Understanding Electronics Basics #2

[Muttley600]

I've gotta get my math sorted, cause your showing me * & calling it division????
This is another 'oh my god, you can't short a live wire out moment'
I'll nail it tomorrow & we can go forwards

Thanks for sim CBB, will have a play

On the morrow guys, gotta catch up on sleep then get back to this after work

 

[KeepItSimpleStupid]

The first 1000 prime numbers are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997...

When you factor, you try to get as many of these (prime numbers, they go on forever) to divide evenly into the number.

So for 16. It's even, so it's divisible by 2. and you get 2*8

8 is even so it;s divisible by 2, so you get 2* (2 * 4)

4 is even, so it's divisible by 2.

So you get 16 = 2* 2 *2 * 2

 

[Muttley600]

ok, that took a while & I still might have it wrong, are you saying you keep breaking a number down until only prime numbers fit into it **broken link removed**

 

[KeepItSimpleStupid]

Yep, That's called "prime factorization".

You can "factor" any which way you like though. e.g. 100 = 10 *10 = 50*2.
You can say that 2, 10, 20, 50 and 5 are "factors" of 100.
That just means that the "factors" divide evenly.

Both concepts are useful. In algebra, there is a lot of "Find the two factors of X which when added or subtracted equal Y.

So we have:
Factors - numbers that divide evenly into the number x
Factoring - numbers that multiplied together equal the number x
Prime Factoring - primes multiplied together equal the number x

 

[Muttley600]

Some other things (√ )
√8=2√2;
√10=√10;
√11=√11;
√12=2√3;
√13=√13;
√14=√14=√2√7;

I've deleted the ones I understand but what are these, they don't make sense

 

[Muttley600]

Both concepts are useful.

So we have:
Factors - numbers that divide evenly into the number x
Factoring - numbers that multiplied together equal the number x
Prime Factoring - primes multiplied together equal the number x

Your going to be very sad that I don't know why you've taught me that because I still don't see the logic or need behind it, what are you showing me & why**broken link removed**

 

[KeepItSimpleStupid]

Remember the √192? and you could not get their answer of something like 8√3 or something like that?
---
Ok, the √8 = 2√2; 8 factored is 2*2*2, so you can take out a pair of 2's from under the √symbol as a 2; so you get 2√2.
11 and 13 are prime so there is nothing to take out.
√10 = sqrt(2 * 5) and there isn't a pair of anything to take out.
√14 =√2√7. I threw that one in to throw you. You can't take out a pair, but you can take out each of the terms as a √. This isn;t something you would normally do.

 

[KeepItSimpleStupid]

If we were dealing with cube roots, factoring 27 would give 3 * 3 * 3 and thus the cube root of 27 is 3.

 

[Muttley600]

I think we are at it again, remember how I wondered what hit me when you put formulas up, I learnt a bit of algebra & grasped enough basic to get me through, while we've hit the runway half way along again (sorry been on phone sorting help for work)
I somehow need to be able to relate to this, what does it come under so I can look it up & try to understand it a bit better?

 

[Muttley600]

If we were dealing with cube roots, factoring 27 would give 3 * 3 * 3 and thus the cube root of 27 is 3.

ok, lets try working on this, show me the formula for this, I can see numbers work but if I'm guessing correct your gonna put a divide somewhere in formula thats going to throw me & can you do this on calculator?

 

[KeepItSimpleStupid]

You can if you have a button that can take the nth root of a number. There is usually a super scripted n before the √ symbol.

If you can take LOGs in base 10, you can also do it.
Log10(27) = 1.431363764
Divided by 3 = 0.477121255
10^ 0.477121255 = 3

Oops, too complicated,

anyway
Factoring 27
You get 3 * 9
and then 3 * 3 * 3
Cube roots just require 3 numbers to be multipled together, so the answer is 3.'

We can do the cube root of 100 the same way and get: 4.641588834 so 4.641588834
*4.641588834*4.641588834 = 100

 

[Muttley600]

Lol, I knew it, you simply divide the answer, but I still need to relate better to that square root symbol, let me have another look
& what is that thing that looks like a house roof that keeps appearing?

 

[KeepItSimpleStupid]

The house roof or carrot is this symbol "^". It denotes exponentiation in computer land.

In Math land it's [latex]x^{n}[/Latex]

thus x^n is equivalent to [latex]x^{n}[/Latex]

The cube root of x is denoted by [Latex]\sqrt[3]{x}[/Latex]

 

[Muttley600]

The house roof or carrot is this symbol "^". It denotes exponentiation in computer land.

In Math land it's [latex]x^{n}[/Latex]

thus x^n is equivalent to [latex]x^{n}[/Latex]

The cube root of x is denoted by [Latex]\sqrt[3]{x}[/Latex]

See, I look at that & can instantly relate to it
Yes, I can hear that sigh of relief **broken link removed**

 

[Muttley600]

[latex]\sqrt{16^{2}-8^{2}}=\sqrt{192}=\sqrt{(2^{2})(2^{2})(2^{2})(3)}=8\sqrt{3}[/latex]

ok, (so first one is) 256 - 64 = (second) 192 (third) 4*4*4 (64) *3

I'm not giving up if I have to do this 100 times until I remember it, don't panic, got it for the second time, I shall promise not to ask how to solve this until thursday at the earliest now **broken link removed**

so we basically are working out the cube, taking one side then cubing that

**broken link removed** we're not even doing that, relating back, we are just cubing bottom measurement, why didn't you say that **broken link removed**

Now before we go any further, I need to carry on learning special triangles so I can put names of sine/cosine etc to them, we have movement **broken link removed** I'll get there in the end **broken link removed**

 

[Muttley600]

A few comments.

Mathematics is all about precision and following lots of rigorous rules. There are fundamental principles called proofs and corollaries. Answers in math generally have to be presented in a "simple form". The √192 isn't a simple form, 8√3 is. Using language that could be said as 8 radical 3 or 8 times the cube root of 3. It's even equivalent to 8 * 3 raised to the 1/3 power.

Damn, you'd given me the answer, I just didn't see it at the time, sorry for doubting **broken link removed**

 

[Muttley600]

just double checking
8 cubed * 3 = 192

So other triangle shown on post #45

5 squiggle 3 would be 5 cubed * 3 = 75

is that right? not that I don't trust myself or anything

 

[KeepItSimpleStupid]

No. 8 √3 = √192 ~= 13.85640646 No cubic anything.

5√3 would be 5 * 1.732050808 ~= 8.660254038

The ~= means approximately equal to.

 

[Muttley600]

ok, slightly misunderstood, so:
5 cubed * 3 = 75 so if I change it to mean sqrt of 75 = 8.660254038

now I see it **broken link removed**

 

[KeepItSimpleStupid]

Huh? 5 cubed = 5 * 5 * 5 = 125;

multiplied by 3 = 375

75 factored is 5 * 5 * 3
If you wanted to take √75 exactly, you would end up with 5√3 or your 8.66 number