All Answers 358516 Answers

Honestly, i wasn't too sure.

So i read this site.

http://www.geteasysolution.com/what-is-14.5-percent-of-215

Mon 18/5/15

If you would like to comment on other site issues please do so on the Lantern Thread.  Thank you.    

FTJ means 'For the juniors' 

Interest Posts:

$${\mathtt{\pi}} = {\mathtt{3.141\: \!592\: \!653\: \!589\: \!793\: \!2}}$$

This is an approximation :)

3.14 rounded

I TRIED TO PUT ALL THIS INTO A TABLE BUT THE TABLE DID NOT COPE VERY WELL   

FOUR IN A ROW

$${\mathtt{2}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}^{{\mathtt{4}}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right) = {\frac{{\mathtt{32}}}{{\mathtt{243}}}} = {\mathtt{0.131\: \!687\: \!242\: \!798\: \!353\: \!9}}$$

$${\mathtt{3}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}^{{\mathtt{4}}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}^{{\mathtt{2}}} = {\frac{{\mathtt{16}}}{{\mathtt{243}}}} = {\mathtt{0.065\: \!843\: \!621\: \!399\: \!177}}$$

FIVE IN A ROW

$${\mathtt{2}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}^{{\mathtt{5}}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right) = {\frac{{\mathtt{64}}}{{\mathtt{729}}}} = {\mathtt{0.087\: \!791\: \!495\: \!198\: \!902\: \!6}}$$

$${\mathtt{2}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}^{{\mathtt{5}}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}^{{\mathtt{2}}} = {\frac{{\mathtt{64}}}{{\mathtt{2\,187}}}} = {\mathtt{0.029\: \!263\: \!831\: \!732\: \!967\: \!5}}$$

SIX IN A ROW

$${\mathtt{2}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}^{{\mathtt{6}}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right) = {\frac{{\mathtt{128}}}{{\mathtt{2\,187}}}} = {\mathtt{0.058\: \!527\: \!663\: \!465\: \!935\: \!1}}$$

$${\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}^{{\mathtt{6}}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}^{{\mathtt{2}}} = {\frac{{\mathtt{64}}}{{\mathtt{6\,561}}}} = {\mathtt{0.009\: \!754\: \!610\: \!577\: \!655\: \!8}}$$

SEVEN IN A ROW  

$${\mathtt{2}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}^{{\mathtt{7}}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right) = {\frac{{\mathtt{256}}}{{\mathtt{6\,561}}}} = {\mathtt{0.039\: \!018\: \!442\: \!310\: \!623\: \!4}}$$

EIGHT IN A ROW

$${\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}^{{\mathtt{8}}} = {\frac{{\mathtt{256}}}{{\mathtt{6\,561}}}} = {\mathtt{0.039\: \!018\: \!442\: \!310\: \!623\: \!4}}$$

$${\frac{{\mathtt{32}}}{{\mathtt{243}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{16}}}{{\mathtt{243}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{64}}}{{\mathtt{729}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{64}}}{{\mathtt{2\,187}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{128}}}{{\mathtt{2\,187}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{64}}}{{\mathtt{6\,561}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{256}}}{{\mathtt{6\,561}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{256}}}{{\mathtt{6\,561}}}} = {\frac{{\mathtt{112}}}{{\mathtt{243}}}} = {\mathtt{0.460\: \!905\: \!349\: \!794\: \!238\: \!7}}$$

If you mean inverse tan for instance then it is 

[2nd] [atan]

arc tan is the same as inverse tan

$$a^2*9=9a^2$$

3ab + 6c - 2cd + 4c - 11cd² - 5 - 2d²c

=3ab     + 6c + 4c      - 2cd   - 5     - 2d²c- 11cd²

I will rearrange so that the like terms are together.  

=3ab     + 6c + 4c      - 2cd   - 5     - 2d²c- 11cd²

NOTE:      cd² is the same as d²c

=3ab     + 10c      - 2cd   - 5     -13cd²

How did you do it MathsGod1 ?

Great answer MathsGod1  

This is how I would do it with an equation

60% of X = 22

$${\mathtt{0.6}}{\mathtt{\,\times\,}}{\mathtt{X}} = {\mathtt{22}}$$

$${\frac{{\mathtt{0.6}}{\mathtt{\,\times\,}}{\mathtt{X}}}{{\mathtt{0.6}}}} = {\frac{{\mathtt{22}}}{{\mathtt{0.6}}}}$$

$${\mathtt{X}} = {\frac{{\mathtt{22}}}{{\mathtt{0.6}}}}$$

$${\frac{{\mathtt{22}}}{{\mathtt{0.6}}}} = {\frac{{\mathtt{110}}}{{\mathtt{3}}}} = {\mathtt{36.666\: \!666\: \!666\: \!666\: \!666\: \!7}}$$

So the original price was $36.67  

hi Gibsonj338,

$$0=x^4(x-43)+40x^2(18x-145)+16(1375x-1884)$$

I do not know any way to do this without expanding first and then looking for factors

in this case (x-12) is a factor.

12 is the only real solution.  There are 2 irrational solutions and 2 complex solutions

what is the numbers that satisfies the pythagoras theorem ?

Hi MathsGod1

Here is a video you should watch and absorb :)

YES Civonamzuk - this is true.

Otherwise he may need to purchase a helicopter.   

I have added this one to our Puzzle thread

I really like your explanation here Chris!

They will both be equally contaminated!

I have added this to the "Great answers to Learn From" sticky thread 

In scientific notation this is 1.7004*10²

Put the decimal point after the first non-zero integer and multiply by 10 to the power of whatever is required to match the original number (2 in this case).

.

To sketch this, calculate the values at a number of different values of x.  In particular, try 5^0 (= 1), 5^∞ (=∞) and 5^-∞ (=0).  If you can't tell the shape from these three, try a few more positive and negative values of x until you can!

.

.

If f(x) = x² then f(-3) = (-3)² = 9

If you meant fx) = x*2 then Anonymous is right that f(-3) = -6

.

Thanks Radix and anon,

I like this question, it is a difference of 2 squares question.   (Just like Radix said )

$$\\\sqrt{7-4\sqrt3}\times \sqrt{7+4\sqrt3}\\\\
=\sqrt{(7-4\sqrt3)(7+4\sqrt3)}\\\\
=\sqrt{(7)^2-(4\sqrt3)^2}\\\\
=\sqrt{49-16\times 3}\\\\
=\sqrt{49-48}\\\\
=\sqrt{1}\\\\
=1$$

Hi Radix,

Welcome to the English forum.  It is great to see you answering questions here.    

x^2 + 2xy + y^2 =  (x + y)(x + y) =  (12)(12) =  144

(x + 3)^2 - (x +  1)^2    =    [ (x + 3) + (x + 1) ] [ (x + 3) - (x + 1) ]  =  [2x + 4] [ 2] = 2[x + 2] [2]  = 4[x + 2]  = 4x + 8

(1/b - 1/a) x (b/a - a/b)  =  [ 1/a - b/a^2 - a/b^2 + 1/b]     [there are other possible forms]

x^2 + x + 1/4  = (x + 1/2)(x + 1/2)  = (x + 1/2)^2

It is a nonsense statement.

Multiply both by 4 and you get     3:1