which of these are not yet a habit for you? what can you do to turn them into daily habits?

The hare can afford to nap for a maximum time of 6.67 seconds without losing the race if his speed is 15 m/s.

After running for 7 seconds, the hare has covered a distance of:

\(d_h = v_h * t = 15 m/s * 7 s = 105 m\)

The hare is now 895 m away from the starting line and 100 m away from the finish line. The tortoise is 895 m away from the starting line and moving towards the finish line at a speed of 0.27 m/s.

The hare needs to cover a distance of 100 m to reach the finish line, while the tortoise needs to cover a distance of 895 m. If the hare takes a nap for a certain amount of time, the tortoise will continue to move towards the finish line and may eventually cross the finish line before the hare wakes up.

We can calculate the time it would take the tortoise to reach the finish line by dividing the distance by its speed:

\(t_t = d_t / v_t = 895 m / 0.27 m/s = 3314 s\)

The hare needs to wake up and cover the remaining distance to the finish line before the tortoise does. The distance the hare needs to cover is:

\(d_h = 100 m\)

The maximum speed of the hare is 15 m/s, which means the time it would take the hare to cover the distance is:

\(t_h = d_h / v_h = 100 m / 15 m/s = 6.67 s\)

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Answer:

-2.0 m/s2

Explanation: D

Answer:

Actions that underlie mathematical rules, patterns or probability distributions.

For example how fast something falls at any given point or time.

More complex actions, such as human decision making in single individuals would be way too complicated to describe in physical terms.

But note that there can be physical models of such things as traffic when we can assume statistical knowledge of behavior.

Also physical models are used to plan such things as emergency exits in big stadiums, because many thousands of people can be described as particles flowing under a given pressure.

Every time we can gain good statistical knowledge and can therefore see patterns and rules in action, we can build theoretical models to make predictions and simulations (and games btw)

Since it's fair to say that mathematics is the science of patterns, it is plausible that physical descriptions often come in mathematical formulations, so that it can be understand as an efficient language of physics.

Neighboring disciplines like chemistry relay on physical theories to build on them,and then add shortcuts to fit their needs and interests, generating an own language for their field of study. But physicists may refer to them as anadd-on to physics.

Physics can basically explain all actions wich you can express in numbers.

But note that on a fundamental level physics describes 'how' things work, not necessarily 'why' they do it this way. The source of the basic and most fundamental physical constants and rules remains a mystery till this day.But of course there are theories on that as well, wich mostly can neither be proved or falsified.

The text is my own work and based of my general knowledge and quintessence of lectures on physics and other fields I attended.

(I would really appreciate the brainliest)

Answer:

the answer is D

Explanation:

Answer:

The answer is D

Explanation:

yes

When the masses are released from rest, the block of mass m will accelerate downwards with a force of mg, where g is the acceleration due to gravity. This will cause the cord to move and the block of mass 2m will accelerate upwards with a force of 2mg. Since the pulley is massless and frictionless, the tension in the cord will be the same on both sides of the pulley.

The force exerted by the table on the stand can be found using Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. Therefore, the normal force exerted by the table on the stand is equal in magnitude and opposite in direction to the weight of the entire system.

The weight of the system can be found by adding up the weights of all the components. The block of mass m has a weight of mg, the block of mass 2m has a weight of 2mg, and the stand has a weight of 4mg. Therefore, the total weight of the system is 7mg.

Therefore, the normal force exerted by the table on the stand is 7mg upwards.

To find the normal force that the table exerts to support the entire system, we'll consider the following terms: massless frictionless pulley, frictionless bearings, stand of mass 4m, massless cord, block of mass m, and block of mass 2m.

Step 1: Identify the forces acting on the system.
The entire system consists of the stand (4m) and the two blocks (m and 2m). The force acting on the system is gravity, pulling each mass downward. The total gravitational force is (4m + m + 2m) * g, where g is the acceleration due to gravity (9.81 m/s²).

Step 2: Calculate the total gravitational force.
Total gravitational force = (4m + m + 2m) * g = (7m) * g

Step 3: Determine the normal force exerted by the table.
The normal force is equal in magnitude and opposite in direction to the total gravitational force acting on the system. Since the system is at rest on the table, there is no net vertical force, meaning that the normal force must balance out the gravitational force.

Normal force = Total gravitational force = (7m) * g

So, the normal force exerted by the table to support the entire system is (7m) * g.

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Answer: "Surface tension is a film of a liquid caused by the attraction of the particles in the surface layer by the bulk of the liquid, which tends to minimize surface area."

Hope this helps!

Answer:

Explanation:

Surface tension is the property of a liquid surface. It is an effect where the surface of the liquid is strong.

example - small insects can walk on water as they do not have enough weight to penetrate it.

This image might help you

Hope it helps

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The magnification is positive, indicating that the image is upright.

Since the magnification (m) is greater than 1, the image is magnified compared to the object. Additionally, since the image distance (d_i) is positive, the image is formed on the opposite side of the mirror (real image).

To determine the position of the image formed by a concave spherical mirror and the characteristics of the image, we can use the mirror formula:

1/f = 1/d_o + 1/d_i,

where f is the focal length of the mirror, d_o is the object distance (distance of the object from the mirror), and d_i is the image distance (distance of the image from the mirror). The sign conventions for distances are as follows: object distance (d_o) is positive for objects placed in front of the mirror, image distance (d_i) is positive for real images, and the focal length (f) is negative for a concave mirror.

Object height (h_o) = 4.0 cm,

Object distance (d_o) = -18.0 cm (negative since the object is in front of the mirror),

Focal length (f) = -20.0 cm (negative for a concave mirror).

First, let's calculate the image distance (d_i):

1/f = 1/d_o + 1/d_i

1/-20.0 cm = 1/-18.0 cm + 1/d_i

-1/20.0 cm + 1/18.0 cm = 1/d_i

(18.0 - 20.0)/(18.0 * 20.0) = 1/d_i

-2.0/(18.0 * 20.0) = 1/d_i

d_i = -18.0 * 20.0 / -2.0

d_i = 180.0 cm

The image distance (d_i) is positive, indicating that the image is formed on the opposite side of the mirror (real image).

Next, we can determine the characteristics of the image. To do so, we can calculate the magnification (m) using the formula:

m = -d_i / d_o

m = -180.0 cm / -18.0 cm

m = 10.0

The magnification is positive, indicating that the image is upright.

Since the magnification (m) is greater than 1, the image is magnified compared to the object. Additionally, since the image distance (d_i) is positive, the image is formed on the opposite side of the mirror (real image).

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a. The electric flux through each of the six faces of the cube is zero.

To answer this question, we must use Gauss' Law.

The electric flux is calculated as follows:

Adding all of these values together, we see that the electric flux through the cubical surface is zero,

as Gauss' Law predicts, since there is no net charge within the cube.

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The mass of the truck is 12,974.4kg .

As a measure of inertia, which is a fundamental characteristic of all matter, mass is used in physics. Effectively, it is the resistance a body of matter offers to a change in its speed or position as a result of the application of a force.

Measures a substance's resistance to acceleration in physics. A measure of an object's mass is roughly equivalent to counting the atoms that make up the object. The kilogram serves as the fundamental mass unit. Mass multiplied by the gravitational acceleration equals weight.

50km/h =50×5/18 m/s= 13.88 = 13.9

momentum (p)=180,345 kg.m/s

P=mv

180,345= m X 13.9

m = 180345/13.9

m = 12,974.46

m = 12,974.4

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The mass of air vented out of the bathroom in one day is 3328.64 kg.

The volume flow rate of the fan is given as 32 L/s, which can be converted to cubic meters per second (m^3/s) as follows:

32 L/s × (1 m^3 / 1000 L) = 0.032 m^3/s

The mass flow rate of the air vented out of the bathroom can be calculated as follows:

mass flow rate = volume flow rate × density

mass flow rate = 0.032 m^3/s × 1.20 kg/m^3

mass flow rate = 0.0384 kg/s

To determine the mass of air vented out in one day, we need to convert the mass flow rate to a daily basis. There are 86400 seconds in a day, so:

mass vented out in one day = mass flow rate × 86400 s/day

mass vented out in one day = 0.0384 kg/s × 86400 s/day

mass vented out in one day = 3328.64 kg/day

Therefore, the mass of air vented out of the bathroom in one day is 3328.64 kg.

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The speed of the boat relative to the water is 9.08 m/s, when the boat takes 14 minutes to cross the river.

We can decompose the velocity of the boat into two components: one parallel to the river, and one perpendicular to it. Let's call the parallel component \(v_p_a_r\) and the perpendicular component \(v_p_e_r_p\):-

\(v_p_a_r = v_b_o_a_t cos\theta\)

\(v_p_e_r_p = v_b_o_a_t sin\theta\)

The boat will travel a distance of 102 m across the river, which will take 14 minutes or 840 seconds. Therefore, the distance traveled parallel to the river will be:

\(d_p_a_r = v_p_a_r * t = v_b_o_a_t cos\theta * 840 s\)

The distance traveled perpendicular to the river will be:

\(d_p_e_r_p = v_p_e_r_p * t = v_b_o_a_t sin\theta * 840 s\)

The boat will end up at a point directly north of its departure point on the south bank, which means that \(d_p_e_r_p = 102 m\). Therefore, we can solve for \(v_b_o_a_t\) as follows:

\(v_b_o_a_t sin\theta * 840 s = 102 m\)

\(v_b_o_a_t sin\theta = 102 m / 840 s\)

\(v_b_o_a_t sin\theta = 0.1214 m/s\)

To solve for \(v_b_o_a_t\):-

\(tan\theta = d_p_a_r / d_p_e_r_p\)

\(tan\theta = (v_p_a_r * t) / (v_p_e_r_p * t)\)

\(tan\theta = v_p_a_r / v_p_e_r_p\\tan\theta = v_b_o_a_t cos\theta / (v_b_o_a_t sin(\theta))\\\)

Reserving the value of \(d_p_e_r_p\) and solving for \(\theta\):-

\(\theta = arctan(v_p_a_r / (102 m / 840 s))\\\theta = arctan(v_b_o_a_t cos(\theta) / 0.1214 m/s)\)

\(v_p_a_r^2 + v_p_e_r_p^2 = v_b_o_a_t^2\\(v_b_o_a_t cos(\theta))^2 + (v_b_o_a_t sin(\theta))^2 = v_b_o_a_t^2\)

\(v_b_o_a_t^2 (cos^2(\theta) + sin^2(\theta)) = v_b_o_a_t^2\\v_b_o_a_t^2 = 102^2 / (cos^2(\theta) + sin^2(\theta))\\v_b_o_a_t = \sqrt{[102^2 / {cos^2(\theta) + sin^2(\theta)}]}\)

Reserving the value of \(\theta\):-

\(v_b_o_a_t = \sqrt{[102^2 / {cos^2(\theta) + sin^2(\theta)}]} \\v_b_o_a_t = 9.08 m/s\)

Therefore, the speed of the boat relative to the water is 9.08 m/s.

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If a rocket blasts off. in 10.0 seconds it's at 10,000 ft, traveling at 3600 mph. assuming the direction is up, the acceleration of the rocket is 528 ft/s². T

The correct answer is option (b)

a = Δv / Δt

a =  acceleration

Δv =  change in velocity

Δt =  change in time.

1 mile = 5280 feet

1 hour = 3600 seconds

3600 mph = 3600 * 5280 ft / 3600 s = 5280 ft/s

Therefore , a = Δv / Δt substituting these, we have:

a = Δv / Δt = (5280 ft/s - 0 ft/s) / 10.0 s

a= 528 ft/s²

In conclusion, the acceleration of the rocket is 528 ft/s²

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The ratio of total work done to total time consumed is defined as average power. P represents it. Watt is the average power unit in the SI system of measurements. An instrument called a wattmeter is used to gauge average power.

To calculate the average power required for a harmonic wave traveling on a string of mass density, we need to use the formula:

P = (1/2)ρAv^2

where P is the power, ρ is the mass density of the string, A is the amplitude of the wave, and v is the velocity of the wave.

Since we know that one half wavelength is defined by the length of the string, we can use the formula for the velocity of a wave on a string:

v = √(T/μ)

where T is the tension in the string and μ is the linear mass density of the string (mass per unit length).

Since one half wavelength is defined by the length of the string, we know that the wavelength is twice the length of the string:

λ = 2L

where L is the length of the string.

Since the wavelength and the length of the string are related by λ = 2L, we can use this to find the frequency of the wave:

f = v/λ = v/2L

Now that we have the frequency, we can find the amplitude of the wave using the equation for the displacement of a harmonic wave:

y = A sin(2πft)

where y is the displacement and t is time. Since we know that the length of the string is one half wavelength, we can write:

y = A sin(πx/L)

where x is the distance along the string. At x = L/2, the displacement is maximum and equal to A.

Using the above equations and substituting the given values, we can calculate the average power required for the wave.

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The nucleus of an atom will have a positive charge due to the existence of protons, which are positively charged subatomic particles.

Protons and neutrons are present in an atom's nucleus. We are aware that a proton has a charge of + 1 and a neutron has a charge of 0 (or no charge). As a result, the atom's nucleus will always be positively charged. A nucleus is a name for the dense area in the middle of an atom. Because there are positively charged subatomic particles present, the nucleus usually has a positive charge. The subatomic particles, which are present in atoms but far smaller than atoms, are there. Protons, neutrons, and electrons are the three primary subatomic particles found in matter. An atom's nucleus contains protons and neutrons, while its outermost nucleus contains electrons. Neutrons are subatomic particles with a charge of zero, whereas protons are positively charged.

Therefore, the nucleus of an atom will always have a positive charge. Consequently, an atom's nucleus has a positive charge because of the presence of protons.

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If the point charge is placed at point \(E_W\) is equal to \(E_X\).

The electric field inside a conducting cubic shell is zero. When a point charge is placed outside the shell, the electric field outside the shell is greater than the electric field inside the shell which is zero.

We can deduce the following;

Thus, the only correct statement is, If the point charge is placed at point \(E_W\) is equal to \(E_X\).

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The center of mass of a thin plate with constant density δ covering a given region can be found by integrating the product of the density function and the position coordinates over the region and then dividing by the total mass. The region is bounded by the given curves or lines, and the density function is given as a constant or a function of x and/or y.

To find the center of mass, we need to calculate the following integrals:

Integrate δ * x over the region and then divide by the total mass.

Integrate δ * y over the region and then divide by the total mass.

The result of these integrals will give us the x-coordinate and y-coordinate of the center of mass, respectively. The density of the thin plate is given as a constant δ or a function of x and/or y. The center of mass will be located at the point (x, y) that satisfies the above integrals. The exact coordinates of the center of mass can be determined by solving the integrals and rounding to the nearest hundredth.

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the answer for the question is D. all of the above

The force that the spring exerts is = 1.31 N

The spring force in the spring depends on the spring's displacement and the force constant of the particular spring. The below expressions show the force that the spring exerts,

\(F=kx\)

Here, we are given,

k= The spring constant of a spring = 8.75 N/m.

x= The displacement of the string is = 0.150 m

Now, we replace the known values in the above equation, we can find :

\(F=kx\)

Or, \(F= 8.75 \times 0.150\)

Or, \(F= 1.3125 N\)

Or, F≈ 1.31 N

Now, from the above calculation we can conclude that the force that the spring exerts is 1.31 N.

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Explanation:

Soil is formed by the method of rock weathering. Weathering is the breaking of rocks into tinier bits as it comes in contact with water, air, or living things. It can happen physically, biologically, or chemically.

Physical weathering: Disintegration of rocks into tiny bits with no modification in their atomic structure. Air and water are factors of physical weathering. When the wind blows on rocks, heavy rain, water waves from the sea can promote a continuous fragmentation of rock bits to debris which ultimately become soil.

Chemical weathering: Chemical reactions in rocks make adjustments in their mineral makeup. Examples of chemical reactions causing weathering are hydrolysis, carbonation, oxidation, and hydration.

Biological weathering: Biological organisms help rock fragmentation. Tree tubers and mosses grow or pierce through rocks and make hole areas that continuously pull rocks apart. Creatures burrow through rocks and form disintegration. Microorganisms discharge chemicals which break down rock minerals.

The correct answer is c. 758,000,000. The 7.58e8 is the scientific notation, also known as exponential notation, which is a way of expressing very large or very small numbers

The letter "e" in a decimal number, indicates scientific notation. The "e" stands for the exponent of 10, and the number following it represents the power to which the number 10 is raised.

7.58e8 in scientific notation represents 7.58 x 10^8  .In this case, 8 is the exponent, meaning that the number 7.58 is multiplied by 10 to the power of 8, or 10^8, resulting in 758,000,000.

Using exponential notation, we may delete zeros and represent a number in a compact form by taking use of the fact that multiplication or dividing by multiples of 10 moves the decimal point of a number to the left or right.

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Answer: He was labeled as one of Africa's cruelest dictators because during his eight year reign many civilians were massacred. He drove out Uganda's Indian and Pakistani citizens and spent large amount of money on the military which led to the economic decline of the country.

Explanation:

Answer:

Color, Streak, luster, cleavage and fracture, hardness, crystal shape, and density.

Explanation:

The speed of the electron required to experience an acceleration along the x-axis is given by the equation v = E/B, where v is the speed, E is the electric field, and B is the magnetic field.

To determine the speed of the electron that would result in acceleration along the x-axis, we need to consider both the electric and magnetic fields acting on the electron. The electric field, E, causes acceleration along the x-axis, while the magnetic field, B, causes a force perpendicular to the electron's motion. The net force acting on the electron will be zero when these two forces balance each other.
Step 1: Determine the electric field, E, and the magnetic field, B, acting on the electron along the x-axis. These values should be given in the problem statement or can be calculated from the given information.
Step 2: Use the formula v = E/B to calculate the speed of the electron that results in acceleration along the x-axis.

By following these steps, you can find the required speed of the electron in meters per second (m/s) to experience an acceleration along the x-axis in the given fields.

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Answer:

A and D

Explanation:

The two benefits of this model are that it represents a complex process more simple, and the second is that it represents something that takes a long time to observe directly. So, options A and D are correct.

The water cycle explains how water vapor from the earth's surface rises into the atmosphere, cools and condenses to form rain or snow in clouds, and then falls back to the earth's surface as precipitation. Water that rains on land gather in lakes, rivers, soil, and porous rock strata. A large portion of this water then flows back into the oceans, where it will again evaporate. An important factor in Earth's weather patterns is the movement of water in and out of the atmosphere.

Using a diagram to explain this process is a good idea because it is a time taking process as well as a very complex process too, but with the help of a diagram it will be easy to visualize things, and it will give a wider aspect of the process.

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Explanation:

Relative density of mercury = 13600 Kgm-3/1000 kg m-3 = 13.6.

Gravitational force between two masses m, and m, is represented as F = Gm₂ m₂ / r^2 where r = xi+yj + zkG, m, m₂ are nonzero constants and let's assume that I = 0

a) Calculation:For F = Gm₂ m₂ / r^2.

Using r = xi+yj + zk and let r^2 = x^2 + y^2 + z^2∴ F = Gm₂ m₂ / (x^2 + y^2 + z^2), Where G, m, m₂ are nonzero constants. Divergence of F = ∇ · F= 1/r^2(d/dx(r^2Fx) + d/dy(r^2Fy) + d/dz(r^2Fz))= 1/r^2(d/dx(r^2Gm₂ m₂ x/(x^2+y^2+z^2)^(3/2)) + d/dy(r^2Gm₂ m₂ y/(x^2+y^2+z^2)^(3/2)) + d/dz(r^2Gm₂ m₂ z/(x^2+y^2+z^2)^(3/2)))= 1/r^2(d/dx(r^2Gm₂ m₂ x/(x^2+y^2+z^2)) * (x^2+y^2+z^2)^(3/2) + d/dy(r^2Gm₂ m₂ y/(x^2+y^2+z^2)) * (x^2+y^2+z^2)^(3/2) + d/dz(r^2Gm₂ m₂ z/(x^2+y^2+z^2)) * (x^2+y^2+z^2)^(3/2))= 1/r^2(Gm₂ m₂ [2x(x^2+y^2+z^2)-3x^2]/(x^2+y^2+z^2)^(5/2) + Gm₂ m₂ [2y(x^2+y^2+z^2)-3y^2]/(x^2+y^2+z^2)^(5/2) + Gm₂ m₂ [2z(x^2+y^2+z^2)-3z^2]/(x^2+y^2+z^2)^(5/2))= 1/r^2(Gm₂ m₂ [(2x^2+2y^2+2z^2-3x^2)/(x^2+y^2+z^2)^(3/2)] + [2x^2+2y^2+2z^2-3y^2]/(x^2+y^2+z^2)^(3/2)] + [2x^2+2y^2+2z^2-3z^2]/(x^2+y^2+z^2)^(3/2)])= 1/r^2(Gm₂ m₂ [x^2+y^2+z^2]/(x^2+y^2+z^2)^(3/2))= 0.

Curl of F = ∇ × F= i(d/dy(Fz) - d/dz(Fy)) - j(d/dx(Fz) - d/dz(Fx)) + k(d/dx(Fy) - d/dy(Fx))= i(d/dy(Gm₂ m₂ z/(x^2+y^2+z^2)) - d/dz(Gm₂ m₂ y/(x^2+y^2+z^2))) - j(d/dx(Gm₂ m₂ z/(x^2+y^2+z^2)) - d/dz(Gm₂ m₂ x/(x^2+y^2+z^2))) + k(d/dx(Gm₂ m₂ y/(x^2+y^2+z^2)) - d/dy(Gm₂ m₂ x/(x^2+y^2+z^2)))= i(Gm₂ m₂ [-2xz]/(x^2+y^2+z^2)^(5/2)) - j(Gm₂ m₂ [-2yz]/(x^2+y^2+z^2)^(5/2)) + k(Gm₂ m₂ [(x^2+y^2-2z^2)]/(x^2+y^2+z^2)^(5/2))

b) Calculation:The line integral of F along a curve C can be evaluated by the following formula∫C F.dr = ∫∫ ( ∇ x F) ds, Where r is the position vector of the curve, s is the scalar parameter representing the curve, and the integral is evaluated from the initial point to the final point.

Using the curl of F obtained in part a) and for the surface with ∂S as C∫C F.dr = ∫∫ ( ∇ x F) ds= ∫∫ curl(F) ds= ∫∫ (-2xz i -2yz j + (x^2+y^2-2z^2)k) ds...[1]

Let's consider the surface S as a plane perpendicular to the z-axis of the form ax+by+c=0 and the curve C as the intersection of the plane and the cylinder x^2 + y^2 = a^2.

Let's choose the unit normal to the surface S as k (along the z-axis).

The curl of F is a vector field perpendicular to the plane and along the direction of k.

Thus the integral can be written as∫C F.dr = ∫∫ ( ∇ x F) . k ds= ∫∫ (x^2+y^2-2z^2) ds...[2]

Now let's evaluate the integral over the given plane ax+by+c=0. We can write x = t, y = (c-at)/b and z = 0, where t is the scalar parameter along the line of intersection of the plane and the cylinder (x^2 + y^2 = a^2).

Since the curve C is on the cylinder of radius a, we have x^2+y^2 = a^2 ⇒ t^2+(c-at)^2/b^2 = a^2On solving for t, we have t = (bc±ab √(a^2-b^2-c^2))/[a^2+b^2].

Substituting t in x and y, we get the curve C in the x-y plane as a function of the scalar parameter s asx = (bc±ab √(a^2-b^2-c^2))/[a^2+b^2]y = (c-at)/b= (c-(bc±ab √(a^2-b^2-c^2))/[a^2+b^2])/b.

Now we can evaluate the integral over the curve C, which is along the intersection of the plane and the cylinder.

Integral over C (x^2+y^2-2z^2) ds= ∫t₁^t₂ [(t^2 + [(c-at)^2]/b^2 - 2(0)^2)^(1/2)] dt= ∫t₁^t₂ [(a^2-b^2-c^2)t^2+2bc(c-at)+b^2c^2-a^2b^2]^(1/2) dt.

Now we can choose the value of t₁ and t₂ such that the square root in the integrand is minimized (so that the integral is path-independent).

This can be done by choosing the value of t that gives the minimum value of (a^2-b^2-c^2)t^2+2bc(c-at)+b^2c^2-a^2b^2 over the range of t from t₁ to t₂.

On differentiation with respect to t and equating to 0, we get the value of t = bc/(a^2+b^2).

Substituting this value of t in the integrand, we get the minimum value of the square root in the integrand to be |c| √(a^2+b^2)/|b|.

Thus the integral over C is given by∫C F.dr = ∫∫ (-2xz i -2yz j + (x^2+y^2-2z^2)k) ds= ∫∫ (x^2+y^2-2z^2) ds= ∫t₁^t₂ |c| √(a^2+b^2)/|b| dt= |c| √(a^2+b^2)/|b| (t₂-t₁).

Now we can see that the integral is path-independent as it depends only on the end points t₁ and t₂ and not on the path taken to reach them.

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Objects of the same volume can have different masses due to variations in their **density**.

Density is defined as mass per unit volume and represents how much mass is packed into a given volume. If two objects have the same volume but different densities, their masses will differ.

For example, consider two cubes of the same size, but one is made of iron and the other is made of aluminum. Iron is denser than aluminum, which means that for the same volume, the iron cube will have more mass compared to the aluminum cube.

The density of an object depends on its composition, arrangement of particles, and the forces acting between them. Different materials can have different densities due to variations in their atomic or molecular structure.

Therefore, even though objects may occupy the same volume, their masses can differ if their densities vary. It is the density of the material that determines how much mass is contained within a given volume.

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Answer:

dormant

Explanation:

Answer:

dormant

Explanation:

Answer:

D. 1×10⁻⁸ M

Explanation:

[H⁺] [OH⁻] = 10⁻¹⁴

(1×10⁻⁶) [OH⁻] = 10⁻¹⁴

[OH⁻] = 1×10⁻⁸

The concentration of hydroxyl ion will be  \(10^{-8}\)M.

The amount of a chemical substance in a mixture is expressed by the substance's concentration.

Calculation of concentration.

Given data:

Concentration of H+ =  1 x \(10^{-6}\) M.

It is known that,

[\(H^{+}\)][\(OH^{-}\)] = \(10^{-14}\)M

Now, put the value of concentration of [\(H^{+}\)] in above equation.

[1× \(10^{-6}\)][\(OH^{-}\)] =  \(10^{-14}\)M

[\(OH^{-}\)]  =   \(10^{-14}\) / [1× \(10^{-6}\)]M

[\(OH^{-}\)]  = \(10^{-8}\)M

Therefore, the concentration of hydroxyl ion will be  \(10^{-8}\)M.

Hence, the correct answer will be an option (D).

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