Melody

The first bit is almost correct  anon  

$$\\1000=500(1+0.03)^n\\
2=1.03^n\\
log2=log1.03^n\\
log2=nlog1.03\\
n=log2/log1.03$$

$${\frac{{log}_{10}\left({\mathtt{2}}\right)}{{log}_{10}\left({\mathtt{1.03}}\right)}} = {\mathtt{23.449\: \!772\: \!250\: \!437\: \!735\: \!9}}$$

It will be worth 1000 in 24 lots of 6 months = 12 years

Sorry Chris that was on the Latex that i lost.

But here is the formula

I just did a whole page of latex and lost the whole lot so now I will do a condensed version. 

Heureka, Your answer looks great but I don't understand it so I will do it my way.

Maybe you can explain your way?

Anyway here goes- again

Find the value of  x such that the area of a triangle whose vertices have coordinates

P(6, 5), Q(8, 2) and R( x, 11) is 15 square units.

distance PQ=sqrt(13)

Equation of line PQ is

3x+2y-28=0

Now I need the perp distance from R to PQ

a=3, b=2, c=-28, x1=x, y1=11

$$\\d=\frac{|3x+22-28|}{\sqrt{13}}\\\\
d=\frac{|3x-6|}{\sqrt{13}}\\\\
d=\frac{|3x-6|}{\sqrt{13}}\\\\$$

$$\\\mbox{perpendicular distance from R to PQ}=\frac{|3x-6|}{\sqrt{13}}\\\\
Area=\frac{1}{2}\times \sqrt{13} \times \frac{|3x-6|}{\sqrt{13}}\\\\
15=\frac{1}{2} \times |3x-6|\\\\
30=|3x-6|\\\\
30=3x-6\qquad or \qquad 30=6-3x\\\\
36=3x\qquad\qquad or \qquad 24=-3x\\\\
x=12\qquad\qquad \;\;or \qquad x=-8\\\\$$

Below are the 2 possible triangles.  :)

 Hi Chris,

The sum of the roots of a polynomial of degree n is   

$$\mbox{sum of the real roots }= -\frac{\mbox{coefficient of }x^{n-1}}{\mbox{coefficient of }x^n}$$

but there is a lot more to this Chris.

Have a look  at this

Hi Chris,

What Heureka has done has many implications.  it can be used on polynomials of degree higher than 2.

although I'd need to 'think' with it if I was asked a question with a higher degree.

I think it can be used in probablility too although again I am very rusty   

the negative and the take away are the same button :)

There are 180 degrees in a triangle

5+3+1=9

180 divided by 9=20

so the angels are 

1x20

3x20   and

5x20    degrees

Your meaning is not clear 

What are you integrating with respect to ?

Hey JewishNerd

That must be aboiut the most ugly animal i ever saw.  LOL