help-49

[bitter tide]

u know that integral of 1/u is ln(u)

so u want to do u=ax+b

which then u get du=adx right?

[vocal briar]

ln|u| / a +C

[bitter tide]

u can plug that back into ur base problem and solve from there

yea and go back to initial variable x

[vocal briar]

yeah so ln|ax+b| / a +C

[bitter tide]

✅

[vocal briar]

oh ok this makes sense

thank you both

.close

[midnight plank]

Channel closed

Closed by @vocal briar

Use .reopen if this was a mistake.

[midnight plank]

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.

[molten bay]

8 sides so choosing two vertices would be 8C1?

[hybrid zealot]

if you are choosing two vertices

would it not be 8C2

[lyric charm]

better to phrase it as "8C1 ways to choose the shared side"

or just 8

(unless you really like writing $n$ as ${}^n C_1$ all the time)

[grand pond]

Ann

[molten bay]

yeah

if i choose one side then two vetices automatically selected

[lyric charm]

yes

it is just a bit more direct to say it this way

[molten bay]

so what is the next step?

we have 6 vertices left

8 into 6?

48

[grim vector]

and the third one can't be the one next to them

so for one side you will have 4 possibilities of third point

figuring out by drawing

[molten bay]

why not?

[grim vector]

draw it

and see what happen

[molten bay]

yes i did

it can make a triangle

[grim vector]

you have more than one common side

with the octogon

[molten bay]

only one

ahha

[grim vector]

so applying this to all the sides of the octogon

you have 8 sides where each sides have ? possible triangle

[molten bay]

we have only 4 points

32

[grim vector]

does it make sense ?

[molten bay]

yeah

[grim vector]

perfect

[molten bay]

tq yakubros

[grim vector]

you're welcome

[molten bay]

what exam are you preparing?

[grim vector]

hell

[molten bay]

🤭

[grim vector]

kekw

[molten bay]

is this combinatronics?

or p&C question

[grim vector]

what does p&C means

probability?

its 99% combinatronics here

and maybe like 1% geometry

[thin tree]

permutation and combination

[molten bay]

hahaha

[grim vector]

ah

[molten bay]

what a pfp

scary

[thin tree]

What

[grim vector]

well both cuz i don't do differences between both

[thin tree]

❤️ don't fear

[molten bay]

which book did you read btw?

[grim vector]

i don't read math books

[molten bay]

whoa

i don't want to read too

😅

you stopped learning?

[grim vector]

never

never stop learning

[molten bay]

thanks

.close

[midnight plank]

Channel closed

Closed by @molten bay

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.

[slim wedge]

Help

[grim vector]

Whats your math question

[slim wedge]

Does anyone know the answer to this question?? The only thing i figured out is I think a is 9 but Im not sure

[prime hornet]

what have you done?

[grim vector]

,rccw

[slim wedge]

Huh😭😭

[slim wedge]

Lol

[prime hornet]

as in, what’ve you tried? :p

[slim wedge]

Idk i think I did it wrong😭😭

[grim vector]

Show

[prime hornet]

b should be fairly quick to get

[slim wedge]

How?😭

I forgor how I did it

[grim vector]

Pythagora

[slim wedge]

Pythagream Theorem?

[grim vector]

Yes

[heady bluff]

omg pythagorean

[slim wedge]

Pluh it didn't automatically correct it 💔💔💔

[heady bluff]

do you know what it is

[slim wedge]

No..

[heady bluff]

learn it first

[slim wedge]

Bro why so mean

I gotta turn this in tmrw and I wasn't in school for a week

So idk what's going on

[heady bluff]

how was i mean bro what

[prime hornet]

the Pythagorean theorem states that if you have a right triangle with sides of length a and b, with a hypotenuse of side length c, then a^2 + b^2 = c^2

[heady bluff]

you dont learn math by spoon feeding man

[slim wedge]

Idk it sounded mean in my head bc you earlier said omg

[prime hornet]

this fact will be super useful in this problem

[slim wedge]

Im scared please don't eat my food man

[slim wedge]

Wow thank you that's so beautiful

[slim wedge]

What the sigma

So b is 28?

[subtle zinc]

how did you get 28

[prime hornet]

can you show your work?

[midnight plank]

@slim wedge Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[midnight plank]

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.

[peak abyss]

so how would we do this

[midnight plank]

@peak abyss Has your question been resolved?

Channel closed

Closed by @peak abyss

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.

[novel sky]

Is there a way to express P(A^c | B) in terms of P(A), P(B | A) and P(B | A^c) ? this feels like enough information but I can't wrap my head around it 😦

[midnight plank]

@novel sky Has your question been resolved?

[next bramble]

bayes theorem

[midnight plank]

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.

[ancient wyvern]

i dont get this

[fossil knot]

There are 13 ways to choose which number/face is the pair

and then you want to choose 3 more cards, each of a different face value

so that's 12 ways for the first card, 11 for the second, and 10 for the third, but their order doesn't matter so you divide by 3!

[ancient wyvern]

i dont get it

dont i want 5 cards

[fossil knot]

yes

[ancient wyvern]

i chose the type of card

that i want to be a pair

OH

i see

suits arent included

so i choose type of card

from the 13

and suits arent considered so like

all i care about is that i get a different type of card

so i get 3 more and not 4 because i alr chose what the type for the pair would be

am i getting that right ? @fossil knot

[fossil knot]

you're on the right track yes

[ancient wyvern]

.stop

.end

ion rememer

[flat veldt]

".close"

[midnight plank]

@ancient wyvern Has your question been resolved?

Channel closed

Closed by @ancient wyvern

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.

[white orchid]

hello

[white orchid]

Not sure how to do questiob b)

[gaunt plume]

What have you tried?

[white orchid]

I havent tried anything the question isnt making any sense to me tbh

[gaunt plume]

Okay, do you understand what it's asking for?

[white orchid]

no

does tangent just mean the 2 lines are touching ?

[gaunt plume]

A tangent is a line like this

Touches but doesn't really intersect

[white orchid]

does the tangent have to touch the vertex for it to be a tangent ?

[gaunt plume]

or more precisely, only intersects at one point

No not at all

[white orchid]

oh so its any singular point on the quadratic

ah ok thanks that makes alot more sense

[gaunt plume]

It's just easier to draw

This is a tangent too

[white orchid]

tbh the question makes no sense still

its saying use your answer to part a

then telling us 2 different equations

[gaunt plume]

What's the difference?

[white orchid]

since its tangent we are comparing 2 different equations but im not sure which 2

[lavish venture]

are you wasted rn

[gaunt plume]

No I mean literally what is the difference

And mayyybe

Part a doesn't directly tell you the answer (unless I missed something) but it simplifies the calculation

[white orchid]

so am i doing 3x - 2 = 3x^3 - 11x^2 + 11x+2

[gaunt plume]

Yeah you need to do that

If line a is tangent to line b, then you need them to intersect at some point, but you also need the slope to be the same

[white orchid]

ok i got (x-2) (3x+1) (x-2)

[white orchid]

how do i know its tangent with that information above

[gaunt plume]

Yep I think that's right

Well that's not the whole calculation

That's just part of it

[white orchid]

oh

wait ik i gota solve for P but for the first part how do i proove that its a tangent ?

[gaunt plume]

I don't know how your teacher defined tangent lines for you, but the definition I was taught was that a line is tangent to a curve at point p if (a) they intersect at point p and (b) the slope of the line is equal to the slove of the curve at point p

So you just have to show those two things

For some point p

Have you learnt about derivatives yet? bc if not then you're definitely going to struggle

[white orchid]

oh that seems confusing

Yeah my A level exams in 2 months 🤣 and I cant do the 1st year stuff

the thing im doing right now is first year

[gaunt plume]

Ouch

Good lucku

[white orchid]

thx

[gaunt plume]

It's not that confusing once you break it down I promise

Where do the two lines intersect? From what you've done already

[white orchid]

do they intersect at x = 2 because (x-2) is a repeated root

[gaunt plume]

They do but not because x=2 is a repeated root

Just because x=2 is a root

[white orchid]

ah

oh i just realised equal slopes means change in gradient

my college uses very different terminology

[gaunt plume]

Ah yes okay sorry

Gradient and slope are equal in the 1d case

So yeah just find where the gradients are the same

[white orchid]

i got dy/dx to equal 3

when i subsuited x = 2

ah ok tysm this helped me alot @gaunt plume I understand it now

.close

[midnight plank]

Channel closed

Closed by @white orchid

Use .reopen if this was a mistake.

[gaunt plume]

Np

[midnight plank]

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.

[lost talon]

can someone please just give me the answer ive tried everything and dont know how to do this

[sleek cloud]

What have you tried

[lost talon]

like nothing

idk what to do

this type of math is not possible

im convinced

[lavish venture]

for sure

[sleek cloud]

What comes to mind with instantaneous rate of change

[lost talon]

idk

increase?

[lavish venture]

d

[sleek cloud]

Do you know about derivatives?

[lavish venture]

who are you asking

[sleek cloud]

Oh I meant to tag @lost talon

[lost talon]

oh

nah

just kidding

i do know derivatives

but this question is impossible

[midnight plank]

@lost talon Has your question been resolved?

[midnight plank]

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.

[real minnow]

how is A even possible, it's obviously not gonna move sincce 4 kg>1 kg

and this questoin doesnt even give me coefficient of friction

[prime hornet]

we're assuming that the surface and the pulley are frictionless (it's stated in the problem)

so the 4kg block will definitely move

if the coefficient of friction were high enough, then it wouldn't

but it's 0, so that doesn't matter anymore

[real minnow]

so

is it

4a=Ft

a=-9.81+Ft

？

[prime hornet]

I have no idea what you did

I personally prefer to do these problems by treating the entire system as one object accelerating to the left and down

[real minnow]

i got the sign wrong

[real minnow]

our teacher dont want that

they want to treat each object

as itself

so basically for the 4 kg one

its

4kg = -Ft

for the 1 kg one

its

1*a = -9.81+Ft

[prime hornet]

where's this coming from?

[real minnow]

for the 4 kg mass

[prime hornet]

the tension force isn't balancing gravity

[real minnow]

f=ma

so

4a=-Ft

plug in

[prime hornet]

F_x = -F_t

F_y = 0

there are always two equations in F = ma problems

the force in the x direction, and the force in the y direction

F_y = 0 because F_n = mg

F_x is not 0, because there's a tension force, but nothing balancing it

so F_x = -F_t = 4a

[real minnow]

my answer is 1.96 [CW}

[prime hornet]

the way you wrote it is kinda confusing because you didn't specify the direction

[real minnow]

whats ur answer?

[prime hornet]

but other than that, it seems okay

[real minnow]

my answer sheet says

2

idk if im wrong or not

[prime hornet]

I uh, aren't actually solving the problem

[real minnow]

ok

[prime hornet]

I was hoping you could do all the number crunching haha

[real minnow]

ok ill figure out

ty

.close

[midnight plank]

Channel closed

Closed by @real minnow

Use .reopen if this was a mistake.

[midnight plank]

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.

[native ruin]

Might be a stupid question, but how do you determine what the slope is here...

[native ruin]

I'm reading how, but I just can't wrap my head around it, can someone kinda help talk me through on how you determine the correct spot (though I don't think there is?) and how you determine it

[midnight plank]

@native ruin Has your question been resolved?

[fickle oriole]

Slope is y2-y1/x2-x1

y=mx+b

You know the slope

You slope in any set of clean cords points

Like 16,60

And find b

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[native ruin]

so the bottom would be 2 and the side 110 which you could then properly determine the slope?

Im sorry, I came late, I am still a bit confused...

[midnight plank]

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.

[native ruin]

can I steal back 🙏

[fickle oriole]

that 2nd value is 60

not 50

160-60=100

[native ruin]

I'm sorry... I saw the bot close as I was writing and thought I couldn't chat anymore and rushed it

but the idea is basically to find the correct points, do the math with the bottom points to determine the correct variable, and then figure the slope from there. Did I mostly do that correctly besides from the writing the side portion incorrectly?

[fickle oriole]

ye

[native ruin]

alr ty, rlly appreciate it

.close

[midnight plank]

Channel closed

Closed by @native ruin

Use .reopen if this was a mistake.

[midnight plank]

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.

[warped kindle]

hey

[warped kindle]

um i need help in regards to revising

im doing financial math and algebra and quadratics

please lmao

[rocky storm]

Shoot it

[prime hornet]

well, we can't exactly help you with entire subjects, only specific problems x.x

[warped kindle]

oh alright

[prime hornet]

if you've got a problem you need help with, do send it!

[warped kindle]

was just wondering if you could like flashcard me on some basic principals

[rocky storm]

Do you have Quizlet?

You can find an algebra Quizlet to refresh your memory

[warped kindle]

my test is next period

but thank you anyway :))

[rocky storm]

I would say download Quizlet like fast

[warped kindle]

kay thanks

[rocky storm]

Ofc

[midnight plank]

@warped kindle Has your question been resolved?

[midnight plank]

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.

[unborn trout]

how do i finish this?

[unique juniper]

what's the problem?

[unborn trout]

i finsheds it

i had to prove trianlge bad to cda

i forgfot ot put all right angles ewual

.close

[midnight plank]

Channel closed

Closed by @unborn trout

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.

[golden holly]

Hill cipher

we know that buzzing ( represents a character from a - z) is some where in this encrypted text (like idk 128 letters long).
_buzzing would be split into _b | uz | zi | ng

key is a 2x2 unknown matrix
K = [a c; b d]

how would you solve for the key?

[midnight plank]

@golden holly Has your question been resolved?

[golden holly]

.close

[midnight plank]

Channel closed

Closed by @golden holly

Use .reopen if this was a mistake.

[midnight plank]

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.

[midnight plank]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[midnight plank]

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.

[upper grove]

Hey anyone this message may concern,

I have a PSMT for Specialist Maths but I am stuck with finding the solution and I don't know where to start and I would like some assistance to get started.

Kind Regards,
Clixqlofy

[midnight plank]

Please don't occupy multiple help channels.

[lyric charm]

.close (duplicate #help-5 )

[midnight plank]

Channel closed

Closed by @lyric charm

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.

[gleaming quail]

For context I am solving this exercise from Abbot's book, understanding analysis.

So I am trying to understand the very last step in in showing the implication g(x_m) = (m+1)1/2^m. However if I rewrite this finite sum to start at n=1 instead, because when n=0, 1/2^0=1, then the finite sum from n=1 to m would just equal m/2^m.

Essentially I dont fully understand why the finite sum is equal to m+1, I can see the intuition that you take an extra step from 0 to 1, but from my logic of rewriting the sum above this isn't making sense?

[gleaming quail]

oh nevermind, I didn't realize the index where different summing from n=0, over 1/2^m

[midnight plank]

@gleaming quail Has your question been resolved?

Channel closed

Closed by @gleaming quail

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.

[void lily]

i dont really knwo what to do frm here

like how to get rid of x

sorry ignore the first line

[pale vapor]

do you know about the power property for logarithms

logₐ(xⁿ) = n * logₐ(x)

[void lily]

oh yes

how do i use that for this

[pale vapor]

write ln(a^x) = xln(a)

[midnight plank]

@void lily Has your question been resolved?

Channel closed

Closed by @void lily

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.

[void lily]

this doesnt seem right

[pale vapor]

first step

[valid sinew]

Why

Oh didn't see the previous image

[tawny apex]

You could simplify if more

[pale vapor]

first step is wrong

[void lily]

should i have left the 3?

[pale vapor]

you can take it

(2x)^3

[valid sinew]

Divide 3

[pale vapor]

is not 2x^3

[valid sinew]

I will end up simpler

[void lily]

does this seem right so far?

[void lily]

ah

[valid sinew]

The 3 is divided by the whole part on the right side not just 1

[void lily]

sorry i meant to bring lna to the other side first

then divide by 3

or does that still make it lna/3

actually does this seem right

[topaz urchin]

it's (2x)^3

which is equal to 8x^3

[pale vapor]

no

lna - lnb isnt ln(a-b)

its ln(a/b)

[midnight plank]

@void lily Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[midnight plank]

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.

[golden maple]

Anybody know what this is called so I can study on this

[shrewd tusk]

similarity

[lethal steeple]

Congruency

[shrewd tusk]

yeah its congruency mb

[amber marlin]

MaThanos is replying to Thanos

[golden maple]

Alright

.close

[midnight plank]

Channel closed

Closed by @golden maple

Use .reopen if this was a mistake.

[midnight plank]

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.

[molten bay]

How to start this problem?

[junior light]

1st, did u tick it?

[molten bay]

Nope

[junior light]

apply nCr

take n as 25 and r as 2

and nCr = n!/(r![n-r]!)

do u know permutation and cobination or not

in this we'll take two lines at a time.

[molten bay]

Broooo

I know all of the things but the main problem is that I didn't understand the question properly

[unique stream]

So solved? 😄

[molten bay]

I didn't understand the question?

@unique stream

[unique stream]

Ah it sounded like now you understood it

[molten bay]

And i am sure the n=25 and n=2 is wrong

Definitely

[unique stream]

You have 25 lines and the parallel condition means that each line intersects with each other

and the concurrent condition means each intersection is unique

Envision it iteratively:

The first line must intersect 24 times

because it is parallel with no other line

and all of those intersections are different, since there are no concurrent triplets

meaning the first line must have 24 unique intersections with other lines

so let's now ignore the first line

the second line must intersect 23 times, uniquely again

continue this process :]

24+23+22+...+1

= 24 * 25 / 2 via sum formula

= 300

remains unclear? @molten bay :]

[molten bay]

The graph is unclear

Can you show me with 5 lines?

[unique stream]

I'm currently not on my setup so I can't send images, try drawing arbitrary five lines

you just need them to intersect uniquely and not be parallel

then the conditions are met

then take any line as starting line

and you'll see it has 4 intersections, since there are 4 other lines

[molten bay]

So if I draw a line and then four other lines will intersect it at different points and those lines will also intersect each other because our condition is they are not parallel

[unique stream]

yes the important part is that if you have 5 lines and you look at any line, each must have 4 intersections with each other

which means if you want to count the total number of intersections

you can count all intersections with the first line

then erase the first line

then count all intersections with the second line

then erase the second line

etc

which gives you
4

+3

+2

+1

+0

= 4+3+2+1

and this generalizes to any amount of lines

[molten bay]

I got the idea

Thanks

[junior light]

but

please don't try to draw the diagram

it will take time

[unique stream]

Purely thinking about a solution with the given information abstractly is better yeah, of course needs a trained mind to avoid viewing everything with a visual lense 🙂

[molten bay]

Yes

Close

. close

.close

[midnight plank]

Channel closed

Closed by @molten bay

Use .reopen if this was a mistake.

[midnight plank]

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.

[last slate]

Would like my proof to be checked for this question

[grand pond]

Edmund Cloudsley

Edmund Cloudsley

[last slate]

and I prove this further for:

--> a > 0, b <0
--> a < 0, b > 0
--> a < 0, b < 0

Since what is 4a^3 < -27b at the moment would do the sign flippity flip for negative values of b, this logic also works for other cases

Does this proof make any sense

?

Thanks in advance

<@&286206848099549185>

[ashen sequoia]

what if a=0 or b=0?

and also, i'm not sure what does alpha<0 and gamma<0 mean

it was supposed to be index and suddenly its a number

[midnight plank]

@last slate Has your question been resolved?

Channel closed

Closed by @dawn crater

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.

[pallid wyvern]

can sb help with this one? I am stuck. I don't know how to get rid of the root

[lyric charm]

there are at least two options here

one is slightly weird but easier, and the other one is more "standard" but harder imo

[pearl hull]

🏥

[pallid wyvern]

the thing is, I'm in highschool and we havent learnt it yet

[pearl hull]

I see

[lyric charm]

the slightly weird option is to substitute $t:=\sqrt[3]{x+4}$, then $t^3=x+4$ and thus $x=t^3-4$; and also $t\to 2$

[grand pond]

Ann

[pallid wyvern]

hmm

[lyric charm]

you get a much nicer limit without any roots at all

tho you will have to know some algebraic identities for cubics

like a^3-b^3

(but third powers would be involved no matter what)

[pallid wyvern]

idk i tried running it through photomath and it wanted me to multiplied it by some weird fraction and i didn't understand how and why to get rid of the root

[lyric charm]

that's the "standard but hard" way

[pallid wyvern]

my enemy is the 3rd powers

[lyric charm]

you know how in limits with square roots you can often get good results by multiplying num and denom by the conjugate?

[pallid wyvern]

ye

[lyric charm]

you can sorta do that for cube roots too but the "conjugate" is much uglier then

cause then you are setting up the identity (a-b)(a^2+ab+b^2) = a^3 - b^3

[pallid wyvern]

yes and that's what photomath gave me. and since i struggle with remebering the formulas, i didn't understand it

[pallid wyvern]

so...i need to multipy by this part then (a-b)(a^2+ab+b^2)?

[lyric charm]

mmm

if you do it the hard way then yes

[pallid wyvern]

well i believe it's what my teacher would tell me to do

[pallid wyvern]

but im still thinking ab this. Why is t=2

[midnight plank]

@pallid wyvern Has your question been resolved?

Channel closed

Closed by @pallid wyvern

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.

[twilit field]

so We have $\grad{f} = \left( \pdv{f}{x}, \pdv{f}{y} \right )$.

[grand pond]

What a wonderful world !

[twilit field]

Wait, I'm not sure

hmm

[next bramble]

$\nabla f$ denotes the direction of steepest ascent, so $-\nabla f$ would be the direction of steepest descent

[grand pond]

Shuba

[next bramble]

Why is $\nabla f$ the direction of steepest ascent? Well, $\pdv{f}{x}$ is the ascent over an infinitescimal distance in $x$, and $\pdv{f}{y}$ is the same for $y$. So the direction of steepest ascent would be the sum of $(\pdv{f}{x},0)$ and $(0,\pdv{f}{y})$.

[grand pond]

Shuba

[twilit field]

I was instead, thinking I'd find the directional derivative tbh

[sinful topaz]

would it be helpful to you to consider the directional derivative?

do you know the formula of it?

[next bramble]

directional derivative also works

[twilit field]

yea

I just realoised it's a unit vector

that's what was stopping me all this time

let $\norm{v} =1$.
\
We then have $\grad{f} \cdot v = \grad{f} \norm{v} \cdot \sin(t) = \grad{f} \sin(t)$.
\
Minimizing this we set $\sin(t)=-1$
\
We thus conlude the direction of greatets decrease is along $\grad f( \bf{x})$

[grand pond]

What a wonderful world !

[next bramble]

So, consider an arbitrary vector $v$ at angle $\theta$. We calculate the rate of change in the direction of $v$ as
$$D_v f = \nabla f \cdot v = |\nabla f| |v| \cos \theta$$
Obviously, this is maximised when $\theta = 0$ - i.e. when $v$ points in the same direction as $\nabla f$.

[grand pond]

Shuba

[twilit field]

oops

yea

got it

[sinful topaz]

remember to tailor that to your question though

[next bramble]

I'm not sure how mathematically rigerous you want the answer

[twilit field]

Not very

this is for a calc 2 class

[next bramble]

Technically, nabla f is the direction of steepest ascent, and the directional derivative is defined as a function of nabla f. So, I'm not sure if they wanted you to proove nabla f is indeed the direction of steepest ascent.

[twilit field]

I doubt it

[sinful topaz]

seems fairly rigorous to me

as long as someone proves the formula for the directional derivative, then just maximise/minimise the value

[next bramble]

At least, to me, the directional derivative never really added anything of interest

everything of interest is coded in the vector \nabla f

though nobody really teaches tensor calculus

[twilit field]

fair

.close

[midnight plank]

Channel closed

Closed by @twilit field

Use .reopen if this was a mistake.

[midnight plank]

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.

[wheat eagle]

Are these 4 right? :333

[midnight plank]

Please don't occupy multiple help channels.

[dreamy lichen]

you should only use one channel

[wheat eagle]

Sorry ah I didn’t mean to open a second and close the other

[dreamy lichen]

but you can check most of those yourselves using wolfram alpha

[wheat eagle]

What is that? :3

[dreamy lichen]

,w integrate 1/(x^2 + 3x)

this

[grand pond]

Results provided by WolframAlpha

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

Requested by methisalwaysright

[dreamy lichen]

https://www.wolframalpha.com

[wheat eagle]

Ohh is it AI? I try to avoid using apps like that cuz of the sustainability aspect hehe but no shame to anyone who does!!!

[dreamy lichen]

Nope, it's not really AI

at least afaik

[tribal temple]

(You may wanna check the bottom 2, or justify them a bit more ) [retracted]

[dreamy lichen]

def not the chatgpt type (WA is accurate, you can rely on it in 99% of cases)

[wheat eagle]

Like the last 2 questions or bottom 2 boxes of a certain question? :3

[violet dune]

its more like a really good calculator that can do a lot of things

[tribal temple]

The bottom pictures

[wheat eagle]

Ok! Thank u sm! Are the first 2 all good to go

[tribal temple]

The top left is fine, I haven’t checked the top right one

Actually I think I’m happy with the bottom left, just noticed they said “or expressions” for it

[wheat eagle]

Do I have to download wolf farm alpha or like pay for it or smth

[tribal temple]

You don’t have to pay for most features, see

Some parts (e.g. worked solutions) are paid if I recall, but unless you want those

[wheat eagle]

This is my work for it

[dreamy lichen]

There is still a way to get around that because it shows you the first step, so i always just reinsert the first step and it will show me the next step

[wheat eagle]

I still don’t see how it’s wrong tho :(((

[tribal temple]

Ah no you’re fine, I’m just tired you’re right

[wheat eagle]

Oh oki no problemo :3

[tribal temple]

Can I make you show your work for the top right one please?

(I’m laying in bed and too lazy to get up to do it )

[wheat eagle]

Yes I got u lemme pull it up

[dreamy lichen]

the top right one seems to be correct

[wheat eagle]

Ok thank u guys sm!

I really appreciate all your time and effort :3

.close

[midnight plank]

Channel closed

Closed by @wheat eagle

Use .reopen if this was a mistake.

[midnight plank]

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.

[rancid vigil]

How to find this limit

[rancid vigil]

$\lim_{x \to -\infty} \frac{e^{-x(n-1)}}{x}$

[grand pond]

<rajel />

[rancid vigil]

n is an integer

Positive

[grim vector]

What happen if you simplify it

[rancid vigil]

How

[grim vector]

e^-xn * e^x

All over x

[rancid vigil]

How would that help

[lyric charm]

n is a positive integer but is it known whether n = 1 or not

[grim vector]

||Well the exponential win over the x||

[lyric charm]

||yeah but if n=1 then...||

[wary thorn]

||I want to look secretive too||

[grim vector]

||Indeed im pretty sure its missing data here||

[midnight plank]

@rancid vigil Has your question been resolved?

[rancid vigil]

n is indeed bigger than one

[lyric charm]

note that we did not know this until you said it

[rancid vigil]

Yeah , terribly asked my question

[lyric charm]

but ok in that case you have $e^{-(n-1)x}$ on the top, and $x \to -\infty$ \ thus $-(n-1)x \to +\infty$

[grim vector]

It ok

[grand pond]

Ann

[grim vector]

Something called compared growth

[rancid vigil]

But on the bottom it's also infinity

-infty

[lyric charm]

i did not tell you the full thing

merely remarking that the numerator grows exponentially

[rancid vigil]

So thats enough to say that the limit goes to -infty ?

Because the denominator is negative

And the numerator is exponentialy growing

Or I need to prove it even more ?

@lyric charm

[lyric charm]

no i think that is enough-ish

[grim vector]

Its enough

[rancid vigil]

Someone marked x to my message lol

[grim vector]

Thats way better than hôpital

[rancid vigil]

Ok fine

[rancid vigil]

Weren't even allowed to use that

[grim vector]

Good thing

[rancid vigil]

Thx y'all

[grim vector]

Yw

[rancid vigil]

.close

[midnight plank]

Channel closed

Closed by @rancid vigil

Use .reopen if this was a mistake.

[midnight plank]

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.

[main owl]

is that a piano on a pully

[tidal turret]

don't think so

no pulleys

[main owl]

yea its just brute force

what are you confused about

[tidal turret]

is hard

[main owl]

do you know what formulas you need to use

you also need to make a free body diagram to get the net forces

[lethal steeple]

Did you draw the free body diagram (fbd)?

[tidal turret]

drawing as of rn

T1 = 1800 N

[lethal steeple]

Yeah you are going right

[tidal turret]

wait but same tension in x and y direction?

how is that possible

[lethal steeple]

Because the angle is 45

That's when cos45=sin45=1/√2

There is no problem in that, the forces in x and y directions can be same

[lethal steeple]

I just noticed, you forgot to consider the weight force (mg) of the piano

[tidal turret]

im stupid thanks

[lethal steeple]

Nah you're not. People miss something sometimes. Anyways you would have come to know it because that's exactly what you have to find

[tidal turret]

yeah ok

let me correct it

[lethal steeple]

Did you get it?

[tidal turret]

im doing the trigonométry

[lethal steeple]

Okay okay

[tidal turret]

is hard

[lethal steeple]

What forces did you get in y direction?

And in x?

[tidal turret]

we dont know anything about T2

fucking internet bro messages are not sending

[lethal steeple]

But you know about T1

[lethal steeple]

Find T1x then T2x and then T2.

[tidal turret]

T2 = ?

how does T2x help

[lethal steeple]

Wait a min

[tidal turret]

ohh trigonometry

but maybe i am missing some info, let me see

[tidal turret]

samee hahaha

[tidal turret]

yep

let me do the trig

maybe there is some value we know other than T2x

[lethal steeple]

You just need T2x tho

Cos70=T2x/T2

[tidal turret]

with this we can figure out T2

and knowing T2 and T2x we can figure out T2y

[lethal steeple]

Yes

[tidal turret]

i need to go to philosophy class

will be back in 2h

srry

[lethal steeple]

I might not be here then, srry. It's my bedtime now so

[tidal turret]

is okay you helped me a lot, i appreciate it!!

gn

[buoyant yoke]

hf :3

[midnight plank]

@tidal turret Has your question been resolved?

[buoyant yoke]

bro, just close the channel

and make a new one when youre available again

[tidal turret]

ok

.close

[midnight plank]

Channel closed

Closed by @tidal turret

Use .reopen if this was a mistake.

[midnight plank]

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.

[glossy compass]

Couldn't the graph be drawn like the red aswell

Cause it's not bounded by x = 0

[lavish venture]

you’re rotating that region around the line x = 6?

what does x = 0 have to do with this

[tired osprey]

just you try to have sqrt(x) with negative x

[subtle zinc]

there is nothing on the other side of x=0

what's the red thing u drew, are the vertical lines x=4,x=6?

[glossy compass]

yes

[subtle zinc]

well it's a different graph

clearly

[glossy compass]

well i know its a different graph lol

[subtle zinc]

idk what u mean by can it be drawn like this aswell

[lavish venture]

you’re misunderstanding volume of revolution

i think they mean the volume or area would be the same?

not sure exactly what they’re getting at

[glossy compass]

but why does the shaded area have to be drawn between x=0 and x=4

[subtle zinc]

x=6 is not bounding ur region

[lavish venture]

it’s the region

[subtle zinc]

it's what ur rotating around

i get her question

[subtle zinc]

for y = sqrt(x) there's nothing when x<0 so x=0 is a default bound from y=sqrt(x) which ur given

[glossy compass]

oh

ty

.close

[midnight plank]

Channel closed

Closed by @glossy compass

Use .reopen if this was a mistake.

[midnight plank]

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.

[twilit knoll]

Apologize for it being sideways, I believe I forgot the formula in regard to the two circled problems. May someone check these or help me with the formula?

[sharp coral]

,rccw

[twilit knoll]

,close

• Figured it out.

17. is 10 as you divide the 2, oops.

,close

.close

[midnight plank]

Channel closed

Closed by @twilit knoll

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.

[safe onyx]

First I calculated the velocity of the block and bullet using conservation of momentum in an inelastic system (the objects stick together)

$P_1 = P_2$ \\
$m_b v_b + m_w v_w = v (m_b + m_w)$ \\
$2.25 = 1.005 v$ \\
$v = 2.239$ m/s \\

[grand pond]

smeagol

[safe onyx]

Then I used conservation of energy to calculate the velocity after the bullet leaves

$E_2 = E_3$ \\
$K_t = U_g + K_b + K_w$ \\
$\frac 1 2 m_t v^2 = m_t y g + \frac 1 2 m_b v_b^2 + 0$ -- Kinetic energy of block is 0 because it is at the peak of the pendulum motion \\
$ 2.519 = 0.0374 + 0.0025 v_b^2$ \\
$ \sqrt{\frac{2.519 - 0.0374}{0.0025}} = v_b$ \\
$v_b = 31.5$ m/s

I messed up somewhere but idk where

[grand pond]

smeagol

[midnight plank]

@safe onyx Has your question been resolved?

[safe onyx]

I need to sleep if someone has advice please ping me. I'll come back to this

[midnight plank]

@safe onyx Has your question been resolved?

[midnight plank]

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.

[twilit field]

Find the point $(x,y)$ and the directions for which the direction derivative of $f(x,y) = 3x^2+5y^2$ has its largest value, if is restricted to be on the ellipse $9x^2+4y^2=36$

[grand pond]

What a wonderful world !

[hard shard]

important question: on or inside?

[kindred zenith]

it says on

[hard shard]

yeah just making sure

[twilit field]

I would think along the boundary

[kindred zenith]

or that

[hard shard]

does the question say on?

[twilit field]

yea

[hard shard]

ok cool thanks

apologies, carry on

[twilit field]

my idea is find grad f, and then paramatrize the ellipse, then maximise the dot product

[hard shard]

you can

but i think you can also do a substitution to make a function in one var

[twilit field]

We start by determining $\grad f = (6x,10y)$
\
The ellipse can be parametrized by $(2 \cos(t), 3 \sin(t))$
\
The directional derivative is maximised along the gradient, we thus wish to maximise $(12 \cos(t) + 30 \sin(t))$
\
The maxima is $6 \sqrt{29}$

[grand pond]

What a wonderful world !

[twilit field]

huh?

[hard shard]

if im not mistaken, you can sub in y^2=(36-9x^2)/4 into f(x,y)

[twilit field]

hmm, yea

I could

[hard shard]

since all the information about y is encoded in the substitution

[twilit field]

that would work well too, yea

thanks

[hard shard]

both shoukd work and give the same answer

[twilit field]

This shouldn't be too bad, either

[hard shard]

hopefully they do

yeah its definitely doable

[twilit field]

so I have $-12\sin (t) = - 30 \cos(t)$; so $tan(t) = \frac{15}{6} = \frac{5}{3}$

[grand pond]

What a wonderful world !

[twilit field]

so the maxima occurs at $t = 12 \cos(\arctan ( 5/3))$

yeah, that's it

x= 2 \arctan(5/3)

[grand pond]

What a wonderful world !

[twilit field]

$y= 30 \sin(\arctan(5/3))$

[grand pond]

What a wonderful world !

[twilit field]

got it

thanks

.close

[midnight plank]

Channel closed

Closed by @twilit field

Use .reopen if this was a mistake.

[midnight plank]

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.

[twilit field]

A differentiable scalar field $f$ has , at the point $(1,2)$ directional derivative $+2$ towards (2,2) and $-2$ towards (1,1).
\
Find the gradient at $(1,2)$ and find the directional derivative towards $(4,6)$

[grand pond]

What a wonderful world !

[merry peak]

so we know the directional derivative towards (2,2) is +2

and towards (1,1) is -2

so

let's just say that the gradient at (1,2) is ∇f(1,2) = (a,b)

[twilit field]

[
\left( \pdv{f}{x} , \pdv{f}{y} \right) \cdot \frac{(2,2)}{2\sqrt{2}} = 2
]
[
\left( \pdv{f}{x}, \pdv{f}{y} \right) \cdot \frac{(1,1)}{\sqrt{2}} = -2
]'

[grand pond]

What a wonderful world !

[twilit field]

is this even solvable?

as (1,1) and (2,2) are parallel, I doubt it

[lethal path]

the change of f(x, y, z) in the direction of (1, 0) is +2
and in the direction of (0, - 1) is -2

so equivalently the change in the direction of (0, 1) is +2

[twilit field]

huh?

[lethal path]

(2, 2) - (1, 2) = (1, 0) right

[carmine sigil]

The direction isn't coming from the origin

[twilit field]

so what do I do

anyway, have a class now

so gtg

thanks though

.close

[midnight plank]

Channel closed

Closed by @twilit field

Use .reopen if this was a mistake.

[midnight plank]

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.

[chilly cobalt]

consider the sequence
7, 9, 19, 39, 71, 117, 179. Find the 13th term

[chilly cobalt]

i cant seem to find anything..

oh wait i subtracted numbers wrong sorry😭

.close

[midnight plank]

Channel closed

Closed by @chilly cobalt

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.

[twilit field]

Fine the values of the constants $a,b,c$ such that the directional derivative of $axy^2+byz+cz^2x^3$ at $(1,2,-1)$ has a maximum value of $64$ in a direction parallele to the $z-axis$

[grand pond]

What a wonderful world !

[twilit field]

$\grad{f} = (ay^2+3cx^2z^2,2axy+bz, by+2czx^3)$

[grand pond]

What a wonderful world !

[twilit field]

evaluvating at $(1,2,-1)$

[grand pond]

What a wonderful world !

[twilit field]

yeah, nvm

I can do this

.close

[midnight plank]

Channel closed

Closed by @twilit field

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.

[twilit field]

in $\R^3$ let $\mathbf{r}(x,y,z) = x \mathbf{i} + y \mathbf{j} + z \mathbf{k}$. Let $r(x,y,z) = \norm { \mathbf{r}(x,y,z)}$

[grand pond]

What a wonderful world !

[twilit field]

Prove that $\grad{r(x,y,z)}$ is a unit vector along $\mathbf{r}(x,y,z)$

anyway

uh

[carmine sigil]

mathbf not fb

[twilit field]

yea

typo

[grand pond]

What a wonderful world !

[lyric charm]

[twilit field]

so $\grad{r}=( \frac{x}{ \sqrt{x^2+y^2+z^2}}, \frac{y}{\sqrt{x^2+y^2+z^2}}, \frac{z}{\sqrt{x^2+y^2+z^2}})$

[carmine sigil]

So what have you tried so far?

[grand pond]

What a wonderful world !

[lyric charm]

oh grad of r the scalar function

[twilit field]

I could improve the formatting, but yeah

[carmine sigil]

Ok, so it's asking you to prove that this is a unit vector

Just use the distance formula, right?

[twilit field]

I mean the defn of the norm works

[carmine sigil]

Yup

Also it's along bold-r because it's a scalar multiple of it

The scalar being the denominator

[twilit field]

yea

[carmine sigil]

GG then? Or are you still dissatisfied somehow?

[twilit field]

GG

thanks

.close

[midnight plank]

Channel closed

Closed by @twilit field

Use .reopen if this was a mistake.

[midnight plank]

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.

[inland patio]

Let $\mathsf T^t:\mathsf W^\ast\to\mathsf V^\ast$ be the transpose of $\mathsf T:\mathsf V\to\mathsf W$. Then $\mathsf T^t$ is onto iff $\mathsf T$ is one-to-one. Now consider the forward direction. Suppose $\mathsf T^t$ is onto and for contradiction, that $\mathsf T$ is not one-to-one. Then there is some nonzero $x\in\mathsf V$ such that $\mathsf T(x)=0$. It is claimed that we can construct a nonzero linear functional $\mathsf g\in\mathsf V^\ast$ such that $\mathsf g(x)\neq 0$. Since $\mathsf T^t$ is surjective, there is some $\mathsf f\in\mathsf W^\ast$ such that $\mathsf T^t(\mathsf f)=\mathsf g$ and then $$0=\mathsf f(\mathsf T(x))=\mathsf T^t(\mathsf f)(x)=\mathsf g(x)\neq0,$$contradiction. But why is it possible that we can construct $\mathsf g$ in the first place?

[grand pond]

psie

[coral zodiac]

hello

is is channal availible

[inland patio]

no, but you can open up a new one by clicking here --> #❓how-to-get-help

.close

[midnight plank]

Channel closed

Closed by @inland patio

Use .reopen if this was a mistake.

[midnight plank]

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.

[chilly cobalt]

how do i solve this? ive never seen it before

[chilly cobalt]

i know it involves some roots of a polynomial, i think?

[lyric charm]

are the lower arguments supposed to increase by 3 from each term to the next

[chilly cobalt]

yes

[lyric charm]

ok, so let's try thinking of it this way first: if you wanted to calculate the sum of ALL binomial coefficients with top argument 2024, i.e. C(2024,0) + C(2024,1) + C(2024,2) + ... + C(2024,2024)

would you see how to do it

[chilly cobalt]

i think so? its 2^2024

[tough shale]

I think she meant the process

[lyric charm]

i did cause i wanted to build off of that

[chilly cobalt]

oh

[lyric charm]

cause i want to build up to considering the function f(x)=(1+x)^2024

[chilly cobalt]

i dont really know that..💔

[lyric charm]

2^2024 is f(1)

and f(x) = sum C(2024,k) x^k

yeah?

[chilly cobalt]

yea

[cedar mason]

this is a binomial combination?

[chilly cobalt]

wdym?

[cedar mason]

just confirming

[chilly cobalt]

its a sum, yeah

[lyric charm]

@chilly cobalt yeah ok so here is a wild idea

evaluate f at the complex cube roots of unity

[chilly cobalt]

?

why would that work?

[lethal path]

you stole my thunder haha

[lyric charm]

try it. see what happens with each term in the expansion.

the powers of omega will repeat with period 3

[chilly cobalt]

okay

[cedar mason]

this is so interesting

[chilly cobalt]

ohh im seeing it now

.close

[midnight plank]

Channel closed

Closed by @chilly cobalt

Use .reopen if this was a mistake.

[tough shale]

💀

How're we supposed to get the idea lol

[chilly cobalt]

the general sum is 2 mod 3

so the root of unit will remove the terms unneeded i guess

[midnight plank]

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.

[regal barn]

dy/dx=2x

what should I do next?

normal would be -1/2x

[tough shale]

Find the equation of normal

And that point should be satisfying it

[regal barn]

..

[grave wasp]

then just use the distance formula i think

i feel that plotting it would be easier

[royal grove]

i think we have to call the shortest point(x;y) then find distance, and then find minimum value of that function

[dusty portal]

Distance formula minimization

[grave wasp]

yup

[dusty portal]

Using normal is so-so

[regal barn]

but what I do with -1/2x

[tough shale]

That's just the slope, isn't it?

[dusty portal]

(Discard it for now)

[regal barn]

yes

[dusty portal]

Do you know how to find the distance between the curve and the point?

Not the minimal, just in general

[regal barn]

actually no

forgot

[dusty portal]

Ah.

Do you know the distance formula?

[regal barn]

yeah

of course

[dusty portal]

Ok

So every point on x^2=y-7 has coordinate (x, x^2+7)

?

[regal barn]

(x-3)^2+(x^2+7-7)^2=y^2

and i will use derivative for minima

[dusty portal]

👍

[dusty portal]

Yep

[regal barn]

why slope thing failed?

[dusty portal]

I mean, I suppose it works

But it’s not very direct per se

You know the straight line to point formula right

If you do, I suppose you could use that and find the normal that contains (3, 7) on the graph

Find the tangent to the curve

Then use the formula

But it’s lengthy

[grave wasp]

but the possibility of it lying on the curve itself would not be accounted for then?

[dusty portal]

Tangent line is at a specific point on the graph

We measure the distance from that point