for one-dimensional, steady-state conduction in a cylindrical or spherical shell without heat generation, is the radial heat flux independent of radius? is the radial heat rate independent of radius?

If the position of an object as a function of time is given by x=2t^3+(4-5t^2)m.

a. The position of the object at t=3s is 9m.

b. The velocity of the object at t=3s is 24 m/s.

c. The acceleration of the object at t=3s is 26 m/s^2.

a) Position:

At t=3s

the equation x=2t^3+(4-5t^2)m:

x = 2(3)^3 + (4 - 5(3)^2)m

x= 54 + (4 - 45)m

x= 9m

b) Velocity:

v = dx/dt = 6t^2 - 10t m/s

At t=3s

v = 6(3)^2 - 10(3) m/s

v= 54 - 30 m/s

v= 24 m/s

c) Acceleration:

a = dv/dt = 12t - 10 m/s^2

At t=3s

a = 12(3) - 10 m/s^2 = 36 - 10 m/s^2

a = 26 m/s^2

Therefore the  position of the object at t=3s is 9m.

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220 times 9 equals 1,980. 5 times 1,980 yields 396. 396 degrees plus 32 is 428 degrees Fahrenheit.

Here is a short tip you can use if you need to rapidly convert from Celsius to Fahrenheit: The (calculated) temperature to degrees Fahrenheit is obtained by multiplying the thermometer in degrees C by 2, then by 30.

The greatest temperature about which people can survive is generally accepted to be 108.14 degrees Fahrenheit, or 42.3 degrees Celsius. Higher temperatures have the potential to denature proteins and harm the brain permanently. Simply said, the human body has the potential to become scrambled.

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Explanation:

To calculate the amount of heating oil needed, we need to first determine the amount of energy required to heat the water. We can use the formula for calculating the energy required to heat a substance:

Q = mcΔT

where

Q is the energy required,

m is the mass of the substance,

c is the specific heat capacity of the substance, and

ΔT is the change in temperature.

For water, the specific heat capacity is 4.18 J/g°C.

Plugging in the values:

Q = 245 kg * 4.18 J/g°C * (68.0°C - 12.0°C) = 45,082,000 J

Next, we need to consider the efficiency of the boiler. The boiler is only 62% efficient, which means that only 62% of the energy released from the heating oil will actually be used to heat the water.

So the actual amount of energy required from the heating oil would be:

Q / 0.62 = 45,082,000 J / 0.62 = 72,619,355 J

Finally, we can use the heat energy released by 1 kg of heating oil to calculate the mass of heating oil required:

72,619,355 J / (4.15 x 107 J/kg) = 17.5 kg

So the boiler would need approximately 17.5 kg of heating oil to heat 245 kg of water from 12.0°C to 68.0°C.

When a wave is absorbed, the matter takes in energy from the wave and, in doing so, lowers the amplitude

Amplitude is the distance or farthest deviation from the balance point in a sine wave. In the international system, the amplitude is usually denoted by A and has units of meters (m).

In another definition, amplitude is a non-negative scalar measurement of the oscillating magnitude of a wave. The amplitude described earlier is the amplitude in physics. In contrast to the amplitude contained in the world of music.

Amplitude in music is defined as the volume of an audio signal. Wave amplitude is measured from the centerline distance. The results of this measurement are referred to in decibel units.

broadly speaking there are 3 main types of amplitude, including:

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It is True that, the parallelogram law for the addition of forces states that two forces acting on a particle are replaced by a single force, called their resultant, obtained by drawing the diagonal of the parallelogram with sides greater than the given forces.

What is Particle?

Particle is a branch of physics that studies the properties and interactions of particles, which are the fundamental constituents of matter and radiation. Particles are studied in the context of quantum field theory, which is a theoretical framework describing the fundamental forces of nature.

Therefore, It is True that, the parallelogram law for the addition of forces states that two forces acting on a particle are replaced by a single force, called their resultant, obtained by drawing the diagonal of the parallelogram with sides greater than the given forces.

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Solar flux is directly proportional to energy per second. Solar flux is a measure of the amount of energy that a star emits per unit of area per unit of time. Solar flux has units of energy per area per time, such as watts per square meter per second. Thus, solar flux is directly proportional to energy per second.

Solar flux refers to the rate of energy flow per unit area per unit time. It is often used to describe the amount of energy that a star emits, and it is typically measured in units of watts per square meter per second (W/m^2/s). The relationship between solar flux and energy is direct, meaning that as the solar flux increases, the amount of energy per second also increases. The higher the solar flux, the more energy is being emitted by the star. Solar flux is a useful metric in astronomy and space physics as it helps to describe the energy output of stars and other celestial objects. Additionally, it provides important information about the amount of energy that reaches the Earth's atmosphere and how it can impact our planet's climate and environment.

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20 to 22 degrees Celsius is standard room temperature in C.

What is Temperature?

 It is a measure of the degree of hotness or coldness of a body or an environment. It is a scalar quantity that is expressed in units such as Celsius (°C), Fahrenheit (°F), or Kelvin (K). The temperature of an object or environment is a measure of the average thermal energy of the particles that make it up, and it determines the direction of heat flow. High temperatures are associated with high thermal energy and fast molecular motion, while low temperatures are associated with low thermal energy and slow molecular motion. The temperature of an object or environment plays a crucial role in many physical and biological processes, such as chemical reactions, phase changes, and metabolic processes.

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Leaving a gap between the crucible and its lid when heating a sample is important for two main reasons:

1. Ventilation: The gap allows air to circulate and prevents the buildup of pressure inside the crucible, which can cause it to crack or explode. It also allows any fumes or gases generated during heating to escape, reducing the risk of contamination or reaction with the lid.

2. Temperature control: The gap allows for more even heating of the sample and prevents the lid from trapping heat inside the crucible, which can cause hot spots and uneven heating. The gap also allows for the insertion of thermocouples or other temperature sensors to monitor the temperature of the sample during heating.

In conclusion, a gap between the crucible and its lid is an important safety and control feature when heating a sample, allowing for proper Ventilation and temperature regulation

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Force is any influence that causes an object to undergo a certain change, either concerning its movement, direction, or geometrical construction.

What is the name for any long-term change in direction?

Acceleration is the rate at which speed and direction of velocity vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates. Even if the speed is constant, motion on a circle accelerates because the direction is always shifting.

A force has the power to alter an object's motion's direction. A greater force acting on an object will result in a greater change in motion. To undergo the same change in motion, a heavier object needs more force than a lighter thing.

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The plane's new velocity with respect to the ground is 195 km/h, westward.

When a plane is flying in the presence of wind, its velocity with respect to the ground is the vector sum of its velocity relative to the air and the velocity of the wind. In this case, the plane is flying due west at 275 km/h and encountering a wind from the west at 80 km/h.

To find the plane's new velocity with respect to the ground, we need to add the velocity of the plane relative to the air and the velocity of the wind. The velocity of the plane relative to the air is given as 275 km/h due west, and the velocity of the wind is given as 80 km/h from the west.

Adding these two velocities gives us the plane's new velocity with respect to the ground:

Velocity with respect to ground = 275 km/h + 80 km/h = 355 km/h due west.

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Answer: Its close to 1.4 km

Explanation:

In a laboratory setting, it is important to leave a gap between the crucible and its lid when heating the sample for several reasons. Firstly, the gap allows for proper ventilation, which prevents the buildup of pressure inside the crucible.

This is important because if the pressure inside the crucible becomes too high, it can cause the lid to pop off or even explode, potentially causing harm to the experimenter and damaging equipment.

Secondly, the gap allows for proper observation of the sample. If the lid is placed directly on top of the crucible, it can be difficult to observe any changes in the sample as it is being heated. The gap provides a space for the experimenter to observe the sample and monitor any changes that may occur.

Finally, the gap allows for proper temperature control. If the lid is placed directly on top of the crucible, it can trap heat inside the crucible and cause the temperature to become too high, potentially altering the results of the experiment.

The gap allows for the release of excess heat, helping to maintain a stable and controlled temperature inside the crucible.

In conclusion, the gap between the crucible and its lid is an important aspect of heating a sample in the laboratory. It helps to ensure the safety of the experimenter, allows for proper observation of the sample, and helps to maintain proper temperature control.

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C. Corn converts light to chemical energy in a photosynthesis.

The process by which light energy is transformed into chemical energy in the form of sugars is known as photosynthesis. Using light energy, glucose (or other sugars) are created from carbon dioxide and water, with oxygen being released as a byproduct. Organic molecules, most especially carbohydrates, hold the freshly created chemical energy (mostly glucose).

Because corn is a plant and contains chlorophyll in its structures, corn can absorb sunlight and use photosynthesis to transform it into chemical energy. Plants use the process of photosynthesis to create their own sustenance. The plant uses energy from the sun and carbon dioxide from the atmosphere.

Water and carbon dioxide combine in a chemical process during photosynthesis to produce glucose and oxygen. It is obvious that photosynthesis involves a chemical reaction since new chemical species are created.

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in a purely capacitive circuit, current is said to lead the applied source voltage.

If a circuit only contains a pure capacitor in it, it said to be a purely capacitive circuit.

In such circuit, when we apply a potential difference or apply a voltage, the current in the said is said to be leading the applied voltage by an angle of 90 degrees.

Now, this 90 degrees angle difference means that when we will make the phasor diagram for the purely capacitive circuit, and plot the pattern of the current and the applied voltage, we will observe that the current is making an angle of 90 degrees with the voltage and it is also ahead of the applied voltage.

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Maxwell's model is a mechanical representation of the behavior of an ideal gas. It was conceived in the nineteenth century by James Clerk Maxwell. An ideal gas.

according to Maxwell's concept, is made up of a huge number of particles that are in continual random motion and collide with each other and the container's walls. These particles are classified as point masses, which means they have no volume or structure. The model assumes that collisions are fully elastic, which means that no energy is wasted and the particle speed remains constant. Maxwell's model may be used to predict the behavior of an ideal gas in a variety of thermodynamic states, including pressure, temperature, and volume. It also enables us

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An independent variable, often known as a predictor variable, is one that is postulated to be the cause of an effect therefore, option a is the right choice.

In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables.

Dependent variables get their name because, during an experiment, their values are examined under the assumption or requirement that they are dependent on the values of other variables due to some law or rule (for example, a mathematical function). In the context of the experiment in question, independent variables are those that are not perceived as dependent on any other factors.

Time, space, density, mass, fluid flow rate, and prior values of some observed value of interest (such as the size of the human population) are examples of typical independent variables that can be used to forecast future values (the dependent variable).

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Mercury-centric models refer to models or theories that center around the planet Mercury, specifically in the context of astronomy and celestial mechanics.

These models may describe the dynamics, orbit, or other physical properties of Mercury or its interactions with other celestial bodies such as the Sun or other planets. For example, a Mercury-centric model might describe the planet's orbit and how it evolves over time due to the gravitational influence of other bodies in the Solar System. These models play a critical role in our understanding of the Solar System and its evolution over time.

Mercury-centric models are important because they help us understand the origin and evolution of the planet and its place in the Solar System. These models take into account various physical properties of Mercury such as its size, mass, and orbit, as well as the gravitational influence of other bodies in the Solar System, such as the Sun and the other planets.

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If a car is travelling east and we define east as the positive direction, the acceleration will be negative when the car is travelling west.

Acceleration is defined in physics as the change in velocity over elapsed time (a = Δv/t). Velocity is equal to displacement x over time t (v = x/t). Acceleration, velocity and displacement are all vector quantities because they have both magnitudes and directions.

We can use positive and negative signs to indicate direction. They are opposite to one another. So if an object (like a car) is travelling east and it is the positive direction, then the negative direction is the west.

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The magnitude of the electrical force exerted on the object at the top corner due to the two objects at the base of the triangle can be calculated using Coulomb's law.

The equation for Coulomb's law is F = k * q1 * q2 / r^2, where F is the force, k is the Coulomb's constant (8.99 * 10^9 Nm^2/C^2), q1 and q2 are the charges of the two objects, and r is the distance between them.

To calculate the force, you must first determine the charges of the two objects and the distance between them. Once these values are known, you can plug them into the equation and calculate the magnitude of the force.

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1.57 *10^-3Ω−m is the resistivity of the material in the wire

What is resistivity?

Electrical resistivity is a measurement of a material's degree of resistance to current flow. The SI unit for electrical resistivity is the ohm meter (m). It is frequently represented by the Greek letter rho. Materials that easily transmit current and have a low resistance are called conductors.

The resistance serves as a gauge for how challenging it is to transfer current through a component or wire. Resistivity affects resistance.

V = IR

R = V/I

V = 2V

I = 4A

R = 2/4 = 0.5

ρ= R A/L

R= Resistance

L= Length of wire

A= Cross sectional area of wire

Cross sectional area of cylinder (A)=Πr^2

⇒A=π×(1) ^2

A = 3.14mm^2

L is 1.0m

ρ=  0.5*3.14 *10^-3/1.0

ρ=  1.57 *10^-3Ω−m

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Acceleration is the result of the graph .

What is acceleration ?

Acceleration is a measure of how quickly an object changes its velocity, or speed and direction. It is a vector quantity and is expressed in units such as meters per second squared (m/s^2), feet per second squared (ft/s^2), or g (where g = 9.8 m/s^2 is the acceleration due to gravity at the surface of the Earth). Acceleration is a result of a force acting on an object and can be calculated using Newton's second law of motion as follows: acceleration = force / mass. Positive acceleration means that the object is speeding up, while negative acceleration means that the object is slowing down. Acceleration is an important physical quantity that is used to describe the motion of objects and to calculate the velocity and position of an object over time. It plays a crucial role in many areas of science and engineering, including mechanics, rocket science, and vehicle design.

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The electric field is strongest at the point of closest proximity between two opposite charges. The electric field will decrease in strength with increasing distance from the point of closest proximity.

Where the lines are spaced apart the most, the field is strongest. Charge 1 is negative and charge 2 is positive because the electric field lines converge towards charge 1 and away from charge 2, respectively. The density of electric field lines directly relates to the strength of an electric field. The strength of the electric field depends on how closely the field lines are spaced from one another; the weakest electric field results from field lines that are far apart.

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The required number of days when the hours are given and they are to be converted into days is 2.65 days.

Days and hours are the measure of time. They can be interconverted from one form to another. In this problem, we are asked to convert hours to days.

The number of hours in a day is known to be = 24 hours

So, 1 day = 24 hours

Number of days in 63.6 hours = ?

Let us convert hours to days.

The required number of days = 63.6 hours/24 hours = 2.65 days

Therefore, the required number of days when the hours are given and they are to be converted into days is 2.65 days.

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Tides occurs on earth as a result of the gravitational attraction between the moon, sun, and earth.

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The acceleration due to gravity on Mars is about 0.025 g, where g is the acceleration due to gravity on Earth.

Significant figures, also known as significant digits, are the meaningful digits in a measured or calculated value. They indicate the degree of precision of a measurement or calculation and include all digits that are known with certainty, plus one uncertain digit.

The acceleration due to gravity is proportional to the mass of the planet and inversely proportional to the square of its radius. Thus, the ratio of the acceleration due to gravity on Mars to that on Earth can be calculated as:

gMars/gEarth = (Mass of Mars) / (Mass of Earth) × (Radius of Earth)² / (Radius of Mars)²

Since the mass of Mars is one-ninth of the mass of Earth and the radius of Mars is half the radius of Earth, we can simplify the expression to:

gMars/gEarth = (1/9) × (1/2)² = 1/9 × 1/4 = 1/36

So, the acceleration due to gravity on Mars is about 1/36 of that on Earth. To express the answer using one significant digit, we can round to:

gMars/gEarth = 1/40

This means that the acceleration due to gravity on Mars is about 0.025 g, where g is the acceleration due to gravity on Earth.

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Speed is an example of measurement that considers velocity.

What is velocity?

Velocity is a vector measurement of the rate and direction of motion or the speed of an object in a given direction. It is the magnitude of the rate of change of an object’s position, and is usually expressed in meters per second (m/s). Velocity is defined as the rate of change of the position of a body with respect to time. An example of velocity is a car traveling at 30 miles per hour.

It is a measure of how quickly an object is moving across a given distance, usually measured in meters per second or kilometers per hour. This is because speed is a measure of how quickly an object is moving, which is related to its velocity. Speed is calculated by dividing the distance traveled by the time it takes to travel that distance, which includes the velocity of the object.

Therefore, Speed is an example of measurement that considers velocity.

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The angle that the vector sum makes with north. The direction the ship must travel is this angle, measured west of north.

We need to determine the angle that the vector sum of the ship's velocity relative to the sea and the ocean current creates with north in order to determine the direction the ship must go in order to have a velocity that is directly north relative to the earth.

Call the angle between the north and the ocean current. The east-west and north-south components of the ship's velocity in relation to the sea may be separated out.

The component along the east-west direction is 5.5 * cos(θ),

and the component along the north-south direction is 5.5 * sin(θ).

Adding the ocean current,

Which has a magnitude of 1.5 and direction 40º north of east, we get:

East component = 5.5 * cos(θ) + 1.5 * cos(40º)

North component = 5.5 * sin(θ) + 1.5 * sin(40º)

Dividing the North component by the magnitude of the vector sum and taking the inverse tangent.

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(1) Two materials that can be scratched by an iron mail are zinc and aluminum.

(2) The substance that can be scratched by an iron nail but not a penny is  Nickel.

The hardness of a material is defined as its ability to resist deformation due to mechanical scratching, abrasion, or indentation.

A material having a higher Mohs hardness number is able to scratch other materials which have a lower Mohs hardness number.

Based on this scale of hardness, iron has a hardness number of 4.5, zinc has a hardness number of 2.5, and aluminum has a hardness number between 2.5 to 3.

Thus, iron can scratch both, Zinc and Aluminum.

A penny is made from copper-plated material and copper has a hardness number of 3 on the Mohs scale. Whereas Nickel has a hardness number of 4. Therefore, a penny cannot scratch a material made of Nickel.

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Projectiles must therefore travel at a speed of at least 8000 meters per second in order to form an or satellite.

The direction of motion of a body as well as object is determined by its velocity. Speed is essentially a scalar quantity. In actuality, velocity is an vector quantity. What it is is the rate of change of distance. It gauges how quickly the displacement is changing.

The rate at which distance and time change is what is meant by speed. It has the aspect of temporal and spatial distance. The mix of the fundamental units of distance and time is what is described also as SI unit of speed. As a result, our Si system of speed is the meter per second.

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Increasing the temperature of the reaction solution can increase the rate of hydrolysis of sucrose, as higher temperatures can increase the rate of molecular motion.

Sucrose is a naturally occurring carbohydrate found in plants and fruits. It is also known as table sugar, or simply sugar. It is a disaccharide composed of glucose and fructose molecules joined together by a glycosidic bond. Sucrose is the most commonly used sweetener in food and beverage production and is found in many processed foods. It is used in baking, sweetening beverages, and as a preservative in some products. Sucrose is used as an energy source for the body. It is broken down by enzymes in the small intestine, releasing glucose and fructose which are then absorbed into the bloodstream and used for energy. Sucrose has a wide variety of uses in the food industry as a preservative, flavor enhancer, and sweetener.

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