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$$\\log_{10} 10000^2 - log_{10} \frac{1}{100^2} \\\\
=2*log_{10} 10000 - log_{10} 100^{-2} \\\\
=2*log_{10} 10^4 -\; -2*log_{10} 100 \\\\
=2*4*log_{10} 10 +2*log_{10} 10^2 \\\\
=8*1 +2*2*log_{10} 10 \\\\
=8 +4 \\\\
=12$$

@@ End of Day Wrap    Sun 22/2/15     Sydney, Australia   Time 1:15 am  (Really mon morning)    ♪ ♫

Hi everyone,

Great answers today from ChaosBolt, CPhill, Lizzylizard7, Tetration, alan, Rosala, Mathematician, Heureka and SevenUp.  Thanks all.  

Interest Posts:

They are attracted by an Equal Number of protons!

Mon 23/2/15

$$\sqrt[5]{8-15i}$$

I saw Alan do one like this recently.  I will give it a go.

$$\sqrt{8^2+15^2}=17$$

$$\\8-15i = 17\left(\frac{8}{17}-\frac{15}{17}i\right)=17(cos\theta+isin\theta)=17e^{i\theta}\\\\
cos\theta=\frac{8}{17}\\
sin\theta=-\frac{15}{17}\\
\theta $ must be in the 4th quad $\\
tan\theta=-\frac{15}{8}\\
\theta\approx -61.9275\\\\
\sqrt[5]{8-15i}\\
=(17e^{i\theta})^{1/5}\\
=17^{1/5}e^{(\theta/5)i}\\
=17^{1/5}e^{(-61.9275/5)i}\\
=17^{1/5}e^{(-61.9275/5)i}\\
=1.7623e^{-12.3855i}\\$$

now these angles are in degrees abd 360/5=72degrees

-12.3855+72=59.61

59.61+72=131.61

131.61+72=203.61

203.61+72=275.61

275.61+72=347.61

so the radius of the polar co-ordinates is 1.7623 and $$\theta$$ = 59.61, 131.61, 203.61, 275.61 and 347.61

these polar co-ordinates are graphed on this page

no number ccan be divided by zero its just not defined

The answer is : OH SH- YOU DIVIDED BY ZERO!

Answer is not a number :P

Alan, could you please take a look at this question.  

I think 315 and SevenUp are both keen to see your answer.   

10x+15

=5*2x+5*3

=5(2x+3)

Here is a good explanation.  :))

use [2nd] asin   on this calc

arc sine and inverse sine are the same thing.

$$\\7x^{1/3}=7*\sqrt[3]{x}\\\\
6x^{-4}=\frac{6}{x^{+4}}\\\\
12x^{-3/2}=\frac{12}{x^{+3/2}}=\frac{12}{x^{1+1/2}}=\frac{12}{x\sqrt{x}}$$

Here are more examples

$${\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{3.14}} = {\frac{{\mathtt{314}}}{{\mathtt{25}}}} = {\mathtt{12.56}}$$

19$${\mathtt{10}}{\mathtt{\,\small\textbf+\,}}{\mathtt{9}}$$

$${\frac{{\mathtt{2}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{1\,000}}{\mathtt{\,-\,}}{\mathtt{0.9}}\right) = {\mathtt{1.999\: \!739\: \!305\: \!980\: \!944\: \!7}}$$

This question made me think 

$$\\cos\;\frac{\pi}{2}=0,\qquad cos\;\frac{-\pi}{2}=0,\qquad and \qquad f(0)=0\\\\$$

Now since g(x)=f(x)*cosx it follows that g(x)=0 when x  = -pi/2, 0 or pi/2

Hence g(x) must be at least one turning point between  -pi/2 and 0  and at least one between 0 and pi/2

If you are not sure about this, plot the 3 points and think about what the graph will have to look like.

NOW  when g(x) turns the gradient of the tangent must be 0 SO g'(x)=0 

HENCE

1 and 3 must both be correct. 

Thanks TOK002 and anon. 

I like it when people provide questions and answers in physics that are basic enough and clear enough for me to learn from.  

This is a good question and has made me think.  

If the line was at 90 degrees to the tangent of the earth (that means vertical) then the curvature of the Earth would make no difference.

If the line were not perpendicular I still do not think it would make any difference.  A line is not a solid, it has no substance and hence it not affected by gravity. So in theory at least the line could just go in any direction and not be effected by the the planet on which it originates.

Others may have a different view.  I will include this question in my next wrap.     

1 radian =57.3 DEGREES 

then 3 radians =  57.3*3  degrees

$${\mathtt{180}}{\mathtt{\,-\,}}{\mathtt{42}}{\mathtt{\,-\,}}{\mathtt{80.4}} = {\frac{{\mathtt{288}}}{{\mathtt{5}}}} = {\mathtt{57.6}}$$

You are right it does :))

This is because the calc is giving you the option of a fraction answer (in this case an improper fraction)  and a decimal answer.   That is all :))

It is not really a part of the working - just an alternate answer.   

Heureka, could you (or someone else) explain the phi function to me please?

I thought phi was an irrational number like pi.     

Yeah....we "Gods" get droppings from "doGs".......this is only a slight permutation.....I don't think Sorasyn would mind.........

After all...."Nauseated" does almost permute to "Seated A**s".....well....give or take an "s" or two......Mmmmmm.....I'm beginning to see EXACTLY where those droppings are originating from, now.......

And before it's pointed out....yes "CPhill" almost permutes to "Phallic".....give or take an "a"...or two....which is only one step away from being  "Richard Cranium"......  I'll let the "slower ones" use Google Translate for further understanding.....

Yes well Nauseated, you are correct about one thing, troll droppings are the only private offerings that us moderator 'Gods' are ever given. 

Doesn't really pay to be a 'God' does it.  

To find the midpoint of the x coordinate......add the x values and divide by 2

Then....do the same with the y coordinates....so you should have....

( [1/4 + -.4]/ 2 , [3.2 +1.7]/ 2 ) =

([1.4 - .4] / 2 , [3.2 + 1.7] / 2 ) =

( 1/2  ,  4.9/2 ) =

(1/2 , 2.45)