Qualification > Reference Material

Add Maths June 8, 10 2010

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J.Darren:
Rules of Differntiation :

x^n = nx^(n-1)
e^2x = 2e^2x
ln x = 1 / x
sin x = cos x
cos x = -sin x
tan x = sec^2 x

Chain rule (Composite function):

y = ln (2x + 1)

y = ln (u)
u = 2x + 1

dy/du = 1/u
du/dx = 2

dy/du x du/dx = dy/dx

1/(2x + 1) * 2 = 2/(2x + 1)

Quotient rule :

y = u / v

dy/dx = (vu' - v'u) / v^2

Product rule (Multiple functions):

y = u x v

dy/dx = v'u + u'v

y = 3x^2 x e^x

v = 3x^2
u = e^x

v' = 6x
u' = e^x

dy/dx = 6xe^x + 3x^2e^x

J.Darren:
Second derivative :

If smaller than 0 - Maximum
If equals to 0 - Point of inflexion
If greater than 0 - Minimum

Rules of Integration :

e^2x = 1/2 x e^2x
cos ax = 1/a x sin x
sin ax = 1/a x -cos x

Add constant c when integrating an indefinite integral

x^n = [x^(n+1)]/(n+1)

(ax+b)^n = [(ax+b)^n+1]/[a*(n+1)]

1/(ax+b) = [ln(ax+b)]/a

J.Darren:
Solving simultaneous equation using matrices :

AX = C
A–1 AX = A–1C
IX = A–1 C
X = A–1 C

Finding the inverse of a 2 x 2 matrix :

cooldude:

--- Quote from: jellybeans on May 30, 2010, 08:30:19 am ---HIIII, lol. could you see what i did .. wrong please? :/

--- End quote ---

see the question is  basically asking what is the time taken for the boat to travel the dist AC, dist BC=54 because the speed of the liner is 36 km/h and the time it travels is 1.5 hrs thus the dist=1.5*36=54, the dist AC can be found out by the cosine rule, x=angle ABC
A^2=B^2+C^2-2ABcosx
A^2=90^2+54^2-(2*54*90*cos 135)
A=AC=133.75 km
therefore the speed of the boat = 133.75/1.5=89.2 km/h

Ghost Of Highbury:
isnt it 28.9 km/h?

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