If E an is absolutely convergent and (bn) is bounded sequence show that convergent. Gabn is absolutely Give an example to show that if the convergence 0l (n is conditional and (bn) is bounded sequence then anbn may diverge. Liii) Give A example of a convergent series (n,Such that 02 is not convergent

The force of friction between an object and the surface upon which it is sliding can be expressed as:

frictional force = coefficient of friction × normal force

where the normal force is the force exerted by the surface on the object perpendicular to the surface. We can use this equation to solve for the weight of the object.

frictional force = 12 N

coefficient of friction = 0.70

frictional force = coefficient of friction × normal force

12 N = 0.70 × normal force

normal force = 12 N / 0.70

normal force = 17.14 N

Since weight is the force exerted by gravity on the object, we can now calculate the weight of the object:

weight = mass × gravitational acceleration

We need to know the mass of the object to calculate its weight. We can use the formula:

weight = mass × gravitational acceleration

mass = weight / gravitational acceleration

The standard value for the acceleration due to gravity is 9.81 m/s²

weight = mass × 9.81 m/s²

mass = weight / 9.81 m/s²

Substituting normal force for weight, we get:

mass = normal force / 9.81 m/s^2

mass = 17.14 N / 9.81 m/s²

mass = 1.75 kg

Therefore, the weight of the object is:

weight = mass × gravitational acceleration

weight = 1.75 kg × 9.81 m/s²

weight = 17.15 N

The weight of the object is 17.15 N.

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The weight of the object is according to the given question is  17.16N.

Calculation of the given problem :-

The force of friction between an object and the surface can be found using the formula:

friction = coefficient of friction x normal force

where the normal force is the force perpendicular to the surface that the object is resting on.

In this case, we know that the friction force is 12N and the coefficient of friction is 0.70. Therefore, we can rearrange the formula to solve for the normal force:

normal force = friction / coefficient of friction

normal force = 12N / 0.70

normal force = 17.14N

The weight of the object is equal to the force of gravity acting on it, which is given by:

weight = mass x gravity

where gravity is approximately 9.81 m/s^2. We need to find the mass of the object in order to calculate its weight.

mass = normal force / gravity

mass = 17.14N / 9.81 m/s^2

mass = 1.75 kg

Therefore, the weight of the object is:

weight = mass x gravity

weight = 1.75 kg x 9.81 m/s^2

weight = 17.16N (rounded to two decimal places)

So the weight of the object is approximately 17.16N.

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Answer:

A. Four times

Explanation:

Gravitational Potential Energy (PE) is given as PE=mass*gravity*height

setting the equations of potential energy equal to each other for each object you get

m1gh=m2gh

then you can cancel out the gravity and height and get

m1=m2

then we know the mass of the second object is 4 times the mass of the first object so

m2=4m1

it will take 30.65 minutes for the thermocouple to read 99 percent of the initial temperature difference. (∅/∅i = 0.01).

The temperature of a gas stream is to be measured by a thermocouple whose junction can be approximated as a 1.2-mm-diameter sphere. So, the radius, r = 0.6 mm = 0.0006 m, the volume of the sphere, V = (4/3)πr³, and the area of the sphere, A = 4πr².

The properties of the junction are k = 35 W/m °C, p = 8500 kg/m³, and Cp = 320 J/kg °C, and the heat transfer coefficient between the junction and the gas is h = 65 W/m² °C.

We have, thermal conductivity of the sphere = k = 35 W/m °C, density of the sphere = p = 8500 kg/m³, specific heat of the sphere = Cp = 320 J/kg °C, and heat transfer coefficient between the sphere and the gas, h = 65 W/m² °C.

The initial temperature difference is given by, ΔT₀ = 1°C = 1 K. Let, the time taken for the thermocouple to read 99% of the initial temperature difference, ΔT99 = 0.99 K.

Let, the thermal diffusivity of the sphere be,

α = k / (pCp) = (35 W/m °C) / (8500 kg/m³ x 320 J/kg °C) = 0.000012868 m²/s.

And, the Biot number is given by, Bi = (h x A) / k = [(65 W/m² °C) x 4π(0.0006 m)²] / (35 W/m °C) = 0.0492.

The equation for the unsteady-state temperature profile of a sphere is, θ(r,t) = Σ [(-1)n+1 / n] exp(-n²π²αt / r²) sin (nπr / R), where R is the radius of the sphere. We can estimate the time taken for the thermocouple to read 99% of the initial temperature difference using a semi-log plot of θ/ΔT vs. t/ti.

This plot is linear and of the form, θ/ΔT = 1 - A exp (-Bt/ti), where A = 0.01 and B = (nπ/R)².So, θ/ΔT = 0.99 = 1 - A exp (-Bt/ti), or 0.01 exp (-Bt/ti) = 0.01/0.99, or exp (-Bt/ti) = 1/99, or -Bt/ti = ln (1/99), or t/ti = ln (99).

Therefore, the time taken for the thermocouple to read 99% of the initial temperature difference is, ti = t / ln (99) = (0.000012868 m²/s) (0.6 mm)² / (35 W/m °C) ln (99) = 1838.98 s or 30.65 minutes.

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An airplane flies due west at an airspeed of 425 mph and the wind is blowing from the northeast at 40 mph, the ground speed of the airplane is 385 mph, and the bearing of the airplane is 285°.

We can use the equation

GS = AS + (Wind x cos(Θ)),

Where GS is the ground speed, AS is the airspeed, and Θ is the angle between the wind and the heading of the airplane. the airspeed is 425 mph, the wind is blowing from the northeast at 40 mph, and the heading of the airplane is due west. The angle Θ is 90°. Plugging these values into the equation, we get

GS = 425 + (40 x cos(90°)) = 385 mph.

To calculate the bearing of the airplane, we can use the equation

Bearing = 180° - (Θ + (Wind ÷ AS) x 180°).

Θ is 90°, the wind is 40 mph, and the airspeed is 425 mph.

Plugging these values into the equation, we get

Bearing = 180° - (90° + (40 ÷ 425) x 180°) = 285°.

Hence , airplane flies due west at an airspeed of 425 mph and the wind is blowing from the northeast at 40 mph, the ground speed of the airplane is 385 mph, and the bearing of the airplane is 285°.

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The work done by friction is 20 J.

According to the law of conservation of energy, the total mechanical energy of a system remains constant if no external work is done on the system. In this case, we can use this law to calculate the work done by friction as follows

The initial mechanical energy of the ball at the top of the hill is

Ei = PE = 100 J

The final mechanical energy of the ball at the bottom of the hill is

Ef = KE + PE = 80 J, where KE is the kinetic energy of the ball.

Since the ball is at rest at the top of the hill, its initial kinetic energy is zero. Therefore, the initial and final kinetic energies are

Ei = 0 J

Ef = KE = 80 J

The work done by friction is equal to the difference between the initial and final mechanical energies

Wf = Ei - Ef = 100 J - 80 J = 20 J

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Answer:

The habitable zone

Explanation:

The habitable zone is the area around a star where conditions are right for liquid water to exist on a planet's surface.

Answer: poop

Explanation:

"Water from photosynthesis provides the electrons for the light reactions in photosynthesis."

The process of photosynthesis is used by plants, algae, and some microbes to produce food from sunlight, carbon dioxide, and water. The substance chlorophyll can be found in an organelle called the chloroplast or in the membrane of organisms that can perform photosynthesis.

The light reactions and the dark reactions are the two major stages of photosynthesis. Utilize sunshine to produce the energy-containing molecules required for the dark reactions during the light reactions. Electrons from chlorophyll are excited to the electron transport pathway during the light reactions. The chlorophyll, which is loaded with electrons from water, has a hole left by the electrons. When water breaks apart, the chlorophyll fills with electrons, and two oxygen atoms join forces to create oxygen gas. The factory releases this as a waste product.

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The correct option that describes the relationship between the new moon phase and constellations is: During the new moon phase, constellations are on the same side of the earth as the sun.

New Moon Phase and ConstellationsThe moon revolves around the Earth, and the Earth revolves around the sun. Because of this motion, the sun and the moon occupy different locations in the sky during various periods of the day and night.New moon phase: A new moon occurs when the moon is located between the Earth and the sun. During the new moon phase, the side of the moon that faces Earth is dark, and we cannot see the moon because the sun's light does not reflect off it towards Earth.Constellations: The term "constellation" refers to a particular configuration of stars that appears to be connected from Earth's perspective. Constellations have no physical connection; they are just stars that appear to be close to each other.New Moon Phase and Constellations RelationshipDuring the new moon phase, the Earth is between the sun and the moon. So, constellations are on the same side of the Earth as the sun, and are thus hidden from view. Therefore, the correct option that describes the relationship between the new moon phase and constellations is: During the new moon phase, constellations are on the same side of the earth as the sun.

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Concentrated sulfuric acid will result in excruciating burns if it comes in contact with your skin and can permanently harm your eyes if it gets in your eyes.

Thus,  Vinegar, or acetic acid, may also burn your skin and eyes, but it is insufficiently potent to serve as a drain cleaner.

Water is certainly not a particularly strong acid, despite the fact that we know it can serve as a proton donor.

It has a proton to provide, even hydroxide ions may theoretically act as acids. However, this is not a response that we often regard to be significant in all but the most extreme circumstances.

Thus, Concentrated sulfuric acid will result in excruciating burns if it comes in contact with your skin and can permanently harm your eyes if it gets in your eyes.

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The correct answer is the car that is turning experiences no net force.

A net force is the sum of all forces acting on an object, taking into account their magnitude and direction. If an object is not in equilibrium, it experiences a net force, which causes it to accelerate. In physics, a net force, often known as unbalanced force, is defined as the total sum of all forces that act on an object. If the forces acting on an object are balanced, meaning they are the same size but opposite in direction, the object will maintain a constant speed with no acceleration.

In this scenario, the car speeding up experiences the greater acceleration. The car that is turning, on the other hand, experiences no net force since the force acting on the car, the centripetal force, is equal to the force required to maintain its motion.

Therefore, the answer is option D. The car that is turning experiences no net force.

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The closer the loop is to the straight wire, the greater the magnetic field it produces, producing the current I2.

Since the nearest edge of the square loop and the current in an infinitely long wire both flow upward, there is an attraction between the two objects.

The magnetic field created by a straight wire increases along with the current. The loop's flux is expanding and getting stronger. The generated current should only cause internal flux.

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a(t) = v'(t) = \frac{d}{dt} [5 + 5^{\frac{t}{3}}] = 0 + \frac{5}{3} \cdot 5^{\frac{t}{3}-1}

We are asked to find the acceleration of the particle at time t=4, so we substitute t=4 into the acceleration function:

a(4) = \frac{5}{3} \cdot 5^{\frac{4}{3}-1} = \frac{5}{3} \cdot 5^{\frac{1}{3}} \approx 1.265

Therefore, the answer is (C) 1.265.

The outer edge of the photosphere of the sun is the region where all the photons produced in the sun's core are absorbed. Therefore, the correct option is (C) Photosphere.

The photosphere is the outermost region of the sun's atmosphere that is visible. It is a thin layer of gas that generates the visible light that we see. It is the region of the sun that has the greatest intensity of light and the lowest temperature.

The light that passes through the photosphere of the sun is then absorbed and re-emitted at various wavelengths by the other parts of the sun's atmosphere, such as the chromosphere and corona. Consequently, the photosphere is the only region of the sun that we can directly observe.

The sun's core is the area where the fusion of hydrogen atoms takes place, producing tremendous amounts of energy that are emitted as light and heat. The core of the sun is the primary source of energy for all the planets in the solar system, as well as for life on Earth.

The core of the sun has a temperature of roughly 15 million degrees Celsius and a density of about 150 times that of water. It is shielded from us by the sun's outer layers, making it impossible to see it directly. However, through studying the light and other radiation emitted by the sun, scientists can gain a better understanding of the processes that occur in the sun's core.

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It will take 0.82sec to reach the edge of the table if the system is free to move. If mB=1.0 kg, 99 kg mA must be used if the system's acceleration is to be kept above 1/100 g.

(a) mA = 11 kg

mB = 7 kg

T = mA mB g / (mA+mB) = 77*9.8 / 18 = 41.92 N is the formula for cord tension.

In the case of mA, we have T = mA*a

acceleration of mA, a = T / mA = 41.92 / 11 = 3.81 m/s²

For mB, we have mB*a = mB*g - T a = (mB*g - T) / mB

                                  a = (7*9.8 - 41.92) / 7 = 3.81 m/s²

(b) Initial velocity of mA, u = 0

The distance traveled by mA, s = 1.3 m

We have,

[tex]s = u t + (1/2) a t^2\\ s = at^2 / 2\\ t = (2s / a)^(1/2) = (2*1.3 / 3.81) (1/2) = 0.82 sec[/tex]

(c) mB = 1 kg

The system's acceleration, a = g/100

The system's acceleration is given by the formula a = mB*g / (mA+mB).

mA = [mB*g / a] - mB = [ 1*9.8*100/9.8 ] - 1 = 99 kg

Acceleration is the rate at which velocity changes with respect to time. It is a vector quantity whose magnitude denotes the amount of change in velocity per unit of time.

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Price elasticity of demand for radios is 1 and total revenue from radio sales will remain constant.

Price elasticity of demand is calculated as the percentage change in quantity demanded divided by the percentage change in price. Using this formula, we can calculate the price elasticity of demand for radios as follows:

Price elasticity of demand = (percentage change in quantity demanded) / (percentage change in price)

Given that when the price of radios decreases by 5%, quantity demanded increases by 5%.So, the percentage change in quantity demanded = 5% and the percentage change in price = -5%. (Because price has decreased by 5%.)Price elasticity of demand = (5% / -5%) = -1.The negative sign indicates that the demand is elastic. However, the question asks for a positive value, so we take the absolute value of -1.Price elasticity of demand = 1.

Therefore, the price elasticity of demand for radios is 1.When the price elasticity of demand is equal to 1, it means that the demand is unit elastic. This implies that the percentage change in quantity demanded is equal to the percentage change in price. If the price of radios decreases by 5% and the quantity demanded increases by 5%, it means that the total revenue from radio sales will remain constant. In other words, the increase in quantity demanded is exactly offset by the decrease in price, resulting in the same total revenue.

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The current in the battery increases and the magnetic field generated is stronger, which causes a larger induced current in the wire loop. This current will also be in the opposite direction of the battery current.

A circuit with a battery and a variable resistor near a loop of wire will cause an induced current in the loop when the resistance of the resistor is decreased. This is known as electromagnetic induction, which occurs when the current in the loop of wire changes, generating a changing magnetic field. This magnetic field then causes a current in the nearby wire loop. In this case, when the resistance of the resistor is decreased,

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The energy dissipated an AC voltage source with peak Output of 262 V due to heat in the resistor is 1471 W.

The rate of peak output voltage from the AC voltage source is 262 V. The energy dissipated due to heat in the resistor can be calculated using the formula P=V²/R, where P is the power (in Watts), V is the voltage (in Volts), and R is the resistance (in Ohms). So, using the values provided, we have:

P = 262²/33.02

P = 1471 W

Therefore, the energy dissipated due to heat in the resistor is 1471 W.

We know that the peak voltage (Vp) of an AC voltage source is given asVp = √2 × VrmsVp = √2 × 262Vp = 371.7V. The voltage across the resistor is given by the peak voltage of the source, which is 371.7V.The resistance of the resistor is 33 ΩWe know that the formula to calculate power (P) is given as P = V² / R Where V is the voltage across the resistor R is the resistance of the resistor. As the power is given, we can find the energy by using the formula:E = P × t Where E is the energy dissipated due to heat in the resistor, P is the power, t is the time.

*Complete question: An AC voltage source with peak Output of 262 V, is connected to a 33-02 resistor. What is the rate of energy dissipated due to heat in the resistor? . 2080 W 1040 W C. 520 W D. 1471 W 662 W

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The constant angular deceleration of the centrifuge is 225 rad/s².

Given data:

Now, we need to find the constant angular deceleration of the centrifuge.

Since the angular deceleration is constant, we can use the formula of angular displacement:θ = ω1t - (1/2)αt²

Where:

Let's calculate the total time taken by the centrifuge to come to rest.Number of revolutions made by the centrifuge after the motor is switched off = N = 50 revolutions.

The time period of one revolution = T = 60 s / 3600 rev. = 1/60 s/rev. The time taken to complete N revolutions = t = N × T = 50 × 1/60 = 5/6 s

Let's plug in the given values in equation (1):0 - 3600(5/6) = (1/2)α(5/6)²

On solving the above equation, we get:

Therefore, the constant angular deceleration of the centrifuge is 225 rad/s².

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Answer:

Explanation:

Graphic Method:

To solve this problem graphically, you will need to draw a vector diagram. Draw the two forces 10N and 20N as vectors originating from the same point, with the angle between the vectors being 60°. Then, draw the resultant vector that joins the tail of the first vector to the head of the second vector. The magnitude of the resultant vector is the magnitude of the resultant force.

Mathematical Method:

To solve this problem mathematically, you will need to use the law of cosines. The law of cosines states that:

R² = A² + B² - 2ABcosϴ

Where R is the magnitude of the resultant vector, A and B are the magnitudes of the two vectors, and ϴ is the angle between the two vectors.

So, in this case, R² = 10² + 20² - 2(10)(20)cos60°

R² = 100 + 400 - 400cos60°

R² = 500 - 200

R = √300

Therefore, the magnitude of the resultant vector is √300N.

If the two forces are now made to be inclined at 120° to each other, the law of cosines states that:

R² = A² + B² - 2ABcosϴ

Where R is the magnitude of the resultant vector, A and B are the magnitudes of the two vectors, and ϴ is the angle between the two vectors.

So, in this case, R² = 10² + 20² - 2(10)(20)cos120°

R² = 100 + 400 - 400cos120°

R² = 500 + 200

R = √700

Therefore, the magnitude of the new resultant vector is √700N.

The frequency of the sound heard is about 438.12 Hz and the frequency at which you are singing is 397 Hz.

Since the sound is propagating towards you at a speed of v = 347 m/s, the frequency detected by an observer with a velocity of u = 24.3 m/s (you) can be calculated with the Doppler effect equation:

fobs = fsrc × (v + u) / (v + usrc)

where, fsrc = 401 Hz (source frequency), usrc = 0 (velocity of the source), u = 24.3 m/s, v = 347 m/s

Replacing the given values we have: fobs = 401 × (347 + 24.3) / (347 - 0) = 466.93 Hz

The frequency that you hear is 466.93 Hz.

In this case, the source is you and you are moving towards your friend with a velocity of 24.3 m/s. Therefore, the frequency detected by your friend with a velocity of v = 347 m/s can be calculated as:

fobs = fsrc × (v + usrc) / (v - u)

where, fsrc = 400 Hz (source frequency), usrc = 0 (velocity of the source), u = 24.3 m/s, v = 347 m/s

Replacing the given values we have:

fobs = 400 × (347 + 0) / (347 - 24.3) = 438.12 Hz

The beat frequency can be calculated by taking the absolute difference of the two frequencies. In this case, the beat frequency is 3 Hz. Since the beat frequency is given by:

beat frequency = |f1 - f2|

We can write the following equation: f2 = f1 - beat frequency

where, f1 = frequency of your friend = 400 Hz, beat frequency = 3 Hz

Replacing the given values we have: f2 = 400 - 3 = 397 Hz

Therefore, the frequency you are singing is 397 Hz.

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Some potential drawbacks of switching from incandescent to compact fluorescent light bulbs are higher initial cost, sensitivity to temperature, and potential health hazards. Here is a more detailed explanation of these drawbacks:

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We can see the moons should be ranked in the following order from oldest to youngest:

A moon is a natural satellite that orbits a planet. Moons are typically much smaller than their parent planets and are held in orbit by the planet's gravity. They come in a variety of sizes and shapes, and can be composed of a wide range of materials, such as rock, ice, or a mixture of both.

Moons play an important role in our solar system. They help stabilize the orbits of planets, contribute to tidal forces, and may even play a role in the formation and evolution of planets themselves.

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When a star depletes its core supply of hydrogen and enters the red giant stage, helium dominates in the core, and hydrogen dominates in the atmosphere.

Let's discuss this in detail. Star depletes its core supply of hydrogenWhen a star exhausts its core supply of hydrogen, it begins to convert helium into carbon and oxygen in its core. This process leads to the formation of a heavier core which contracts and increases in temperature. As a result, the temperature of the core increases to the point where it can initiate helium fusion, producing carbon and oxygen. At the same time, the outer shell of the star cools and expands. Dominates in the core and dominates in the atmosphere in the core of a red giant star, helium dominates since this is where helium fusion occurs. The star's atmosphere is, on the other hand, dominated by hydrogen because it is cooler and less dense than the core. The helium-burning phase is shorter than the hydrogen-burning phase in a star's life cycle. When a star enters the red giant phase, it indicates that the core of the star has depleted its hydrogen and is now converting helium to heavier elements. This stage will not last long as the core will continue to contract and heat up, resulting in the production of heavier elements.

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E = mgh

where m is the mass of the sled, g is the acceleration due to gravity, and h is the height of the hill.

At the bottom of the hill, all of the potential energy has been converted into kinetic energy, which is given by:

E = (1/2)mv^2

where v is the velocity of the sled at the bottom of the hill.

When the sled reaches the level stretch, the kinetic energy is converted into work done by the friction force, which is given by:

W = fd

where f is the friction force and d is the distance traveled across the level stretch.

Setting the potential energy at the top of the hill equal to the work done by the friction force on the level stretch, we have:

mgh = fd

Solving for h, we get:

h = (fd)/(mg)

Substituting the given values, we get:

h = (0.27)(m)(9.8 m/s^2)(19 m)/(m)(9.8 m/s^2)

Simplifying, we get:

h = 5.13 m

Therefore, the height of the hill is 5.13 meters.

The velocity of wreckage immediately after impact = 9.68 m/s and the compass heading is 45 deg (for the second answer).

Mass of 1950 kg Oldsmobile = 1950 kg

Velocity of Oldsmobile = 15.4 m/s

Mass of a truck hauling animal feed = 3992 kg

Velocity of a truck hauling animal feed = 9.9 m/s

Conservation of Momentum Formula Used,

Momentum before collision = Momentum after collision(m1 × v1) + (m2 × v2) = (m1 + m2) × V'

Calculation for Momentum before Collision = (m1 × v1) + (m2 × v2)

Momentum before Collision = (1950 kg × 15.4 m/s) + (3992 kg × 9.9 m/s)

Momentum before Collision = 30129 + 39560.8

Momentum before Collision = 69689.8 kg-m/s

Let V' be the velocity of the wreckage immediately after the impact.

Velocity after Collision is V'

Calculation for Velocity after Collision = (m1 × v1) + (m2 × v2) / (m1 + m2)V'

= (1950 × 15.4) + (3992 × 9.9) / (1950 + 3992)V'

= 57606.8 / 5942V'

= 9.68 m/s

Given, the 1950 kg car was traveling East on Saginaw Street which means the wreckage was moving North-East (45 degrees)

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The length is 2.78 mm if the 0. 100-mm diameter tungsten filament in a light bulb is to have a resistance of 0. 200 ω at 20 degrees.

The length tungsten filament is 2.78 mm to have a resistance of 0. 200 ω at 20. degrees.

The given data is as follows:

Diameter of tungsten = 0.100 mm

resistance of tungsten = 0.200ω

The resistance (R) of a conductor is calculated by using the formula,

R = ρ × (L/A)

ρ =   resistivity of the material

L =  length of the conductor

A  =  cross-sectional area.

By rearranging the formula to calculate the length,

L = (R × A) / ρ

A = π × r²

A = 3.14 × (5.0 x [tex]10^{-5}[/tex])²

A = 7.85 x [tex]10^{-9}[/tex] m²

The resistivity of tungsten at 20.0°C  =  5.6 x [tex]10^{-8}[/tex] Ωm

L = (0.200 × 7.85 x [tex]10^{-9}[/tex]) / (5.6 x [tex]10^{-8}[/tex])

L = 2.78 x [tex]10^{-3}[/tex] m

L = 2.78 mm

Therefore we can conclude that the length is 2.78 mm to have a resistance of 0. 200 ω at 20 degrees.

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The volume of the solid obtained by rotating the region in the first quadrant bounded by the curves x = 0, y = 1, x = y^7 about the line y = 1 is 0.

To determine the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves x = 0, y = 1, x = y^7 about the line y = 1, we need to use a specific integral formula.

The volume of the solid is calculated by multiplying the area of the cross-section of the solid, which is perpendicular to the axis of rotation, with the distance traveled by the center of mass of the cross-section. And, when this product is summed up across the length of the solid, we get the volume of the solid.

To solve the given problem, the area of the cross-section of the solid is [tex]\pi (r)^2[/tex], where r is the distance from the line y = 1 to the curve [tex]x = y^7[/tex]. Since the cross-section is a circle, we know the area of the cross-section can be represented by the equation of a circle with radius r, which is [tex]\pi (r)^2[/tex].

To find the value of r, we will equate  [tex]x = y^7[/tex] to the line y = 1. By solving for y, we get: [tex]y = 1^{1/7} = 1[/tex].

Hence, r = 1 - 1 = 0.

We can now compute the volume of the solid using the integral formula:

[tex]V =\int_0^1 \pi (r)^2 dy\\V = \int_0^1 \pi (0)^2 dy\\V = \int_0^1 0 dy\\V = 0[/tex]

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