Word Problems (Quadratic Function) Mathematics N3

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Angular Motion Engineering Science N4

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  Chapter 4 Angular Motion 4.1 Introduction   Angular displacement unlike linear displacement is displacement that is defined by number of rotations or number of revolutions per unit second about a fixed point or center (shaft).                                   The diagrams below illustrate the fact that the radius or diameter of the rotating component is considered when there is a conversion of angular velocity into linear velocity.                                                                ...
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Boiler Efficiency (Steam Power Plant)

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Definition of the Cubic Function

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  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...
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