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You can ask Apple to make an app for you!

you take or give groups of the number that is being multiplied/divided to.

The answer is 10! :)

10

Im learning about this in one of my classes! :)

I dont really know how, 

Find f(-5) if f(x) = |x + 1|.

six

Very interesting observation!! Did you come up with this scheme yourself? It would have been much more interesting if Row 3 produced ONLY primes, instead of listing all the counting numbers from 1 to infinity, such as this famous observation by Euler: x^2 + x + 41. If you start with 1 and sub it into the equation, it will produce only prime numbers up to 41. Beyond that, it was proven by two mathematicians, that up to 10,000,000 the equation gives 50% primes and 50% composites!.

Another observation. If 705 in Row 3 produces a number in Rows 1 and 2 that is 148 digits long, how big a number would the 1,000,000th number in Row 3 produce in Row 1 and 2?

Is this some new observation or has been known to number theorists for a while? With such large numbers in Rows 1 and 2, maybe number theorists can prove or disprove it in a much more clever ways.

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

Its 4!

I dont really know why its out of fashion now!

I suspect  you meant   something else besides 333  and  252525    ....that is not reality....it looks like you typed in too many digits.    It is more closely   33/252 = 13 %

Use the Pascal triangle:

what is (2x-2)3    [is not \((2x-2)^3\)]

\((2x-2)3=6x-6=(x-1)6\)

  !

Your question , as written, makes no sense......did you transcribe it correctly?

Thank you EletricPavlov

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 :)))))

-4x < 32     divide both sides by -4  (when you divideor multiply by a negative the < sign gets reversed)

x > -8

Anything > -8 will solve this equation  -7  -2   4  6    etc all satisfy this equation

7y  x  8y  =  56 y^2

tan45° = 1

I have the same thing happening. if you copy paste the boxes into google it will tell you that it is in fact, a bat emoji

that would be 59049

9*9*9*9*9

Hello Herr Heureka,

It seems odd that a barn (or even an airplane hangar) would have such a high and massively large roof for a short length.

Wouldn’t you just integrate from -20 to 20 --the width of the barn? This would make the roof area 4701 Ft² for a 40’ x 100’ barn.  This seems more aesthetic and consistent with common barn structures.

Gruß Ginger