An equilateral triangle is a triangle with all three sides of equal length. All of the angles in an equilateral triangle are equal.

What is the measure of angle θ in the triangle shown?(Figure 1) Recall that the sum of the angles in a triangle equals 180∘.

Prism index of refraction is 2.40 if it is deflected by 22.6degrees by a 30-60-90 prism.

Refraction of light is perhaps of the most ordinarily noticed peculiarity, however different waves like sound waves and water waves additionally experience refraction. Refraction makes it feasible for us to have optical instruments, for example, amplifying glasses, focal points and crystals. It is likewise a result of the refraction of light that we can shine light on our retina..

Applying Snell's law at the point of refraction we get

μ₁sinθ₁ = μ₂sinθ₂

where μ₁ is refractive index of the prism,

μ₂ is the refractive index of the air,

sinθ₁ is the angle made by light with prism

and sinθ₂ is the angle made by light beam with air medium.

Now,we know that μ₂=1,θ₁ =22.6°,θ₂=90° - 22.6°=67.4°,μ₁=?

On putting we,get

=>μ₁ ˣ sin(22.6°)= 1 ˣsin(67.4°)

=>μ₁=sin(67.4°)/ sin(22.6°)

=>μ₁=0.923/0.384

=>μ₁=2.403

Hence, prism index of refraction is 2.403.

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The 2 springs should be connected in parallel so that the spring Constant for the combination is 1 Twice that of a single Spring.

How does Hooke's law work?

In accordance with Hooke's law, a principle of elasticity, for relatively minor deformations of an object, the displacement or size of the deformation is directly proportional to the deforming force or load

A system of two parallel springs connected in accordance with Hooke's Law is equivalent to a single Hookean spring with a spring constant of k. The formula that applies to capacitors linked in parallel in an electrical circuit can be used to determine the value of k.

If spring 1 and 2 have spring constants k1 and k2 respectively,

k is k1+k2

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Answer:

Gravitational.

Explanation:

In Earth, everything have a volume and mass, or downward force of gravity, which Earth's mass exerts on them.

Answer:

Many objects are designed specifically to store elastic potential energy, for example: The coil spring of a wind-up clock. An archer's stretched bow. A bent diving board, just before a divers jump

Explanation:

Answer:

Elastic Potential Energy is stored in elastic items.

A example of Elastic Potential Energy is a rubber band. When you stretch it, and it shoots off your finger. Where the rubber band gives off Elastic Potential Energy, is when you stretch it on your fingers, before you let it go.

A hockey puck can transfer kinetic energy by

When a hockey player hits the puck with their stick, they transfer kinetic energy to the puck.

The puck then moves across the ice, and if it collides with another object (such as the boards or another player's stick), some of the kinetic energy from the puck is transferred to that object through touch.

This demonstrates that kinetic energy can move from one item to another and that energy transfers from materials through touch.

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10% of more girls are likely to work than boys.

option A.

The percentage of girls who are more likely to work than boys are calculated as follows;

Total number of boys = 18 + 12 = 30

Number of boys who works = 18

Percentage = 18/30 x 100% = 60%

Total number of girls = 14 + 6 = 20

Number of girls who works = 14

Percentage = 14/20 x 100% = 70%

Difference = 70% - 60% = 10%

So 10% of more girls are likely to work than boys.

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The H-R diagram, also known as the Hertzsprung-Russell diagram is a graph that demonstrates the relationship between luminosity, temperature, classification, and spectral types of stars. This diagram shows the life cycle of stars. The life cycle of stars begins with their formation, followed by a sequence of changes leading to the death of a star. The location of a star on an H-R diagram enables us to determine the mass, temperature, and luminosity of the star.

The following can be determined from the location of a main-sequence star on the H-R diagram- The position of a star on the H-R diagram is determined by the star's mass. More massive stars are placed to the left of the diagram, while less massive stars are placed on the right. Temperature can be calculated by looking at where the star falls on the horizontal axis of the H-R diagram. The temperature ranges from cool to hot, left to right. By studying the location of the star on the vertical axis, we can determine its luminosity. The luminosity ranges from dim to bright, from bottom to top.

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TNT has a heat of combustion of -3406 kJ/mol compared to sugar's -5639 kJ/mol.

what is heat of combustion?

The quantity of heat released when a specific amount of a substance undergoes burning is known as the heat of combustion, also known as the calorific value or the energy value. In most cases, the terms "heat of combustion" and "calorific value" are interchangeable. Calorific value is the term used to describe the total amount of energy released during the complete combustion of a given mass of a substance in the presence of (an adequate amount of) oxygen under typical conditions of pressure and temperature.

TNT has a heat of combustion of -3406 kJ/mol compared to sugar's -5639 kJ/mol.

TNT is an explosive because it explodes more quickly due to its lower heat of combustion. Sugar is not explosive and will take a lot longer to heat up or burn.

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Answer:

When we have irregular objects, it may become very hard to calculate the volume of the object, as we actually can not use any simple equation to find it.

The mass is less tricky, just find a scale and wheight it, now we know the mass of the irregular object.

One way to measure the volume of the object is using water... how we do it?

Get some recipient with water, measure the height of the water.

Introduce your object into the water and totally submerge it, now the level of the water will rise. This is because as you introduce the object under the water, you are displacing up a given volume of water that has the same volume as the irregular object.

Now that you know the height of the water before and after you put your object, you can easily calculate the volume of water displaced, and that will be the volume of the object (the tricky part may be totally submerging the object if, for example, is wood and it floats, here you can use a thin wire to push it down but it will affect a little bit the measures.)

Answer:

v = 15.23 m/s

Explanation:

Given that,

Mass of a car, m = 1110 kg

Initial velocity, u = 21 m/s

Force,F = -8000 N

Time, t = 0.9 s

We need to find the final velocity of the car.

Force, F = ma

\(F=\dfrac{m(v-u)}{t}\\\\v-u=\dfrac{Ft}{m}\\\\v=\dfrac{Ft}{m}+u\\\\v=\dfrac{-8000\times 0.8}{1110}+21\\\\v=15.23\ m/s\)

So, the final velocity of the car is 15.23 m/s.

Carol's speed in kilometers per hour in order to get to her uncles house in 40 minutes by motorcycle is 36km/hr.

The average speed of a moving body can be calculated by dividing the distance moved by the time taken.

According to this question, the distance between Carol's house and her uncle's house is 24 km. The speed it will take her to get to her uncle's house in 40 minutes by motorcycle is as follows:

Average speed = 24km ÷ 40/60 hour

Average speed = 36km/hr

Therefore, Carol's speed in kilometers per hour in order to get to her uncles house in 40 minutes by motorcycle is 36km/hr.

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Incomplete question. Correct question read;

The motion of plates in Ridge-Trench Transform Fault is______________ .

Answer:

Transform faults

Explanation:

Remember, a Fault as used in geology refers to an area that has an abrupt decline in the volume of rock due to rock movements. So, as the name implies, transform fault describes the kind of motion in Ridge-Trench.

The absorption and reflection of waves, such as sound and light is called as wave interaction or wave behavior.

The absorption and reflection of waves, such as sound and light, are fundamental properties that determine how waves interact with different materials and surfaces.

Absorption occurs when a wave transfers its energy to a medium or material, causing the wave to diminish in intensity. The absorbed energy is converted into other forms, such as heat. Different materials have varying abilities to absorb waves, depending on their physical properties and composition. For example, materials with porous structures or soft surfaces tend to absorb sound waves more effectively, leading to reduced sound reflection.

Reflection, on the other hand, refers to the bouncing back of waves when they encounter a surface or boundary. When a wave encounters a reflective surface, a portion of the wave's energy is reflected back into the medium from which it originated. The remaining energy may be absorbed or transmitted through the material, depending on its properties. Smooth and polished surfaces are often good reflectors of both sound and light waves.

The balance between absorption and reflection determines the behavior of waves in various environments. It influences factors such as the audibility of sound, visibility of objects, and the quality of acoustics in architectural spaces. Understanding and controlling absorption and reflection properties is crucial in fields such as architecture, materials science, audio engineering, and optics.

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The potential difference across the lamp as calculated is 116.6 volts.

Given: Resistance (R) = 136 ohms, Power (P) = 1.00 x 10² W. We need to calculate the potential difference across the lamp. We know that; Power = (Potential Difference)² / Resistance.

We can write the above formula as, Potential Difference = √(Power x Resistance)By substituting the values in the above formula; Potential Difference = √(100 x 136)Potential Difference = √13600Potential Difference = 116.6 volts.

Therefore, the potential difference across the lamp is 116.6 volts.

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The Doppler effect can be used to measure radial motion, which refers to the motion of objects along the line of sight. In the context of stars, the Doppler effect allows astronomers to determine the radial velocity of stars, which is their motion towards or away from the observer.

When a star moves towards an observer, the observed wavelengths of the light emitted by the star are compressed, resulting in a blue shift. On the other hand, when a star moves away from an observer, the observed wavelengths are stretched, leading to a red shift. By analyzing the shift in the wavelengths of the star's spectral lines, astronomers can determine the star's radial velocity.

The Doppler effect is a valuable tool for studying the motion of stars, including the motion of binary star systems, the rotation of stars, and even the motion of galaxies. It allows astronomers to investigate the dynamics and kinematics of celestial objects and gain insights into their behavior and interactions.

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The kinetic energy of the ejected electron (photoelectron) is equal to the energy of the photon minus the work function (E required to eject the photoelectron).

The  process of final kinetic energy of the electron upon reaching the anode compare to its initial potential energy immediately after it has been ejected -

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Answer:

D

A machine can help decrease the input force and increase the output force.

Answer:

it'sD:)

Explanation:

Answer:

:) :::::::::::::::::::::::::::::::))))

The major ionic species present in an aqueous solution of FeCl3 is Fe³⁺.

Conventionally, the charge of an electron is thought to be negative; this charge is equal to and opposite to the charge of a proton, which is thought to be positive. Because the total number of electrons in an ion is more than the total number of protons, the net charge of an ion is not zero.

A negatively charged ion called an anion has more electrons than protons compared to a positively charged ion called a cation. Electrostatic force causes opposite electric charges to be drawn towards one another, causing cations and anions to attract one another and easily form ionic compounds.

Hence, The major ionic species present in an aqueous solution of FeCl3 is Fe³⁺.

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Answer:

See the explanation below.

Explanation:

Solving the first image question:

C ) The resulting force is defined by Newton's second law which tells us that the sum of the forces on a body is equal to the product of mass by acceleration. That is, there must be a force that acts on a body to produce an acceleration. If there is no acceleration it is because there are no external forces or developed by the body. And if there is no acceleration the body moves at a constant speed, in a straight line, so the response is C.

For the second image, we must remember that weight is defined as the product of mass by gravitational acceleration.

W = m*g

where:

W = weight [N]

m = mass [kg]

g = gravity acceleration [m/s²]

Now we have

m = 50 [kg]

ge = Earth gravity acceleration = 10 [m/s²]

gp = Distant planet gravity acceleration = 4 [m/s²]

We = ge*m

We = 10*50 = 500 [N]

Wp =gp*m

Wp = 4*50 = 200 [N]

Therefore the answer is D

For the third image, The mass is always going to be preserved, regardless of where the body or object is in space, its weight is the only one that changes since the gravitational force is modified. That is, the mass on the moon and on Earth will always be the same.

m = 70 [kg]

First, we must calculate the acceleration, by means of the following equation of kinematics.

\(v_{f} =v_{o} +a*t\)

where:

Vf = final velocity = 20 [m/s]

Vo = initial velocity = 0 (because stars from the rest)

a = acceleration [m/s²]

t = time = 4 [s]

20 = 0 + a*4

20 = 4*a

a = 5 [m/s²]

Now using Newton's second law which tells us that the total force acting on a body is equal to the product of mass by acceleration.

F = m*a

where:

F = force [N] (units of Newtons)

m = mass = 2 [kg]

a = acceleration = 5 [m/s²]

F = 2*5

F = 10 [N]

The body of Figure D, since a total force of 25 [N] to the left acts on it, in the rest of cases the force is zero or much less than 25 [N]

50 + 40 - 35 - 30 = F

F = 25 [N]

Answer:

29.41%

Explanation:

Given that,

In 1630 at the beginning of European settlement, about 425,000,000 hectares of the United States were covered with trees.

By 2017, the area covered by trees was reduced to 300,000,000 hectares.

We need to find the percentage decrease in the area covered by trees between 1630 and 2017.

The percentage decrease in any value is given by :

\(\%=\dfrac{300,000,000 -425,000,000 }{425,000,000 }\times 100\\\\=29.41\%\)

So, the percentage decrease in the area covered by the trees is 29.41%.

It's none of the above hope this helps

Answer:

It obeys Newton's third law of motion.

Explanation:

The experiment obeys Newton's third law of motion because when the air in the balloon is released, the air moves in the downward direction which is an action of the balloon so in the reaction, the balloon moves in upward direction   so both action and reaction forces are equal in magnitude but moves in opposite direction which obeys Newton's third law of motion.

The spring constant of the spring is 32 N/m

From the question given above, the following data were obtained:

The spring constant, K for the spring can be obtained as follow:

E = ½Ke²

16 = ½ × K × 1²

16 = ½ × K

Cross multiply

K = 16 × 2

K = 32 N/m

Thus, the spring constant is 32 N/m

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The actual volume of the cone is 160/3 cm3, and it increases from the center of the base to the tip. The form of a cone with a dotted line.

The amount of quantity that is gained by the solid or object when it is located in three-dimensional space is referred to as the volume of the solid.

The volume of the cone may be calculated using the formula below, which is as follows:

\(V=\frac{\pi r^2 h}{3}\)

The radius of the cone's base is denoted by the symbol (r), while the height of the cone is denoted by the symbol (h).

The picture of the cone, the volume of which has to be determined, is attached further down.

The height of the cone is 10 centimeters, while the radius measures 4 centimeters. Thus, enter these numbers into the formula shown above as,

\(& V=\frac{\pi(4)^2(10)}{3} \\& V=\frac{160}{3} \pi \mathrm{cm}^3\)

As this is the case, the precise volume of the cone in which the outline of a cone with a dotted line rises from the center of the base to the tip is 160/3 cm3.

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The Tully-Fisher relation, which correlates the rotation speeds of galaxies with their luminosities or masses, only works for spiral galaxies.

The Tully-Fisher relation is an empirical relationship between the rotation speed (velocity) of a spiral galaxy and its luminosity or mass. It suggests that there is a tight correlation between the two properties, meaning that galaxies with higher rotation speeds tend to be more luminous or have larger masses.

This relation is primarily applicable to spiral galaxies, as their rotation speeds can be accurately measured from the Doppler shifts of their spectral lines. Other types of galaxies, such as elliptical or irregular galaxies, do not exhibit the same well-defined correlation between rotation speed and luminosity/mass.

The Tully-Fisher relation provides valuable insights into galaxy formation and evolution, helping astronomers understand the link between a galaxy's structure, its rotation, and its overall properties.

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Answer:

Explanation:

Electric generators work on the principle of electromagnetic induction. A conductor coil (a copper coil tightly wound onto a metal core) is rotated rapidly between the poles of a horseshoe type magnet. The magnetic field will interfere with the electrons in the conductor to induce a flow of electric current inside it.

Answer: Aaron and john have 56 m of rope altogether. Aaron's rope is 3 times as long as john's rope. Then the length of Aaron's rope is 42m.

Explanation: To solve this problem, we need some basic mathematic problems relating variables.

                     \(L_A+L_J=56m\)        , where La is the length of Aron's rope   and Lb is that of John's rope.

                           \(L_A=3L_J\)

                      \(3L_J+L_J=56\\4L_J=56\\L_J=\frac{56}{4}=14m\)

                    \(L_A=3*L_J=3*14=42 m\)

Thus, from the above calculations, we can conclude that, the length of Aaron's rope is 42m.

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In sport, perfectionism is usually conceptualized as comprising four dimensions: perfectionistic strivings, perfectionistic concerns, parental pressure to be perfect, and coach pressure to be perfect