Monkey Raptor V.2

This is a brain teaser. The rule is we are only allowed to use the the grid line (the border of each box) to reach the destination . Finding the Shortest Path Let's right away find the shortest path to reach the destination. We need to pick only two directions from all four directions: up-down-right-left. And the two must be perpendicular to each other. If we start from the top left, to go diagonally to the bottom right, we will have two options to move, those are: down — right . Other than those, we won't be going on the shortest path. If we start from the bottom left, and we have to reach the top right, then we'll have two options, those are up — right . I put different colors, green and red, so you can see them. In that example, we have 6 steps as our shortest path. How to Actually Get the Shortest Route (Steps)? By counting along the side borders of the grid. Or Adding the total rows and columns. Let's generalize the method....

This is a bread. ANYWAY, the numeral system we always use is the Decimal System , which consists of ten different numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 The Binary System is the base in computational world, to represent the bit encoded data. This numeral system only consists of 2 numbers: 0 and 1 Binary to Decimal Conversion It's easier if I just put an example of this. But before we start, to indicate the different system, usually the number has a subscript thingy so we won't be confused between those two. Like so: 1001 2 or 11001 2 for binary numbers, and 1024 10 or 2357 10 for decimal . Binary to Decimal Conversion Examples 101 2 = ( 1 x 2 2 ) + ( 0 x 2 1 ) + ( 1 x 2 0 ) 101 2 = ( 4 + 0 + 1 ) 10 101 2 = 5 10 11101 2 = ( 1 x 2 4 ) + ( 1 x 2 3 ) + ( 1 x 2 2 ) + ( 0 x 2 1 ) + ( 1 x 2 0 ) 11101 2 = ( 16 + 8 + 4 + 0 + 1 ) 10 ...

The quadratic equation, ax² + bx + c = 0 , is a non-linear ( 2 nd degree polynomial, a ≠ 0) equation that always has two roots as the solution. Sometimes the roots are different, sometimes they're twins. Sometimes they all have real numbers or complex numbers, or just imaginary number. Methods To find the roots (the solution), we can choose between these four different methods : Factoring Completing the square Using quadratic formulation Drawing the graph : this can be achieved by writing your own loop-n-plot computer script, or using pre-programmed Mathematical software, or just using a pencil and a paper then create a table of values, continued with plotting the values on the Cartesian plane (2D x-y axis). A glimpse about the function f(x) graph Discriminant (∇) This is the expression that will tell us if a quadratic function crosses an axis. Because this is f(x) (the function of x values axis), then the discriminant here will tell us whether a  fun...

Basic Identities: Pythagorean and Ratios sin² A + cos² A = 1 tan² A + 1 = sec² A 1 + cot² A = cosec² A tanA = sinA / cosA cosecA = 1 / sinA secA = 1 / cosA cotA = cosA / sinA cotA = 1 / tanA Co-function Identities: Shifts sin[(½)π - A] = cosA sin(90° - A) = cosA cos[(½)π - A] = sinA cos(90° - A) = sinA tan[(½)π - A] = cotA tan(90° - A) = cotA Odd-Even Identities: Reflection sin(-A) = - sinA cos(-A) = cosA tan(-A) = - tanA Addition Formulas: Angle Sum and Difference sin(A + B) = sinA·cosB + cosA·sinB sin(A - B) = sinA·cosB - cosA·sinB cos(A + B) = cosA·cosB - sinA·sinB cos(A - B) = cosA·cosB + sinA·sinB tan(A + B) = ( tanA + tanB ) / ( 1 - tanA·tanB ) tan(A - B) = ( tanA - tanB ) / ( 1 + tanA·tanB ) Double-Angle Formulas sin2A = 2·sinA·cosA cos2A = cos² A - sin² A cos2A = 1 - 2·sin² A cos2A = 2·cos² A - 1 tan2A = ( 2·tanA ) / ( 1 - tan² A ) ...

In mathematics, the trigonometric functions (also called the circular functions) are functions of an angle. They relate the angles of a triangle to the lengths of its sides. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications. Dear Wikipedia Basic : Sin, Cos, Tan Let's take a look at a right angled triangle (a triangle that has a right angle : 90°) below : And let's take the triangle's corner A as our angle reference. SINE function (abbreviated as sin ) is the length ratio between the opposite (a) and the hypotenuse (h) side. Sin A = opposite (a) / hypotenuse (h) COSINE function (abbreviated as cos ) is the length ratio between the adjacent (a) side and the hypotenuse (h). Cos A = adjacent (b) / hypotenuse (h) TANGENT function (abbreviated as tan ) is the length ratio between the opposite (a) side and the adjacent (h) side. Tan A = opposite (a) / adjacent (b) It also ...