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by the way -4^2 does = 16, not -16 because -4*-4=16. 2 negatives make a positive, duhhhh!!!! dont hit the minus, hit the negative

Yes I understand now because in class we are doing Exponential Growth and Decay.

if you used 1/3 you will have 2/3 left

 2   /   3

\/       \/

2(120/3)

2(40)

$80    left

25(12*42)

25(504)

12600

Why does -4^2 equal -16 and not +16 ?

$$-4^2 = (-1)[(4)^2]=(-1)[16]=-16\\\\
(-4)^2 = [(-1)*(4)^2]=(-1)^2*(4)^2=1*16=16\\$$

If the RR Lyrae stars in a globular cluster have apparent magnitudes of 18, how far away is the cluster ?

You need the absolute magitude too.

$$d = 10^{0.2(m-M+5)} \quad
\small{\text {where d is in pc }}\\
m = \small{\text { Apparent magnitudes }} \\
M = \small{\text { Absolute magnitudes }} \\
\small{\text{ 1 pc = 3.26 light years }}$$

what is the solution of -2(8x-4)<2x+5

$$-2(8x-4)<2x+5 \\
-16x+8 < 2x+5 \\
-16x+8 < 2x+5 \quad | \quad +16x\\
8 < 2x+16x+5 \\
8 < 18x+5 \\
8 < 18x+5 \quad | \quad -5\\
8 -5< 18x \\
3< 18x \\
3< 18x \quad | \quad :18\\
\frac{3}{18}< x \\
\frac{1}{6}< x \\
x > \frac{1}{6}$$

-2(8x-4)<2x+5  simplify the left side

-16x + 8 < 2x + 5      subtract 5, add 16x to both sides

3 < 18x                     divide both sides by 18

3/18  < x                   reduce 3/18

1/6  < x

or, expressed another way......

x > 1/6

$${\frac{{\mathtt{127}}}{{\mathtt{247}}}} = {\mathtt{0.514\: \!170\: \!040\: \!485\: \!83}}$$

hi Tenacious,

Your third line is missing =0

The conclusion you have drawn is incorrect.

Heureka's answer is correct.  See if you can work out the logic of why.

We may need to discuss it.

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Your fourth and fifth lines are just checking that the factorising is correct so if you want to include it at all you should insert the words "checking factorization ".  
Or something like that. :)   

You can check the finished answer - that would be better anyway.

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I'll let you think about it a bit and then I will give you the full worked answer with explanation if you want me to.     

Thanks Chris,  I have added this to the puzzle thread :)

A little money logic from CPhill     (23/1/15)

Oh heck, heureka....I forgot about the bottom and top..I think I really must have "CDD"..!!! Thanks!!!

"None of those fromulas have got just  s  a u and t   ..."

Errm!  Have a look at formula [2]

.

x²+7x=18

x²+7x-18=0

(x-2)(x+9)=0  So x=+2 or x=-9   Edited because I had the + and - the wrong way round originally, now correct. Thanks to Melody for pointing that out.

x²+9x-2x-18

x²+7x-18

By the time I saw this there were other answers so too late but I purposefully avoided looking at them, no point in cheating. I only saw the first two posts, the question and Melody's hints. I doubt I would have done this so easily without those hints Melody, so thanks. I think this is the first time I have encountered a quadratic trinomial in a practical ish situation. Up till now I have only encountered them as isolated exercises. It is useful to see how they can actually be used and be of benefit.

How to find surface area of a cylinder ?

$$\\ \small
\begin{array}{ll}
\text{ Area of the top is } & \pi r^2 \\
\text{ Area of the bottom is } & \pi r^2 \\
\text{ Area of the side is } & 2\pi rh \\
\boxed{A = 2\pi r^2 + 2\pi rh }
\end{arry}
}$$

Or it could be 3^(2^x) = 195 in which case

Take logs:

(2^x)ln(3) = ln(195) or 2^x = ln(195)/ln(3)

Take logs again:

xln(2) = ln( ln(195)/ln(3) )

x = ln( ln(195)/ln(3) )/ln(2)

$${\mathtt{x}} = {\frac{{ln}{\left({\frac{{ln}{\left({\mathtt{195}}\right)}}{{ln}{\left({\mathtt{3}}\right)}}}\right)}}{{ln}{\left({\mathtt{2}}\right)}}} \Rightarrow {\mathtt{x}} = {\mathtt{2.262\: \!941\: \!541\: \!431\: \!602\: \!2}}$$

.

Oops...thanks, Alan...

Don't worry, the + and - are pretty close together, easy to do.

For info:

€ =Euro

£ = pound

.

Since it's compounded quarterly, the interest rate per period is 12% / 4  = 3% = .03

Sa_c = 2 * pi * r * h       where  r is the radius and h is the height.....

[ In essence, we just "stacking" a bunch of like "perimeters" on top of each other...!!!]

Let x be the number that paid 35 pounds and y be those that paid 45 pounds

So we have this system of equations

x + y = 500

35x + 45y = 20500

And using the first equation, we can rearrange it as y = 500 - x....and subbing this in for y in the second equation, we have

35x + 45(500 - x) = 20500   simplify

35x + 22500 - 45x = 20500  combine like terms on the left side

-10x + 22500 = 20500       subtract 22500 from each side

-10x = -2000    divide both sides by -10

x = 200.....and this is the number of people who paid 35 pounds

One left.......two remained....!!!

You are right.

It did come from me and it was a typo.  Sorry.