All Answers 358087 Answers

Thanks Alan, do you know how to get ρ to display in LaTex?   I do not know what it is called :/

I suppose I could just google greek letters. :/      $$\rho$$      got it!    

Well, if you right-click over the question mark icon and then choose Copy image URL you can paste the result (a URL) into the search box and it seems to find some questions.

You can also choose Open image in new tab and then copy the URL at the top.

Not sure if this is what you are after!

Is the question mark icon only available to moderators?

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Alan, can you find a way that we can bring up questions with the ? icon using the search feature?

If you could that would be really good.  I ask you because you seem to be best at this type of thing. :)

Is your study list as long as mine Chris :(

Still is is much better to have a list that is too long than a list that is too short :D

I was just having some fun with you Zac,

I really like all the great answers that you have been presenting :)

Excellent explanation SevenUp!  All I would add is that ρ is the electrical resistivity (it has SI units of ohm-metres).

And Melody's integration is, of course, correct (though the usual symbol for resistivity is the Greek letter ρ, rather than an upper case P!)

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Here is an explanation of the double summation and a couple of practice double summations Melody:

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Didn't you lose a minus sign after the first line of your second group anonymous?

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Factors of 2¹⁴⁵-3 are 29,  51690246276649  and 29753822786092084791696150649

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$$11r+18=51$$

$$11r=33$$

$$r=3$$

Thanks Zac

Complex numbers have nothing to do with this question.

I am sorry Alan, I just don't get it.

If I want to know how many ways I can put 3 identical b***s 9 different boxes such that there was a maximum of 1 ball in each box then I would say

1.       9C3=84        or

2.       $$\frac{9*8*7}{3!}=84$$

Now , you have said

So               $$1+3+6+10+15+21+28 =$$   $$\frac{9*8*7}{3!}=84$$

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OR

I am really struggling with this Alan.   

I totally understand that the answer to this is 84 (doing it my way) but I just can't understand the logic that you use to do it your way.

ALSO  can you show me how to expand this triple summation please.  I have no idea :(
I have always had trouble with sigma notation.  As soon as it is above the most basic level I get lost :/

Maybe you could throw me a couple of double summations that I could try on my own. :)

have you ever heard of complex numbers ??? (i)^2=-1

w=21

or 2w-1=21    2w=22    w=11

4x=11.2

11.2/4 = x

2.8 =x

thats for x>0

or

-4x=11.2

x=11.2/4

x=2.8

thats for x<0

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{282}}}{{\mathtt{137}}}}\right)} = {\mathtt{64.088\: \!795\: \!240\: \!146^{\circ}}}$$

64 degrees

4x=11.2<<get x by itself

11.2/4 = x

2.8 =x

Absolute value is the distance between a number and the origin

You have to write it like this in the calculator: (-5)^2

$${\left(-{\mathtt{5}}\right)}^{{\mathtt{2}}} = {\mathtt{25}}$$

If you simply type -5^2 it takes it as -(5^2)

$${\mathtt{\,-\,}}\left({{\mathtt{5}}}^{{\mathtt{2}}}\right) = -{\mathtt{25}}$$

$$\frac{5}{8}\times\frac{-72}{1}$$

$$\frac{5\times{-72}}{8}$$

$$\frac{-360}{8}$$

$$-45$$

I have no understanding of the initial  part but

Given that P and L are constants then

$$\\ \displaystyle\int_{a}^{b}\frac{P}{2\pi rL}\;dr\\\\
=\frac{P}{2\pi L}\displaystyle\int_{a}^{b}\frac{1}{r}\;dr\\\\
=\frac{P}{2\pi L}\;[ln(r)]_a^b\\\\
=\frac{P}{2\pi L}\;[ln(b)-ln(a)]\\\\
=\frac{P}{2\pi L}\;\left[ln\left(\frac{b}{a}\right)\right]\\\\$$

This is how I interpret it. (Elucidating comments from Alan are always appreciated)

This is called radial current flow. It is calculated via an infinite number of “shells” radiating out from the point of origin. As the current flows out from the center, each shell has a progressively greater surface area and a lower corresponding resistance. The shells’ surface areas, and its corresponding resistances, are summed to calculate the total resistance. However, because the area, and the rate of area, increases as the current moves outward, the cross-sectional area formula is integrated to effectively make the area uniform over predefined distances.

For DC circuits this phenomena seems trivial. For AC circuits it becomes important because the current flow moves closer to the surface of a conductor as the frequency increases. Where it really becomes interesting is in the conduction of signals in biology, specifically nerve cells that are mediated by sodium, potassium, and calcium channels. Understanding this is a brain strain (and a nerve pinch), and how anyone ever figured it out in the first place is mind boggling. 

_7UP_

$$m=-475t+2650$$

Substitute $$[m=1500]$$

$$1500=-475t+2650$$

$$-1150=-475t$$

$$t\approx2.421$$

(0.421*60=25.26)

t is aproximately 2 hours and 25 minutes, so the most correct answer is A.

David, what are u doing here????????

I am the cousin of Denzel, so dont worry, he is saying the truth...

Good work!