Write the equation of the plane with normal vector n = i _ k passing through the point (5,2, 8) in the scalar form ax + by + cz = d. (Express numbers in exact form. Use symbolic notation and fractions where needed. Give the equation in scalar form in terms of x, %, and equation:

(a)(i) To calculate the change in wavelength of light received by an observer on the Earth, we can use the formula for redshift:

z = ∆λ/λ = v/c

where z is the redshift, ∆λ is the change in wavelength, λ is the original wavelength, v is the velocity of the galaxy, and c is the speed of light.

Substituting the given values, we get:

z = ∆λ/6.2 × 10−7 m = 3.9 × 104 km/s / 3.0 × 105 km/s

Solving for ∆λ, we get:

∆λ = λz = 6.2 × 10−7 m × 3.9 × 104 km/s / 3.0 × 105 km/s

∆λ = 8.06 × 10−11 m

Therefore, the change in the wavelength of the light received by an observer on Earth is 8.06 × 10−11 m.

(ii) The wavelength of the light that is received by the observer on Earth can be calculated using the formula:

λ' = λ + ∆λ

where λ' is the new wavelength and λ is the original wavelength.

Substituting the given values, we get:

λ' = 6.2 × 10−7 m + 8.06 × 10−11 m

λ' = 6.2008 × 10−7 m

Therefore, the wavelength of the light received by the observer on Earth is 6.2008 × 10−7 m.

(b) The redshift of galaxies supports the Big Bang theory in two ways:

1. According to the Big Bang theory, the universe is expanding. As the universe expands, galaxies move away from each other, and their light is redshifted. The greater the redshift, the faster the galaxy is moving away from us. The observation of redshift in distant galaxies provides evidence that the universe is indeed expanding.

2. The Big Bang theory predicts that the early universe was much denser and hotter than it is now. This high density and temperature would have caused the universe to emit a lot of radiation, including light. As the universe expanded, this radiation would have cooled and stretched, leading to a cosmic microwave background radiation that fills the universe. The observed spectrum of this radiation is consistent with the predictions of the Big Bang theory. The redshift of distant galaxies provides further evidence for the Big Bang theory, as it is consistent with the idea that the universe was much denser and hotter in the past.

Answer:

Sorry for the bad drawing, as you have not specified whether is should be open switch or close I have drawn both

I hope it helps.

Total heat supplied to the system within this temperature range is 10040 J.

Heat refers to the energy that is released or absorbed during any chemical reaction.

Melting of the ice:

Amount of heat required to melt the ice is given by the equation: Q = mLf

Q is heat required, m is mass of the ice, and Lf is specific latent heat of fusion of water.

Q = (0.02 kg) × (3.34 × 10^5 J/kg)

Q = 6680 J

Therefore, the heat required to melt the ice is 6680 J.

Heating of the water:

Amount of heat required to raise the temperature of the water from 0°C to 40°C is given by the equation: Q = mcΔT

Q is heat required, m is mass of the water, c is specific heat capacity of water, and ΔT is change in temperature.

Q = (0.02 kg) × (4200 J/kg.K) × (40°C - 0°C)

Q = 3360 J

Therefore, heat required to heat the water from 0°C to 40°C is 3360 J.

Qtotal = Qmelting + Qheating

Qtotal = 6680 J + 3360 J

Qtotal = 10040 J

Therefore, total heat supplied to the system within temperature range is 10040 J.

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Answer:

a

 \(a = 21.7 \ m/s^2\)

b

\(F = 108.5 \ N\)  

Explanation:

From the question we told that

   The mass is  m  =  5 kg

    The initial speed \(u = 5 m/s\)

    The time taken to attain \(v = 70 \ m/s\) is  t =  3 s

Generally from kinematic equation we have that

     \(v = u + at\)

=> \(70 = 5 + a * 3\)

=>  \(a = 21.7 \ m/s^2\)

Generally  the force acting is mathematically represented

        \(F = m * a\)

=>      \(F = 5 * 21.7\)  

=>      \(F = 108.5 \ N\)  

149,597,871 kilometres

hope it helps...!!!

Answer:

The reaction absorbs energy from its surroundings.

Explanation:

An endothermic reaction is any reaction in which energy is absorbed by the reaction system.Thus implies that energy is withdrawn from the environment A cold pack's function is based on an endothermic chemical reaction.

The absorption of energy by the reaction system means that the environment feels cool in an endothermic reaction.This manifests in a decrease in the temperature of the cold pack.

Answer:

An animal that doesn’t eat meat is called a herbivore. An few examples would be cows, rabbits, horses, and goats.

:)

Answer:

a. Pure white

b. Pure black

c. Hybrid

The unknown resistor Rx to make the circuit "balance" is 6.08kΩ.

To determine the value of the unknown resistor Rx, we need to analyze the circuit shown in the figure. The circuit is said to be "balanced" when the voltage across the resistor RD is zero. This occurs when the ratio of the resistances in the two arms of the Wheatstone bridge is equal.

In this case, the coarse setting reading is 5 and the fine setting reading is 67. The ratio of the resistances in the two arms can be calculated using the formula: Rx/RD = (coarse setting)/(fine setting).

By substituting the given values, we have Rx/RD = 5/67. To find the value of Rx, we rearrange the equation as Rx = (5/67) * RD. Given that RD is 9.95kΩ, we can calculate Rx as approximately 6.08kΩ.

The circuit shown in the figure is not balanced.

To determine if the circuit is balanced or not, we need to check if the ratio of the resistances in the two arms is equal to the ratio of the resistances in the other two arms of the Wheatstone bridge.

If the ratio of the resistances is equal, the circuit is balanced. However, if the ratio is not equal, the circuit is unbalanced.

In this case, since the readings of the coarse setting and fine setting are given, we can calculate the ratio of resistances in the two arms of the bridge. If this ratio is different from the ratio of resistances in the other two arms, then the circuit is unbalanced.

Unfortunately, the given information does not provide sufficient details to determine whether the circuit shown in the figure is balanced or not.

The formula to find the unknown resistor RA is (RB + RC) × RD.

To find the unknown resistor RA, we need to consider the relationship between the resistances in the Wheatstone bridge. The general formula for the Wheatstone bridge is (RB + RC) / (RA + RD) = (VB / VA), where RB, RC, RA, and RD are the resistances, and VB and VA are the voltages across the corresponding arms of the bridge.

By rearranging the formula, we can solve for RA: RA = ((RB + RC) / (VB / VA)) × RD.

Thus, the formula to find the unknown resistor RA is (RB + RC) × RD.

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The model house on remote renewable energy will generate (20mmm + 30sss) kilowatt-hours of energy in 10 years.

Given:

Remote Renewable House= 2 windmills + 3 turbines

1 windmill generate mmm kilowatts-hours in a year

Therefore,

2 windmills will generate,

2×mmm=2mmm kwh in a year

In 10 years, 2 windmills will generate

10×2mmm=20mmm

1 solar panel generate sss kilowatt-hour each in 1 year

3 solar panels will generate yearly

3×sss=3sss

In 10 years, 3 solar panels will generate

10×3sss=30sss

Therefore, the total energy generated in the renewable model house is in 10 years

(20mmm+30sss)  kwhr

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Given :

Velocity of bullet, \(v_b=300\ m/s\).

Mass of bullet, m = 0.005 kg.

Mass of rifle, M = 5 kg.

To Find :

The recoil velocity of the rifle.

Solution :

Since, their is no external force is acting.

So, momentum of the system will be conserved :

Initial momentum = Final momentum

m(0) + M(0) = m(300) + Mv

\(v=-\dfrac{300m}{M}\\\\v=-\dfrac{300\times 0.005}{5}\\\\v=-0.3 \ m/s\)

Therefore, recoil velocity of the rifle is 0.3 m/s.

Hence, this is the required solution.

Answer:

The Egg

Explanation:

personally the Chicken who would lay the egg would have to come from an Egg itself, then It would have to grow up and then Produce an egg that will produce a chicken and so on.

Answer: Epidermis tissue.

Explanation: Layer of cells covering surface of entire plant, what it does is Acts as a barrier to fungi and other microorganisms and pathogens. the thin layer because it Allow for light to pass through, thereby allowing for photosynthesis in the tissues below

Answer:

Explanation:

Since work = magnitude of the force times the displacement, then

W = 43.0(5.00) so

W = 215 N*m

To solve this, we must be knowing each and every concept related to fundamental force. Therefore,  215 Nm is the work done on a bookshelf being pulled 5.00 m at an angle of 37.0° from the horizontal.

Nature is governed by four fundamental or universal forces. All stuff in the universe would disintegrate in the absence of these forces. Any pull or push that causes an item to change its physical condition is referred to as force (in terms of motion or deformity).

Mathematically, the formula for work can be given as

work = force × displacement× cos(Θ)

W = F × D × cos(Θ)

force= 43.0 N

Θ=37.0°

displacement=5.00 m

substituting all the given values in the above equation, we get

W =  43.0  × 5.00  × cos(37.0°)

W = 215 Nm

Therefore,  215 Nm is the work done on a bookshelf being pulled 5.00 m at an angle of 37.0° from the horizontal.

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Answer:

blue and purple light

Explanation:

Light waves have very, very short wavelengths. Red light waves have wavelengths around 700 nanometers (nm), while blue and purple light have even shorter waves with wavelengths around 400 or 500 nm.

A 2.0-kilogram cart traveling at a constant speed in a horizontal circle of radius 3.0 meters. The magnitude of the centripetal force of the cart is 24 newtons. The speed of the car is 6 m/s. Thus, Option A is the correct answer.

To find the speed, the given values are,

Mass m = 2 Kg

Radius r =3 meters

Centripetal force = 24 Newtons.

A centripetal force is the force which is made up of two Latin words centrum which means center and peterum which means to seek.

It is defined a force which make a body to follow a curved path. The direction of this force is always orthogonal to the body's motion and it is always towards the fixed point which is instantaneous center of the path's curvature.

Centripetal force is expressed according to the formula;

F = mv²/r

m is the mass of the body

v is the speed of the cart

r is the radius

Substituting the values into the formula and get v,

24 = 2v²/3

24×3 = 2v²

72 = 2v²

v² = 72/2

v² = 36

v =√36

v = 6m/s

Hence, the speed of the cart is 6m/s. Thus, Option A is the correct answer.

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Answer:

C. a disturbance that travels through a medium with a transfer of energy and without a transfer of matter

Explanation:

A wave is any disturbance that transfers energy from one location to the other via a substance called medium. It is important to note that a wave only conveys energy and not matter. For example, sound wave is a type of wave that carries sound energy from one place to another via mediums such as water, air etc.

Hence, according to this question, a wave can be described as a disturbance that travels through a medium with a transfer of energy and WITHOUT A TRANSFER OF MATTER.

Answer:

The tangental acceleration of the flywheel of  radius 2.12 cm with a final angular velocity of 1820 rev/min and an angular acceleration of 16.2 rad/s is 0.34 m/s².

This is the rate of change of tangental velocity of an object in circular motion.

To calculate the tangental acceleration, we use the formula below.

Formula:

Where:

From the question,

Given:

Subsitute these values into equation 1

Hence, The tangental acceleration of the flywheel of  radius 2.12 cm with a final angular velocity of 1820 rev/min and an angular acceleration of 16.2 rad/s is 0.34 m/s².

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A discordant igneous intrusion cuts across bedding planes. Here is the detailed explanation of the given question:Explanation:The Discordant igneous intrusion is the formation of an igneous rock mass when magma is injected into a host rock and cools there.

This form of igneous intrusion does not conform to the stratification or layering of the existing rock mass because it cuts across it.Therefore, a discordant igneous intrusion cuts across bedding planes.Option (a) is correct. It is the only option that describes the features of discordant igneous intrusion. Hence, the correct answer is option (a).

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Dropping a ball of dough onto a kitchen counter, its energy store of potential energy is converted into kinetic energy as it falls. Upon impact, the kinetic energy is converted into potential, thermal, and sound energy.

When a ball of dough is dropped onto a kitchen counter, there is a change in the energy store of the dough. Initially, the dough has potential energy due to its position above the counter. As the dough is dropped, this potential energy is converted into kinetic energy, or energy of motion. As the dough falls, it gains speed and thus increases in kinetic energy.

When the dough strikes the counter, the kinetic energy is converted into a combination of potential energy and thermal energy. The dough compresses and deforms upon impact, increasing its potential energy. The compression and deformation also generates heat, which increases the thermal energy of the dough. A portion of the kinetic energy is also converted into sound energy as the dough makes contact with the counter.

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Answer: the stopping distance for an initial speed of 15 m/s with a constant deceleration of 3.9 m/s² is approximately 57.7 meters.

Explanation:

To calculate the stopping distance, we need to use the following equation of motion:

v² = u² + 2as

where:

v is the final velocity (in this case, it is 0 because the car stops)

u is the initial velocity (15 m/s)

a is the deceleration (-3.9 m/s²)

s is the stopping distance (what we want to find)

Substituting the given values in the equation, we get:

0² = 15² + 2(-3.9)s

Simplifying and solving for s, we get:

s = (15²) / (2 × 3.9) ≈ 57.7 meters

looking at the graph,

1) Displacement includes direction

Displacement from 8s to 16s = 15 - 6 = 9

Displacement fbetween 16s and 24s = 0 - 15 = - 15

Displacemet between 8s and 24s = 9 - 15

Displacemet between 8s and 24s = - 6m

2)

Distance does not include direction

from 8s to 16s,

distance travelled = 15 - 6 = 9 m

From 16s to 24s,

distance travelled = 15 - 0 = 15

Total distance between 8s and 24s = 9 + 15

Total distance between 8s and 24s = 24 m

Wavelength is a measure of the distance between two consecutive peaks or troughs of a wave. It is an important property of light and other electromagnetic radiation, and can be used to calculate their energy.

The most common way to calculate the wavelength of radiation is using the equation

c=λν, where c is the speed of light (3 x 10^8 m/s), λ is the wavelength and ν is the frequency.

Frequency is the number of wave peaks that pass a certain point per second, and can be measured in hertz (Hz).

To calculate the wavelength, start by finding the frequency of the wave. This can be done by counting the number of wave peaks that pass a certain point in one second, or measuring the time between two wave peaks and dividing one second by that time. Once the frequency is known, plug it into the equation c=λν to calculate the wavelength.

For example, if the frequency of a wave was measured to be 10 Hz, the wavelength can be calculated by solving the equation c=λν, giving λ = 3 x 10^8/10 = 3 x 10^7 m.

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As the rollercoaster moves from point A to point B, the correct answer is option c: The kinetic energy increases and the potential energy decreases.

At point A, the rollercoaster is at its highest position, which corresponds to the maximum potential energy and minimum kinetic energy. As the rollercoaster moves downwards towards point B, it gains speed and its height decreases.

This results in a decrease in potential energy since the height is decreasing. At the same time, the rollercoaster's speed increases, leading to an increase in kinetic energy.

The conservation of energy principle states that the total mechanical energy (the sum of potential energy and kinetic energy) of a system remains constant in the absence of external forces.

In this case, as the rollercoaster moves from point A to point B, the decrease in potential energy is equal to the increase in kinetic energy, keeping the total mechanical energy constant.

Therefore, the correct answer is option c: The kinetic energy increases and the potential energy decreases.

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Troposphere, stratosphere, mesosphere, thermosphere and exosphere.

Earth's atmosphere has five major layers.

From lowest to highest, layers are the troposphere, stratosphere, mesosphere, thermosphere and exosphere.

a) What are the conditions in the troposphere?

The atmospheric temperature descends upward with a slope of ~10 K km−1 for dry air and ~7 K km−1 for wet air in troposphere.

The temperature of troposphere decreases with an increase in height.

B) What sort of temperatures would she experience in the stratosphere? What other layer is found within the stratosphere?

The temperature in the stratosphere ranges from- 60° F at the troposphere boundary to -5°F at the top.

The temperature increase is due to the ozone layer that absorbs ultraviolet light from solar radiation.

C)What sort of temperatures would she experience in the mesosphere?

The temperature in the mesosphere ranges from -2.5°C to -90°C

The temperature decreases because of a decrease in the absorption of penetrating solar radiation.

The atmosphere gets cooler with an increase in altitude because an increase in distance from the Earth's surface.

D)What sort of temperatures would she experience in the thermosphere? What other layer is found within the thermosphere?

4,500°F is the temperature of thermosphere.

Temperatures climb sharply in the lower thermosphere , then level off and hold fairly steady with increasing altitude above that height.

Temperatures in the upper thermosphere can range from about 500° C (932° F) to 2,000° C (3,632° F) or higher.

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With the use of Ohm's law formula and some assumption, the answers are

(a) V2 = 30v

(b) I2 = 5 A

(c) R1 = 1 Ω

(d) R2 = 6 Ω

(e) RT = 4 Ω

Current can simply be defined as the rate at which charges flow in a conducting material. It is measured in Ampere.

From the given circuit,

a) V2 and V3 are in parallel, so they will have the same voltage. The voltage dropped in V1 should be taken away from the total voltage. That is,

V2 = VT - V1

V2 = 40 - 10

V2 = 30v

b) The current produced from the battery is assumed to split equally on R2 and R3. Therefore, I2 = 5 A

c) The total current will flow through I1. That is,

I1 = 10 A

Using Ohm's law V1 = I1 × R1

10 = 10 × R1

R1 = 10/10

R1 = 1 Ω

d) From Ohm's law, V2 = I2 × R2

30 = 5R2

R2 = 30/5

R2 = 6 Ω

e) By using Ohm's law again

VT = IT × RT

40 = 10 × RT

RT = 40/10

RT = 4Ω

Therefore, The resistance in R1, R2 and R3 are 1Ω, 6Ω and 6Ω

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