Melody

The calc will do natural logs - what do you want with log tables.  They have not been used since the 1970s.

oh well,

here are som natural logs

It is more than 6 units from A to B if you go in a straight line.

the diagonal of this square is  

$${\sqrt{{\mathtt{36}}{\mathtt{\,\small\textbf+\,}}{\mathtt{36}}}} = {\mathtt{8.485\: \!281\: \!374\: \!238\: \!570\: \!3}}$$

So there are definitely NO paths that are only 6 units in length!

I assume you mean.  How many distict 5 digit numbers can be made with the digits 4,5,5,6,and 7

Well, for the first digit there are 5 numbers to choose from.

for the second there are 4 numbers and so on so this is

5*4*3*2*1 ways  = 120 ways

However,  there are 2 5's so there are really half this number because, for instance, 

45567 is the same as 45567

so there will be  120/2 = 60 ways.

the more general formula for this is   5!/2!

Yes, that 'looks' really good MathsGod 

Here is a different question.

Dora has 2 brothers and 2 sisters.  How many Permutation of the family can there be (from Dora 's point of view)

For instance Dora could have 2 older brothers and 2 younger sisters. That is one possibility.  :)

When you get sick of answering these questions you can either tell me or you can just stop answering.

I won't mind :)

Good work anon

but it would have been quicker if you had made p^2 the common denominator in the first place.   :)

good try anon but not quite right

(28w + 1) /4 = -5

$$\\\frac{(28w + 1) }{4} = -5 \\\\
28w + 1 = -20 \\\\
28w + 1-1 = -20-1 \\\\
28w = -21 \\\\
w=\frac{-21}{28}\\\\
w=\frac{-3}{4}$$

Not quite anon

(6x+5)  -1(4x-6 )

=6x+5-4x+6

=2x+11

$$\sqrt{94}+20$$   

can't be simplified

$$\\ln \frac{(e^x)}{(1+e^x)}\\\\
ln (e^x)-ln(1+e^x)\\\\
x-ln(1+e^x)\\\\$$