All Answers 358093 Answers

A pie is a warm baked dish made from a pastry dough.

If you meant Pi, Pi is the number used to define various measures in circles and spheres.

Some examples:

circumference of a circle =$${\mathtt{\pi}}{\mathtt{\,\times\,}}{\mathtt{diameter}}$$

area of a circle = $${\mathtt{\pi}}{\mathtt{\,\times\,}}{{\mathtt{radius}}}^{{\mathtt{2}}}$$

volume of a sphere = $${\frac{{\mathtt{4}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}{\mathtt{\pi}}{\mathtt{\,\times\,}}{{\mathtt{radius}}}^{{\mathtt{3}}}$$

area of a sphere = $${\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{\pi}}{\mathtt{\,\times\,}}{{\mathtt{radius}}}^{{\mathtt{2}}}$$

Pi is an irrational number, meaning you can't write it's exact value as it has an infinite amount of decimals.

Most people just use the first two to five decimals (3.14159), if you want to be thorough you might use the first 100 digits:

Note

3^1 = 3

3^2 = 9

3^3 = 27

4^4 = 81

And this pattern repeats

So

2189 / 4 = 547 + 1/4

So...the last digit is 3

That looks very impressive Heureka :))

3x+2y=4           (remove 2y from both sides)

3x=4-2y            (divide by 3 on both sides)

x=(4-2y)/3

This expression isn´t equal to a specifik number as long as you don´t know what number y is. 

No there isn't one.

Degrees and radians are different units to measure angles in.

It is like you can measure distance in either kilometres or miles.

6.8 kg = 6800 g

Equally divided among 6 students this is 6800/6 = 1133 g each, to the nearest gram.

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1 - cos(2x) + cos(6x) - cos(8x) = 0       x =?

$$\small{\text{$
\begin{array}{rcl}
1-\cos{(2x)}+\cos{(6x)}-\cos{(8x)}&=&0\\
1-\cos{(2x)} &=&\cos{(8x)}-\cos{(6x)}\\
&&$Formula:\\
&&
$~\boxed{\mathbf{ \cos{2x}=1-2\sin^2{(x)} \quad or \quad 1-\cos{2x}=2\sin^2{(x)} }}\\
2\sin^2{(x)} &=& \cos{(8x)}-\cos{(6x)}\\
&&$Formula:\\
&&
$~\boxed{\mathbf{
\cos{(a)}-\cos{(b)}=2\sin{ \left( \dfrac{a+b}{2} \right)}\sin{ \left( \dfrac{b-a}{2} \right)}
}}\\
&&
\cos{(8x)}-\cos{(6x)}=2\sin{ \left( \dfrac{14x}{2} \right)}\sin{ \left( \dfrac{-2x}{2} \right)}\\
&&
\cos{(8x)}-\cos{(6x)}= -2\sin{ (7x) }\sin{(x)}\\
2\sin^2{(x)} &=& -2\sin{ (7x) }\sin{(x)}\\
\sin^2{(x)} &=& -\sin{ (7x) }\sin{(x)}\\
\sin^2{(x)} +\sin{ (7x) }\sin{(x)} &=& 0\\
\sin{(x)} \left[ \sin{(x)} + \sin{ (7x) } \right] &=& 0\\
&&$Formula:\\
&&
$~\boxed{\mathbf{
\sin{(a)}+\sin{(b)}=2\sin{ \left( \dfrac{a+b}{2} \right)}\cos{ \left( \dfrac{b-a}{2} \right)}
}}\\
&&
\sin{(x)}+\sin{(7x)}=2\sin{ \left( \dfrac{8x}{2} \right)}\cos{ \left( \dfrac{6x}{2} \right)}\\
&&
\sin{(x)}+\sin{(7x)}=2\sin{ (4x) }\cos{ (3x) }\\
\sin{(x)}\cdot 2 \cdot\sin{ (4x) }\cos{ (3x) } &=& 0\\
\end{array}
$}}$$

The solution set of the given equation is:

$$\\\boxed{\mathbf{
\sin{(x)}=0 \qquad \textcolor[rgb]{150,0,0}{x = k\cdot\pi \qquad k \in \mathrm{Z} }
}}\\
\boxed{\mathbf{
\sin{(4x)}=0 \qquad 4x = k\cdot \pi \qquad \textcolor[rgb]{150,0,0}{x = k\cdot \dfrac{\pi}{4} \qquad k \in \mathrm{Z} }
}}\\
\boxed{\mathbf{
\cos{(3x)}=0 \qquad 3x = \pm \dfrac{\pi}{2}+ k\cdot 2\cdot \pi \qquad \textcolor[rgb]{150,0,0}{x = \pm\dfrac{\pi}{6}
+ k\cdot \dfrac{2}{3}~\pi \qquad k \in \mathrm{Z} }
}}$$

Bad choice of word I would have just preferred to factorise rather than use the formula. 

You are nearly right zacismyname.  However, you should take a closer look at your calculation of $$1^2-4\times3\times-80$$ under the square root sign.  It isn't 960 (almost, but not quite!).

You've nothing to be ashamed of!

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. . . I'm a bit ashamed I didn't see those factors 

The length of a room is 1 more than 3 times its width. The area of the room is 80 square meters. Find the demensions.

$$w\times{l}=A$$

$$w\times({3w+1})=80$$

$$3w^2+w=80$$

$$3w^2+w-80=0$$

$$w=\frac{-1+\sqrt{1^2-4\times{3}\times{-80}}}{2\times{3}}$$ or $$w=\frac{-1-\sqrt{1^2-4\times{3}\times{-80}}}{2\times{3}}$$

$$w=\frac{-1+\sqrt{961}}{6}$$ or $$w=\frac{-1-\sqrt{961}}{6}$$

$$w=\frac{{-1}+31}{6}$$

$$\mathbf{w=5}$$

$$l=3\times{5}+1}$$

$$\mathbf{l=16}$$

Fixed!

Let L be the length and W the width

L = 3W + 1                (1)   (I assume the room is 1 metre longer than 3 times the width)

L*W = 80                  (2)

Using (1) in (2)

(3W + 1)W = 80

Rearrange

3W² + W - 80 = 0

This factors as

(3W + 16)(W - 5) = 0

Since we can't have a negative width for the room, the only valid solution is W = 5m

Using (1) this means that L = 3*5 + 1 = 16m

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If P(5 - 3n) = 5/6 - 1/3n then P = (5/6 - 1/3n)/(5 - 3n), so P is a function of n.

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This is too general a question to be answered briefly here.

Provide a specific example of the sort of probabilistic problems you want to solve.

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