Melody

20% of Turnover = 90000

0.2T=90000

2T=900000

T=$450,000

(x^3 + x^2*a + x + b)/ x^2 - 4 

$$if \;\;lim(f(x))\Rightarrow 5\;\; with \;\;x\Rightarrow 2$$

This is what I think :/

$$\\\displaystyle\lim_{x\rightarrow2}\;\frac{x^3+ax^2+x+b}{x^2-2}=5\\\\
\displaystyle\lim_{x\rightarrow2}\;\frac{x^3+ax^2+x+b}{x^2-2}*(x-2)=\displaystyle\lim_{x\rightarrow2}\;5(x-2)\\\\
\displaystyle\lim_{x\rightarrow2}\;\frac{x^3+ax^2+x+b}{x+2}=\displaystyle\lim_{x\rightarrow2}\;5x-10\\\\
\displaystyle\lim_{x\rightarrow2}\;x^3+ax^2+x+b=\displaystyle\lim_{x\rightarrow2}\;(5x-10)(x+2)\\\\
8+4a+2+b=0\\\\
4a+b=-10$$

$$2log(1/3)=2log3^{-1}=-2log3$$

$${\mathtt{\,-\,}}\left({\mathtt{2}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{3}}\right)\right) = -{\mathtt{0.954\: \!242\: \!509\: \!439\: \!324\: \!9}}$$

tan theta = 82/62

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{82}}}{{\mathtt{62}}}}\right)} = {\mathtt{52.907\: \!162\: \!702\: \!958^{\circ}}}$$

find the equation of the line though C(5, 8) perpendicular to AB. AB is 8x+5y-1=0

8x+5y-1=0

5y=-8x+1

y=(-8x+1)/5

gradient = -8/5

gradient of perpendicular is  5/8       also through   (5,8)

y-8=(5/8)(x-5)

8y-64=5x-25

5x-8y-25+64=0

5x-8y+39=0

you need to check it :)

Mmm,

Mat's first method is for equations on degree 2

Factorization method can be used if you can work out the factors.  

You can use remainder theorem / factor theroem to help find them.

Given a 15% world wide web usage in 2005 , a 30 % world wide web usage in 2010 and a 40 % world wide web usage in 2014.., during what year would the entirety of earth become connected to the world wide web?

I am confused  

I don't think that it  will ever really get there.

The model would be logatithmic i guess with an asymptote at y=100%

What kind of model are you expected to use?

$$\\log x=y\\
then\\
x=10^y\\\\
eg\\
logx={17}\\
x=10^{17}$$

100-15=85

$${\mathtt{0.85}}{\mathtt{\,\times\,}}{\mathtt{84}} = {\frac{{\mathtt{357}}}{{\mathtt{5}}}} = {\mathtt{71.4}}$$

100+7=107

$${\mathtt{1.07}}{\mathtt{\,\times\,}}{\mathtt{71.4}} = {\mathtt{76.398}}$$

$76.40