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$$\\\frac{(r^n)^2}{r^{6-2n}}\\\\
=\frac{(r^{2n})}{r^{6-2n}}\\\\
=r^{2n-(6-2n)}\\\\
=r^{2n-6+2n)}\\\\
=r^{4n-6}\\\\$$

$${\frac{{{\mathtt{r}}}^{{\mathtt{2}}{n}}}{{{\mathtt{r}}}^{\left({\mathtt{6}}{\mathtt{\,-\,}}{\mathtt{2}}{n}\right)}}}$$

$${\frac{{{\mathtt{r}}}^{{\mathtt{4}}{n}}}{{{\mathtt{r}}}^{{\mathtt{6}}}}}$$

= $${{\mathtt{r}}}^{\left({\mathtt{4}}{n}{\mathtt{\,-\,}}{\mathtt{6}}\right)}$$

$$\frac{1}{2}x^{-1/4}=\frac{1}{2x^{0.25}}=\frac{1}{2\sqrt[4]{x}}$$

$${\frac{{\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{a}}}{{\mathtt{5}}}}{\mathtt{\,\times\,}}{\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{c}}}{{\mathtt{4}}}} = {\frac{{\mathtt{14}}{\mathtt{\,\times\,}}{\mathtt{ac}}}{{\mathtt{20}}}}$$

=  $${\frac{{\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{ac}}}{{\mathtt{10}}}}$$

there are 360 degrees in a revolution.

and

there are  $$2\pi$$     radians in a revolution.

you can't        .......

YES it is

but slope is diff in y/diff in x

y has to be on the top!

How did CPhill work this out?

what multiplies to get -143 and adds up to -2?

They mult to a negative so one is negative and one is positive

If they add up to -2 the numbers must be close together and the 'bigger' one is negative

sqrt(143)=almost 12

143/11=13

so the numbers are -13 and +11

Look at the sticky topics

That sounds interesting anon, I did not know about this. 

I ran a few solids through in my head and it worked for them 

Thank you anon,

That is really nice of you,  I am really glad that we can help you. 

Why don't you join up properly.  It is really easy and you do not have to give any personal information.

You just have to choose a username and a password.

You get your own watchlist which is really helpful and you can access the message centre and best of all we will get to know you.  :))

Your Mum

Im doing trigonometry and there is a question for example : the area of a sector of a cirlce of radius 8cm is 40cm(squared).
Find, in radians, the measure of the angle in this sector.

So to find the answer I have to put : $${\frac{{\mathtt{1}}}{{\mathtt{2}}}}$$  (8)squared.θ = 40

Why would you want to do that?

Any number that divides into itself and 1 ONLY :) 

Write the same thing in calculator and the click = but I think you already know what it is.

what is the ones digit of 9^40 ?

$$9^{40}\mod 10\\
=( \underbrace{9^2}_{=1\mod 10} )^{20}\mod 10 \qquad | \qquad 9^2\mod 10 =\ 81 \mod 10 =\ 1 \\\\
=1^{20}\mod 10 \qquad\qquad | \quad 1^{20} = 1 \\
=1\mod 10$$

A composite shape is just more than one shape put together.

A perimeter is just the distance around the outside.

There is no set formula.  It depends on what the shapes are. :)

2a/5*7c/4 = 14ac/20

The critical angle (assuming the light is travelling from the glass to air with a refractive index of 1) is given by sin^-1(1/1.74)

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{1}}}{{\mathtt{1.74}}}}\right)} = {\mathtt{35.079\: \!510\: \!940\: \!524^{\circ}}}$$

Perform the indicated operations and simplify the expression.

$$\small{\text{
$
\left( x^{\frac{1}{4}} + 1 \right)
\cdot
\textcolor[rgb]{1,0,0}{\left( \dfrac{1}{4}x^{-\frac{1}{4}} \right)}
-
\left( x^{\frac{1}{4}} - 1 \right)
\cdot
\textcolor[rgb]{1,0,0}{\left( \dfrac{1}{4}x^{-\frac{1}{4}} \right)}
$}}\\
\small{\text{
$
=
\textcolor[rgb]{1,0,0}{\left( \dfrac{1}{4}x^{-\frac{1}{4}} \right)}
\cdot
\left[
\left( x^{\frac{1}{4}} + 1 \right)
-
\left( x^{\frac{1}{4}} - 1 \right)
\right]
$}}\\\\
\small{\text{
$
=
\left( \dfrac{1}{4}x^{-\frac{1}{4}} \right)
\cdot
\left(
\not{x^{\frac{1}{4}}} + 1
- \not{x^{\frac{1}{4}}} + 1
\right)
$}}\\\\
\small{\text{
$
=\left( \dfrac{2}{4}x^{-\frac{1}{4}} \right)
$}}\\\\
\small{\text{
$
=\left( \dfrac{1}{2}x^{-\frac{1}{4}} \right)
$}}$$

We need to find the proportionality constant, k.

So we have

V = kAH

4 = k(6)(2)

4 = k(12) 

4/12 = k = 1/3

So, when A = 9  and H = 4, we have

V = (1/3)(9)(4)

V = (1/3)(36)

V = 12 

Let B's rate = x  ...then A's rate = x + 4 

The distance that A runs is ..... time x rate = 2(x + 4)

The distance that B runs is..... time x rate = 2x

And using the Pytagorean Theorem, we have

(2x)^2 + [2(x + 4)]^2  = 40^2

4x^2 + 4(x^2 + 8x + 16)  = 1600

4x^2 + 4x^2 + 32x + 64 = 1600

8x^2 + 32x - 1536  = 0  divide through by 8

x^2 + 4x - 192  = 0     factor

(x +16) ( x - 12) = 0

And setting each factor to 0, we have that x = -16 and x = 12

Reject the -16

So ... A's speed = x + 4 = 12 + 4 = 16 km/hr