an Earth Day Math Problem

[tuckerkao]

This math problem will be easy if you have a calculator and understands College Algebra -

 

[Truthy]

Earth is the exoplanet

Spoiler :

I mean, you just gotta make sure the units are right, so I set them up first and then plugged in d = 12.
(I shortened exoplanet years, months, etc to just years, months, etc)
earth days/year = (d months / year)(4 weeks / month)(6 days / week)(d^3 min / day)([that formula] earth min / min)(1 earth day / 60*24 earth min)
= d(4)(6)(d^3)(1 + 8/d^2 + 2/d^3 + 3/d^4) / (60*24)
= (1/60)(d^4 + 8d^2 + 2d + 3)
And "d = Dozen"...
So 365.25 earth days per exoplanet year
I dunno, I was kinda guessing that (or just 365) would be the answer before I did anything. Not sure how obvious that was.

 

[Hygro]

Tuckerkao you are a CFC:OT hero

 

[tuckerkao]

Here's another math trivia -

232,792,560

Find the smallest positive integer that is not a factor of the 9-digits number above.

 

[Arakhor]

Trivia is information of little relevance, not random maths problems.

 

[Hrothbern]

Here's another math trivia -

232,792,560

Find the smallest positive integer that is not a factor of the 9-digits number above.

It is the first prime after the last prime that is a factor in your number (it is 23)
or stated otherwise: your number is the result of the multiplication of all primes below the prime 23 multiplied with the first integer above 23.

But how do you come at that number by Math ?

 

[AmazonQueen]

Trivia is information of little relevance, not random maths problems.

And it makes my head hurt.
I could do this sort of stuff 40 years ago but now? Not a chance.

 

[Truthy]

Trivia is information of little relevance, not random maths problems.

That problem does involve "math trivia" - apparently that number is the first positive integer that's evenly divisible by all of the first 20 positive integers (well first 22, really, given Hrothbern's answer). It's the answer this Project Euler problem

 

[tuckerkao]

It is the first prime after the last prime that is a factor in your number (it is 23)
or stated otherwise: your number is the result of the multiplication of all primes below the prime 23 multiplied with the first integer above 23.

But how do you come at that number by Math ?

I used a different base, then converted it back to decimal at the end.