We can write 256 as 2⁸ and we can write 8 as 2³

So we have    (2³)^x  =  2⁸

And, equating exponents, we have

3x = 8      divide on both sides by 3

x = 8 / 3

$$\\2log20^2 -(log5+log8)\\
=log400^2-(log40)\\
=log160000-(log40)\\
=log(160000/40)\\
=log(4000)\\
=log1000+log4\\
=3+log2^2\\
=3+2log2$$

$$Sn = \frac{(a1+an)*n}{2}

S = the sum of the numbers

a1 = first number

an = last number

n = quantity of numbers

an = a1 + d(n-1) [d = 1 = the common difference of successive members)

201 = 101 - 1(n-1)

n = 101

S101 = [(101+201)*101]/2

S101 = 15251$$

This problem is an altered form of an easier problem, which I will explain first before I'll move on to your problem.

Suppose we want to add the numbers 1 to 10. 

Then we could go about this by simply calculating

$$\begin{array}{lcl}
1+1 = 2\\
2+3 = 5\\
5+4 = 9\\
9+5 = 14\\
\mbox{etc.}
\end{array}$$

Since this takes quite a long time, we can also try to find a more logical way to solve this.

Let's try to find pairs which make it easier for us to solve this summation.

$$\begin{array}{lcl}
0+10 = 10\\
1+9 = 10\\
2+8 = 10\\
3+7 = 10\\
4+6 = 10\\
\ \ \ \ \ \ 5 = 5\\
\_\_\_\_\_\_\_\_\_\_\_\_\_ \\
1+...+10 = 55\\
\mbox{Hence the sum of all the numbers between 1 and 10 is 55}\\
\end{array}$$

$$\begin{array}{lcl}
\mbox{Note that we could also write this as } 10\times \frac{10}{2}+\frac{10}{2}\\
\mbox{This again can be rewritten to} \frac{10 \times 10 + 10}{2}\\
\mbox{and } \frac{10 \times 10 + 10}{2} = \frac{10 \times (10+1)}{2}
\end{array}$$

Try to see for yourself that this idea doesn't just hold for the sum of the numbers 1 to 10, but also for numbers 1 to n. where n is any number you want to choose. Therefore

$$1+2+...+n = \frac{n(n+1)}{2}$$

Now find the sum of 1 to 201, the sum of 1 to 100 and then substract the second from the first :D

Then you can find the sum of 1 to 201.

Good luck!

You formula is correct

normally it is written as

$$C=\frac{5}{9}(F-32)$$

but your formula is exactly the same. :)

C=(98.6-32)/1.8 = 37 degrees Celcius

$${\frac{\left({\mathtt{98.6}}{\mathtt{\,-\,}}{\mathtt{32}}\right)}{{\mathtt{1.8}}}} = {\mathtt{37}}$$

Nice work 4X  

$$\frac{a^{2}}{4} + \frac{a^{2}}{4} = 2*\frac{a^{2}}{4} = \frac{a^{2}}{2}$$

2% = 2/100 

2% of 400 = 

(2*400)/100 = 8

For volume:

 $${\mathtt{V}} = {\mathtt{\pi}}{\mathtt{\,\times\,}}{{\mathtt{r}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{\mathtt{h}}$$

For surface area:

$${\mathtt{A}} = {\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{\pi}}{\mathtt{\,\times\,}}{\mathtt{r}}{\mathtt{\,\times\,}}{\mathtt{h}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{\pi}}{\mathtt{\,\times\,}}{{\mathtt{r}}}^{{\mathtt{2}}}$$

For lateral surface:

$${\mathtt{L}} = {\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{\pi}}{\mathtt{\,\times\,}}{\mathtt{r}}{\mathtt{\,\times\,}}{\mathtt{h}}$$

this is going to be a major effort has I have to revise matrices from the beginning LOL

Talk about making life difficult fo myself.

I viewed this you tube clip before I started.

$$\\f(x)=2x^2-4x+9\\
f(x)=2\times x^2-4\times x+9\\\\
$for f(3) you have to put a 3 everywhere that there was an x$\\
f(3)=2\times 3^2-4\times 3+9=2\times 9-12+9=18-12+9=15\\\\
$for f(-3) you have to put a -3 everywhere that there was an x$\\
f(-3)=2\times (-3)^2-4\times (-3)+9=2\times 9+12+9=18+12+9=39\\
so\\
2f(3)+3f(-3) = 2*15+3*39 = 30+117 = 147$$

@@ End of Day Wrap    Tues 11/11/14      Sydney,   Australia       Time 7:40 pm             ♬

Hi all,

There has  been about a million questions today.

great answers were given by CPhill, pachecachu, happy7, TayJay, geno3141, Kaepernicks and kitty<3.  Thank you all  

I collect most of the worthwhile unanswered question and put them here.

Wed 12/11/14

1) Rosala's back  Hip Hip Horray!

okay so what does your teacher say is the answer?

Does someone else want to take a look at this one?

Nice answer Gino :)

I'd like to see this one answered using matrices.  

I'd like to do it myself but there arer too many questions and i do not have time      

(25.48-26.22) billion

5.693*10^4

that was a big effort Gino :)

divide 

$$\\125=5*5*5=5^3\\\\
25x=\frac{\sqrt{125}}{5}\\\\
125x=\sqrt{125}\\\\
x=\frac{\sqrt{125}}{125}\\\\
x=\frac{5\sqrt{5}}{125}\\\\
x=\frac{\sqrt{5}}{25}\\\\$$

9*3+27

so what is 16*3

9*3=27 

so what is 16*3 ?

3 parts cement to 1 part gravel = 4 equal parts

1/4 * 208 = 52 lbs of gravel

$$\\y=\frac{4}{x}\\\\
y=log x\\\\
y=3^x-6$$