Country Boy

Well, for God's sake (and you own) make a paper copy of what you can get, whatever the font. If nothing else, you can write what you see on the screen by hand. Even if you have to copy the information in the file by hand, then type it into a new file, that's better than losing it. I'm not sure what you mean by "Changing the font, however, is no option. Don't feel like doing that." Why not? It is the information in the file that is important. I would try changing the font, if that is necessary, save it to a different file, open that new file in WORD and see if I couldn't change the font back in that new file.

"Casting out nines' says that if you add the digits of any number, and, if the result has more than one digit, add digits again, repeating until you have a single digit, the result will be the remainder when the original number is divided by 9. For example, the sum of digits of 3242747 is 3+ 2+ 4+ 2+ 7+ 4+ 7= 29, 2+ 9= 11, 1+ 1= 2. 9 divides into 3242747 360305 times with remainder 2. As you can see from the Wikipedia article studio links to, this method is over a thousand years old.

I don't know exactly what you are asking but surely it is NOT about a "ceiling fan". A ceiling fan uses electricity to cool a room. It does not produce or store electricity so CANNOT be used for "power backup".

But there is something wrong with asking if an observer would notice a change in the light "as it approaches". While the light is approaching the observer he cannot yet observe it! If "as it approaches" refers to approaching the black hole, again, the observer won't notice any "change", he only sees the light at one instant.

If you are thinking of the wave property of light as an "up down motion" in space then, yes, you are misunderstanding. The "wave" is an "increase, decrease" of the electro-magnetic field strength.

No "shock wave" would be involved. It just means that since the light from the sun takes a little more than 8 minutes to travel the approximately 93 million miles from the sun to the earth, we would see the sun "go out" only a little more than 8 minutes later. I don't know what "shockwave" you are talking about.

You give a single example and call it a "trend". What "trend" are you talking about and what evidence do you have that it is a "trend"?

I don't know why you are using "brute force" as you call it when you already had the solution staring at you! You have "either x+ 2y= 5 or x- 2y= 1". If x+ 2y= 5 then, for every y, x= 5- 2y. Solutions, in (x, y) form, are (5, 0). (3, 1), (1, 2). (-1. 3), ..., (5- 2y, y) for y non-negative and (7. -1), (9. -2). (11, -3),... for y negative. If x- 2y= 1 then, for every y, x= 2y+ 1. Solutions are (1, 0), (3, 1). (5, 2), (7, 3), ... for y non-negative and (-1, -1), (-3, -2), (-5, -3), ... for y negative. Those at are the solutions: $\{(5- 2y, y)\}\cup\{(2y+1, y)\}$ for y any integer.

Not quite. The "wavelets", as you call them, are not "an electric and magnetic field". They are waves in the ambient electro- magnetic field that pervades space.

Do your homework for you?

I'll just add this: you say "I'm not about pursuing writing as a career. I'm thinking about doing nuclear engineering." What nuclear engineers do most is write! In fact, what physicists, mathematicians, engineers in general, etc. etc. do most is write. They all may do many different kinds of things but they are of no use if they are not conveyed to other people. A nuclear engineer, for example, will spend most of his time writing proposals, reports, etc.

The problem appears to be that you are using the word "dimension" in a very strange, non-standard, way. What is your definition of "dimension"?

"but all the matrix examples I've seen so far seem to use much simpler, single digit numbers". So it is the arithmetic that is stopping you? Using x, y, and z as unknowns, the equations are 2270x+ 1800y= 15. -1800x+ 3480y- 680z= 0 -680y- 1150z= -8 Noticing that "y" is the only unknown to appear in all three equations, I would solve the first and third equation for x and z in terms of y: x= (15- 1800y)/2270= (3- 160y)/454. z= (8- 680y)/1150= (4- 340y)/575. So the middle equation becomes -1800((3- 160y)/454)+ 3480y- 680((4- 340y)/575)= 0. Use a calculator if those numbers are too much for you.

What does this, "a force of .5kg at 40 meters /sec velocity", mean? A mass moving at a given speed has momentum, not "force". Are you talking about the force the mass applies to the floor, say, when it hits the floor (and is equal to the force the floor applies to stop it). That depends upon the time required to stop which itself depends upon the elasticity of the floor- mass duo.

I am going to hope, very seriously, that you are fourteen or 15 year old high school student doing this for a class project. If you really are "a scientist working for a government organization on producing new energy sources for the planet" then I cringe for our planet. Even a college student should be able to do calculations, which you say you have done, to show that the energy cost of putting a satellite in orbit, then bring it back to discharge a battery, will far greater than any energy that battery could hold!

I have no idea what you mean by "centroid of a single variable function". "Centroid" is a geometric concept-there must be a region in the plane or an object in three dimensions. I presume you have some kind of curve that bounds a region (but then it couldn't be a "function").

I like to think of "energy" as a "book-keeping device". We have the "kinetic energy" but then define "potential energy" so that as "kinetic energy" decreases, we can still say that "total energy" stays the same. But as soon as you introduce friction, "kinetic energy" and "potential energy" are not enough so we introduce "heat energy" to balance the equation. Every time we have a situation where energy does not seem to be conserved, we introduce another kind of energy!

aSorry, I am still trying to be "polite' but this simply makes no sense to me. When you say "Let z1 be the multiplicative property of 0 ", what does that mean? z1 is a "number" in this system, not a "property". The "multiplicative property" of 0, in any algebraic system that has both multiplication and addition with more than 1 number and "0" is the additive identity, is that 0 times anything is equal to 0. When you say "Let z2 be the multiplicative identity property of 1" do you mean that z2 is the multiplicative identity? But then you say "Let 0 have both properties". What happened to z1 and z2? If you mean that this "number", is both the additive identity and the multiplicative identity, then, as I said before, there must exist only one number in your system, 0. Proof: let "0" be the additive identity. Then x+ 0= x. So, by the "distributive law", for any a, a(x+ 0)= ax+ a(0)= ax. Subtracting ax from both sides, a(0)= 0. Does your "number system" not satisfy the distributive law? If so that sharply restricts its usefulness! Now, suppose it is true that "0" is also the multiplicative identity. That is, a(0)= a for any a in the system. From above, a(-0)= 0= a. That is, assuming that your system satisfies the distributive law, every member member of the system is equal 0. Again, I did not check to see if your system satisfies the "distributive law". If it does, then "Let 0 have both properties" is impossible. If it does not, then it simply won't be very interesting!

If you let u= x+ 1, x= u- 1 and x+ 2= u+ 1. So what is f(u)? What is f(x) for any x?

First "Coriolis" is an adjective, not a noun! You mean "Coriolis force". That is the (imaginary) force that causes large scale motion of the atmosphere to circulate, clockwise in the northern hemisphere and counter-clockwise in the southern hemisphere. It is responsible for the rotary motion of large storms and, in particular, typhoons and hurricanes. Of course, it is NOT responsible for the strength of the winds in such storms- that is due to the energy picked up from warm tropical waters- so I don't know that it has any particular effect on plants and animals. It is responsible for the trade winds as J.C.MacSwell says.

Follow 3 "How things can exist win two or more places at once in the quantum level" is explained in quantum physics. That has nothing to do with where God exists or not.

So x is a function of t. v= dx/dt= Aw cos(wt) and a= dv/dt= -Aw^2 sin(wt)= -w^2 x. In your original post you had a=-kx/m so w^2= k/m.

You say "some mathematicians consider this to be a proof that 0 is in fact an even number" but your "this" appears to refer to "certain middle-level theorems in mathematics require that the number 0 be treated as an even number". I don't know of any mathematician who would think that. I am not sure what you mean by "mathematician" but I would expect any undergraduate math major to know that "0 is even" because 0= 2*0.