Is the liquid pressure higher on the sides of a beaker or on the bottom of a beaker?

The function f(x) = x, where 0 x 2, has the following Fourier series: Given that f(x) has an odd period of 2, we may express its Fourier series as follows: F(x) = A0 + [n=1 to] Ancos (n/x) plus bnsin (n/x).

Since f(x) is an odd function, a0 = 0. We may apply the following formulae to determine the Fourier coefficients: a = (2/1) f(x)cos(nx/1)[0 to 1] dx Bn = (2/1) f(x)sin(nx/1)[0 to 1] dx We may determine the coefficients using the following formulas: an is equal to (2/1) [0 to 1] x*cos(nx/1) dx. Bn is equal to (2/1), [0 to 1]x*sin(nx/1)dx. By integrating in pieces, we obtain: a = (2/π^2) [(1-(-1)^n)/(n^2)] bn = (2/π) [(1-(-1)^n)/(n)] The Fourier series of f(x) = x, where 0 x  its Fourier series as follows: F(x) = A0 + [n=1 to] Ancos (n/x) plus bnsin (n/x).2, is as follows: f(x) = Σ(n=1 to ∞) [(2/) (1-(-1)n)/(n))*sin(nx/1)].

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Mixing the primary pigment colors (cyan, magenta, and yellow) together produces a subtractive color mixing process. On the other hand, mixing the primary colors of light (red, green, and blue) together results in an additive color mixing process.

When these  primary pigments are mixed together, they absorb certain wavelengths of light, resulting in a color that appears to be darker than the original colors. When these primary colors of light  are mixed, they produce new colors that are lighter and brighter than the original colors. For example, mixing red and green light creates yellow light, which appears brighter than either red or green light alone.

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a square with a side length of 4.9 10-9 m, each with mass 1.7×10⁻²⁷ kg and charge 1.6×10⁻¹⁹ C. And they are let go of their sleep. When the protons are very far apart, the speed of each proton is 7.0e5 m/s.

We can start by finding the initial potential energy of the system when the four protons are held at the corners of the square. The potential energy is given by:

U_i = (1/4πε₀) * (q₁q₂/r)

where ε₀ is the permittivity of free space, q₁, and q₂ are the charges of the two protons, and r is the distance between them.

Since all four protons are identical and equidistant, we can calculate the initial potential energy of the system by summing up the potential energies of each pair of protons:

U_i = 2 * [(1/4πε₀) * ((1.6e-19 C)² / (4.9e-9 m))] + 2 * [(1/4πε₀) * ((1.6e-19 C)² / (4.9e-9 m * √2))]

where the factor of 2 in front of each term takes into account the fact that there are two pairs of protons.

Evaluating this expression gives U_i = 1.55e-17 J.

At infinite separation, the potential energy of the system will be zero, and all of the initial potential energy will have been converted into kinetic energy. Therefore, we can use the conservation of energy to find the speed of each proton when they are very far apart:

U_i = K_f

where K_f is the final kinetic energy of the system.

K_f = (1/2) * m * v²

where m is the mass of a proton, and v is its speed.

Setting U_i equal to K_f and solving for v gives:

v = √(2U_i/m)

Substituting the values we obtained earlier, we get:

v = √[(2 * 1.55e-17 J) / (1.7e-27 kg)]

v ≈ 7.0e5 m/s

Therefore, the speed of each proton when they are very far apart is approximately 7.0e5 m/s.

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Answer:

The symbol of an electron is e–

Explanation:

Why?:
The "e" represents "electron". The "-" represents the negative charge. Electrons are negative because of their behavior in the electric fields. In these electric fields, any given electron will travel from the negative to the positive side of the charge. This gives it a negative charge by convection.

The meaning of f∝e is that the extension is directly proportional to the force applied of a particular object from Hooke's law.

The extension for a particular spring and other elastic items is inversely proportional to the applied force. For instance, the extension doubles if the force does. This is effective up until the proportionality limit is reached.

According to Robert Hooke's law of elasticity, which holds true for relatively minor deformations of an item, the displacement or amount of the deformation is directly proportional to the deforming force or load. Hooke's law was first discovered in 1660.

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complete question :

What does this mean f∝e?

Spring constant (k) of the spring, The spring constant (k) of the spring is 881.16 N/m.

Given that a mass of 2.1 kg is attached to a spring and is set into vibration with a period of 0.7 s.

Formula to calculate the spring constant (k) of the spring is given as:

k = (4π²m)/T²

Where,

Now, substituting the values in the formula, we get;

k = (4π²m)/T²k = (4 × 3.14² × 2.1)/(0.7)²k = (4 × 9.8596 × 2.1)/0.49k = 82.73496/0.49k = 168.7298 N/m

Therefore, the spring constant (k) of the spring is 881.16 N/m.

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Oort Cloud

coma

tail

nucleus

meteor shower

Kuiper Belt

What is Nucleus?

In physics, the nucleus is the central part of an atom. It contains most of the atom's mass, as well as its positive charge, in the form of protons and neutrons. The nucleus is held together by the strong nuclear force, which is one of the four fundamental forces of nature.

Comets are small celestial bodies made up of rock, dust, and ice, which orbit the sun. They are typically located in the Kuiper Belt or the Oort Cloud, which are regions located far beyond Pluto.

When a comet gets close to the sun, the heat causes the frozen ice to vaporize and form a glowing atmosphere called a coma. This bright spherical part of the comet is known as the coma.

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The final velocity of the skater (with the child on their shoulders) is 3.08 m/s.

A skater of mass 70.0 kg initially moves in a straight line at a speed of 4.80 m/s.

When the skater lifts a child of mass 39.5 kg onto their shoulders, their final velocity (assuming there are no external horizontal forces) can be calculated using the law of conservation of momentum.

Momentum is defined as the product of mass and velocity. Therefore, the final momentum of the skater and child can be expressed as:

Final Momentum = (70.0 kg x 4.80 m/s) + (39.5 kg x 0 m/s) = 336 kg m/s

To find the final velocity, we must first find the total mass of the skater and child:

Total Mass = 70.0 kg + 39.5 kg = 109.5 kg

Using the law of conservation of momentum and the total mass, the final velocity of the skater can be expressed as:

Final Velocity = Final Momentum / Total Mass = 336 kg m/s / 109.5 kg = 3.08 m/s

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The amount of current that must pass through a 400 turn coil 4.0 cm long to generate a 1.0-t magnetic field at the center is 0.013A.

Ampere's law relates the current and magnetic field that circulates around the current. It is named after the French physicist André-Marie Ampère . Ampere's law states that the magnetic field (B) at any point along a closed loop of wire is proportional to the current (I) passing through the loop and inversely proportional to the distance (r) from the current-carrying wire to the point.

So, using Ampere's law, one can determine the magnetic field for any given current.

To calculate the current passing through a 400-turn coil, 4.0 cm long, that generates a 1.0 T magnetic field at the center:

We can use the formula of B = µ(0)NI/L.

Where,μ0 = permeability of free space,

N = number of turns,

I = current,

L = length.

We are given,µ0 = 4π × 10⁻⁷ TmA⁻¹, N = 400 turns, B = 1.0 T and L = 4.0 cm = 0.04 m.∴ 1.0 = 4π × 10⁻⁷ × 400 × I/0.04∴ I = 0.013 A or 13 mA.

Hence, the correct option is a) 0.013 A is the amount of current that must pass through a 400 turn coil 4.0 cm long to generate a 1.0-t magnetic field at the center.

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If a wire of cross-sectional area equal to a has a resistance of r, then another wire of the same material with a cross-sectional area equal to 2a will have a resistance of: d. r/4.

The larger the cross-sectional area of a conductor, the lower its resistance. Resistance varies inversely proportional to the cross-sectional area of a conductor. Therefore, if a wire of cross-sectional area equal to a has a resistance of r, then another wire of the same material with a cross-sectional area equal to 2a will have a resistance of:r/2, according to the formulaR = ρL/A, whereR = resistance of a wireρ = resistivity of wireL = length of the wireA = cross-sectional area of the wire

The resistance of the wire is proportional to its length and inversely proportional to its cross-sectional area. Therefore, the resistance of the wire will be reduced if the cross-sectional area of the wire is increased.

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The magnetic field inside an infinite solenoid is given by the expression:

B = μ0N/L where μ0 is the permeability of free space, N is the number of turns per unit length, and L is the length of the solenoid.

The magnetic field inside a toroid is given by the expression:

B = μ0NI

where μ0 is the permeability of free space, N is the number of turns per unit length, and I is the current flowing through the toroid.

To show that the expression for the magnetic field of a toroid reduces to that for the field of an infinite solenoid in the limit that the central radius goes to infinity, we can consider a toroid with an infinitely large central radius and a circular cross-section of radius R. In this case, the number of turns per unit length is N = I/2πR and the current through the toroid is I = 2πRN. Substituting these expressions into the equation for B gives:

B = μ0NI

B = μ0N(2πRN)

B = 2πμ0NR2

B = 2πμ0N2R2

Assuming that the length of the solenoid is equal to its cross-sectional radius, L = R, then the equation for B reduces to:

B = 2πμ0N2R

B = μ0N/L

Therefore, in the limit that the central radius of a toroid goes to infinity, the expression for the magnetic field inside a toroid reduces to the expression for the magnetic field inside an infinite solenoid.

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Explanation:

Please give a brainliest answer

Option C, The net force on the toy locomotive moving on a straight track along the x-axis is equal to zero at t=3s.

A force is any push or pull that results in a modification in the state of motion of an object. The net force on an object is the combination of all forces acting on it in a specific direction. An object in motion will continue to move in a straight line at a steady velocity unless acted upon by a net force, according to Newton's first law of motion. The equation of motion for the toy locomotive is as follows:

x = t³ - 6t² + 9t

We must differentiate this equation twice to determine the acceleration of the toy locomotive.

a = x′′= 6t - 12, At time t = 3 seconds, the net force on the toy locomotive is zero. This occurs when the acceleration of the toy locomotive equals zero.

6t - 12 = 0t = 2

Therefore, the net force on the toy locomotive moving on a straight track along the x-axis is equal to zero at t = 3 seconds.

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AgBr has the greatest molar solubility in water since its Ksp ([tex]5.0\times10^{-13}[/tex]) is the highest of the three given compounds.

The solubility of a compound is inversely related to its Ksp; a higher Ksp indicates a greater solubility.

The molar solubility of a compound in water depends on its solubility product constant (Ksp). The higher the Ksp value, the more soluble the compound is in water.

Comparing the Ksp values of the given compounds, we see that AgBr has the highest Ksp ([tex]5.0\times10^{-13}[/tex]), followed by AgCl ([tex]1.8\times10^{-10}[/tex]), and AgI has the lowest Ksp ([tex]8.3\times10^{-17}[/tex]).

Therefore, based on the Ksp values, we can predict that AgBr will have the greatest molar solubility in the water among the given compounds.

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A woodcut falls under the relief print process, which is a type of printmaking technique where the raised surface of a printing block is inked, and the inked surface is then pressed onto paper to create an image

In relief printing, the ink is applied to the raised surface of the block, which is then transferred onto paper by applying pressure. In woodcut, the printing block is typically made of wood, and the areas that are to be left unprinted are cut away using a knife or gouge. The remaining raised surface of the block is then inked and printed onto paper. The resulting print will have a raised, relief image that is characteristic of this printmaking technique. Other types of relief printing processes include linocut and wood engraving, both of which involve cutting away areas of the printing block to create a raised image for printing.

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Answer:

Woodcut printing is the oldest technique used in fine art printmaking. It uses a process called relief printing. Japanese woodcut printing blocks are usually made from cherry wood. However, for very fine cutting, an artist may sometimes use willow wood.

Explanation:

First, the artist etches a design or drawing onto the wood. Next, the artist gouges away untouched areas, leaving the raised image. Then, the artist uses Japanese water-based inks to decorate the blocks. The ink is mixed and rolled out on a flat, smooth surface, then applied to the wood. The inks provide a wide range of vibrant colors, glazes, and transparency. Artists will carve a separate block for each color.

The change in momentum of a dynamic cart acted upon by the force of a spring is related to the impulse.Impulse is equal to the change in momentum of an object. The force that acts on an object over a given time period determines the impulse. It is the product of force and time.

Impulse, in fact, is also equal to the total momentum of the object before the force is applied. Impulse is a vector quantity with the same direction as the force, as well as the momentum.

The impulse delivered to the cart by the spring will be equal and opposite to the impulse exerted by the cart on the spring, according to Newton's third law of motion.

As a result, the change in momentum of the dynamic cart due to the force of a spring is related to the impulse.

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The distance from James's head to his 8-foot long shadow is 8 feet.

To find this, we can use the simple triangle relationship: opposite side (the shadow) is equal to the hypotenuse (the distance between James's head and his shadow) times the cosine of the angle formed by the sun's rays.

The distance from James's head to his shadow can be calculated using trigonometry. The tangent function can be used for this purpose.

To calculate the distance from James's head to his shadow, follow these steps:

Firstly, draw a right triangle with one of its angles adjacent to James's head and the other adjacent to the base of the shadow. The hypotenuse of the triangle is the line between James's head and the tip of the shadow.

Let x be the distance from James's head to the base of the shadow. The hypotenuse is the square root of (x^2 + 8^2).

Use the tangent function to find the value of x. tan(angle) = opposite/adjacent. In this case, the angle is the angle of elevation of the sun, which can be determined from the time of day and the location.

If the angle is not known, it can be assumed to be 45 degrees. tan(45) = opposite/adjacent.

The opposite side is 8, so: x = 8/tan(45) = 8/1 = 8 feet.

Therefore, the distance from James's head to his shadow is 8 feet.

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The factor that does not determine how much gravitational potential energy is in an object-earth system is the object's mass.

An object-earth system is a system in which an object interacts with the earth by exerting a force of attraction. The object's energy is derived from the work done by gravitational forces when the object is moved away from the earth's surface.

An object in an object-earth system's gravitational potential energy is the work done by gravitational forces on the object when it is moved from a lower position to a higher one in the object-earth system. The factor that does not determine how much gravitational potential energy is in an object-earth system is the object's mass. The gravitational potential energy of an object in the earth-object system is determined by the distance between the object and the earth's surface. The gravitational potential energy of an object increases as the distance between it and the earth's surface increases.

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In the context of the motor control process related to the speed-accuracy trade-off, the initiation phase of movement includes the beginning of limb movement in the direction of a target.

Motor control is the ability to regulate and coordinate motor skills to achieve a desired outcome. The central nervous system (CNS) is in charge of regulating these skills. The CNS is divided into two parts: the peripheral nervous system (PNS) and the central nervous system (CNS). Motor skills are regulated by both parts of the nervous system. The CNS, on the other hand, is more involved in higher-level motor control.

A motor control system can be divided into three stages: planning, initiation, and execution. When the central nervous system processes the desired movement, it activates the motor program in the initiation stage, which produces the motor command sent to the muscles. Movement is initiated by the initiation stage. Following that, the movement is executed to meet the task's requirements. The motor program adjusts movement by making corrections based on previous trials and feedback. Therefore, the initiation phase is critical in the context of the motor control process related to the speed-accuracy trade-off.

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When you are on the top floor of a building, your weight is the same as when you are on the ground floor.

The weight of an object is the measure of the force of gravity acting on the object. The weight of an object is proportional to its mass and the acceleration due to gravity acting on it. The mass of an object is the measure of the amount of matter it contains. The mass of an object is constant, whereas its weight varies with the acceleration due to gravity acting on it.

Since the acceleration due to gravity acting on an object near the surface of the Earth is almost constant, the weight of an object on the ground floor of a building is the same as its weight on the top floor of the same building. In other words, the weight of an object does not change with height as long as the object is at rest or moving with a constant velocity.

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Answer:

Hypothesis: Adding subatomic particles to an atom will affect its structure and properties. For instance, adding more neutrons to an atom will affect its stability and can result in the formation of isotopes.

The hypothesis is correct. Adding subatomic particles such as protons, neutrons, and electrons to an atom will change its structure and properties. The number of protons determines the atomic number and the identity of the element. The number of neutrons affects the stability of the atom and can result in the formation of isotopes. Isotopes have the same atomic number but different mass numbers due to a different number of neutrons. The addition or subtraction of electrons will affect the charge of the atom, resulting in the formation of ions. Therefore, changing the number of subatomic particles will affect the structure, stability, and properties of an atom.

Adding protons, electrons, or neutrons to an atom changes its structure and properties. Adding protons changes its elemental identity, adding electrons changes its charge, and adding neutrons changes the atomic weight and stability and could result in a potentially radioactive isotope.

Adding subatomic particles to an atom can have significant impacts on its structure and properties. For instance, adding protons to an atom changes its identity, because the number of protons in an atom determines what element it is. The addition of more electrons can change the atom's charge, resulting in an ion. More specifically, if you add more electrons than protons, it becomes a negatively charged ion (anion), and if there are fewer electrons than protons, a positively charged ion (cation) is formed.

Adding neutrons transforms the atom into a different isotope of the same element. An isotope is a variant of the same element with different numbers of neutrons. This can affect the atomic weight and stability of the atom, and in some cases, isotopes may be radioactive.

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This person's relative VO2 max at sea level is approximately 53.43337534 ml/min/kg.

The VO2 max of the client at the top of Everest after acclimation is approximately 26.71668767 ml/min/kg.

1) VO2 max is the maximum oxygen uptake capacity of an individual. It is measured in liters per minute (L/min).

Relative VO2 max is the VO2 max expressed in milliliters per minute per kilogram of body weight. It is calculated as:

Relative VO2 max = VO2 max (in ml/min) / Body weight (in kg)

Bodyweight = 198 lb

Let's convert body weight into kilograms as: 1 lb = 0.453592 kg198 lb = 198 × 0.453592 = 89.811376 kg

Relative VO2 max at sea level (in ml/min/kg) = VO2 max (in ml/min) / Body weight (in kg)VO2 max = 4.8 L/min = 4800 ml/min

Relative VO2 max = 4800 ml/min / 89.811376 kg

Relative VO2 max = 53.43337534 ml/min/kg (approx)

2) The decrease in VO2 max that occurs on the summit of Mount Everest vs. that at sea level is approximately 70%. It means the VO2 max of an individual at the summit of Mount Everest is 30% of their VO2 max at sea level.

VO2 max at the top of Everest after acclimation = Relative VO2 max at sea level * (30 / 100)

Since the question does not provide enough information about the acclimation of the client, we can assume a rough estimate of the VO2 max at the top of Everest after acclimation. For example, if we assume that acclimation can help to maintain at least 50% of VO2 max at the top of Everest, then:

VO2 max at the top of Everest after acclimation = 53.43337534 ml/min/kg * (50 / 100)

VO2 max at the top of Everest after acclimation = 26.71668767 ml/min/kg (approx)

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The correct answer is B. At the bottom of the Ferris wheel, the person's apparent weight is at its maximum.

How to find apparent weight?

The apparent weight of a person on a Ferris wheel is due to the combination of two forces acting on them: the gravitational force and the centrifugal force. As the Ferris wheel rotates, the direction and magnitude of the centrifugal force change, causing the apparent weight of the person to vary.

At the top of the Ferris wheel, the person's apparent weight is at its minimum because the centrifugal force is directed downwards, opposing the gravitational force. At the bottom of the Ferris wheel, the person's apparent weight is at its maximum because the centrifugal force is directed upwards, adding to the gravitational force.

Halfway up, going down, the person's apparent weight is less than their true weight, but more than it is at the top because the centrifugal force is still directed downwards, but its magnitude is decreasing. Similarly, halfway up, going up, the person's apparent weight is less than their true weight, but more than it is at the bottom because the centrifugal force is still directed upwards, but its magnitude is decreasing.

Therefore, the correct answer is B. At the bottom of the Ferris wheel, the person's apparent weight is at its maximum.

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The true strain at the onset of necking can be obtained from the Hollomon equation as follows: true strain = (K/S)^(1/n).

Here, K is the strength coefficient, S is the stress, and n is the strain hardening exponent. Thus, given the values of these parameters, we can calculate the true strain at the onset of necking.

The Hollomon equation is a mathematical expression for the true stress-true strain curve that relates the true stress to the true strain in a material. It is expressed as follows: true stress = K(true strain)^n. Here, K is the strength coefficient and n is the strain hardening exponent.

The true strain at the onset of necking is the strain at which the material starts to deform plastically instead of elastically. This can be obtained from the Hollomon equation by rearranging it to the form true strain = (K/S)^(1/n). Thus, given the values of the parameters K, S, and n, we can calculate the true strain at the onset of necking.

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Acceleration due to gravity is 9.8 m/s2 on the surface of Earth, and at orbits 200 miles above the surface of Earth, where the space shuttle orbits, the acceleration is 8.78 m/s².

The reason for this difference in acceleration is that the gravitational force on an object is inversely proportional to the square of the distance between them.

Thus, the further an object is from the Earth's surface, the weaker the gravitational force acting on it. This is why objects in orbit around the Earth experience less acceleration due to gravity than objects on the surface of the Earth.

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As moist air rises in the atmosphere, it cools and expands, which causes the moisture in the air to condense into clouds and precipitation.

A moist air mass is a volume of air with a high water vapor concentration. It is usually humid and can be found in tropical regions, where the temperature is high and the air is often saturated with water vapor. When this air mass rises in the atmosphere, it cools, and the water vapor begins to condense into clouds.

As the moist air mass rises in the atmosphere, it cools due to a decrease in pressure. The cooling causes the water vapor in the air to condense into clouds, and the clouds can then produce precipitation. The amount of precipitation that is produced will depend on factors such as the temperature, humidity, and the amount of moisture in the air mass.

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There is continuity in the flow as the velocity distribution is constant in the x-direction, but it can vary in the y-direction.The Navier-Stokes equations are thus valid. Finally, p(x,y)p(x,y) if the pressure at the origin is p0p0​ is $$ p(x,y) = p_0 - \rho V^2 \frac{xy}{h^2} $$.

(a) Check continuity:Let v (x) be the velocity distribution. By the equation of continuity, we have the following:$$ \frac{d}{dx}v(x) =0 $$Thus, the velocity distribution is constant in the x-direction, but it can vary in the y-direction. Therefore, there is continuity in the flow.

(b)The Navier-Stokes equations are valid. (c) write down the Navier-Stokes equations:

$$ \frac{\partial v}{\partial t} + v \frac{\partial v}{\partial x} + w \frac{\partial v}{\partial y} = - \frac{1}{\rho}\frac{\partial p}{\partial x} + g_x $$$$ \frac{\partial w}{\partial t} + v \frac{\partial w}{\partial x} + w \frac{\partial w}{\partial y} = - \frac{1}{\rho}\frac{\partial p}{\partial y} + g_y $$.Since there is no gravity, we have that g x = g y = 0. Then, we can rewrite the equations as follows:

$$ \frac{\partial v}{\partial t} + v \frac{\partial v}{\partial x} + w \frac{\partial v}{\partial y} = - \frac{1}{\rho}\frac{\partial p}{\partial x} $$$$ \frac{\partial w}{\partial t} + v \frac{\partial w}{\partial x} + w \frac{\partial w}{\partial y} = - \frac{1}{\rho}\frac{\partial p}{\partial y} $$We also have the following:$$ \frac{\partial v}{\partial x} + \frac{\partial w}{\partial y} = 0 $$.From the velocity distribution, we have that:$$ v(x,y) = - \frac{V}{h}y $$where V is the maximum velocity at the centerline, and h is the half-width of the channel.

Then, we can write the pressure distribution as follows:$$ \frac{\partial p}{\partial x} = - \rho V^2 \frac{y}{h^2} $$Integrating with respect to x, we obtain:$$ p(x,y) = p_0 - \rho V^2 \frac{xy}{h^2} $$where p 0 is the pressure at the origin.

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

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

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

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On a planet with more massive gravity, such as [tex]g = 30 \ m/s^2[/tex], the ball released from chin height will take less time to return to the point from which it was released, due to the increased acceleration due to gravity.

It will take less time to return to the point from which it was released. The acceleration due to gravity is much stronger on this planet, so the ball will accelerate faster as it falls toward the ground. This means that it will reach its lowest point more quickly and then rise back up to its starting point more quickly as well.

Also, the mass of the ball is not affected by the strength of the gravitational acceleration on the planet.

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Answer:

Work is negative on the way up and positive on the way down.

Explanation:

Work is positive if displacement and the force are in the same direction.

Work is negative if displacement and the force are in opposite directions.

(Note that work is zero if displacement is perpendicular to the force.)

In this question, the gravity on the object points downwards at all times.

On the way up, the position of the object is above where it was launched. Hence, displacement would point upwards.

Since the direction of gravity is opposite to that of displacement on the way up, the work on the object would be negative.

In contrast, displacement of the object points downward on the way down. Since displacement is in the same direction as the force of gravity, the work on the object would be positive.