All Answers 358601 Answers

Here's one generated from Wolframalpha : https://www.wolframalpha.com/input/?i=exponential+equation++(1,1),+(2,2),+(3,4),+(4,8)

y = 0.5 e^(0.693147 x)

Here's the graph : https://www.desmos.com/calculator/flgzerupyk

8 + 1/4  = 

32/4 + 1/4 = 

33/4

We can set this up as a proportion where x is the thickness of one sheet

60mm / 500   = x / 1         cross-multiply

60  = 500x            divide both sides by 500

60/500mm  = x =  6/50mm   =  12/100mm =  .12mm

-14-13(-1)  =

-14 - [-13]   =

-14 + 13  =

-1

Yes, thanks

Er... no..   (•^-^•)

Do you understand it all Daniel?

There is one other person who used to call me "Miss Melody"  Eloise.  Do you remember who that was?

Hey! Only I call Miss Melody, "Miss Melody"! Hmph! 

Ok I will start.

43210 is a pretty big number, am I allowed to do that OR do you need to be used as single digits?

4--3--2--1=10

Do I need to use all the digits?

Anwyway, that is a start, I am sure someone can do much better :)

Hi Daniel, :)

\(a-b=5\\ (a-b)^2=25\\ a^2-2ab+b^2=25\qquad but\;\;ab=2\\ a^2 -2*2+b^2=25\\ a^2 -4+b^2=25\\ a^2 +b^2=29\\~\\ (a^2 +b^2)^2=29^2\\ a^4+2*a^2b^2 +b^4=841\\ a^4+b^4+2ab*ab =841\\ a^4+b^4+2*2*2 =841\\ a^4+b^4+8 =841\\ a^4+b^4=833\\\)

how is algebra connected with maths???

The letters in algebra are called pronumerals.   

Losely translated the pro means 'in place of'

and 'numerals' are numbers.

So the letters just represent numbers of unknown value.

In primary school you might write     3+  box = 8

then you put the answer 5 in the box.

Well algebra is just the same only you say 3+x=8  and then the answer is x=8

So algebra is a very important branch of mathematics :)

I hope that helps :)

-659+14946581*1+659*2 / 2

Hi GA,  no I didn't lose any of my marbles but the asker did find some more of his.  

Maybe he will find such questions easier in the future.   

It is always easier when you have all, or even more of, your marbles     

More info needed. 

Yes, I see. Annoying!

That is such a relief, Miss Melody!! I was thinking you had lost some of your marbles. 

GA

Press [2nd]   MOD is over on the right :)

Hi Alan,

The question has been edited.  (With no polite word to say so)

I copied the original question into my response.  The numbers have since been changed :/

Thanks Heureka,

I had not thought to do it as a GP  :))

Compute.

\(i+i^2+i^3+\cdots+i^{258}+i^{259}.\)

geometric series:
\(\begin{array}{|rcll|} \hline a &=& i\\ r &=& i \\ n &=& 259 \\\\ s &=& i\cdot \dfrac{(1-i^{259}) }{1-i}\\\\ s &=& \dfrac{i-i^{260} }{1-i} \qquad & | \qquad i^{4m} &=& 1 \\\\ s &=& \dfrac{i-i^{4\cdot 65} }{1-i} \qquad & | \qquad i^{4\cdot 65} &=& 1 \\\\ s &=& \dfrac{i-1}{1-i} \\\\ s &=& -\dfrac{1-i}{1-i} \\\\ s &=& -1 \\ \hline \end{array} \)

I think the question is meant to be interpreted as follows:

Total marbles = T

T = 36 + 72 +(5/8)T

(3/8)T = 108

T =  288

Thomas has (5/8)T → (5/8)*288 → 180

(no broken marbles!)

.

If john had 36 marbles and sally had 64 marbles and thomas has 5/8 of the total marbles,how many marbles does thomas have? 

Well if John, Sally and Thomas have all the marbles then 

36+64=100

3/8 of the marbles is 100

\(\frac{3}{8}x=100\\ x=\frac{100*8}{3}\\ \frac{5}{8}x=\frac{5*100*8}{3*8}\\ \frac{5}{8}x=\frac{500}{3}\\ \frac{5}{8}x=166\frac{2}{3}\\\)

Thomas has 166 whole marbles plus 2/3 of a marble.  I guess some of the marbles are broken!     

6 5/9 - 3 1/4

=(6+5/9)-(3+1/4)

put into the web2 calc

(6+5/9)-(3+1/4) = 3.3055555555555556 = 119/36 = 3 and 11/36