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Forum ยป Any of you boys good with Math? Need some help. (Intervals)
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Thread: Any of you boys good with Math? Need some help. (Intervals)

post 1690843893 09-28-2023, 06:26 PM
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#31
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Originally Posted By ZyraThornrise⏩
Number of cells you want to fill minus 1
You can also write it as 31-1 and it'll function the same but I got lazy lol
My mistake thought you would have n starting at 1 and not magically arrive at 30. As to how you arrived at the number of elements, no one knows

If the goal was just to write all the numbers between 53 and 13 OP would have been better off inputting each one into the spreadsheet manually.

If the goal is to write a proper formula, then your formula shouldn't be missing all the logic you used to calculate the number of elements or break if you changed a single value such as the value of A1, B1 or the decrement,

How did you calculate the number of elements in a finite series? Seems like a pretty important part of the formula to me just saying. Magically getting the number 30 means half your formula is missing
post 1690843943 09-28-2023, 06:28 PM
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#32
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Originally Posted By BigGuyTruth⏩
Find the slope
post 1690844723 09-28-2023, 06:43 PM
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Originally Posted By outfoxxed⏩
My mistake thought you would have n starting at 1 and not magically arrive at 30. As to how you arrived at the number of elements, no one knows

If the goal was just to write all the numbers between 53 and 13 OP would have been better off inputting each one into the spreadsheet manually.

If the goal is to write a proper formula, then your formula shouldn't be missing all the logic you used to calculate the number of elements or break if you changed a single value such as the value of A1, B1 or the decrement,

How did you calculate the number of elements in a finite series? Seems like a pretty important part of the formula to me just saying. Magically getting the number 30 means half your formula is missing
How many cells are between A1 and A31?

Say he had 34 at A1 and 13 at A45, the formula would then be (45-1) in that slot of the formula
Dragging the formula into the empty spaces then fills that formula automatically, there is no additional math

My formula wouldn't work for what he was asking, anyway, because I misread as mentioned above
There's no magical way I came up with the numbers, you just go down the column and you can see the number to put in the N space

With what he is wanting to do, I'm not sure really how to make that work in a singular column
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post 1690845343 09-28-2023, 06:56 PM
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#34
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Originally Posted By ZyraThornrise⏩
How many cells are between A1 and A31?

Say he had 34 at A1 and 13 at A45, the formula would then be (45-1) in that slot of the formula
Dragging the formula into the empty spaces then fills that formula automatically, there is no additional math

My formula wouldn't work for what he was asking, anyway, because I misread as mentioned above
There's no magical way I came up with the numbers, you just go down the column and you can see the number to put in the N space

With what he is wanting to do,I'm not sure really how to make that work in a singular column
I would start by swapping the 13 and the 34 around, and use the formula 13 + 21n(n-1)/992
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post 1690846713 09-28-2023, 07:27 PM
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Originally Posted By DuracellBunny⏩
I would start by swapping the 13 and the 34 around, and use the formula 13 + 21n(n-1)/992
That would just end up getting you 13.3, though, not do anything to fill the cells
Also why the 992?
Not saying you're incorrect by any means, just not sure where you're going with it
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post 1690847243 09-28-2023, 07:39 PM
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Is there a way to do this with a pencil & paper, fellas? I'm not specifically looking for an Excel formula, just want to know how to get the answer.
R.I.P. Bert
post 1690847263 09-28-2023, 07:39 PM
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Originally Posted By ZyraThornrise⏩
That would just end up getting you 13.3, though, not do anything to fill the cells
Also why the 992?
Not saying you're incorrect by any means, just not sure where you're going with it
Go back to my first post.

What he is talking about is triangular numbers, like balls on a pool table. The first row you have 1, the second you have 2 etc and the total numbers of balls is n(n+1)/2

so it starts at 13 and you then add one ball for the 2nd row, 3 for the 3rd, 6 for 4th, 10 for the 5th etc

The problem being that we can't use whole balls. He wants to add 21 balls over 31 rows. so we have to use fractions of balls

y31(31+1)/2=21
y992=42
y=42/992

so the rows would be

13
13 + 42/992
13 + 42/992 + 2x42/992
13 + 43/992 + 2x42/992 + 3x42/992
13 + n(n-1)/2 x 42/992 or 21n(n-1)/992 (using n and n-1 instead of n+1 and n as we don't start adding "balls" until row 2

Then by the time we go through 31 rows it will have the value of 34
Screw nature; my body will do what I DAMN WELL tell it to do!

The only dangerous thing about an exercise is the person doing it.

They had the technology to rebuild me. They made me better, stronger, faster......
post 1690847563 09-28-2023, 07:46 PM
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#38
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Originally Posted By DuracellBunny⏩
Go back to my first post.

What he is talking about is triangular numbers, like balls on a pool table. The first row you have 1, the second you have 2 etc and the total numbers of balls is n(n+1)/2

so it starts at 13 and you then add one ball for the 2nd row, 3 for the 3rd, 6 for 4th, 10 for the 5th etc

The problem being that we can't use whole balls. He wants to add 21 balls over 31 rows. so we have to use fractions of balls

y31(31+1)/2=21
y992=42
y=42/992

so the rows would be

13
13 + 42/992
13 + 42/992 + 2x42/992
13 + 43/992 + 2x42/992 + 3x42/992
13 + n(n-1)/2 x 42/992 or 21n(n-1)/992 (using n and n-1 instead of n+1 and n as we don't start adding "balls" until row 2

Then by the time we go through 31 rows it will have the value of 34
Damn. Nice.
I was limiting my thinking to Excels formula capabilities to make it a couple button clicks and you're done lol

Also you explained that incredibly well
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post 1690848873 09-28-2023, 08:16 PM
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#39
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Originally Posted By DonVonDuck⏩
Is there a way to do this with a pencil & paper, fellas? I'm not specifically looking for an Excel formula, just want to know how to get the answer.
Checking in.

Because I still see people struggling with this, I'll give a full answer.

What you have is the recurrence relation

a[n] = a[n-1] - nr

with the boundary conditions

a[0] = a0
a[N] = aN

In this case, it's fairly easy to solve without much formal knowledge.

If you write out the first few terms and you'll notice a pattern

a1 = a0 - r
a2 = a1 - 2r
a3 = a2 - 3r
...

summing up the equations

SUM(a[n], n=1, n=N) = SUM(a[n], n=0, n=N-1) - r * (1 + 2 + ... + N)

which simplifies to

aN = a0 - (1/2)N(N+1)r

Now use your boundary conditions to solve for r

r = 2(a0 - aN) / (N * (N+1))

and so for an arbitrary n, you have

a[n] = a0 + n(n+1)/(N(N+1)) * (aN - a0)


Applying this to your toy example,

a[0] = 53
a[12] = 14

and so

a[n] = 53 - 39/156 * n(n+1)

plugging in values for n, we see

a[0] = 53, a[1] = 52.5, a[2] = 51.5, a[3]=50, ..., a[12] = 14

as desired
Physics crew
post 1690849033 09-28-2023, 08:20 PM
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#40
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Originally Posted By DuracellBunny⏩
Go back to my first post.

What he is talking about is triangular numbers, like balls on a pool table. The first row you have 1, the second you have 2 etc and the total numbers of balls is n(n+1)/2

so it starts at 13 and you then add one ball for the 2nd row, 3 for the 3rd, 6 for 4th, 10 for the 5th etc

The problem being that we can't use whole balls. He wants to add 21 balls over 31 rows. so we have to use fractions of balls

y31(31+1)/2=21
y992=42
y=42/992

so the rows would be

13
13 + 42/992
13 + 42/992 + 2x42/992
13 + 43/992 + 2x42/992 + 3x42/992
13 + n(n-1)/2 x 42/992 or 21n(n-1)/992 (using n and n-1 instead of n+1 and n as we don't start adding "balls" until row 2

Then by the time we go through 31 rows it will have the value of 34
Wouldn't it be 30 instead of 31? Since nothing is being added to the first number.
R.I.P. Bert
post 1690849293 09-28-2023, 08:28 PM
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#41
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Originally Posted By DonVonDuck⏩
Wouldn't it be 30 instead of 31? Since nothing is being added to the first number.
Yeah, my bad. I'm multi-tasking.

so just swap 30x31 for 31x32 or 930 for 992, so 13 +21n(n-1)/930
Screw nature; my body will do what I DAMN WELL tell it to do!

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post 1690849413 09-28-2023, 08:30 PM
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#42
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So, taking that to apply to the first set, it'd be
A[0]=34
A[30]=13

Right?

Literally never had to use a problem like this and I want to make sure I've got it down lol
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post 1690849453 09-28-2023, 08:32 PM
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#43
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Originally Posted By DuracellBunny⏩
Yeah, my bad. I'm multi-tasking.

so just swap 30x31 for 31x32 or 930 for 992, so 13 +21n(n-1)/930
I really appreciate it. Helped me out a lot. I knew the Misc would come through for me . Wouldn't ever have figured it out.



EDIT: Did it backwards.
R.I.P. Bert
post 1690849573 09-28-2023, 08:33 PM
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#44
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Curious, but what is this being applied to?
Seems useful AF but also niche lol
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post 1690850543 09-28-2023, 08:53 PM
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Originally Posted By DonVonDuck⏩
I really appreciate it. Helped me out a lot. I knew the Misc would come through for me . Wouldn't ever have figured it out.



EDIT: Did it backwards.
You're welcome. Misc is quite varied and it depends on who is on at what time and sees what thread as to whether you get help. It's hit and miss.
Screw nature; my body will do what I DAMN WELL tell it to do!

The only dangerous thing about an exercise is the person doing it.

They had the technology to rebuild me. They made me better, stronger, faster......
post 1690851133 09-28-2023, 09:04 PM
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#46
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