All Answers 358087 Answers

$$\frac{4}{3}x-\frac{1}{2}=0$$

I would do this question by multiplying both sides by the lowest common denominator which is 6.

That way you get rid of all the fractions right from the begining.  

$$\begin{array}{rll}
6\times \left(\frac{4}{3}x-\frac{1}{2}\right)&=&0 \times 6\\\\
\frac{6\times 4}{3}x-\frac{6}{2}&=&0\\\\
8x-3&=&0\\\\
8x&=&3\\\\
x&=&\frac{3}{8}\\\\
\end{array}$$

Yes they are correct.  I've never seen them written on a unit circle backward before but they are right.

(8.76 x 109)(6.52 x 10-3)/13.27 x 105

Enter as: [(8.76*10^9)(6.52*10^-3)]/(13.27 x 10^5) = 43.040844009042954.

Alan answered this a couple of days ago. 

Angle EOB is just 180° - angle EOD, so yes, subtract!

I like

$$\begin{array}{l}
$$\mathbf{P}arachute\\\mathbf{E}xpert\\\mathbf{M}y\\\mathbf{D}ear\\\mathbf{A}unt\\\mathbf{S}ally
\end{array}$$

:)

(2.4 x 10^-9) (4.0 x 10^23) 

= (2.4*10^-9)*(4.0* 10^23)

= 960000000000000

= $$\mathbf{9.6*10^{14}}.$$

Yes, Please Excuse My Dear Aunt Sally.

Here, we just need to get x alone, or in other words, x = something.

$$\begin{array}{l}
\frac{4}{3}x-\frac{1}{2}=0\qquad\mbox{Add $\frac{1}{2}$ to both sides}\\
\frac{4}{3}x=\frac{1}{2}\qquad\mbox{Divide both sides by $\frac{4}{3}$}\\
x=\frac{1}{2}\div\frac{4}{3}\qquad\mbox{Remember, when diving two fractions, multiply by the reciprocal (flip-flop the second fraction)}\\
x=\frac{1}{2}\times\frac{3}{4}\qquad\mbox{Multiply the left side out}\\
x=\frac{3}{8}

\end{array}$$

To check this, put in $$\frac{3}{8}$$ for x!

$$\begin{array}{l}
\frac{4}{3}x-\frac{1}{2}=0\\
\frac{4}{3}\times\frac{3}{8}-\frac{1}{2}=0\\
\frac{12}{24}-\frac{1}{2}=0\qquad\mbox{Reduce the first fraction}\\
\frac{1}{2}-\frac{1}{2}=0\\
0=0

\end{array}$$

It works, because 0 does equal 0!

The answer is 19/30.

What? Could you ask this differently?

I have no idea what your question is...

merci

asin is the same as sin^-1

acos is the same as cos^-1

atan is the same as tan^-1

$$\frac{d}{dx}\sin x = \cos x\\\\
\frac{d}{dx}\cos x = -\sin x$$

These should be committed to memory!

NinjaDevo sent me a message about this.  Here's a copy of the reply I sent him:

The default for the LaTeX box on the site is to be in "Display" math mode. I often switch this off to begin with by inserting $$ right at the start. If I then type words it comes out as text. 

In the "average slope" case I wanted to start with some "Inline" math, which requires a single $ immediately before and immediately after the math (so it looks like I started the whole thing with 3 dollar signs - 2 to switch off the default "Display" mode and 1 to switch on the "Inline" mode). 

Putting $$ immediately before and after the math produces "Display" mode math, where the math appears centred on a new line. 

You switch off math mode and enter text mode by using either $ (for "Inline" math) or $$ (for "Display" math). 

Hope this helps. 
PS I'm no LaTeX expert - I just use trial and error and see what results!

what about the coordinates in the second graph ! 

the place which I put in question mark ? 

The cubed root button is the little ³√x button, you can find it here (highlighted):

To use it, type in the number you want cube-rooted, click the button, and click the equal sign!

All looks good to me.

Remember. If you take any point on the unit circle,  cos will be the x value and sin will be the y value

It is easy to see why this is true because the hypotenuse is one.

Alan is here so he can tell us!  Please Alan.

I actually don't think that Alan's $ signs did anything.

If you are working with LaTex away from a forum you need to put $ signs around the maths made parts.

On forums this is effectively done for you.  I know Alan writes a lot of his Latex and coppies it over.  He probably didn't here but the $ signs would just be a habit that he is in.

I don't know why he has put the 2 extra dollar signs at the front.  I think he would b e happy to tell us though.

This was your code Alan

$$$\int dx$

$$$\int dx$$$

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

The other day Heureka used something else instead of \mbox{} 

It had the same purpose.  I cant remember what it was but it would be referred to in the LaTex thread for sure. I have been faily consciencious about updating and adding to the LaTex thread.  Although I will admit that it is a bit of a mess.  

yep that's it!

You are better off to put the original amount in the one with the hight interest rate.

Say you have an original amount of $1000.  Is it better to get 3% on this or 5%.  The highter percent is better of course.  This is assuming that there is not funny little account catches of course. 

Thanks Melody.

I think it's for the roman numerals. It's kind-of a clever nickname actually.

xvxvxv 

x = 10

v = 5

xv=15

xvxvxv=15x3

Is this what you mean?

(-2p/q)*(-q)^4*2/5 p^2

$$\frac{-2p}{q}*(-q)^4*\frac{2}{5} p^2\\\\
=\frac{-2p}{q}*\frac{q^4}{1}*\frac{2p^2}{5}\\\\
=\frac{-2p}{1}*\frac{q^3}{1}*\frac{2p^2}{5}\\\\
=\frac{-4p^3q^3}{5}\\\\$$

BRAIN TEASERS                      (posted by Reinout-g   15/5/2014) 

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