a solenoid with a self-inductance has an induced emf described by . which of the given equations describes the current carried by the coil?
a. I = - bt/L + C
b. I = - bt^2 / 2L + C
c. I = - Lb
d. I = - bt/2L +C

The power series representation for the function f(x) = ln(7 - x) is f(x) = ln(7) - ∑(n=0 to ∞) [(x - 7)^n / (n+1)].

To find the power series representation, we can use the Taylor series expansion of the natural logarithm function ln(1 + x):

ln(1 + x) = x - (x^2 / 2) + (x^3 / 3) - (x^4 / 4) + ...

In this case, we have the function f(x) = ln(7 - x), which can be rewritten as f(x) = ln(1 + (x - 7)).

Using the Taylor series expansion, we substitute (x - 7) in place of x:

f(x) = (x - 7) - [(x - 7)^2 / 2] + [(x - 7)^3 / 3] - [(x - 7)^4 / 4] + ...

Simplifying, we can write this as:

f(x) = -∑(n=0 to ∞) [(x - 7)^n / (n+1)]

Next, we add ln(7) to the series to account for the constant term:

f(x) = ln(7) - ∑(n=0 to ∞) [(x - 7)^n / (n+1)]

The radius of convergence, R, can be determined by using the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms in the series is L, then the series converges absolutely when L < 1 and diverges when L > 1.

In this case, we take the absolute value of the terms in the series and calculate the limit:

lim(n→∞) |(x - 7)^(n+1) / [(n+2)(x - 7)^n]|

Simplifying and taking the limit, we find:

lim(n→∞) |x - 7| / (n + 2)

Since this limit approaches zero for any value of x, the series converges for all values of x. Therefore, the radius of convergence, R, is infinity.

The power series representation for the function f(x) = ln(7 - x) is f(x) = ln(7) - ∑(n=0 to ∞) [(x - 7)^n / (n+1)]. The series converges for all values of x, indicating that the radius of convergence, R, is infinity.

To know more about Power Series, visit

https://brainly.com/question/32654795

#SPJ11

This soil sample is one that is primarily clay, with some portions of silty clay and sand.

It has little of the clay loam category, that has a balanced mixture of clay, silt, and sand.

The soil triangle shows soil texture using sand, silt, and clay. Based on given percentages, soil sample has 40% silt, 40% sand, and 20% clay. It's silty sand or sandy loam soil.

Clay loam soil has a balanced blend of clay, silt, and sand. Moderate water-holding, good drainage, favorable nutrient retention. Sandy clay is a mixture of sand and clay. Retains sandy soil traits with better water hold from clay.

Learn more about soil triangle from

https://brainly.com/question/30763246

#SPJ1

Answer:

Y = 4.775 x 10⁹ Pa = 4.775 GPa

Explanation:

First, we calculate the stress on the rod:

[tex]stress = \frac{Force}{Area} = \frac{3000\ N}{\pi r^2} \\\\stress = \frac{3000\ N}{\pi (0.01\ m)^2}\\\\stress = 9.55\ x\ 10^6\ Pa = 9.55 MPa\\[/tex]

Now, we calculate the strain:

[tex]strain = \frac{Change\ in Length}{Original\ Length}\\\\strain = \frac{0.501\ m - 0.5\ m}{0.5\ m}\\\\strain = 0.002\\[/tex]

Now, we will calculate the Young's Modulus (Y):

[tex]Y = \frac{stress}{strain}\\\\Y = \frac{9.55\ x\ 10^6\ Pa}{0.002} \\[/tex]

Y = 4.775 x 10⁹ Pa = 4.775 GPa

Answer:

Energy moves between the particle of the medium.

Explanation:

The additional volume of ethanol that can be put into the tank is 0.0136 m³.

The given informations are,

Part A

When the tank and its contents have cooled to 20.0 °C, the volume of ethanol decreases due to the decrease in temperature.

Let's assume the volume of ethanol at 33.0 °C be V1 and at 20.0 °C be V2 and coefficient of cubical expansion of ethanol be α.

From the temperature coefficients of cubical expansion, we can say that the volume of ethanol decreases with decrease in temperature.

So, the additional volume of ethanol which can be put into the tank is,

Additional volume = V1 - V2

The volume of ethanol changes due to the change in temperature,

V2 = V1 / [1 + α (T2 - T1)]

where T1 and T2 are the initial and final temperatures of the ethanol in degree Celsius.

The coefficient of cubical expansion of ethanol, α = 1.12 × 10^-3 / °C.

Now, let's substitute the given values in the above equation:

V2 = 1.60 m³ / [1 + (1.12 × 10^-3 / °C) × (33.0 °C - 20.0 °C)]

V2 = 1.5864 m³

Therefore, the additional volume of ethanol that can be put into the tank when the tank and its contents have cooled to 20.0 °C is,

Additional volume = V1 - V2= 1.60 m³ - 1.5864 m³

                              = 0.0136 m³

Hence, the additional volume of ethanol that can be put into the tank is 0.0136 m³.

Learn more about the ethanol:

brainly.com/question/31742303

#SPJ11

The groups aren't well formatted ;

The groups are ;

(-3, -1, 0, 2, 7) ; (9, 7, 6, -5, -4) ; (8, -6, 5, -4, 1) ; (-3, -4, -7, -8, -9)

Answer:

(-3, -4, -7, -8, -9)

Explanation:

Given the following group of numbers :

Evaluating each group of values for which is correctly arranged from greatest to least.

(-3, -1, 0, 2, 7) : - 1 is greater than - 3 (the group isn't arranged from greatest to least)

(9, 7, 6, -5, -4) : - 4 is greater than - 5 ; hence, the group isn't arranged from greatest to least

(8, -6, 5, -4, 1) : 5 is greater than - 6 ; hence, the group isn't arranged from greatest to least

(-3, -4, -7, -8, -9) ; the group of numbers here is arranged from greatest to least ;

(-3 > -4 > -7 > -8 > -9) ; hence, the correct group

Answer:

[tex]\frac{60kgm}{s}[/tex]

Explanation:

momentum = mass * velocity

= 20kg * 3m/s

= 60kgm/s

-50F is the air temperature at which the speed of a sound wave is closest to 1,000 feet per second. It is option D.

The speed of a sound wave depends on the temperature of the medium through which it travels. The formula for calculating the speed of sound in air is given by: v = 331 m/s + 0.6 m/s °C × t

t = temperature in degrees Celsius  

v = velocity of the sound wave in meters per second.

Therefore, to answer the question, we need to convert the temperatures from Fahrenheit to Celsius and use the above formula to determine the velocity of the sound wave at each temperature.

A. -46F = -43.33°C

Speed of sound = 331 + 0.6 x (-43.33)≈ 304.4 m/s

B. -48F = -44.44°C

Speed of sound = 331 + 0.6 x (-44.44)≈ 303.6 m/s

C. -49F = -45°C

Speed of sound = 331 + 0.6 x (-45)≈ 303 m/s

D. -50F = -45.56°C

Speed of sound = 331 + 0.6 x (-45.56)≈ 302.5 m/s

Therefore, the air temperature at which the speed of a sound wave is closest to 1,000 feet per second is option D.-50F.

To know more about Sound Wave at:

https://brainly.com/question/29071528

#SPJ11

Increasing number of photons per second striking the surface and increasing the frequency of the incident light lead to increase in maximum kinetic energy of ejected electrons in the photoelectric effect.

Increasing the number of photons per second striking the surface:

The maximum kinetic energy of the ejected electrons depends on the total energy transferred to the electrons by the incident photons. Increasing the number of photons per second increases the total energy transferred, resulting in an increase in the maximum kinetic energy of the ejected electrons.

Increasing the frequency of the incident light:

The maximum kinetic energy of the ejected electrons is directly proportional to the frequency of the incident light. According to the equation E = hf, where E is the energy of a photon, h is Planck's constant, and f is the frequency of the light, increasing the frequency of the incident light increases the energy of each photon. This, in turn, leads to an increase in the maximum kinetic energy of the ejected electrons.

Using photons whose frequency fo is less than Wo/h, where Wo is the work function of the metal and h is Planck's constant:

If the frequency of the incident light is less than the threshold frequency (fo) required to overcome the work function of the metal, no electrons will be ejected regardless of the intensity or number of photons. Therefore, using photons with a frequency less than the threshold frequency does not lead to an increase in the maximum kinetic energy of the ejected electrons.

Selecting a metal that has a greater work function:

The work function of a metal represents the minimum amount of energy required to eject an electron from its surface. Selecting a metal with a greater work function would result in a higher energy threshold for electron ejection. While it affects the threshold for electron ejection, it does not directly influence the maximum kinetic energy of the ejected electrons.

Increasing the number of photons per second striking the surface and increasing the frequency of the incident light lead to an increase in the maximum kinetic energy of the ejected electrons in the photoelectric effect. However, using photons with a frequency less than the threshold frequency and selecting a metal with a greater work function do not contribute to an increase in the maximum kinetic energy of the ejected electrons.

To know more about Photoelectric effect visit:

https://brainly.com/question/1359033

#SPJ11

The crank OB is horizontal and has a clockwise angular velocity of 0.8 rad/sec. The objective is to find the speed of the guide roller A and the angular velocity of the connecting rod AB link.

To solve this problem, let's first draw the mechanism diagram. [tex]\frac{d\theta_{1}}{dt}[/tex] and [tex]\frac{d\theta_{2}}{dt}[/tex] are the angular velocities of OB and AB, respectively. We can apply the kinematic equations to find these unknowns.

In this case, the kinematic equations of the mechanism are Vb = Va + AB * [tex]\frac{d\theta_{2}}{dt}[/tex] (1)0 = AB * cos β - OA * [tex]\frac{d\theta_{1}}{dt}[/tex] (2.).

Now, we can evaluate [tex]\frac{d\theta_{1}}{dt}[/tex] and [tex]\frac{d\theta_{2}}{dt}[/tex] using the given angular velocity of crank OB.

It is given that [tex]\frac{d\theta_{1}}{dt}[/tex] = 0.8 rad/sec.

Using equation (2), we can obtain AB = OA * cos β / [tex]\frac{d\theta_{1}}{dt}[/tex].

Putting the value of [tex]\frac{d\theta_{1}}{dt}[/tex] = 0.8 rad/sec, OA = 60 mm and β = 60° in equation (2),

We get:AB = 60 * cos 60 / 0.8 = 43.3 mm.

Now, using equation (1), We can find the speed of the guide roller Va as Vb = Va + AB * [tex]\frac{d\theta_{2}}{dt}[/tex]Vb - Va = AB * [tex]\frac{d\theta_{2}}{dt}[/tex]Va = Vb - AB * [tex]\frac{d\theta_{2}}{dt}[/tex].

We know that Vb = R * [tex]\frac{d\theta_{1}}{dt}[/tex] = 60 * 0.8 = 48 mm/sec.

Hence,Va = 48 - 43.3 * [tex]\frac{d\theta_{2}}{dt}[/tex].

Now, we need to find [tex]\frac{d\theta_{2}}{dt}[/tex]. We can find it using the kinematic equation of link AB, which is given as AB * sin β * [tex]\frac{d\theta_{2}}{dt}[/tex] = Va.

But, we don't know the value of Va yet. So, we can use the velocity diagram of the mechanism to relate the velocities of points A and B.

Using the vector law of addition of velocities, we can write Va^2 = (Vb cos β)^2 + (Vb sin β - R [tex]\frac{d\theta_{1}}{dt}[/tex])^2Putting the values of Vb, β and R, we get: Va^2 = (48 cos 60)^2 + (48 sin 60 - 60 * 0.8)^2Va = 52.4 mm/sec.

Now, putting the value of Va in the kinematic equation of link AB, we get AB * sin β * [tex]\frac{d\theta_{2}}{dt}[/tex] = 52.4d[tex]\theta_{2}[/tex] / dt = 52.4 / (43.3 * sin 60)d[tex]\theta_{2}[/tex] / dt = 0.639 rad/sec.

Hence, the speed of the guide roller A in the slot is 52.4 mm/sec and the angular velocity of the AB link is 0.639 rad/sec.

Learn more about vector law of addition here ;

https://brainly.com/question/14454864

#SPJ11

As the time needed to run up a flight of stairs decreases, the power initially increases and then decreases.

The power generated during an activity can be calculated using the equation: Power = Work / Time. In the context of running up a flight of stairs, the work done is the force exerted to overcome gravity and move the body vertically against it. When the time needed to complete the task decreases, it means the individual is able to generate more power.

Initially, as the person improves their running ability and becomes more efficient, they can complete the task in less time. This reduction in time indicates an increase in power output since the work done remains relatively constant. The individual is exerting more force in a shorter amount of time, resulting in higher power.

However, there is a limit to how much power a person can generate. As the person continues to improve their running speed, they reach a point where their power output plateaus or even decreases. This decline can occur due to various factors, such as muscle fatigue or biomechanical limitations. At this stage, further decreases in time may not be achievable without sacrificing power output. Therefore, the power initially increases as time decreases, but eventually levels off or decreases as the person reaches their physiological limits.

To learn more about power refer:

https://brainly.com/question/11569624

#SPJ11

Therefore, the focal length of the converging lens is approximately 9.33 cm or 21 cm (rounded to the nearest whole number).

To determine the focal length of the converging lens, we can use the lens formula:

1/f = 1/v - 1/u

where f is the focal length, v is the image distance from the lens, and u is the object distance from the lens.

Given that the object is placed 28 cm in front of the lens (u = -28 cm) and the image is formed 14 cm behind the lens (v = 14 cm), we can substitute these values into the lens formula:

1/f = 1/14 - 1/(-28)

Simplifying the equation:

1/f = 1/14 + 1/28

Finding a common denominator:

1/f = 2/28 + 1/28

Combining the fractions:

1/f = 3/28

Inverting both sides of the equation:

f = 28/3

Converting the fraction to decimal form:

f ≈ 9.33 cm

Therefore, the focal length of the converging lens is approximately 9.33 cm or 21 cm (rounded to the nearest whole number).

The focal length of the converging lens is approximately 21 cm.

To know more about Converging lens visit:

https://brainly.com/question/15123066

#SPJ11

Answer:

3 m/s²

Explanation:

Initial Velocity, u = 18

Final velocity, v = 36

Time, t = 6 seconds

Acceleration is the change in velocity of a body with time. It obtained using the relation :

Acceleration = (v - u) / t

Acceleration = (36 - 18) / 6

Acceleration = 18 / 6

Acceleration = 3m/s²

Hence, acceleration of the skier is 3m/s²

Answer:  TRUE /   IT IS TRUE

Explanation:

Answer:

11 cm and concave

Explanation:

edge 2021

Answer:

it is -21, The top part is correct it is only the second part this is the first part.

Explanation:

All supernova explosions leave stars in the same condition after the process has finished which is false.

Supernova explosions do not leave stars in the same condition after the process has finished. Supernovae are incredibly powerful explosions that occur at the end of a massive star's life or in the aftermath of a white dwarf's accretion. The outcome of a supernova depends on various factors, such as the mass of the star and the nature of the explosion. There are two main types of supernovae: Type I and Type II.

In a Type I supernova, the star is completely destroyed, leaving behind either a neutron star or a black hole. These explosions occur in binary star systems where a white dwarf accumulates matter from a companion star, eventually reaching a critical mass and triggering a runaway nuclear reaction.

In a Type II supernova, the massive star collapses under its own gravity, resulting in a powerful explosion. After the explosion, what remains can vary. It could leave behind a neutron star or even a black hole. The remnants may also include a rapidly expanding cloud of gas and dust called a supernova remnant, which can enrich the surrounding space with heavy elements.

Therefore, it is incorrect to say that all supernova explosions leave stars in the same condition after the process has finished. The specific outcome depends on various factors and can lead to the formation of different celestial objects.

To learn more about supernova explosions click here

https://brainly.com/question/14018571

#SPJ11

The line, 100 mm in length, is parallel to and 40 mm above the h.p. Its ends, positioned 25 mm and 50 mm in front of the v.p., are connected to form projections. The inclination with the v.p. is 48.59°.

To draw the projections of the line, we start by drawing the plan view (H₁) and the front view (V₁).

In the plan view (H₁), we draw a horizontal line of 100 mm length. The line is parallel to the horizontal plane (h.p.), so it remains at the same height as the h.p.

In the front view (V₁), we draw a vertical line to represent the height above the h.p. Since the line is 40 mm above the h.p., we draw a line 40 mm long above the ground line. Then, we draw the line segments representing the ends of the line.

The first end is 25 mm in front of the vertical plane (v.p.), and the second end is 50 mm in front of the v.p. We connect these ends to the top of the vertical line to complete the front view.

To find the inclination of the line with the v.p., we use the right triangle formed by the height of the line (40 mm) and the distance from the v.p. to the second end of the line (50 mm). We can calculate the inclination angle using the tangent function:

tan(θ) = opposite/adjacent = 40/50

Solving for θ, we find:

θ = tan^(-1)(40/50) = 48.59°

To know more about tangent function, refer here:

https://brainly.com/question/30162652#

#SPJ4

Answer: Biotic

Explanation: Because it's bacteria.

Answer:

The moon doesn’t have light of its own, the moon lights up because of the sun. So at night, as the light of the sun doesn't reach the grass directly because of the moon, it doesnt reflect any color off the grass, and so our eyes detect grass as black.

Explanation:

Sun appears white, but it is made up of the colors: red, orange, yellow, green, blue, indigo, and violet. When white light hits an object, it absorbs some colors and reflect the others. Grass appears green because it absorbs all the wavelengths except green. Green is reflected off the grass, so we see grass as green.

Answer:

Nepal is one of the least developed countries. Solar power is well-founded than electricity. It's better to use solar power because it's a clean resource, the sun provides more energy than we will ever need.

Explanation:

The height of the cannon where the objects are launched from is 18 feet.

The canons of page construction are historical reconstructions, based on careful measurement of extant books and what is known of the mathematics and engineering methods of the time, of manuscript-framework methods that may have been used in Medieval- or Renaissance-era book design to divide a page into pleasing proportions. Since their popularization in the 20th century, these canons have influenced modern-day book design in the ways that page proportions, margins and type areas (print spaces) of books are constructed.

To determine the height of the cannon where the objects are launched from, we need to find the value of "h" when "t" is equal to zero.

Given the equation: h = (-1/5)×t^2 + 5×(t) + 18

Substituting t = 0 into the equation, we have:

h = (-1/5)×(0)^2 + 5(0) + 18

= 0 + 0 + 18

= 18

Therefore, the height of the cannon where the objects are launched from is 18 feet.

To know more about canons:

https://brainly.com/question/14010693

#SPJ4

Answer:

Efficiency of the inclined plane is 56%

Explanation:

efficiency = (work output / work input) x 100%

efficiency = ([load force x load distance] x [effort force x effort distance]) x 100%

efficiency = (250 kg x 10 m) / (180 kg x 25 m) x 100%

efficiency = (2500kg/m) / (4500kg/m) x 100%

efficiency = 0.555 = 0.56 x 100%

efficiency = 56%

a. The potential at 5.50 cm from the center of the sphere is 9.00 x [tex]10^7[/tex] V.

b. The potential at 30.0 cm from the center of the sphere is 1.65 x [tex]10^8[/tex] V.

c. The potential at 16.0 cm from the center of the sphere is 2.47 x [tex]10^8[/tex] V.

To find the value of the potential at different distances from the center of the sphere, we can use the equation for the electric potential of a uniformly charged sphere.

Given:

Total electric charge (Q) = 5.50 nC

Radius of the sphere (R) = 30.0 cm = 0.30 m

a) To find the potential at 5.50 cm from the center of the sphere:

Distance from the center of the sphere (r) = 5.50 cm = 0.055 m

The equation for the electric potential of a uniformly charged sphere is:

V = k × Q / r

where V is the potential, k is the Coulomb's constant (8.99 x [tex]10^9[/tex] N m²/C²), Q is the total charge, and r is the distance from the center of the sphere.

Substituting the given values into the equation:

V = (8.99 x [tex]10^9[/tex] N m²/C²) × (5.50 x [tex]10^{-9[/tex] C) / 0.055 m

Calculating the value:

V = 9.00 x [tex]10^7[/tex] V

Therefore, the potential at 5.50 cm from the center of the sphere is 9.00 x [tex]10^7[/tex] V.

b) To find the potential at 30.0 cm from the center of the sphere:

Distance from the center of the sphere (r) = 30.0 cm = 0.30 m

Using the same equation as above:

V = (8.99 x [tex]10^9[/tex] N m²/C²) × (5.50 x [tex]10^{-9[/tex] C) / 0.30 m

Calculating the value:

V = 1.65 x [tex]10^8[/tex] V

Therefore, the potential at 30.0 cm from the center of the sphere is 1.65 x [tex]10^8[/tex] V.

c) To find the potential at 16.0 cm from the center of the sphere:

Distance from the center of the sphere (r) = 16.0 cm = 0.16 m

Using the same equation as above:

V = (8.99 x [tex]10^9[/tex] N m²/C²) × (5.50 x [tex]10^{-9[/tex] C) / 0.16 m

Calculating the value:

V = 2.47 x [tex]10^8[/tex] V

Therefore, the potential at 16.0 cm from the center of the sphere is 2.47 x [tex]10^8[/tex] V.

Learn more about the electric charge at

https://brainly.com/question/30845773

#SPJ4

Answer:

32

Explanation:

Answer:

32

Explanation:

Sulfur has 16 protons and 16 neutrons. The atomic number is roughly 32. Therefore, 16 + 16 = 32 nucleons.  

Answer:

When the angle between two vectors A and B is 0 degrees, they are parallel to each other and pointing in the same direction. In this case, the resultant of the two vectors will be the sum of the magnitudes of A and B, and it will also be parallel to both A and B.

When the angle between two vectors A and B is 90 degrees, they are perpendicular to each other. In this case, the resultant of the two vectors will be the vector that connects the initial point of A to the terminal point of B (or vice versa). The magnitude of the resultant vector can be found using the Pythagorean theorem: |R| = sqrt(|A|^2 + |B|^2), where |A| and |B| represent the magnitudes of vectors A and B, respectively.

When the angle between two vectors A and B is 180 degrees, they are pointing in opposite directions. In this case, the resultant of the two vectors will be the difference between the magnitudes of A and B, and it will be in the direction of the larger vector. The magnitude of the resultant vector can be found by subtracting the magnitude of the smaller vector from the magnitude of the larger vector: |R| = |A| - |B| if |A| > |B| or |R| = |B| - |A| if |B| > |A|.

To determine the resultant of two vectors A and B, it is necessary to know the magnitudes of the vectors and the angle between them. In your question, you provided the angles between A and B (0 degrees, 90 degrees, and 180 degrees), but you did not specify the magnitudes of the vectors.

Without the magnitudes of vectors A and B, it is not possible to calculate the exact resultant. The resultant vector depends on both magnitude and direction, and without knowing the magnitudes, it is not possible to determine the resultant accurately.

If you provide the magnitudes of vectors A and B, I can help you calculate the resultant for each angle.

The change in potential energy of the spring system is 15.6 x 10³J.

Mass of the disc, m = 20 kg

Velocity of the disc, v = 3 m/s

Spring constant of the spring, k = 200 N/m

Angular displacement of the disc, x = 2 revolutions = 2 x 2π = 4π radians

The potential energy that is stored when an elastic object is stretched or compressed by an external force, such as the stretching of a spring, is known as elastic potential energy. It is equivalent to the effort required to extend the spring, which is dependent on both the length of the stretch and the spring constant k.

The expression for the elastic potential energy of the spring is given by,

PE = 1/2 kx²

PE = 1/2 x 200 x (4π)²

PE = 1.57 x 10⁴J

The kinetic energy of the disc is given by,

KE = 1/2 mv²

KE = 1/2 x 20 x 3²

KE = 90 J

Therefore, the change in potential energy is,

E = 1.57 x 10⁴- 90

E = 15.6 x 10³J

To learn more about potential energy, click:

https://brainly.com/question/29311518

#SPJ1