Cubic Functions N3

Definition of a Compressor  A compressor is a machine that takes up air at a lower pressure (Usually at atmospheric pressure) at the induction stroke and compresses it to a higher pressure (compression stroke). The air is stored at this higher pressure. A bicycle pump is a very good example of a compressor. This pump is used to inflate the tire of a bicycle. The inflation of an automobile is also done by a compressor. These compressors are motor driven compressors. This is, therefore, a criteria for classifying the compressor calculations (manually driven and motor driven compressors) The Graph of a Compressor One of the most fundamental procedures of compressor problems is the graphs  of compressors (PV Diagram). The numbering of the graphs in terms of the different processes is very fundamental. Induction Process 1-2   Constant Pressure Compression 2-3 Compression 3-4   Constant Pressure Induction 4-1  Classifications of Compressor Problems. The crit...

  Second Order Differential Equations The most basic classification of the second order differential equation is in terms of the the following: a) real and imaginary solution (Complex Number Solution) Refer to Equations b) Basic solution of the quadratic formula The basic formula of a second order DE is stated in terms of the following: a)  b)  ax^2+bx +c=0 or   am^2+bm+c=0   (x = m) Classification of DE problems Complex Number Solution and Basic Quadratic Equation Formula Solution General Solution and Particular Solution

  Definition of the Cubic Function The cubic function is a function or graph (curve) is defined by the two formulas below: a) y= ax^3+bx^2+cx+d    (expanded standard form) b) y= (x+1)(x+2)(x+3)     (factorized form)  (factors of the cubic function)  The cubic curve or function has three x intercepts. For the  factorized cubic function as stated earlier y= (x+1)(x+2)(x+3) the x intercepts are x=-1, x=-2 and x= -3. The relationship between the two cubic formulas as stated above is based on the expansion of the factorized cubic formula, y= (x+1)(x+2)(x+3). The expansion of the cubic function y= (x+1)(x+2)(x+3) is calculated thus:       y= (x+1)[(x(x+3) +2(x+1)] y= (x+1)[x^2+3x+2x+1] y= (x+1)[x^2+5x+1] y= x[x^2+5x+1]+1[x^2+5x+1]  y= [x^3+5x^2+x]+x^2+5x+1] add like terms  y= [x^3+5x^2+x^2+x+5x+1] y=...................................................... The intercepts of the cubic functions are evaluated from the facto...