  15.2s = 2934 m.

What is velocity ?

velocity is the prime indicator of the position as well as the rapidity of the object

Sol-

1. 0.5gt^2 = 2010 m.

4.9t^2 = 2010.

t = 20.3 s. = Fall time.

D = Xot. = 193m/s 20.3s = 3909 m.

2. V=sqrt(Xo^2+Yo^2)=sqrt(193^2+58^2) = 202 m/s.

3. Vot + 0.5gt^2 = 2010 m.

58t + 4.9t^2 = 2010.

4.9t^2 + 58t - 2010 = 0.

Use the  quadratic formula we are get  

t = 15.2 s. = Fall time

D = 193m/s  15.2s = 2934 m.

D = 193m/s  15.2s = 2934 m.

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At constant temperature pressure is inversely proportional to volume, so pressure will increase.

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All different kinds of electrical wires and cables are routinely tested by measuring insulation resistance. This test is frequently used as a customer acceptance test in production settings.

This test is frequently used as a customer acceptance test in production settings, with the customer frequently defining the minimum insulation resistance per unit length.

In contrast to a real HIPOT test, the results of the IR Test are meant to provide information on the quality of the bulk insulation material rather than being helpful in identifying specific insulation flaws.

Many wire and cable manufacturers use the insulation resistance test to track their insulation manufacturing processes and identify emerging issues before process variables stray outside of permitted limits, even when it is not needed by the end customer.

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1year is the orbital period of this planet.

The orbital period  is the quantity of time a given astronomical object takes to complete one orbit around every other object. In astronomy, it generally applies to planets or asteroids orbiting the solar, moons orbiting planets, exoplanets orbiting different stars, or binary stars.

Kepler's third law - indicates the relationship among the length of an items orbit and the common distance that it's far from the issue it orbits. this could be used  for something clearly orbiting round another factor.

Entire revolution is known as the orbital duration. At 200 km that is approximately ninety minutes. The orbital duration will increase with altitude for two motives. First, as the altitude increases, Earth's gravity decreases, so the orbital speed had to stability it decreases.

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Electronic Configuration:

Normally, the electronic configuration will be written through the atomic number of the particular element. The electrons fill in this accruing to the energy level and orbitals like s, p, d, and f

The atomic number for the Beryllium is 4. So, the electronic configuration of beryllium is

In option B, the s block has two electrons and both are having an upward spin orientation. This is incorrect, as one must be in the upward orientation and the other will be in the downward orientation

The charge of 15 Chas been flowing through a circuit with current of 2 A for a time period of 7.5 s

Q = I t

Q = Electric charge

I = Electric Current

t = Time

Q = 15 C

I = 2 A

t = Q / I

t = 15 / 2

t = 7.5 s

Electric current is the rate of flow of charge. In a circuit the current always flows from the negative terminal to the positive terminal. Its unit is Ampere ( A ) which is C / s.

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The red light is the least refracted by the prism.

Each beam of light with a particular wavelength is slowed differently by the glass. Since violet light has a shorter prism wavelength, it is brake more than the longer wavelengths of red light. accordingly, violet light is bent the most while red light is bent prism the least. Prism on dispersion, the light rays with longer wavelengths bend less than ones with shorter wavelengths. Since red has the longest wavelength, it bends the least. prism Among the 7 constituent colors of light, violet light has the least wavelength and hence it deviates the most, and red light having the largest wavelength deviates the least. Hence, prism the required order is violet, indigo, blue, green, yellow, orange, and red.

So we can conclude that in a prism, the red light is less refracted.

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Fraction of the initial kinetic energy is lost in the collision f = 3/4.

Two balls of masses M and 3M kinetic energy

Initially before collision:

Speed of ball of mass M = −V0 (Right direction is taken as negative)

Speed of ball of mass 3M = +V0

Finally after collision: Speed of ball of mass M = v

Speed of ball of mass 3M = V02

[tex]Finding the fraction(f) of initial kinetic energy lost in the collisionf=1−Final Kinetic EnergyInitial Kinetic Energyf=1−12×M×(v02)2+12×3M×(v02)212×M×(−v0)2+12×3M×(v0)2f=1−v024v02f=1−14=34[/tex]

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The theory is that:

H0: The amount of salt added to ice has no bearing on how quickly it melts.

H1: The amount of salt added to ice will have an impact on how quickly it melts.

By altering the rate at which salt is introduced to the equation, the independent variable can be modified.

The ice, which is the dependent variable, will alter or melt in response because it will get smaller as the rate at which salt is injected rises.

The boiling point of water, or the temperature at which it may erupt, rises when salt is added to it. For every 58 grams of dissolved salt per kilogram of water, the temperature required to reach boiling rises by around 0.5 C. This is an illustration of an elevated boiling point, which is not just a property of water.

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The 50 N force applied at an angle to the crate may be broken down into horizontal and vertical force components. As the angle created by the rope, e, increases from 0° to 90°, the horizontal component, Fx, drops and the vertical force component, Fy, increases.

The components of a force are the force parts acting in perpendicular directions, horizontal and vertical, that combine to give the specified force.

The direction the crate is sliding = The horizontal, x-direction

The force exerted by the man = 50 N

The angle of the rope

The components of the force are therefore:

Horizontal component, Fx = 50 × cos(8)

Vertical component, F₁ = 50 x sin(0)

The value of cos(e) and sin(e) as the angle the rope makes with the horizontal,

e, increases from 0° to 90° are as follows:

Therefore, the horizontal component of the force exerted by the man, Fx has a maximum value at = 0, and decreases to 0, as increases from 0° to 90°.

The vertical component of the force exerted, Fy, has a minimum value of O at → = 0°, and the value of sin(e) and therefore Fy, increases to a maximum of (sin(90°) 1) 50 N as increases to 90°.

Please find attached the graph showing the components of the force, Fx, and Fy, exerted by the man as the angle formed by the rope increases from 0° to 90°

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We may not consider the use of hair samples today because DNA analysis is more modern.

The term DNA refers to the molecule that contains the genetic material of the living things. Hence, we could use the DNA sample to be able to solve very difficult cases. This is because the DNA sample can be able to tell the exact identity of the person that involved,

Before the advent of the DNA, the hair sample was one of the very reliable ways be which evidence could be gathered to solve  crimes. Hence; Modern DNA analyses have made testimony using hair samples obsolete.

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Missing parts;

Which of the following statements is most true regarding the use of testimony on hair samples in courts today?

Hair samples are replacing DNA as an easily available, go-to source for identifying suspects

Modern changes in the discipline mean that any police officer can provide testimony on hair samples

Modern DNA analyses have made testimony using hair samples obsolete

There’s solid research that should lead us to be skeptical of testimony based on hair samples

The dependent variable in the experiment in which the weight of each fish is recorded daily is the fish' weight.

A dependent variable is the variable that cannot be controlled in an experiment. An independent variable is the controllable variable/factor in an experiment.

In this experiment, the amount of food fed and how often the food fed can be controlled. The fat gained by the fish and the weight of fish cannot be controlled.

Therefore, in this experiment the dependent variable is weight of fish.

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