help-33

[chrome jacinth]

Okay sweet, so

https://media.discordapp.net/attachments/907022703230345237/1447876859886047322/2025-12-09_20_05_24-Untitled_Diagram_-_draw.io_-_Brave.png?ex=693937e7&is=6937e667&hm=a741308880a0df1c3e6464c9001950b383b396fb97a1d8bcadb28deb16400328&=&format=webp&quality=lossless&width=1590&height=455

Now let's go back to this problem.

Now I told you that the inequality will be in the form:
Starting Value < x < Ending Value

First of all, what is the "ending value" on the yellow part?

[still temple]

Infinity, nothing

[chrome jacinth]

Wait when I mean ending value, it refers to the right most bit

Like

[still temple]

ohh the arrow confused me LOL

[chrome jacinth]

Would you agree that 4 is like the 'ending value' of this line?

[still temple]

So it'd be 4

[chrome jacinth]

You're good 👍

Nice!

Now,

I said

Well, you said

That the starting value is actually infinity, it should be negative infinity because it is going to the left side.

[still temple]

okay yeah

[chrome jacinth]

So, how would you write it in this format?

The final inequality?

[still temple]

How do you write infinity

[chrome jacinth]

Oh you can just say "infinity" on the chat

I'll know what you mean :)

[still temple]

Okayy

So, -infinity < x < 4 I completly did that wrong didnt i LOL

[chrome jacinth]

Good! No that's exactly right

[still temple]

Oh awesomeee

[chrome jacinth]

Literally the starting value is -infinity, and the ending value is 4

So the answer is literally just that

(Maths is not supposed to be some giant leap. Usually the answers are pretty straight forward)

[still temple]

What about the right bit

[chrome jacinth]

Anyway

Wait before we go to the right bit

The yellow portion is

-infinity < x < 4

Now as you said, -infinity isn't really something a number can "stop at"

So what we can do is

We can just get rid of the -infinity

That is, the final inequality would just look like:
x < 4

[still temple]

ohh ok

[chrome jacinth]

And in a way, this kind of makes sense:
x < 4 is saying that x is a random number that is less than 4.

Well, we do actually see that in the image -

The line expands to everywhere before the point 4.

So yeah, you don't need to write infinities when doing inequalities (but you will need to for interval notation, but that's for another day).

Anyway.

Yeah

[still temple]

yeahh okay

[chrome jacinth]

https://media.discordapp.net/attachments/907022703230345237/1447876859886047322/2025-12-09_20_05_24-Untitled_Diagram_-_draw.io_-_Brave.png?ex=693937e7&is=6937e667&hm=a741308880a0df1c3e6464c9001950b383b396fb97a1d8bcadb28deb16400328&=&format=webp&quality=lossless&width=1590&height=455

How would you write the second interval?

I mean, the second line on the right?

Hint: What is the starting value, and what is the ending value?

[still temple]

I think it would be infinity < x < 5

[chrome jacinth]

Close! The starting value is not infinity :)

[still temple]

I thought it would be since its an arrow going on beyond

[chrome jacinth]

Yeah well the problem is,

The arrow is going to the right.

By the way, when I mean 'start' and 'end values' what I really should say is 'left' and 'right' values.

So the starting value is the leftmost point and the ending value is the right most value.

[still temple]

the start is the 5 or the one further to the right

[chrome jacinth]

The start is the one on the left.

[still temple]

is that because we are doing the right side now

[chrome jacinth]

Oh no the starting value was always the left one

[chrome jacinth]

Well technically yeah

[still temple]

So it'd be 5 < x < infinity?

[chrome jacinth]

Perfect!

[still temple]

Yipee

[chrome jacinth]

How do you simplify this inequality?

[still temple]

Oh gosh

No idea to be honest

[chrome jacinth]

Hint: Remember what I said here.

[still temple]

Oh we get rid of the infinity?

So it'd be 5 < x?

Or

[chrome jacinth]

Yep!

Literally just get rid of the infinity

So good!

What you end up with is these two inequalities

[still temple]

Would it be all together x < 4 and 5 < x?

[still temple]

So the top left one?

[chrome jacinth]

Not quite

Wait before you choose your answer

One thing further I will say

[chrome jacinth]

Dont use the word 'and' here

Use the word 'or'

[still temple]

okayy

[chrome jacinth]

The short reason is

You cant use 'and' here

Because you don't want both of these things to be true

As in

A number cant be less than 4 and bigger than 5

So instead, use the word 'or'.

It is possible a number is less than four or bigger than five

[still temple]

okayy

I dont actually get which one it would be

x < 4 or x > 5?

[chrome jacinth]

Yeah!

Because

What we had was

x < 4 or 5 < x

But that second inequality is just x > 5

[chrome jacinth]

Like you can swap everything around like an equation

I.e

You know how 2x = 4 is the same as 4 = 2x?

You can do the same thing with inequalities

5 < x is the same as x > 5

[still temple]

Uhhhh

i think

ye

ish

[chrome jacinth]

One more thing

You may find this helpsheet useful

It is sort of a 'summary' of the things we discussed

[chrome jacinth]

The common thing to note is that intervals always start on the left, and end on the right.

[still temple]

okay

[chrome jacinth]

That's why a is always on the left.

[still temple]

yeah

awesome okay

[marsh citrus]

@still temple Has your question been resolved?

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[dull spire]

how to solve this without using lhopital?

[dull spire]

limit x-->0

[stone fulcrum]

Use Taylor series expansion

[dull spire]

alright

thanks

.close

[marsh citrus]

Channel closed

Closed by @dull spire

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[limpid oxide]

no idea as to how i ought to even begin with this question, please help

[atomic ruin]

squeeze theorem?

[winged geode]

i think this may be squeeze theorem hinting

[atomic ruin]

try to find lim x->inf for the function on the left and right

[winged geode]

^

[atomic ruin]

if they are equal, by squeeze theorem lim x->inf of f(x) must be equal to the limits

[winged geode]

i don't think they'd put f(x) between two functions if it wasn't squeeze theorem and if the two functions didn't have the same limit

[limpid oxide]

lim x->infinity for the left = 5?

atleast that's what I got

[atomic ruin]

yes

and the right?

[winged geode]

i just checked

it's 5 for both

therefore it's 5 for the one in the middle as well by squeeze theorem

[limpid oxide]

also 5

is what I'm getting

[limpid oxide]

oh okay

alright thanks

[winged geode]

npp

[limpid oxide]

.close

[marsh citrus]

Channel closed

Closed by @limpid oxide

Use .reopen if this was a mistake.

[blissful kestrel]

5?

[serene bramble]

My guy the question's been answered

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
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[quick shell]

what have you tried?

[covert prism]

wdym

[quick shell]

exactly what I said. have you tried to solve the question, and if so, what have you tried?

[covert prism]

i've tried doing 4g+90=180

but i think that's wrong

[quick shell]

where are you getting that from

[quick shell]

for reference I'll add a point P

so you are saying that 4g + 90 = 180 because that's the sum of angles in triangle ABP... but aren't you forgetting a third angle down there?

regardless, I don't think it's necessary

[covert prism]

whats the third angle

[quick shell]

angle ABP?

you know, the one sitting at the bottom of the triangle

[covert prism]

yeah

[quick shell]

you've neglected to include it in your sum

and even if you did, you don't know what it is

so that route is kinda a no-go

[covert prism]

ok

[quick shell]

you can do this an easier way by tackling angle DCA and angle ACB instead

[covert prism]

alternate interior angles?

[quick shell]

that is, these two angles marked here

[quick shell]

hold on there. you gotta specify which pair(s)

can't just throw out terms and hope they'll stick

[covert prism]

ok

what now

[quick shell]

^

you can't just say "alternate interior angles". which two angles fit the bill?

[covert prism]

i don't really

get it

sorry

i'm tired

@quick shell

[quick shell]

if you want to specify a pair of angles as alternate interior angles, also say which pair you mean

(also you don't have to tag me. I'll respond if and when I'm able)

[covert prism]

A and C

[quick shell]

I accept angle A being labelled that way, but not angle C

there are three angles there, so you should probably specify which angle on C

[covert prism]

the red one

[quick shell]

correct

that would be angle DCA for your reference

[covert prism]

ok

[quick shell]

cool, so you've realized that angle DCA is an alternate interior angle partner to angle A

what about the blue angle (angle ACB)?

hint: look at lines AB and CB

[covert prism]

they're congruent

i see

[quick shell]

so you get it now?

[covert prism]

i just know that they're congruent

still don't know how to get it

[quick shell]

they = what?

which two angles?

[covert prism]

AB and CB

[quick shell]

ok the sides are congruent. so what does that mean for the blue angle?

hint: what kind of triangle has two sides of the same length? what angle property does it have?

[covert prism]

wdym by angle property

[quick shell]

answer the first question first

[covert prism]

ok

[quick shell]

thanks for spoiling the solution

I guess I'll let you take over then

[plain moat]

No

Do

[cobalt lion]

lmao bro coudn't wait

[covert prism]

hey man

you explain

you said the solution

[plain moat]

you see there are two sides of that triangle equal right?

[covert prism]

yeah

[plain moat]

Therefore it's an isosceles triangle

[covert prism]

yes

[plain moat]

If you know what that is

So this triangle has a special property where the angles opposite to equal sides are also equal

Angles opposite to equal sides. Remember

That means angle BAC = angle ACB

Easy?

[covert prism]

wdym by angles opposite to equal sides

[plain moat]

Take one of the two equal sides

[covert prism]

ok

[plain moat]

The angle opposite to it

Exactly opposite

[blissful kestrel]

Can u please resend the question 😅
I might help u

[covert prism]

^

[plain moat]

We got the answer dw

[blissful kestrel]

Oh oki

[odd agate]

given how Koyuki has already helped like a big chunk of the way and then prqt intercepted the rest, I think we have enough manpower

[plain moat]

you can also prove it with congruency

[blissful kestrel]

Okay someone already answered me chill

[covert prism]

can you illustrate which one is 4g and 2g

like

in the solution

[plain moat]

Ok

[covert prism]

draw where it is

[odd agate]

why not we have you try drawing it instead, and we can confirm what you drew

[covert prism]

how is lower red =4g?

[plain moat]

.

Isosceles triangle

angles opposite to equal sides

Are equal

[odd agate]

btw just a minor note: if a helper is already helping like quite a long way, try not to barge in with the direct solution straight away, esp. if no explanations are provided

[plain moat]

I didn't know all these rules, I've seen people millions of times interrupting

If that hurt u or anyone I'm sorry

in the end you learn what u see

[odd agate]

well for one, generally direct solutions are kinda frowned upon unless the helpee and helper are really going nowhere
and for another it kinda undermines the effort of the existing helper to try to get them to understand the topic by themselves

but you may continue here ofc

[covert prism]

okay i'm sorry for not understanding but what do you mean by opposite sides

like B and C are opposite?

[plain moat]

It's "angles opposite to sides"

The side which you see opposite of angle A

Is BC

Right?

Wait I'll draw

[covert prism]

ok

[plain moat]

See this triangle for example

The side opposite to angle C

Is AB

[covert prism]

ooh

so

C is = AB??

[plain moat]

Yeah

And Side opposite to angle B is AC

[covert prism]

ohhhh

i see it

[plain moat]

Therefore Angle B and Angle C are equal

For every isosceles triangle

[covert prism]

the base is always equal

for every isosceles?

[plain moat]

The angles

Angle B and C

[plain moat]

Same in this case

[covert prism]

then why is it 2g and 4g

[plain moat]

Forget about the 2g

See there are two angles = 4g

[covert prism]

yeah

B =AC?

[plain moat]

Those angles are equal

BC = BA

[covert prism]

ah yep

mb

[plain moat]

You get why that angle was 4g now?

And for the 2g angle
It's because
AB is parallel with CD

So that's why angle CDE = ABC

[covert prism]

ohhh

is it corresponding angles

[plain moat]

Yep

[covert prism]

icicic

[plain moat]

Now just use angle sum properly of triangle

[covert prism]

you couldve told me that in the first place lol

[plain moat]

mb

So 2g + 4g + 4g = 180

[plain moat]

Same question

[plain moat]

Just replaced 2g with 3g

[plain moat]

Yep

[covert prism]

so 3g+3g+3g=180

[plain moat]

Yep

g = 20

[covert prism]

thank u bro

[plain moat]

Ur welcome

[cobalt lion]

btw

[marsh citrus]

If you are done with this channel, please mark your problem as solved by typing .close

[covert prism]

can I ask 2 more questions

problems

i mean

sorry

this the first oen

[plain moat]

Btw sorry @quick shell

Oh

[cobalt lion]

yes

[quick shell]

just keep going atp.

[plain moat]

Sorry sorry sorry 😔😔😔

You're mad at me

[quick shell]

no apologies needed. my only objective is to see OP learn, so if you can do it, sure.

[plain moat]

😔👍🏻

[plain moat]

Spot the isosceles triangle

[covert prism]

here's some notes i made

i forgot to draw the angle for 3x

just imagine its between 3x and 12x

[plain moat]

This is the question?

[covert prism]

yes

find x and y

[plain moat]

Do you know what's linear pair?

[covert prism]

yea

[plain moat]

Where do u see it

You can get x easily from there

[covert prism]

3x+3x+12x

[plain moat]

Yea

[covert prism]

x=10

?

[plain moat]

Yeah

There's other linear pair with 5y if u see

[covert prism]

5y+5y=180???

[plain moat]

No

5y + angle APB = 180

[covert prism]

5y+3x=180?

[plain moat]

.

[plain moat]

No

[covert prism]

wdym by APB

the interior angles of APB?

[plain moat]

The angle C should be 5y

[plain moat]

That blue game

And if u do the linear pair property, you get that angle as 180-5y

If u ask how I got that

Assume that angle is z
So 5y + z = 180

So z = 180-5y

[covert prism]

hmm

so what is y

[plain moat]

Now just use angle sum property of triangle

[covert prism]

3x+5y-180-5y=180?

[plain moat]

3x + 5y + 180-5y = 180

Wait what

Is the question wrong or something

[covert prism]

idk

[plain moat]

I think it is

It's not possible

Did u make it on your own?

[covert prism]

no

it just gave that

[plain moat]

It's not possible

We are getting x = 0 and 10 at the same time

[covert prism]

there's a give up option

do I click it

[plain moat]

Yes

Im completely sure it's wrong

[plain moat]

Or ur labelling is wrong

[plain moat]

Yep

Your labeling is wrong

[plain moat]

Angle C should be 5y

[covert prism]

@plain moat

[plain moat]

Um

[covert prism]

so x =10

[plain moat]

How

[cobalt lion]

eh how's it 4y

[plain moat]

First thing

Spot the isosceles triangle

AC = AB

[covert prism]

can you explain how to get y

[plain moat]

Ok

Is that small angle 3x again?

Angle P

[covert prism]

angle p is not 3x

[plain moat]

Ok

[covert prism]

it looks like its 4y

but last time i was wrong

[plain moat]

Got it

[plain moat]

No

What can u say about angle C

Remember I told u about isosceles triangle properly

[covert prism]

c = 4y?

[plain moat]

Yep

[covert prism]

p=4y?

[plain moat]

Nop

[plain moat]

They are not parallel

P will be 90 degree

Another property

[covert prism]

wdyn

wdym

OHH

BISECTOR

[plain moat]

Kinda

Yeah

[covert prism]

6x+4y+4y=180??

@plain moat

sorry am in a rush

[plain moat]

6x?

3x + 4y + 90 = 180

We are talking about the smaller triangle APC

You'll get 3x + 4y = 180

[covert prism]

can u solve this?

[plain moat]

Now for the 2nd part
We will use the exterior angle property

[covert prism]

idt u can

[plain moat]

4y + 4y = 12x

[covert prism]

can u give me the equation for y

[plain moat]

Do you know how to solve linear equations in two variables

[covert prism]

i think so

systems of equations?

[plain moat]

3x + 4y = 180
And
8y = 12x

Find x and y

6x = 180
x = 30

[odd agate]

this is crossing into nosols territory, just a reminder

[plain moat]

Im gonna get a warning probaby

[plain moat]

He's in a rush

[covert prism]

is y = 15??

[odd agate]

still, I believe OP can attempt it himself

[indigo nest]

Doesn't matter, nosols still applies

[odd agate]

but again, guess you've said it so it stays

[plain moat]

Techanically finding y was the solution

[cobalt lion]

working on this?

[sacred idol]

you could also say triangle ACP is congruent to triangle ABP and find angle PAB
finding x and y would be easy from there by completing the remaining angles

[plain moat]

I did

He wants to know it deeper

[sacred idol]

no you did not

[plain moat]

Why like that

[plain moat]

..

[odd agate]

finding x directly leads to y and you're doing part of the calculation that he could have done himself
but whatever, you've sent it already

[sacred idol]

different qn though...

[plain moat]

Literally the similar question

[cobalt lion]

mm.. what they did goes similar tbh

[sacred idol]

yeah but not like he directly pointed out congruence in this question

[plain moat]

At least he learnt something about why it happens that way

[sacred idol]

idk man BISECTOR is kind of a weird way to put it

[plain moat]

yep they are bisectors and also in linear pair

I also mentioned it's a property of all isosceles triangles

So please 🙏🏻

[sacred idol]

okay..

[plain moat]

@covert prism dude close this channel, people are yapping here

He went away, his doubts are over

[cobalt lion]

bro went to sleep

[covert prism]

sorry gais gotta close it

.close

[cobalt lion]

he's back

[marsh citrus]

Channel closed

Closed by @covert prism

Use .reopen if this was a mistake.

[cobalt lion]

and gone

[plain moat]

phew

WHAT

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
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• Type the command .close to free the channel when you're done.
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[blissful pond]

There are 2 coins in a bin. When one of them is
flipped, it lands on heads with probability .6, and
when the other is flipped, it lands on heads with
probability .3. One of these coins is to be randomly
chosen and then flipped. Without knowing which
coin is chosen, you can bet any amount up to 10
dollars, and you then either win that amount if the
coin comes up heads or lose it if it comes up tails.
Suppose, however, that an insider is willing to sell
you, for an amount C, the information as to which
coin was selected. What is your expected payoff
if you buy this information?

Note that if you buy it and then bet x, you will end up either winning
x− C or−x− C (that is, losing x + C in the lat-
ter case). Also, for what values of C does it pay to
purchase the information?

[blissful pond]

<@&286206848099549185>

[odd agate]

!15m please.

[marsh citrus]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[blissful pond]

my question hasnt for 1 hour rn

i opened up again

[obtuse umbra]

what the hell is this paragraph

!status

[marsh citrus]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[obtuse umbra]

choose

[blissful pond]

idk where to begin

[blissful pond]

<@&286206848099549185>

[marsh citrus]

@blissful pond Has your question been resolved?

[blissful kestrel]

👋 hi

u there?

the probability of heads is .5*(.6)+.5(0.3)

which is .45

u need to calculate the expectation of the bet(win/loss)

if u bet x( anything between 0 and 10)

u will recieve x with a probability of .45

and u will lose x with a probability of .55

so x(.45)-x(.55)

=(-0.1)*x

@gilded ice

this is without buying info

[cobalt lion]

hmm.. and -C

[blissful kestrel]

that we will come in with info case

with info

case 1

u get the coin with head probability 0.6

so the tail probability would be 0.4

expectation is x*(0.6-0.4)

= 0.2*x

it will be optimal if u bet x=10

ur payoff would be 2-C

ad do the same thing with case 2 the coin with .3 probab of tail

and u will find the best values for each case and optimal value of C for u

[blissful pond]

thank u brotha

.close

[marsh citrus]

Channel closed

Closed by @blissful pond

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[fossil oasis]

Find the volume of the solid that results when the region
enclosed by the given curves is revolved about the x-axis.

[marsh citrus]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[fossil oasis]

,w integrate pi * e^(2y) from 0 to 1 w.r.t y

[elfin berry]

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[fossil oasis]

idk if this is correct

[wanton slate]

Why wouldn't it be

[fossil oasis]

well, the question asks me to revolve it around x axis

and im doing the integration wrt y

[gloomy merlin]

I dont think it is

[fossil oasis]

the answer is correct but the method is not

i must integrate wrt x

[wanton slate]

Oh mb mb i thought you were saying if the result given by wolfram alpha was correct or not

[gloomy merlin]

I can't see how the answer is correct, either? I believe it should be 2pi, but maybe I could be mistaken. What makes you sure of your answer?

[fossil oasis]

what method did you use to get 2pi

[gloomy merlin]

Shell

,w integrate 2piye^y from 0 to 1

[elfin berry]

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Requested by lexqa

[wanton slate]

It's this region right

[fossil oasis]

okay but, how did you identify that this was a shell problem?

[fossil oasis]

why cant i just integrate from pi * e^ 2y from 0 to 1 in this

it makes sense tho

[wanton slate]

The question asks to revolve that around x axis

[gloomy merlin]

Well if you used washer youd need to split your integral

[fossil oasis]

no but @gloomy merlin says that its incorrect, even if i do it wrt y

[wanton slate]

This seems to give the volume found by revolving the region around y axis

[fossil oasis]

isnt that wat we want

[wanton slate]

Nah

Your question asks x axis

[gloomy merlin]

,, V = \int_0^1 (\t{cylinder})\dd x+ \int_1^e(\t{washer})\dd x

[gloomy merlin]

Because the bottom boundary changes

[fossil oasis]

can you explain why we cant do what i did

[fossil oasis]

this

[gloomy merlin]

Well its what Ishmam said

You revolved it around the wrong axis

Disks are always prependicular to the axis of rotation

[fossil oasis]

cant i use washer then

[gloomy merlin]

You can

[gloomy merlin]

But this happens

[fossil oasis]

its gonna be 1-lnx ^ 2

why is there still a cylinder there

[fossil oasis]

alright i get it now

but i am more comfortable doing it with washer

first i will do from 0 to 1

[gloomy merlin]

Because it's a part of the shape? You cant hust ignore it and focus on the washer

[fossil oasis]

wait, that woul involve integrating lnx squared

[gloomy merlin]

You gotta ibp it

Thats why washer is bery much so less than ideal here

Lol

[fossil oasis]

what abt shelll

[gloomy merlin]

Thats what I did above

[fossil oasis]

what would be the integral in that case

[gloomy merlin]

[gloomy merlin]

This

[fossil oasis]

so you integrate wrt y?

[gloomy merlin]

Yes

[fossil oasis]

is shell method kinda inverted

[gloomy merlin]

Wdym

[fossil oasis]

the question asks for x axis

but we're doin dy

[gloomy merlin]

But you can switch that easily

[fossil oasis]

but you are integrating wrt y

waaat

[gloomy merlin]

Okay maybe saying that wasnt helpful

[fossil oasis]

lmao

[gloomy merlin]

Yeah which is why I integrated with respect to y as well

[gloomy merlin]

Oh I see what youre asking now

[fossil oasis]

wat

[gloomy merlin]

But yeah basically if you are rotating around the y axis you integrate with respect to x in shell and vice versa

[fossil oasis]

thats weir

[gloomy merlin]

Weirder that you understand washer but not shell as thats usually the "harder" one

[fossil oasis]

shell is un intuitive

ik washer and disk and am comfortable wid it

also kno shell but its kinda weird

[gloomy merlin]

Okay well

Do you want me to walk you through how I set up that intehral or do you get it

[fossil oasis]

how can i tell if this is the situation to use a shell instead of washer?

can all shell problems be done using washers

[gloomy merlin]

Both are identical

You get the same result

[gloomy merlin]

Its about which variable is easier tk integrate across

[fossil oasis]

like in this one

i have to ibp lnx ^ 2 if i use washer

[gloomy merlin]

Washer requires you to integrate over x here when rotating around the x axis

Problem is: boundaries of the function change as you move along thr x axis! You'd need to consider two different integrals

On the other hand, shells require you to integrate over y when rotating around x. This is good here because the y boundaries are static between 0 and 1

[fossil oasis]

alr i messed up

the question is abt y axis

[gloomy merlin]

Yeah

Okay

Well

[fossil oasis]

can you tell me what do you mean by boundaries of the function change as you move along thr x axis

[gloomy merlin]

Guess the prior conversation is pointless

[fossil oasis]

learning new stuff is never pointless for me

[gloomy merlin]

Like

[gloomy merlin]

Look at the lower boundary of the shaded blue area

From x = 0 to x = 1 its just the x axis isnt it?

[fossil oasis]

oh

ahh k

[gloomy merlin]

But suddenly at x = 1, you switch to the curve

[fossil oasis]

gothca

[gloomy merlin]

Yeppie

[fossil oasis]

alr what if we integrate the shell, wrt x?

what region would that give us

[gloomy merlin]

Thatd give u the volume if the region was rotated around the y axis

Which should match what u got

The first time

[fossil oasis]

if i am revolving the shell around the x axis i integrate 2pi y f(y) dy
and i the shell is around y axis then i do 2pix f(x) dx

is that righ

[gloomy merlin]

Ye

[fossil oasis]

alright tx

ty

.close

[marsh citrus]

Channel closed

Closed by @fossil oasis

Use .reopen if this was a mistake.

[gloomy merlin]

Well

Just to be clear its not always x or y

[fossil oasis]

wat

[gloomy merlin]

Its a function of the height

Like

[fossil oasis]

aight ill come back when i reach the shell questions

[gloomy merlin]

Lol ok

[fossil oasis]

im speedrunning calc js a min

[gloomy merlin]

Yeah uh

Good luck with that

[marsh citrus]

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[elfin badger]

Can someone help me Integrate this

[ionic ferry]

it's pretty direct

Do you know the integral of x^n

[stoic saddle]

do you know the integral of x^n

oh sniped

[ionic ferry]

jinx

[pale dagger]

Ones on phone, the other on latop

[ionic ferry]

what?

[pale dagger]

First letter of your sentence

Lets not talk abt that here now

[cobalt lion]

Twist it was tablet

[elfin badger]

Yeah

X^n-1/n-1

[pale dagger]

... no.

Thats not its intefration

[elfin badger]

Oops

I meant that

[pale dagger]

Even that isnt

The integral of x^n

Youre mixing up intdegration and derivation

[ionic ferry]

Sorry I don't get this

[elfin badger]

I meant x^n+1/n+1

[pale dagger]

sure
Anyways

Now u integrate the individual terms

And add em up

[elfin badger]

So

[dim forge]

i also dont get it, is this ragebaiting or sum?

[pale dagger]

On phone, whenever you write a sentence the first letter is capitalised,
This is not the case with laptop/pc users

[elfin badger]

2x^6/6

[pale dagger]

Yep

Continue

[ionic ferry]

I see

[elfin badger]

Then 4x-2/-2

[dim forge]

omg waht the hail

[pale dagger]

Yes

[elfin badger]

I'm only stuck on the second term

Oh is that it

[pale dagger]

Youre correct though!

Keep going

[elfin badger]

,w integrate -1/(4x^3)

Hmm

[elfin berry]

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Requested by zarahx123

[pale dagger]

I gotta ask(dont take it offensivsly), are you an undergrad?

[elfin badger]

Most certainly not

[pale dagger]

Your role says you do..

[elfin badger]

I meant am

Mb

Anyways

Why is this different to my answer?

[pale dagger]

....

Its not

?

[elfin badger]

Um

[elfin badger]

.

[pale dagger]

Write it properly

4 is on numerator, x - 2

These are all typing errors

[elfin badger]

4x^-2/-2

=

[pale dagger]

The question dictates 4 on the denominator....

[elfin badger]

-2x^-2

[pale dagger]

Read the question pleasd

[dim forge]

isnt this it

[pale dagger]

!noans

[marsh citrus]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[elfin badger]

It is

BUT

I'm trying to understand why

[marsh citrus]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[pale dagger]

My guy

Please read the question

[elfin badger]

OK

[pale dagger]

4 is on the denominator yet somehow magically you're putting on the numerator.

[elfin badger]

So it's -4x^-3

?

[pale dagger]

1/(4x^3)

Integrate this

[dim forge]

it is (1/4) x^-3

[elfin badger]

Ok

[pale dagger]

<@&268886789983436800> can you check this channels deleted messages?

[quiet anvil]

sure

[pale dagger]

Pretty sure someone sent an nsfw post

[cobalt lion]

Eh why

[dim forge]

i m sur, something sus came through

[elfin badger]

1/4*1/x^3

[dim forge]

abuout omni man

[pale dagger]

Yes

Integrate it

[pale dagger]

@gaunt gulch it was this guy

[quiet anvil]

I found it.

[delicate prairie]

b&

[elfin badger]

x^-3 > x^-2/-2

[cobalt lion]

Ban evader

[pale dagger]

Yes

Continue

Now multiply 1/4 with this

[pale dagger]

[elfin badger]

Also maths is not my major so yes I am doing a undergraduate but not in maths

[pale dagger]

But if you are taking a science degree, it should be expected of you to know this kuch integration
(Again, not tryna offend you)

[elfin badger]

I know integration

[pale dagger]

Nice

Doesnt that now look familiar to wolfram alphas answer

Just integrate tje 3rd term now

[elfin badger]

I only needed help on the second term

[pale dagger]

Alrighty then

!done

[marsh citrus]

If you are done with this channel, please mark your problem as solved by typing .close

[elfin badger]

I'm assuming your a maths major

[pale dagger]

Im not : )

[elfin badger]

Then

[pale dagger]

The role doesnt imply you have to be a math major

Just means you study ug math

And that I do

[elfin badger]

Okay

[pale dagger]

Part of my branch's curriculum

[elfin badger]

Thanks

[pale dagger]

[elfin badger]

.close

[marsh citrus]

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[marsh citrus]

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[wheat yew]

for this question, in the answer key, they told to take substitution as x= pi/2 - h

why?!and how do we figure out what exactly to substitute?

[gloomy merlin]

What is the question asking?

[wheat yew]

Find the value of k

[gloomy merlin]

What information about f are you given? Is f continuous?

[void elm]

it says that f is continuous at x = pi/2

[wheat yew]

yes it is continous at x= pi/2

[void elm]

you need the two functions to be equal at pi/2 for continuity

[wheat yew]

ehh

ohhh

so how do we get that

for LHL why do we take substitution as x= Pi/2 - h

[void elm]

well, we need to have kcos(x)/(pi - 2x) = 3 at x = pi/2 for f(x) to be continuous, but both cos(x) and pi - 2x are equal to 0 at that point, so our first step must be to compute the limit cos(x)/(pi - 2x) as x approaches pi/2

"limit of cos(x)/(pi - 2x) as x approaches pi/2" is the same as "limit of cos(pi/2 - h)/(pi - 2(pi/2 - h)) as h approaches 0"

so that's where the motivation for taking x = pi/2 - h comes from

once you have the value for that limit, you can easily find what k is

[wheat yew]

Okayyy

lemm e try

[marsh citrus]

@wheat yew Has your question been resolved?

[marsh citrus]

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[vale ermine]

need clue for number b

[vale ermine]

<@&286206848099549185>

[torpid swallow]

what i can think is divide by ZX on both the sides

then you seem to get some similarility proportion, maybe you can work that out

also what do the hints mean?

[marsh citrus]

@vale ermine Has your question been resolved?

[dreamy steppe]

just add point W' as projection of Q on ZX

[marsh citrus]

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[still temple]

can i get a hint for this? im stuck

[plush elk]

Write AE in terms of AC and AB

[amber birch]

it's easier if you let AC = x and AB = y

[plush elk]

And write AQ in terms of AC and AB

[amber birch]

then AE = AC + 2/5 * CB and now you can get CB in terms of x, y

AQ is c * AE by definition (scalar multiple)

then you'll also need to consider CQ = k * CD for some constant k

[plush elk]

||AE=(3/5)AC+(2/5)AB||, ||AQ=(1/2)AC+(1/2)AD=(1/2)AC+(1/3)AB||

[oak oxide]

There's a powerful formula to solve problems with collinear points, but w/o it you can express every other vectors in term of 2 vectors

[still temple]

i think wrting AQ in terms of AC and AB and AE in terms of AC and AB will give the answer

[amber birch]

solve the simultaneous equations

[still temple]

lemme try

yo i got the answer

but how do i know what to do

[amber birch]

the idea is always to find two equations for AQ

one equation is AQ = c * AE

[still temple]

like the expression of what its asking for?

[amber birch]

the other comes from approaching Q from CQ

[amber birch]

do you not understand that you have to solve simultaneous equations in two variables?

[still temple]

wdym

i just didnt know what to do cos it looked hella complicated

anyways thx

.close

[marsh citrus]

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[amber birch]

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

watch these worked examples

[still temple]

bruh i know how to do ts

[marsh citrus]

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[gaunt lake]

Hi

[gaunt lake]

Oop wrong channel

[sinful crest]

bro what

[gaunt lake]

Uhh i thought this was discussy TwT

.close

[marsh citrus]

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[marsh citrus]

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[oak oxide]

\begin{cases}
x^2 + xy +y^2 = 9 \
y^2 + yz + z^2 =16 \
x^2 + xz + x^2 =25 \
\end{cases}
With out solving the above system of equations, Find $ xy+yz+xz $

[elfin berry]

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

[oak oxide]

okay I have no idea what's wrong with my LateX

[cobalt lion]

we get it dw

[gloomy merlin]

[
\begin{cases}
x^2 + xy +y^2 = 9 \
y^2 + yz + z^2 =16 \
x^2 + xz + x^2 =25 \
\end{cases}
]
With out solving the above system of equations, Find $xy+yz+xz$

[oak oxide]

I have tried complete the square , add the first 2 and subtract the third

[oak oxide]

But it didn't go anywhere

[proper wagon]

It is $x^2+xz+x^2$ and not $x^2+xz+z^2$? Just asking

[elfin berry]

Adhi

[oak oxide]

oh

[chrome jacinth]

Hi! Here's a hint: You should think about the question geometrically.

[proper wagon]

The last equation

[oak oxide]

lmao I meant x^2 + zx + z^2

[proper wagon]

yeah

[oak oxide]

Typo mb

[oak oxide]

Have thought about that didn't know what to do tho

[chrome jacinth]

||Consider what formula x^2 + xz + z^2 = 25 represents if you were to link it to geometry.||

Maybe if I rewrite it this way

||9 = x^2 + y^2 - 2xy(-1/2)||

[cobalt lion]

*9

[gloomy merlin]

Triangles

[chrome jacinth]

Oh whoops

Yes

[gloomy merlin]

Good hint

[chrome jacinth]

25 not 9

I mean

9 not 25.

[oak oxide]

Got it

.close

[marsh citrus]

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[oak oxide]

Thanks y'all

[marsh citrus]

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[echo scaffold]

I don’t understand how my teacher was able to solve for the a value ( the 2 ) without any point to plug in

[echo scaffold]

And how she was able to know to add ( x+2) to the numerator if that is not given information

This is all I have right now

[jagged relic]

The 2 comes from the horizontal asymptote

And it does say that the (x+2) factor can vary

[echo scaffold]

Huh

But the horizontal asymph don’t come from the factors

It comes from the Degr tee

Degree

I don’t understand how I am supposed to know that without the answer key

[jagged relic]

Not sure what you mean

[echo scaffold]

My teacher did not teach us this she was not here so I’m confused

[jagged relic]

,, y = \frac{\textcolor{red}{2}(x\textcolor{blue}{-3})(x\textcolor{blue}{+2})}{(x\textcolor{blue}{-4})(x\textcolor{blue}{+1})}

[echo scaffold]

I am not sure how I would know to put a two or any point if it is not in the given information on a test without an answer key

[elfin berry]

Nel

[jagged relic]

When you take the limit at -inf or +inf, the blue parts become insignificant

[pseudo flax]

horizontal asymptote is the value the function approaches as the x values tend to infinity or negative infinity

[jagged relic]

All you're left with is 2 x^2/x^2 = 2

(which is the red factor)

[echo scaffold]

I’m really confused sorry

I don’t really undestand what you mean

[echo scaffold]

Yea I know that but we are not given any pictures or points to help determine the value of it

And I cant plug in points because I don’t have a complete equation I only have one intercept on the graph

[blissful pond]

,rcw

[echo scaffold]

So how would I know if the infinite asymptote on the rigjt is above or below the y axis ish.

[blissful pond]

eh

[echo scaffold]

Yea we are given the horizontal asymph but no information to know where the line is

And I don’t know how I would know it has to be -2 or below

[jagged relic]

Wdym "where the line is"

[echo scaffold]

Like the intimate asymph line curve

[jagged relic]

It's a horizontal asymptote

[echo scaffold]

I don’t have a complete equation to know anymore points

[jagged relic]

A horizontal line that corresponds to the value 2

Of course it's the line y = 2

[echo scaffold]

I know that but there are also the curved lines

Not the dotted lines

The red lines

[jagged relic]

The red curve is h

That's what you're supposed to find

The asymptotes are given to you

[echo scaffold]

Yea but I cant find any more points on the line because I don’t have a complete equation

If I had a complete equation I would plug in -2,-3,-4, etc to know the line

[jagged relic]

I'm having a hard time understanding what you think the exercises is about

It's asking for a rational function with some properties

There aren't enough properties to make the answer unique, but you can still give an answer

[echo scaffold]

Sorry I’m just confused cus we where taught this lesson

And I don’t understand how we know there is an x intercept at any value below and including -2

It seems like is a guess and hope it is rigjt

Why cant the x intercept be at 1.5?

[jagged relic]

It does not include -2

[jagged relic]

.

[echo scaffold]

But there’s a point at (-2,0)

Yea but I don’t know how are expected to know there is a x interpet and where it should be

And I just don’t know how I would know on a test if I have to make up an x intercept, or a point, or a y intercept

[jagged relic]

The only one you know is (3,0)

That's given to you from h(3) = 0

The other one, you can choose as long as the other properties hold

Example: https://www.desmos.com/calculator/sipowoxr6v

As long as b > 1, that a valid formula for h(x)

[echo scaffold]

Ugh I hate that tbh I wish there was just a concrete answer

[jagged relic]

Note that I added an x-intercept at 1.5 but that's completely arbitrary

[echo scaffold]

idk why my teacher thought it was a good idea to give us a lesson packet without being there to teach the lesson 😭

Also jf if I had another set of info that included a hole disconunity would I plug in the x value of the hole and set it to the y value to find the a value

[jagged relic]

For a removable discontinuity (a hole) at x = d, you would just add (x-d) to both the numerator and the denominator

[echo scaffold]

Yea but we also have to find an a vlue

Value

So in this one 12 and idk how they got 12

And for another one the sub told me to plug in the hole value

[jagged relic]

You just solve the limit

[echo scaffold]

So in this case I would set the equation to 2 and plug in -1 go x

[echo scaffold]

How do you solve a unit?

[jagged relic]

$p(x) = \frac{a(x-1)}{(x+3)(x-5)}$, solve $p(-1) = 2$

[elfin berry]

Nel

[echo scaffold]

But I don’t get 12

I get six

[jagged relic]

,w x(-1-1)/((-1+3)(-1-5)) = 2

[elfin berry]

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[jagged relic]

You made a mistake I guess

[echo scaffold]

This is how I did it yesterday

[jagged relic]

,rccw

[jagged relic]

... that's not the same question

[echo scaffold]

Yea I know but I am saying I used the same process yesterday and it worked

[echo scaffold]

Why is there an extra x ? Is that a

Ok now I some how have -12

This happened yesterday also I orginally got the - version of the right answer

I think I maybe found the issue

[jagged relic]

Yes, for WA to understand what to solve for

[echo scaffold]

What’s WA?

[jagged relic]

Wolfram Alpha

[echo scaffold]

ohh

[jagged relic]

That's correct (though you shouldn't really say f(-2) since that's undefined)

[echo scaffold]

When we use the equation to find points on the graph we use the reduce version right? So in this case we would take out the factor (x+1) in the numerator and denominator

[jagged relic]

Yes, you remove the discontinuity

since it's a removable discontinuity

In other words you plug the hole

[echo scaffold]

Waittt that’s a cool way of putting it

[jagged relic]

It's no longer the same function though, so be careful how you write it

[echo scaffold]

kk is it likely supposed to be another letter instead of f . Is usually our teacher doesn’t care about that kind of stuff

[jagged relic]

You can use another letter, or you can write the limit each time

[marsh citrus]

@echo scaffold Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[marsh citrus]

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[junior owl]

what ex2 second question means

[junior owl]

what are the characteristics of the vector velocity when t1=1s

[plain moat]

Dude we need full translation

[stoic saddle]

i think it isn't even a matter of "translation" so much as "french math terminology doesnt translate well and we also need to know WTF is meant by characteristics of a vector"

[junior owl]

yeah thats what am asking

[stoic saddle]

to help everyone else not break their eyes at the combination of poor typesetting and low resolution, i'm going to transcribe the problem

An object M moves in a rectangular coordinate system. Its acceleration vector is constant and equal to a = 8j.
At time t=0, M goes through the point (4, 7) with velocity v_0 = -3i + 3j.

1. Find the equations of motion of the object (i.e. its x and y coordinates as functions of t).
2. Give the characteristics(???) of the velocity vector v_1 at time t = 1 s.

[plain moat]

How do u write so fast

[junior owl]

should i ask chatgpt about the characteristics

[plain moat]

Maybe characteristics of vector means the components along x y and z axis

[junior owl]

only x nd y

[stoic saddle]

90 wpm, idk.

[stoic saddle]

you can probably ask it to explain what "caractéristiques d'un vecteur" is supposed to mean and/or post a text version of the problem in original french

[night relic]

i must admit this is a guess, but usually we want to know the magnitude and direction in physics

[junior owl]

what original french

[night relic]

and if they wanted components they would have said "composants du vecteur", no?

[plain moat]

What else could characteristic possibly mean