All Answers 358514 Answers

That was good logic JonyMyster.  When there is a squared term there are often 2 answers.  

The C stands for combinations.

how many combinations of 4 can you choose from 7 items.

$$\\1200=600(1.06)^n\\\\
2=1.06^n\\\\
log(2)=log(1.06^n)\\\\
log(2)=nlog(1.06)\\\\
n=\frac{log(2)}{log(1.06)}$$

$${\frac{{log}_{10}\left({\mathtt{2}}\right)}{{log}_{10}\left({\mathtt{1.06}}\right)}} = {\mathtt{11.895\: \!661\: \!045\: \!941\: \!876\: \!8}}$$

there you go, leave it in the bank for 12 years.

I did this with a 3 by 3 grid - not including headings    (like a times table grid)

The headings along the top are left right and total

The headings down the side are like jazz, dislike Jazz and total

Then i filled in what I was given and worked out the rest.   

$${\frac{{\mathtt{13}}}{{\mathtt{7}}}}{\mathtt{\,\times\,}}{\mathtt{100}} = {\frac{{\mathtt{1\,300}}}{{\mathtt{7}}}} = {\mathtt{185.714\: \!285\: \!714\: \!285\: \!714\: \!3}}$$

185.7%

23^(1/3)

It is an irrational number so this is an approximation.

$${{\mathtt{23}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)} = {\mathtt{2.843\: \!866\: \!979\: \!851\: \!565\: \!4}}$$

we must have had this question 100 times already,   

      $${\mathtt{6}}{!} = {\mathtt{720}}$$

and

ABC

ACB

BAC

BCA

CAB

CBA 

It is easier if you do a little sketch of the triangle.

I do not understand the question.

I didn't know what aquarenumbers were either BlackNinja,  It is just as well there are mathematics forensic experts amoung us.   Like JonyMyster 

sin90 + sin90

=1+1

=2

OH,OH Revenge is in the shadows! HAHAHA!

I wondered why this was so complicated. Most of the time I can figure the answer just by looking. Along with the clothespin, a pair of untinted spectacles might help.

Well, CPhill, it looks like we have the same strain of CDD.

Thanks Alan!

 The missing Phi constant is a pain, but here are some great ones I use all the time.

The 220 lattice spacing of silicon constant. I use this one the most. It’s especially useful for efficiently sweeping sand out of my beach house.

The Sackur-Tetrode constant (1 K, 101.325 kPa). I use this one to estimate the size of the vacuum cleaner I need.

The Shielded proton mag. mom. to Bohr magneton ratio. I use this one to calculate how close I can stand to my household-sized nuclear reactor that powers the vacuum cleaner.

The electron-tau mass ratio. This is used as a substitute for the dominant hadronic tau decays for the heaver particles that escape the shielded proton magneton generator. It also allows for a basis to make optimum adjustments for when my mother-in-law visits.

Atomic unit of 1st hyperpolarizability This one tells me how hyper-polarized I am in person.

Atomic unit of 2nd hyperpolarizability This one tells me how hyper-polarized I am on line.

Phi estimates the potential effect this has on others. I have to enter the number manually --what a bummer!

I would give an example, but the equations are proprietary, I can’t share them.

LMAO! You could be a standup comedy writer, CPhill --or at least a sit down comedy writer.

Who would ever think permutations could generate so much humor? But they do:

Thanks Alan,

-----------------------------

My goodness Nauseated, it seems you have become contaminated very badly with CDD.

You must be hospialised and quarantined immediately.

Do not fret the nurses wear face masks and nose pins so that they can handle the stench!  

Plus it is their calling so they shall nurse you back o health while they struggle to control their nausea.   

Thanks Alan for that great matrix answer.  

I need to have a proper look at all of these solutions.

We have not heard from the anon that asked this question.  I wonder which answer they were after?

Hmm!  Your first expression isn't right either Nauseated.

$$\\ \frac{1}{x}+\frac{1}{4x}=\frac{5}{12}\\\\\frac{4}{4x}+\frac{1}{4x}=\frac{5}{12}\\\\\frac{5}{4x}=\frac{5}{12}\\\\4x=12\\\\x=3$$

.

sin90+cos90

(sin90=1.cos90=0)

1+0

1

Well, Anon, maybe you should take off the blinders instead of putting more on. But I guess this is normal for you because you are a m***n. Too bad there isn’t a “close pin on the nose” emoto. One reason for the nausea of CDD is the stench. Morons with CDD are very foul!

$$\Text {solution :} \\\\
\hspace*{1em} \dfrac{1}{x}+\dfrac{1}{(x+4)}\;= \; \dfrac{5}{12}
\hspace*{3em} \Leftarrow \; \text {Solve} \\\\
\hspace*{1em} 12(x+4)+12x=5x(x+4)\hspace{10pt} \Leftarrow \; \text {simplify using 12x(x+4) } \\\
\hspace*{3em} 24x+48=5x^2+20x \hspace{16pt} \Leftarrow \; \text {expand } \\
\hspace*{3em} -5x^2+4x+48=0
\hspace*{1em} \; \Leftarrow \ {Subtract}\; 5x^2+20x \; \text {and set = 0}\\\\
x = \dfrac{-(4)\pm \sqrt{((4^2)-4 \times(-5)(48))}}{2(-5)} \hspace*{1em} \Leftarrow \; \text { Use quadratic formula}\\\\\\\\$$

$$\text {. .}\
\\\
\hspace{1pt} \qquad -4 \pm \dfrac {\sqrt{976}}{-10}}\\\\
\hspace{1pt} \qquad \text {x = -2.7240998703626618} \\\
OR \\
\hspace{34pt}\text {x = 3.5240998703626616} \\$$

You have given the right formula TJM!!!

.

$$\\a^{3b}-1 = 63\\ a^{3b}=64\\(a^b)^3=64\\a^b=64^{\frac{1}{3}}\\a^b=4\\x=4$$

.

x + 5 + 4/x = 0

Multiply all terms by x

x² + 5x + 4 = 0

This factorises as:

(x + 1)(x + 4) = 0

So the two solutions are:  x = -1  and  x = -4

.

$$\sqrt{x^3y^4z^6}=\sqrt{x\times x^2\times (y^2)^2\times (z^3)^2}=xy^2z^3\sqrt{x}$$

Note:  There aren't any denominators!

.

NO Definitely not!