All Answers 358098 Answers

the answer is 600

Distance  / Rate   = Time   .....so...

17.5 /  7   =  2.5 hours

Also, by this simple method:

0.1 = 2^-(500,000/h)

1/10 = 2^-(500,000/h) take the reciprocal of both sides,

10 = 2^(500,000/h)       take the log of both sides

500,000/h =log(10) / log(2)

500,000/h =3.321928...

h =500,000 / 3.321928

h ~ 150,515 years - the half-life of this element.

By simple inspection, we have:

a=1   and  x=1

a=5   and  x=5

a=7  and  x=7

a=11 and x=11

You gave me a heart attack.

Thank you Melody. I shall take it from here.

I see Alan beat me to it :))

Integrate the following:  ∫x^2 sin^3 (x) dx. Also, please show steps of solution.

I thank you for any help.

\(\int\;x^2sin^3x\;dx\\ =\int\;x^2sinx\;sin^2x\;dx\\ =\int\;x^2sinx\;sin^2x\;dx\\ \qquad \qquad cos2x=cos^2x-sin^2x\\ \qquad \qquad cos2x=1-2sin^2x\\ \qquad \qquad 2sin^2x=1-cos2x\\ \qquad \qquad sin^2x=\frac{1-cos2x}{2}\\ =\int\;x^2sinx\;\frac{1-cos2x}{2}\;dx\\ =\int\;\;\frac{x^2sin(x)-x^2sinxcos(2x)}{2}\;dx\\ =\frac{-1}{2}\int\;[x^2sin(x)cos(2x)-x^2sin(x)]\;dx\\ \)

\(\qquad \qquad sin(\alpha-\beta)+sin(\alpha+\beta)\\ \qquad \qquad =sin(\alpha)cos(\beta)-sin(\beta)cos(\alpha)+sin(\alpha)cos(\beta)+sin(\beta)cos(\alpha)\\ \qquad \qquad =2sin(\alpha)cos(\beta)\\ \qquad \qquad so\\ \qquad \qquad 2sin(x)cos(2x)=sin(x-2x)+sin(x+2x)\\ \qquad \qquad 2sin(x)cos(2x)=sin(-x)+sin(3x)\\ \qquad \qquad 2sin(x)cos(2x)=sin(3x)-sin(x)\\ \qquad \qquad sin(x)cos(2x)=\frac{1}{2}[sin(3x)-sin(x)]\\ =\frac{-1}{2}\int\;[x^2sin(x)cos(2x)-x^2sin(x)]\;dx\\ =\frac{-1}{2}\int\;\frac{x^2}{2}[sin(3x)-sin(x)]-x^2sin(x)]\;dx\\ =\frac{-1}{2}\int\;[\frac{x^2}{2}sin(3x)-\frac{x^2}{2}sin(x)-x^2sin(x)]\;dx\\ =\frac{-1}{2}\int\;[\frac{x^2}{2}sin(3x)-\frac{3x^2}{2}sin(x)]\;dx\\ =\frac{-1}{4}\left(\int\;[x^2sin(3x)]dx\;-\;\int[3x^2sin(x)]\;dx\right)\\ \text{Now work out each of these two integral seperately using integration by parts.}\)

Maybe I will finish it later  (it is 1:36am)  anyway, that is a good start for you :)

4x - 3y = -24    (1)

x = 2y - 11       (2)

Substitute (2) into (1)

8y - 44 - 3y = -24

5y - 44 = -24

5y = 20

y = 4

Use this in (2)

x = 8 - 11

x = -3

.

Use N/N0 = e^-(ln2*t/h)

0.1 = e^-(ln2*500000/h)

ln0.1 = -ln2*500000/h

h = -ln2*500000/ln0.1 ≈ 150515 years

.

Thank you Alan.

Third part:

Second part:

First part:

Well, atleast you are being rational.

Im not a "mathbitch". I dont do it because math is "sacred" and other things arent. I dont care about your hobbies, i dont care if you love math, hate math, i simply dont care. but people need to stick to the topic of the forum. its called "WEB2.0CALC" for a reason, d**n it. If you want do talk about other things, open a new forum, that's what my alternative is. Unfortunately, you turned down my offer, because theres a "off topic" button, and you could "simply" flag every post that is irrelevant. Of course by that you have to go over the forum again and again, but for some reason its more effective, or more 5-years-old-friendly. Couldnt you open that forum? couldnt you ATLEAST give them the option to flag themselves as irrelevant if they feel so? you really are beating your head against the wall for no reason.

I didnt get the whole "Batshit stupid" thing. Go ahead, if thats what you think, flag me.

I also think you've misunderstood me. When you read my posts you're probably picturing an old angry man slamming his keyboard. Im simply proposing a better way to arrange this forum.

There is one thing that is clear: The Clown Prince is dealing with his chaotic dark passengers well more efficiently than you are dealing with yours. You are making yours worse!

 No thanks. I dont need you to tell me how to live my life. Im not asking you to know my, because you wont. Dont your energy writing idiotic sentences.

The funny thing is, Mystical jaycat Had another solution that doesnt rely on you- she opened a discord chat. Why cant you go there instead? is it too hard to type a few words and click your mouse twice?

I come out evil and annoying in your comment, while other arent, because they seem positive or because it seems they are very nice.

Theres one thing i ask you to do. Enter the discord chat mysticalcat added, scroll all the way up and read. 

The number e is a famous irrational number, and is one of the most important numbers in mathematics. The first few digits are: 2.7182818284590452353602874713527 (and more ...) It is often called Euler's number after Leonhard Euler. ... e is the base of the Natural Logarithms (invented by John Napier).

Hi all,

I know everyone here has their own ideas on what the proper use of this forum is.

Some people want it to be a serious and dedicated help site for young people who really want to learn mathematics.

I want that too of course but I want the forum to have a lighter side as well. 

I have always wanted it to be like a after school drop in centre for students who enjoy mathematics and who want to be with others who are like minded.  As such it would (and is) a social centre for many people, including myself. I have never minded people socializing here so long as it does not monopolize the forum or diminish the forum's vaue as a place to learn, teach and enjoy mathematics. 

I am pleased that ClownPrinceofChaos and HighSchoolCalculus have shared their music with the rest of us.

Thanks guys :)

Yes Ehrlich, CPC does write irritating posts: He often states the obvious as if it is some esoteric knowledge, and he magnifies the offal of social communication to the point where one can smell it.  Even so, all of his posts combined still have less of an offensive smell than any one of yours.  That you would choose the only post CPC made that is outside the above description to post your comments is very telling. 

Your comments are like throwing water on a grease fire—a very stupid thing to do.  You are the neighbor that bìtches about another neighbor’s yapping dog. So now, we get to listen to the yapping dog and the neighbor’s bìtching. 

Notwithstanding your impassioned objections, Herr Massow allows for social comments on this forum. He made a filter-controlled, provisional label for it: Off-topic. When it’s used, it does work. You need your own label, Ehrlich. A year ago, the forum’s Troll suggested one.

I really like this Matthew, I didn't know you wrote music !! 

This is an interesting and pleasant piece of _minimalistic music. With this, you demonstrate clearly the aphorism that “_less is ^more,” still lives. 

Why did you switch the treble and bass clefs on the piano section? Is this part of your “chaotic” nature?

Wheels required  =  4 * 236  = 944      (1)

Wheels available =  748      (2)

Wheels needed  =  (1) - (2)  = 196

Cars that wll have no wheels  =  196 / 4  =  49

Thanks!!!!!!!!!!!!!!!

Easy, 236*4=944 944-784=160(a).      Last: 784/2=392 392-236=158(b) simple :) wish you good luck brother bye:)