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modulus is not absolute function!

Use the function abs().

For example, type in abs(-6) to get 6

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There are two positive solutions that can be obtained numerically as follows:

There is also a negative solution that could be obtained by the bisection method (x ≈ -0.82667)

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Like so:

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\(^nC_r=\frac{n!}{r!(n-r)!}\\ so\\ ^8C_5=\frac{8!}{5!*3!}\\ ^8C_5=\frac{6*7*8}{1*2*3}\\ ^8C_5=\frac{7*8}{1}\\ ^8C_5=56\)​

2x2x2x2=16

what's 8C5? amd how to do it without using a calculator?

\(\begin{array}{rcll} && ^8C_5 \\\\ &=&\dbinom{8}{5} \\\\ &=&\dbinom{8}{8-5} \\\\ &=&\dbinom{8}{3}\\\\ &=&\dfrac{8}{3}\cdot \dfrac{7}{2} \cdot \dfrac{6}{1}\\\\ &=&\dfrac{8}{2}\cdot \dfrac{7}{1} \cdot \dfrac{6}{3}\\\\ &=&4\cdot 7 \cdot 2\\\\ &=& 56 \end{array} \)

miles per hour means      miles divided by hours

how many ways 15 student can be sit where 2 talkative students never sit together?

Are they sitting in a row or in a circle or what?

It just means square the R's and add the squares together.  

For it to have any more meaning woud depend on the exact question.

Hi Heureka,

I have added the fabulous thread to the Latex sticky thread.

A great trig diagram from Heureka.                                 26th June 2016

http://web2.0calc.com/questions/sine-law_1

Hallo Melody,

the diagram is in Latex.

My new version:

The Latex package is:

\usepackage{tikz}

\usetikzlibrary{  calc,   positioning,   automata, ... }

The source code is:

Hallo Melody,

the diagram is in Latex.

My new version:

The Latex package is:

\usepackage{tikz}

\usetikzlibrary{  calc,   positioning,   automata, ... }

The source code is:

\(\begin{tikzpicture} % Hilfslinie \coordinate[ ] (D) at (6.14300380421,0); %Punkte \coordinate[label=left:$P$] (P) at (0,0); \draw [dashed,color=red,line width=0.5pt] (P)--(D); \coordinate[label=right:$Q$] (Q) at (31:6); \coordinate[label=right:$R$] (R) at (5.14300380421,4.47074499954); \draw [dashed,color=red,line width=0.5pt] (3.14300380421,4.47074499954)--(R); % Winkel\)
\(\begin{scope}[shift={(P)}] \draw (0,0) -- (0:2.00cm) arc (0:31:2.00cm); \draw (15.5:2.35cm) node {$31^{\circ}$}; \draw[fill=green] (0,0) -- (0:1.25cm) arc (0:41:1.25cm); \draw (20.5:1.55cm) node {$41^{\circ}$}; \end{scope}\)

\(\begin{scope}[shift={(R)}] \draw[fill=green] (0,0) -- (-180:1.25cm) arc (-180:-139:1.25cm); \draw (-160:1.55cm) node {$41^{\circ}$}; \end{scope}\)
\(\draw [color=blue!50,line width=1.5pt] (P)--(Q)--(R)--cycle; \coordinate[label=right:$h$] (h) at ($(R)!.5!(Q)$); \draw ($(P)!.7!(Q)$) node [below,rotate=31]{$600\ m$}; \draw [fill=blue!50] (0,0) circle [radius=1.5pt]; \draw [fill=blue!50] (31:6) circle [radius=1.5pt]; \draw [fill=blue!50] (R) circle [radius=1.5pt]; \end{tikzpicture}\)

Hallo Melody,

the diagram is in Latex.

My new version:

The Latex package is:

\usepackage{tikz}

\usetikzlibrary{  calc,   positioning,   automata, ... }

The source code is:

\begin{tikzpicture}
% Hilfslinie
\coordinate[ ] (D) at (6.14300380421,0);

%Punkte
\coordinate[label=left:$P$]  (P) at (0,0);
\draw [dashed,color=red,line width=0.5pt] (P)--(D);

\coordinate[label=right:$Q$] (Q) at (31:6);
\coordinate[label=right:$R$] (R) at (5.14300380421,4.47074499954);
\draw [dashed,color=red,line width=0.5pt] (3.14300380421,4.47074499954)--(R);

% Winkel
\begin{scope}[shift={(P)}]
   \draw (0,0) -- (0:2.00cm) arc (0:31:2.00cm);
   \draw (15.5:2.35cm) node {$31^{\circ}$};
   \draw[fill=green] (0,0) -- (0:1.25cm) arc (0:41:1.25cm);
   \draw (20.5:1.55cm) node {$41^{\circ}$};
\end{scope}

\begin{scope}[shift={(R)}]
   \draw[fill=green] (0,0) -- (-180:1.25cm) arc (-180:-139:1.25cm);
   \draw (-160:1.55cm) node {$41^{\circ}$};
\end{scope}

\draw [color=blue!50,line width=1.5pt] (P)--(Q)--(R)--cycle;

   \coordinate[label=right:$h$] (h) at ($(R)!.5!(Q)$);
   \draw ($(P)!.7!(Q)$) node [below,rotate=31]{$600\ m$};

\draw [fill=blue!50] (0,0) circle [radius=1.5pt];
\draw [fill=blue!50] (31:6) circle [radius=1.5pt];
\draw [fill=blue!50] (R) circle [radius=1.5pt];

\end{tikzpicture}

What is 1,000,000!=8.263931688331240062376646103173 x 10^5,565,708

3x+3(x-2)= 3(x+6)3*x+3*(x-2)= 3(x+6) = x=8

This term does not make sense.

Farmer Fran has 38 barnyard animals consisting of only chickens and goats. If these animals have 116 legs, how many of each type of animal are there?

Let the number of chickens =C

The number of goats =38 - C

2C + 4[38 - C] =116

2C + 152 - 4C =116

-2C=-36 divide both sides by -2

C= -36/-2

C=18 the number of chickens

38 - 18 =20 the number of goats, so that:

[18 x 2] + [20 x 4] =116 legs

wood board 156 centimeters long is cut into three parts. The two longer parts are the same length and are 15 centimeters longer than the shoertest part. How long are the three parts?

Let the shortest part=S

The other two parts=S + 15

S + 2[S + 15] =156

S + 2S + 30 =156

3S=156 - 30 =126 divide both sides by 3

S=126/3

S=42 cm-the shortest wood board

42+15=57cm-the two other wood boards, so that:

42 + 57 + 57 =156 cm

how many radians is 36 degrees

I work it out like this, some people just remember a fromula.

\(180 degrees = \pi radians\qquad so\\ 1 degrees = \frac{\pi}{180} radians\qquad so\\ 36 degrees = \frac{36\pi}{180} radians\qquad so\\ 36 degrees = \frac{\pi}{5} radians\qquad \\ \)

Inverse cos is the same as arc cos

use

[2nd] [acos]