Brodudedoodebrodude

Equation is: sqrt(x) = x - 3

--> x = x^2 -6x + 9

--> 0 = x^2 -7x + 9

Use quadratic formula where a=1 , b=-7, c=9 :

x = (7±sqrt(49-4(1)(9)) / 2 = (7±sqrt(13)) / 2

x = 1.70 or x = 5.30

Just substitute in the values for x and y then you have an equation for a:

           8 - a = sqrt(-2(-8+a))

a^2 -16a+64=-2(a-8)

a^2 -14a+48=0

     (a-6)(a-8)=0 Therefore a = 6 or a = 8

Means x factorial:

x! = x * (x-1) * (x-2)*....* 2 * 1

Eg:

6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

3! = 3 x 2 x 1 = 6

Special cases and notes:

--> 0! = 1

--> Cant get factorials of a negative number or fractions, must be positive whole numbers

Lets say the fencing makes a circle:

Using circumference of a circle:

40 = 2 * pi * r

   r = 6.366.......

Area = pi * radius^2

       = pi * 6.366^2

       = 127.32 meters squared

Area of a triangle is 1/2 Base x Height.

This is an isosceles triangle with base sqrt(28), so you can split it in half to form 2 right angled triangles with base = sqrt(28) / 2  ,  hypotenuse = sqrt(70) and height = x.

Use pythagorus to get the height of the right angled triangle:

x = sqrt[70 - (28/4)] = sqrt(63)

Therefore area of Isosceles triangle = 2 x area of right angled triangle = 2[1/2 * (sqrt28)/2 * sqrt(63)]

                                                                                                    = 21 units ^2

Gahh CPhill beat me to it...

Cheers yeah its straightforward now --> y(t) = (e^3t)/4 + (3e^-t)/4

If gonna let x= the current second of the the cycle that you start watching at at a total of x=63 cycles.

The only times that you will witness a colour change is when:

x=29: G, G, Y

x=30: G, Y, Y

x=32: Y,Y,R

x=33: Y,R,R

x=62: R,R,G

x=63: R,G,G.

There are 6/63 situations where you could witness a colour change therefore the probability is 6/63 or 0.0952

A derivative tells you the rate of change (the gradient) of every point on the curve/line.

For instance take the linear function (a straight line) y = 2x. Rise / Run will show you the gradient equals 2 on any point of the line. The derivative of y (y'=2) also tells you that the gradient will always equal 2 at any point of x.

On a non-linear function however y=x^2 +2x, the gradient changes on every point of the curve and the rise/run method will not work, but the derivative will and it will give you an equation that can tell you the gradient of the function at any point x, in this case the derivative y' = 2x + 2.  At point x=0, y'=2 therefore the gradient at x=0 is 2. At point x=7.5, y'=17 therefore the gradient at x=7.5 is 17 etcetera.

Not a problem man

We know total area is 16, so lets base our equations on that.

Area Sq1:2.0 miles * [ x + (x - 1)] --> 2 * (2x - 1)

Area Sq2:1.2 miles * x

Area Sq1 + Area Sq2 = 16:

2 * (2x - 1) + 1.2x = 16

        4x - 2 + 1.2x = 16

                     5.2x = 18

                          x = 45/13 (exact answer) or 3.46 (rounded)