ROF LOL     ROF LOL

Thanks guys and girls.  That was fabulous forum humour.    

I CAN cook up a great pi too   :)))))

It is my birthday today - this thread was a great gift :))

I'll give you all some points for making me laugh :))

That address does not work MG :/

What colour are the llamas and how much does the roof weigh?

$$\sqrt{-1}=i$$

i is NOT a real number it is an imaginary number.  It is the basic unit of the imaginary number system :)

0.08 *59^1=0.08*59

$${\mathtt{0.08}}{\mathtt{\,\times\,}}{\mathtt{59}} = {\frac{{\mathtt{118}}}{{\mathtt{25}}}} = {\mathtt{4.72}}$$

I don't think that I have seen that before Chris.    

$$6\times 1 \div 6 = 6\div 6 = 1$$

this is a furure value of an ordinary anuity problem.

I am going to assume it is 3% p.a and that there are 52 weeks in a year.

C=100,    i= 0.03/52      n=7*52

Now you can find Future value.

But Sasini, you were asked to leave it as a proper fraction.   

$$\frac{7.25}{26.2}=\frac{7.25*10}{26.2*10}=\frac{72.5}{262}=\frac{72.5*2}{262*2}=\frac{145}{524}$$

hi Sasini, 

$$80008(1+ 0.00625)*12^2$$

$${\mathtt{80\,008}}{\mathtt{\,\times\,}}\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.006\: \!25}}\right){\mathtt{\,\times\,}}{{\mathtt{12}}}^{{\mathtt{2}}} = {\mathtt{11\,593\,159.2}}$$

$${\mathtt{1\,000\,000\,000}}{\mathtt{\,\times\,}}{\mathtt{100}} = {\mathtt{100\,000\,000\,000}}$$

Thanks Heureka,

I have added your table to our Latex thread :)

A nice table drawn by Heureka :)

\small{\begin{array}{c|c}\text{nat\"urliche Zahl} & \text{Dreierpotenz} \\

\hline\\(0) & 0^3 \\1 & 1^3 \\2 & 2^3 \\3 & 3^3 \\4 & 4^3 \\5 & 5^3 \\\cdots & \cdots \\n & n^3 \\\\\hline\end{array}}

$$\small{\begin{array}{c|c}\text{nat\"urliche Zahl} & \text{Dreierpotenz} \\
\hline\\(0) & 0^3 \\1 & 1^3 \\2 & 2^3 \\3 & 3^3 \\4 & 4^3 \\5 & 5^3 \\\cdots & \cdots \\n & n^3 \\\\\hline\end{array}}$$

I would consider the graph

y=(x+3)(2x-1)(2-x)    

The roots are  -3, 1/2, and 2

It is of the form    

 $$\\y=-ax^3+bx^2+cx+d\\\\
$Where a,b,c and d are real numbers and a is positive.$$$

****    I instantly know the shape of this graph.    ****

Refer to this post that I did in the past to understand what I mean.

It will help you enormously if you understand this older post  !!!

I have done another version of the graph    

I have just done this really to demonstrate another feature of Desmos Graphing calculator :)

Nice explanation - thanks :)

Very nice Alan.    

I really like the way you have displayed this.

To get Tina's probabilities, Alan has just  counted the nymber of pairs that would work and divided it by 5C2.

5C2 is the number of ways that 2 numbers can be chosen from 5 where order does not matter.

nCr(5,2)

$${\left({\frac{{\mathtt{5}}{!}}{{\mathtt{2}}{!}{\mathtt{\,\times\,}}({\mathtt{5}}{\mathtt{\,-\,}}{\mathtt{2}}){!}}}\right)} = {\mathtt{10}}$$

$$x^2+2*3x+3^2=(x+3)^2$$

Anon you have found the answer if this polynomial was = 0    

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{15}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{1}}{\mathtt{\,-\,}}{\sqrt{{\mathtt{14}}}}{\mathtt{\,\times\,}}{i}\\
{\mathtt{x}} = {\sqrt{{\mathtt{14}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{1}}{\mathtt{\,-\,}}{\mathtt{3.741\: \!657\: \!386\: \!773\: \!941\: \!4}}{i}\\
{\mathtt{x}} = {\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3.741\: \!657\: \!386\: \!773\: \!941\: \!4}}{i}\\
\end{array} \right\}$$

.

Was bedeutet Dreierpotenzen der natürlichen Zahlen ?

$$\small{
\begin{array}{c|c}
\text{nat\"urliche Zahl} & \text{Dreierpotenz} \\
\hline
\\
(0) & 0^3 \\
1 & 1^3 \\
2 & 2^3 \\
3 & 3^3 \\
4 & 4^3 \\
5 & 5^3 \\
\cdots & \cdots \\
n & n^3 \\
\\
\hline
\end{array}
}$$

B.   √(45 +4) - 3 = √49 - 3  =  7 - 3  = 4.

C. and D. will result in √(x +4) - 3 > 4

A. will result in √(x +4) - 3 < 4

.

On her first step she has a probability of 1/2 of choosing a direction alongside the gray square.  For each of three steps thereafter she has a probability of 1/4 of choosing a direction that keeps her beside the gray square; so her probability is (1/2)*(1/4)*(1/4)*(1/4) = 1/128

.

Here is the graph for  y=csc(x)

You can see that y=0 is an asymptote   

I think you are saying that if the probability of rain tomorrow is 1/11,

then the probablity of there not being any rain tomorrow is 10/11

☻   ☻   ☻

$$\frac{w+8}{w-8}$$      cannot be simplified :)