All Answers 358087 Answers

Wow.....this Fight/Argument is amazing....EXCEPT FOR THE FACT THAT YOU TEENS, KIDS, WHATEVER YOU GUYS ARE, HAVE WRECKED MY HOUSE!!!!!!

To TR: You're cleaning up this mess right now! And I believe there's better things to do right now than to "take over the world"? Maybe you should study for tomorrow's History test? Or taking notes for Friday's English essay? Maybe doing Math HOMEWORK? Instead, I see you making a mess around my house while fighting the rest of the Forums pack. 

However, to be honest, good fighting skills, you seem to be in the Suicide Squad. If you continue your life of 'crime', maybe the Government would take you in the Suicide Squad, besides, the government now needs new Suicide Squad members to execute black op missions, and war seems like your skill.

To 7UP: please give me a 7UP, im getting thirsty after lecturing TR.

To Rosala: Is TR always like this? If he is, he must be crazy and violent. Although he is a genius based on the posts he has done, he seems pretty violent as well, anyways continue what you were going to do for 7UP.

To Nauseated: Yeah, he definetely needs to press Pause from his warfare games, that's why he said earlier not many girls can eat metal, lol im just joking, but seriously, life isn't just about video games, its about work, food, paying bills, taxes, more work, quality time with important or fun people, more work, conferences and meetings, more work, trying to find a soulmate, more work, trying to grab #1 spots, more work, and death. You'll get all of those things if you decide to press pause.

Thx Sis

(please don't ask me or Melody what the numbers mean, we have no reason why except to tell us apart?)

@@ End of Day Wrap    Sun 16/8/15     Sydney, Australia Time   11:40pm      ♪ ♫   

Good day to you all,   

Our great answers today were delivered by Alan, CPhill, Heureka and Dragonlance.  Thank you   

The significance of you post has only just dawned on me.  I mean the colours of the your flag.

That is so cool!

Greeen for faith and fertility.  That makes good sense.

White for purity, truth and peace.  I am not sure why white is widely used to signify purity.  I guess, if it is at all dirty it is not white any more so , that does make sense. 

Saffron I am wondering why/how saffron is linked to courage, sacrafice and spirit :/

Can you explain that Rosala ?

I like your Scarlet Macaw Melody44   

She is a really BIG sister to my Crimson Rosella :))

Thanks Alan, I really like this answer.

I doubt that I have absorbed it but it is the only explanation of electricity that I have ever understood.  :))

I just added this one to our puzzle sticky thread :)  Thanks Maia :))

November = 14118

October = 15107        

That does look rather wet Rosala :))

When did you move?  

September=1999

I understand both answers but I do not understand this statement Geno

To get the answer of 5, change the first '5' into a '2'  

(Sorry I get you now - how on Earth did you figure that out!)

What does that mean and what has it got to do with your graphical solution ?

Your algebra is really neat Alan  

Geno has said that if 

2^{x + 1} + 5·2^{x - 2} = 104 

then 

2^{x + 1} + 5·2^{x - 2} - 104 =0

If we graph 

y=2^{x + 1} + 5·2^{x - 2} - 104 

and we graph

y=0    (this is just the x axis)

then, where the two graphs cross on the x axis will be the solution.

This is a technique that we use all the time but I think many students (even those who use it ) do not really understand what they are doing. :)

Here is the graph.

Well spotted geno!

2^(x+1) + 5*2^(x-2) = 104

2^x*(2 + 5/4) = 104

2^x*13/4 = 104

2^x = 104*4/13

2^x = 32

2^x = 2^5

x = 5

.

Thanks Alan,

I'm still scratching my head on this one. (contemplation and confusion - not nits   LOL )

$$\\2m(3m+1)\\\\
=2m*3m\;\;+\;\;2m*1\\\\
=6m^2\;\;+\;\;2m$$

This is what I get, numerically, using MathCad:

.

10x+3x=13x

so

13x=169

now divide both sides by 13  

7,952/99 = 80.3232323232

100% is 8032.32323232

1% is 80.3232323232 

13 feet

I am jut going to REDO it here   :))

$$\\y=18.5+6sin((9(\pi/12)) - (10(\pi/12)))\\\\
y=18.5+6sin(9\pi/12 - 10\pi/12)))\\\\
y=18.5+6sin(-\pi/12)))\\\\
$ 4th quad so neg$\\\\
y=18.5-6sin(\pi/12)))\\\\
y=18.5-6sin(15^0)\\\\
y=18.5-6sin(45-30)\\\\
y=18.5-6[sin45cos30-cos45sin30]\\\\
y=18.5-6[\frac{1}{\sqrt2}*\frac{\sqrt3}{2}-\frac{1}{\sqrt2}*\frac{1}{2}]\\\\$$

$$\\y=18.5-6[\frac{\sqrt3}{2\sqrt2}-\frac{1}{2\sqrt2}]\\\\
y=18.5-6[\frac{\sqrt6}{4}-\frac{\sqrt2}{4}]\\\\
y=18.5-3[\frac{\sqrt6}{2}-\frac{\sqrt2}{2}]\\\\
y=\frac{37-3\sqrt6+3\sqrt2}{2}\\\\$$

Ok NOW our answers are the same :))

Yes you are right. Thanks for noticing that :)

 Sorry anon  :/

Hello,melody and anon!

I think melody made a mistake.（9pi/12-10pi/12 is in inside of the parentheses)

 y=18.5+6sin((9(pi/12)) - (10(pi/12)))

y=18.5+6sin(9pi/12-10pi/12)

y=18.5+6sin(-pi/12)

y=18.5-6sin(pi/12)

y=18.5-6sin(pi/4-pi/6)

$${\mathtt{y}} = {\mathtt{18.5}}{\mathtt{\,-\,}}{\mathtt{6}}{\mathtt{\,\times\,}}\left(\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\frac{{\mathtt{\pi}}}{{\mathtt{4}}}}\right)}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\frac{{\mathtt{\pi}}}{{\mathtt{6}}}}\right)}{\mathtt{\,-\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\frac{{\mathtt{\pi}}}{{\mathtt{4}}}}\right)}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\frac{{\mathtt{\pi}}}{{\mathtt{6}}}}\right)}\right)$$

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\frac{{\mathtt{\pi}}}{{\mathtt{4}}}}\right)} = {\frac{{\sqrt{{\mathtt{2}}}}}{{\mathtt{2}}}}$$  $$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\frac{{\mathtt{\pi}}}{{\mathtt{6}}}}\right)} = {\frac{{\sqrt{{\mathtt{3}}}}}{{\mathtt{2}}}}$$ $$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\frac{{\mathtt{\pi}}}{{\mathtt{4}}}}\right)} = {\frac{{\sqrt{{\mathtt{2}}}}}{{\mathtt{2}}}}$$ $$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\frac{{\mathtt{\pi}}}{{\mathtt{6}}}}\right)} = {\frac{{\mathtt{1}}}{{\mathtt{2}}}}$$

$${\mathtt{y}} = {\mathtt{18.5}}{\mathtt{\,-\,}}{\mathtt{6}}{\mathtt{\,\times\,}}\left({\frac{{\sqrt{{\mathtt{6}}}}}{{\mathtt{4}}}}{\mathtt{\,-\,}}{\frac{{\sqrt{{\mathtt{2}}}}}{{\mathtt{4}}}}\right) = {\mathtt{18.5}}{\mathtt{\,-\,}}{\frac{{\mathtt{3}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6}}}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{3}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{2}}}}}{{\mathtt{2}}}}$$

Well that is great :)

64x^6-80x^4+8x^3+24x^2-4x-1=0

64*(cos(2pi/11))^6-80*(cos(2pi/11))^4+8*(cos(2pi/11))^3+24*(cos(2pi/11))^2-4*(cos(2pi/11))-1

$${\mathtt{64}}{\mathtt{\,\times\,}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\frac{{\mathtt{360}}}{{\mathtt{11}}}}\right)}}^{\,{\mathtt{6}}}{\mathtt{\,-\,}}{\mathtt{80}}{\mathtt{\,\times\,}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\frac{{\mathtt{360}}}{{\mathtt{11}}}}\right)}}^{\,{\mathtt{4}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{8}}{\mathtt{\,\times\,}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\frac{{\mathtt{360}}}{{\mathtt{11}}}}\right)}}^{\,{\mathtt{3}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{24}}{\mathtt{\,\times\,}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\frac{{\mathtt{360}}}{{\mathtt{11}}}}\right)}}^{\,{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{4}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\frac{{\mathtt{360}}}{{\mathtt{11}}}}\right)}{\mathtt{\,-\,}}{\mathtt{1}} = -{\mathtt{0.000\: \!000\: \!000\: \!004\: \!464\: \!9}}$$

Yes it looks like you might be right - it is certainly is very close to zero :)

I am not so sure that Wolfram|Alpha agrees with you though.  

How comes 153?

9=9

10=1

11=2

12=1

13=4

14=1

15=6

16=1

17=8

18=1

19=10

20=0

21=1

22=0

23=3

24=0

25=5

SUM = 58 Odd integers