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PEMDAS:   Parentheses; Exponents; Multiplication; Division; Addition; Subtraction

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v = √(G*M/r) can be rewritten as v² = G*M/r, which can then be rearranged as r = G*M/v²

$${\mathtt{r}} = {\frac{{\mathtt{6.67}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{\left(-{\mathtt{11}}\right)}{\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{\left({\mathtt{30}}\right)}}{{\left({\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{4}}}\right)}^{{\mathtt{2}}}}} \Rightarrow {\mathtt{r}} = {\mathtt{333\,500\,000\,000}}$$

r = 3.335*10¹¹ m

.

Do you mean this:

(10/14) / (6/7) =   $${\frac{\left({\frac{{\mathtt{10}}}{{\mathtt{14}}}}\right)}{\left({\frac{{\mathtt{6}}}{{\mathtt{7}}}}\right)}} = {\frac{{\mathtt{5}}}{{\mathtt{6}}}} = {\mathtt{0.833\: \!333\: \!333\: \!333\: \!333\: \!3}}$$

$${\frac{\left({\frac{{\mathtt{10}}}{{\mathtt{14}}}}\right)}{\left({\frac{{\mathtt{6}}}{{\mathtt{7}}}}\right)}} = \left({\frac{{\mathtt{10}}}{{\mathtt{14}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{7}}}{{\mathtt{6}}}}\right)$$   =    $${\frac{\left({\mathtt{10}}{\mathtt{\,\times\,}}{\mathtt{7}}\right)}{\left({\mathtt{14}}{\mathtt{\,\times\,}}{\mathtt{6}}\right)}} = {\frac{\left({\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{1}}\right)}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{3}}\right)}} = {\frac{{\mathtt{5}}}{{\mathtt{6}}}}$$

Hallo anonymous!

5 1/2 x 4 3/8 = 11/2 * 35/8 = 385/16 = 24 1/16

:- )

(5+1/2) * (4+3/8) = 11/2 * 35/8 =

$$\left({\frac{{\mathtt{11}}}{{\mathtt{2}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{35}}}{{\mathtt{8}}}}\right) = {\frac{{\mathtt{385}}}{{\mathtt{16}}}} = {\mathtt{24.062\: \!5}}$$

$$\left({\mathtt{5}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right){\mathtt{\,\times\,}}\left({\mathtt{4}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{3}}}{{\mathtt{8}}}}\right) = {\frac{{\mathtt{385}}}{{\mathtt{16}}}} = {\mathtt{24.062\: \!5}}$$

Hallo anonymous!

-3(-4y+3)+7y                                   ( - * - = + )   ( - * + = - )

= 12y - 9 + 7y

= 19y - 9

-3(-4y+3)+7y = 19y - 9

:- ) 

I thought your answer was the same as mine. I thought you gave the complementary angle. :)

Anyway your answer is still very impressive :))

You do so much of work tin...don't you? So many *'s ........and something much more funny......those *'s aren't even interesting -_-

Thank you Melody, i don't need to divide by 16, my mistake!

*scouts the map of Camelot for interesting places to attack

*tries to decide between the Camelot Castle or the Gem Box Paradise base

me:alright, i'm attacking Gem Box Paradise, it contains and only contains green and pink Gems which we can use to improve our base more quickly

and unlike before, where im doing real attacks, this time I got one of SUperCell's Developer iPads and am gonna use it to spawn troops and attack Gem Box Paradise

*waits until 3 am

alright, the paradise is completely unguarded

*pays usual 1k gold to attack

*spawns 300 witches and 300 scorchers

*witches and scorchers steal many gems, eventually all of them have full hands

*sends in 300 goblins

alright, we stole all the gems!

*replaces gems with fake red jewels

alright, lets get out of here!

Well it seems you are the expert anon, :))

Do you do your own brain surgery too?

@@ End of Day Wrap    Thurs 20/8/15     Sydney, Australia Time   12:22pm       ♪ ♫   

Yes it is Friday already  

Hi all,

Our fabulous answers were delivered by Radix, Heureka, Geno3141, Alan, Asinus and MathsGod1. Thank you 

Alright, the Suicide Squad Project is done, for now.....until the next member tries to steal the Queen's throne

alright, time to do a crime

****** *** *****'* ****** (Censored so Melody cant crack the code)

A (p, p +1) and B (2p, p +2)

$$\\gradient=\frac{p+2-p-1}{2p-p}\\\\
gradient=\frac{1}{p}\\\\
y=\frac{x}{p}+b\\\\
Sub\;in\;point\;A\\\\
p+1=\frac{p}{p}+b\\\\
p+1=1+b\\\\
so\;b=p\\\\
$Equation of line is $ y=\frac{x}{p}+p\\\\$$

If p is negative the the y intercept is negative and the gradient is negative so it will cut the negative x axis.

If p is positive the the y intercept is positive and the gradient is positive so it will cut the negative x axis.

Melody: Your logic is srewy! I think you spend too much time on the beach!. A negative integer raised to a positive EVEN integer is ALWAYS positive. A negative integer raised to an ODD positive integer is ALWAYS negative. Case closed.

Well I am not certainly not going to give anyone my phone number or my address !    :)

It is only easy for you anon because you know how to do it :)

Most things are easy when you know how to do them :))

I added this into the "great questions to learn from" sticky thread :)

Let the point (x,y ) be the point where the speed boat intercepts the vessel

Let t be the time taken to intercept.

Let alpha be the angle between East and the direction the speed boat travels (as shown in the diagram)

So the bearing of the speed boat will be  N(90-alpha)E

$$\\x=20cos75+26tcos50\qquad and \qquad x=50tcos\alpha\\
so\\
20cos75+26tcos50=50tcos\alpha\\\\
20cos75=50tcos\alpha-26tcos50\\\\
20cos75=t(50cos\alpha-26cos50)\\\\
\frac{20cos75}{ (50cos\alpha-26cos50)}=t\\\\
AND\\
y=20sin75+26tsin50\qquad and \qquad y=50tsin\alpha\\\\
...\\
\frac{20sin75}{ (50sin\alpha-26sin50)}=t\\
so\\
\frac{(20sin75)}{ (50sin\alpha-26sin50)}=\frac{(20cos75)}{ (50cos\alpha-26cos50)}\\\\$$

$$\\(20sin75)(50cos\alpha-26cos50)=(20cos75)(50sin\alpha-26sin50)\\\\
(20sin75)(50cos\alpha)-(20sin75)(26cos50)=(20cos75)(50sin\alpha)-(20cos75)(26sin50)\\\\
(1000sin75)(cos\alpha)-(520sin75cos50)=(1000cos75sin\alpha)-(520cos75sin50)$$

$$\\(1000sin75cos\alpha)-(1000cos75sin\alpha)=(520sin75cos50)-(520cos75sin50)\\\\
1000(sin75cos\alpha-cos75sin\alpha)=520(sin75cos50-cos75sin50)\\\\
1000sin(75-\alpha)=520sin(75-50)\\\\
sin(75-\alpha)=0.52sin(25)\\\\
75-\alpha=asin(0.52sin(25))\\\\
-\alpha=asin(0.52sin(25))-75\\\\
\alpha=75-asin(0.52sin(25))\\\\$$

$${\mathtt{75}}{\mathtt{\,-\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}^{\!\!\mathtt{-1}}{\left({\mathtt{0.52}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{25}}^\circ\right)}\right)} = {\mathtt{62.304\: \!975\: \!095\: \!575}}$$

$${\mathtt{90}}{\mathtt{\,-\,}}{\mathtt{62.304\: \!975\: \!095\: \!575}} = {\mathtt{27.695\: \!024\: \!904\: \!425}}$$   =     27 degrees 41minutes and 42 seconds

The speed boat needs to set a course for

   $$N\;27^041'42"E$$

What a great question and Heureka and I even agree   :)))

So you mean that you and everyone else will not give their personal information?

$${\mathtt{\,-\,}}{\mathtt{9}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}} = -{\mathtt{8}}$$

Easy one

To simplify you divide the denominator and numerator by a common factor.

this is repeated until they don't have a common factor.

This is the fraction in it's lowest terms.

68/100

/2

34/50

/2

17/25

Can't be reduced anymore.

$$\\44-2(3x+4)=-18x\\\\
44-6x-8=-18x\\\\
36-6x=-18x\\\\
36-6x+6x=-18x+6x\\\\
36=-12x\\\\
-3=x\\\\
x=-3$$

$$6x(3x-4)=18x^2-24x$$