help-42

[oblique current]

that sounds way too general then

[paper bolt]

What do you mean

[oblique current]

its kind of like asking how to simplify a + b + c + d + e where a,b,c,d,e are just any numbers

[leaden thunder]

,calc 1/24

[potent lotus]

Result:

0.041666666666667

[leaden thunder]

Computers seem to handle that fine?

[paper bolt]

Well it has to be in will to optimize

[paper bolt]

Oh my bad, I thought of something different but never mind

Well let's say how would they handle

1 / 1000! ?

That's bad, I would assume

[oblique current]

,w 1/1000!

[potent lotus]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by iCaird#6258

[leaden thunder]

Your question just needs to be scoped better. Solving numerical approximation is different from simplifying fractions

[paper bolt]

Ideally

It would be best to represent it as a factorial

Which is later on going to be multiplied by certain other factorial and scale it back

[leaden thunder]

"best" for what purposes

What problem are you solving

[paper bolt]

My friend and I are trying to make a certain algorithm work

And essentially that thing is part of the algorithm

It's optimization to an already existing thing as far as I Know

and I would have to do the coding part

This is an example expression:

-1/8! + 1/2! * 1/6! + -1/4! * -1/4! + 1/2! * 1/2! * -1/4! + 1/6! * 1/2! + 1/2! * -1/4! * 1/2! + -1/4! * 1/2! * 1/2! + 1/2! * 1/2! * 1/2! * 1/2! = 277/8064

This 277/8064 will be later on multiplied by some factorial

Which will scale it back

[oblique current]

this is different to your original question, you didnt have products of factorials

[paper bolt]

Does that change anything significantly?

[oblique current]

probably not, but it could have

[remote mural]

what language? what algorithm? before we get too far down the xy rabbit hole

[paper bolt]

Any language I would assume, but I am trying to use Python since it's very useful for stuff like this

As for algorithm, I would have to keep that a secret for now :/

[remote mural]

use sympy if you care about the result (but not the speed)

[paper bolt]

Speed would also be important, that's kind of the point of optimization

[remote mural]

you cant have both if the problem that you've proposed is optimal ¯_(ツ)_/¯

[paper bolt]

XD

Thanks for the tip tho, I will take a look at it

But, can we anyhow simplify this mathematically

Mathway has successfully expressed this thing as that fraction up there

[oblique current]

sure, just add the fractions by hand

thats what mathway will have done

[paper bolt]

What do you mean "by hand"

Literally that way?

[oblique current]

like the usual way you add fractions

[paper bolt]

Are you really sure that will ... work optimally xD?

[oblique current]

you are asking whether you can simplify it mathematically

[paper bolt]

To phrase it mathematically, do you think that's simplified enough?

[oblique current]

how more would you simplify it than as one fraction?

[paper bolt]

But to get to that one fraction maybe you will have to calc 1000!

And that's not very great

I am trying to evade that

[oblique current]

which brings me back to the original point of this being way too general. you can't hope for a general simplifcation that's going to work no matter what expression you give

simplifications that will avoid big calculations will be a result of cancelations because of the specific terms in an expression

like how 24/6 = 4, but being able to do that simplification was completely dependent on the numbers being 24 and 6

[paper bolt]

Alright

We will end it at that then xd

Thank you for help

.close

[calm coral]

Channel closed

Closed by @paper bolt

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[exotic arch]

Hi everyone, I hope you all are doing well today!
I am working on a creating some parametric gear drawings by means of code and for that need to use an involute curve.
Calculating the positions is no issue, but finding out where to start an stop is an issue.
To this end I have identified this formula to find out where a given angle would create a point on the involute curve:

involute_position = angle - atan(angle)

Now I am looking for doing the inverse to find out where I should start/stop.
The question would be:
Given the involute position (an angle) how would I find (or approximate) the input angle?

[somber finch]

,w x = y +arctan(y)

[potent lotus]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by sopinha#5309

[somber finch]

hm

'-'

[somber finch]

can you give an example?

[exotic arch]

Of course! Let me draw it up real quick

[teal coral]

are you just trying to solve equations that look like 3 = theta + atan(theta)?

[exotic arch]

I hope this illustrates the question:

[exotic arch]

No, I am looking to approximate theta in the equation 3 = theta - atan(theta) when given the value of 3

[teal coral]

what's the difference between that and what I said

[exotic arch]

My mathematical vocabulary isn't too great, so it might be the same.

Ah, I'm looking for theta - atan(theta) instead of theta + atan(theta) I'm not sure if there's a difference?

[teal coral]

oh yeah my bad typoed that

so you want to solve something that looks like c = theta - atan(theta)

like do you just want numbers for practical purposes or are you looking for a proper analytical solution

[somber finch]

Do you have the tools to calculate theta - atan(theta) given theta? You could use derivative then to aproximate

[exotic arch]

It would be numbers for practical purposes

[teal coral]

practical purposes, you can probably just ask wolframalpha

,w solve 3 = theta - atan(theta)

[potent lotus]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Saccharine#3780

[teal coral]

if you need to write it in code, you can use some numerical optimization methods

[exotic arch]

Ah I see, so that would provide individual values

As 3 would be a dynamic value, I think the analytical solution is probably what I'm looking for then?

[teal coral]

are you writing code for it

[exotic arch]

Yes

[teal coral]

okay then you can use a numerical method

in this case, there are a few ways to do it

one way might be to rearrange the equation to theta = c + atan(theta)

and then solving this amounts to finding a fixed point

[exotic arch]

I see, so I would swap out the function, and then iteratively find the closer value?

[teal coral]

well, hmm idk if that would work so well, since the derivative at the root is 1

you could certainly use something like Newton's method

there are plenty of root-finding algorithms

at the worst, bisection would probably do the trick

in particular, the equation you're solving is really well-behaved; it's monotone nondecreasing

[exotic arch]

That makes sense, I'll try that out!

[teal coral]

so even a simple binary search is guaranteed to converge

[exotic arch]

Thank you, I will try those methods out!

[somber finch]

Bisection can ensure decimal places

[exotic arch]

So if I understand correctly, there's no direct method for inverting this formula, and as such, using some root-finding method is necessary to approximate the values?

Thank you for your help @teal coral and @somber finch!

.close

[calm coral]

Channel closed

Closed by @exotic arch

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sullen heart]

Need help

[frosty compass]

whats the nature of ABCD ?

[sullen heart]

Parallelogram

[calm coral]

@sullen heart Has your question been resolved?

[frosty compass]

is there a way to prove that AM is the bisector of BAC ?

[sullen heart]

Possible if AB:AC = 2:3

[frosty compass]

im looking for another but i cant seem to find one

[sullen heart]

Might be possible with constructing a line

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[frosty compass]

.reopen

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sullen heart]

.

[sullen heart]

Need help

[rotund olive]

well I do have an idea

[calm coral]

@sullen heart Has your question been resolved?

[frosty compass]

enlighten us

[sullen heart]

Yes please

[rotund olive]

nvm it didn't work

[sullen heart]

[rotund olive]

my idea ended up with a conclusion that 5=3qsrt2

[sullen heart]

???!!????!!? What does that mean

[calm coral]

@sullen heart Has your question been resolved?

[frosty compass]

<@&286206848099549185>

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sudden nebula]

I need a hint for how to handle the exponents here

[sudden nebula]

Could I multiply by something to make the math smoother?

[calm coral]

@sudden nebula Has your question been resolved?

Channel closed

Closed by @sudden nebula

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fair rapids]

Good Evening!
Can someone help me to find the approach they used to get that result?
I know that the first fraction is 2 but what about the rest?

[glass heart]

show the original problem statement

but well, it does say quotientenkriterium there

[remote mural]

looks like ratio test

[fair rapids]

I am aware of the criteria, I just dont udnerstand how they transformed the first equation to the second

[glass heart]

well presumably plugged in a_k+1 and a_k

[fair rapids]

And from theory?

[glass heart]

.

[fair rapids]

Because 2^k+1 /2^k is 2

[glass heart]

well the factorials nearly cancel each other out

and just a few factors remain

[fair rapids]

So it says that we need to decide if the series converges

[glass heart]

(k+1)! = (k+1) * k!, the k! cancel and you are left with (k+1) in the numerator

then squared

and (2(k+1))! = (2k+2)! = (2k+2)(2k+1)*(2k)! and the (2k)! cancel

and you are left with (2k+2)(2k+1) in the denominator

[fair rapids]

What is this (2k+2)! = (2k+2)(2k+1)*(2k)!

[glass heart]

well factorial

(2k+2)! is the product of all numbers <= 2k+2

(2k+2)(2k+1)(2k)(2k-1)(2k-2)....3*2*1

but that second part is just (2k)!

[fair rapids]

Holy moly

Never though about it like this

[glass heart]

what did you think factorial was

[fair rapids]

I mean I get the concept for natural numbers

But not in such a way

Thats actually great help!

Appreciate it 👍

[glass heart]

youre welcome

[fair rapids]

.close

[calm coral]

Channel closed

Closed by @fair rapids

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[modest otter]

I am confused and stuck since the first step

.closr

.close

[calm coral]

Channel closed

Closed by @modest otter

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[remote pendant]

If S is normally distributed with mean 1800 and variance 317.4

[remote pendant]

and L is also normally distributed with the same mean and variance

how can u work out the probability that S is atleast 25 units larger than L

textbook has the answer but no workings lol

<@&286206848099549185>

[remote mural]

Very carefully

[remote pendant]

thx

[leaden thunder]

use z score

[calm coral]

@remote pendant Has your question been resolved?

Channel closed

Closed by @remote pendant

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[drowsy flume]

Um hello can I please just have some help??

[calm coral]

Please don't occupy multiple help channels.

[drowsy flume]

sorry

[hasty fiber]

stick to your first channel

.close

[calm coral]

Channel closed

Closed by @hasty fiber

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[eternal mason]

log_10(1/sqrt1000)

[eternal mason]

how do u simplify this

[remote mural]

what is the square root of 1000?

in a more simplified form

[eternal mason]

uhhh

idk

[remote mural]

well okay

[eternal mason]

ik its around 31

[remote mural]

1000 is just 100 times 10 right?

[eternal mason]

yea

[remote mural]

right so what is the square root of 100

[eternal mason]

10

[remote mural]

right

so take that out of the square root

what do you have now

[eternal mason]

10^3

[remote mural]

no

like

[
\s{1000} = \s{100 \cdot 10} = ?
]

[eternal mason]

10sqrt10?

[remote mural]

yep

[eternal mason]

oh alr

then what

1/10sqrt10

[remote mural]

okay so

[
\log_{10}\parens{\f{1}{\s{1000}}} = \log_{10}\parens{\f{1}{10\s{10}}}
]

[remote mural]

now,

[eternal mason]

mhm

[remote mural]

can you write sqrt(10) in exponential form

[eternal mason]

sure

10^1/2

[remote mural]

right

so

you have $10 \cdot 10^{\f12}$

[eternal mason]

yep

which is

[remote mural]

do you know anything in particular we can do with this?

[eternal mason]

10^1/2

bases stay the same

add the exponents

[remote mural]

yes

so

add them up you get what

[eternal mason]

1 and 1/2

?

[remote mural]

yeah

whats 1+ 1/2

[eternal mason]

3/2

[remote mural]

right

so what do you have now

[eternal mason]

3sqrt10

[remote mural]

no

[eternal mason]

oh wait

[remote mural]

where did that come from

[eternal mason]

3/sqrt10

[remote mural]

no

again

where is the 3 coming from

[eternal mason]

1+1/2

[remote mural]

you said bases dont change at all

[eternal mason]

3/2

[remote mural]

we are only dealing with exponents

[eternal mason]

oh ok

so what do we have at the moment

[remote mural]

you have [
\log_{10}\parens{\f{1}{\s{1000}}} = \log_{10}\parens{\f{1}{10\s{10}}} = \log_{10}\parens{\f{1}{10^{\f32}}}
]

[eternal mason]

yea

[remote mural]

i think it is best if you try to continue this on your own

[eternal mason]

why

??

@remote mural

[remote mural]

because i dont want to simply hand the answer to you

you wouldn't be learning anything in that process

why not try and attempt to continue it?

[eternal mason]

walk me through it

im understanding

or

what if i continue and u see if itts correct

[remote mural]

yeah sure

go ahead

[eternal mason]

ok

so

it would be

1log_10(10^3/2)

right?

[remote mural]

uh

where did the fraction disappear

[eternal mason]

oh wait

is it

3/2log_10(1/10)

according to the log rule

[remote mural]

okay sure

continue

[eternal mason]

then

it would equall 3/2

for the answer

or am i wrong

[remote mural]

no

it would not be 3/2

what is log_10(1/10)

[eternal mason]

1?

right?

@remote mural

[remote mural]

no

[eternal mason]

how would u do it

@remote mural

[remote mural]

bring the 10 to the numerator

and please stop pinging me

[eternal mason]

ok

so 10^10?

[remote mural]

no like apply the exponent law of $\f{1}{a^n} = a^{-n}$

[eternal mason]

ohh

so it would be

10^-3/2?

[remote mural]

yes

idk why u brought back the 3/2

but yes

[eternal mason]

so what?

just 10?

[remote mural]

yeah what u were already doing

[eternal mason]

yea

[remote mural]

so what do u have now

[eternal mason]

-1

[remote mural]

yes

apply the log rules

[eternal mason]

-3/2

right?

[remote mural]

yes

thats ur answer

[eternal mason]

ye

wasnt hard

now i got one more question

log_1/9(x)=-1/2

i simplfied it to

log_3^-2(x)=2^-1

idk what to do after

@remote mural

last ping i promise

lol

anyone?

.close

[calm coral]

Channel closed

Closed by @eternal mason

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[drifting vortex]

ive done part a

need some help on b plz

[velvet osprey]

$x_i \geq 0$

[potent lotus]

Ann

[velvet osprey]

2+s-t >= 0, and -4+7s-19t >= 0, and so on...

[drifting vortex]

ok

[drifting vortex]

ight got them

what now?

[velvet osprey]

now graph them

that's what i would have done

it is not yet immediate just from looking at these ineqs that the five halfplanes they describe actually intersect in one single point

[calm coral]

@drifting vortex Has your question been resolved?

[drifting vortex]

i got this

with the credit of chartbit the goat

[velvet osprey]

seems like that works

i mean it would be nice to know what the value of t is too

[drifting vortex]

it says there

t = 0

💀

[velvet osprey]

oh, right. yeah.

[drifting vortex]

another Ann L

[velvet osprey]

🙄

[drifting vortex]

might have to change from rare Ann L to common Ann L

[calm coral]

@drifting vortex Has your question been resolved?

Channel closed

Closed by @drifting vortex

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[karmic ridge]

could i get a hint?

[karmic ridge]

i dont even know where to start

[tacit compass]

maybe use a five digit variable abcde

and when you cross one out and add

you can create a system of equations

[calm coral]

@karmic ridge Has your question been resolved?

[karmic ridge]

so five different equations

??

abcde+bcde=41751 for instance

how do i solve this

[tacit compass]

it looks liek that doesnt work

because e + e cannot end in a 1

so try crossing out a different one

[amber bolt]

that's the answer then

you can;t not cross e

so you must cross e unles that doesn;t work either

must be 1 or 0

only one equation

[tacit compass]

yep

abcde+abcd

use that

[tacit compass]

got it?

[karmic ridge]

why?

[tacit compass]

is e is an odd number

e + e will always end in an even number

the only way you can end in an odd number is by adding an even and odd together

1+1 = 2

3+3 = 6

5+5 = 10

[amber bolt]

e must be 6

and that lets you find d, and it keeps working

[tacit compass]

now?

[karmic ridge]

i understand

[karmic ridge]

how did you get that

[amber bolt]

our equation is
11000a+1100b+110c+11d+e = 41751

e must be such that 41751−e is divisible by 11

i checked all options to find that e=6 makes it divisible by 11

that was pretty dumb of me

like the remainder of division bt 11 would give me 6 directly

at least it worked

now since 11000a+1100b+110c+11d = 41745 we can tell that d is 5, other letters don't even contribute to the last digit

[karmic ridge]

wait how

[amber bolt]

it's a number that you have to subtract to make something divisble

it only gives one number, smallest, so if it was appropriate e could also be 17 and 28 etc.

but it's only 6 thaat can be a digit

[karmic ridge]

pardon...

[karmic ridge]

how did you get 17 and 28....

[amber bolt]

6+11

6+11+11

[karmic ridge]

ah ok

thanks for your help

[karmic ridge]

well they cant be anything

right?

[amber bolt]

right, they don't mess with the last digit

it's only defined by d

[karmic ridge]

but we still have to find the possible digits?

[amber bolt]

i don;t understand

yes

it just keeps working

[karmic ridge]

we have to find the possible values of a, b and c?

[amber bolt]

if d is 5, then 11000a+1100b+110c = 41690
and then c defines that 9

so c is 9

[karmic ridge]

right

so is there only 1 possible number?

[amber bolt]

yes

i checked

[karmic ridge]

what would be the solution for this? 11000a+1100b=41591

[amber bolt]

how did you get that though

i don't know

[karmic ridge]

i subtracted 990 from 41690

@amber bolt since we said c=9

[amber bolt]

40700

[karmic ridge]

oh mb

THANKS

.close

[calm coral]

Channel closed

Closed by @karmic ridge

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wary condor]

I need help understanding how to solve nested quantifiers

[calm coral]

@wary condor Has your question been resolved?

[calm coral]

@wary condor Has your question been resolved?

[wary condor]

<@&286206848099549185>

I don't have a frame of reference on how to solve this

so far I've only been given statements to negate

is it X is even --> x^2 + 1 is even?

idk if my train of thought is correct cause im struggling to find anything online that is similar to the questions im being asked.

But, for negating the statement do I negate everything

or just the 2nd stuff

so would it become
x ≥ −3 −→ x^2 < 9

and false

[pulsar canyon]

well for starters what do you do with the quantifier?

we have a ∀ right?

[pulsar canyon]

how much DO you know about this? because I can walk you through it a little bit (i think, it's been a while)

[pulsar canyon]

This one is phrased as an "if, then" if i'm understanding it correctly, so we flip the quantifier ("for all" gets replaced with "there exists an x" ∃). and then we say x is even AND x^2 + 1 is not odd (can just say even)

https://sites.math.washington.edu/~aloveles/Math300Summer2011/m300Quantifiers.pdf

that's what i'm using to kinda refresh my brain on it

remember that push comes to shove use a truth table

[calm coral]

@wary condor Has your question been resolved?

[wary condor]

hey sorry, I'm absolutely fried rn i'll have to get back to this tomorrow ty for the link it looks like it has a lot of useful stuff for me

[calm coral]

Channel closed

Closed by @wary condor

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[pulsar canyon]

no worries, here's another one that I found for what it's worth
https://www.ccs.neu.edu/home/lieber/courses/algorithms/general/quantifiers.pdf

[pulsar canyon]

.close

[calm coral]

Channel closed

Closed by @pulsar canyon

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[frosty mica]

This is the question I have an issue with.

This is what I have so far.

I understand I need to derive q to get i, but the software is saying my q is wrong.

The lecture on this section was very rushed in that it didn't explain any of the numbers, it just gave the initial top equation with values, then the next line was the q and i, without showing any of the steps in between.

[calm coral]

@frosty mica Has your question been resolved?

[upper sparrow]

Hmmm, that integrating factor is looking a bit

[teal coral]

QC = V on a capacitor, is it not?

nvm I'm an idiot

Q = CV

but yeah your differential equation looks wrong, because q(0) = 0 is one of the boundary conditions

[upper sparrow]

Also seems like you implies that $\frac{1}{5\times 10^{-6}} = 5\times 10^{6}$ on that first line actually

[potent lotus]

@upper sparrow

[teal coral]

should look something like q(t) = k(1-e^(-t/RC)) iirc

[frosty mica]

I'm not entirely sure, this entire section was not really explained whatsoever.

It's an online class so the teacher just assumes you know everything they don't explain, which I don't.

[frosty mica]

Where does it say that?

.close

[calm coral]

Channel closed

Closed by @frosty mica

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[frosty mica]

This is what I'm stuck on

[frosty mica]

This is what I have tried

I'm just trying to wrap my head around all of the different variables/constants because the book is so egregiously awful at explaining it, that it doesn't seem to actually explain it, in my mind.

I understand that K is the limiting capacity, but r is just described as f(0), but I have no idea what f(t) represents.

[teal coral]

what do you mean by K and r

[frosty mica]

It's what's given in the book\

The book doesn't really explain anything clear enough for me to understand

K = carrying capacity, r is a constant where f(0) = r

f(P) =(r-rP/k)

[teal coral]

is that like the growth rate or something

and P is the population?

[frosty mica]

It would seem so, yes.

[teal coral]

it seems like rP/K is just a fudge factor to delete some offspring

[frosty mica]

I am assuming N and P are interchangeable here

For the purposes of the answer to the question

[teal coral]

not interchangeable, just different names for the same thing

[frosty mica]

Yeah

[teal coral]

the question doesn't talk about P

[frosty mica]

Yeah

I'm just extremely confused because this section is so poorly explained

I'm mainly confused on the N(0) = and the N(1) =

How do I tie those into the original equation to find r?

Or are those values for c?

[teal coral]

wait so are you confused where the form of the logistic equation comes from

or are you confused about how to actually solve the problem

[frosty mica]

Essentially, yes.

Both?

I don't really know where to find resources on this, since I haven't been in college in 5 years.

I am quite out of the loop.

[teal coral]

I dunno if it's that important for passing to know where the equation comes from

but as for actually solving the problem, you just need to know what the general form of the logistic equation looks like

[frosty mica]

I would assume that dN/dt = N(r-rN/K). Do I need to integrate that to get N(t)?

[teal coral]

and then find the constants like you would any other function

[teal coral]

this is a differential equation

you need to solve it to get N(t)

[frosty mica]

Is that not the logistic equation?

Oh

The book didn't say that at all

[teal coral]

you see that there's a derivative of N on the left side and the actual N on the right side

so you can't just integrate

solve it like you would any other initial value problem

[frosty mica]

Separate it for N on one side, t on other?

Would it have to be a Bernoulli equation since N is a denominator?

Oh never mind

I forgot you can integrate like that

[frosty mica]

Kinda like this, but if I integrated correctly?

Somethin more like that I think

[frosty mica]

Am I not supposed to have a P^2? The book is saying I'm wrong.

[calm coral]

@frosty mica Has your question been resolved?

Channel closed

Closed by @frosty mica

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[bitter plover]

?

[pseudo wedge]

?

[dry surge]

?

[pseudo wedge]

they factored the denominator

[bitter plover]

how

[pseudo wedge]

well

$a = x^2 + 1, b = x, (a+b)(a-b) = (x^2+1)^2 - x^2$

[potent lotus]

kheerii

[bitter plover]

thx

.close

[calm coral]

Channel closed

Closed by @bitter plover

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[astral mural]

Huh

[calm coral]

Channel closed

Closed due to the original message being deleted

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[mint cloud]

how can u tell when certain letters are reffering to certain meanings

[mint cloud]

im starting to notice letters being used for multiple definitions

can you only tell based on the other letters around it?

[exotic falcon]

Normally you only know that a letter means anything if the problem tells you what it means

I could give you a question and say, "let x = the number of rubber ducks" or a different question and say, "let x = the number of cars"

and the only reason you know what "x" means is because I told you what it means for that specific question

Letters start to get used a lot for the same things and there will be patterns, so if sometimes you don't get an explicit explanation but you recognize what the letter probably means, it might be safe to guess.

[mint cloud]

hmmm ok thank you

so the letters that DO change are called variables correct?

and the ones that do not are Constants?

[oblique current]

"variable" and "constant" are not attributes assigned to letter, just to quantities themselves

i.e. there are not letters that are constants and letters that are variables

but in a specific setup, you can choose to represent variables and constants by whatever letters you choose

e.g. the speed of light in a vacuum is constant and we usually use the letter c for that

but that does not mean c is always representing a constant value

[exotic falcon]

yes and you can have an equation like this

[potent lotus]

AustinU

[exotic falcon]

where a, b, and c are "constants" but x is a variable

although they are all letters

so it is entirely context-dependent, just like the definition of what the letters themselves signify

[calm coral]

@mint cloud Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[whole swallow]

the one with the truss

[rotund olive]

What's a truss

[whole swallow]

it's something that supports the roof

but in the image it's the one above. #2

[calm coral]

@whole swallow Has your question been resolved?

Channel closed

Closed by @whole swallow

Use .reopen if this was a mistake.

[whole swallow]

.close

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[calm coral]

Channel closed

Closed by @gray oar

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[dense idol]

is the null space of a matrix just the # of free variables?

[exotic falcon]

the dimension of the null space can be thought of as the # of free variables

I believe

[dense idol]

and then the col / row space dimensions are just the # of pivotal columns

which is also the rank

right?

[runic fjord]

... wait a sec

[exotic falcon]

Yes

[runic fjord]

that's not how I was taught it but that works fine, yea...

[dense idol]

thank god im not in medical school lmao

[runic fjord]

LOL wym

[dense idol]

i would probably explode with the amount of memorization i'd have to do

i hope i wont have to use this later

[exotic falcon]

linear algebra can be useful

[calm coral]

@dense idol Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[glacial elk]

if you have an operator that acts on f(x), what is the significance of a '^' above an x in its definition (like in the example below)

[glacial elk]

ive seen operators where if the goal was O(f(x) = x * alpha * f(x) they would write the x without the hat on top

so i'm confused as to why i'm seeing x hats in operators and if they mean something specific

[calm coral]

@glacial elk Has your question been resolved?

[calm coral]

@glacial elk Has your question been resolved?

[calm coral]

@glacial elk Has your question been resolved?

[solar spruce]

do you have more context?

[glacial elk]

i'm trying to understand notation so that i can do a question for a piece of coursework

(which is testing linearity of operators)

i dont really think i understand the topic enough to phrase it in a way that makes more sense

i guess since i'm unsure of how vague the term 'operator' even really is

this is for example the hamiltonian operator [using the same field/definition of 'operator' i am studying and attempting to understand]

but i'm referring to any operator O that has notation 'x^' within it

[stark sable]

hey

that’s acutely really simple

so you see

use chat gpt👍

[calm coral]

@glacial elk Has your question been resolved?

[calm coral]

@glacial elk Has your question been resolved?

[warped rampart]

operators in quantum mechanics are just given a hat on top to show that they are operators. in the example of the position operator $\hat{x}$ we just have that this operator just happens to be the position, $x$, so $\hat{x}=x$. a different operator like momentum is not just defined as the "momentum" (whatever that would be in quantum mechanics since velocity is not well defined) but as $$\hat{p}=-i\hbar\pdv{x}$$ or more generally $$\hat{p}=-i\hbar\nabla$$

[potent lotus]

Duh Hello

[warped rampart]

so in this case $\hat{O}$ is just multiplying some function $f(x)$ by $\hat{x}\cdot\alpha$ (from the left). since $\hat{x}=x$ then this operator is just regular multiplication. so this O operator is just scaling a function by a factor $x\alpha$

[potent lotus]

Duh Hello

[warped rampart]

to test for a linear operator you just need to check if this holds where $\alpha, \beta$ are scalars, $A$ is the operator and $x,y$ are the functions, vectors or tensors etc.

[potent lotus]

Duh Hello

[calm coral]

@glacial elk Has your question been resolved?

[rigid kettle]

No, we do not encourage people to use chatgpt thanks. Read the rules.

[rigid kettle]

I believe this is dependent on context - given none, I'd guess unit vector perhaps???
I'd probably advise asking in the relevant topic-specific channel

[warped rampart]

its quantum mechanics, $\hat{x}\equiv x$

[potent lotus]

Duh Hello

[warped rampart]

unless they just threw in the qm hamiltonian for no reason

[glacial elk]

Sorry, wasn't here for your answer, this explains it perfectly thanks 👍

[calm coral]

Channel closed

Closed by @glacial elk

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fresh mountain]

I have 29 and 30

<@&286206848099549185>

..

ok then?

I'll wait

[mossy anchor]

What do you want help with?

[fresh mountain]

this

[mossy anchor]

Which part? Where are you stuck? What have you tried?

[fresh mountain]

I'm trying to find the points of the triangle on 29

e

[calm coral]

@fresh mountain Has your question been resolved?

[fresh mountain]

...

ok?

.close

[calm coral]

Channel closed

Closed by @fresh mountain

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[turbid osprey]

anyone knows how I get from left to right?

[calm coral]

@turbid osprey Has your question been resolved?

[leaden thunder]

Find eigenvalues and eigenvectors of the matrix

[turbid osprey]

why is it allowed to say that it is x1 and x2 on the underlined red line ?

[leaden thunder]

Follows from matrix multiplication rules

[turbid osprey]

oh wait did he just multiplied it?

so he made it row echelon form and multiplied it by that [x1, x2] at first step right?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sleek prawn]

Hello, I’m practicing some logic questions in preparation for a competition in March. One of these questions is the following:

[sleek prawn]

You can see in the figure the sides of the rhombus divided into four equal parts and, inscribed inside the rhombus, the dark rectangle. What is the ratio (expressed as a decimal number) between the area of ​​the rectangle and that of the rhombus?

[low owl]

well i'd start trying to compute the small side of the rectangle

considering the soze of the rhombus is one

each equal parti is 1/4

using pythagoras

that rectangle's small side is 1/sqrt(8)

[leaden thunder]

Does the answer not depend on the angle?

If not, just treat it like a square

[low owl]

hm

[sleek prawn]

I’m trying to set up an equation starting from the triangles next to the rectangls

[low owl]

you'r correct

[sleek prawn]

The answer must be a numerical value

I’ll do what I can think of and let y’all know

[low owl]

we now for sure that the triangle is isoscele

[sleek prawn]

Yeah

[low owl]

oh wait

imagine

deleting that rectangle

from the total area

is it possible to compute the new area ?

[sleek prawn]

Calling x every fourth part of the side of the rhombus, and α the vertex angle of the small triangle next to the rectangle, the total area of the rhombus is as follows:

indeed, I precisely calculated the total WHITE area

I think I got the result!

I checked and it’s correct, thank you guys!

The other question I need help with is this:

Number 2020 admits 12 divisors. If you write them in ascending order, the seventh is a prime number. What other year of the twenty-first century will in the future admit twelve divisors with the same property (if they are ordered in ascending order, the seventh is a prime number)? Can you name at least two?

[calm coral]

@sleek prawn Has your question been resolved?

Channel closed

Closed by @sleek prawn

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[oblique ferry]

ChatGPT seems to have called out an issue with this equation's units not actually equal to m^3/s. I am confused because it seems to actually be right. There is a left over 1/2 of this portion of the equation, so that means it has to be higher than m^3?

[teal coral]

nah the units do seem to be

chatgpt says that sqrt(9.8m/s^2) has units of m/s, but it has units of sqrt(m)/s

[oblique ferry]

Interesting so the square root of units has its own rules you have to learn as well?

[leaden thunder]

Don't use chatgpt for math

[teal coral]

what rules

sqrt(m/s^2) is just the rules for fractions

[teal coral]

chatgpt the best for math

[oblique ferry]

Gotcha

This makes sense now thank you guys for your help I guess chatGPT can’t help with everything

.close

[calm coral]

Channel closed

Closed by @oblique ferry

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sick blade]

could someone please look through my solution to verifty it? no answers were posted for this set ):

nvm can just use chatgpt!

.close

[calm coral]

Channel closed

Closed by @sick blade

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[old falcon]

can you define dividend?

what piece of the problem are we looking for

thats where id start

,w dividend

[potent lotus]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by jan Niku#2119

[old falcon]

so i wonder

if $\frac{\text{dividend}}{\text{divisor}} = \text{quotient}$

[potent lotus]

jan Niku

[old falcon]

and we're given quotient and divisor

what can we do

the remainder contains the divisor

think of how you write them

are you sure it was simplified?

its not simplified

try it yourself

youll get your answer

no

think about what the quotient and the divisor are here

we know the structure of the remainder gives us the divisor

which part is the quotient

and the remainder

okay

now if dividend/divisor = quotient

give me a formula for dividend

yup

so we know quotient, its that whole thing plus remainder

and divisor is x-3

its $(x-3)\qty( 2x^2 + 7x + 21 + \frac{67}{x-3})$

[potent lotus]

jan Niku

[old falcon]

does that help?

well $A(C+D) = AC + AD$

[potent lotus]

jan Niku

[old falcon]

this is the distributive property

so we can do some distributinvg

[old falcon]

OH

haha

well it just cancels the fraction right

$(x-3)\frac{67}{x-3} = 67$

[potent lotus]

jan Niku

[old falcon]

is this what youre asking

yup

so we have 3 pieces

[potent lotus]

jan Niku

jan Niku

jan Niku

[old falcon]

youre asking how we have a +4

since we know we have a +67 floating around from the remainder

that means were hunting for a -63

can you see where we might pick this up?

where do we have just a number times just a number, with no x's

yup

so getting +4 makes sense

np

[calm coral]

Channel closed

Closed by @warm mason

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[winged forge]

Hello, so I'm in 9th grade and I was just revewing my teacher's correction of a test that didn't count until I saw that she multiplied the numerator and denominator by four on the red circled part.

I'd like to know why she mutiplied it by four.

[winged forge]

I'm pretty sure she explained why during class but I forgot what she said 💀

[prisma mango]

To get a common denominator to add the fractions

[winged forge]

Ohhhh I'm so stupid

[winged forge]

It's because of the other fraction's denominator correct?

[prisma mango]

Yes

[winged forge]

Alright thank you very much

.close

[calm coral]

Channel closed

Closed by @winged forge

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hearty silo]

How do i do solve b?

[hearty silo]

do i do 2pi = tpi/6?

How do i do this?

@warped rampart

[muted marlin]

its where the function starts repeating

[hearty silo]

so from here to here?

[warped rampart]

note that you cannot include the point where it has repeated

[hearty silo]

i feel like it should be [0,12)

yeah right?

[warped rampart]

yeah

[hearty silo]

but why is it including it

in the question [0, r]

[warped rampart]

no idea, seems weird

[hearty silo]

in that case wouldnt it be 6

when we reach the first bottom tide

cuz we only want one y value associated to one x

so if we go back up to the 2nd high tide we use the same y-values

where these lines are

@warped rampart

[muted marlin]

yeah

we want the domain to be such that d(x) is 1-1

[warped rampart]

yeah ur right, mb was thinking about it wrong

[hearty silo]

all good

last question how do you do this

.close

[calm coral]

Channel closed

Closed by @hearty silo

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[junior stag]

so i have a quadratic formula worksheet here and i know how to do it most but i have to break down the 60, i broke it down into 10 and 6, then 3 and 2 (for the 6) then 5 and 2 for the 10, but i forgot how what to do next

[exotic bone]

you are trying to simplify the square root right?

[exotic bone]

oh wait, you did the formula wrong

[junior stag]

i did?

[exotic bone]

yeah, in the radical

check that again

[junior stag]

what’s that

[exotic bone]

square root*

[junior stag]

6 squared it’s 36

[exotic bone]

yep

[junior stag]

this is the formula

[exotic bone]

yah, you did the formula right, but the math is wrong

[junior stag]

a is 1, b is 6, c is -7

[exotic bone]

you have this equation right? $\frac{-6\pm\sqrt{36-4\left(1\right)\left(-7\right)}}{2}$

[potent lotus]

Judgemental Snail

[junior stag]

yeah

[exotic bone]

we can first multiply 1 and -7

getting this

$\frac{-6\pm\sqrt{36-4\left(-7\right)}}{2}$

[potent lotus]

Judgemental Snail

[junior stag]

oh i didn’t know that

[exotic bone]

ah ok, redo it then i can check your answer

[junior stag]

thanks

[exotic bone]

np 🙂

[junior stag]

@exotic bone so i broke 64 down

[exotic bone]

you dont need to do that

64 is a perfect square

meaning you can evaluate the square root and get a whole number

[junior stag]

ohhh i see

[exotic bone]

what number would you get if you do so?

[junior stag]

1 right?

[exotic bone]

no

[junior stag]

or 8

[exotic bone]

^

8

because 8^2=64

[junior stag]

yeah but don’t you simplify that to 8/8 and then 1/1?

[exotic bone]

taking a square root is asking yourself, what number, times itself results in the number in the root

so in this case, what number, times itself results in 64

[junior stag]

8 times itself

[exotic bone]

yep, so the square root of 64 would be 8

does that make sense?

[junior stag]

yeah i know square roots but i forgot what to do next

[exotic bone]

well we can replace sqrt(64) with 8 because sqrt(64)=8

$\frac{-6\pm\sqrt{64}}{2}\to\frac{-6\pm8}{2}$

[potent lotus]

Judgemental Snail

[junior stag]

this this

[exotic bone]

yep

[junior stag]

and then just one last question

[exotic bone]

whats the question?

[junior stag]

for this do i do -12 on both sides to make the other side equal to 0

[exotic bone]

yep, did you get your answer for this though?

[junior stag]

that way i can label A B and C and use it for the quadratic formula

[junior stag]

i have to do it out but yeah i will get the answer once i do it out

[exotic bone]

k

[junior stag]

but for the last one yes

thank you

[exotic bone]

np, but yeah you will subtract both sides by 12

[junior stag]

and to get approximate answers how do i do it on a ti84

the teacher taught us on a ti83 how to get what x is approx. but doing the same doesn’t work on my ti84

she showed me i have to do it differently but i’m not sure how

[exotic bone]

solve it first using the quadratic formula

then plug what you got into the TI84

[junior stag]

i tried that with another one but it said non real answers

[exotic bone]

for which one?

[junior stag]

ohhh it’s because i didn’t do the formula right

i see

[exotic bone]

k

[calm coral]

@junior stag Has your question been resolved?

Channel closed

Closed by @junior stag

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[muted marlin]

$\int_0^1 f(x) x^n dx = 0$ Prove that $f(x) = 0$ on [0,1]

[potent lotus]

please request a new nickname

[muted marlin]

and n is some positive integer

[calm coral]

@muted marlin Has your question been resolved?

[calm coral]

@muted marlin Has your question been resolved?

[pallid halo]

presumably this has to be true for all positive integers n?

it's easy to find counterexamples if it's only true for one n

[muted marlin]

yeah for all n

[pallid halo]

proof by contradiction seems viable, suppose f(x) > 0 at some point

find a polynomial which has no roots in [x-epsilon, x+epsilon]

and hence has the same sign throughout [x-epsilon, x+epsilon]

[muted marlin]

but wouldnt you lose generality if you suppose f is some polynomial

would it help if i mentioned that we're learning sequences of functions

[muted marlin]

ok so looks like i have to learn a theorem before i can try this problem

.close

[calm coral]

Channel closed

Closed by @muted marlin

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fierce cradle]

Can someone help me with the circled question

[fierce cradle]

Using this formula:

[marsh agate]

Just compute it I think

According to my mental math, y is chosen for integral to give a nice perfect square to remove the square root

[fierce cradle]

I would find derivative of the function first. I’d get this, right?

And then I’d evaluate from there?

[marsh agate]

Yes

[fierce cradle]

I’m not good here…would I foil what’s in the paranthesis?

[marsh agate]

Yes

How else could you possibly try to rewrite this

[fierce cradle]

Like this?

[marsh agate]

You're not telling me you're trying to find the length of a curve through integration yet need to be hand-held to expand a square

[fierce cradle]

Well alrighty.

Thanks for your time.

.close

[calm coral]

Channel closed

Closed by @fierce cradle

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[thorn stag]

I think I have created a "new" type of best fit plot for an asymptotic data set (think something like a box office graph), and I want to know how to improve it. I found an approximate slope at each point by taking the average slope of the two surrounding points, then entered this data into an exponential best fit calculator. Then, I wrote a function that took an integral of this best fit exponential curve, which gave me a best fit line for the data set. What are the flaws with this approach?

[thorn stag]

data set

function

plot

.close

[calm coral]

Channel closed

Closed by @thorn stag

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fierce mulch]

Hi I'm trying to compute this integral, I need to do it by substitution to "show it"

I attempted first to sub u=x-5, and then from there u=3 sinh t

But I don't believe the answer should have logs, as I believe the integral of sech would have, it should come out as arctan I belive, anyway, any help would be amazing! Thanks

[leaden thunder]

the anti-derivative of this is just something with arctan(u)

[fierce mulch]

Ik by recognition it’s 1/3 arctan (u/3) but I have to show it by substitution I believe

[leaden thunder]

then do u = tan(t)

[fierce mulch]

I forgot about the tan^2 + 1 formula

Thanks for your help

.close

[calm coral]

Channel closed

Closed by @fierce mulch

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[noble cedar]

do I need brackets on this part that I circled after taking the derivative?

[leaden thunder]

yes

[noble cedar]

ty

[leaden thunder]

but also you're doing this the long way

write f(x) as a sum of terms and distribute the derivative to each term and you'll only need to use power rule

[noble cedar]

this is the Chain Rule?

[teal coral]

pwer

[noble cedar]

Oh OK

[pure kayak]

you can split the fraction into 3 separate terms

[leaden thunder]

d/dx (4/x) =?

[noble cedar]

is this always the case for taking derivatives? good practice to keep them in brackets even after you derive? or not always

[teal coral]

the quotient rule is very specific about what needs to be done

i.e. it requires (vu' - uv')/v^2

if taking off the brackets changes the meaning of what you have with the brackets

then clearly that's not acceptable