you are attempting to create a standing wave with n = 7 in a pipe .50m in length and filled with air. the top of the pipe is open to the ait and the bottom of the pipe is barely submerged in water and thus closed. draw the diagram for this standing wave with the proper nodes and antinodes for this open- closed pipe. what is the frequency?

A boat that transitions from salt to fresh water will float at a lower level in the water. due to the fact that fresh water is less buoyant than salt water. The boat will therefore flow less in fresh water.

The force that makes things float is known as buoyant force. It is the force applied to a solid object that is partially or completely submerged in a liquid. The pressure differences occurring on the opposing surfaces of an object submerged in a static fluid are what cause buoyancy. Additionally called the buoyant force. It is pretty inevitable that an object's bottom will always be deeper in a fluid than its top, which is why there is a buoyant force.

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Temperature rise will be there in cylinder B more than in cylinder A because of internal energy.

what is internal energy?

The sum of the kinetic and chemical potential energies of all the particles in the system is the internal energy. Particles accelerate and pick up kinetic energy when energy is applied to increase the temperature.

Briefing:

Cylinder A uses the heat it absorbs to both work while expanding and to increase internal energy (or temperature).

While cylinder B solely uses the heat it absorbs to increase its internal energy 

As a result, cylinder B's temperature rise is greater than cylinder A's.

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I drew the first picture myself, and the second one is the image

The greatest amount of time is going to be achieved when the volleyball is hit with its maximum velocity and that's his maximum vertical component.

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Answer:

magnetic force F = q

Explanation:

The projection of the mg on the inclined roof is mg*sin (36), which must be equal to the friction force of 390: When we solve for mass m using mg*sin (36) = 390, we obtain m=390/ (9.8*sin (36)) = 67.70 kg.

A body's mass is used to calculate how much matter it contains. m or M are used to indicate mass. Weight is a unit of measurement for the force that gravity's acceleration has on a mass. W typically stands for weight.

Given that Mass (m) = 1000 kg and Acceleration (a) = 5 m/s 2, what is Force (F)? We are aware that F = m a = 1000 k g 5 m / s 2 = 5000 k g m / s 2 Therefore, the needed force is equal to 5000 m/s2 or 5000 N.

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The femur, which is the thighbone, and the pelvis, which consists of the ilium, ischium, and pubis. The femoral head creates the ball of the hip joint, and the acetabulum creates the socket.

What tissues connect to the iliac crest?

Hip flexors, internal and external abdominal oblique muscles, erector spinae muscles, latissimus dorsi, transversus abdominis, and tensor fasciae latae are just a few of the significant abdominal and core muscles that are linked to the iliac crest.

What are the pelvis' four components?

The coccyx and sacrum make up the pelvic spine. The innominate bones are the pubic bone, ischial bone, and iliac bone that connect on either side.

Is the iliac crest the hip bone?

The largest of the three bones that make up the hip bone or bony pelvis, the ilium, has a conspicuous section called the iliac crest. A person will occasionally rest their hands on the curved section of the pelvis that creates the wing-like feature of the hip and lies close to the skin.

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E4 = kQ.[2/a2 + 1/a2] appears to reflect the electric field at the fourth corner as a result.

A characteristic of matter called an electric discharge generates multiple objects to either attract or repel each other depending on how it is charged (positive or negative). A region of space surrounding a static electricity particle or object known as an electrostatic potential is one in which an electricity would experience force.

A personality electromagnetic field like light also requires a grasp of the electric field idea. We now have a mechanism to explain how starlight traverses enormous stretches of vacant desert in order to reach our eyes thanks to the electric field notion.

Number of point charges = 3

E4 = E1 + E2 + E3

E4 = kQ/a2 + kQ/√(2a2) + kQ/a2

E4 = kQ.[ 1/a2 + 1/√(2a2) + 1/a2 ]

E4 = kQ.[ 2/a2 + 1/a√2 ]

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The amount of space a wave covers in a certain amount of time, such as the number of meters it covers in a second, is known as its speed of wave.

The formula Speed = Wavelength x Frequency relates wave speed to both wavelength and wave frequency. The formula wave speed = frequency x wavelength relates wave speed to wavelength, frequency, and period. The speed of light, or roughly 300,000 kilometers per second, is the absolute speed limit at which a wave can move according to Einstein's theory of special relativity. A change in the medium is truly necessary to modify the wave's speed since the wave's speed is a feature of the medium. The wave speed is constant if the medium does not alter during the wave's motion.

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The first law of thermodynamics, which states that you cannot produce or destroy matter or energy, is broken by this. Critics assert that the big bang theory implies the universe didn't exist before the big bang.

According to a theoretical hypothesis known as the Big Bang theory, the cosmos first existed in a state of extreme density and heat. The evolution of the observable universe from the earliest known times through its later large-scale form is explained by a variety of cosmological models of the Big Bang. These models provide a thorough justification for a wide variety of known phenomena, including the abundance of light elements, cosmic microwave background (CMB) radiation, and large-scale structure. Cosmic inflation, or the abrupt and extremely rapid expansion of space during the Universe's early moments, provides an explanation for the flatness problem, or the appearance of uniformity over the whole cosmos. The initial conditions of the Big Bang, however, are not currently well modeled by any commonly accepted quantum gravity theory.

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In other words, pH equals the negative log of the KW value given at 2.35 times 10 to the negative 14 -30H given at 4.75°C temprature. We also obtain 888.

The pH scale determines how acidic or basic water is. The range is 0 to 14, with 7 representing neutrality. Acidity is indicated by pH values below 7, whereas baseness is shown by pH values above 7. In reality, pH is a measurement of the proportion of free hydrogen and hydroxyl ions in water.

A solution's pH is a significant indicator of its chemical composition. The pH can affect how readily available nutrients are, how biological processes work, how bacteria behave, and how chemicals behave.

If Kw = [H⁺][OH⁻] = 2.5 x 10⁻¹⁴, then

log₁₀ [H⁺] + log₁₀ [OH⁻] = log₁₀ (2.5 x 10⁻¹⁴), or

-log₁₀ [H⁺] - log₁₀ [OH⁻] = -log₁₀ (2.5 x 10⁻¹⁴), which is

pH + pOH = -log₁₀ (2.5 x 10⁻¹⁴) = 13.60

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The freshwater reservoirs on earth are ranked by volume, with the one with the biggest volume at the top is-

1. ice caps; 2. groundwater; 3. lakes; 4. rivers.

The atmosphere, the earth's surface, and the earth's interior are the three main locations where water can be kept.

Thus, the freshwater reservoirs on earth are ranked by volume, with the one with the biggest volume at the top is-

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(a)Vt =r=(288)(0.32)=92.2m/s is a straightforward formula that may be used to calculate the dragster's linear speed at a distance of df = 384 m.

(b) We utilize the following two kinematic equations to determine the angular acceleration of the dragster's wheels during this time: delta theta = 1/2 at2 and wf = at.

Simply said, magnitude is "distance or amount." It shows the size or direction that an item travels in either an absolute or relative sense. It is a way of expressing something's size or scope.

Size is referred to as magnitude. A automobile is traveling more quickly than a bike, for instance, when it comes to speed. The extent of the car's speed in this situation.

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Self Inductance:

1.11 x 10^-7 H is the solenoid inductance

The characteristic of a current-carrying coil that opposes or resists a change in the current running through it is called self-inductance. This mostly happens because of the self-induced emf that the coil produces. In layman's words, we can also state that self-inductance is a phenomenon where a voltage is induced in a wire that carries current.

Given;

The spring's dimensions are

length L=  5 cm (0.05 m),

diameter = d 0.15 cm

radius = r = 0.075 cm (0.00075 m).

There are 50 coils in the spring.

N = 50;

The spring's area is determined using the formulas below;

A = π [tex]r^{2}[/tex]

A = 3.14 × (0.00075)^2

A = [tex]1.77[/tex] × [tex]10^-6[/tex] [tex]m^2[/tex]

The inductance of a solenoid is;

L = [tex]\frac{N^2 A}{l}[/tex]

L = [tex]1.11[/tex]×[tex]10^-7[/tex] H

1.11 x 10^-7 H is the solenoid inductance that needs to be accounted for in the model.

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If all these resistors were light bulbs, 22Ω resistor is greatest, it would be the brightest bulb.

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The centripetal acceleration of the runner is 1.44m/sec²  if he is moving at a speed of 7.20m/sec while bending a radius of 36m.

Centripetal acceleration increase is characterized as the property of the movement of an item, crossing a roundabout way. Any item that is moving all around and has a speed increase vector pointed towards the focal point of that circle is known as Centripetal speed increase.

You probably seen different instances of centripetal speed increase in your regular daily existence. In the event that you drive a vehicle around a circle, your vehicle is going through centripetal speed increase and a satellite circling the earth likewise follows a centripetal speed increase. Centripetal means towards the middle.

Centripetal acceleration increase can be estimated in meters each second as it is the quantity of meters each second by which your speed changes consistently. At the point when an item is moving in a round movement, it very well may be estimated by utilizing the accompanying condition

[tex]a_c[/tex]=(v²)/r

Where,

[tex]a_c[/tex]   is the centripetal acceleration increase in m/sec²

v is the speed in m/sec

r is the sweep in m.

So, we have v=7.20m/sec, r=36m.

So,[tex]a_c[/tex]=(7.20)²/36

=>[tex]a_c[/tex]=(51.84)/36

=>[tex]a_c[/tex]=1.44m/sec²

Hence, centripetal acceleration is 1.44m/sec².

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Answer: Attached JPG

Explanation:

FBD shows the forces acting on an object. If you where given no values (mass, acceleration, μ, etc...) then simply label the various vectors. Vectors show direction and magnitude as in how big the force is.

If you where given the mass you can find the weight and normal force (not inclined plane) by multiplying mass times gravity. Fg=Fn because its not moving in the y dimension (up and down).

If given acceleration and told no friction then the force applied would be mass times acceleration.

If given friction force you have to set up the equation m*a=Fa-Ff and then plug in variables.

It gets more complicated when you are given μ. To find these force then you have to set up the equation Ff=μFn. Plug in variables to find Ff, then set up previously listed equation.

Hope this helps

Minimizing static friction coefficient to prevent slipping if the turntable had experienced radius of gyration continuous angular acceleration when it was at rest.

In general, the radius of gyration is the distance from a body's center of mass at which the entire mass could be concentrated without changing the body's moment of rotational inertia about the axis through the center of mass.

Equation for Radius of Gyration

The following is the formula for moment inertia in terms of gyroscope radius: I is the moment of inertia and m is the body's mass, and I = mk2 (1). The radius of gyration is given as follows as a result. k = I m ( 2 ) ( 2 ).

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The speed of the bullet is determined as 800 m/s.

The speed of the bullet is calculated by applying Newton's second law of motion as shown below.

F = ma

where;

The acceleration of the bullet is calculated as follows;

a = F / m

a = ( 4000 N ) /  ( 0.05 kg )

a = 80,000 m/s²

The speed of the bullet is calculated as follows;

v = at

where;

v = 80,000 m/s²   x   0.01 s

v = 800 m/s

Thus, the speed of the bullet at the given acceleration and time of motion is determined by applying first kinematic equation as shown above. The speed of the bullet measures the rate of change of distance of the bullet with time.

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The ratio of the newly allowed intensity to the previously allowed intensity is 3.1623 x 10⁻³.

Banks says a leaf blower makes 64 to 78 decibels at 50 feet. To the operator's ear, the noise is 95-115 decibels. According to Dangerous Decibels, a public-private partnership aimed at reducing hearing loss, typical speech is around 60 decibels, washing machines 75 decibels, and chainsaws 115 decibels.

Performance that fits your needs. Setting the motor to a low speed makes less noise. According to the American Green Zone Alliance, an organization dedicated to zero-emission landscaping, the average fan produces about 65 dB of noise. Compare this to the average noise level of a traditional gas backpack blower.

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The surface area of the filament is  4.66*10⁻⁴ m².

P = e*σ*A*T⁴

where,

P = radiating energy at a rate

e=  emissivity

σ = Stefan's Constant (5.67 *10⁻8 W/m².K⁴)

A= Surface Area

T = Temperature of the glowing filament (absolute temperature °K)

P = 60 w.

T  = 1500°C+ 273°K

   =1773°K

e= 0.23.

substituting into the equation:

P = e*σ*A*T⁴

60 w = 0.23. * 5.67 *10⁻8 W/m².K⁴ * A * (1773°K)⁴

Making A subject of the formula we have:

A =                  60 w                          

      0.23. * 5.67 *10⁻8 W/m².K⁴ * (1773°K)⁴

A =                             60 w                          

      0.23. * 5.67 *10⁻8 W/m².K⁴ * (9.88*10¹² °K)

A = 4.66 *10⁻⁴ m²

Hence, the surface area is   4.66 *10⁻⁴ m².

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The separation between the fifth maximum and seventh minimum from the central maximum is 2.457mm

Seperation between 5th and 7th minima

=2X(wavelength)x(Distance of screen) / (slit seperation)

=(2x 585x10^-9 x21x10^-2 )/ 0.1x10^-3 =2.457mm

The double-slit experiment shows that light and matter can exhibit properties of both classically defined waves and particles. Furthermore, it demonstrates the fundamental stochastic nature of quantum mechanical phenomena. This kind of experiment was first performed by Thomas Young in 1802 to demonstrate the wave behavior of visible light [1]. At the time, light was thought to consist of waves or particles. With the advent of modern physics about 100 years later, it was recognized that light can indeed exhibit behavior characteristic of both waves and particles. We have demonstrated that it exhibits the same behavior as extended to molecules . Thomas Young's light experiments were part of classical physics long before the concept of quantum mechanics and wave-particle duality was developed. He believes that this proves that the wave theory of light is correct, and his experiment is sometimes called Young's experiment  or Young's slit.

This experiment belongs to the general class of "double-path" experiments, in which a wave is split into two separate waves (a wave usually consists of many photons and is better known as a wavefront). .The wave properties of a single photon ), which later combine into a single wave. Changes in the path length of both waves lead to phase shifts that create interference patterns. Another version is a Mach-Zehnder interferometer that splits the beam with a beam splitter.

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The effect that this will have on the amplitude of your oscillation.is b.) The amplitude of oscillation will decrease.

The amplitude of an oscillating system is the magnitude of change in the oscillating variable with each oscillation. Sound waves in air, for example, are oscillations in atmospheric pressure, and their amplitudes are proportional to the pressure change during one oscillation.

When a wave travels through a medium, it loses energy as it moves. As the distance between the wave and its source grows, it spreads out over a larger and larger area. As the wave spreads through the medium, it loses energy and its amplitude decreases.

In this case, at the point of equilibrium, the cart and the skater will have maximum kinetic energy. By dropping the same bag, the energy is reduced. The amplitude of an oscillating pendulum decreases with time because of friction due to air

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On a whim, you are trying to stand in a cart attached to a strong spring. The spring is compressed and then released, and you oscillate back and forth, trying to maintain your balance. There is a sand bag in the cart.

At the instant you pass through the equilibrium (x=0) location of the spring, you drop the sandbag onto the ground, out of the cart.

Question: If you drop the sand bag out of the cart right at the equibrium location, what effect will that have on the amplitude of your oscillation? (choose correct choice):

a.) The amplitude of oscillation will increase.

b.) The amplitude of oscillation will decrease.

c.) There will be no effect on the amplitude.

Wavelengths are 310 nm , 827 nm , 496nm

Wavelength is the distance between identical points (adjacent crests) in the adjacent cycles of a waveform signal carried in space or over a wire.

According to the given information

E = hc/wavelength [tex]10^{-19}[/tex]

a) n=3  to n=1

E = 4.0 - 0.0 = 4.0 eV = 4×1.602 × [tex]10^{-19}[/tex]= 6.40×[tex]10^{-19}[/tex] J

  = wavelength = 19.86×[tex]10^{-26}[/tex]/(6.40×[tex]10^{-19}[/tex]) = 3.10×[tex]10^{-7}[/tex]  = 310 nm

b) n=2  to n=1

E = 1.5 - 0 = 1.5 eV = 1.5×1.602× [tex]10^{-19}[/tex] = 2.40×[tex]10^{-19}[/tex] J

  = wavelength = 19.86×[tex]10^{-26}[/tex]/(2.40×[tex]10^{-19}[/tex])  = 8.27×[tex]10^{-7}[/tex]= 827 nm

c) n=3 to n=2

E = 4.0  - 1.5 = 2.5 eV = 2.5×1.602×[tex]10^{-19}[/tex] = 4×[tex]10^{-19}[/tex] J

  = wavelength = 19.86×[tex]10^{-26}[/tex](4×[tex]10^{-19}[/tex]) = 4.96×[tex]10^{-7}[/tex] = 496nm

Wavelengths are 310 nm , 827 nm , 496nm

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The net reaction of force on each of fore wheels = 113.5 N

In physics, a force is an effect that can modify the velocity of an object. A mass-containing object can alter its velocity, or as a result of a force, accelerate. One way to think of force is as a push or pull. Due to the fact that it has both a magnitude and a direction, a force is a vector quantity.

According to the given information

Calculate the mass of tractor.

[tex]m_1 & =\frac{2100 \mathrm{lb}}{32.2 \mathrm{ft} / \mathrm{s}^2} \\[/tex]

     [tex]& =65.217 \mathrm{lb} \cdot \mathrm{s}^2 / \mathrm{ft}[/tex]

Calculate the mass of gravel.

[tex]m_2 & =\frac{900 \mathrm{lb}}{32.2 \mathrm{ft} / \mathrm{s}^2} \\[/tex]

     [tex]& =27.950 \mathrm{lb} \cdot \mathrm{s}^2 / \mathrm{ft}[/tex]

[tex]& \sum F_x=m a_x \\[/tex]

[tex]& 2 F=\left(m_1+m_2\right) a \\& F=\frac{1}{2}\left(m_1+m_2\right) a \\[/tex]

& F = [tex]\frac{1}{2}\left(65.217 \mathrm{lb} \cdot \mathrm{s}^2 / \mathrm{ft}+27.950 \mathrm{lb} \cdot \mathrm{s}^2 / \mathrm{ft}\right)\left(2 \mathrm{ft} / \mathrm{s}^2\right) \\& \quad[/tex]=93.167[tex]\mathrm{lb} \\[/tex]

[tex]& \sum F_y=0 \\[/tex]

[tex]& 2 N_A+2 N_B-2100-900=0 \\[/tex]

[tex]& N_A+N_B=1500 \mathrm{lb} \\[/tex]

Consider the algebraic sum of moments about A treating counter-clockwise moments to be positive

[tex]& \sum M_A=I_G a+\sum m a(d) \\[/tex]

[tex]& -2100(20)+2 N_B(60)-900(110)=0-m_1 a(20)-m_2 a(40) \\[/tex]

[tex]& -2100(20)+2 N_B(60)-900(110)=0-(65.217)(2)(20)-(27.950)(2)(40) \\[/tex]

[tex]& 120 N_B-141000=-4844.7 \\[/tex]

[tex]& N_B=1134.6 \mathrm{lb}[/tex]

Substitute [tex]$1134.6 \mathrm{lb}$[/tex] for[tex]$N_B$[/tex] in equation (1).

[tex]& N_A+1134.6=1500 \mathrm{lb} \\[/tex]

[tex]& N_A=365.4 \mathrm{lb}[/tex]

Calculate the net reaction on each of the rear wheels.

[tex]F_R & =\sqrt{N_A^2+F^2} \\[/tex]

     [tex]& =\sqrt{(365.4)^2+(96.138)^2} \\[/tex]

     [tex]& =377.83 \mathrm{lb}[/tex]

Calculate the angle made by the resultant reaction force with the horizontal at the rear wheels.

[tex]\theta & =\tan ^{-1}\left(\frac{365.4}{93.168}\right) \\[/tex]

  [tex]& =75.7^{\circ}[/tex]

Calculate the net reaction on each of the for wheels.

[tex]& F_B=N_B \\& F_B=1135 \mathrm{lb}[/tex]

The net reaction of force on each of fore wheels = 113.5 N

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The highlighted artery has two terminal branches are Basilic vein.

The basilic vein travels from the palm of your hand up your arm, passing by the side of your pinky and ulna (a long bone that runs from your elbow to your finger). Due to its proximity to the skin's surface, the basilic vein is regarded as superficial. The inner arm frequently exhibits it. The dorsal venous network's ulnar region is where the basilic vein first appears. The vena mediana cubiti connects to it at the anterior surface just below the elbow as it ascends the basilic vein of the forearm, which goes up the posterior surface of the ulnar side of the forearm.

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His apparent weight will be the greatest when the elevator accelerating upward.

acceleration is the rate of to the  change of the velocity of an object with respect by  time.

When a person stand in an elevator moving upwards, he feels heavier because the elevator's floor presses harder on his feet, and the scale will show a higher reading than when the elevator is at rest.

According to Newton's second law

R = mg + ma

where;

R is the reading of the scale = apparent weight of the person

mg is the normal weight of the person

ma is the upward force acting on the person

Therefore, his apparent weight will be the greatest when the elevator is accelerating upward

(c) is accelerating upward

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The reason why Saturn's rings appear bright is because sunlight reflects off the ring material.

Because the ice particles in Saturn's rings scatter and reflect sunlight, the rings appear dazzling. Astronomers have long known that when Earth is directly between Saturn and the sun, Saturn's rings reflect sunlight with the greatest intensity. When light reflects off flat, polished surfaces (like a mirror or a pond) in a specific direction, it might appear exceptionally bright. The rings' actual nature becomes clear upon closer inspection. A mix of factors, such as gravity and collisions between the ring particles themselves, account for the rings' appearance of uniformity. Although the planets appear to be perfectly spherical, their spin causes them all to slightly bulge around the equator. The Saturnian ring system is the largest ring system in the Solar System. They are made up of innumerable tiny particles that orbit Saturn and range in size from micrometres to meters. With the exception of a small amount of stony material, the ring particles are virtually exclusively comprised of water ice.

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The acceleration due to gravity at a distance r = 2RM from the center of Mars will be 0.933 m/s².

What is acceleration?

In mechanics, acceleration is the rate of change of an object's velocity with respect to time. Acceleration is a vector quantity (as long as it has magnitude and direction). The direction of an object's acceleration is given by the direction of the net force acting on that object. As described by Newton's second law, the magnitude of an object's acceleration is the combined effect of two causes. ) The mass of this object is inversely proportional to the mass of the object, depending on the material the object was made from.

The SI unit of acceleration is meters per second square.

Therefore, The acceleration due to gravity at a distance r = 2RM from the center of Mars will be 0.933 m/s².

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The area of Surface = [tex]{ }^3 k \pi\left[\frac{\ln (1+\sqrt{2})+\sqrt{2}}{x}\right]=3 \pi[\ln (\sqrt{2}+1)+\sqrt{2}] \\[/tex]

A vector equation is a linear combination of vectors with possibly unknown coefficients.

Vectors are defined as quantities that have both magnitude and direction. Examples include weight, acceleration, force, displacement, and velocity. Scalar quantities are those that merely have magnitude and no direction.

According to the given information

r(u, v) =[tex]\langle u \cos v, u \sin v[/tex], [tex]v\rangle \quad 0 \leqslant u \leqslant 1[/tex]

[tex]0 \leqslant v \leqslant 6 \pi \\[/tex]

[tex]& \gamma_u=\langle\cos v, \sin v, 0\rangle \\[/tex]

[tex]& r_v=\langle-u \sin v, u \cos v, 1\rangle \\[/tex]

[tex]& r_u \times r_v[/tex] = [tex]\left|\begin{array}{ccc}\hat{i}_i & \hat{j} & \hat{k} \\\cos v & \sin v & 0 \\-u \sin v & u \cos v & 1\end{array}\right| \\[/tex]

= [tex]\hat{\imath}[\sin v-0]-\hat{\jmath}[\cos v]+\hat{k}\left[u \cos ^2 v+u \sin ^2 v\right] \\[/tex]

[tex]& =\langle\sin v,-\cos v, u\rangle \\& \left\|\gamma_u \times \gamma_v\right\|=\sqrt{\sin ^2 v+\cos ^2 v+u^2}=\sqrt{1+u^2} \\[/tex]

[tex]& A_{r e}=\iint\left\|r_u \times r_v\right\| d A \\& =\int_0^1 \int_0^{6 \pi} \sqrt{1+u^2} d v d u \quad=\int_0^1 \sqrt{1+u^2} d u[v]_0^{6 \pi} \\& =6 \pi \int_0^1 \sqrt{1+u^2} d u=\frac{6 \pi}{2^2}\left[\frac{1}{2}\left(x \sqrt{1+u^2}+\ln \left(\sqrt{1+u^2}+1\right)\right]_0^1\right. \\& ={ }^3 k \pi\left[\frac{\ln (1+\sqrt{2})+\sqrt{2}}{x}\right]=3 \pi[\ln (\sqrt{2}+1)+\sqrt{2}] \\[/tex]

So

The area of Surface = [tex]{ }^3 k \pi\left[\frac{\ln (1+\sqrt{2})+\sqrt{2}}{x}\right]=3 \pi[\ln (\sqrt{2}+1)+\sqrt{2}] \\[/tex]

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