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Sin(θ-β)-2sin(2(θ-β))-sin(2θ)=0

0°<​θ<90°

0°<β<90°

wolframalpha:

plot sin(y-x)-2sin(2(y-x))-sin(2y) = 0 ( 0<x<pi/2 ) (0<y<pi/2)

Not a firm "proof," but

(x + y ) - y  =         

x +  y  - y    =

x + ( y - y )  =

x  +  0   =

x

This cannot be reduced because 71 is a prime number and shares no common factors with 25........we could  express this as :    - (2 + 21/25)

Now Dragonlance,

Your opening sentence was good but you do not need to get rude with people.

Anon, I think it is great that you had a go at LaTex.  I am always trying to encourage people to use it and you cannot learn it all at once :)

So please keep up your great efforts   

There are a lot of ways to put spaces between words.

Dragonlance has done it with this code:

{$This is how it should look }

$${$This is how it should look }$$

I have never used code exactly the same as Dragonlance's.

I may have used \mbox{This is how it should look }

$$\mbox{This is how it should look }$$

\ says a function is following and mbox stands for messsage box :)

Here is another way

This\; is \;how\; it\; should\; look

$$This\; is \;how\; it\; should\; look$$

Using log(m*n) = log(m) + log(n)  and log(m^n) = n*log(m) we get:

3log(A) + x*log(a) = 12log(a)

x*log(a) = 12log(a) - 3log(A)

x = 12 - 3log(A)/log(a) 

(If A and a are meant to be the same then this reduces to x = 9)

.

√108 = 6√3

√18 = 3√2

√12 = 2√3

So Manuel owes Rico  6√3 - 3√2 +2√3 = 8√3 - 3√2 pesos

.

What is the value of x? A^3a^x = a^12

$$\small{\text{$
\begin{array}{rcl}
A^3a^x &=& a^{12} \\
a^x &=& \dfrac{a^{12}}{A^3} \qquad | \qquad b=\dfrac{a^{12}}{A^3} \\\\
a^x &=& b \qquad | \qquad \ln{()} \\
x\ln{(a)} &=& \ln{(b)}\\\\
\mathbf{x} &\mathbf{=}& \mathbf{\dfrac{ \ln{(b)} }{\ln{(a)} } }\quad $
and $ \mathbf{ \quad b=\dfrac{a^{12}}{A^3} }\\\\
\end{array}
$}}}$$

Yea, but then I will have to wear two layers of titanium armor if both Rosala and TR come after me.

Maybe it's worth it.

“Titanium F*g” is funnier !!! hahahahaha

I dieing from laughter again!

see the solution in german forum:

I meant “Titanium Fang” LOL . . . . . like vampire fangs.

“Titanium F*g” hahahahaha  

Good question.

What do you think of “Carpathia Rome” and “Titanium F*g”?

Assuming you refer to the change of base formula for logarithms:

Most calculators only determine logs with a base of 10. Ex: log₁₀10000  = 4

To determine a log value with a different base, such as log₂8, you would use the change of base formula, which states that:

log_ax = log_bx / log_ba

b in this case could be 10 (or e) to let you find the value on a calculator.

So log₂8

= log₁₀8 / log₁₀2

= 3

*On the website calculator, you could write in log₂8 as log(8,2) and get the same answer:)

I think Rosala will k**l your butt. hahahaha

What about names for your children?

((100*12)*12/100)*20. Hope this helps :)

Solve the following system of equations.

8x + 5y = -84

3x + y = -21

A. x = -12, y = -3

B. x = 5, y = -24.8

C. x = 12, y = -57

D. x = -3, y = -12

The answer is D. x = -3 and y = -12

$$\small{
\begin{array}{lrcl}
(1) & 8x + 5y &=& -84 \\
\hline
(2) & 3x + y &=& -21 \qquad | \qquad \cdot 5\\
(2) & 15x + 5y &=& -105 \\
\hline
(2)-(1)& 15x-8x +5y-5y &=& -105 -(-84) \\
& 15x-8x &=& -105 + 84 \\
& 7x &=& -21 \qquad | \qquad :7\\
& \mathbf{x} & \mathbf{=} & \mathbf{-3} \\
\hline
&3x+y &=& -21\\
&3\cdot(-3) + y &=& -21\\
&-9 + y &=& -21\\
& y &=& -21 + 9 \\
& \mathbf{y} &\mathbf{=} & \mathbf{-12}
\end{array}
}$$

That’s cool you have so many who care about you.

“Bed Sores and Blood Clots” You know, Lance, that sounds like a good title for a short story about a whirlwind romance of a vampire and a werewolf. Now what could their names be?

I might extend the trading of DNA to that of a love child -- maybe two. Do you think Rosala will like it?

The doctor say I hafe to stay in bed for at least a week and I have a traction thing pulling on my legs I call it the rack. Then I not allowed lift anything heavy for a month. That means I can’t work on the ranch for a month. I finally get into real school and now I stuck in bed and can’t go. This will be my second week of h**l this year. Every year I have at least two weeks of h**l.

Not everything is horrible. My sister make me 5 get well cards so far and I probably have a 100 before this is over. Morticia visit with me most all of yesterday. Tonight she have a long ballet rehearsal. She send me some texts. She probably be on line later.

I get out of this bed 4 or 5 times a day. I get bed sores and blood clots if I stay in it all the time. I go crazy too.

How to calculate ( 1/a - 2/b ) / ( 2/a - 1/b )

$$\dfrac{ ( \frac{1}{a} - \frac{2}{b} ) } { ( \frac{2}{a} - \frac{1}{b} ) }\cdot \left( \dfrac{ab}{ab} \right) \\\\\\
=
\dfrac{ ( \frac{1}{a} - \frac{2}{b} ) \cdot ab} { ( \frac{2}{a} - \frac{1}{b} ) \cdot ab }\\\\\\
=
\dfrac{ ( \frac{1}{a}\cdot ab - \frac{2}{b}\cdot ab ) } { ( \frac{2}{a}\cdot ab - \frac{1}{b}\cdot ab ) }\\\\\\
=
\dfrac{ ( b- 2a) } { (2b - a) }\\\\\\$$

Holy c**p! How long do you have to stay in bed?

Where’s Morticia? Is she taking care of you? :)

Hi 7UP.

Yeh. I fall off the hay loft and k**l my back. I not know how bad I was hurt until the next morning and I couldn’t walk. I felt like I was in the middle of a stampede. My mom freaked out and called 911 and the paramedics take me to the hospital.

The doctor give me a ct scan and then a MRI. After that he give me 2 two shots and one he say is in my spine and will hurt but I have to stay still while he give it. Well he not kidding it hurt, it feel like the devil is raping me. But after an hour my back not hurt so much and I could feel my legs better and walk some too.

That’s really funny, DL. Your other post is great, too. Your latex is excellent. I really need to start using it on here.

You’ve been on here a lot in the last few days.

What do you do with the other 75% of the money?

$${\frac{{\mathtt{729}}}{{\mathtt{12}}}} = {\frac{{\mathtt{243}}}{{\mathtt{4}}}} = {\mathtt{60.75}}$$

$${{\mathtt{60.75}}}^{{\mathtt{3}}} = {\mathtt{224\,201.671\: \!875}}$$

answer: 224, 201.671, 875