for what value of xaxle will the two forces provide 1.3 n m of torque about the axle?

Answers

Answer 1

The value of the axle for the two forces that provide 1.3 N m of torque about the axle is 0.5 m.

Given values are:

Torque: 1.3 N m

Force1: 0.8 N

Force2: 1 N

We need to find the value of the axle.

To find the answer, we will use the formula for torque:

τ= r × FTorque

τ is given as 1.3 N m.

Force F1 is given as 0.8 N.

Force F2 is given as 1 N.

The distance between the two forces (axle) is unknown.

Let's denote axle as r.

Now, substitute all the known values into the formula for torque to get:

1.3 N m = r × (0.8 N + 1 N)1.3 N m = r × 1.8 N2F multiplied by r on both sides of the equation and solve for r:

r = (1.3 N m) ÷ (1.8 N) r = 0.722 m

But we have assumed that the distance between the two forces is r.

But the problem states that the distance between the two forces is axle.

Hence we can write, r = axle/2r = axle/2r × 2 = axle

Therefore, axle = 2r = 2(0.722 m) = 1.44 m

Therefore, the value of axle for the two forces that provide 1.3 N m of torque about the axle is 0.5 m.

So, the answer is 0.5 m.

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Related Questions

1 a Suggest three things you can do to change your mass. b How could you change your weight without changing your mass? 2 Use information from the table in question 3 to work out the gravitational field strength on: a Venus b Mars c Earth 3 Complete the gaps in this table, using your answers to question 2 to help you. Tool Mass (kg) Spacesuit 70 Rover vehicle 200 Rock samples 50 Spanner 0.06 Screwdriver j Weight on Earth (N) Weight on Venus (N) 686 C e g 0.049 a W mg d 445 h k Weight on Mars (N) b 740 f i​

1 a Suggest three things you can do to change your mass. b How could you change your weight without changing

Answers

Answer:

1. Increase your caloric intake, reduce your caloric expenditure, and engage in regular physical activity.

2. Eat a balanced diet and focus on nutrient dense foods such as vegetables, protein and healthy fats.

3. Monitor your progress with a food diary and weigh-in, so that you can track any changes in your weight.

To change your weight without changing your mass, you can increase or decrease the gravitational field strength on the planet. For example, if you were to travel to the Moon, your weight would decrease due to the weaker gravitational pull.

Using information from the table in question 3, the gravitational field strength on Venus is 8.87 m/s2, on Mars it is 3.71 m/s2, and on Earth it is 9.81 m/s2.

Complete the gaps in this table, using your answers to question 2 to help you:

Tool Mass (kg) Spacesuit 70 Rover vehicle 200 Rock samples 50 Spanner 0.06 Screwdriver j Weight on Earth (N) 686 Weight on Venus (N) 693 Weight on Mars (N) 445

An object of mass m is initially at rest and free to move without friction in any direction in the xy-plane. A constant net force of magnitude F directed in the x direction acts on the object for 1 s. Immediately thereafter a constant net force of the same magnitude F directed in the y direction acts on the object for 1 s. After this, no forces act on the object. Write down the vectors that could represent the velocity of the object at the end of 3 s, assuming the scales on the x and y axes are equal

Answers

The graph would look like a series of two linear slopes, one going up and one going down.

A linear slope, also known as a straight-line slope, refers to the rate of change of a linear function, which is represented by a straight line on a graph. In mathematical terms, the slope is defined as the ratio of the change in the vertical coordinate (y) to the change in the horizontal coordinate (x) between any two points on the line.

The slope of a linear function is constant throughout the line, meaning that the rate of change remains the same regardless of the position on the line. Linear slopes are used in a variety of mathematical applications, including geometry, physics, engineering, and economics, among others. They are particularly useful for modeling relationships between two variables, such as distance and time, or price and quantity.

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what force could you put on a 2-kg see-saw to cause a torque of 200 N-m when applied straight down. 2 meters away from the center fulcrum?

Answers

The force that will cause the given torque on the see-saw is 100 N.

The given parameters:

Mass of the see-saw, m = 2 kgTorque applied, τ = 200 N-mRadius of the fulcrum, r = 2 m

The force that will cause the given torque on the see-saw is calculated as follows;

τ = Fr

\(F = \frac{\tau}{r} \\\\F = \frac{200}{2} \\\\F = 100 \ N\)

Thus, the force that will cause the given torque on the see-saw is 100 N.

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A measurement of a change
in distance over time

Answers

Explanation:

Speed is the rate of change of distance with time.

A car's engine changes
Mechanical energy to chemical energy
O Chemical energy to mechanical energy

Answers

Answer:

Chemical energy to mechanical energy

Explanation: uses gases and fluids to make it thermal then mechanical

Chemical energy to mechanical energy

I am pushing on a box with 15 N of force, and my younger cousin is pushing the box (in the same direction as me) with 10 N of force. How much is the net force on the box?


Help

Answers

25N
:)
Hope this helps

based on scientist 2’s discussion, an imbh nearby but not at the direct center of a galaxy would most likely:

Answers

An intermediate-mass black hole (IMBH) nearby but not at the direct center of a galaxy would most likely have a significant impact on the dynamics of stars in its vicinity.

Scientist 2 likely discussed how an IMBH, while not having the gravitational pull of a supermassive black hole at the center of a galaxy, would still have a significant impact on the dynamics of stars in its vicinity due to its strong gravitational pull.

As stars orbit around the IMBH, they would experience gravitational perturbations that could cause them to change direction or even be ejected from the galaxy entirely. This could have observable effects on the overall shape and structure of the galaxy, as well as the distribution of stars and gas within it.

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What is the difference between FIR AND IIR filter?

Answers

Digital filters are important in digital signal processing. FIR and IIR filters are two types of digital filters. The main difference between FIR and IIR filters is that FIR filters are known as non-recursive filters, while IIR filters are recursive filters. In this answer, we will explore more about the differences between FIR and IIR filters.

FIR Filters FIR stands for finite impulse response. FIR filters are also called non-recursive filters. In an FIR filter, the output depends only on the current input and the previous inputs. FIR filters are also known as moving average filters. FIR filters have a linear phase response, which makes them useful in audio and image processing. FIR filters have more stable responses compared to IIR filters, which means they are more predictable.

IIR filters are more efficient than FIR filters because they use feedback loops. IIR filters have nonlinear phase responses, which make them useful in signal processing and control systems. IIR filters are less stable than FIR filters, which means they are less predictable.

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Ayuda porfavor :( doy corona

Answers

Answer:(:

Explanation:

1.   19685

2. 26400

3. 47244.1

4. 15.53428

5. 2.1336

6. 3.61111

7. 42240

8. 560

9. 24.384

10. 54

What is the basis for the sounds referred to as korotkoff sounds?.

Answers

Answer:Korotkoff Sounds. -tapping sounds created by turbulent blood flow in arm. -pressure is slowly being released from cuff, so systolic pressure is above that of the cuff, but diastolic is still below, so the artery opens in systole and collapses in diastole.

Explanation:

Ice is put in a cooler to cool the contents. to speed up the cooling process, the ice can be?

Answers

Crushing increases the ice's surface area. Additionally, cooling from ice happens as a result of convection, which is proportional to area. Thus, breaking up the ice expedites the cooling process.

What is cooling process?

When precise and consistent temperature control inside a process is necessary, this sort of cooling is used. Because they can offer cooling capacity independent of variations in the ambient temperature, heat load, and flow needs of the application, chillers are frequently employed to remove heat from a process.

It's important to properly regulate the heat load in many industrial operations. Different components of the whole application might need to be cooled.

Major locations for cooling include:

Direct product cooling

During the molding process, plastic

milling metal products

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How does the launch angle affect the maximum height reached by a ground launched projectile?​

Answers

Answer:

The maximum height is determined by the initial vertical velocity. Since steeper launch angles have a larger vertical velocity component, increasing the launch angle increases the maximum height.

Explanation:

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A 75 kg motor cycle is moving at 10m/s makes a head-on collision with a 45kg bicycle travelling at 8 m/s. assuming that there are no external forces acting on the system, what are the velocities of the two masses after impact? (Assume coefficient of restitution e= 0.5)

Answers

After the collision, the motorcycle's velocity is around 3.42 m/s, and the bicycle's velocity is approximately -1.42 m/s in the opposite direction.

To solve this problem, we can apply the principles of conservation of momentum and the coefficient of restitution. The conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision.

Let's denote the initial velocity of the motorcycle as v1, the initial velocity of the bicycle as v2, the final velocity of the motorcycle as v1f, and the final velocity of the bicycle as v2f.

The total momentum before the collision can be calculated as:

Initial momentum = (mass of the motorcycle * initial velocity of the motorcycle) + (mass of the bicycle * initial velocity of the bicycle)

= (75 kg * 10 m/s) + (45 kg * 8 m/s)

= 750 kg·m/s + 360 kg·m/s

= 1110 kg·m/s

According to the conservation of momentum, the total momentum after the collision is equal to the initial momentum:

Total momentum after the collision = (mass of the motorcycle * final velocity of the motorcycle) + (mass of the bicycle * final velocity of the bicycle)

= (75 kg * v1f) + (45 kg * v2f)

Now, let's consider the coefficient of restitution (e = 0.5). The equation for the coefficient of restitution is:

Coefficient of restitution (e) = (relative velocity of separation) / (relative velocity of approach)

= (v2f - v1f) / (v2 - v1)

Since it's a head-on collision, the relative velocity of approach is the sum of the velocities of the two masses before the collision:

Relative velocity of approach = v2 - v1

To find the relative velocity of separation, we can use the equation:

Relative velocity of separation = e * (relative velocity of approach)

= e * (v2 - v1)

Substituting these values into the equation for conservation of momentum, we have:

1110 kg·m/s = (75 kg * v1f) + (45 kg * v2f)

Since we have two unknowns (v1f and v2f), we need another equation to solve for them. Using the equation for the relative velocity of separation, we have:

v2f - v1f = e * (v2 - v1)

45 kg * v2f - 75 kg * v1f = 0.5 * (45 kg * 8 m/s - 75 kg * 10 m/s)

Now we have a system of two equations with two unknowns. Solving these equations simultaneously will give us the final velocities of the motorcycle (v1f) and the bicycle (v2f) after the collision.

By solving these equations, we find that the final velocity of the motorcycle (v1f) is approximately 3.42 m/s, and the final velocity of the bicycle (v2f) is approximately -1.42 m/s. The negative sign indicates that the bicycle is moving in the opposite direction after the collision.

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A motorcycle traveling at 87.3 mi/hr for 0.85
hours, what is the acceleration if the final-
velocity is 120 mi/hr?

Answers

A motorcycle traveling at 87.3 mi/hr for 0.85 hours, the acceleration of the motorcycle is 38.47 miles per hour squared (mi/\(hr^2\)) if the final- velocity of a motorcycle is 120 mi/hr.

What is the calculation of the acceleration?

The acceleration of the motorcycle= (final velocity - initial velocity) / time

(initial velocity=at the beginning of the time interval, final velocity= velocity at the end of the time interval, time= the duration of the interval)

Here, initial velocity =87.3 mi/hr, the final velocity = 120 mi/hr, and the time interval = 0.85 hours.

acceleration = (120 mi/hr - 87.3 mi/hr) / 0.85 hours

acceleration = 32.7 mi/hr / 0.85 hours

acceleration = 38.47 mi/\(hr^2\)

     

Hence, the acceleration of the motorcycle is 38.47 miles per hour squared  (mi/\(hr^2\)) if the final velocity is 120 mi/hr.

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Help meeee is for tomorrow, plssss!!!
2) For the association of resistors below:
a) The equivalent resistor between A and B.
b) The total electric current that runs through the circuit, knowing that the electrical voltage between terminals A and B is valid 21 V(volts).
c) The value of the electric current passing through the resistor of 1.0 Ohm.
d) The power dissipated through the 8.0 Ohm resistor.

Help meeee is for tomorrow, plssss!!!2) For the association of resistors below:a) The equivalent resistor

Answers

(a) The equivalent resistance of the circuit is 0.52 ohms.

(b) The total electric current that runs through the circuit is 40.38 A.

(c) The value of the electric current passing through the resistor of 1.0 Ohm is 21 A.

(d) The power dissipated through the 8.0 Ohm resistor is 55.13 W.

Equivalent resistance of the circuit

The equivalent resistance of the circuit is calculated as follows;

1/R = 1/(1 + 1) + 1/(2 + 2 + 2) + 1/(6) + 1/(2) + 1/8 + 1/8 + 1/6 + 1/6

1/R = 1/2 + 1/6 + 1/6 + 1/2 + 1/8 + 1/8 + 1/6 + 1/6

1/R = 1 + 2/3 + 1/4

1/R = 23/12

R = 12/23

R = 0.52 ohms

Total current through the circuit

V = IR

I = V/R

I = 21/0.52

I = 40.38 A

Current through 1 ohm resistor

V = IR

I = V/R

I = 21/1

I = 21 A

Power dissipated through 8 ohm resistor

P = V²/R

P = (21)²/8

P = 55.13 W

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Thin lenses. Object O stands on the central axis of a thin symmetric lens. For this situation, each problem in the table (below) gives object distance p (centimeters), the type of lens (C stands for converging and D for diverging), and then the distance (centimeters, without proper sign) between a focal point and the lens. Find (a) the image distance i and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real or virtual, (d) inverted from object O or noninverted, and (e) on the same side of the lens as object O or on the opposite side.

Answers

The image distance i  is - 8.6 cm and  the lateral magnification m of the object, including signs is +0.39  .

How is it calculated ?

For a diverging (D) lens we know that the focal length value should be negative ( f=–14cm).

1. The image distance :

i = \(\frac{pf}{p-f}\)

∴ i = [22 × (-14)] / [22 -(-14) ]

∴ i = -8.6 cm

​2. The magnification :

m = - i / p

∴ m = - (-8.6 / 22)

∴ m = +0.39

3.The image distance being a negative number indicates that the image is virtual (V).

4.A positive magnification value indicates that the image is not reversed (NI).

5.The image is on the same side of the object as the object.

6. This problem's ray diagram is similar to the one depicted in Figure. The lens is diverging, creating a virtual image with the same orientation as the object and on the same side.

What is ray diagram ?Ray diagrams are a visual representation of light propagation in physics. They can help us understand and visualize a variety of scenarios, such as light reflecting off a mirror or changing direction while passing through a lens.A ray diagram is a simplified representation of light that is used to analyze its journey as it moves from one place to another.

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the daily tidal range is greatest during what period of the lunar cycle?

Answers

The daily tidal range is greatest during the period of the lunar cycle when the moon is either full or new.

During these lunar phases, the gravitational pull of the moon and the sun are aligned, which results in higher tidal bulges and lower tidal troughs. This alignment, known as the spring tide, occurs approximately twice a month during the full and new moon phases. During other phases of the lunar cycle, such as the quarter moons, the gravitational pull of the sun and the moon are perpendicular, which results in lower tidal bulges and higher tidal troughs. Thus, the daily tidal range is greatest during the spring tides that occur during the full and new moon phases.

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When light is incident on a boundary between two mediums, it often slows
down or speeds up. When it does this, the path the light travels can change.
This is called:
A. diffraction
B. reflection.
c. translocation.
D. refraction

Answers

Answer:

the answer is

D.refraction

2. At 6:00 AM a hopital ued it cyclotron to make 1 milligram of the iotope fluorine-18 for ue a a diagnotic tool with it PET canner. The half-life of F-18 i 1. 8 hour. How much F-18 i left at 3:00 PM? At midnight? Should the hopital plan to make more F-18 the next morning?

Answers

Cyclotron to make 1 milligram of the isotope fluorine-18 for use a a diagnostic tool with it PET scanner. It seems that the hospital should plan to make more F-18 the next morning, as the amount remaining at midnight is very small.

The half-life of F-18 is 1.8 hours, so after 1.8 hours, half of the original amount of F-18 will remain. After 3.6 hours, a quarter of the original amount will remain, and so on.

At 3:00 PM (9 hours after the F-18 was made), the hospital will have

= 1/2^(9/1.8)

= 1/2^5

= 1/32

= approximately 0.03125 milligrams of F-18 remaining.

At midnight (18 hours after the F-18 was made), the hospital will have

= 1/2^(18/1.8)

= 1/2^10

= 1/1024

= approximately 0.0009765625 milligrams of F-18 remaining.

While using cyclotron, based on these calculations, it seems that the hospital should plan to make more F-18 the next morning, as the amount remaining at midnight is very small.

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Each of these flasks contains the same number of gas molecules. In
which container is the pressure highest?
Flask 1
Flask 2
Flask 3
Flask 4
Flask 3
Flask 4
Flask 2
Flask 1
Page

Each of these flasks contains the same number of gas molecules. Inwhich container is the pressure highest?Flask

Answers

Answer:

Flask 1

Explanation:

when volume goes down pressure goes up, and the first flask has the smallest volume therefore the greatest pressure

We have that from the ideal gas equation that the flask with the lowest volume will have the highest pressure therefore

Flask one has the lowest Pressure

Option D

From the question we are told

Each of these flasks contains the same number of gas molecules. In

which container is the pressure highest

Generally the equation for an Ideal gas given as   is mathematically given as

The ideal gass equation

\(PV=nRT\)

Where

P=pressure

V=Volume

n=No of mole

R=Gas Constant

T=temperature

Therefore We have that from the ideal gas equation that the flask with the lowest volume will have the highest pressure therefore

Flask one has the lowest Pressure

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A champion weightlifter raises a 240kg barbell a distance of 2.1m. How much potential energy has the barbell gained?

Answers

The weightlifter lifts a barbell, they are doing work on the barbell, which results in the transfer of energy to the barbell. This energy is known as potential energy and is determined by the height and mass of the object.



The case, the weightlifter has raised a barbell with a mass of 240kg to a height of 2.1m. To calculate the potential energy gained by the barbell, we can use the equation: Potential Energy PE = Mass (m) x Gravity (g) x Height (h) Where m = 240kg, g = 9.8m/s² (acceleration due to gravity), and h = 2.1m PE = 240kg x 9.8m/s² x 2.1m PE = 4,998.24 Joules (J) Therefore, the champion weightlifter has transferred 4,998.24 Joules of energy to the barbell by raising it a distance of 2.1m. This potential energy can be converted to other forms of energy, such as kinetic energy, as the weightlifter begins to lower the barbell.

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Which of the following is NOT a negative effect of the way we use science? A. Climate Change B. Pollution C. Overuse of resources D. Damage to the sun

Answers

Answer:

D

Explanation:

Damage to the sun is not a negative effect of the way we use science because we can't affect the sun due to its long distance from us.

How we negatively affected environment with the use of science?

Humans negatively affected environment by using science because with the help of science we made new technologies which leads to Climate Change, Pollution and Overuse of resources.

So we can conclude that option D is the right answer.

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what is friction? effect of force​

Answers

Answer:

Force

Explanation:

Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. Dry friction is a force that opposes the relative motion of two solid surface in contact.

the specific heat of silver is 0.24 . how many joules of energy are needed to warm 4.37 g of silver from to ?

Answers

The amount of energy (in joules) required to warm 4.37 g of silver by ΔT degrees Celsius can be calculated using the equation Q = 1.0488 * ΔT.

The specific heat capacity (C) of a substance is the amount of energy required to raise the temperature of 1 gram of that substance by 1 degree Celsius. In this case, the specific heat capacity of silver is 0.24 J/g°C.

To calculate the energy required to warm 4.37 g of silver, we need to multiply the mass (m) by the specific heat capacity (C) and the change in temperature (ΔT). The change in temperature is not provided in the question, so we'll assume it is given.

Let's assume the change in temperature is ΔT°C. The formula to calculate the energy (Q) is:

Q = m * C * ΔT

Substituting the given values:

Q = 4.37 g * 0.24 J/g°C * ΔT

The units of grams cancel out, and we are left with:

Q = 1.0488 J/°C * ΔT

So, the amount of energy (in joules) required to warm 4.37 g of silver by ΔT degrees Celsius can be calculated using the equation Q = 1.0488 * ΔT.

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Write a c program inputs three integers. find and display to the screen the max and min of three given integers

Answers

Here's a C program that takes three integers as input and finds the maximum and minimum values among them:

What is an integer ?

An integer  is a whοle number (nοt a fractiοnal number) that can be pοsitive, negative, οr zerο. Examples οf integers are: -5, 1, 5, 8, 97, and 3,043.

c

#include <stdio.h>

int main() {

   int num1, num2, num3;

   int max, min;

   printf("Enter three integers: ");

   scanf("%d %d %d", &num1, &num2, &num3);

   // Assume num1 is the maximum and minimum initially

   max = num1;

   min = num1;

   // Check if num2 is greater than current max

   if (num2 > max) {

       max = num2;

   }

   // Check if num3 is greater than current max

   if (num3 > max) {

       max = num3;

   }

   // Check if num2 is smaller than current min

   if (num2 < min) {

       min = num2;

   }

   // Check if num3 is smaller than current min

   if (num3 < min) {

       min = num3;

   }

   printf("Maximum value: %d\n", max);

   printf("Minimum value: %d\n", min);

   return 0;

}

In this program, we declare variables num1, num2, and num3 to store the input integers. We also declare max and min to keep track of the maximum and minimum values, respectively.

The scanf function is used to take input from the user. The user is prompted to enter three integers, which are stored in num1, num2, and num3.

Next, we compare each input integer with the current maximum and minimum values. If an input is greater than the current maximum, we update the max variable. If an input is smaller than the current minimum, we update the min variable.

Finally, we display the maximum and minimum values on the screen using the printf function.

When you run the program and enter the three integers, it will output the maximum and minimum values among them.

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5.4.2 Test (CST): Earth's Resources
Question 5 of 15
▬▬
The human population grows by about 2 percent each year, showing
growth.
OA. exponential
OB. linear
OC. cubic

Answers

The human population which grows by about 2 percent each year, is showing linear growth.

What is linear increment?

A linear increment occurs when a sequence increases gradually with a constant value.

If a population increases at the rate of 2%, the incremental rate or constant factor is 2%, thus, we can conclude that the human population which grows by about 2 percent each year, is showing linear growth.

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1. How should you begin an exercise routine?
by increasing endurance
by eating
Hard right from the start
By stretching
2. True or False. You have to go to the gym to get exercise.
True
False
3. Which of the following is an advantage to exercising?
building stronger muscles and bones
increasing blood pressure
increasing body fat
4. Which of the following is an example of exercise?
riding your bike
watching basketball
playing chesss

Answers

Answer:

1. By streching

2. false

3. building stronger muscles and bones

4. riding your bike

Explanation:

The routine of exercise begins with the usual basic step of stretching the body.

What is meant by exercise ?

An essential component of a healthy lifestyle is exercise. Exercise can help you cope with stress and prevent health issues while also enhancing energy and strength. It can also help you control your appetite and keep your weight in a healthy range.

Here,

1. The routine of exercise begins with the usual basic step of stretching the body.

2. People don't have to necessarily go to the gym to get exercise, because exercise includes the activities from the basic one to difficult methods. So, you can do some kind of exercise at the home itself. So, the statement is false.

3. An advantage to exercising is building stronger muscles and bones.

4. Riding your bike is an example of exercise.

Hence,

The routine of exercise begins with the usual basic step of stretching the body.

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Dry steam at 100° is bubbled into 500g of water originally at 20° . what will be the temperature of water after 30g of steam has condensed .(Specific latent heat of steam=2.26×10^6Jkg,specific heat capacity of water =4200Jkgk)​

Answers

The temperature of the water after 30g of steam has condensed will be approximately 52.14°C.

To solve this problem, we need to consider the energy transfer that occurs when steam condenses into water. The energy released by the condensing steam will be absorbed by the water, resulting in a temperature change.First, let's calculate the energy released when 30g of steam condenses. The specific latent heat of steam is given as 2.26 × 10^6 J/kg, so the energy released by 30g of steam can be calculated as:

Energy released = (30g) × (2.26 × 10^6 J/kg) = 6.78 × 10^7 J

Next, we need to calculate the energy required to raise the temperature of the water from 20°C to the final temperature. The specific heat capacity of water is given as 4200 J/kgK, and the mass of the water is 500g. Therefore, the energy required can be calculated as:

Energy required = (500g) × (4200 J/kgK) × (final temperature - 20°C)

Since the energy released by the steam is equal to the energy required by the water, we can set up the equation:

6.78 × 10^7 J = (500g) × (4200 J/kgK) × (final temperature - 20°C)

Now, we can solve for the final temperature:

(final temperature - 20°C) = (6.78 × 10^7 J) / ((500g) × (4200 J/kgK))

(final temperature - 20°C) = 32.14°C

final temperature = 32.14°C + 20°C

final temperature ≈ 52.14°C

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How to integrate 1/ 1 + x2

Answers

The integral of 1/(1 + x²) is (1/2)ln|1 + x²| + C where C is the constant of integration.

Integration is a mathematical process of finding the antiderivative of a function. To integrate the given expression 1/(1 + x²), we will use the substitution method.

Let u = 1 + x², du/dx = 2x dx, then dx = du/2x and the integral becomes:

∫1/(1 + x²) dx = ∫1/u * (1/2x) du= (1/2)∫1/u du

The antiderivative of 1/u is ln|u| + C, where C is the constant of integration.

Therefore, the final solution of the integral is (1/2)ln|1 + x²| + C.

Let us work through the steps:

Step 1:Let u = 1 + x² and then differentiate both sides with respect to x to obtain du/dx. du/dx = 2x

Substitute 2x dx = du into the integral ∫1/(1 + x²) dx to get the integral in terms of u:∫1/u * (1/2x) du = (1/2) ∫1/u du

Step 2:Calculate the antiderivative of 1/u, which is ln|u|. Thus, the final solution is (1/2)ln|1 + x²| + C, where C is the constant of integration. The constant C will vary depending on the initial conditions of the problem.

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Many college students have a mini-fridge in their dorm room. A standard mini fridge costs roughly $100, uses about 100 watts of electricity per hour when it is running, and can be expected to last for 5 years. The refrigerator is plugged into an electrical socket 24 hours a day, but is usually running only about 12 hours per day. Assume that electricity costs $0.10/kWh.
(a) Calculate the lifetime monetary cost of owning and operating the refrigerator.
(b) Assume that the electricity used to power the refrigerator comes from a coal-burning power plant. One metric ton of coal contains 29.3 GJ (8,140 kWh) of energy. Because of the inefficiency of electricity generation and transmission, only one-third of the energy in coal reaches the refrigerator. How many tons of coal are used to power the refrigerator during its lifetime?
(c) Assume that 15 percent of the mass of the coal burned in the power plant ends up as coal ash, a potentially toxic mixture that contains mercury and arsenic. How many tons of coal ash are produced as a result of the refrigerator's electricity use over its lifetime?
(d) What externalities does your answer from part (a) not include? Describe one social and one environmental cost associated with using this appliance.
(e) Describe two ways a college student could reduce the electricity use associated with having a mini fridge in his or her dorm room.

Answers

The amount of coal burnt to operate the mini fridge is 0.81 metric tons.

What is energy cost?

The term energy cost refers to the monetary cost of operating a particular electrical appliance. Let us now answer the questions one after the other.

a) Power consumption per hour = 100 watt or 0.1kW. To operate it for an hour we have  0.1kWhr × $0.10/kWh = 0.01$ Since it operates for twelve hours a day 12(0.01$)= 0.12$ per day. In five years; 0.12$× 5 × 365 = 219 $.

b) Electricity used for the five years = 5 × 365 × 12 × 0.1kWhr = 2190 kWhr

Since 1 metric ton of coal produces 2713 kWh(considering energy losses)

x metric tons of coal produces 2190 kWhr

x = 1 metric ton × 2190 kWhr/2713 kWh

x = 0.81 metric tons

c) In part 1 we did not include the cost of the environmental damage caused by the mining of coal and the social inconveniences caused by the sound of the mini fridge.

d) The college student could reduce the electricity use associated with having a mini fridge in his or her dorm room by turning it off for some hours within the day.

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