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@@ End of Day Wrap          Tues 3/2/15 Sydney,        Australia Time      10:25 pm          ♪ ♫

Hi all,

There were a lot of questions today.  Many did not get answered.    Still we had lots of people answering so it could have been much worse.  Today our fantastic answerers were Happy7, TayJay, Alan, awsomenes, Mathematician, shaniab29544, CPhill, Heureka, Anima, Saseflower, Jillybean, Mikado, sasini and Bertie.  Thank you.  

Interest posts:

Wed 4/2/15

When I tried to look at that site Chris I was told that I needed a plug in.

It did not specify which one  

Does anyone know how I can fix this problem?

So how do you do your one Bertie?  (or anyone else)   

$$\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1+\dots$$

Thanks, Bertie......

The "Illuminati".......LOL!!!

BTW....do you recognize this symbol????.....if so....you may REALLY be part of  "THE ILLUMINATI"

That I think is the second of these nested expansions in just a couple of days.

Here is, probably(?), the first problem of this type to appear in print.

Find the value of

$$\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1+\dots$$

Yep...the "formula" is

[ 1 + √5 ] / 2  ≈ 1.618

And the reciprocal of this is "phi"   (i.e., "little Phi").....which =  just the decimal part of Phi = .618   !!!

Here's a website that explains how Phi can be derived from the diagonals of a pentagon.....

Let the expression on the left hand side = N = 9

Square both sides

x + N  = 81  

x + 9 = 81    subtract 9 from both sides

x = 72

That's not much of a hill!!.... anyway, we have that

tan 25  = x / 130    where x is the distance from the boat to the base of the hill   

Multiply both sides by 130

130* tan 25 = x  = about 60.62cm

Very nice, Mathematician and heureka....!!!

Because you can work all the others out from thosw ones.

y=x^2 is a concave up parabola with vertex at (0,0)

y=-x^2 is its reflection in the x axis.  That is it is a concave down parabola with vertex at (0,0)

See if this helps

y=(x-1)(x-2)(x-(3/5))

y=a(x-1)(x-2)(5x-3)     where 'a' is a constant

That is really neat Heureka, thank you 

Sasini, any normal number raised to the power of zero is 1  

Thanks Mikado, perhaps you should give some instruction on how to do it by hand. :)

I like that one.  Thanks awsomenes 

subtract 2/3 from both sides

then

multiply both sides by -5

They all go into 36 so it is 36  

[2nd]  [atan]  (17/19) =

$${\frac{\left({\frac{{\mathtt{4}}}{{\mathtt{7}}}}\right)}{\left({\frac{{\mathtt{3}}}{{\mathtt{5}}}}\right)}} = {\frac{{\mathtt{20}}}{{\mathtt{21}}}} = {\mathtt{0.952\: \!380\: \!952\: \!380\: \!952\: \!4}}$$

you will have to divide both sides by 500 first

and then take the log (base e is easiest) of both sides.

Whenever the exponent is unknown you can/will use logs to solve it.