On your first day at work as an electrical technician, you are asked to determine the resistance per meter of a long piece of wire. The company you work for is poorly equipped. You find a battery, a voltmeter, and an ammeter, but no meter for directly measuring resistance (an ohmmeter). You put the leads from the voltmeter across the terminals of the battery, and the meter reads 12.1 . You cut off a 20.0- length of wire and connect it to the battery, with an ammeter in series with it to measure the current in the wire. The ammeter reads 6.50 . You then cut off a 40.0- length of wire and connect it to the battery, again with the ammeter in series to measure the current. The ammeter reads 4.50 . Even though the equipment you have available to you is limited, your boss assures you of its high quality: The ammeter has very small resistance, and the voltmeter has very large resistance.
What is the resistance of 1 meter of wire?

Answer: 20m

Explanation:

We will solve this question by applying the law of conservation of energy which states that the sum of potential energy and kinetic energy is always the same.

The PE is 0 at surface and maximum at top while the KE is maximum at surface and 0 at top.

From the question,

PE = mgh = 50 J -(1)

mg* 10 = 50

mg = 50/10

mg = 5

The total energy at that point = PE + KE = 50 + 50 = 100 J

Therefore, at topmost point, the PE will be 100 J

mgH = 100J , H is the needed height

Using the value of mg obtained above, we have

H= 100/5

H = 20 m

Answer:

265.9Hz

Explanation:

In an open pipe, both ends of the pipes are opened. The fundamental frequency in an open pipe is expressed as fo = V/2L where;

f is the frequency of the wave

V is the velocity of the wave = 343m/s

L is the length of the pipe = 1.29m

Substituting the value to get the fundamental frequency in the open pipe we have;

Fo = 343/2(1.29)

Fo = 343/2.58

Fo = 132.95Hz

Harmonics are integral multiples of the fundamental frequency e.g 2fo, 3fo, 4fo, 5fo...

The first harmonic in the open pipe will be f1 = 2fo

Since f1 =2(132.95)

f1 = 265.9Hz

The frequency of the first harmonic if the pipe is open at each end is 265.9Hz

Answer:

132.95 Hz.

Explanation:

Given:

v = 343 m/s

L = 1.29 m.

Since the pipe is open at both ends,

L = λ/2

λ = v/f = 2L

= 2 × 1.29

= 2.58 m

f = 343/2.58

= 132.95 Hz.

Answer:

[tex]372.3 J/^{\circ}C[/tex]

Explanation:

First of all, we need to calculate the total energy supplied to the calorimeter.

We know that:

V = 3.6 V is the voltage applied

I = 2.6 A is the current

So, the power delivered is

[tex]P=VI=(3.6)(2.6)=9.36 W[/tex]

Then, this power is delivered for a time of

t = 350 s

Therefore, the energy supplied is

[tex]E=Pt=(9.36)(350)=3276 J[/tex]

Finally, the change in temperature of an object is related to the energy supplied by

[tex]E=C\Delta T[/tex]

where in this problem:

E = 3276 J is the energy supplied

C is the heat capacity of the object

[tex]\Delta T =29.1^{\circ}-20.3^{\circ}=8.8^{\circ}C[/tex] is the change in temperature

Solving for C, we find:

[tex]C=\frac{E}{\Delta T}=\frac{3276}{8.8}=372.3 J/^{\circ}C[/tex]

Final answer:

The heat capacity of the calorimeter, determined by applying a constant voltage and measuring the temperature change, is calculated to be 372.3 J/°C.

Explanation:

To calculate the heat capacity of the calorimeter, we first need to understand the amount of heat (q) added to the system. This can be determined using the formula q = IVt, where I is the current (2.6 A), V is the voltage (3.6 V), and t is the time (350 seconds). So, the heat added to the system is q = 3.6 V * 2.6 A * 350 s = 3276 J. The temperature change (ΔT) observed in the calorimeter is from 20.3°C to 29.1°C, which is a change of 8.8°C. The heat capacity (C) of the calorimeter can then be calculated as C = q/ΔT = 3276 J / 8.8 °C = 372.3 J/°C. This indicates the amount of heat required to raise the temperature of the calorimeter by one degree Celsius.

Incomplete question as we have not told which quantity to find.So the complete question is here

A solenoid used to produce magnetic fields for research purposes is 2.2 mm long, with an inner radius of 25 cmcm and 1300 turns of wire. When running, the solenoid produced a field of 1.5 TT in the center.Given this, how large a current does it carry?

Answer:

[tex]I=2.021A[/tex]

Explanation:

Magnetic field B=1.5 T

Length L=2.2mm =0.0022m

Number of turns N=1300 turns

To find

Current I

Solution

From the magnetic at the center of loop we know that:

[tex]B=uI\frac{N}{L}[/tex]

Substitute the given values

[tex]B=uI\frac{N}{L}\\ as\\u=4\pi *10^{-7} T.A/m\\So\\B=uI\frac{N}{L}\\I=\frac{LB}{Nu}\\ I=\frac{0.0022m(1.5T)}{(1300)(4\pi *10^{-7} T.A/m)}\\I=2.021A[/tex]

Answer:

In chemical compounds, atoms tends to have the electron configuration of a noble gas.

Explanation:

The noble gases are unreactive because of their electron configurations. This noble gas neon has the electron configuration of 1s22s22p6 . It has a full outer shell and cannot incorporate any more electrons into the valence shell.

The octet rule states that atoms tend to form compounds in ways that give them eight valence electrons and thus the electron configuration of a noble gas. An exception to an octet of electrons is in the case of the first noble gas, helium, which only has two valence electrons.

The octet rule states that atoms (excluding some exceptions like hydrogen and helium) in a compound strive for eight electrons in their valence shell, making it stable. This is achieved by sharing, accepting or donating electrons. For instance, oxygen in a water molecule gains two electrons from two hydrogen atoms through covalent bonding.

The octet rule is a principle in chemistry which states that atoms in chemical compounds tend to achieve a stable electron configuration with eight electrons, a complete 'octet', in their valence shell. Atoms will donate, accept, or share electrons to fulfill this rule. For example, oxygen, which has six electrons in its valence shell, will react with other atoms so as to gain two more electrons, completing its octet. This is achieved through covalent bonding, where electrons are shared between atoms, such as in a water molecule H2O. It is important to note that there are exceptions to this rule, notably hydrogen and helium which are stable with two and helium with two electrons in their valence shell respectively.

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Answer:

dehydration reactions

Final answer:

Dehydration reactions decrease entropy within a cell by building larger molecules from smaller units, unlike catabolic reactions like digestion and respiration which increase entropy by breaking down molecules.

Explanation:

The type of reaction that would decrease the entropy within a cell are dehydration reaction. Entropy is a measure of disorder or randomness in a system, and dehydration reactions are anabolic processes that build larger molecules from smaller ones, thus decreasing entropy. In contrast, catabolic reactions, such as digestion, hydrolysis, and respiration, generally increase entropy in a system by breaking down complex molecules into simpler ones and releasing energy in the process.

Answer:

Smoky Mountains specific spots--such as a factory's smokestacks--where large quantities of pollution are discharged

Explanation:

Point source pollution is characterized by the following components:

From the options, Smoky Mountains specific spots--such as a factory's smokestacks--where large quantities of pollution are discharged ticked all the necessary box for a point source pollution.

Answer:

1 V / div

Explanation:

Solution:

- The vertical scale has eight divisions.  

- If each division is set to equal 1 volt, the display will show 0 to 8 volts.  

- This is okay in a 0 to 5 volt variable sensor such as a throttle position (TP) sensor.  

- The volts per division (V/div) should be set so that the entire anticipated waveform can be viewed.

Answer:

Ptolemy made geocentric model of the solar system using epicycles

Explanation:

Ptolemy made geocentric model of the solar system using epicycles.

This model accounted for the apparent motions of the planets in a very direct way, by assuming that each planet moved on a small circle, called an epicycle, which moved on a larger circle, called a deferent.

Therefore, Ptolemy is the answer.

Answer:

a) [tex]v=313.209\ m.s^{-1}[/tex]

b) [tex]v_t=3751.79\ m.s^{-1}[/tex]

Explanation:

Given:

a)

[tex]v=\sqrt{2g.h}[/tex]

[tex]v=\sqrt{2\times 9.81\times 5000}[/tex]

[tex]v=313.209\ m.s^{-1}[/tex]

b)

given that:

diameter of the drop, [tex]d=4\ mm=0.004\ m[/tex]

density of the air, [tex]\rho=1.18\ kg.m^{-3}[/tex]

the terminal velocity is given as:

[tex]v_t=\sqrt{\frac{2m.g}{\rho.A.c_d} }[/tex]

where:

m = mass

g = acceleration due to gravity

[tex]\rho=[/tex] density of the medium through which the drop is falling (here air)

A = area normal to the velocity of fall

[tex]c_d=[/tex] coefficient of drag = 0.47 for spherical body

[tex]v_t=\sqrt{\frac{2\times 5\times 9.81}{1.18\times \pi\times 0.002^2\times 0.47} }[/tex]

[tex]v_t=3751.79\ m.s^{-1}[/tex]

Final answer:

The emission spectrum corresponds to energy emitted by electrons as they fall back from an excited state to a lower energy state. Energy levels are the quantized orbits around the nucleus, and quantum refers to the specific amount of energy in these processes. The excited state is a temporary, higher energy level for an electron.

Explanation:

Lets match the vocabulary with their definitions:

Now, to give a more in-depth understanding:

Answer:

The first eagle hear a frequency of 4.23kHz and the second eagle hear a frequency of 3.56kHz

Explanation:

Given that

both eagle are flying towards one another

speed of the first eagle v1 = 15m/s

speed of the second eagle v2 = 20m/s

frequency emitted by the first eagle f1= 3200Hz

frequency emitted by the second eagle f2 = 3800Hz

speed of sound v = 330m/s

[tex]F_1 = (\frac{v + v_2}{v - v_1} )f_1\\F_1 = (\frac{330 + 20}{330 - 15} )(3200)\\= 3.56 \times 10^3Hz\\= 3.56kHz\\[/tex]

the second part

[tex]F_1 = (\frac{v + v_2}{v - v_1} )f_1\\F_1 = (\frac{330 + 15}{330 - 20} )(3800)\\= 4.23 \times 10^3Hz\\= 4.23kHz\\[/tex]

The first eagle hear a frequency of 4.23kHz and the second eagle hear a frequency of 3.56kHz

Explanation:

When coil is placed in the magnetic field , the flux attached with it can be found by the relation . Flux Ф = the dot product of magnetic field and area of coil .

Thus Ф = B A cosθ

here B is magnetic field strength and A is the area of coil .

The angle θ is the angle between coil and field direction .

When coil rotates , the angle varies . By which the flux varies . The emf is produced in coil due to variation of flux . The relation for this is

The emf produced ξ = - [tex]\frac{d\phi}{dt}[/tex] =  B A sinθ [tex]\frac{d\theta}{dt}[/tex]

Now in the given problem

5 = 0.38 x A x [tex]\frac{d\theta}{dt}[/tex]                            I

Now if the magnetic field is 0.55 T and all the other terms are same , the emf produced

ξ = 0.55 x A x [tex]\frac{d\theta}{dt}[/tex]                              Ii

dividing II by I , we have

[tex]\frac{\xi}{5}[/tex] = [tex]\frac{0.55}{0.38}[/tex] = 1.45

or ξ = 7.2 V

Answer:

Explanation:

The distance of the student from the wall is L

After hearing the reflection she claps her hand again

A complete cycle is the distance to the wall and back to the boy, so the total distance travel then is 2L, then the wave length is 2L

λ=2L

So the frequent is f

Then using wave equation

v=f λ

Since our λ=2L

Then, v=f×2L

v=2fL

The speed of sound in air is 2fL

Final answer:

To find the speed of sound in air based on the frequency of clapping and its reflection off a wall, we can use the rearranged equation V = 2fL, where V is the speed of sound, f is the frequency of clapping, and L is the distance to the wall.

Explanation:

The question involves calculating the speed of sound in air based on the frequency at which a person claps their hands and the time it takes for the sound to reflect off a wall and travel back to them. To solve this, we can use the formula f = ½(V / L), where f is the frequency of clapping (in Hz), V is the speed of sound in air (in m/s), and L is the distance from the person to the wall (in meters). However, the provided formulas from various attempts don't directly address the question but hint at the relationship between the speed of sound, frequency, and distance. Thus, by understanding that the sound needs to travel twice the distance (L) to reach the person again and taking into account the time interval represented by the frequency of clapping, we can rearrange the formula to solve for the speed of sound as V = 2fL. It's understood that the time taken for the sound to travel to the wall and back is inversely related to the frequency of clapping.

Answer:

Electric flux

Explanation:

The electric flux measures the amount of electric field passing through a surface. For any closed surface, the electric field passing through it (electric flux) is given by Guass law. The mathematical relation between electric flux and the enclosed charge is known as Gauss law for the electric field. Electric flux may also be visualised as the amount of electric lines of force passing through an area.

Answer:

Therefore the required solution is

[tex]U(t)=\frac{2(2-\omega^2)^2}{(2-\omega^2)^2+\frac{1}{16}\omega} cos\omega t +\frac{\frac{1}{2}\omega}{(2-\omega^2)^2+\frac{1}{16}\omega} sin \omega t[/tex]

Explanation:

Given vibrating system is

[tex]u''+\frac{1}{4}u'+2u= 2cos \omega t[/tex]

Consider U(t) = A cosωt + B sinωt

Differentiating with respect to t

U'(t)= - A ω sinωt +B ω cos ωt

Again differentiating with respect to t

U''(t) =  - A ω² cosωt -B ω² sin ωt

Putting this in given equation

[tex]-A\omega^2cos\omega t-B\omega^2sin \omega t+ \frac{1}{4}(-A\omega sin \omega t+B\omega cos \omega t)+2Acos\omega t+2Bsin\omega t = 2cos\omega t[/tex]

[tex]\Rightarrow (-A\omega^2+\frac{1}{4}B\omega +2A)cos \omega t+(-B\omega^2-\frac{1}{4}A\omega+2B)sin \omega t= 2cos \omega t[/tex]

Equating the coefficient of sinωt and cos ωt

[tex]\Rightarrow (-A\omega^2+\frac{1}{4}B\omega +2A)= 2[/tex]

[tex]\Rightarrow (2-\omega^2)A+\frac{1}{4}B\omega -2=0[/tex].........(1)

and

[tex]\Rightarrow -B\omega^2-\frac{1}{4}A\omega+2B= 0[/tex]

[tex]\Rightarrow -\frac{1}{4}A\omega+(2-\omega^2)B= 0[/tex]........(2)

Solving equation (1) and (2) by cross multiplication method

[tex]\frac{A}{\frac{1}{4}\omega.0 -(-2)(2-\omega^2)}=\frac{B}{-\frac{1}{4}\omega.(-2)-0.(2-\omega^2)}=\frac{1}{(2-\omega^2)^2-(-\frac{1}{4}\omega)(\frac{1}{4}\omega)}[/tex]

[tex]\Rightarrow \frac{A}{2(2-\omega^2)}=\frac{B}{\frac{1}{2}\omega}=\frac{1}{(2-\omega^2)^2+\frac{1}{16}\omega}[/tex]

[tex]\therefore A=\frac{2(2-\omega^2)^2}{(2-\omega^2)^2+\frac{1}{16}\omega}[/tex]   and        [tex]B=\frac{\frac{1}{2}\omega}{(2-\omega^2)^2+\frac{1}{16}\omega}[/tex]

Therefore the required solution is

[tex]U(t)=\frac{2(2-\omega^2)^2}{(2-\omega^2)^2+\frac{1}{16}\omega} cos\omega t +\frac{\frac{1}{2}\omega}{(2-\omega^2)^2+\frac{1}{16}\omega} sin \omega t[/tex]

Answer:

In 3 hours, the cars will be 297 miles apart.

Explanation:

Speed=Distance/Time

Distance= Speed X Time

Speed of 1st Car=44 miles/hr

Distance=44 X Time taken = 44t

Speed of 2nd Car=55 miles/hr

Distance=55 X Time taken = 55t

Total Distance Covered by both Cars = 44t + 55t = 99t

The cars are 297 miles apart, therefore:

99t = 297

t = 3 hours

It means that in 3 hours, the distance between the cars is 297 miles.

Answer:0.754m

Explanation:

F=kq1q2/r^2

R^2= kq1q2/f

R^2= 9*10^9*7.9*10^-6*6.0*10^-6/0.75

R^2= 9*7.9*6*10^-3/0.75

R^2=0.4266/0.75

R^2=0.5688

R=√0.5688

R=0.754m

Answer: B) Light

Explanation: light waves are Electromagnetic waves. Visible light is one of the many types of electromagnetic waves. The others are mechanical waves.

Answer:

The orientation b has the largest magnetic torque.

Explanation:

As the complete question is not given, the complete question is attached herewith

From the diagram

[tex]|\mu_a|=|\mu_b|=|\mu_c|=|\mu|[/tex]

Also the angles for the 3 orientations are given as

[tex]\theta_a>90\\\theta_b=90\\\theta_c<90\\[/tex]

Now as the torque τ is given as

[tex]\tau=|\mu||B|sin\theta[/tex]

As the value of μ and B is same so value of τ is maximum for sin θ is maximum so

[tex]sin \theta_{max}=1\\\theta_{max}=90[/tex]

So the orientation b has the largest magnetic torque.

The orientation with the largest magnetic torque on the dipole is Orientation B (See attached image).

The torque on the dipole is defined as:

τ = µ×B,

where B is the external magnetic field.

The magnitude of this torque is µB sinθ, where θ is the angle between B and µ

Magnetic Torque is highest when;

→     →

µ ⊥ β

That is when θ  = 90°. Hence B is the correct answer. Please see attached image.

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Answer:

The energy stored in this new capacitor is [tex]4.4514\times10^{-9}\ J[/tex]

Explanation:

Suppose, Two parallel plates, each having area A = 2180 cm² are connected to the terminals of a battery of voltage [tex]V_{b}= 6\ V[/tex] as shown. The plates are separated by a distance d = 0.39 cm.

We need to calculate the charge

Using formula of capacitance

[tex]C=\dfrac{Q}{V}[/tex]

[tex]\dfrac{Q}{V}=\dfrac{\epsilon_{0}A}{d}[/tex]

[tex]Q=V\times\dfrac{\epsilon_{0}A}{d}[/tex]

Put the value into the formula

[tex]Q=6\times\dfrac{8.85\times10^{-12}\times2180\times10^{-4}}{0.39\times10^{-2}}[/tex]

[tex]Q=2.968\times10^{-9}\ C[/tex]

The distance between the plates is doubled.

We need to calculate the new capacitance

Using formula of capacitance

[tex]C'=\dfrac{\epsilon_{0}A}{d}[/tex]

Put the value into the formula

[tex]C'=\dfrac{8.85\times10^{-12}\times2180\times10^{-4}}{0.78\times10^{-2}}[/tex]

[tex]C'=2.473\times10^{-10}\ F[/tex]

We need to calculate the energy stored in this new capacitor

Using formula of energy

[tex]U=\dfrac{1}{2}C'V^2[/tex]

Put the value into the formula

[tex]U=\dfrac{1}{2}\times2.473\times10^{-10}\times(6)^2[/tex]

[tex]U=4.4514\times10^{-9}\ J[/tex]

Hence, The energy stored in this new capacitor is [tex]4.4514\times10^{-9}\ J[/tex]

Answer:

Explanation:

A fire alarm notification appliance is an active fire protection component of a fire alarm system. The primary function of the notification appliance is to alert persons at risk.

If want the audible public mode signal to be hear clearly then, we need to have a sound level that is at least 15dB above the average ambient sound level or 5dB above the maximum sound level of at least 1minute

In this case the,

The average ambient sound level is 62dB,

And the maximum sound level is 68dB

Then, the public mode signal should be at least

1. 62dB+ 15dB=77dB

Or

2. 68dB +5dB =73dB.

Then the public mode signal hearing must be at least 77dB.

Explanation:

Below is an attachment containing the solution.

Answer: c. they will hit the ground at the same time

Explanation:

The volume of both objects is almost the same, so the force of friction will be the same in each one, so we can discard it.

Now, when yo drop an object, the acceleration of the object is always g = 9.8m/s^2 downwards, independent of the mass of the object.

So if you drop two objects with the same volume but different mass, because the acceleration is the same for both of them, they will hit the ground at the same time, this means that the density of the object has no impact in how much time the object needs to reach the floor.

So the correct option is c

Answer:

True

Explanation:

If there's no preference over the string case (upper case or lower case), one can convert both strings to upper case or to lowercase and then compare the converted strings to test if they're equal or not.

An Illustration is

string a = "Boy"

string b = 'bOy"

if(a.ToUpper() == b.ToUpper() || a.ToLower() == b.ToLower())

{

Print "Equal Strings"

}

else

{

Print "Strings are not equal";

}

The above will first convert both strings and then compare.

Since they are the same (after conversion), the statement "Equal Strings" will be printed, without the quotes

The statement is true. Most programming languages include methods to convert strings to either lower or upper case. This feature is useful to make comparisons case-insensitive.

This statement is true. In many programming languages, there are methods to convert a string to either lower case or upper case. These methods are often utilized to make string comparisons case-insensitive, eliminating any discrepancy caused by case differences.

For example, in Java, the methods are toLowerCase() and toUpperCase(), while in Python, they are lower() and upper(). This is particularly useful when a program is designed to interact with human input, as it allows the program to accept input regardless of the case used.

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Answer:

Explanation:

Given that we have two cars

First car has mass =m

Second car has mass = 4m

They are driving at constant speed

Given that the radius of curve is R

Both cars maintain the same acceleration.

Let velocity of small car be vS

Velocity of big car be vL

From centripetal acceleration

a=V²/R

V²=aR

Then since both car have the same accelerating and bashing through the same curve of radius R

Then, We can say, V² is constant

vL² = vS²

Then taking square root of both side

vL=vS

The speed of the small car vS is greater than the speed of the large car vL as they round the curve due to the difference in their masses and the application of the same acceleration.

The speed of the small car vS is greater than the speed of the large car vL as they round the curve. This is because both cars have the same acceleration a, but the small car has less mass than the large car. According to Newton's second law, F = ma, the force required to maintain the same acceleration is greater for the larger car, which means it has a greater speed as it rounds the curve.

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Explanation:

The field at the center of circular current can be calculated by

B = [tex]\frac{\mu _0 I}{r}[/tex]

here μ₀ is permeability constant and is equal to 4π x 10⁻⁷

I is the current in circular path and r is the radius of circle

Thus I =[tex]\frac{90x10^-^1^2x12x10^-^2}{4\pi x 10^-^7 }[/tex] = 8.8 x 10⁻⁵ A

Answer:

Protein molecules

Explanation:

Ribosomes are the cell organelles that are responsible for the synthesis of protein in the cell. Proteins are the fundamental building blocks and help in repair and damage of cell in the body.

Ribosome is a complex which is made up of protein and RNA. Ribosomes can be found floating within the cytoplasm or attached to the endoplasmic reticulum.

The situation can be modeled with a differential equation taking into account the inflow and outflow rates of carbon dioxide. By resolving this equation, we obtain a function representing the CO2 quantity over time. This can be easily converted into percentage by dividing by the room's volume and multiplying by 100.

This problem can be solved using a mathematical model called a differential equation. The percentage of carbon dioxide in the room changes over time due to the input of fresher air and the removal of mixed air.

Let's denote the quantity (not the percentage, the actual quantity) of carbon dioxide in the room at time t by Q(t). Initially, we have Q(0) = 0.0025 * 180 = 0.45 m³.

Carbon dioxide flows into the room at a rate of 0.0005 * 2 = 0.001 m³/min and flows out at the rate proportional to the total quantity present, which is (Q(t) / 180) * 2 = (Q(t) / 90) m³/min. Therefore the situation can be modelled by the differential equation dQ/dt = 0.001 - Q(t) / 90. Here, 0.001 represents the rate on inflow of carbon dioxide, and Q(t) / 90 represents the rate of outflow.

By solving this differential equation, we can obtain the function Q(t) which gives the quantity of carbon dioxide in the room at each moment, and the percentage of carbon dioxide can be obtained by dividing Q(t) by the volume of the room and multiplying by 100 to get a percentage, i.e., p(t) = Q(t)/180 * 100.

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The percentage of carbon dioxide in the room over time can be calculated using differential equations. The resulting function is[tex]p(t) = 0.005 * e^{(t/90)} + 0.02 * e^{(-t/90)}[/tex]. This takes into account both the inflow of fresh air and the mixture exiting the room.

To determine the percentage p of carbon dioxide in the room as a function of time t (in minutes), we need to use principles from differential equations to model the mixing process.

Initially, the volume of the room is 180 m³ containing 0.25% carbon dioxide. Fresh air with 0.05% carbon dioxide flows into the room at 2 m³/min.

Let's denote the amount of carbon dioxide in the room at time t by C(t), measured in cubic meters. The concentration of carbon dioxide p(t) is given by:

The rate of change of the carbon dioxide in the room can be written as:

The inflow of carbon dioxide is:

The outflow of carbon dioxide depends on the concentration in the room:

Thus, the differential equation becomes:

This simplifies to:

[tex]or, dC/dt = 0.001 - (C/90)[/tex]

To solve this, we use an integrating factor. The integrating factor is:

Multiplying both sides by the integrating factor:

This simplifies to:

Integrate both sides:

Hence,

To find K, use the initial condition C(0):

Initial amount of CO2:

Thus,

Therefore, [tex]K = 0.36[/tex].

The solution is:

The percentage of CO2 is:

This simplifies to:

Hence:

[tex]p(t) = 0.005 * e^{(t/90)} + 0.02 * e^{(-t/90)}[/tex]

Answer:

(a) increase

Explanation:

On a line graph; we have the x-axis to the positive side and the negative side .In a positive x-axis direction, the force is usually positive, vice versa the negative side as well.

The change in the potential energy of a charge field-system can be given as:

[tex]\delta U= -q(EdsCos \theta)[/tex]

where;

q = positive test charge

E = Electric field

ds = displacement between thee charge positions

θ  = Angle between the electric field and the displacement.

Given that:

Charge of the particle = -q

displacement = (60.0 -20.0)cm = 40.0 cm

θ = 0

Replacing our values in the above equation, we have:

[tex]\delta U = -(-q)(60Cos 0)[/tex]

[tex]\delta U = qEds[/tex]

Since the potential energy of the system is positive, therefor the electric potential energy also increases.

The electric potential energy of a system consisting of a negatively charged particle in a uniform electric field increases when the particle is moved in the same direction as the field.

The electric potential energy of the charge-field system increases as a negatively charged particle is moved in the same direction as the electric field. This is because work is done to overcome the force of the electric field, which opposes the movement of the negatively charged particle. The uniform electric field produces a constant force, and since work is force times distance, the amount of work (and hence energy) increases.

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