Tetration

I guess it depends on whether it involves corruption or not...  :/

3x(x+2)²      Recall that: (a + b)² = a² + 2ab + b²:

3x(x² + 4x + 4)        

You have to multiply 3x w/ all the terms inside the paranthesis. You can start off w/ only the x, to avoid careless mistakes.

3(x³ + 4x² + 4x)      multiply all the terms inside the paranthesis by 3:

3x³ + 12x² + 12x

(30(-7))-(210(-3))

First, dispose of unneccesary paranthesis:

30(-7) - (210(-3))       Multiply what's inside the paranthesis:

-210 - (- 630)         Recall that: - (-x) = x:

-210 + 630

630 - 210 = 420     

Full tank: n gallons

Amount bought today: 4.25 gallons

Before she filled the motorcyle we know that:

* It must be a non-negative amount of gas in the tank. 

* It was at most n - 4.25 gallons of gas in the tank before she filled it.

(she filled 4.25 gallons into the tank after all)

Therefore the amont of gas g, in gallons can be expressed as follows:

0 ≤ g ≤ n - 4.25         or equaly:         g ∈ [0, n - 4.25]

How many people are there ?

10.25/15 = 0.68(3) ≈ 0.68

Percent means "per hundred". X percent means X/100.

So when you have a decimal that you want to convert into percentages, simply multiply by 100.

10.25/15 = 0.68(3) ≈ 0.68 = 68/100 = 68 %

We see that: 2500 = 25 * 100

We know that: √(a * b) = √a * √b

Thus: √2500 = √(25 * 100) = √25 * √100 = 5 * 10 = 50

The formula for the volume of a cylinder is:

V = pi * r²h

So in our case:

V = pi * 15² * 3 = 3pi * (10 + 5)² , Using this formula: (a + b)² = a² + 2ab + b², we get:

V = 3pi * (100 + 100 + 25) = 3pi * 225 = 675 * pi = <your answer>

Would be very helpful if you could specify what geometric object you would like to know the area of.

Nontheless here are a few formula for the area of polygons and circles:

square: A = s², s: length of one side

rectangle: A = lw, (length * width)

circle: A = pi * r², r: radius

triangle: A = bh/2, b: base, h: height

quadrilateral: A = pq sin t, (p and q are the length of the diagonals, and t is the angle between them)

parallelogram A = bh (base * heigth)

rhombus: A = pq/2 (p and q are the length of the diagonals)

trapezoid: (a + b)h/2 (a and b are the length of the parallel sides, h is the heigth)

ellipse: pi * ab, (a and b are the semi-major and the semi-minor axes)

I'm not sure what you're after :( ...

The exponent in this expression is pretty large: 10^999999999999

n/4 - 2 = 3    Add 2 to both sides:

n/4 = 5       Multiply both sides by 4:

n = 20

Test: n/4 - 2 = 20/4 - 2 = 5 - 2 = 3, seems ok, :)

Use this formula:

A = bh/2

Where b is the base and h is the height