Other have explained the frame of reference part but let's look at the square part.

The reason is the square of the velocity is at high speed you need to apply the force for a longer distance.

(1) W = F *s

where W =Work (transferred enerergy), F = force and s= applied distance

(2) s = v *t

Where v is the speed and t is the time.

(3) a= F/m => F =m *a

where a is the acceleration and m is the mass.

(4) v= a * t => t= v/a

Consider if you an object with a mass of 1 kg that you accelerate with a force of 1N that means the acceleration is 1m/S

If you start at a speed of 0 the speed after 1 second is 1m/s so the average speed for that second is(0+1)/2= 0.5 m/s and you only travel 0.5m That is the distance you apply the force. So the work is 1 N * 0.5m = 0.5 Joules.

If you start at 10m/s the speed after 1 second is 11m/s so the average speed is (10+11)/2=10.5m/s . So you traveled 11.5m. That means the work is 1 N * 11.5m = 11.5 joule

If we just have constant acceleration 0 to v the average speed is v/2.

Combine 1 and 3 and we get (5) W= m *a *s

If we use 2 with the average speed you get (6) s= v/2 *t

Combine 5 and 6 and we get (7) W= m *a * v/2 *t

Combine 7 with 4 and we get W= m *a * v/2 * v/a = m * v/2 *v * a/A = m * v/2 *v = (m * v^2)/2

So the square is a result of that you need to apply the force over a longer and longer distance the higher the speed is and the work gets larger and larger.

It can also explain what we see in a different frame of reference. When a car slowed down from 120 to 90 by applying breaks the force is applied from the road. So from your point of view, the car change is speed but pushing on something that moved backward at a speed of 120 relatives to you. You need to include that the ground is not stationary compared to you.

For it to do less work whilst slowing down it needs to apply force to something that moves at the same speed as you.

You can compare this to you walkin' in a train where you start waking forward in the direction of the moment. Your feet apply the force relative to the train so the distance is short. But at the same time, the train needs to apply the same force relative to the ground, if it did not it would slow down.

Compare it to walking in a canoe on the water next to the dock. It has very little friction from the water and the mass close to you. If you stand up and walk forward you push the canoe backward. When you reach the front of the canoe you have walked a short distance relative to the dock. So if you use the canoe as the frame of reference you need to consider how it moves relative to the dock. You moving in a train change it a moment too but it will be a lot less compared to you because its mass is many times higher than you

So if you jump off the train and hit the ground, the difference in energy from you walking forward versus stationary when you hit the ground from the work the train needed to do to keep its speed constant.

So it all works out regardless of the frame of reference. You just need to consider everything like what you apply a force relative to and what your action has on the frame of reference

How can a single ear drume in you ear hear multiple frequencies at the same time?

Sound is a pressure in air and when the pressure waves from multiple sources interact you get the sum of all those waves. So the pressure wave that reaches your ear is a combination of all sound sources and results in a single pressure on your eardrum at each moment in time. Over time the eardrum move following the combined pressure of all the sound waves.

If a force a speaker membrane to move just like your eardrum did it will produce a pressure wave just like the one that reached your ear and you will hear the same sound.

Mathematically you can show that any periodical movment that is just not a single sine wave can be described as the sum of multiple sine waves. So unless it will perfectly move as just a single sine wave it will produce multiple frequencies. You can show the same thing for no period signals but then you can never have a single frequency, if you did it would be a periodic sine wave.

There is multiple way to calculate a square root https://en.wikipedia.org/wiki/Methods_of_computing_square_roots The simples to understand is iterative methods. The general idea is make a guess and then improve it.

without using any specific algorithm let's try to calculate the square root of 26. Let's find a to large and to small number and test the average of them. If the average is to small replace the smaller number, if it is to larger replace the larger

Let's first guess at 5 5 ^(2) =25, that is too low lets call it S

The second guess at 6 6^(2) =36 is to large let's call it L .

Let's try the midpoint (S+ L)/2 =(5+6)/2 = 5.5 and 5.5^2 =30.25 which is to large so replace S with it.

The next average is (5+5.5)/2=5.25 Let's repeat it in the table below. I rounded all numbers to 6 or less decimals

S        L        (S+L)/2        ((S+L)/2)^2
5        6           5.5            30.25        To large
5        5.5         5.25           27.5625      To large
5        5.25        5.125          26.265625    To large
5        5.125       5.0625         25.628906    To small
5.0625   5.125       5.09375        25.946289    To small
5.09375  5.125       5.109375       26.105716    To large
5.09375  5.109375    5.101563       26.02594     To large
5.09375  5.101563    5.097659       25.986102    To small
5.097659 5.101563    5.099611       26.006032    To large
5.097659 5.099611    5.098635       25.996079    To small
5.098635 5.099611    5.099123       26.001055    To large
5.098635 5.099123

Let's stop at this point. We can see that the square root is in between 5.098635 and 5.099123 so we know it to be two decimals as 5.09. We could continue this forever and get closer and closer. Many roots like this will have an infinite number of decimals so wee needs to stop.

The algorithm above is not an especially efficient one because it converges quite slowly but it is a good example of an iterative way do numerical find a solution to an equation.

The guesses I made were so you quickly get some decimals correctly. But you can pick a conservative guess like 1 and the number /2 that will work for any number we look for a root for that is larger than 1

Newton-Rapson https://en.wikipedia.org/wiki/Newton%27s_method method is faster, but exactly why you choose that formulais a lot harder to explain.

Let's call x the guess and a number we look for the root of in this case a=26. The next guess can be calculated 1/2( x + a/x) let's start with 5 and calculate the next number as 1/2 (5+26/5) = 5.1 . The next step is 1/2 (5.1+26/5.1)

I added a space among the decimal at the point it is longer accurate

5
5.1
5.099019 6078431372549019607843137254901960784313725490196078431372
5.09901951359278 57010906650681807043140270913210506275188406452756
5.099019513592784830028224109022 8563911005788636011794938296893309
5.099019513592784830028224109022781989563770946099596407584970804 9


The square root is
5.0990195135927848300282241090227819895637709460995964075849708044...

The number of accurate decimals doubles in each step. That is a very efficient way to find a square root of a number

>Light minutes, on the other hand, are a unit of time, not distance.

Light minutes are a unit of distance just like a light year is. In SI base units are speed is in m/s and time is in seconds so speed * time =m /s * s =m

A light second is exactly 17,987,547,480 m

That is because the speed of light is by definition 299,792,458 m/s so just multiply that by 60 seconds and you ger the distance above. If we improve measurement it is the meter that changes not the speed of light. A meter is the distance light travels in 1/299,792,458 of a second in a vacuum.

The buttons work by sending out two tones, the combination is unique for each key. The equipment on the other end interprets the tone.

You can see the tone and how they are used at https://en.wikipedia.org/wiki/Dual-tone_multi-frequency_signaling#Keypad

The same for trips to Mars. If we have an experiment that tries to detect life on anybody we do not what contamination from the earth can give a false positive.

it is the derivate of y in regards to x.

if y =x^2 the dy/dx = 2x

The second derivative is d^2 y /dx^2 =2

You could derivate in regards to another variable dy/dt = 0 because y do not depend on t.

The notation is common when you have a function that depends on multiple variables as was created by Leibniz in 1675

Multivitamins can't target part of the body. Vitamins and medicine will be distributed all around the body, medicine might have been designed so they interact with a single part but it will go everywhere.

There is an exception to going everywhere that is crossing the blood-brain barrier, so stuff might reach muscles but not the brain.

The devices that scan the luggage with X-rays are shielded so very little leaks out. They are large metal boxes with a scanner inside and the wall of them absorbs X- rays. The ray is also going in one direction, up or down so not toward where the baggage enters and exits.

The curtains the luggage passes through are rubber with lead in them and are X-ray shields. You have multiple of them per side if I am not mistaken.

So the number of X-Rays that leak out is minimal.

We do not use a small contained unit like that for humans because it would be quite impractical and not a great experience for the patient. We use larger protective boxes that fit humans and are not claustrophobic this is whole rooms

>Spacecraft need to eject mass to move forward. Essentially they are pushing off parts of themselves, and leaving it behind.

They do not need to. Light sails exist and have been used by some satellites. So you can just let the light from the sun push you.

To feel the forces of the water do a belly flop by jumping from just above the water's surface and you will notice the water can have quite a high force on you and take time to move away

Space is not a perfect vacuum, it is just a system with very low pressure. You will find atoms even between galaxies.

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The solar wind is particles that is ejected from the sun and move away from it in all direction in space. There is very little interaction between the particle not like on earth where there is quite a lot of interaction. So wind is a bit of a metaphor. The solar wind is more like the sun spraying out particles in all directions.

The solar wind does interact with other stuff in the solar system. It is in large part charged particles and some will be redirected by earth's magnetic field. Northern/Southern light is a result of the interaction with the solar wind and the top of our atmosphere

It is not a fraction of an inch, it is a logarithmic scale based on the number of time you draw it through the die that reduces the diameter with the same percentage in each step

The dimater will be 0.005 * 92 ^((36-n)/39)

Should is subjective. The origin of the system is from how the wires are made.

You can make a wire but draw to conical holes that rescue the wire size it is called,https://en.wikipedia.org/wiki/Wire_drawing The wire gets thinner and longer in each step.

The AWG system is based on the number of times you draw it through a die to get the wire.

Each time you draw it in the system the diameter reduces to 92% of the previous.

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I am not sure why the system starts with a Nr. 0000 at 0.46 inches in diameter and end with Nr. 36 awg at 0.005 inches in 40 steps and not 1 to 40 but that is the way it was done

A " birthrate has declined by 20%" do not mean there is not an increase in population, if it was high enough to begin with you can still have an increase it is just slower.

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Even if you have a birth rate that over a long time would result in a stable population it can still increase. Let say it would end with 10 000 births and 10 000 deaths per year. The population is 10 000 x average lifespan, so if the life expectancy increases the population can grow even if the birth rate is constant.

The average human lifespan on earth during the 20th century increased from 48 to 74 years for men, and from 51 to almost 80 years for women. that is close to 35% increase for both. That is a major part of the population increase on the earth

But there is another major factor for population density other than birth rate is migration both inside and between countries.

So even if the birth rate in your country would result in minimal growth migration from other countries can increase the population.

The general trend today is people moving to large cities from the countryside and smaller cities. So if you live in a large city you will see a population increase that primarily is a result of people moving there. The change is not primarily because if birth but migration.

If you were out in the countryside you would likely see a population decrease. It is a result of people moving to cities. Because young people are more likely to move than old the demographics can become quite uneven and as a result, the number of deaths can be a lot higher than the number of births.

On the north pole, there is only south, the is no east-west or north. Talk instead of what latitude line the sun is over.

For any 12 hours period, the sun will move 180 degrees The angular speed of the sun is 15 degrees per hour regardless of where on earth you and what time of year. The sun's angular movement is a result of earth's rotation and it orbits around the sun, not the location on earth

Technically it changes a tiny amount because the time between two solar noons are 24 hours +-30s because the orbit is the ecliptic. The rate it move close to the horiont changes a bit to because of atmospheric refraction.

But the general idea of the angular speed of the sun in the sky is very close to 15 degrees per out is very close to correct for any location and day on earth, That is when the sun is in the sky.

The sun will move in a line very close to a line from due east to due west, directly overhead. It is "close to" not "exactly in".

The problem is the equinox is a moment in time it is not a day. If you look at https://en.wikipedia.org/wiki/Equinox you can see the time was in March 20 15:33 UTC and on September 23 is was 01:04 UTC, those time are rounded to minutes. The day of the equinox is the day it occurs not that is during the whole day.

So it is only one moment in time the equator is in line with the ecliptic.

If we assume the rate of change of axial tilt is constant we can calculate the cage during the day, I believe this is an approximation because of the elliptic orbit of Earth but it is a good enough approximation for my point.

The change in a year is 4 x 23.4 degrees = 93.6 degrees. Per day it is 93.6/365 =0.27 degrees. So on the day of the equnox the sun is up close to 12 hours and the equator change relative to the ecliptic is 0.27/2 =0.135 degrees.

So during the time the sun is up on the day of the equinox, the equator will change its tilt relative to the ecliptic by around 0.14 degrees. So even if the sunrise is exactly due west it will set a small bit off due west. The difference can be even higher because for half of the equator it will be night when the equinox occurs so will be off it even before the day start or before depending on you relative direction, let's double the error and ger a max error of around 0.3 degrees

So if due east and due west mean within 0.3 degrees then the sunrise and sunset direction are correct. If it is 0 error then it is only one spot on earth it is true for sunset and one for sunrise, the spots when the events are on the moment of the equinox.

James web have looked at exoplanets. But it will at best see them as a few pixels what can be done is to analyze the spectrum of the atmosphere. That way we can detect what gases are there and we live free oxygen is an indicator of life. https://www.sciencenews.org/wp-content/uploads/2022/09/090122_lg_jwst_feat-1030x580.jpg is a exoplanbet it observe. It is a gas gignat 20x the mass of Jupiter. This is the resolution it can get of a expolnaet

Planets are tiny and very far away. Here can you see Pluto from Hubble and New Horizons The max resolution of an optical system depends on the diameter of the aperture. For Hubble, it is 2.4 meters, and James Webb has 6.5 meters let's call that 3x the diameter. So Jamers Webb could only manage 3x the resolution of Pluto and compared to any exoplanet Pluto is large in the sky. This is ignoring any effect of the longer wavelength light that James Webb observe that reduces the increase relative to Hubble. New Horizons was very close to the Plut so it can have a lot higher resolution

The image from Jamew Webb and another telescope you see in the sky are surprisingly large. An extreme example is https://apod.nasa.gov/apod/image/0612/m31abtpmoon.jpg the moon and the Andromeda galaxy to scale. It might be 2.4 million lightyears from us but is a galaxy of billions of stars. It is the second largest thing in the sky after out own galactic core, the milky way. The sun are the same size of the moon in the sky. You can see the center of it with your naked eye as a white fuzzy area. It is hard to see because it is dim not because it is small.

IF you look at a image https://www.nasa.gov/image-feature/goddard/2022/nasa-s-webb-reveals-cosmic-cliffs-glittering-landscape-of-star-birth it is not the size of planets is is a gas cloud man

>Called the Cosmic Cliffs, Webb’s seemingly three-dimensional picture looks like craggy mountains on a moonlit evening. In reality, it is the edge of the giant, gaseous cavity within NGC 3324, and the tallest “peaks” in this image are about 7 light-years high.

The closes star to earth, except for our sun, is 4.3 light years. Pluto is 0.00055041 light years from us. Our solar system would be in around 1 pixel in that image. The image width is enough to include another star system

The Cosmic Cliffs is a part of https://en.wikipedia.org/wiki/NGC_3324 that is 11 arcmin in size 1 degree = 60 arcminute so 11 arcmins =11/60 =0.18 degrees wide The moon is 0.5 degrees.

If it was bright enough you would see it as more than a dot with your naked eye, you would see some structure. The angular resolution of a human eye is around 1 arcminute = 0.02 degree. It is not too small to see with a nake eye in the sky, it is just too dim for your naked eye

Pluto is 0.06 to 0.11 arcseconds. 1 arcminut = 60 arcsecond so when closed to earth it is 0.11/60/60 = 0.00003 degrees

This mean NGC_3324 is =0.18/0.00003=6000 times larger in the sky the Pluto

Humans have resolved a few stars to more than a single do look at https://en.wikipedia.org/wiki/List_of_stars_with_resolved_images where 1 mas =0.001 arcsecond. Pluto is 110 mas in size when larges resolved star except for out sun is 50 mas.

So James Webb has and will observer more exoplanets. The are at best a few pixels in size. The stuff you see it the image that fills the frame is surprisingly large in the sky, we talk about lighyear across. it is just dim and the telescope is very good at collecting light

The pauses are of different lengths. How long a pause in between the dots and dashes depends if you are in a character (letter, digit, or other symbols), between characters, and between words. So if you learn it you will be able to tell the pauses apart

The timing is includes how long the dots and dashes are themself

• dot 1 unit
• dash 3 units
• Pause between dots and dashes within a character 1 unit.
• Pause between characters in a word 3 units.
• Pause between words 7 units

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https://morsecode.world/international/timing.html

You can use a website like https://www.meridianoutpost.com/resources/etools/calculators/calculator-morse-code.php? and generate the sound, it is quite clear at low speed that it is different even for a novice. It is noticeable even at high speed that pauses are not identical even if you might not there the it exactly right.

51 x 52 = ( 50 + 1 ) x (50 +2)

(a + b) x (c +d) = a x (c + d) + b x (c + d) = a x c + a x d + b x c + b x d

It is this expansion you need to use. Think of it each variable in the first parent multiplied by each variable in the second and add them together

( 50 + 1 ) x (50 +2) = 50 x (50 + 2) + 1 x ( 50 + 2) = 50 x 50 + 50 x 2 + 1 x 50 + 1 x 2 = 50 x 50 + 3 x 50 + 2 = 2500 + 150 + 2 = 2652

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I would not ever get to 50 x 50 if tried to do it by hand or in my head 50 x 52 + 1 x 52 would be my start. 1 x 52 is 52 so we just add it at the end

Then try to get to a multiple of 10. 50 is 100 /2 so 50 x 52 = (100 * 52) /2 = 5200/2. You can directly get it is 2600 but you can split it too.

Ignore the 00 at the end. 52 / 2 = 26 or 50 / 2 + 2/2 = 25+1 =26. We cannot just add back the 00 at the end and get 2600

The result is no 2600 +51= 2651.

Tying to get to a multiple of 10 other another number that will be easy is a good idea 99 x 52 is directly hard but 100 x 52 - 1 x 52 is not. You get 5200 - 52 and you can get 5148 from that