help-27

[foggy topaz]

isnt -1/3 0.3333333

[placid rover]

???

[foggy topaz]

then its zero or 1

[placid rover]

-0.333333...

[foggy topaz]

yea

then its 0 or1

[placid rover]

Ok, but we've established 0 is an integer

1 is also an integer

yes?

[foggy topaz]

zero isnt an integer

[placid rover]

..........

[foggy topaz]

owait

[placid rover]

Read carefully

[foggy topaz]

nvm

[placid rover]

I'm stating this as a fact

(that hopefully should be in your notes)

[foggy topaz]

my test is in 12 hours

[placid rover]

in words, this is what the integers are

[foggy topaz]

so its 0

ans = 0

[placid rover]

..., -3, -2, -1, 0, 1, 2, 3, ...

yes it is.

[foggy topaz]

o

thank you

.close

[devout snow]

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[blissful elk]

Time for me to return with a question I'm struggling with
Topic is Number Theory
Struggling to figure out a way to solve this question using information I learnt in lecture. I already have an answer that works. I'm just struggling with...getting to that point

So far my workings looks like:
6x+9y = 126
6y+9x = 114

Then attempted to use GCD (not useful, can find the GCD in 2 iterations)

Anyone got a better idea to solve this?

[topaz axle]

isn't this just algebra

hm

[blissful elk]

Not simple algebra, no no lol

The general theme seems to be Greatest Common Divider with this style of question

But through some trial and error I got the answer

[topaz axle]

2x+3y = 42
2y+3x = 38

x+y = 16

[blissful elk]

But because this is university level, They kiiinnndddaaa want your workings rather than just the answer

[topaz axle]

then you find x-y

y-x = 4

so y = 10, x = 6

[blissful elk]

Surely it can't be that easy

All that'll require is me finding the GCD (which is 3)
Dividing through
Then simultaneous equations

[topaz axle]

it doesn't require knowing gcd

but it let me do it without calculator

nvm i can even do 15x+15y=240 in my head
#overmind

if you figure out how to do it with number theory i'd be interested

[devout snow]

@blissful elk Has your question been resolved?

[fathom thicket]

You would use sin(a/π x) if the relevant point is an integer

Sin(x/2π) means that it repeats every x = 1 , 2 , 3...

[blissful elk]

Huh...pretty smart. Time to close this channel then

[devout snow]

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[carmine fable]

hello

[carmine fable]

i am trying to solve an integral

but after a substitution, the bounds are equal (i'm substituting t = e^(ix) and the bounds are 0 and 2pi, so after the sub the bounds would both be 1)

[restive river]

whats the original integral?

[sonic smelt]

Then the substitution is illegal most likely

[restive river]

(also i'm so tempted to tag riemann)

[sonic smelt]

Splitting up the original integral can help with that

[carmine fable]

https://cdn.discordapp.com/emojis/801309853116923924.gif?size=48&quality=lossless

[pastel pasture]

That looks like something I'd enter into Desmos as a 10 year old

[carmine fable]

lmao

[sonic smelt]

Including the integral?

[pastel pasture]

Nope

[pastel pasture]

I didn't know what an integral was

[carmine fable]

how should i split it

[pastel pasture]

Complex numbers always fuck things up huh 😔

[carmine fable]

they just like me fr

[restive river]

,w int e^(cos x)cos(sin x) from 0 to 2pi

[woven radish]

Results provided by WolframAlpha

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

Requested by Toby#2275

[restive river]

$\tau$

[pastel pasture]

2π

[woven radish]

Toby

[sonic smelt]

I would try picking the intervals from 0 to pi and pi to 2pi or smth

[pastel pasture]

Disgusting

[carmine fable]

i was thinking about that

[low holly]

also the real part of the integral is the integral of the real part

[sonic smelt]

Let's see,
[
\int_0^\pi e^{e^{ix}}dx + \int_\pi^{2\pi} e^{e^{ix}}dx = \int_0^\pi e^{e^{ix}}dx + \int_0^\pi e^{e^{i(\pi - x)}}dx
]

[woven radish]

A Lonely Bean

[sonic smelt]

e^i(pi - x) is the same as -e^ix, right?

[carmine fable]

when you do the substitution on the split up integral the whole thing is 0 i think

[sonic smelt]

Oh sorry meant x - pi here

[carmine fable]

,tex Before substitution: $\int_0^\pi e^{e^{ix}}dx + \int_\pi^{2\pi} e^{e^{ix}}dx$\newline After substitution: $\int_1^{-1}{ e^t t^{-1}dx} + \int_{-1}^1{ e^t t^{-1}dx}$

[sonic smelt]

{-1}

\int_

[carmine fable]

yeah i copied from your message and discord formatting moment

wow i forgot the actual substitution

[sonic smelt]

You are doing t = e^(ix) btw, right?

[carmine fable]

yes

[woven radish]

what is an riemann?

[pastel pasture]

dt

[carmine fable]

yes

[sonic smelt]

Maybe
[
\int_0^{2\pi}e^{e^{ix}}dx = \frac12\int_0^\pi e^{e^{2ix}}dx
]
?

[carmine fable]

hm

how would i prove that

[sonic smelt]

Sub for x/2

Oh, wait

Should be 2ix up there then

[woven radish]

A Lonely Bean

[sonic smelt]

Let's see, t = e^(2ix) dt = e^(2ix) * 2idx = 2it * dx
dx = -i/2 dt/2

Same dounds

Imma come back to this after a while

[carmine fable]

okay

thanks

[pastel pasture]

Have you considered using the Taylor series for e^x

[carmine fable]

i don't think evaluating the sum would be more pleasant tbh

[pastel pasture]

True

But it's something to do

[carmine fable]

now i'm getting e wtf

[restive river]

?

[carmine fable]

use the function

spoiler: the function is even

[restive river]

Don’t know what that means I’ll be honest lmao

[carmine fable]

uh

just replace x with the values in the table and evaluate it

[carmine fable]

an even function is a function where f(-x) = f(x)
so in this case you'll find the same for -2 and 2

[devout snow]

@carmine fable Has your question been resolved?

[sonic smelt]

I found a video on this exact integral from flammable maths, here is the link if you want to check it out
https://www.youtube.com/watch?v=X40nssSbcHs

[carmine fable]

pog

https://cdn.discordapp.com/emojis/802002483152289822.gif?size=48&quality=lossless

[devout snow]

@carmine fable Has your question been resolved?

[carmine fable]

i guess

friendship ended with real methods, residue theorem is my new best friend

[devout snow]

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[devout snow]

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[lucid kernel]

Apparently there is something wrong with this equation. Does anyone know which step has been done wrong and on which line?

[lofty glacier]

what is X+? in the power of 2 @lucid kernel ??

[lucid kernel]

2 to the power of x+1

[lucid kernel]

It’s a „1“, if you mean that, 2 to the power of x+1

[lofty glacier]

just take log to the base 2

it will simply everything

dont take ln (log to the base e) take log2

[lucid kernel]

But ln has to be used, I can’t change the equation, I just have to find out what has been done wrong

[lofty glacier]

okok

1 min then

[lucid kernel]

Okay

[lofty glacier]

well you have solved it the right way

i dont see any problem

@lucid kernel

[lucid kernel]

Hm, weird, the assignment says „something has been done wrong, correct the problem“

but if you say everything is correct then I believe you

thank you @lofty glacier

[lofty glacier]

can you send the ss of assignment

@lucid kernel

[lucid kernel]

We’ll, the assignment is not written in English, but I’ll translate the screenshot to English and paste it over it

1 min

[lofty glacier]

1 min you have done all steps right but you got wrong answer

check your calculations

@lucid kernel

[lucid kernel]

„a student solved the exponential equation as follows:“

„Describe the mistake he made and correct the calculation.“

[lofty glacier]

can i call you?

[lucid kernel]

Sorry, but no

[lofty glacier]

okok

then in 2nd line

you cannot seperate log

like log(a+b) ~= log a + log b

this is incorrect in 2nd line

[lucid kernel]

Do you mean like this? Is this how it should be done?

[lofty glacier]

yes

[lucid kernel]

So this is now the correct equation?

[lofty glacier]

yes

do not separate log

[lucid kernel]

Okay

Thank you so much @lofty glacier

!!!

<3

[lofty glacier]

dm me if you have any doubt

[lucid kernel]

Okay, thank you

.close

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[nova ibex]

need to find the G.S.

using the Particular Integral method thingy

[restive river]

!status

[devout snow]

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

[restive river]

@nova ibex

[nova ibex]

ohhh

[restive river]

have you already found the homogeneous solution?

(or complementary solution, if you will)

[nova ibex]

no , im doing the PI first

but gimme a sec ill do the homogenous one

[restive river]

Good idea.

Use the ansatz $e^k = s(t)$

[woven radish]

45

[restive river]

You should get a quadratic equation

[nova ibex]

$Ae^{-2t}+Be^{-0.5t}$

[woven radish]

ikraamampampam

[restive river]

Cool

now let's do the particular solution

[restive river]

given the fact that you posted this, I am assuming you want to use undetermined coefficients and not variation of parameters

so, let's take a look at which type of function we have on the RHS

[nova ibex]

2e^-t - 3e^t

[restive river]

So what's our guessing function?

[nova ibex]

i was gonna use the trial Ce^-t - De^t

[restive river]

Ce^{-t} + De^t, I think.

[nova ibex]

why + ?

[restive river]

Because we don't care about the coefficient of the exponential function(s)

We are solving for it

[nova ibex]

ok

so i guess we take first and second derivtives now

[restive river]

Indeed

[nova ibex]

sec

is that right?

[restive river]

Yes

[nova ibex]

now sub?

[restive river]

Yep

[restive river]

Looks right to me

Now expand and combine like-terms

[nova ibex]

ok

am i meant to be doing something like this

combinig all C's and D's

[restive river]

exactly.

Except you made a mistake on the RHS

you should have 2e^{-t}

[nova ibex]

OOPS

is it meant to look something like this?

[restive river]

No

9De^t = -3e^t

-Ce^{-t} = 2e^{-t}

Now find D and C

[nova ibex]

OHHHH ok

[restive river]

Yes.

[nova ibex]

this is right i think

[devout snow]

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[keen moss]

I understand the limit law for

where n is a positive integer

but I'm not sure what to do when it's aa function

[unreal thunder]

Limit will go inside

$[\lim_{x\to a}f(x)]^{g(x)}$

[woven radish]

Dubleyou

[keen moss]

right

so then I after 0 raised to g(x)

but I don't know what g(x) is

[devout snow]

@keen moss Has your question been resolved?

[keen moss]

<@&286206848099549185>

[devout snow]

@keen moss Has your question been resolved?

[keen moss]

still need help

[winter brook]

well assuming g(x) is non-zero 0^g(x) should be 0

if g(x) = 0 then 0^0 = 1

uhhh

if u have multiple attempts, I'd say 0 tbh

[keen moss]

ok

.close

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[hybrid snow]

Okay so far I've gotten the jacobian and what xyz is equal to

[hybrid snow]

But like

The evaluation is ass because it just becomes $\int_1^2\int_1^3\int_1^4(abc)^{-\frac 14} \dd c \dd b \dd a$

[woven radish]

Umbraleviathan

[magic thicket]

I've never done triple integrals by hand, but doesn't this just have nice antiderivatives ? Like (abc)^-1/4 -> 4/3 (ab)^-1/4 c^3/4

[winter brook]

it should be fine as long as ur keeping track of them

[magic thicket]

Yeah exactly

[hybrid snow]

Crying

Crying inside

The rest of the worksheet are rigged problems

[lusty sapphire]

[restive river]

lol

[hybrid snow]

This would be so much better if the integrand was 2xyz

I'm just saying

Then it would be 6

Holy shit I got the answer

Horrible

Horrible horrible

.close

[devout snow]

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[restive river]

⚠️ please remember to type .coose to coose your channel

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[frozen horizon]

this is what i’ve done so far

idk where to go from here

also on the last row that should say q1

[devout snow]

@frozen horizon Has your question been resolved?

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@frozen horizon Has your question been resolved?

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[placid sandal]

How do I make a table for the limits when the left side of the number is the same as the limit?

[devout snow]

@placid sandal Has your question been resolved?

[devout snow]

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[vast finch]

Can someone help me with these I am confused on how to do them. I would greatly appreciate it.

[devout snow]

@vast finch Has your question been resolved?

[devout snow]

@vast finch Has your question been resolved?

[lusty sapphire]

@vast finch do you know volume formula for pyramid?

Start there

[devout snow]

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[exotic gazelle]

Hello, I need help with converting equations

[exotic gazelle]

I forgot how to convert to vector form as it states here

please help ive been stuck on the hw about transform matices for hours

please let me know if my question isnt clear

<@&286206848099549185>

[devout snow]

@exotic gazelle Has your question been resolved?

[exotic gazelle]

<@&286206848099549185> please guys i kinda need to turn this in

[devout snow]

@exotic gazelle Has your question been resolved?

[exotic gazelle]

no mr bot sir it has not

[jagged harbor]

salut

if your parametric form of a line is (x, y) = (at + u, bt + v), then the line is equivalently given by (x, y) = (akt + u, bkt + v) for any nonzero k

(why?)

[exotic gazelle]

ok.. so iwhat would i have to plug into those equations?

youre gonna have to spell it out for me ive been doing work all day im dead inside

[jagged harbor]

that's fair

if you accept that one non-integer solution is to say the blanks are 37/16 and 16/37 respectively, then you can multiply those numbers by anything you want to make it an integer

[exotic gazelle]

so by the lcm?

[jagged harbor]

that is what I did actually yeah lol

my silence was me working this out I hadn't done it in quite a bit

[exotic gazelle]

so both numbers would be 592?

[jagged harbor]

like 592 is final answer in both slots?

if so, you lose the slope of your line

[exotic gazelle]

nope

[jagged harbor]

I guess I was confused by your wording sorry, the lcm of 37 and 16 is just their product of 592, yeah

[exotic gazelle]

wait im dumb one sec

for some reason i thought 37/16 * 592 = 592

instead of 37^2

[jagged harbor]

ah ok yeah lol

[exotic gazelle]

nope

[jagged harbor]

also like, hold up, because I think that other guy was wrong, because surely your values would become like, 37^2 and 16^2, meaning your slope is (37/16)^2 or something

[exotic gazelle]

which isnt right

the slope is 37/15

16

[jagged harbor]

yeah

so I think you can just doctor it and just remove the squared bit

so says hindsight

[exotic gazelle]

so put 37/16 for both?

nope

[jagged harbor]

well you still wouldn't want that because 1) they ask for integers, and 2) your slope would still not be 37/16

also is this a linear algebra setting or just a school math thing?

[exotic gazelle]

linear algebra setting

[jagged harbor]

oh ok

[exotic gazelle]

on transform matrices

i need help on everything

[jagged harbor]

I'm more comfortable with writing lines of the form P + Vt where P is a point and V is your direction vector

then the coordinates just fall right out

but also, if V is a direction vector, then kV is also a direction vector for all nonzero k

[exotic gazelle]

ok...

so what no?

now/

[jagged harbor]

sorry I'm confusing myself; you can make a slope argument like we've been doing and try to fix it so that your entries are integers and the slope of your line is correctly 37/16, or you can try other things

personally I brute forced it by just letting x = -9 + at and y = -13 + bt and then solve for a,b so that you get an equation that's always true

[exotic gazelle]

these are parts a and b if that heps

[jagged harbor]

because I didn't immediately think about slopes lol

[exotic gazelle]

ok so i would just like

wait but how do i know what t is?

i mean it doesnt have a value

but i really dont understand how to get that

[jagged harbor]

t is just your parametric variable, it ranges over R so that every real value of t you plug in corresponds to a point on the line

also, dang, I really don't think I've ever heard of a projection onto a line before

that is sad

[exotic gazelle]

right... normally i just say haha x = t then just replace x with t for the y one

but i cant do that here so

idk

[jagged harbor]

this was my setup

[exotic gazelle]

ok got it

how do i solve for 2 variables in 1 equation though?

[jagged harbor]

I think this way isn't very sophisticated but it works lol

well that's the cool part: you can't! and indeed it makes sense that you're not able to obtain a unique solution, because your choice of u and v correspond to your direction vector of the line, which we've already said isn't unique since you can just scale it

so really you whittle it down into a nice equation and then just choose numbers that are nice

like... you can find one solution for some equation down the line fairly easily, then just multiply by something to both to make them both integers

I say fairly easily, but just by staring it down

[exotic gazelle]

somehow i feel like it shouldnt take that long...

idk

[jagged harbor]

I believe you're right, because yeah this really is not a sophisticated or cool way to go about this sorry lol

[exotic gazelle]

i might just ask the teacher for an extension

[jagged harbor]

oh no I mean it's still possible, it's just arguably not cool probably

[exotic gazelle]

ill try i guess

but wait i mean

at the end ill end up with like t = uv * some constant

what will i do then?

[jagged harbor]

you shouldn't have u * v, but you would have a multiple of u + a multiple of v

after distribution and killing constants, this is what I was left with

[exotic gazelle]

so then u would be 16 and v would 37

thats what i got

[jagged harbor]

yeah

and that solution isn't unique but they sure are integers that make it work

[exotic gazelle]

i dont think that worked though....

let me check and plug in numbers

did not work

[jagged harbor]

rats

[exotic gazelle]

so i said x = 1 and y = 5.5

which works

if x = 1 that means t = 5/8

37* 5/8 = 23.125

23.125 - 13 = 10.125

10.125 != 5.5

[jagged harbor]

I see

well that sucks, I'm not really seeing it yet

[jagged harbor]

74 - 32(5.5) + 250 = 74 - 176 + 250 = 148 != 0

so (1, 5.5) is not on the line

[exotic gazelle]

it is, plug those values into the orginal equation

[jagged harbor]

on m? I did

[exotic gazelle]

i plugged those in and got it

[jagged harbor]

m : 74x - 32y = -250
74(1) - 32(5.5) = -102 != -250

[exotic gazelle]

the equation 74x - 32y = -250 is true when x = 1 and y = 5.5?

WAIT

its - 1

im so dumb

-1, 5.5

[jagged harbor]

ahh ok that makes more sense

I still don't know why the machine isn't taking this vector though, it looks good to me

maybe it's falsely complaining that the vector for m is incorrect when it's really just m' being missing?

[exotic gazelle]

RIGHT?? im getting my roommate he took this course years ago he might be able to help

[exotic gazelle]

.close

[devout snow]

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[fast helm]

how do i solve 17c

[pastel pasture]

$\tan 2x + \frac{1}{\tan 3x} = 0$

[woven radish]

NEONPerseus

[fair minnow]

Try using the Cosine addition angle formula

It should simplify down nicely

[pastel pasture]

Cosine?

$\tan 2x \tan 3x = -1$

[woven radish]

NEONPerseus

[fair minnow]

after tan=sin/cos

[pastel pasture]

Ah that way

Yeah that's rule 0 of trig

[pastel pasture]

Although this should be it

If the product of the tangents is -1, it means the arguments add up to pi/2

[fair minnow]

that also works plenty lol

[fast helm]

did this but its wrong

only one answer

[fair minnow]

from sin2xsin3x + cos3xcos2x

using cos(a-b) = sinasinb + cosacosb

you have cos(3x-2x) = cos(x)

cos(x)=0

your trig expressions were correct i think you just simplified it down into cos wrong, there

[pastel pasture]

,w cot (3pi/2)

[woven radish]

Results provided by WolframAlpha

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

Requested by NEONPerseus#2128

[pastel pasture]

Yup you're good

[fast helm]

which line?

[fair minnow]

im not really sure what you tried to do underneath

[fast helm]

product to sum

but i see what you did

and its correct

[fair minnow]

i see what you're trying to do by making them all cos

[fast helm]

i couldve just simplfied it

[fair minnow]

i'll try and find your error using this if you're interested

[fast helm]

this whole chapter was product to sum and sum to product

[fair minnow]

but yeah, typically qs like this can be solved via just basic addition and double angle formulas

[fast helm]

so i didnt think of doing that

[fair minnow]

oh, that's completely fair

let me have a look at your sum and product method, then

[fast helm]

ye it just expands it more

alr thanks man

[fair minnow]

you made a mistake with -s and +s

i believe

let me double check what you wrote real quick

if you'll excuse the mspaint

this is right

cos(A-B) is either going to be -x and x depending on

[fast helm]

o

[fair minnow]

whether you make A 2x

or A 3x

what you've done is in your product sum of sinsin made A 2x

and in your product sum of coscos made A 3x

they have to be the same

thats why you have cos(-x) on one side, and cos(x) on one side

[fast helm]

but usually cos(-x)

just simplfies to cos(x)

doesnt it?

[fair minnow]

yeah since cos is symmetric

cos(x) = cos(-x) for all x

thats why it doesnt matter whether (a-b) is in any order

it'll be the same

though you've got a point there actually

let me read past that, i wonder how you didnt simplify that

[fast helm]

i just messed up that -5x

wtf

why did i change a negative to positive

[fast helm]

i see my mistake

[fair minnow]

ah if you see it thats fine

[fast helm]

ok thanks

.close

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[dusk sand]

I plugged in x into function and still got it wrong, even rounded up or down, accordingly. any ideas?

[pseudo basin]

rounded up or down, accordingly.

can you post the instructions in full?

this might be some stupid/bureaucratic input requirement that you're missing.

[dusk sand]

no instructions

[pseudo basin]

no instructions whatsoever?

then where is this a(n) coming from?

thin air?

[dusk sand]

but if you must have context

[pseudo basin]

yes, that'd be good. let's see.

,calc 95 + 13000/100

[woven radish]

Result:

225

[pseudo basin]

,calc 95 + 13000/200

[woven radish]

Result:

160

[pseudo basin]

,calc 95 + 13000/5000

[woven radish]

Result:

97.6

[pseudo basin]

,calc 95 + 13000/10000

[woven radish]

Result:

96.3

[pseudo basin]

ok, so all of your values are correct.

[dusk sand]

i rounded down and up

trust me

[pseudo basin]

what?

there would not even be any rounding here.

[dusk sand]

98, and 96

oh

[pseudo basin]

you aren't told to round to the nearest dollar here.

[dusk sand]

ohh

[pseudo basin]

are you told which of your 5 answer boxes have incorrect values?

you said it got rejected, or so much i gathered.

[dusk sand]

but you know whats strange

look at c)

well

nvm

when i got the answer wrong

it told me to graph it

and plug in the values for x there

[pseudo basin]

can you show the error message

[dusk sand]

sure

error: invalid. 1.quit, 2:goto. attempted to use a variable or function where it is not valid.

(95x+13000)/x

[pseudo basin]

that's what it said...?

[dusk sand]

thats what i graphed

[pseudo basin]

no, hold on, this isn't what i'm asking you.

i'm gonna go bureaucrat mode again.

[dusk sand]

ok

[pseudo basin]

you submitted these answers for part c. yes or no?

[dusk sand]

yes

[pseudo basin]

your answers for part c were rejected in part or in full. yes or no?

[dusk sand]

it accepted it

[pseudo basin]

THEN WHY ARE YOU TELLING US YOU GOT IT WRONG

[dusk sand]

previously

when i rounded

it was wrong

but a message popped up

[pseudo basin]

so you misled us......

[dusk sand]

explaining how to get the answer

[pseudo basin]

if you're gonna say you got something wrong,

[dusk sand]

misunderstanding

[pseudo basin]

then tell us WHAT it was that you got told is wrong

otherwise it's miscommunication

[dusk sand]

bad communication on my part

so to be clear i got it right but as i was saying when i got it wrong, i got a message that said how to solve it, and in that message, it said "graph it into calculator and find x values"

and i trolled into the calculator settings, pushed some buttons

and i got the error code for x>200

,graph (95x+13000)/x

[pseudo basin]

ok, so do you or do you not want to resolve the issue you're having with your calculator?

[dusk sand]

i want to know why my calculator gave me an error message

compared to when i solved for x manually

[pseudo basin]

okay, in that case:

show us your calculator.

and show us exactly what you are entering into it.

[dusk sand]

(95x+13000)/x

exactly like that

into y=

[pseudo basin]

SHOW don't tell.

you are having a technical issue.

[dusk sand]

then went "2nd" "trace" and "1:value", typed 200, and pressed enter

error 404

.close

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[dense steeple]

calcular= calculate

[pseudo basin]

are you sure "si" translates as "yes" and not "if" here

[haughty orchid]

x = sqrt(3)/2 + i/2

or sqrt(3)/2 - i/2

[quaint citrus]

It’s “if”

[dense steeple]

sorry, if

[devout snow]

@dense steeple Has your question been resolved?

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@dense steeple Has your question been resolved?

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[burnt thunder]

I tried to determine α so that ΣUn converges

I found that for α > 1 the serie converges

But in the solution by the Prof he found that it should be greater that -1 so it converges

What s wrong with my method

The Prof's method

<@&286206848099549185>

[devout snow]

@burnt thunder Has your question been resolved?

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@burnt thunder Has your question been resolved?

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[hollow stream]

I’m stuck idk

[hollow stream]

What’s the equation?

[jagged kestrel]

$x=v_0t+\frac{1}{2}at^2\
\text{and}\
v=v_0 + at$

gravity has an acceleration of 9.81 m/s^2 (negative in your case)

[woven radish]

Dogecode

[hollow stream]

I’m a bit confused

[hollow stream]

Which equation do I use?

What’s V0?

[jagged kestrel]

you need both to solve it

[hollow stream]

Oh

[jagged kestrel]

starting velocity (100m/s)

[hollow stream]

Is it a U or V?

And which one do I do firsthand?

[jagged kestrel]

v for velocity

x is the position

[hollow stream]

Sorry if I’m a bit slow

[jagged kestrel]

when it reaches its maximum height, v=0
For an instant in time it’s neither going up or down
which you’ll use in the v equation

[hollow stream]

Which position?

[jagged kestrel]

thats what you want to find

But you don’t have all the information to use that equation yet

think about what you need to find using the velocity equation

[hollow stream]

So v and v0 are different?

V=0?

[jagged kestrel]

at the exact moment it stops traveling upwards yes

[hollow stream]

So t=10?

0=100-10t

[jagged kestrel]

ye

then you can plug t (time) into the other equation to find x, the distance the bullet traveled

[hollow stream]

I got 1500

[jagged kestrel]

ye that looks right

[hollow stream]

Ah tu

Ty

[jagged kestrel]

specifically 1490.5 meters but I assume you rounded it

[hollow stream]

Yeah

We use 10 and gcse instead of 9.8

Appreciate your help

[jagged kestrel]

np

[hollow stream]

U mind if I ask another question?

Or 2 more

[jagged kestrel]

don’t a2a

though i might have to go

im sure someone else will help though

[hollow stream]

Ty

Is 3a correct and how do I do b?

5 confuses me as well

[inland vault]

The bullet question. If the acceleration is given by a(t) = -10 shouldnt the velocity be v(t) = -10t + 100 and position s(t) = -5t^2 + 100t thus max height s(10)= -5*100 + 1000 = 500 ?

[hollow stream]

Damn

Ur correct

I didn’t see that

[hollow stream]

Ty

Any clue on the others?

[devout snow]

@hollow stream Has your question been resolved?

[hollow stream]

Nope

[devout snow]

@hollow stream Has your question been resolved?

[hollow stream]

Nope

[devout snow]

@hollow stream Has your question been resolved?

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[zenith orchid]

hi

[zenith orchid]

so i have question

[restive river]

[zenith orchid]

f(f(x)) = log2(x)

solve for f(x)

oh never mind my parents are calling me to dinner and being annoying

um bye

[restive river]

.close

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[restive river]

how do i approach solving this

[devout snow]

@restive river Has your question been resolved?

[vast rain]

what's your proof so far?

[restive river]

i dont even know if i understand what the q is asking

[vast rain]

which things inside do you not understand

[restive river]

How to prove it arbitrarily and also [] refers to the image right

[vast rain]

yeah

[restive river]

where do i start

because A and B are just any sets

[vast rain]

A and B don't matter that much

you should probably be more concerned that S, T are any subsets of A

[restive river]

the powerset of A

[vast rain]

S, T elements of power set of A mean that S, T are subsets of A

[restive river]

right..

and its the intersection

which is logical and

im still sorta confused on where to start

[restive river]

where should i start

[devout snow]

@restive river Has your question been resolved?

[upper schooner]

Well this is an if and only if proof, so you have to show both ways

[restive river]

im so confused lol this type of math is painful

[upper schooner]

Maybe assume that $f$ is injective, and then assume you have some $y\in f[S] \cap f[T]$

[restive river]

i should give up lol

[upper schooner]

No, you shouldn't

Give it a go

You know the definition of being injective, right?

[restive river]

i have been at this for tooo long hehehe

yes

injective is like

everything in the domain maps to distinct elements

[woven radish]

@upper schooner

[upper schooner]

[prefer the letter y haha]

Anyways, you're in the intersection of these, so you know that y would have to be in both of those sets, right?

[restive river]

right

intersection is logical and

[upper schooner]

Yep yep, so you know that you have $y\in f[S]$ and $y\in f[T]$, what does that mean?

[woven radish]

@upper schooner

[restive river]

f[s] and f[t] are the images

[upper schooner]

Yep yep, so there should be some element of S that gets mapped to y, and similarly there should be an element of T that gets mapped to y, you agree?

[restive river]

ye

yes

[upper schooner]

Could you write that for me a tiny bit more explicitly for me, in terms of symbols?

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[warm sierra]

I did the questions but i am struggling with the highlighted ones

Can anyone help please

[wicked acorn]

I can

[warm sierra]

thanks

appreciate it

[wicked acorn]

I'll help for a few so you can get the concept, but I have to go soon

so I'll do what I can

[warm sierra]

okay

[wicked acorn]

So, our first one, $\left(-2\sqrt{7}\right)\cdot3\sqrt{7}$

[woven radish]

Starphile

[warm sierra]

yes

[wicked acorn]

Let's remove the parenthesis: $-2\sqrt{7}\cdot3\sqrt{7}$

[woven radish]

Starphile

[warm sierra]

yes..

[wicked acorn]

We can split this into 2 parts:

a) $-2\cdot3$

b) $\sqrt{7}\cdot\sqrt{7}$

[woven radish]

Starphile

[warm sierra]

hmm

okay

[wicked acorn]

Part "a" will have the normal numbers, and part "b" will have all of the roots

[warm sierra]

root 7 * root 7 is 7

[wicked acorn]

Correct

[warm sierra]

$-2\cdot3+7$

[woven radish]

Dhyan99

[wicked acorn]

Not quite

[warm sierra]

or is is *7

[wicked acorn]

Yes

[warm sierra]

$-2\cdot3\cdot7$

[woven radish]

Dhyan99

[wicked acorn]

It's best to solve part a, then part b, then multiply

but that works

[warm sierra]

hmm

never was taught that

thanks

[wicked acorn]

there's many ways to teach math

as for your second one

this will be funny

just pretend to laugh

What's 2*3?

[warm sierra]

6

[wicked acorn]

then take the root

sqrt(6)

done

boom

[warm sierra]

$\sqrt6$

[woven radish]

Dhyan99

[warm sierra]

wow

[wicked acorn]

easy

[warm sierra]

thats actually scarily easy

[wicked acorn]

yep

[warm sierra]

,calc -237

[woven radish]

Result:

-42

[wicked acorn]

now, $\sqrt{2}+\sqrt{3}$ is not the same as $\sqrt{5}$

[woven radish]

Starphile

[warm sierra]

not?

[wicked acorn]

Correct, they are not equal

[wicked acorn]

since square roots and multiplication are similar to each other, it only works for sqrt(x) * sqrt(y) and sqrt(x) / sqrt(y)

[warm sierra]

so then how would it be for addition

?

[wicked acorn]

for addition it doesn't simplify

sqrt(2) + sqrt(3) just is itself

simplified

very annoying

but

[warm sierra]

oh

thats very annoying

[wicked acorn]

$\sqrt{x}\cdot\sqrt{y}=\sqrt{x\cdot y}$

$\sqrt{x}\div\sqrt{y}=\sqrt{x\div y}$

[woven radish]

Starphile

[wicked acorn]

two helpful equations

x and y can be anything

[warm sierra]

this serber doesnt have bookmnark bot

sed

screenshotted it

[wicked acorn]

and you can go further:

$a\sqrt{x}\cdot b\sqrt{y}=\left(a\cdot b\right)\sqrt{x\cdot y}$

$a\sqrt{x}\div b\sqrt{y}=\left(a\div b\right)\sqrt{x\div y}$

[woven radish]

Starphile

[wicked acorn]

basically plug in a, b, x, and y

and you get your answer

[warm sierra]

so now $2\sqrt2\cdot\sqrt11$ the same rule will apply?

[woven radish]

Dhyan99

[wicked acorn]

Yep:
a=2
b=1
x=2
y=11

plug them in and boom

$\left(2\cdot1\right)\sqrt{2\cdot11}$

[woven radish]

Starphile

[wicked acorn]

just simplify

[warm sierra]

$2\sqrt22$

[woven radish]

Dhyan99

[wicked acorn]

yep

good work

[warm sierra]

and thats simplest?

no * 2

[wicked acorn]

Correct

but the *2 is on there

$\sqrt{22}*2$

[woven radish]

Starphile

[warm sierra]

okay

[wicked acorn]

yep

make sense?

[warm sierra]

yes

perfect sense now

[wicked acorn]

now, there is one that I didn't mention

Problem "3j"

[warm sierra]

a classic but wait.... theres more

[wicked acorn]

yep

it's easy(ish) though

so let's start basic:

$\left(\sqrt{x}\right)^{y}=\sqrt{\left(x^{y}\right)}$

[woven radish]

Starphile

[warm sierra]

$\left(2\sqrt2)\right..........

okay

[wicked acorn]

Example: $\left(\sqrt{2}\right)^{3}=\sqrt{\left(2^{3}\right)}=\sqrt{\left(8\right)}$

[woven radish]

Starphile

[warm sierra]

soo

2 sqrt(8) * 5 * sqrt(3)

and as you taught me

a) $2\cdot 5$

b) $\sqrt 8\cdot\sqrt 3$

[woven radish]

Dhyan99

[wicked acorn]

You are doing great, but before you go further

I led you into a trap

[wicked acorn]

see, that's true

but if it was something like $\left(5\sqrt{2}\right)^{3}$ it would be different

[woven radish]

Starphile

[wicked acorn]

that's where it gets harder-but-not-really

we just use another equation:

$\left(a\sqrt{x}\right)^{y}=\left(a^{y}\right)\sqrt{\left(x^{y}\right)}$

[woven radish]

Starphile

[wicked acorn]

For example, $\left(5\sqrt{2}\right)^{3}$

a = 5

x = 2

y = 3

So we get $\left(5\sqrt{2}\right)^{3}=\left(5^{3}\right)\sqrt{\left(2^{3}\right)}$

[woven radish]

Starphile

[warm sierra]

ok im back

[wicked acorn]

which is $125\sqrt{8}$

[woven radish]

Starphile

[warm sierra]

hmm

oh okay

so lemme chanw a bit

a) $8\cdot 5$

b) $\sqrt 8\cdot\sqrt 3$

[woven radish]

Dhyan99

[wicked acorn]

perfect

[warm sierra]

a) $40$

b) $\sqrt 24$

[woven radish]

Dhyan99

[wicked acorn]

yep

now, in this case

we can simplify a bit

[warm sierra]

$40$$\sqrt 24$

[woven radish]

Dhyan99

[wicked acorn]

what are some factors of 24?

[warm sierra]

$10$$\sqrt 6$

4

no

non

non on

[wicked acorn]

not quite, but closeish

[warm sierra]

$\sqrt 24*40$

[woven radish]

Dhyan99

[warm sierra]

960

$\sqrt (960)$

[woven radish]

Dhyan99

[wicked acorn]

ok slow down for a sec

[warm sierra]

okay

[wicked acorn]

yes that's correct, but that's not simplified

[wicked acorn]

that is a more simplified version

since we want in the form $a\sqrt{x}$

[woven radish]

Starphile

[wicked acorn]

so, some factors of 24:
1 * 24
2 * 12
3 * 8
4 * 6

right?

[warm sierra]

yes

[wicked acorn]

so, let's focus on that last one

we could write it as $\sqrt{4\cdot6}$

[woven radish]

Starphile

[warm sierra]

$40$$\sqrt{4\cdot 6} $

[woven radish]

Dhyan99

[wicked acorn]

yep, but we can do more

see how 4 is the same as 2^2?

[warm sierra]

$40$$\cdot2\cdot \sqrt 6 $

[woven radish]

Dhyan99

[wicked acorn]

yep

$\sqrt{24}=\sqrt{4\cdot6}=\sqrt{4}\cdot\sqrt{6}=2\cdot\sqrt{6}$

[woven radish]

Starphile

[warm sierra]

so $80$$\sqrt 6 $

[woven radish]

Dhyan99

[wicked acorn]

perfect

and we can't break 6 down since 2 * 3 doesn't give us anything useful

[warm sierra]

yep

[wicked acorn]

so it's simplified

so

key takeaways:

oops

[warm sierra]

oops

[wicked acorn]

$a\sqrt{x}\cdot b\sqrt{y}=\left(a\cdot b\right)\sqrt{x\cdot y}$

$a\sqrt{x}\div b\sqrt{y}=\left(a\div b\right)\sqrt{x\div y}$

$\left(a\sqrt{x}\right)^{y}=\left(a^{y}\right)\sqrt{\left(x^{y}\right)}$

Factor $\sqrt{x}$ to be $a\sqrt{y\cdot z}=a\sqrt{b^{2}\cdot z}=a\sqrt{b^{2}}\cdot\sqrt{z}=a\cdot b\cdot\sqrt{z}=ab\sqrt{z}$

Note: $y$ and $z$ are factors of $x$, meaning $y\cdot z=x$. Try to look for factors where $y$ is a perfect square (meaning it can be written as a^{2})

[warm sierra]

$a\sqrt{x}\cdot b\sqrt{y}=\left(a\cdot b\right)\sqrt{x\cdot y}$

$a\sqrt{x}\div b\sqrt{y}=\left(a\div b\right)\sqrt{x\div y}$

$\left(a\sqrt{x}\right)^{y}=\left(a^{y}\right)\sqrt{\left(x^{y}\right)}$

Factor $\sqrt{x}$ to be $a\sqrt{y\cdot z}=a\sqrt{b^{2}\cdot z}=a\sqrt{b^{2}}\cdot\sqrt{z}=a\cdot b\cdot\sqrt{z}=ab\sqrt{z}$

Note: $y$ and $z$ are factors of $x$, meaning $y\cdot z=x$. Try to look for factors where $y$ is a perfect square (meaning it can be written as a^{2})

[woven radish]

Dhyan99

$a\sqrt{x}\cdot b\sqrt{y}=\left(a\cdot b\right)\sqrt{x\cdot y}$

$a\sqrt{x}\div b\sqrt{y}=\left(a\div b\right)\sqrt{x\div y}$

$\left(a\sqrt{x}\right)^{y}=\left(a^{y}\right)\sqrt{\left(x^{y}\right)}$

Factor $\sqrt{x}$ to be $a\sqrt{y\cdot z}=a\sqrt{b^{2}\cdot z}=a\sqrt{b^{2}}\cdot\sqrt{z}=a\cdot b\cdot\sqrt{z}=ab\sqrt{z}$

Note: $y$ and $z$ are factors of $x$, meaning $y\cdot z=x$. Try to look for factors where $y$ is a perfect square (meaning it can be written as a^{2})
```Compilation error:```! Missing $ inserted.
<inserted text> 
                $
l.65 ...ct square (meaning it can be written as a^
                                                  {2})
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.```

[wicked acorn]

$a\sqrt{x}\cdot b\sqrt{y}=\left(a\cdot b\right)\sqrt{x\cdot y}$

$a\sqrt{x}\div b\sqrt{y}=\left(a\div b\right)\sqrt{x\div y}$

$\left(a\sqrt{x}\right)^{y}=\left(a^{y}\right)\sqrt{\left(x^{y}\right)}$

Factor $\sqrt{x}$ to be $a\sqrt{y\cdot z}=a\sqrt{b^{2}\cdot z}=a\sqrt{b^{2}}\cdot\sqrt{z}=a\cdot b\cdot\sqrt{z}=ab\sqrt{z}$

Note: $y$ and $z$ are factors of $x$, meaning $y\cdot z=x$. Try to look for factors where $y$ is a perfect square (meaning it can be written as b^{2})

[woven radish]

Starphile
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[wicked acorn]

nope

wait

one more edit

$a\sqrt{x}\cdot b\sqrt{y}=\left(a\cdot b\right)\sqrt{x\cdot y}$

$a\sqrt{x}\div b\sqrt{y}=\left(a\div b\right)\sqrt{x\div y}$

$\left(a\sqrt{x}\right)^{y}=\left(a^{y}\right)\sqrt{\left(x^{y}\right)}$

Factor $a\sqrt{x}$ to be $a\sqrt{y\cdot z}=a\sqrt{b^{2}\cdot z}=a\sqrt{b^{2}}\cdot\sqrt{z}=a\cdot b\cdot\sqrt{z}=ab\sqrt{z}$

Note: $y$ and $z$ are factors of $x$, meaning $y\cdot z=x$. Try to look for factors where $y$ is a perfect square (meaning it can be written as b^{2})

[woven radish]

Starphile
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[wicked acorn]

this VVVVVVVVVVVVVVVVVVVVVVVV

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

that was a lot to type

but there you go

[warm sierra]

sorry for the trouble

[wicked acorn]

nah its ok

[warm sierra]

ima save the link https://cdn.discordapp.com/attachments/903486480075354182/1078551770218909716/866423709467803659.png

[wicked acorn]

yep

anyways

i have to go

hope this helps!

[warm sierra]

thank you so so much

[wicked acorn]

yep!

[warm sierra]

this helped tons

ima spped through my hw now\

[wicked acorn]

good luck!

bye!

[warm sierra]

thanks, you too!

[wicked acorn]

!close

/close

[warm sierra]

!close

.close

[devout snow]

Channel closed

Closed by @warm sierra

Use .reopen if this was a mistake.

[wicked acorn]

whelp

[warm sierra]

byeee

[wicked acorn]

I'm smart I promise

byeee

[warm sierra]

[devout snow]

Available help channel!

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[dull egret]

Find the LCM of 12, 15 and 21 by the method of prime factorization.

[dull egret]

Can anyone help with this?

How to solve?

[restive river]

it will be good if u learn how to do it

[dull egret]

But I don't know

I'm confused

GCD AND LCM

[restive river]

do u know how to do prime factorisation

[dull egret]

Yes.

[restive river]

greatest common divisor and lowest common multiple

[dull egret]

Yes

[restive river]

whats their prime factorisation

[dull egret]

A metal memento has to be prepared by placing a solid sphere on a solid
cylinder as shown in the figure. Find quantity of the metal required to
prepare this memento, such that the radius of the cylinder is 6cm and its
height is 14cm and the radius of the sphere is 2.1cm. And also calculate
the cost of painting the surface of the sphere with golden colour at the
rate of 10 paise per cm2
.
6cm
14cm
2.1cm

This ?

[restive river]

so it is 2.1

or 21

[dull egret]

2.1

[restive river]

okk

so i think u should do one thing

convert them into millimeter

and than calculates its lcm

and than convert that in cm

[dull egret]

Ok?

Then?

[restive river]

u get ur ans?

isnt it

[dull egret]

But which formula to be used?

CSA of cylinder ?

[restive river]

show figure

[restive river]

i think volume

but will it full the cylinder

[dull egret]

Oh.

[devout snow]

@dull egret Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• 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.

[restive river]

If the vector field of electric charge is not a open simply connected ...because its not defined at origin ...how can we call it conservative ?