math
Determine if the function below is continuous.

graph of a piecewise function, with 2 pieces. The first piece is a line that starts at negative infinity and goes through point (-4,5) and ends with an open dot at (1,0). The second piece is a line that starts with a closed dot at (1,-1), goes through point (2,1) and continues to infinity.

A. not continuous at x = 1
B. not continuous at x = 0
C. not continuous at x = -1
D. continuous

Answer:

When a passenger is sitting in a stationary bus it is under the law of inertia of rest that is the body resists any change in its state of rest.

Explanation:

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Personally, the barriers I face that interfere with my performance are:

These can all be addressed by

People can face various barriers that can interfere with their personal performance. Some of the common barriers that people face include:

Lack of motivation or direction: People may struggle with finding motivation or a clear direction for their goals, which can hinder their personal performance.

Lack of resources: People may face financial or other resource constraints that limit their ability to pursue their goals or develop their skills.

Physical or mental health issues: Physical or mental health issues can impact a person's ability to perform at their best, affecting their energy levels, focus, and overall well-being.

Personal or environmental distractions: People may be distracted by personal or environmental factors such as noise, social media, or family obligations that can interfere with their ability to focus on their goals.

To address these barriers, there are various plans that people can take, such as:

Setting clear goals: By setting specific and measurable goals, people can have a clearer sense of direction and motivation for their personal performance.

Seeking support: People can seek support from friends, family, or professionals to help them overcome resource or health-related barriers.

Developing healthy habits: Practicing healthy habits such as exercise, mindfulness, and good sleep hygiene can improve physical and mental health and increase energy and focus.

Managing distractions: People can create an environment that is conducive to their personal performance by minimizing distractions, prioritizing their time, and creating routines that support their goals.

Overall, addressing these barriers requires a combination of self-reflection, planning, and taking action to overcome obstacles and achieve personal growth and success.

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The current that is supplied by the batteries is 0.01333 Amp.

An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor. It is measured as the net rate of flow of electric charge through a surface or into a control volume.

Eeq = E1 + E2 ( batteries in series )

=> Eeq = 3+4.5 = 7.5 V

Veq = V1 + V2 + V3 ( resistances in series )

=> V3 = 7.5 - 2 - 3.5 = 2 V

=> current = V/R = 2/150 = 0.01333 Amp

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The magnitude of the damping coefficient is = 0.277 Ns/m

We can use the formula for the damped harmonic motion of a spring-mass system:

At t=0, the displacement of the egg is x = 0.300 m, and at t=5.00 s, the displacement has decreased to x = 0.100 m.

The angular frequency of the motion is:

w = sqrt(k/m) = sqrt(25.0 N/m / 0.0500 kg) = 10.0 rad/s

The equation for the amplitude of the motion at time t is:

A = x / cos(wt + delta) * e^(bt/2m)

At t=0, we have:

A = 0.300 m / cos(0 + delta) * e^(b0/20.0500 kg) = 0.300 m / cos(delta)

At t=5.00 s, we have:

A = 0.100 m / cos(10.0 rad/s * 5.00 s + delta) * e^(b5.00 s/20.0500 kg)

Dividing these two equations, we get:

0.300 m / cos(delta) / (0.100 m / cos(10.0 rad/s * 5.00 s + delta) * e^(b5.00 s/20.0500 kg)) = e^(b5.00 s/20.0500 kg)

Simplifying, we get:

cos(10.0 rad/s * 5.00 s + delta) * e^(b5.00 s/20.0500 kg) / cos(delta) = 3.00

Taking the natural logarithm of both sides, we get:

ln(cos(10.0 rad/s * 5.00 s + delta) * e^(b5.00 s/20.0500 kg) / cos(delta)) = ln(3.00)

Using the properties of logarithms, we can simplify this to:

ln(cos(10.0 rad/s * 5.00 s + delta)) + b*5.00 s / 0.0500 kg / 2 - ln(cos(delta)) = ln(3.00)

We can rearrange this equation to solve for b:

b = (2/5.00 kg) * (ln(3.00) - ln(cos(10.0 rad/s * 5.00 s + delta)) + ln(cos(delta)))

The phase angle delta is unknown, but it cancels out when we take the difference between the two equations for A. Therefore, we can choose any value of delta and still get the correct value of b.

Let's choose delta = 0 for simplicity. Plugging in the values, we get:

b = (2/0.0500 kg) * (ln(3.00) - ln(cos(10.0 rad/s * 5.00 s)) + ln(cos(0)))

b = 0.277 Ns/m

Therefore, the magnitude of the damping coefficient is = 0.277 Ns/m

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A 50.0-g hard-boiled egg moves on the end of a spring with force constant k=25.0N/m. It is released with an amplitude 0.300 m. A damping force Fx=−bv acts on the egg. After it oscillates for 5.00 s, the amplitude of the motion has decreased to 0.100 m.Calculate the magnitude of the damping coefficient b.

The pressure of the system, that the large piston produces a force of 37775 pounds is 3007.56 pound / in²

The following data were obtained from the question:

Pressure is defined as force per unit area as shown by the following formula

Pressure  = Force / Area

Inputting the value of the force and area, we have

Pressure of system = 37775 / 12.56

Pressure of system = 3007.56 pound / in²

Thus, from the calculation made above, we can conclude that the pressure of the system is 3007.56 pound / in²

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Answer:

13.6569 minutes

Explanation:

The eagle flies east for 4 minutes and then north for 4 minutes. This creates a right triangle with sides of 4 and 4. You can find the other side of a right triangle (hypotenuse) by using the Pythagorean theorem, a^2 + b^2 = c^2

C is the hypotenuse which is the longest side, and A and B are the other two sides. So C equals 4^2 + 4^2 = c^2. c=5.6569. So the total distance traveled is 4+4+5.6569=13.6569

The intensity increases by a factor of 16.

option D.

According to the inverse-square law of sound propagation, the intensity of a sound wave decreases proportionally to the square of the distance from the source.

I ∝ 1/r²

where;

when distance from the source is reduced by a factor of 4, the intensity of the sound wave becomes;

I ∝ 1/4²

I ∝ 1/16

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The ball exerts a force on the wall, and the wall exerts an equal and opposite force on the ball. So, the correct answer is A.

Newton's 3rd law of motion states that for every action, there is an equal and opposite reaction. The action is the force that the ball exerts on the wall, and the reaction is the force that the wall exerts back on the ball. When the ball hits the wall, it exerts a force on the wall. This force is equal in magnitude but opposite in direction to the force that the wall exerts back on the ball. This is why the ball reverses course. Therefore, option A is correct.

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--The complete Question is, Which of the following statements is true according to Newton's 3rd law when a ball hits a wall and reverses course?

A) The ball exerts a force on the wall, and the wall exerts an equal and opposite force on the ball.

B) The ball exerts a force on the wall, but the wall does not exert a force on the ball.

C) The wall exerts a force on the ball, but the ball does not exert a force on the wall.

D) The ball and the wall do not exert any forces on each other. --

The distance the ball was thrown is 52.22m by A quarterback throws a pass at an angle of 35° above the horizontal with an initial speed of 25 m/s. The ball is caught by the receiver 2.55 seconds later.

Every motion under constant acceleration is projectile motion

Angle above horizontal Ф = 35°, initial speed v1 = 25m/s , time 2.55s

Substituting value in the below equation

x=x₁ + (v₁*cosθ)(t)+1/2 *a*t²

a= 0 as acceleration in horizontal direction is zero

x= 25*cos(35)*2.55

x=52.22 m

Projectile motion is a form of motion in which object influenced when it is launched into the gravitational force from the surface of Earth along a curved path.

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Given: v = 341 m/s, t = 2.9 s.

Substitute into equation 2

x = 341(2.9)/2

x = 494.45 m.

The characteristics of sound waves should be the starting point for studying sound. Transverse and longitudinal waves are the two fundamental forms of waves, and they are distinguished by how they move through space.

Particles that are vibrating make up sound waves. These collide with other particles, causing them to vibrate, which allows the sound to escape the source. Your ear drums vibrate as a result of air vibrations, which allows you to perceive sound. This vibration is transformed into messages, which proceed to your brain via a nerve.

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Answer:

When unpolarized light is reflected off a non-metallic surface at a specific angle of incidence, the reflected light becomes polarized. This angle of incidence is known as Brewster's angle and can be calculated using the formula:

tan θp = n

where θp is Brewster's angle and n is the refractive index of the medium the light is passing into.

In this case, the light is passing from air (which has a refractive index of approximately 1) into water with a refractive index of 1.3. Therefore, we can plug in the values into the formula and solve for θp:

tan θp = 1.3

θp = tan^-1(1.3)

Using a calculator, we get θp = approximately 53.1 degrees.

Therefore, light reflected from water will be completely polarized at an angle of incidence of approximately 53.1 degrees.

Answer:

Therefore, the voltage required is 20 volts

Explanation:

To find the voltage that will send a current of 5 amperes through a bell circuit with a resistance of 4 ohms, we can plug in the values into the equation and solve for V: V=IR

V=(5A)(4Ω)

V=20V

The  frequency of the mass spring system would decrease by a factor of  3 if length of the spring is cut into one third.

Frequency is described as the number of occurrences of a repeating event per unit of time which is also occasionally referred to as temporal frequency for clarity, and is distinct from angular frequency.

The energy equation is shown as E = hν.

where E = energy,

h =  Planck's constant (6.626 x 10 -34 J · s),

and  v= frequency.

The energy equation shows  a direct relationship between frequency and energy because as frequency increases,  energy also increases.

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Answer:

the magnitude of the electrostatic force between these two charged particles is 4.32 x 10^-28 N.

Explanation:

F = k * (q1 * q2) / r^2

where:

F is the electrostatic force

k is the Coulomb's constant (9 x 10^9 Nm^2/C^2)

q1 and q2 are the charges of the particles

r is the distance between the particles

Plugging in the given values:

q1 = 8 x 10^-19 C

q2 = 4.8 x 10^-19 C

r = 1.2 x 10^-4 m

k = 9 x 10^9 Nm^2/C^2

we can calculate the electrostatic force:

F = (9 x 10^9 Nm^2/C^2) * (8 x 10^-19 C) * (4.8 x 10^-19 C) / (1.2 x 10^-4 m)^2

F = 4.32 x 10^-28 N

The electrostatic force between these two particles is therefore calculated to be **1.44x10⁻¹⁴ N**1 using Coulomb's equation of electrostatic force.

With a force proportional to the product of the charges and inversely proportional to the square of the distance between them, Coulomb's law states that like charges repel and opposite charges attract. There is a formula that may be used to calculate the force between two point charges. Charles-Augustin de Coulomb created Coulomb's law in 1785

The electrostatic force between two charges is inversely proportional to the square of the distance between them and directly proportional to the product of their magnitudes1.

The centers of the two tiny charged particles in this example are separated by a distance of **1.2x10⁻⁴ meter**, with charges of **8x10⁻¹⁹** and **4.8*10⁻¹⁹**, respectively.

F is the electrostatic force

k is the Coulomb's constant (9 x 10⁹ Nm²C²)

q1 and q2 are the charges of the particles

r is the distance between the particles

Plugging in the given values:

q1 = 8 x 10⁻¹⁹ C

q2 = 4.8 x 10⁻¹⁹C

r = 1.2 x 10⁻⁴ m

k = 9 x 10₉ Nm²/C²

we can calculate the electrostatic force:

F = (9 x 10⁹Nm²/C²) * (8 x 10⁻¹⁹ C) * (4.8 x 10⁻¹⁹ C) / (1.2 x 10⁻⁴ m)²

The electrostatic force between these two particles is therefore calculated to be **1.44x10⁻¹⁴N**1 using Coulomb's equation of electrostatic force.

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The battery Peukert constants, n and, are around 1.223 and 2.486, respectively.

Wilhelm Peukert, a German physicist, proposed Peukert's law in 1897, which quantifies a battery's capacity in terms of the rate of discharge. The battery's useful capacity reduces as the rate of discharge rises. The supplied capacity decreases as discharge rate increases.

C = I⁽⁻ⁿ⁾ * t * λ

log(C) = -n * log(I) + log(λ) + log(t)

log(C1) = -n * log(I1) + log(λ) + log(t1)

log(C1) = -n * log(25) + log(λ) + log(10)

Similarly, for the second measurement, we have:

log(C2) = -n * log(I2) + log(λ) + log(t2)

log(C2) = -n * log(45) + log(λ) + log(4)

log(C1) - log(C2) = -n * (log(25) - log(45)) + log(10/4)

Simplifying, we get:

log(C1/C2) = n * log(45/25) + log(2.5)

Substituting the values, we get:

log(25/45) = n * log(45/25) + log(2.5)

Solving for n, we get:

n = (log(25/45) - log(2.5)) / log(45/25)

n = 1.223

log(C1) = -1.223 * log(25) + log(λ) + log(10)

log(C1) = -1.223 * 1.39794 + log(λ) + 1

Solving for log(λ), we get:

log(λ) = log(C1) + 1.223 * 1.39794 - 1

log(λ) = log(25) + 1.223 * 1.39794 - 1

log(λ) = 0.39794

Therefore, λ = 2.486.

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During the earliest stages of the universe, the only things that existed were subatomic particles such as protons, neutrons, and electrons. These particles came together to form the first atoms, which were primarily hydrogen and helium.

The universe was also filled with a hot, dense plasma of particles and radiation, known as the cosmic microwave background radiation.

Hence, as the universe expanded and cooled, these atoms and radiation would play a key role in the formation of galaxies, stars, and the larger structures we see today.

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To calculate the final temperature of an air-metal mixture, we need to use the principle of heat transfer.

The heat transfer equation states that the heat gained by the metal is equal to the heat lost by the air. This equation can be written as:

mcΔT = mairCpΔT

To make a prediction of the final temperature, we need to consider factors such as the thermal conductivity of the metal and air, the specific heat capacities of the materials, and the heat transfer coefficients at the metal-air interface. Additionally, the shape and size of the metal object and the surrounding environment can affect the final temperature.

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Claims that if temperature is kept constant, the end result of both volume and pressure is constant. The new level is 1036 Pa, which is how this can be expressed.

So either a strong force or a strong force applied over a short area can cause a lot of pressure. When we stand up compared to when we are walking, more of our feet are in proximity to the earth. Pressure would be lower if there was more surface area in contact.

An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude. There are both living things and non-living objects in the concept of a force.

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The resulting angular speed of the flat, uniform circular disk is 0.237 rad/s.

Angular momentum is a fundamental concept in physics that describes the rotational motion of an object around an axis. It is defined as the product of the moment of inertia of an object and its angular velocity with respect to a chosen axis.

We can use conservation of angular momentum to solve this problem. The initial angular momentum of the disk is zero because it is stationary. The final angular momentum of the system (disk + person) is:

L = Iω

where I is the moment of inertia of the disk and person about the axis of rotation, and ω is the resulting angular speed of the disk.

The moment of inertia of the disk about its axis is:

I_disk = (1/2)mr²

where the disk's radius is r and its mass is m.  Substituting the given values, we get:

I_disk = (1/2)(150 kg)(5.44 m)² = 2226.24 kg·m²

The moment of inertia of the person about the axis can be approximated as:

I_person = mr²

where r is the distance from the axis to the person. Substituting the given values, we get:

I_person = (47.0 kg)(1.54 m)² = 109.64 kg·m²

The total moment of inertia of the system is:

I = I_disk + I_person = 2226.24 kg·m² + 109.64 kg·m² = 2335.88 kg·m²

The final angular momentum of the system is:

L = Iω

where ω is the resulting angular speed of the disk. Substituting the given values, we get:

(2335.88 kg·m²)ω = (197.64 kg·m²/s)(2.80 m/s)

Solving for ω, we get:

ω = (197.64 kg·m²/s)(2.80 m/s) / (2335.88 kg·m²) = 0.237 rad/s.

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Answer:

The resistance is 6 ohms

Explanation:

V = 12V

I = 2A

Use ohm's law:

R = V / I

R = 12V / 2A

R = 6 ohms

The angular speed of the object when your hand has risen to a height of y = 0.73 m above the floor is approximately 26.83 radians/s.

What is Mass?

Mass is a fundamental property of matter that quantifies the amount of matter in an object. It is a scalar quantity that describes the resistance of an object to acceleration when subjected to an external force. The mass of an object is a measure of the total amount of material or substance that it contains, and it is usually expressed in kilograms (kg) or other appropriate units.

The final potential energy is given by:

PE_final = m * g * y_final

where y_final is the final height of the object above the floor.

Setting the initial mechanical energy equal to the final mechanical energy and rearranging the equation, we get:

g = 9.8 m/[tex]s^{2}[/tex] (acceleration due to gravity)

(1/2) * 0.02 * [tex](15)^{2}[/tex]^2 + 0.5 * 9.8 * 0.22 = (1/2) * 0.02 * [tex]w_final ^{2}[/tex] + 0.5 * 9.8 * 0.73

w_final = sqrt((2 * ((1/2) * 0.02 * (15)^2 + 0.5 * 9.8 * 0.22 - 0.5 * 9.8 * 0.73)) / 0.02)

Plugging in the given values and solving for w_final, we get:

w_final ≈ 26.83 radians/s (rounded to two decimal places)

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The direction cosines of a→ - b→ are:

l_x = 1 / √46

l_y = 3 / √46

l_z = -6 / √46

The direction cosines of a vector can be found by dividing the components of the vector by its magnitude.

Here's how you can find the direction cosines of the vector a→ - b→:

Step 1: Subtract the vectors a→ and b→ to get a new vector, let's call it c→:

c→ = a→ - b→

In this case, a→ = 4i^ + 7j^ - 5k^ and b→ = 3i^ + 4j^ + k^, so we can subtract them component-wise:

c_x = 4 - 3 = 1

c_y = 7 - 4 = 3

c_z = -5 - 1 = -6

So, c→ = 1i^ + 3j^ - 6k^.

Step 2: Find the magnitude of vector c→ using the formula:

|c→| = √(c_x^2 + c_y^2 + c_z^2)

Substituting the values we found earlier:

|c→| = √(1^2 + 3^2 + (-6)^2)

|c→| = √(1 + 9 + 36)

|c→| = √46

Step 3: Divide the components of vector c→ by its magnitude to find the direction cosines:

l_x = c_x / |c→|

l_y = c_y / |c→|

l_z = c_z / |c→|

Substituting the values we found earlier:

l_x = 1 / √46

l_y = 3 / √46

l_z = -6 / √46

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the direction cosines of the vector a→ - b→ are (0.155, 0.466, -0.932).

we first calculate the vector a→ - b→:

a→ - b→ = (4i^ + 7j^ - 5k^) - (3i^ + 4j^ + k^)

= (4-3)i^ + (7-4)j^ + (-5-1)k^

= i^ + 3j^ - 6k^

Next, we find the magnitude of the vector a→ - b→:

|a→ - b→| = √(1^2 + 3^2 + (-6)^2) = √46

We then find  the direction cosines of the vector a→ - b→:

cos α = (1/√46) = 0.155

cos β = (3/√46) = 0.466

cos γ = (-6/√46) = -0.932

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The correct answer is (2) mechanical energy - electrical - chemical.

What is Energy?

Energy is a fundamental property of the universe that allows things to happen or work. It is the ability to do work, cause changes, or produce an effect. Energy can be found in many different forms, including kinetic energy (energy of motion), potential energy (stored energy), thermal energy (heat), electrical energy, chemical energy, nuclear energy, and more.

In an operating electric motor, electrical energy is converted into mechanical energy through electromagnetic interactions, resulting in the motor's mechanical motion. The mechanical energy is then used to perform work, such as turning a shaft or driving a load. In some cases, the motor may also generate electrical energy through processes such as regenerative braking or back-EMF (electromotive force) during deceleration or when acting as a generator.

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Answer:

The force between the wires used to connect the battery of a car to the motor can be calculated using the equation F = I*L, where F is the force, I is the current, and L is the length of the wires. In this case, the force would be calculated as F = 200A * 0.15m = 30N.

Using the length of the string and nodes, the wavelength of the string is 2m.

The relationship between wavelength, length of string, and nodes is a fundamental concept in physics, specifically in the study of waves and vibrations.

In the case of a vibrating string, the wavelength is the distance between two consecutive points in the wave that are in phase, meaning they are at the same point in their cycle of vibration. The length of the string is the distance between the two fixed endpoints of the string that are not vibrating.

The number of nodes, on the other hand, refers to the points along the string that are not vibrating. These points are also known as points of zero displacement. The number of nodes is determined by the frequency of the vibration, which is determined by the tension and mass of the string, as well as the length of the string.

The relationship between these three variables can be described by the formula:

wavelength = 2 x length of string / number of nodes

This equation shows that as the length of the string increases, the wavelength also increases, while the number of nodes decreases. Conversely, if the length of the string decreases, the wavelength also decreases, and the number of nodes increases.

In this problem, the nodes = 5

wavelength = 2 * 5 / 5

wavelength = 2m

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It promotes enjoyable experiences for both guests and hosts; It lessens the negative effects of tourism on the environment; It increases local residents' access to work and financial prospects; It promotes conservation by offering financial advantages in its direction.

The World Tourism Organization defines ecotourism as all forms of nature-based travel in which visitors' primary interests are in observing and appreciating the environment as well as the local cultures that are still practiced in natural settings.

Here are a few instances of ecotourism:

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The change in the system kinetic energy during the jump is 576.32 J.

Kinetic energy refers to the energy that an object in motion possesses due to its movement and is influenced by the object's velocity and mass.

The initial potential energy of the child-Earth system is given by mgh, where m = 37 kg is the mass of the child, g = 9.8 m/s^2 is the acceleration due to gravity, and h = 1.6 m is the height of the fence. Thus, the initial potential energy is (37 kg)(9.8 m/s^2)(1.6 m) = 576.32 J.

At the bottom of the fence, all of the initial potential energy is converted into kinetic energy. Since the child is at rest initially, the initial kinetic energy is zero. Using the law of conservation of energy, the final kinetic energy can be calculated as equal to the initial potential energy, or 576.32 J.

The change in kinetic energy during the jump is therefore:

Final kinetic energy - Initial kinetic energy = 576.32 J - 0 J = 576.32 J.

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The complete question should be:

A 37-kg child jumps to the ground from the top of a fence that is 1.6 m high. You analyze the problem using upward as the positive x direction. Taking x = 0 to be at the bottom of the fence, what are the initial potential energy of the child-Earth system and the change in the system kinetic energy during the jump? Enter your answers numerically separated by a comma.

If enough experimental data supports a hypothesis, it is considered a well-supported scientific theory, but it is not considered to be 100% true or proven. Scientific theories are always open to further investigation and revision based on new evidence. Therefore, option C ("Is proven 100% true") is incorrect.

Option A ("Is accepted as true until proven false") is also incorrect because scientists do not accept a hypothesis as true until it has been rigorously tested and supported by a large body of evidence. Even then, scientists recognize that any scientific theory is subject to revision or falsification if new data or evidence emerges that contradicts it.

Option B ("Becomes an Observational Law") is also incorrect because scientific laws are typically descriptive, rather than explanatory. They describe what happens in a given set of circumstances, but they do not explain why it happens. Hypotheses and theories, on the other hand, attempt to explain why certain phenomena occur, and they are supported by experimental evidence.

Therefore, none of the options are completely accurate, but the most appropriate answer is that the hypothesis becomes a well-supported scientific theory.

Answer:The period of a pendulum, as measured by an observer moving at a relativistic velocity with respect to the pendulum, can be calculated using the concept of time dilation from special relativity.

The formula for time dilation in special relativity is given by:

Δt' = Δt / sqrt(1 - (v^2 / c^2))

where:

Δt' is the time interval measured by the moving observer

Δt is the time interval measured in the rest frame of the pendulum

v is the relative velocity between the pendulum and the moving observer

c is the speed of light in vacuum

In this case, the relative velocity between the pendulum and the moving observer is 0.95c, where c is the speed of light in vacuum (approximately 3 x 10^8 meters per second). Let's assume the period of the pendulum as measured in its rest frame is 3 seconds.

Plugging in the values into the formula:

Δt' = 3 / sqrt(1 - (0.95c)^2 / c^2)

Simplifying the expression:

Δt' = 3 / sqrt(1 - 0.95^2)

Using a calculator to evaluate the square root and simplify further, we get:

Δt' = 3 / sqrt(0.0975)

Δt' = 3 / 0.3125

Δt' ≈ 9.6 seconds

So, the period of the pendulum, as measured by an observer moving at a speed of 0.95c (95% of the speed of light) with respect to the pendulum, would be approximately 9.6 seconds. This demonstrates the concept of time dilation in special relativity, where the observed time interval changes due to relative motion at relativistic velocities.

Explanation: