How old was isaac newton when in 1666 he formulated the theory of universal gravity?

The given polar equation is r = 3 sin(4), where r is the distance from the origin and θ is the angle in radians.

To sketch the curve, we can first sketch the graph of r as a function of x in cartesian coordinates. We can do this by substituting x = r cos(θ) into the equation r = 3 sin(4). This gives us:

r = 3 sin(4)

r = 3 sin(4) * cos(θ)

r = 3 * cos(4θ)

x = r cos(θ)

y = r sin(θ)

We can then use the slope-intercept form of the graph to sketch the curve. The slope of the line is given by the derivative of the function, which is:

dy/dx = d/dx (r sin(θ)) = -r sin(θ) * cos(θ) = -r cos(4θ)

So the slope of the line is -r cos(4θ).

To sketch the curve, we can first plot the point (0, 0) on the graph and then find the slope of the line passing through this point. We can then use the slope to draw the line and extend it to the right to get the entire curve.

The resulting curve is a circle with radius 3 and center at the origin. The angle θ is measured in radians, so the curve will be symmetric about the x-axis. The y-intercept of the curve is 0, since the distance from the origin to the center of the circle is 0.  

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Used in generators and electric motors, electromagnetic induction explains how a changing magnetic field can produce an electric current and, conversely, how an electric current generates a magnetic field around it. The most accurate option is:

a.

Yes, effective thermal conductivity of an insulation system accounts for heat transfer by conduction.

What do you mean by thermal conductivity?

Thermal conductivity is a property of a material that describes its ability to conduct heat. It is typically measured in units of watts per meter per kelvin (W/m·K). The thermal conductivity of a material is affected by various factors, such as temperature, pressure, and the presence of impurities or defects.

The effective thermal conductivity of an insulation system is a measure of its ability to resist heat transfer by conduction. It does not take into account other forms of heat transfer, such as convection or radiation.

The value of the thermal conductivity is typically measured by determining the rate of heat flow through a sample of the insulation material under specific conditions of temperature and pressure.

The lower the thermal conductivity, the better the insulation's ability to resist heat transfer by conduction.

Hence, effective thermal conductivity of an insulation system accounts for heat transfer.

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3Kg is the mass of the fish.

rotational equilibrium

(3.5)(9.8)(L/2) + m(9.8)(L/4) – (5)(9.8)(L/2) = 0

34.3(L/2)+9.8m(L/4)-49(L/2)=0

34.3(L/2)-49(L/2)+9.8m(L/4)=0

-14.7(L/2)+9.8m(L/4)=0

-7.35L+2.45mL=0

2.45mL=7.35L

m=7.35L/2.45L

m = 3 kg

Mass is used in physics to express inertia, a fundamental characteristic of all matter. Essentially, it is a mass of matter's resistance to changing its direction or speed in response to the application of a force. The change that an applied force produces is smaller the more mass a body has. The kilogram, the unit of mass in the International System of Units, corresponds to 6.62607015 1034 joule seconds using Planck's constant (SI). One joule is produced by multiplying one kilogram by one square meter per second. The kilogram is determined by exact measurements of Planck's constant since the second and the meter have previously been defined in terms of other physical constants.

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Physical properties such as color, shape, size, weight, odor, melting point, boiling point, and density can be observed without destroying the substance.

Physical properties are characteristics of a substance that can be observed and measured without changing the substance's chemical composition. Examples of physical properties include color, density, hardness, melting point, boiling point, and electrical conductivity. These properties are determined through experiments and/or observations. Physical properties can be used to identify and classify a material. They can also be used to differentiate between different forms of the same material, such as different allotropes of the same element. Physical properties are also important for understanding how materials interact with each other and how they respond to the environment.

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Answer:

true

Explanation:

Answer: True

Explanation:

The force lies in the negative y direction, that is in the third quadrant.

Since the force does positive work on a particle that has a displacement pointing in the x direction, we can conclude that the force must be pointing in the same direction as the displacement, which is in the positive x direction.

Similarly, since the force does negative work on a particle that has a displacement pointing in the y direction, we can conclude that the force must be pointing in the opposite direction as the displacement, which is in the negative y direction. Therefore, the force lies in the negative y direction, which corresponds to the third quadrant.

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Magnesium [Mg] + Oxygen [O2] --> Magnesium oxide [MgO]

See, When magnesium is burned in air,it reacts with oxygen, here both of them(Mg & O) gets combined with each other, thus it is a combination reaction.

Now, balance this equation first;

Now, as you can see that 2 molecule of magnesium gets combined with one molecule of oxgyen and forms 2 molecules of magnesium oxide. And let us understand how they are bonded with each other;

Mg × × • • • •

• O • • O •

• • • •

Mg × ×

and as 2 Mg are bonded with 2 oxygen, they will together result in 2 molecules of magnesium oxide.

Answer:

To find the average distance of the numbers you provided (255cm, 242cm, 245cm), you can add all the numbers together and divide by the number of numbers in the set.

In this case, you would add 255cm + 242cm + 245cm = 742cm, and then divide by 3 (the number of numbers in the set) to get an average distance of 244cm.

You can also use this formula: (255 +242 + 245) /3 = 244

Answer:

1 work is scalar quantity

2 it si unit of work is joule

3The equation of caculate is work= Force× Displacement

1 power is scalar quantity

2 it si unit of power is watt

3 the equation of calculateis power= work \time

Answer:

The positive charges point away from each other

Explanation:

Why?

Arrows point away from the positive charge and toward the

negative charge.

Explanation:

Suppose that you rubbed a balloon with a sample of animal fur such as a wool sweater or even your own hair. The balloon would likely become charged and its charge would exert a strange influence upon other objects in its vicinity. If some small bits of paper were placed upon a table and the balloon were brought near and held above the paper bits, then the presence of the charged balloon might create a sufficient attraction for the paper bits to raise them off the table. This influence - known as an electric force - occurs even when the charged balloon is held some distance away from the paper bits. The electric force is a non-contact force. Any charged object can exert this force upon other objects - both charged and uncharged objects. One goal of this unit of The Physics Classroom is to understand the nature of the electric force. In this part of Lesson 1, two simple and fundamental statements will be made and explained about the nature of the electric force.

Perhaps you have heard it said so many times that it sounds like a cliché.

Opposites attract. And likes repel.

These two fundamental principles of charge interactions will be used throughout the unit to explain the vast array of static electricity phenomena. As mentioned in the previous section of Lesson 1, there are two types of electrically charged objects - those that contain more protons than electrons and are said to be positively charged and those that contain less protons than electrons and are said to be negatively charged. These two types of electrical charges - positive and negative - are said to be opposite types of charge. And consistent with our fundamental principle of charge interaction, a positively charged object will attract a negatively charged object. Oppositely charged objects will exert an attractive influence upon each other. In contrast to the attractive force between two objects with opposite charges, two objects that are of like charge will repel each other. That is, a positively charged object will exert a repulsive force upon a second positively charged object. This repulsive force will push the two objects apart. Similarly, a negatively charged object will exert a repulsive force upon a second negatively charged object. Objects with like charge repel each other.

The activity where to explore the relationships between the electricity field charged with particles and those of the hockey field

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answer

64 is C (c) 1-Bromo-3-methylbutane

63 is D

i is secondary ii is primary

The new volume of the gas after heating it to a temperature of 227°C is approximately 66.67 cm³.

It is determined using the ideal gas law, which states that the product of the pressure (P) and volume (V) is directly proportional to the product of the number of moles (n) and the temperature (T) in Kelvin. Given that the initial volume (V1) is 40 cm³, the initial temperature (T1) is 27°C (or 300 K), and the final temperature (T2) is 227°C (or 500 K), we can set up the equation: (P1 * V1) / T1 = (P2 * V2) / T2. Since the vessel is freely expandable, the pressure remains constant. Therefore, we can simplify the equation to: V2 = (V1 * T2) / T1. Substituting the values, we get the new volume of the gas.

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Answer:

Once static friction gives up, it allows the box to begin sliding across the floor, the frictional force acting on the box, is now the force of sliding friction exerted by the floor on the box

Explanation:

.

Copper is used in wiring and cookware because it can conduct electricity and heat well. The property which allow this  is call high conductance .

Conductivity is defined as a material's ability to conduct electricity or heat.

High Conductance  is the property of copper that allows it to do this . Copper is a metal and have free electrons which help in good conduction of heat and electricity .

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The rate of change of displacement is known as velocity. The rate at which velocity changes is called acceleration. Due to the fact that it includes both magnitude and direction, velocity is a vector quantity. Acceleration is likewise a vector quantity as it is only the rate of change of velocity.

Speed serves as the baseline for both velocities and acceleration measurements. Speed is a scalar quantity that measures the amount of distance traveled over a period of time. Acceleration and velocity are both vector quantities, which means they both employ magnitudes and a designated direction. The rate of motion of an object is measured by both speed and velocity. The fact that speed is a scalar quantity, nevertheless, means that it can be quantified.

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When the cart travels towards the origin, the magnitude of its exact position reduces with time.

The cart will be at -2 m (origin) 2s later.

When the cart travels towards the origin, the magnitude of its exact position reduces with time.

The formula of speed is given as

S = d/t ................. (1)

Where S = speed of the cart,

d = distance covered by the cart over a certain time.

t = time taken to cover the distance.

Where d the subject of the equation,

d = St ................. (2)

Given: S = 2.0 m/s, t = 2.0 s

Substitute into (2)

d = 2(2)

d = 4 m.

From the above, the cart covered a distance of 4 m in 2s.

The exact position of the cart = Initial position - distance covered

x' = x - d ............ (3)

Where x' = exact position of the cart 2s later,

x = initial position of the cart, and

d = distance covered by the cart in 2.0 s

Given: x = 2.0 m, d = 4 m.

Substitute into (3)

x' = 2.0 - 4

x' = -2 m.

Therefore the cart will be at -2 m (origin) 2s later.

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Answer:

a) The distance each child ran is approximately 0.232 m

b) The angular acceleration is 0.21\(\overline 6\) rad/s²

Explanation:

The given parameters of the merry-go-round are;

The mass of the merry-go-round, m = 240-kg

The diameter of the merry-go-round, d = 4.00 m

The number of children pushing tangentially on the merry-go round = Four children

The spinning rate of the merry-go-round, n = 2.14 rev/minute

a) Given that the force exerted by each child = 26 N, we have;

The total force applied by the four children, F = 26 N × 4 = 104 N

The tangential acceleration, \(a_t\) = F/m = 104 N/240-kg = 0.4\(\overline 3\) m/s²

The angular acceleration, α = \(a_t\)/r

Where, the radius of the merry-go-round, r = d/2

∴ r = 4.00 m/2 = 2.00 m

α = 0.4\(\overline 3\) m/s²/(2.00 m) = 0.21\(\overline 6\) rad/s²

We have;

ω² = ω₀² + 2·α·Δθ

The merry-go-round starts from rest, therefore; ω₀ = 0 rad/s

ω² = 2·α·Δθ

Δθ = ω²/(2·α)

n = 2.14 rev/minute

∴ ω = 2·π×2.14/60 rad/s ≈ 0.22410 rad/s

∴ Δθ = (0.22410 rad/s)²/(2 × 0.21\(\overline 6\) rad/s²) ≈ 0.11589 rad

Therefore, the angle each child ran, θ = 0.11589 rad

The distance each child ran = r·θ

∴ The distance each child ran = 2.00 m × 0.11589 rad ≈ 0.232 m

b) From part 'a' above, the tangential acceleration, \(a_t\) = 0.4\(\overline 3\) m/s²

Angular acceleration, α = \(a_t\)/r

∴ α = 0.4\(\overline 3\) m/s²/(2.00 m) = 0.21\(\overline 6\) rad/s²

The angular acceleration = 0.21\(\overline 6\) rad/s²

When light travels from one medium to another, its speed, direction, and wavelength can change, while its frequency remains constant. These changes are due to differences in the refractive indices of the two media.

As light travels from one medium to another, several of its properties change, including its speed, direction, and wavelength. The speed of light changes because the refractive index of each medium is different, which alters the velocity of the wave. The direction of the light may also change, a phenomenon known as refraction, as it enters a medium with a different refractive index. The amount of refraction depends on the angle of incidence, the angle between the incoming light and the normal line to the surface of the medium. Finally, the wavelength of the light may also change due to the refractive index of the medium, a phenomenon known as dispersion. This results in the separation of white light into its component colors when it passes through a prism or other refracting medium.

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Optical fiber is a type of cable that can be used to transmit data as light signals. It is made up of thin glass or plastic fibers that are bundled together to create a pathway for light to travel.

The refractive index of a material is the ratio of the speed of light in a vacuum to the speed of light in that material. It's a dimensionless number that's always greater than or equal to Critical angle

Critical angle is the smallest angle of incidence that allows total internal reflection to occur when light is traveling from a more dense medium to a less dense medium.

It is given by θc = sin⁻¹(n₂/n₁).

Explanation

When the refractive index of a material increases, the critical angle decreases.

Step 1: Let n1 be the refractive index of the fiber and n2 be the refractive index of the cladding.

Step 2: The critical angle θc is given by θc = sin⁻¹(n₂/n₁).

Step 3: Substitute the values to get θc = sin⁻¹(1.53/1.66) = 64.26°.

Therefore, the critical angle, in degrees, for total internal reflection is 64.26°.

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Answer:

The height of the image of the candle is 20 cm.

Explanation:

Given that,

Size of the candle, h = 12 cm

Object distance from the candle, u = -6 cm

Focal length of converging lens, f = 15 cm

To find,

The height of the image of the candle.

Solution,

Firstly, we will find the image distance of the candle. Let it is equal to v. Using lens formula to find the image distance.

\(\dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u}\)

v is image distance

\(\dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u}\\\\\dfrac{1}{v}=\dfrac{1}{f}+\dfrac{1}{u}\\\\\dfrac{1}{v}=\dfrac{1}{15}+\dfrac{1}{(-6)}\\\\v=-10\ cm\)

If h' is the height of the image. Magnification is given by :

\(m=\dfrac{h'}{h}=\dfrac{v}{u}\)

\(h'=\dfrac{vh}{u}\\\\h'=\dfrac{-10\times 12}{-6}\\\\h'=20\ cm\)

So, the height of the image of the candle is 20 cm.

Answer:

&3?.&.)/&282/8//8338/.)9

Explanation:

Andrew's displacement while visiting his grandparents is 35 miles to the east.

The displacement is the shortest distance travelled by the particle. It is the vector quantity which represents both the magnitude and direction.

Given Andrew drives to his friend's house, which is 60 miles to the east. After visiting, he travels 25 miles to the west to visit his grandparents.

The displacement will be

60 miles to the east - 25 miles to the west = 35 miles to the east

Thus, the Andrew's displacement is 35 miles to the east.

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Answer: it’s increasing in size and hydrogen fusion reactions are occurring in a shell around the core

The size of Arcturus is expanding, and its core is undergoing hydrogen fusion processes.

After a star exhausts its hydrogen fuel for nuclear fusion and starts to die, a red giant develops.

Here,

The brightest star in the constellation Boötes (the herdsman), Arcturus is a red giant star in the Northern Hemisphere of the Earth's sky. One of the brightest stars that can be seen from Earth is Arcturus.

At the conclusion of its existence, Arcturus will become a white dwarf, according to astronomers.

However, Arcturus is cooler than the sun, therefore a large portion of the red giant star's energy is released as heat. Arcturus really emits 215 times more heat than the sun does when this is taken into consideration.

The star is nearing the end of its existence. Arcturus, a red giant that has stopped fusing hydrogen in its core like the sun does, is now thought to be fusing heavier elements like carbon, according to astronomers.

Hence,

The size of Arcturus is expanding, and its core is undergoing hydrogen fusion processes.

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The distance between two adjacent nodes in terms of the wavelength λ of the standing wave is B) The distance between the two adjacent nodes = λ/2.

A standing wave is a wave that appears to be standing still, resulting from the interference of two waves of identical wavelength and frequency traveling in opposite directions.

In standing waves, the nodes are located at fixed points of the wave, with no displacement at the nodes. Standing waves are created by the superposition of two waves of the same amplitude and frequency traveling in opposite directions in a medium, resulting in a wave that appears to be standing still.

The distance between the two adjacent nodes is equal to half of the wavelength λ of the standing wave, according to the formula,

Distance between the adjacent nodes = λ/2.

Therefore, option B is correct.

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To repeat the same sound clip one after another, the method used is to concatenate the sound sample arrays. By concatenating the sound sample arrays, you create a new array that contains multiple copies of the original sound clip, effectively repeating it one after another. Therefore the correct option is b. Multiply the sound sample arrays by a scalar value less than 1.

When you want to repeat the same sound clip, one after another, you can achieve this by concatenating the sound sample arrays. Here's a step-by-step explanation:

1. Load the sound clip into MATLAB and convert it into a sound sample array.

2. Determine the number of times you want to repeat the sound clip.

3. Use the concatenation operator `[ ]` to join the sound sample arrays together.

4. Repeat the sound sample array as many times as desired by appending it to itself using the concatenation operator. For example, if you want to repeat the sound clip three times, you would write `[soundClip, soundClip, soundClip]`.

5. Store the concatenated sound sample array in a new variable.

6. If needed, you can then play the repeated sound clip using the `sound()` function in MATLAB.

By concatenating the sound sample arrays, you create a new array that contains multiple copies of the original sound clip, effectively repeating it one after another.

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Answer:

Explanation:

This is a 2D problem (parabolic) so we have to think that way. We have to split up the problem into its 2 dimensions to solve it. Think "y-stuff" and "x-stuff".

In the y-stuff category:

v₀ = 0 (initial upwards velocity is 0 since we are told the penny is thrown horizontally)

Δx = -10.0 m (this displacement is negative because the penny lands 10.0 m below the point from which it was thrown)

a = -9.8 m/s/s

t = ? (we need to find the time in this dimension so we can use it in the x dimension to find the displacement, our unknown)

In the "x-stuff" category:

v₀ = 7.25 m/s (this is given)

Δx = ???

a = 0 (acceleration in this dimension is ALWAYS 0)

t = (we will solve for this in the y-dimension and plug it in here).

In the y dimension:

Δx = v₀t + \(\frac{1}{2}at^2\) and plugging in from the y-dimension info:

\(-10.0=0t+\frac{1}{2}(-9.8)t^2\) which simplifies to

\(-10.0=-4.9t^2\) so

\(t=\sqrt{\frac{-10.0}{-4.9} }\) which, to 2 significant digits is

t = 1.4 seconds

Now we will do the same in the x-dimension, using t = 1.4:

Δx = v₀t + \(\frac{1}{2}at^2\) and filling in the x-stuff:

Δx = \(7.25(1.4)+\frac{1}{2}(0)(1.4)^2\) Notice that the stuff after the + sign goes to 0 cuz of the multiplication of 0, so what we are left with is another form of the d = rt equation:

Δx = 7.25(1.4) + 0 so

Δx = 1.0 × 10¹ m (That's rounded correctly to 2 sig dig's: 10 m from the base of the building).

Answer:

30.2

Explanation:

When fundamental frequency, length and tension is given then the wire's mass per unit length is 9.23 * 10 ^-3 g/m.

The fundamental frequency is defined as the lowest frequency of a periodic waveform. Fundamental frequency is defined as the average number of oscillations per second and is expressed in Hertz.

Given ; length , l= 0.54m Tension, T = 1373N

Frequency , f = 357 Hz

f= (1/2l)*(√T/m)

m = T/(4l² f²)

= 1373/(2*0.54² * 357²)

m= 9.23 * 10 ^-3 g/m

The wire's mass per unit length in grams/meter is 9.23 * 10 ^-3 g/m.

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To determine the initial speed required for a bullet fired at a 45° angle to hit the top of a 110m tower located 190m away, we can use the following kinematic equations:

Horizontal motion: x = v₀x * t
Vertical motion: y = v₀y * t - (1/2) * g * t²

Here, x represents the horizontal distance (190m), y represents the vertical distance (110m), v₀x and v₀y are the horizontal and vertical components of the initial velocity, t is time, and g is the acceleration due to gravity (approximately 9.81m/s²).

Since the angle of projection is 45°, v₀x = v₀ * cos(45°) and v₀y = v₀ * sin(45°). Since sin(45°) = cos(45°), we have:

x = v₀ * cos(45°) * t
y = v₀ * sin(45°) * t - (1/2) * g * t²

Substitute the values of x and y:

190 = v₀ * cos(45°) * t
110 = v₀ * sin(45°) * t - (1/2) * 9.81 * t²

Solve these equations simultaneously to find the initial velocity (v₀) required for the bullet to hit the top of the 110m tower./

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