Vector & has a magnitude of 3.2 units and makes +45° with the +x-axis. Vector b has a magnitudeof 2.4 units, and makes +290° with the +x-axis. What is the dot product of the two vectors?A) -3.2(B -2.5c 3.2D) 2.4E 5.6

The force exerted by b on a is given by 1.90N along the left.

Let the charge of the particle 'a' and 'b' be q and Q respectively.

Given,

The force exerted ([tex]F_{ab}[/tex]) when the two particles are at distance (d = 12.9 mm) is 2.66 N from a to b.

So, [tex]F_{ab} = \frac{kqQ}{d^2} \hat{x}[/tex] (along the right)

[tex]\implies F_{ab} \times d^2 = kqQ\\\implies kqQ = 2.66 N \times 12.9 mm\\\implies kqQ = 34.314 Nmm[/tex]

Now after the separation between them is 18 mm

The force on a due to b when the distance between them is (D = 18mm) is ([tex]F_{ba}[/tex])

i.e. [tex]F_{ba} = \frac{kqQ}{D^2}(-\hat{x})[/tex] (along the left)

[tex]\implies kqQ = -F_{ba}\times D^2 \\\implies 34.314 Nmm = -F_{ba} \times 18mm\\\implies F_{ba} = -1.90 N[/tex]

Hence the force exerted by b on a is given by 1.90N along the left.

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The spring constant k can be determined using the equation:

Therefore, k = (30 × 9.81 + 20) × 0.3/(0.3^2 - 0.1^2) = 301.53 N/m .

The equation is a mathematical expression that states the equality of two expressions. It is typically written using symbols and numbers and is used to find the solution to a problem. Equations are used in all fields of mathematics, from basic algebra to calculus and beyond. They can also be used to find the relationships between variables, explore trends, and make predictions. Equations are a powerful tool for understanding and manipulating the world around us.

k = (mg + mA)h/(h2 - h1)

where m is the total mass of the system (m = mA + mB), g is the acceleration due to gravity, h is the height of the system in equilibrium, and h1 and h2 are the heights at which the spring is unstretched and stretched, respectively.

In this case, m = 30 kg, g = 9.81 m/s2, h = 0.3 m, h1 = 0.1 m, and h2 = 0.3 m.

Therefore, k = (30 × 9.81 + 20) × 0.3/(0.3^2 - 0.1^2) = 301.53 N/m .

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Density of mercury The density of liquid mercury is 13.6g cm3 . 68 moles of mercury are there in 1 liter of the metal.

What is density ?

The term "density" refers to the ratio between the volume (the amount of space taken up by an object or substance) and the amount of matter contained therein (its mass). The amount of mass per unit of volume is another method to define density. An object has a high density if it is both heavy and small.

What is mole ?

A mole is the atom's elementary particle, an ion. The mole of the substance is always related to the Avogadro number. The mole is always associated with the weight or mass of the element or substance. The standard unit of a mole is mol. The mole is a significant factor of the reactant and products to form an equation. A mole calculates the atom, ion, and substance weighs.

Therefore, Density of mercury The density of liquid mercury is 13.6g cm3 . 68 moles of mercury are there in 1 liter of the metal.

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calculate the % of L-dopa in the solution, we can use the following equation:

% L-dopa = 100 * (specific rotation of solution - specific rotation of enantiomer) / (specific rotation of L-dopa - specific rotation of enantiomer)

The specific rotation of the enantiomer is the same magnitude as the specific rotation of L-dopa, but opposite in sign. So, the specific rotation of the enantiomer is 39.5.

Plugging in the values:

% L-dopa = 100 * (-19.75 - 39.5) / (-39.5 - 39.5) = 100 * (59.25) / 0 = undefined

Since the denominator is zero, the % L-dopa is undefined.

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Part A.

It is impossible to determine the speed of the test charge at point y based solely on the information provided. The speed of the charge at point y could be greater than, less than, or equal to v0 depending on various factors such as the presence of electric flux or magnetic fields, resistance, or other forces that may have acted on the charge between points x and y. A detailed analysis of the situation taking into account all relevant factors would be required to determine the speed of the charge at point y.

Part B.

The electric flux through a face of a cube can be calculated using the following formula:

where Φ is the electric flux, ε0 is the permittivity of free space (8.854 x 10^-12 C^2/Nm^2), E is the electric field through the face, and A is the area of the face.

Given that the sides of the cube have length L1, the area of one face can be calculated as A = L1^2. Substituting this value into the formula for Φ, we get:

So, the electric flux through one face of the cube can be calculated by multiplying the permittivity of free space, the electric field through the face, and the square of the side length.

Electric Flux is the number of lines of force from the electric field that penetrates a surface, even though the electric field in a conductor is not moving. Electric flux is used to describe and measure the magnitude of the electric field at a certain distance from the test charge.

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Earth's mass is approximately 81 times greater than the Moon's mass. Earth has a mass of approximately 5.97 x 10^24 kilograms, while the Moon has a mass of approximately 7.34 x 10^22 kilograms.

Why Earth's mass is more than Moon's mass?

Earth's mass is much greater than the Moon's due to its larger size and composition. Earth is a terrestrial planet with a dense iron-nickel core, while the Moon is a smaller, rocky satellite.

Earth's greater size allowed it to retain more heat and develop a stronger gravitational field, which in turn allowed it to retain more volatile elements and heavier elements that would have otherwise been lost to space. This led to a more massive planet with a much stronger gravitational pull, which makes it about 81 times more massive than the Moon.

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Customary fluid liter of liquid weighs a substantial 33.814 fluid ounces, or 4 and 2/8 cups' worth.

A fluid ounce, often known as fl oz, fl. oz, or oz. fl, is a unit of liquid volume equal to 1/16 of a US liquids pint, or 1/128 of a US litre in the US system, or 1/20 of a pint and 1/160 of an Oblate spheroid in the imperial system.

Instead, we utilize fluid ounces, teaspoons, pints, quarters, and gallons when determining the density of a solution using U.S. generally utilized units, with gallons serving as the smallest and largest measurement units, respectively.

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Astronauts and their spacecraft still have mass and are subject to the effects of Earth's gravity while they are in space. In this way, even though the gravitational pull of the Earth is weaker in space than it is on Earth's surface, objects still have weight.

All objects fall at the same pace due to gravity in a vacuum. It is irrelevant how much mass the thing has.

"The force that gravity exerts on the item," according to our textbook, is how weight is defined. The astronauts are weightless since space has zero gravity. But since mass is a measure of how much matter is there, they are not massless. Independent of gravity, mass may be measured.

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The direction that the genes are transcribed is shown by the arrows. The arrow directs attention to the 3' end. When creating DNA strands, arrows are crucial.

Using only the nucleotides A, T, G, and C, construct a compact DNA molecule. Because of their antiparallel structure, the two strands of the double helix that make up DNA molecules move in the opposite directions from one another. Humans and unicellular protists are two eukaryotic species that have telomeres, which are repeating regions at the very ends of chromosomes. The telomeres, which function as caps to protect the internal chromosomal regions, lose a small amount of their length with each cycle of DNA replication.

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The correct option is option B) Electronegativity

Electronegativity is a chemical property that determines how strongly an atom attracts electrons toward itself within a bond.

An atom with a higher electronegativity will attract the shared electrons more strongly than an atom with a lower electronegativity. This leads to a partial negative charge on the atom with the higher electronegativity and a partial positive charge on the atom with the lower electronegativity, resulting in a polar covalent bond.

Electronegativity is related to the electron configuration of an atom and its atomic number, with elements towards the right and top of the periodic table typically having higher electronegativities.

It is important to note that electronegativity is not to be confused with other properties such as electron affinity (the energy change that occurs when an electron is added to a neutral atom), ionization energy (the energy required to remove an electron from an atom), and valence (the number of electrons an atom can donate or accept to form a chemical bond).

Therefore, The correct option is option B) Electronegativity

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The momentum of a photoelectron can not be determined solely from the wavelength of light used to irradiate a metal.  The incident light of wavelength 500 nm has a lower energy than the light of wavelength 620 nm, so the momentum of the photoelectron would be smaller in the former case.

The momentum of the photoelectron depends on several factors such as the energy of the incident photon, the binding energy of the electron in the metal, and the interaction between the light and the metal. In general, the larger the energy of the incident photon, the larger the momentum of the photoelectron. The incident light of wavelength 500 nm has a lower energy than the light of wavelength 620 nm, so the momentum of the photoelectron would be smaller in the former case.

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lan can decrease the magnetic force on the washers by increasing the distance between the magnet and the pile of metal washers.

A material or object that creates a magnetic field is called a magnet.

The most noteworthy characteristic of a magnet, a force that pulls on other ferromagnetic elements like iron, steel, nickel, cobalt, etc., as well as the ability to attract or repel other magnets, is caused by this invisible magnetic field.

The strength of the magnetic force produced by a magnet increases when the distance between the magnet and an object experiencing the magnetic force is reduced.

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The magnitude of the net force acting on the car is 33.66 N.

To calculate the net force acting on the car, we can use the formula:

Force = mass x acceleration

where acceleration can be calculated using the change in velocity. To convert the velocity units to SI units, we first convert km/h to m/s:

[tex]48.0 km/h = (48.0 x 1000/3600) m/s = 13.33 m/s\\59.0 km/h = (59.0 x 1000/3600) m/s = 16.39 m/s[/tex]

The change in velocity is then given by:

[tex]Δv = v_f - v_i = 16.39 m/s - 13.33 m/s = 3.06 m/s[/tex]

The acceleration can then be calculated as:

a = Δv / Δt

where Δt is the time taken to cover the 100 m distance. We can assume this to be a constant, so:

[tex]a = Δv / Δd = 3.06 m/s / 100 m = 0.0306 m/s^2[/tex]

Finally, the net force can be calculated as:

Force = [tex]m x a = 1100 kg x 0.0306 m/s^2 = 33.66 N[/tex]

The magnitude of the net force acting on the car is 33.66 N.

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The density of earth is 5500 kg/m3 and the density of sun is 0.256 times the density of Earth.

Given that Earth's volume is 5500 kg/m3,

When comparing the density of the Sun with the Earth, we must split the:

The ratio of Earth's density to that of the Sun is 0.256, or 1410 kg/m3 to 5,500 kg/m3.

The sun has a density that is 0.256 times that of Earth.

The density of the Earth is 5.52 grams per cubic centimeter, as determined by a number of measurement techniques. 5520 kilos per cubic meter is [this value's equivalent. The earth's mass per cubic centimeter is 5.514 g/cm3. r = 6.37 106 meters is the radius of the earth. We may calculate the needed average density of the stuff in the earth as 5.514 gm/cm3 by dividing the mass of the Earth by its volume. Earth has an average density of 51 g/cm3.

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Answer: A moving block , a moving trailer and a rolling block.

Explanation:

The direction of the net force on the charge at the top is downwards.

This is because the electric field created by the charge at the bottom exerts an electric force on the charge at the top, which is directed downwards. This electric force is greater than the force of gravity, which acts upwards, resulting in a net force directed downwards. This is a result of the inverse square law of electrostatics, which states that the force between two point charges is proportional to the inverse of their distance squared. Thus, the force between the charges is stronger when they are closer together, resulting in a net force directed downwards.

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The eccentricity of the red planet is 1.3175 x 10¹² m².

The eccentricity of the red planet is the product of the Semi-Major axis (a) and the linear eccentricity (c).

The Semi-Major axis (a)  is given as 1,550,000 m and the linear eccentricity (c) is given as 850,000 m.

The eccentricity of the red planet is calculated as follows;

e = ca

e = 850,000 m x 1,550,000 m

e = 1.3175 x 10¹² m²

Thus, the eccentricity of red planet is a function of the Semi-Major axis (a)  and the linear eccentricity (c) .

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The density of cube is 300000 kg/m^3.

We know that density of a substance is : Mass/volume

Given,

Mass = 51.84g = 51.84 / 1000 kg

Volume = 0.012* 0.012* 0.012 m^3

Putting these values in above equation we get;

Density =  300000 kg/m^3.

So the density of cube is  300000 kg/m^3.

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The energy per degree of freedom of a gas particle at temperature 376K is 3/2 kT, where k is the Boltzmann constant and T is the temperature in Kelvin.

Hence, the energy per degree of freedom at 376K is 3/2 x 8.6173 x 10-5 x 376 = 0.007845 ev.

What is temperature?

Temperature is a physical quantity which measures the degree of hotness or coldness of an object. It is measured on the Celsius (°C), Fahrenheit (°F) or Kelvin (K) scales. Temperature is related to the amount of thermal energy in a system, and is an important factor in many fields of science, such as physics, chemistry, meteorology, and engineering. Temperature affects the rate of many chemical reactions, and is a key factor in the functioning of living organisms. It also plays an important role in the Earth's climate and weather pattern.

Therefore, energy per degree of freedom at 376K is 3/2 x 8.6173 x 10-5 x 376 = 0.007845 ev.

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At distance 319m from the foot of the cliff does it strike the ground.

It strikes the ground 3.2x10^4 meters from the base of the cliff

Let's write our given variables:

initial velocity  (V)=600m/s

angle of incline  (θ)=30°

initial height  (h)=20m

acceleration due to gravity  (g)=9.81m/s2

To Find:  we first need to understand that there are two basic types of motion for this type of projectile motion. Accelerated vertical (or "y-axis") motion and smooth horizontal (or "x-axis") motion. The vertical component of motion is affected by gravitational acceleration, but the projectile's horizontal velocity remains the same throughout. We unrealistically assume that drag is ineffective without drag because there are too many unknown factors that need to be resolved. Find the initial vertical and horizontal velocities.

Sinθ = opposite/hypotenuse

        = V(y)/V

V(y) = V(Sinθ)

V(y) = 600m/s × Sin(30°)

V(y) = 300m/s

This vertical speed will be altered over time by the Earth's gravity.

Cosθ = adjacent /hypotenuse

         =V(x)/V

V(x) = V(Cosθ)

V(x) = 600m/s × Cos(30°)

V(x) = 519.6152423m/s

Since this is a uniform horizontal velocity, to solve for horizontal distance using the formula v=d/t

All we need to do is find the time the projectile is in the air. First, solve for the time it takes for the projectile to reach the summit, which is known to have a velocity of 0 m/s because it is perfectly stationary for a moment.

V(f) = V + at = V(y) + gt₁

t₁ = (V(f)−V(y) /g

t₁ = (0m/s−300m/s)/(−9.81m/s2)

t₁ = 30.58103976s

Next,  the time for it to reach the ground, and for this we need total height at the apex, which will be the vertical distance travelled plus the initial 20m of the cliff:

d = (V(f)+V)/2)t₁ + 20m

d = (0m/s+300m/s)/2) × 30.58103976s + 20m

d = 4607.155963m

With this distance we can find the time it takes for the projectile to reach the ground from its apex:

d = V(t) + (1/2)

t₂ = (2d−Vit2)/g

t₂ = √((2(4607.155963m)−(0m/s×t2))/(9.81m/s2))

t₂ = 30.64763391s

Now, we put the two times together:

t =t₁+t₂ = 30.58103976s + 30.64763391s

t = 61.22867367s

Finally, we go back to the x-axis and use this time to solve for the horizontal distance the projectile has moved to the point of impact:

V = d/t

d = V (x) (t)

d = 519.6152423m/s × 61.22867367s

d = 319 m

The projectile strikes the ground at a distance of 3.2x10⁴ meters from the base of the cliff.

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The acceleration of the body after 5 seconds is  2 m/s².

The acceleration of the body after 5 seconds is the rate of change of velocity of the body with time.

Mathematically, the formula for the acceleration of an object is calculated as follows;

a = ( Δv ) / ( Δt )

a = ( v - u ) / ( t₂ - t₁ )

where;

a = ( 10 m/s - 0 m/s ) / ( 5 s  - 0 s )

a = 2 m/s²

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The top speed of a cheetah is generally approximately 120 km/h (75 mph). However, this speed is only possible over short distances, usually around 460 meters (500 yards), and the cheetah may attain it in a matter of seconds. Its speed decreases after that distance as it becomes fatigued.

Speed is the pace at which an item moves along a route in time, whereas velocity is the rate and direction of movement. In other words, velocity is a vector, whereas speed is a scalar number. The pace at which an object's location changes in any direction. Speed is defined as the ratio of distance traveled to time spent traveling. The direction of movement of the body or item is defined by velocity. Speed is fundamentally a scalar number. Velocity is, in essence, a vector quantity. It is the pace at which distance changes. It is the displacement rate of change.

Here,

A cheetah's peak speed is usually around 120 km/h (75 mph). However, this speed is only achievable over short distances, often approximately 460 meters (500 yards), and the cheetah may reach this speed in a couple of seconds. Its speed slows after that distance as it tired.

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When designing a ship and spacesuits for astronauts to use in zero gravity, it is important to take into consideration Newton's laws of motion. For instance, the ship and spacesuits should be designed to minimize or eliminate the effects of inertia, which will allow the astronauts to move more easily.

Additionally, the ship and suits should be light and streamlined to minimize air resistance and drag in the vacuum of space. Finally, the ship and suits should be designed to provide adequate protection from the extreme temperatures of space. All of these design considerations should take into account Newton's laws of motion to ensure the safety and comfort of the astronauts.

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The electric field does -423.85 × 10^-6 J of work in moving the -7.7 µC charge from ground to a point whose potential is 55 V higher.

The work done by an electric field on a charge can be calculated using the equation:

W = qΔV

where W is the work done, q is the charge of the object, and ΔV is the change in potential energy.

For the given situation, q = -7.7 µC and ΔV = 55 V. Thus,

W = (-7.7 × 10^-6 C) × (55 V) = -423.85 × 10^-6 J

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The location of the CM of a system ( 0.5l , 0.25l )

x = (m1.x1 +m2.x2 +m3.x3) / ( m1 + m2 +m3)

x = ( m x 0 + m x 0 + 2m x l ) / ( m+m+2m)

x = 2m x l / 4m

x = 0.5 l

y = (m1 x y1 +m2 x y2 +m3 x y3) / ( m1 + m2 +m3)

y = (m x 0) + m x l + 2m x 0 ) / ( m + m + 2m )

y = m x l / 4m

y = 0.25 l

A position established in relation to an object or set of objects is the center of mass.

It represents the system's average location as weighted by each component's mass.

The center of mass for straightforward stiff objects with homogeneous density is found at the centroid.

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The acceleration due to gravity near the surface of the hypothetical planet is 9.79 m/s^2, which is the same as the acceleration due to gravity near the surface of the Earth.

The acceleration due to gravity near the surface of a planet is given by the formula:

g = G * M / R^2

where G is the gravitational constant (6.67 x 10^-11 Nm^2/kg^2), M is the mass of the planet, and R is the radius of the planet.

Since the mass of the hypothetical planet is the same as the Earth, we can use the mass of the Earth for M. The radius of the hypothetical planet is 1.98 times the radius of the Earth, so we can use the following for R:

R = 1.98 * 6380 km = 12618.4 km

We can now substitute these values into the formula for g:

g = 6.67 x 10^-11 Nm^2/kg^2 * 5.98 x 10^24 kg / (12618.4 x 10^3 m)^2

Simplifying this expression gives us:

g = 9.79 m/s^2

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Kepler's second law states that a planet moves most quickly during perihelion and most slowly at aphelion. The orbit's total period (T) is related to the cube of the planet's average distance from the Sun (R).

According to Kepler's Second Law, as a planet rounds the Sun, an arbitrary vertical connecting them sweeps across the same amount of space at the same rate. In essence, this means that asteroids do not travel throughout their revolutions at a constant speed.

The speed of the planet as it travels through its elliptical orbit is governed by Kepler's second law. Kepler demonstrated that no matter where in the orbit the planet is, the region that it "sweeps out" over a period of time is the same.

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A) The population of Alaska is expected to be 1083.173 thousand at the end of year 2022.

B) Alaska’s population is expected to reach 850,000 at the end of 14.160 years after the end of 2000.

Population of Alaska at the end of x years is given as: A(x) = 0.638x^2 + 6.671x + 627.619 thousand people……..(i)

To find the population of Alaska in the year 2022,

x= 0 in the year 2000

therefore, x= 22 in the year 2022

putting value in x in equation (i),

A(22) = 0.638(22^2) + 6.671*22 + 627.619= 1083.173 thousand people

The number of years it will take for Alaska to exceed 850000 people is,

Since the population equation is provided in thousand, the equation now becomes:

A(x) = 0.638x^2 + 6.671x + 627.619= 850

0.638x^2 + 6.671x – 222.381= 0

Using Sridhar Acharya’s formula,

x=(-b±√(b^2-4ac))/2a

x= (-6.671 ± √((6.671^2)- 4*(0.638*(-222.381))))/2*0.638

x = (-6.671 ±  √(44.502 +567.51))/1.276

x = (-6.671+ 24.739)/1.276 or (-6.671 - 24.739)/1.276

x= 14.16 or -24.61

therefore, the number of years that Alaska will take to exceed its population above 850000 is 14.16 years from 2000

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A vector measurement of the rate and direction of motion is how physics defines velocity.

Thus, velocity is a measurement of the speed at which an object is moving. The velocity equation is defined as the change in an object's position, divided by the passage of time. When you use the velocity formula, you obtain more clearance.

The rate of change in displacement over time is referred to as the velocity.

The velocity formula in physics is as follows:

                              [tex]v = d/t[/tex]

V= 9 m/s

Time= 19.25 s

distance = 9 / 19.25 = 2.138

Velocity Equation:

 Initial Velocity 2.138 m

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The density of an object can be calculated using the equation density = mass / volume.

Density is a measurement of the mass per unit volume of an object. Or it could also be interpreted as a comparison between the mass and volume of an object, as reported by the Ministry of Education and Culture's Learning Resources website.

The higher the density of an object, the greater the mass of each volume. The average density of each object is the total mass divided by the total volume.

An example of an object that has a higher density is iron, while an example of an object that has a lower density is water.

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