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@@ End of Day Wrap    Wed 12/8/15     Sydney, Australia Time   8:50pm    ♪ ♫

Hi everyone,

Our fabulous answers were contributed by CPhill, Heureka, Rubenhh, Alan, jdh3010, Dbg4thebest, luigiboi, Shaniab29544 and  Geno3141.  Thankyou   

There seems to be some disagreement here.    

Thanks Chris, of course Chris is correct :)

The derivative cannot be expressed as a function of x but it can certainly be expressed as a function of y.

Ok so why is such a bid deal made of functions verses non function ?

The question i have is that to make a drink you need a ratio (3:1) of juice to water.

If ou wanna make 1200 ml how much juice do yu need??? 

9-9 sin^2 x become 9(1-sin^2 x)

hopefully your are comfortable with this:

9-9y

= 9*1-9*y

=9(1-y)

I have factored out the 9    

Ok now lets look at yours

$$\\9-9 sin^2 x\\\\
=\textcolor[rgb]{0,0,1}{9}*1-\textcolor[rgb]{0,0,1}{9}*sin^2 x\\\\
=\textcolor[rgb]{0,0,1}{9}(1-sin^2 x)
\textcolor[rgb]{0,0,1}{}$$

Again I have factored out the 9   :))

$${\frac{\left({{\mathtt{6}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{{\mathtt{4}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{{\mathtt{8}}}^{{\mathtt{2}}}\right)}{{\mathtt{\,-\,}}\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{8}}\right)}} = {\frac{{\mathtt{11}}}{{\mathtt{16}}}} = {\mathtt{0.687\: \!5}}$$

Thanks Chris,

This is what I would do with this question.

$$\\36 \le 1-5z>-21\\
$subtract 1 throughout$\\
35 \le -5z>-22\\
$divide throughout by -5 but you will have to turn the signs around$\\
-7 \ge z<-4.4\\
$now I will separate them because this really doesn't make much sense.$\\
-7\ge z \qquad and \qquad z<-4.4\\
z\le -7 \qquad and \qquad z<-4.4\\
so\\
Z\le -7$$

This original line  $$\\36 \le 1-5z>-21\\$$     IS NOT normal or good presentation.

It should have been presented as 

$$\\36 \le 1-5z \qquad and \qquad 1-5z >-21\\$$

In Australia I would call it an interval but line segment sounds best out of those answers.

There is no question here   

Take a look at this   :)

I am not sure what you mean?

perhaps

whats 0.667 x 10's exponential form

$$\\10^x=6.67\\
x=log(6.67)\\
x=0.824125833\\
so\\
6.67=10^{0.824125833}$$

Equivalent Ratios 2:6=   :18=10:    =    :72=200:

$$\small{\text{$
\begin{array}{rclcl}
&&\dfrac{\textcolor[rgb]{0,0,1}{2}}{\textcolor[rgb]{0,0,1}{6}} &=& \dfrac{1}{3}\\\\
&=&\dfrac{1}{3}\cdot \dfrac{6}{6} &=& \dfrac{\textcolor[rgb]{1,0,0}{6}}{\textcolor[rgb]{0,0,1}{18}}\\\\
&=&\dfrac{1}{3}\cdot \dfrac{10}{10} &=& \dfrac{\textcolor[rgb]{0,0,1}{10}}{\textcolor[rgb]{1,0,0}{ 30}}\\\\
&=&\dfrac{1}{3}\cdot \dfrac{24}{24}&=& \dfrac{\textcolor[rgb]{1,0,0}{ 24}}{\textcolor[rgb]{0,0,1}{72}}\\\\
&=&\dfrac{1}{3}\cdot \dfrac{200}{200} &=&\dfrac{\textcolor[rgb]{0,0,1}{200}}{ \textcolor[rgb]{1,0,0}{ 600}}
\end{array}
$}}$$

2:6 = 6:18 = 10:30 = 24:72 = 200:600

$$\\\frac{4x}{9}\le -27$$

multiply both sides by  9/4

Really TR ?  You like the forum better when it is quiet?

I thought you would like it much better when there are more kids about.

You have surprised me. :/

0.667*100 = 66.7 = 6.67*10¹

$${\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{5}} = {\mathtt{60}}$$

r^2=0.785

Root both sides

r=$${\sqrt{{\mathtt{0.785}}}}$$

So, r= 0.886002 or -0.886002

Find all values of  such that .

$$\small{\text{$
\begin{array}{rcl}
\sqrt{4x^2}-\sqrt{x^2} &=& 6\\
\sqrt{4}\sqrt{x^2}-\sqrt{x^2} &=& 6\\
2\sqrt{x^2}-\sqrt{x^2} &=& 6\\
\sqrt{x^2} &=& 6 \qquad | \qquad 1^2\\
x^2 &=& 36 \qquad | \qquad \pm\sqrt{}\\
x_{1,2} &=& \pm\sqrt{36} \\
x_{1,2} &=& \pm6 \\
\mathbf{x_1} & \mathbf{=} & \mathbf{6}\\
\mathbf{x_2} & \mathbf{=} & \mathbf{-6}
\end{array}
$}}$$

77.5/3.09*10^19

=2.5080906148867313915857605177993527 5080906148867313915857605177993527...*10^18

(5080906148867313915857605177993527) repeating

0.667*100=667*10^(-1)

1.236*100=1236*10^(-1)

425/1000=425*10^(-3)