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f(x+h) = [(x + h)^2 - 2(x + h)] = [x^2 + 2xh + h^2 - 2x - 2h]

So we have

[f(x+h) - f(x)]/h =

[(x^2 + 2xh + h^2 - 2x - 2h) - x^2 + 2x]/ h =

(2xh + h^2 - 2h) / h  =

h (2x + h - 2) / h =

(2x + h - 2)

And if we let h → 0, then we have

2x - 2

And this is the "derivative" of f(x) = x^2 - 2x

(5+9z^3-3z^4)-(7z^4+4)-(6z^3+8z^2)    simplify, fitst

5 + 9z^3 -3z^4 - 7z^4 - 4 -6z^3 - 8z^2   collect like terms

 -3z^4 -7z^4 + 9z^3 - 6z^3  -8z^2 + 5 - 4   simplify again

-10z^4 + 3z^3 -8z^2 +1

Yes, xvxvxv, e is correct for the second question.

As to your hypothesis...let's see if this it is true that cos(n*pi + x) = cos(x)

Using a trig identity, we have

cos(n*pi + x) =

cos(n*pi)cos(x) - sin(n*pi)sinx  =

cos(n*pi)cos(x)

Notice that this equals cos(x) only when n = 0, 2, 4, 6......

yes Math is really wonderful!

You know Aziz before coming to this website i not at all liked maths!My whole class hates math until some maths is getting in their brains!but after joining the site i have expeerienced that how wonderful n easy Math is!im really happy with this change!

But you know none of us are grown ups , we dont know properly what right we start liking that thing which we understand nicely and is good to us and so  is Maths to me , sometimes when i dont understand something not at all in Maths i feel that math is so hard and is of no use and all and the moment i understand it and get it nicely then i fell "oh maths is soo easy, its the best subject"!

And now i hope with this u might have got the idea what sometimes is our behaviour!

But the truth is Maths is really nice (but again this feeling will come to the only person whose good in maths or has some interest in it)!

nice alan .. so question 2 the answer is e ! right ? 

and I want to ask ... from your amswer in question 6 I Concluded this law                                                                   cos(npi + x ) = cos(x)    ...  n mean any Integer number ( 0 , 1 , 2 , 3 ....... ) 

2du/dt=u^2, u(0)=1

Separating the variables, we have

1/(u^2) du  = (1/2)dt       Now integrate

∫u^-2 du = ∫ (1/2) dt

-1/u = (1/2)t + C    so we have

1/u = -((1/2)t + C) = -(t + 2C)/2

u(t) = -2/(t + 2C)

And

u(0) = 1

So

-2/(0 + 2C)  = 1

-1 = C

So we have

u = -2/(t - 2)   or

u = 2/(2 - t)

Great questions Rosala.

When I see people questioning answers like you often do I know that learning is taking place. And that, really pleases me. 

Have you tried doing it on the site calc on the home page? 

Another ambiguous question, because of the lack of brackets.  Again, making assumptions about what is wanted we have:

This would be easier if you used brackets to clarify what is and isn't a power!  However, I'll make the assumption that the following is what you are looking for:

Oh please don’t delete these. They are so funny. I have not ever read troll posts as funny as the ones on this site. The chimp and banana ones still make me laugh.

I don’t mean to be rude to you Stu, but these really are funny. Think about all the people on here who might be a target and this troll picks you. In a way, it is really a compliment. Your answers make them more funny. Until you made this post, I thought you might be doing it to yourself. Maybe that’s part of it. If you are the one doing it, it is truly funny and awesome.

The most funny one on here is not even a troll post. It’s from a girl named Charlotte. She compliments CPhill and then talks about how someone made a coconut look like her grandmother. She uses bad language, but that is just the way she talks and writes, and I do not think she meant to be offensive. I do think she meant to be sincere. I laughed so hard, I about stabbed myself with a paint brush.

I am an art major. I learn a lot of maths here, but I mainly understand and appreciate art. I really like the art of humor on here. Even your trolls are great fun.

My first post is not about math, but a troll. That is funny too. It is the art of humor, I guess.

Please show how to do summation symbol as i tried and it is not the same as elsewhere. Thanks. Also please say if $$ is input as dollar signs or backslashes and its puoose

I agree that "feel" is somewhat subjective; but, in this case, most people would agree on the effect (I've just tried it myself and it's fairly clear-cut) if not the magnitude of it.  To me, that suggests there is an underlying physical mechanism, related to the material being touched.  My further thoughts on this are as follows:

There are two physical requirements for removal of heat from a finger, say, when it touches a solid surface.

The first is that the material in contact with the finger is capable of conducting the heat away. A better conductor will conduct the heat away better, so one up for thermal conductivity.

However, the second requirement is that there be a temperature difference between the material in contact with the finger and the rest of the material. If the local temperature of the solid doesn't rise, the heat will not flow away no matter how good the thermal conductivity. The local material will rise in temperature quicker and hence start to remove heat more quickly if it has a smaller specific heat capacity. One up for specific heat capacity.

Both properties are involved.

I'm tempted to construct a simple mathematical model of the process!

Moderators please delete the posts that are disrailing the thread. 

Go troll someone else you 4 ft tall a*s.

That is about the height of a bonobo chimpanzee, isn't it?

They are very social chimps. I'm not sure if they make good bartenders. Though maybe it would make a good mate for you, and even help with bartending like reminding you to pick up your banana peals and such.

Dear Anonymous, better than being an a*s like you. You do not know anythimg about me or where I could be coming from. You are a complete a*s. Go eat some hay or something.

I hope your posts make you feel taller! They definatly make me feel happy for my accomplisment and my studying. You keep on telling your self you are tall. Sure you will get there one day when you develop respect for others and what they do as well as for effort they make to reach there goals; and when you don't need to hide from what you say.

A*s:

a hoofed mammal of the horse family, which is typically smaller than a horse and has longer ears and a braying call.

synonyms:donkey; 

From Stu. 

The principle consideration here is definition of the word “feel” used in the test question. This is a subjective quality and is open to a broad range of interpretations.

When it comes to physics and other physical sciences, there is often, if not always, a need to quantify uniformly (as much as possible) a subjective quality. For example, why does a person feel hot at times then cold at other times when subjected to the same temperature?

To give a basis for understanding and eventually controlling environments, a series of equations were developed to quantify environmental effects on living beings (including animals). These equations are generally referred to as psychometric equations. The most recognized of these are the wind-chill factor and Heat index (aka humiture or humidex). Though common in usage, most do not really understand the information these equations present.

Other psychometric equations include the perception of sound and light. Though, not necessarily a psychometric equation, the decibel is used for sound energy because of the way the human ear perceives sound.

Most psychometric equations represent a rate. In the case of the wind-chill factor, it correlates the equivalent rate at which heat is removed by wind to a temperature without wind. A similar relation exists for the heat index. Though theses give values, the equation relates how a person perceives an effect relative to another effect.

The case in point for this question has more to do with how fast heat is removed from a human hand than how fast a substance change temperature for a given amount of heat. Though these two are related, they are not really the same thing.

~~D~~

"Question 1 of my last post. I am not sure why it is positive answer from your post."

The field direction is positive, by convention, going from positive to negative, so it must be going away from the positives spread through the sphere.

"That is that i should or shouldnt use signs when using Fe equations in front of proton charge or electron charge? As well i am unsure what is R^3 in your equation"

Use negative sign when it's an electron and positive when a proton.  R is the radius of the sphere (have a look at the sphere drawn just below the graph), given as 7.04fm (7.04 femto metres = 7.04x10^-15m in your question), R^3 is R raised to the power 3 (or R³).

nice ... I am grateful for you .. alan and david 

Stu, maybe you should consider a change in major. You could take bartending classes. Here, you could make a fair living by wage and tips. I think you might do ok at this after a few years of practice.

The chimp bartender, I comment on, made great tips –mostly bananas, but cash too. After he retired, he lived quite well. He was one of the few who could actually pay for his keep and his keepers. Those who polished his gold-plated monkey bars to a mirror like shine, were his most prized and favored keepers. He rewarded them well, too.

Just something for you to consider.

The answer to question 16 isn't, perhaps, as simple as the person who set the question might have thought.  Here are some links that discuss the problem; some like thermal conductivity, some like specific heat!!

I cannot see why in solution 1 that t+ c falls onto the denominator or why in solution 2 the -1 goes to the numirator. Thank you for the assistance today. Long day for how much i have done. Next i need to resolve null members and null joints. Oh before that i have to work on understanding the integration factor which seems not to hard if i follow the steps. One hopes anyway.

Input this in your calculator, 128*sqrt(e*980), and you will obtain 6606.481884325691648 as your answer.