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If n is the number if days, then 0.01*2ⁿ = 10⁶

Divide both sides by 0.01

2ⁿ = 10⁸

Take log to the base 2 of both sides

$${\mathtt{n}} = {{log}}_{{\mathtt{2}}}{\left({{\mathtt{10}}}^{{\mathtt{8}}}\right)} \Rightarrow {\mathtt{n}} = {\mathtt{26.575\: \!424\: \!759\: \!098\: \!9}}$$

So it takes 27 days!

Rosala made one little mistake, the answer is x=-3 and not x=3

5 and -4 are the two numbers you're looking for

6.

bodmas - division first

6/8= 0.75

multiplication next

0.75 x 8= 6

okay so we'd solve this like 

2(x-3)+9=4-7 ( first we will multiply 2 by x and 3 and also subtract 4 and 7 on the other side)

2x - 6 + 9 = -3            ( and now we will subtract -6 and 9)

2x + 3 = -3    (now we will bring -3 to the other side and also change its sign aswell)

3+3 = 2x     (and now we would simply add them both)

6 = 2x         (and now we shall bring 2 to the other side and then divide it by 6 which would then give us our x)

6/2 = x

3=x        ANSWER

i hope uve understood by now but if not then pls be free to ask!

i hope it helps!

thank you very much alan!thats just gave me the idea of what the question is otherwise it was looking as if only Einstein could solve this!and melody im glad i didnt require to trouble u more as alan took all of it!lol!

points from me for both of you!Thank you!

Thank you Melody now that looks better!

$$\\3(h^3+h^2)=108\\\\
h^3+h^2=36\\\\
\mbox{I don't know how to do this without 'guessing'.}\\
\mbox{So I am going to present if easier for guessing}\\\\
h^2(h+1)=36\\\\
That\; is\;\; 9*4=36\\\\
h=3 \\\\
\mbox{So that is one solution - it is a cubic so there are 2 more but they might be imaginary numbers}\\\\
\\$$

Here are the answers.  There is only one real one.  

Thanks Alan

Your idea of simplfying the numbers as you go will probably be much better for Rosala.

Maybe i should go back an incorporate it into my answer.  Normally I would but the numbers cancelled out so nicely that I didn't force myself to do it that way.  :)

I think i will wait till she comments more.      

The volume is height*length*width so just multiply your three numbers together using the calculator on the home page here.

Ok rosala, I'll have a go, though I doubt I will do better than Melody did!

The question is If √(0.09 * 0.9 * x) = 0.9 * 0.09.√y , then find x/y

First let's simplify how it looks by calculating 0.09*0.9

$${\mathtt{0.09}}{\mathtt{\,\times\,}}{\mathtt{0.9}} = {\frac{{\mathtt{81}}}{{\mathtt{1\,000}}}} = {\mathtt{0.081}}$$

Now replace 0.09*0.9 in the original equation wherever it occurs (noting that 0.9*0.09 is the same as 0.09*0.9)

√(0.081*x) = 0.081*√y

Now square both sides of the equation

Left-hand side:  (√(0.081*x))² = 0.081*x                            ...(1)

Right-hand side:  (0.081*√y)² = 0.081²*(√y)² = 0.081²*y   ...(2)

Equate (1) and (2)

0.081*x = 0.081²*y

Divide both sides by 0.081

x = 0.081*y

Divide both sides by y

x/y = 0.081

Is this any clearer?

Mon 8/9/14

1) This one provided some humour and it is very comforting for a queen to know that her kingdom is so fiercely defended.   

@@ End of Day Wrap:      Sun 7/9/14        Sydney, Australia      Time 6:15pm     ♬

Hi all,

I powered through the questions last night and today (along with Aziz) and at a glance they all seem to have a reasonable answer.  Right back to the last proper wrap which was last Thursday.  I am very pleased about that.     (With the exception of a couple of high end commercial questions)   

Now for the credits.  Our great answerers over these few days have been HaleyWoodall17, Alan, AzizHusain, CPhill, Rosala, NinjaDevo, Honga, Kitty<3, Blazinkurama, DragonSlayer554, DevSeth, Heureka, Helen1709 and LLABlackJack.  A big thank you to each of you.  

Blazinkurama and DevSeth are both new.  I like to take this opportunity to welcome you to web2.0calc forum.  We all hope  that you enjoy yourselves here.   

Now for a few interest threads:

1) is it divisable by 3 - I handy trick to know (Thanks Alan)

Do you want

$$-8/9^3=-8/729\\
or\\
-(8/9)^3=-(8^3/9^3)=-512/729\\
or\\
(-8/9)^3=(-8)^3/9^3=-512/729$$

Okay rosala,

I have improved the layout.  Now let's see if we can work through it.  

yeah u can say that aswell!its just a true statement!

No 9 plus 10 isnt 21 but 19

Yes Melody the answer she got is  0.81 but i just cant understand the steps at all!i am confused on your steps also!if u can help me some more then pls can u simplify the steps more!and can u pls use simple writing style instaed of Latex!that seems a lil crowded to me!

I invite comment on this one.  

Let me see...

15 applicants.    5 sportA,     5 sportB    and     5 sportC

9 will be recruited and not more than 4 from any individual sport

possibilities

441      414      144        I think the number here is  5C4*5C4*5C1 = 3* 5*5*5 = 3*125 = 375

432   423  342   324   234   243   I think the number here is  6*5C4*5C3*5C2 = 6*5*10*10=6*500=3000

333    I think the number here is   1* (5C3)^3  =10^3 = 1000

So there seems to be 10 ways that the numbers from each sport can be chosen.

I think there are  375+3000+1000=4375 different ways that the 9 can  be selected.      

Chang all the units to m before you start.

Actually, it is not so straight forward because I am not sure which two equal sides you are meant to omit, probably the 2 smallest one  

They are just 4 rectangles.  Find the areas and add them up.  

Have a go and if you get stuck post with what you have tried.  

You will find the formula here

Here is the formulary page theat will help you.

It is right here on the web2 site!   

This is very similar to you last question.  only easier.  

You have a go at it by yourself.

. תודה לך -. אני שמח שאתה אוהב את זה

6 sin x − 3 sin 2x=12/π

You can solve this graphically in differnent ways.

The 2 online graphing calculators that I will recommend are Desmos and Wolfram|Alpha.

you can also do some graphing on the web2 calc.