Melody

You do not need a high powered calculator.  Yo can do it yourself.  :)

let   y=256^(1024^3)

1024^3 = 1073741824

\(y=256^{1073741824}\\ log_{10}y=log_{10}256^{1073741824}\\ log_{10}y=1073741824\;log_{10}256\\ log_{10}y\approx 1073741824\;*\;2.408239965\\ log_{10}y\approx 2585827973\\ 10^{log_{10}y}\approx 10^{2585827973}\\ y\approx 10^{2585827973}\\\)

However, here is the answer using wolfram|alpha  :)

Very nicely explained hectictar   

I'd give you more points if I could.  Hopefully Athena will give you some points (stars) too :))

This is where it took me :)  

I like you new icon Omi :))

Kermit goes good with Red.  

Red is my pet dinosaur - my icon is a recent photo of him.

Yes, RED,  it is a funny name for a green dinosaur but he used to be red. 

I dyed him recenly, Red said he had been red for a couple of million years of so and he wanted a change :)

He does look handsome as a green dinosaur with MY red glasses.  He has taken posession of them, he thinks that they make him look sophisticated  LOL

A barn is 100 ft long and 40 feet wide. A cross section of the roof is the inverted catenary y=31-10(e^x/20+e^-x/20). Find the number of square feet of roofing of the barn.

Here is the cross section of my barn, I painted it purple :)

consider the length of the arc of the roof on the 40 foot side.  Using Pythagoras    (this is really cool)

\(dL^2=dx^2+dy^2\\ (\frac{dL}{dx})^2=1+(\frac{dy}{dx})^2\\ \frac{dL}{dx}=\sqrt{1+(\frac{dy}{dx})^2}\\ L=\displaystyle\int_{-20}^{20} \sqrt{1+(\frac{dy}{dx})^2}\;dx\\ \text{So the area of the roof would be}\\ Area=100\displaystyle\int_{-20}^{20} \sqrt{1+(\frac{dy}{dx})^2}\;dx\qquad feet^2\)

so my starting point is now the same as Heurekas except if have got the catenary over the short side which makes more sense to me :)

Heureka has done the rest already :)))))

Yes that is correct except you forgot the +c

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This is how I would enter it

\int\frac{(-1+y)^2}{4y}\;dy

now open up the LaTex button on the ribbon and paste it in :)

\(\int\frac{(-1+y)^2}{4y}\;dy\)

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this might seem a bit complicated to start with if you do not know any LaTex but this forum is a great place for you to learn.

fractions are easy and very handy, so to write 2/3 as a fraction it is just

\frac{2}{3}

and now I will past this into the  LaTex box

\(\frac{2}{3}\)

That is a very cool signal :)  

log3((x)(sqrt(y)))

\(log_3(x\sqrt y)\\ =log_3x+\log_3\sqrt y\\ =log_3x+\log_3(y)^{1/2}\\ =log_3x+\frac{\log_3(y)}{2}\\ =\frac{2logx}{2log3}+\frac{logy}{2log3}\\ =\frac{2logx+logy}{2log3}\)

Look here

Yes, maybe that is it :))

Hi Chris :)