help-23

[stray axle]

man i just realised

im dumb as hell

thanks though

.close

[safe radish]

Channel closed

Closed by @stray axle

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.

[wild ore]

Stuck on last part of q3 anyone have ideas??

[timid fossil]

,rotate

[safe radish]

@wild ore Has your question been resolved?

[wild ore]

<@&286206848099549185>

[candid mortar]

tome un regalo mio tengo una calculador paso paso

https://es.symbolab.com/solver

solo que no dice las propieddes de las radicaciones

[safe radish]

@wild ore Has your question been resolved?

[safe radish]

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.

[half laurel]

So I distributed the 1/3 and got
x/3 - 4/3 < x+8
I have to remove X on both sides but im confused with removing the x on the less than side

[timid pasture]

multiply 3 both sides to simplify it

[half laurel]

before or after removing the x?

[timid pasture]

wdym removing the x?

[pseudo scroll]

Doesn't matter where the x is

[half laurel]

Ok, I multiplied

x/3 - 4/3 < x+8
by 3 on both sides and got
3x-12 < 3x +24

Im confused here, I wanted to add 12 to both sides but I can't subtract 3x from both sides

Starting over
looking at the example the part after removing the x is confusing to me, how does it turn in -5x/6 - 5/2?

<@&286206848099549185>

I see 15/6 gets divided by 3 into 5/2 but im still confused on how removing the x turns into 5x/6

[safe radish]

@half laurel Has your question been resolved?

[hasty wagon]

try this out first, and see what happens

[half laurel]

I keep ending up with

3x-12 < 3x +24

.close

[safe radish]

Channel closed

Closed by @half laurel

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.

[strong radish]

what multiplication equation would be used if a price of something was going to be raised by 10% for an example?

[strong radish]

i know if a price went on sale you can do $200 multiplied by 0.10

if its on sale by 10%

but if the price got raised i don't know what you would multiply the price by

[silver venture]

110% would be * 1.1

[strong radish]

so if a price got raised by 30 percent

its would be 1.3

[silver venture]

yep

[strong radish]

ok tysm

[silver venture]

because youre keeping the previous price (hence the 1.) and adding another percentage (hence the .x)

[strong radish]

yh

ty

.close

[safe radish]

Channel closed

Closed by @strong radish

Use .reopen if this was a mistake.

[safe radish]

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.

[boreal mantle]

hi

[boreal mantle]

The problem says: Calculate the sum of the first 100 terms of the following sequence:
1;3;5;-7;9;11;13;-15;17;19;21;-23

[sand robin]

This is an arithmetic sequence

Do you know the formula for the sum of an arithmetic sequence?

[boreal mantle]

I have tested the formula, but I am confused because there are positive and negative

[sand robin]

Oh! I didn’t see the negatives

[boreal mantle]

yes, then that's my problem

[safe radish]

@boreal mantle Has your question been resolved?

[safe radish]

@boreal mantle Has your question been resolved?

[sacred plover]

use it ignoring the negatives then add 2 sums of negatives

(1+3+5+7+9+...) + 2 * (-7-15-23-...)

[boreal mantle]

thx i will try

using the formula with difference 2 I get an answer that is not in the alternatives

[safe radish]

@boreal mantle Has your question been resolved?

[safe radish]

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.

[cursive warren]

Hello, this is actually a really simple question. I've got two parallel vectors in R^3. How do I get the vector that is perpendicular to both and has an intersection with both, as well?

[cursive warren]

( for visual understanding, I need the violet one)

[safe radish]

@cursive warren Has your question been resolved?

[safe radish]

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.

[edgy shoal]

say i want to create some sort of story that has an answer like (n^2)!/(n!)^n, how could i approach that?

[edgy shoal]

by story, i mean like "place n boxes..."

maybe something like the number of ways to arrange n distinct balls into n distinguishable boxes such that each box has minimum 1 ball?

[safe radish]

@edgy shoal Has your question been resolved?

[edgy shoal]

.close

[safe radish]

Channel closed

Closed by @edgy shoal

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.

[flat spoke]

Hello.

[flat spoke]

I eed help with this and

[fossil panther]

Two angles in between a line and two parallel lines like this will always add to 180

So 3x-5+2x-15=180

[flat spoke]

Okay

WHat about the second one

sorry didn't mean to ping

[fossil panther]

Unfortunately I can’t be much help there I think we use slightly different words in England for the angles

I believe 1 and 5 are corresponding

I have no clue what the other two mean lol

[flat spoke]

Okay thank you so much for your help

[timid fossil]

corresponding means equal

supplementary means adds up to 180

as far as i remember at least

[flat spoke]

Is that for the second or first one?

[timid fossil]

verticals are across but take that with a grain of salt

[timid fossil]

in gneeral

[flat spoke]

Okay

[flat spoke]

Thank you so much

.close

[safe radish]

Channel closed

Closed by @flat spoke

Use .reopen if this was a mistake.

[safe radish]

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.

[lean otter]

On part a, I have no issues on the first part but I can’t figure out if there’s a catch to the condition of x=1. Afaia it still converges via the alternating series test criteria.

[safe radish]

@lean otter Has your question been resolved?

[junior smelt]

Sounds about right, you meet all the criteria for it! Get 1/k^8, nonincreasing sequence which goes to zero, so the "alternating" version of it must converge [at least conditionally]

[lean otter]

Okay cool, that’s what I was able to write out.

[junior smelt]

[in fact you could consider x=-1 as well and that would converge there too]

[lean otter]

Thank you!

.close

[safe radish]

Channel closed

Closed by @turbid axle

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.

[sturdy pine]

Can someone please help me solve this

[shut inlet]

the sin(x) is always between 1 and -1
sooo....

[sturdy pine]

I’m very new to this method so don’t expect much lol

[shut inlet]

okay we know that -1<sin(x)<1 , whatever x is

so

$-1 \le \sin(e^n) \le 1$

[sturdy pine]

Is it supposed to be <1 after e^n

Alright

[flat frigate]

Mehdi_Moulati

[shut inlet]

which means that :

[sturdy pine]

It’s 0?

[shut inlet]

you mean the final answer of the limit ?

[sturdy pine]

Nvm

Bc you said it’s between-1 - 1 I just thought of 0

[shut inlet]

the sin of something is always between 1 and -1

[sturdy pine]

Ok

[shut inlet]

but that doesn't mean that the whole eaquation tend to 0

[sturdy pine]

Makes sense

[shut inlet]

since :
[ -1 \le \sin(e^n) \le 1 ]
we can say that :
[-\frac{\sqrt[3]{n^2}}{n+1} \le \frac{\sqrt[3]{n^2}\sin(e^n)}{n+1} \le \frac{\sqrt[3]{n^2}}{n+1}]

[flat frigate]

Mehdi_Moulati

[shut inlet]

does it make sence ?

[sturdy pine]

Yup

[shut inlet]

if the limit of :
[\lim_{x \to \inf }-\frac{\sqrt[3]{n^2}}{n+1} = \lim_{x \to \inf} \frac{\sqrt[3]{n^2}}{n+1} = L]
then :
[ \lim_{x \to \inf } \frac{\sqrt[3]{n^2}\sin(e^n)}{n+1} = L]

[flat frigate]

Mehdi_Moulati

[sturdy pine]

Does L stand for limit

[shut inlet]

L is a value

[sturdy pine]

Ok

[shut inlet]

real number

[shut inlet]

so you just need to calculate those limits

[sturdy pine]

Can you show me how to do this specific one

I’m not very good with limits in general

[shut inlet]

just factorize by (n^2)^(1/3) in the denominator

,align
\lim_{x \to \inf} \frac{\sqrt[3]{n^2}}{n+1}
&= \lim_{x \to \inf} \frac{\sqrt[3]{n^2}}{\sqrt[3]{n^2}* (\sqrt[3]{n}+\frac{1}{\sqrt[3]{n^2}})} \
&= \lim_{x \to \inf} \frac{1}{\sqrt[3]{n}+\frac{1}{\sqrt[3]{n^2}}}

[flat frigate]

Mehdi_Moulati

[sturdy pine]

Would that be the answer

[shut inlet]

no

i didn't do the final step

[sturdy pine]

Ok

Can you check if I do it right?

[shut inlet]

of course

[sturdy pine]

I got this

((3Sqrtn^2)/(n+1))

[shut inlet]

no bro

[sturdy pine]

What would it be then

[shut inlet]

when n tend to infinity where does 1/n goes ?

[sturdy pine]

0

[shut inlet]

apply that in your limit

[sturdy pine]

How would I apply it tho

[shut inlet]

when n tend to infinity where does 1/sqrt^3(n^2) goes ?

[sturdy pine]

It approaches 0

[sturdy pine]

We’re already basically done can you please show me the answer I’m gonna practice more anyways and I just want an example

[shut inlet]

it's 0

[sturdy pine]

Omg 💀😭

I’m actually an idiot

[flat frigate]

Mehdi_Moulati

[unique fiber]

am i seeing wrong or is everything in the limit just a constant ?

x is tending to infinty of a function that is not in x terms

[shut inlet]

it's just a typo

[unique fiber]

oh ok xD

[safe radish]

@sturdy pine Has your question been resolved?

Channel closed

Closed by @sturdy pine

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.

[trim jackal]

if i am trying to show two vectors which are scalar multiples of each other (i.e. u=av for some scalar a) are linearly dependent, can i assume the scalar a is nonzero, or should i do two cases, one where a is zero and one where a is nonzero?

[trim jackal]

like, when you say one vector is a multiple of another, does the word multiple imply that the multiple is nonzero?

[tawdry fox]

if you assume the scalar can be 0 then 0 is the scalar multiple of every vector

[trim jackal]

right, so are you saying we can assume its a nonzero scalar then?

[tawdry fox]

yeah

[trim jackal]

so for example, i dont have to say, "if a=0, then to satisfy u=av, it must be true that u is the zero vector" ?

[tawdry fox]

no you should include it, its good to be thorough

[trim jackal]

oh okay!

would you mind looking over my proof per chance when i finish it in a minute?

just to make sure it makes logical sense

[tawdry fox]

sure

[trim jackal]

thank you! i know it is wordier than it needs to be, but I struggle to figure out where I can cut things down.

[tawdry fox]

For the second paragraph you can cut out where it says "in the case where a=0...

*third paragraph

[trim jackal]

okay! but wait, why? i thought you were saying it's good to be thorough

[tawdry fox]

so youre trying to show that if u,v are scalar multiples, then they are lin dependent

[trim jackal]

yes

[tawdry fox]

but lin dependent definition only says that two vecs are lin dep if they satisfy
au + bv = 0 for some a,b

[trim jackal]

right

[tawdry fox]

we already assumed a is some real scalar and 1 is obvious real so u-av=0 already satisfies this defint

[trim jackal]

but saying a is some real scalar, doesnt that mean a could be zero?

[tawdry fox]

nothings wrong with that

[trim jackal]

so even in the case where a is zero, it doesnt change that u-av=0 satisfies the definition of linear dependence?

[tawdry fox]

precisely, since this just implies that one of the vectors are 0 and 0 vec is lin dep to any vec

[trim jackal]

okay, so i can just scratch that part then because the case where if a=0 then u must be the zero vector is implied. thank you!

[tawdry fox]

one thing you could do is suppose one of the vectors is 0 vec to start with and follow with, "then the vectors are trivially linearly dependet" or something along those lines and then follow with "then suppose that u,v are nonzero vectors"

if it makes you feel better, but really not necessary

[trim jackal]

okay fosho! ill probably just cut that part like you suggested and then leave it! i appreciate the help tho, thank you!

[tawdry fox]

👍

[trim jackal]

.close

[safe radish]

Channel closed

Closed by @trim jackal

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.

[sturdy pine]

Can someone please help me do this

[sturdy pine]

.close

[safe radish]

Channel closed

Closed by @sturdy pine

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.

[timid goblet]

What did I do wrong

[hexed dune]

your very last one

y -> -infinity, didnt you mean y-> infinity

[timid goblet]

Lmfaooo my eyes

Am so sleepy

💀

[timid goblet]

Wait bro what is this one

Is it -infinity and 2 @hexed dune

[hexed dune]

no i mean litearlly the last one, the end behaviour

[safe radish]

@timid goblet Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

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.

[lean otter]

i dont get question 1 and 2

ive been trying to find the pattern in the second one for ages

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

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 smelt]

$-(k + 1)x + ky - 5k = 1 - 2ky$

[flat frigate]

chartbit

[safe radish]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

@halcyon flume Has your question been resolved?

[halcyon flume]

1

[junior smelt]

Try gathering everything on one side?

[halcyon flume]

.close

[safe radish]

Channel closed

Closed by @halcyon flume

Use .reopen if this was a mistake.

[halcyon flume]

.reopenen

[junior smelt]

.reopen

[halcyon flume]

.reopen

[safe radish]

✅

[halcyon flume]

thank u

i got

🙏

.close

[safe radish]

Channel closed

Closed by @halcyon flume

Use .reopen if this was a mistake.

[safe radish]

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.

[red talon]

Is this B or C

[red talon]

9

[quick breach]

answer this one please

[whole acorn]

don't troll here moai

[red talon]

https://cdn.discordapp.com/attachments/903481106819612714/1073242831520538704/C8E1FE2D-98D9-40E4-82F7-A7C692DBB8CF.jpg

I can’t decide between B and C

[whole acorn]

can you give a screenshot rather than a picture?

[red talon]

No

[whole acorn]

ok

[red talon]

Sorry

[lean otter]

?

[whole acorn]

wrong channel bro

[lean otter]

ik man nobody helps me in my channel 😦 and i aint got no time left

[woeful plume]

That's unfortunate, but someone else is entitled to this channel

[whole acorn]

is it an exam?

[lean otter]

kinda

[woeful plume]

You aren't supposed to get help then

[lean otter]

yerrrrrrrrrrrrrrrrrrr

[lean otter]

i ain't getting help in first place lol

[woeful plume]

👍

[safe radish]

@red talon Has your question been resolved?

[lean otter]

why does my channel doesnt ask this question

[safe radish]

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.

[signal herald]

<@&286206848099549185> If you calculate the discriminant (b2 - 4ac) does the a need to be possitive. So before calculating, do you need to translate the formula into a formula with a possitive a?

[pastel briar]

Don't immediately ping helpers thxxx

[signal herald]

O, sorry

this are the workings by the way. But I had -8 and -6. Why is this wrong?

So in the answers I had a - before the 8 and 6

[timid pasture]

absolutely not

[signal herald]

Yes, I thought so. But why is my answer then wrong?

[timid pasture]

show your working

[timid pasture]

is it this?

[signal herald]

Yes

[timid pasture]

so, the two equations you are talking about are

3x^2 - 8x - 47 = 0 and -ve of that?

[signal herald]

Therse are my workings btw

Well my final anser, but it is on paper and my phone to take pictures is downstaires

[timid pasture]

looks correct except for -6 in denominator

[signal herald]

but you divide by 2a?

So 2 x -3 = -6

[timid pasture]

you've written a = 3 right?

then 2a = 2 * 3 = 6

[signal herald]

These are my workings

[timid pasture]

,rotate

[potent bay]

u just multiplied by -1/-1 so its good too

[signal herald]

So is my answer correct or not?

[timid pasture]

the quadractic formula is $\frac{-b \pm \sqrt{D}}{2a}$

[flat frigate]

numbpy

[timid pasture]

where $D = b^2 - 4ac$

[flat frigate]

numbpy

[timid pasture]

make sure you've used this correctly

[signal herald]

Yes i did, so I guess my answer is correct and the answer book is wrong?:)

[potent bay]

both are correct

u just used -a -b and -c

[timid pasture]

what is your answer and what does the book say?

I am genuinely confused

[signal herald]

Look at the pictures that I send

[potent bay]

you can use -17a -17b and -17c too, u just make it more complicated for yourself

[timid pasture]

This is what you did right?

My question is, what is a? 3 or -3?

[signal herald]

No, I have it correct

,rotate

[signal herald]

So both my answer and the one from the book correct. Only if you write it down in my way you switch x1 and x2 but that really doesn't matter

[potent bay]

indeed

[timid pasture]

yes

[signal herald]

Thanks a lot! @timid pasture @potent bay

.close

[safe radish]

Channel closed

Closed by @signal herald

Use .reopen if this was a mistake.

[safe radish]

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 sandal]

I need help approaching 1

[timid pasture]

Hint: object is at rest when v(t) = 0

[turbid sandal]

Ah so

I set it 0=2t^3…

Should I do that

[timid pasture]

yes, then solve for t

[turbid sandal]

Okok

There are t1 t2 and t3

[timid pasture]

huh?

[turbid sandal]

I solved it, look

[turbid sandal]

What should I do now?

[timid pasture]

Looks correct, notice that time can't be negative so you ignore -5/2

[turbid sandal]

Okok

Do I plug the t values in?

And see if it equals 0?

[timid pasture]

nope, you're done

That's the answer

[turbid sandal]

So I say therefore the times the object is at rest is t=0 and t=3

[timid pasture]

They're asking at what times t, the object is at rest

[timid pasture]

yes, maybe add seconds

or maybe not

they haven't specified the units

I think

[safe radish]

@turbid sandal Has your question been resolved?

[safe radish]

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.

[wet gust]

soo

[wet gust]

im doing calc 2

i have the problem integral from 0 to pi/2

of 2sin2t/4-cos2t dt

and i got it down to integral from 0 to pi/2 of du/u

which means ln of absolute value of u

but the work my teacher gave us the values are now 3 to 5

and idk why

any guesses or my teacher do it wrong

i thought you wouldve just plugged u back into ln of u

then use pi/2 with u minus 0 u in ln and get like ln5/3

nvm i figured it out apparently the way i did it just so happened to work the same but im suppose to convert the domain with my u

.close

[safe radish]

Channel closed

Closed by @wet gust

Use .reopen if this was a mistake.

[safe radish]

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.

[fleet current]

Hello, can someone please help me in this. i have general approach but there are some things im not sure of. if someone is iwlling to solve question with me. thanks in advance

[safe radish]

@fleet current Has your question been resolved?

[safe radish]

@fleet current Has your question been resolved?

[fleet current]

<@&286206848099549185>

[drowsy barn]

Did you think about residue theorem ?

Here the residue is 0 because the function is holomorphic inside the closed path

To compute the integral, you should integrate on each part separatly

You will have three paths and hence three integrals

[safe radish]

@fleet current Has your question been resolved?

[fleet current]

.close

[safe radish]

Channel closed

Closed by @fleet current

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.

[viscid spire]

i think the answer to the first part is no because there's not a pivot in every row of B if you row reduce it

but how would i do the second part

[final halo]

question is weirdly worded

the columns of B are not elements of R^3 so they couldnt possible span it

but they would span some 3 dimensional subspace of R^4 that is isomorphic to R^3

[safe radish]

@viscid spire Has your question been resolved?

[viscid spire]

but idk if that's what it means

[fickle marten]

rows don't span anything, only columns (i.e. vectors) can span a space

[viscid spire]

oh okay

[plucky elk]

this is incorrect

https://en.wikipedia.org/wiki/Row_and_column_spaces

[fickle marten]

This is seemingly for an intro linear algebra course, given how the questions in the screenshot refer to columns

[safe radish]

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.

[elder sage]

just if i have k= f(w)

how would i calculate dw/dk?

.close

[safe radish]

Channel closed

Closed by @elder sage

Use .reopen if this was a mistake.

[safe radish]

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.

[wise saddle]

Must prove

[wise saddle]

If gcd (a,b) =1

Then gcd ( (2^a) -1, (2^b ) -1)=1

I cant understand how to use the fact that a and b dont divide eachother

[oak wraith]

what have you tried so far

[wise saddle]

Not very subtle ways, like getting some products and using gcd linearity

[devout shale]

,, \frac{a}{b}=1 \implies \frac{2^{a}-1}{2^{b}-1}=1

[wise saddle]

But i did it during an oral exam with euclid's lagorithm

[wise saddle]

But i cant remember how it went at all

Not quite that

[devout shale]

yeah I just realized lol

[wise saddle]

Ye np

Im sorry im illiterate when it come to latex so its kind of ugly

.close

[safe radish]

Channel closed

Closed by @wise saddle

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.

[thin vine]

can anyone explain me how sqrt(x)*sqrt(1+49/4x)) = sqrt(x+49/4) pls ?

[empty gyro]

$\sqrt{a}\cdot\sqrt{b}=\sqrt{a\cdot b}$

[flat frigate]

SWR

[empty gyro]

Is that a sufficient reasoning?

[thin vine]

damn

I was thinking way too hard

thanks dude

.close

[safe radish]

Channel closed

Closed by @thin vine

Use .reopen if this was a mistake.

[bold ferry]

maybe think softer next time

[thin vine]

HAHA

[empty gyro]

[safe radish]

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.

[prime orchid]

i need some hlep

[worthy hemlock]

With what?

[prime orchid]

i dont know how did you get to the answer

can you go through it w me

[worthy hemlock]

Is that not your work?

[prime orchid]

no

can i show you how i got it

[worthy hemlock]

Yes

[prime orchid]

i expanded the brackets

4p-8q=3p+2

-2 on each side

4p-8q-2=3p

-8q-2=3p-4p

-8q-2=p(3-4)

-8q-2 over 3-4

= p

[devout shale]

it appears you just solved the question

[prime orchid]

why is the answer on top dif tho

[devout shale]

oh

[worthy hemlock]

What's 3 - 4?

[prime orchid]

the 3p-4p

p(3-4)

[worthy hemlock]

I mean mathematically, what is 3 minus 4?

[prime orchid]

-1

[worthy hemlock]

So you have what now?

[prime orchid]

oh

damn

wow

thanks man

also

one more question

wait no

not his

[inland urchin]

i need help

as well

[prime orchid]

wait not this one

[safe radish]

Please read #❓how-to-get-help

[prime orchid]

this one

i got -y-5z over 2-4

would it still be correct

[worthy hemlock]

What's 2 - 4?

[prime orchid]

-2

2

wiat

-2

wait so i messed up

[worthy hemlock]

Wait, that's a z

[blazing jewel]

i think its a z bro

[worthy hemlock]

Not a 2

[prime orchid]

oh yeah

z

[worthy hemlock]

Show your work

[prime orchid]

wait

[worthy hemlock]

What are your steps?

[prime orchid]

-y-5z over z-4

i did

4x-y=z(x+5z)

-5z

on each

wait

[worthy hemlock]

Yeah that's the same because (z - 4) = -1 * (4 - z)

[prime orchid]

oh so it is

okay thats all i needed thank you

🙂

what do i do now

when im done

and not need help

[blazing jewel]

tap . close

[prime orchid]

wait

one more

thingy

soz

for this one

-8q-2 over -1 = p

does -8q-2 over -1

equal to

2+8q

anyone

....

[blazing jewel]

yeah, i think so

[prime orchid]

okay thanks

.close

[safe radish]

Channel closed

Closed by @prime orchid

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.

[untold yarrow]

X

[untold yarrow]

Is this correct?

x ^ 2 + y ^ 2 = < x ^ 2 + y ^ 2

is true because of the =, so it's reflexive

it's antisymmetric because for all (x, y) and (p, q),
if x ^ 2 + y ^ 2 < = p ^ 2 + y ^ 2
AND
p ^ 2 + y ^ 2 <= x ^ 2 + y ^ 2, then x = p, y = q

and I think why it's transitive is pretty trivial since x < y and y < z obviously means x < z

[safe radish]

@untold yarrow Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

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.

[delicate quail]

does my work make sense

[safe radish]

@delicate quail Has your question been resolved?

[safe radish]

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.

[little kettle]

How do I prove that "(9^x - 2) mod 5 = 2" is only TRUE for odd numbers?

[little kettle]

I may use logic and induction

But I think it's too weak an argument to say "well for the first 10, 9^x ends in either 9 or 1"

It seems 9^x follows a pattern of ending in either 9 or 1, making the above statement true, but I don't have any ideas how to prove it

[empty gyro]

It would help if you kept these mod 5

[lean otter]

Idk how mod works, but I do have general understanding of why it always ends with 1 or 9
I can help u with that ig, but I am not sure how u would formally write it with symbols and stuff

[empty gyro]

You may easier see the pattern

[little kettle]

modulo sorry

[little kettle]

i understand the pattern, though don't know how to prove that they will keep going for infinity

[empty gyro]

mod is the remainder you get after division. 9 mod 5 is 4 because 9/5 is 1 with a remainder of 4

[empty gyro]

what are all of these numbers mod 5?

[little kettle]

it's not mod 5, it's (9^x -2) mod 5

[lean otter]

U can prove it using number theory ig

[little kettle]

so the last digit of the numbers are 7 or 9, which makes mod 5 either 2 or 4

[empty gyro]

I'm asking what is the result of all of those calculations once you mod it by 5?

[little kettle]

and for odd numbers it's 2, making the statement true

[empty gyro]

where do you see 7?

[little kettle]

here

sorry, the table is not ((9^x) - 2) it's just

9^x

[empty gyro]

but all the last digits here are 1 or 9. No 7 to be found

[empty gyro]

ahh

I see I see

[little kettle]

i realized the ambigous -2 lol

[empty gyro]

my bad too. I should have inferred

[little kettle]

Anyway, how would I go about proving the pattern goes on?

[empty gyro]

you have the idea correct with induction

start with x=1

[little kettle]

I'm hoping for a bit more explanation lol

[empty gyro]

show that it's true for x=1

what's 9^1-2 mod 5?

[little kettle]

i guess it should be true for x = 2k-1 only?

because of uneven numbers

so i should prove for k instead

i'm confusing myself

[empty gyro]

yeah that's fine too

You can do it that way

Inductively, that should be easier

Here's a hint, for k=1, you get 9^1-2 mod 5

Show that that's 2 mod

Then for some arbitrary k+1, write $9^{(2(k+1)-1)}-2=9^2\cdot 9^{(2k-1)} - 2$

[flat frigate]

SWR

[little kettle]

it messed up the formatting but i get it

oh you fixed it, nice

thanks a lot for the help! this has been the most fun part of my night so far. Feels cool to use induction 😎

learned about it yesterday

[empty gyro]

nice

If you wanna feel even cooler, you can show that 9 = 4 mod 5, so 9^x=4^x mod 5

Makes the arithmetic a bit easier

[little kettle]

isn't 4 mod 5 = 4?

[empty gyro]

yes that too

so is 9

That's how mod works

[little kettle]

oh hahahaha

@empty gyro

sooo... i got this far

do I just reduce or am I missing something?

nevermind, sorry, i didn't see what you wrote

[little kettle]

I don't get it, how does this prove induction

[little kettle]

also, shouldn't it be "...= 9*9^(2k-1)..."

instead of "...=9^2"

[empty gyro]

Nah. Review exponent properties

[little kettle]

oh dang, missed that

it's x2 i didn't see that

what's the next step from my screenshot?

Because I need to have the modulo part in my proof aswell, right?

[empty gyro]

Just FYI it would be easier to prove 9^(2k-1)=4 mod 5

I'll bbl

I'm eating my fish sticks

[little kettle]

lol nice

enjoy!

[empty gyro]

But yeah. Prove this

[little kettle]

Is the other way around too hard?

@empty gyro Can you confirm this is true?

[safe radish]

@little kettle Has your question been resolved?

Channel closed

Closed by @little kettle

Use .reopen if this was a mistake.

[little kettle]

.reopen

[safe radish]

✅

[safe radish]

@little kettle Has your question been resolved?

[little kettle]

Can someone confirm that this math is true? I just need to know if my operations with (mod 5) are correct

[safe radish]

@little kettle Has your question been resolved?

[empty gyro]

Looks good

I'd say you're all set @little kettle

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

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.

[quaint pelican]

How do I find the diameter

[south epoch]

!statuss

[safe radish]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[quaint pelican]

6

[south epoch]

what is it then

[quaint pelican]

i have no idea what the formula is

to figure out diameter from circumference

[south epoch]

$2 \pi r$ is the Circumference

[flat frigate]

Shockshwat

[quaint pelican]

i already have the circumference

i need the diameter from the circumference

[whole acorn]

yeah, use that formula to find it

[south epoch]

see

diameter = 2r

so

[quaint pelican]

Do i divide by pi or 2 first

[south epoch]

what do you think you should do

[quaint pelican]

divide pi and 2

for r

then multiple r by 2\

[south epoch]

if you are dividing by 2

and then multiplying again by 2 doesnt it mean the same thing

[quaint pelican]

Thats why im dividing

[south epoch]

and then you are multiplying again

[quaint pelican]

how?

im confused

[whole acorn]

ok so you divided by 2 here right?

[quaint pelican]

yes

[whole acorn]

and then you multiplied it by 2 again

[quaint pelican]

oh

[whole acorn]

[quaint pelican]

so then do i just divide by pi

[whole acorn]

yes

[quaint pelican]

okay

it said number incorrect

[whole acorn]

notice that you can rearrange 2 pi r to 2r pi which is just diameter * pi

what did you answer?

[quaint pelican]

2.55

[whole acorn]

round to nearest tenth... not hundredth

[quaint pelican]

oh

im stupid

thks i got it now

.close

[safe radish]

Channel closed

Closed by @quaint pelican

Use .reopen if this was a mistake.

[whole acorn]

[safe radish]

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.

[worldly marten]

what is angle BAC ?

<@&286206848099549185>

nvm

.close

[safe radish]

Channel closed

Closed by @worldly marten

Use .reopen if this was a mistake.

[buoyant charm]

?

[worldly marten]

dont think anyones helping lol so i mightaswell close

[safe radish]

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.

[worthy meadow]

can somebody help me reflect idk where to start

[wintry condor]

can you mark y=-2 on the plane first?

[worthy meadow]

like that?

[wintry condor]

no

y=-2 is a line

it expresses all points on the plane that has a y-coordinate of -2

[worthy meadow]

idk what u mean 😭

it just ends up in a line sideways

[safe radish]

@worthy meadow Has your question been resolved?

[worthy meadow]

.close

[safe radish]

Channel closed

Closed by @worthy meadow

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.

[hot kindle]

yo

[hot kindle]

How do i find the absolute max &min

also the relative max&min

<@&286206848099549185>

[safe radish]

@hot kindle Has your question been resolved?

[hot kindle]

<@&286206848099549185>

[lapis shadow]

in 5 is there a number that this line appears to ALWAYS be above of or below of?

[safe radish]

@hot kindle Has your question been resolved?

[safe radish]

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.

[pseudo peak]

$$
\forall v \in V:
\langle u, v \rangle = 0 \implies u = 0
$$
I know the converse is true but is this true as well?

[flat frigate]

Frisk17

[proper crypt]

I think so

<u, u> = 0 means u = 0

I'm assuming u is also in V

[pseudo peak]

yeah
can you even take inner product of two different vector spaces?

[proper crypt]

well if V is a subspace then ig it would make sense

dont take my word for it

lmao

[pseudo peak]

how can you go about proving this though?

[cerulean patio]

I don't think that is true, if u and v are orthogonal vectors, their inner product is 0 while none of them are

For instance (0, 1) and (1, 0) in R^2

[pseudo peak]

I'm saying this forall vectors v

if the vector u gives 0 inner product

then is u necessarily 0

[cerulean patio]

Indeed, my bad, therefore it is true yes

[pseudo peak]

^ any idea?

[cerulean patio]

It should be true for v = alpha*u since it is true for all (since we assume u in V) with alpha != 0

[pseudo peak]

ah

that makes sense

so basically
$$
\forall \alpha \in F:
\langle u, \alpha u \rangle = \alpha^* \langle u,u \rangle = 0
\implies u = 0
$$

where F is the field associated

with the vector space

[flat frigate]

Frisk17

[pseudo peak]

.close

[safe radish]

Channel closed

Closed by @pseudo peak

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.

[orchid patio]

Complementary angles add up to 90

So you have w + x = 90 and y + z = 90

The question asks for the sum of x + (w + y + z)

[orchid patio]

See if you can use that to help you figure out the sum

[south epoch]

The question asks for the sum of x + (w + y + z)

Question asks what is x and what is w+y+z
I dont think that and is for adding them

[spring horizon]

huh

[thin bridge]

its not possible to determine their individual values
the question wants the special relation between the expressions

[orchid patio]

I thought it was looking for the other word used to describe the sum of angles that is very similar to complementary angles lol (I dont wanna give the answer away incase they want to attempt it first)

[spring horizon]

so all add up to 180

[orchid patio]

Yup and what are angles that add up to 180 called?

[spring horizon]

supplementary

[orchid patio]

Yeah!

[spring horizon]

oh wait is taht it?

[orchid patio]

So those 2 angles are supplementary

Yeah I think that's all it's asking

[spring horizon]

oh okay! tysm

.close

[safe radish]

Channel closed

Closed by @spring horizon

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.

[umbral bobcat]

Any hints on how to solve this

[plucky elk]

,w int 1/(x + x^10)

[flat frigate]

Results provided by WolframAlpha

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

Requested by riemann#2529

[plucky elk]

did you try partial fraction decomposition

[umbral bobcat]

what is that?

[plucky elk]

https://www.youtube.com/watch?v=QKkdYW77xNI

[safe radish]

@umbral bobcat Has your question been resolved?

[safe radish]

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.

[rugged radish]

Trying to find C to complete the equation. What am I doing wrong here?

[pseudo scroll]

$\int e^{2.7u}\dd{u} = \int e^{1.8t}\dd{t}$

[flat frigate]

NEONPerseus

[pseudo scroll]

Is this what you did?

[rugged radish]

Yes

[pseudo scroll]

$\frac{e^{2.7u}}{3} = \frac{e^{1.8t}}{2} + C$

[flat frigate]

NEONPerseus

[pseudo scroll]

Looking good?

[rugged radish]

Shouldn't 2.7 and 1.8 be at the bottom?

[pseudo scroll]

I simplified it

[rugged radish]

$\frac{e^{2.7u}}{2.7} = \frac{e^{1.8t}}{1.8} + C$

Ah oke

[pseudo scroll]

3 = 2.7? Lol

[flat frigate]

MrSomeone

[rugged radish]

Sorry lol

[pseudo scroll]

Yeah so you can multiply by 9/10 throughout

[pseudo scroll]

Now since u(0) = 3.5

$C = \frac{e^{2.7 \times 3.5}}{3} - \frac{1}{2}

Wrong way round argh

[rugged radish]

Wait sorry why did you multiply 9/10?

[pseudo scroll]

To simplify denominators

$C = \frac{e^{2.7 \times 3.5}}{3} - \frac{1}{2}$

[flat frigate]

NEONPerseus

[pseudo scroll]

Did you not get why?

[rugged radish]

Uh yea im not sure

my third from last row i got e to be alone and used ln to put u alone

[pseudo scroll]

Alright have a look

$$\frac{9}{10} \times \frac{e^{2.7u}}{2.7} = \frac{9}{10} \times \frac{e^{1.8t}}{1.8} + \frac{9}{10} \times C$$
$$\frac{9e^{2.7u}}{27} = \frac{9e^{1.8t}}{18} + C$$
$$\frac{e^{2.7u}}{3} = \frac{e^{1.8t}}{2} + C$$

[flat frigate]

NEONPerseus

[rugged radish]

Ohh got it

Sorry im slow lol

[pseudo scroll]

Nah it's alright

[pseudo scroll]

So this is the value of C, and with logs and stuff as you did previously you can find u(t)

[rugged radish]

Is my equation correct? I just need to plug in C to find it right?

[pseudo scroll]

You don't need to have 2.7C

Since 2.7C is just a constant

Rebrand it to C

[rugged radish]

Ah okay

[pseudo scroll]

Other than that it looks alright

[rugged radish]

.close

[safe radish]

Channel closed

Closed by @rugged radish

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.

[dreamy finch]

I need to find the fixed points of this equation

[dreamy finch]

I set that equal to x, and solved it and got (rk -k) / (r - 1)

is that correct so far?

[lean otter]

@dreamy finch you are on the right track to find one of the solutions

you already lost one solution, though

[dreamy finch]

x = 0

[lean otter]

right

[dreamy finch]

okay great

almost forgot about that

so just to make sure i understand, a fixed point is a point in which the iterative value does not change, right?

[lean otter]

that's it

[dreamy finch]

okay great, but the thing that confused me is the stability type. How could a fixed point be unstable?

like if it's unstable, then it's not a fixed point because the value is changing, right?

[lean otter]

no there can be unstable fixed points

[dreamy finch]

that's what confuses me

like what exactly is an unstable fixed point

[lean otter]

try to balance your pen on your finger

[dreamy finch]

im liking the analogy

[lean otter]

if you hold it exactly vertically it will stay, if deviate by the minutest amount it will fall

the verdict "stable/not stable" is speaking more about the vicinity of the fixed point rather than about the point itself

i.e. "do you move towards or away from the fixed point when you start close to it?"

[dreamy finch]

oh okay. So in this case, how would i find the stability type?

Do i just take the derivative of the original equation at the point (rk - k) / (r -1)?

[lean otter]

how much linear algebra do you know?

do the terms "linearization" and "eigenvalues" say you something?

[dreamy finch]

a fair amount, but this course does not use linear algebra

[dreamy finch]

no 😦

i shouldve learned eigenvalues but we ran out of time when i took the course

although i think i know the linearization theorem

is that just determining the derivative at the point and seeing if it's absolute value is less than 1?

[lean otter]

that should work around zero

around the other fixed point at x=k you need to modify your idea slightly

what do you think is x=0 stable/unstable?

what about x=k?

Do you know the concept of a Taylor expansion?

$f(x) \sim f(x_0) + f'(x_0)(x-x_0)+\frac{1}{2!}(x-x_0)^2 + \dots$ as $x\to x_0$

[flat frigate]

Landau08

[lean otter]

$f(x) \sim f(x_0) + f'(x_0)(x-x_0)$

[flat frigate]

Landau08

[lean otter]

$\frac{r x}{1+\frac{r-1}{k}x} \sim r x, \text{ as } x\to 0$

[flat frigate]

Landau08

[lean otter]

and around x=k:

$\frac{r x}{1+\frac{r-1}{k}x} \sim k + \frac1r(x-k), \text{ as } x\to k$

[flat frigate]

Landau08

[lean otter]

I just see, your idea to just check the derivative at the fixed point works just fine also at the x=k fixed point.

(your answer will depend on r, by the way)

[safe radish]

@dreamy finch Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

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.

[granite tusk]

what exactly does it mean to sample elements from a set with pairwise independence. Let's say that we have a set S, and we create a subset R from it such that every element is added independently with probability p, in that case every element has a probability of p of being in R. However, let's say that we sample elements from S to create a subset with pairwise independence, how exactly is it different from the first scenario. Apologies if things aren't completely clear, I needed a clear idea of the concept behind the problem, however I can't share the problem completely as I want to solve it myself.

[safe radish]

@granite tusk Has your question been resolved?

[safe radish]

@granite tusk Has your question been resolved?

[safe radish]

@granite tusk Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

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.

[lean otter]

I do not understand, neither of the lines are touching -2 but none of the answers say that?

[violet thorn]

it looks like the function is going to infinity and negative infinity at the same time at -2

and it cant have 2 values at once

[stray socket]

You're right; it diverges

Look at what happens to numbers around x=-2

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

@stray socket So would A be the answer? I feel like -inf and +inf are a little bit more of than a slight difference like it says so I don’t know for sure if that’s the answer

[safe radish]

Channel closed

Closed by @smoky coral

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.

[solid crow]

Im really only focused on the first entry to the chart, the "last second" one. I'm just really lost so anything would help

I tried setting t=1 and got 12, that was wrong unfortunately. I think just bc it wasnt specifically the last second

If i could just get help with understanding that first chart answer than i think i can do the rest tho

[safe radish]

@solid crow Has your question been resolved?

[violet thorn]

last second would be 1.3229-1 seconds after it started falling

so 0.3229 seconds after it started falling

[solid crow]

Yeah so i basically figured out the height that the orange was at when the time was at 0.3229 seconds

It was 26.332 feet

Which i would think means in the remaining second, it falls that 26.332 feet, meaning its falling at a rate of 26.332 feet per second

But it also said that was wrong :(

[violet thorn]

its asking for the average rate

[solid crow]

Wait would the average be different? If im only worrying about the last second, and in the last second it travels 26.332 feet, wouldnt the average just be 26.332 feet per second?

Or is that wrong

[violet thorn]

try dividing it by 2

[solid crow]

Will do, ill let u know how it goes

[violet thorn]

because at the end its on the floor so 0

[solid crow]

Dang it still said its wrong

I thought that mightve done it

I put 13.166 for the answer

[violet thorn]

it may be wrong

the question

[solid crow]

Yeah thats kinda what i was thinking, ill try and email my professor about it cuz im at a loss trying to solve it

Thanks a ton for trying to help tho!

.close

[safe radish]

Channel closed

Closed by @solid crow

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.

[south leaf]

Show that the lines $\frac{x+1}{3} = \frac{y+3}{5} = \frac{z+5}{7}$ and $\frac{x-2}{1} = \frac{y-4}{3} = \frac{z-6}{5}$ intersect each other. Also find the point of intersection.

[flat frigate]

innocently.innocent.soul

[south leaf]

I know that if lines intersect each other, there would be a common point on both the lines. But how to start? Should I start by assuming the common points to be (a, b, c)?

.close

[safe radish]

Channel closed

Closed by @south leaf

Use .reopen if this was a mistake.

[south leaf]

.reopen

[safe radish]

✅

[south leaf]

<@&286206848099549185>

[noble moat]

Solve the equations $\begin{cases}\frac{x+1}{3} = \frac{y+3}{5} = \frac{z+5}{7}\\frac{x-2}{1} = \frac{y-4}{3} = \frac{z-6}{5}\end{cases}$

[flat frigate]

1048576Prog

[south leaf]

And how would I do that?

By equation $\frac{x+1}{3} = \frac{x-2}{1}$ and so on...?

[flat frigate]

innocently.innocent.soul

[noble moat]

No.

1. solve $\dfrac{x+1}3=\dfrac{y+3}5; \dfrac{x-2}1=\dfrac{y-4}3$

[flat frigate]

1048576Prog

[noble moat]

2. for solution $(x, y)$, calculate $z$

[flat frigate]

1048576Prog

[noble moat]

3. check if $(x,y,z)$ satisfy the equations.

[flat frigate]

1048576Prog

[south leaf]

Ohh Okay

Thanks for the help

I got it

.close

[safe radish]

Channel closed

Closed by @south leaf

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.

[languid garden]

I had assumed 1-6 were True, but I got the answer wrong. Can anyone tell me why I got it wrong?

[sacred plover]

first one is false

it's true for 2 standard deviations

everything else looks fine

[languid garden]

So everything except for the first one is true?

[sacred plover]

and the last one

[languid garden]

Alrighty, thanks!

[languid garden]

.close

[safe radish]

Channel closed

Closed by @languid garden

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.

[uneven epoch]

hi how do i know when to change the symbols

[plush saddle]

If a<b then b>a

[uneven epoch]

what abt x²<18-3x

[plush saddle]

They subtracted 12x and then rotated it like that

Subtract 18 and add 3x and you get something < 0

[uneven epoch]

so it's x²+3x-18<0

ok

[safe radish]

@uneven epoch Has your question been resolved?

[safe radish]

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.

[supple shore]

$u{n}$ defined by $u{0} \geq 0$ and $u{n +1} = \sqrt{u{n}} + \frac{1}{n + 1}$ I need to study the convergence of this sequence but don't know how to do. By recurrence I prove that $u_{n} \geq 1$ for all $n \geq 1$ but don't know how to prove that it converge to 1 and not diverge and also say that it's decreasing from a certain rank

[flat frigate]

phoestaclies

[supple shore]

like if this sequence have a limit, like l so $u_{n + 1} = l$ and $\frac{1}{n + 1}$ tend to 0 so $l = \sqrt{l}$ so $l = 1$ but I don't know if this is correct and I don't know if it can also diverge

[supple shore]

yes sorry for the latex

[flat frigate]

phoestaclies

[supple shore]

I tried to calculate $u_{n+1} - u_{n}$ and I can say that if $u_{n}- u_{n-1}$ is negative so $u_{n+1} - u_{n}$ too

[flat frigate]

phoestaclies

[supple shore]

don't know is this is useful, because I don't know if it's decreasing or not

[safe radish]

@supple shore Has your question been resolved?

[supple shore]

<@&286206848099549185>

[junior smelt]

,w plot sqrt(x) + 1/(x+1) - x

[flat frigate]

Results provided by WolframAlpha

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

Requested by chartbit#3171

[junior smelt]

Poor you. <@&268886789983436800>

[junior smelt]

Actually nooooo I'm being slow, not this

Anyways we would have that $u_{n+1} - u_{n} = \sqrt{u_{n}} - u_{n} + \frac{1}{n+1}$

[flat frigate]

chartbit

[supple shore]

why do you add -x

yes we have that

[junior smelt]

I was being slow and it was the wrong idea there, sorry for that!

[supple shore]

np