Squaddy

I am sorry for any problems you might have had reading, but  "{nl}" is not supposed to be there so just ignore them.

Also I seem to be unable to edit my answer

Assuming the ratio doesn't change, you can divide any of the numbers with the previous one to find the ratio.

For example: {nl} \(150/100=1.5\) {nl} {nl} We can test this by applying this value to the other numbers in the sequence:

\(150*1.5=225\) {nl} \(225*1.5=337.5\) {nl} \(337.5*1.5=506.25\)

We have confirmed that the ratio from one number to the next is 1.5 {nl} To find the percentage we multiply a ratio with 100:

\(1.5*100=150\)

The answer is 150 %. 

The tangent is the ratio between the opposite side and the adjacent side of a right triangle.

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{x}}\right)} = {\frac{{\mathtt{opposite}}}{{\mathtt{adjacent}}}}$$

$$\left({\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{5}}}{{\mathtt{8}}}}\right){\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{9}}}{{\mathtt{16}}}}{\mathtt{\,\small\textbf+\,}}\left({\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{4}}}}\right)$$

$${\frac{{\mathtt{5}}}{{\mathtt{8}}}} = {\mathtt{0.625}}$$        $${\frac{{\mathtt{9}}}{{\mathtt{16}}}} = {\mathtt{0.562\: \!5}}$$      $${\frac{{\mathtt{1}}}{{\mathtt{4}}}} = {\mathtt{0.25}}$$

Start inside the brackets:

$$\left({\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.625}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{0.562\: \!5}}{\mathtt{\,\small\textbf+\,}}\left({\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.25}}\right)$$

$$\left({\mathtt{2.625}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{0.562\: \!5}}{\mathtt{\,\small\textbf+\,}}\left({\mathtt{3.25}}\right)$$

Then you just add the numbers:

$${\mathtt{2.625}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.562\: \!5}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3.25}} = {\mathtt{6.437\: \!5}}$$

In order to find the decimals you simply divide the two numbers:

$${\frac{{\mathtt{8}}}{{\mathtt{20}}}} = {\mathtt{0.4}}$$

The decimal is 0.4

If you want to find the precentage you take the decimal and multiply it by 100:

$${\mathtt{0.4}}{\mathtt{\,\times\,}}{\mathtt{100}} = {\mathtt{40}}$$

The percentage is 40%

Haha , I'm sorry for the confusion!

Where i come frome we say catet (or katet) to describe the two sides that aren't the hypotenuse in a right triangle.

It comes from greek kathetos meaning the same thing.

$${\sqrt{{\mathtt{60\,000\,000}}}} = {\mathtt{7\,745.966\: \!692\: \!414\: \!833\: \!770\: \!4}}$$

Should you however mean to use the comma to mark decimals:

$${\sqrt{{\mathtt{6}}}} = {\mathtt{2.449\: \!489\: \!742\: \!783\: \!178\: \!1}}$$

This IS a calculator site.

Anyway:

$${\frac{\left({\mathtt{64}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}{\left({\frac{{\mathtt{1}}}{{\mathtt{8}}}}\right)}}{\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{3}}}}$$ 

$${\frac{\left({\mathtt{64}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}{{\mathtt{0.125}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{3}}}}$$

64+2/3  64.66667

$${\frac{{\mathtt{64.666\: \!666\: \!666\: \!666\: \!666\: \!7}}}{{\mathtt{0.125}}}}$$517.3333333333333336

517.3333333333333336-1/3  517.0000000000000002667 517

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:

"cos" (short for cosine) is the ratio between the adjecent catet and the hypotenuse in a right triangle. 

$${\frac{{\mathtt{catet}}}{{\mathtt{hypotenuse}}}}$$

When dividing by zero you get something called an indeterminate form. In short, this is a number that can't be determined.

Examples of indeterminate forms are $${\frac{{\mathtt{x}}}{{\mathtt{0}}}}$$, $${{\mathtt{0}}}^{{\mathtt{0}}}$$ and pretty much anything involving infinite (for example ∞/2).

The quadratic formula is as follows:

When the quadratic function equals 0

 $${\mathtt{0}} = {{\mathtt{ax}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{bx}}{\mathtt{\,\small\textbf+\,}}{\mathtt{c}}$$

For example in:

$${\mathtt{0}} = {{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{3}}$$ (a=1, b=2 and c=-3)

For these functions you can use the quadratic formula to find the value of x.

The formula being:

$${\mathtt{x}} = {\frac{\left({\mathtt{\,-\,}}{\mathtt{b}}{\mathtt{\,\small\textbf+\,}}{\sqrt{{{\mathtt{b}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{a}}{\mathtt{\,\times\,}}{\mathtt{C}}}}\right)}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{a}}\right)}}$$

Now you just fill in the values of a, b and c.

For the example I've used it would be:

$${\mathtt{x}} = {\frac{\left({\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\sqrt{{{\mathtt{2}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{1}}{\mathtt{\,\times\,}}-{\mathtt{3}}}}\right)}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{1}}\right)}}$$

$${\mathtt{x}} = {\frac{\left({\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\sqrt{{\mathtt{4}}{\mathtt{\,\small\textbf+\,}}{\mathtt{12}}}}\right)}{{\mathtt{2}}}}$$

$${\mathtt{x}} = {\frac{\left({\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\sqrt{{\mathtt{16}}}}\right)}{{\mathtt{2}}}}$$

Now since the square root of any number (positive of course) can be both positive and negative, we get two solutions: The square root of 16 can be either 4 or -4, since negative negative becomes positive.

The solution would be either

$${\mathtt{x}} = {\frac{\left({\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{4}}\right)}{{\mathtt{2}}}} = {\frac{{\mathtt{2}}}{{\mathtt{2}}}} = {\mathtt{1}}$$

or

$${\mathtt{x}} = {\frac{\left({\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,-\,}}{\mathtt{4}}\right)}{{\mathtt{2}}}} = {\frac{\left(-{\mathtt{6}}\right)}{{\mathtt{2}}}} = -{\mathtt{3}}$$

I'd assume you want to find the value of y in the function f(x) when x=4.

This is simple, all you have to do is to put 4 in where the x's are.

$${f}{\left({\mathtt{x}}\right)} = {\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{4}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{4}}$$

$${f}{\left({\mathtt{x}}\right)} = {\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{16}}{\mathtt{\,-\,}}{\mathtt{8}}$$

$${f}{\left({\mathtt{x}}\right)} = {\mathtt{48}}{\mathtt{\,-\,}}{\mathtt{8}}$$

$${f}{\left({\mathtt{x}}\right)} = {\mathtt{40}}$$

So in the function f(x), when the value of x is four the value of y would be 40. 

In order to calculate based on percentage you need to know how decimals and percentages work.

For example if you've got a whole apple that is 100% of an apple.

If you've got half an apple, 50%, that is 0.5 apples.

You simply divide the percentage by 100 to get the decimal.

100%: 100/100=1
42%: 42/100=0.42

If you have 60 people as you say, and you want to know how many 42% of them are, you simply take the total amount times the decimal.

In this case, the way you solve it would be: 

$${\frac{{\mathtt{42}}}{{\mathtt{100}}}} = {\mathtt{0.42}}$$

$${\mathtt{60}}{\mathtt{\,\times\,}}{\mathtt{0.42}} = {\mathtt{25.2}}$$

And as the previous answer mentioned, you can't have decimals in the answer when talking about number of people, so you round it to the closest whole number: 25.

You have the normal trigonometric functions cos, sin and tan. The invertion is more or less the same for all of these functions.

Let's use cosine for this example.

As you probably know you can use cosine to calculate the ratio and thereby the sides of either an adjecent catet or the hypotenuse. 

I.E.:

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{78}}^\circ\right)} = {\frac{{\mathtt{3}}}{{\mathtt{x}}}}$$ 

3 being the lenght of the catet and x being the unknown hypotenuse. 

Inverse trigonometric functions work the other way around,  if you already know the ratio you can use the inverse trigonometrical functions to find the angle.

The functions are shown in calculators as either

 $$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}^{\!\!\mathtt{-1}}{\left(\right)}$$ 

or

$${acos}\left($$

If the ratio is for example 3.7 you would type $$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}^{\!\!\mathtt{-1}}{\left({\mathtt{3.7}}\right)}$$ in a calculator to get the angle.

Note however that you sometimes have to mark that you want the answer shown in degrees and not in radiuses.