help-10

[misty magnet]

because the power of x^5 is greater than or equal to this power of 3x^4 + 5x^2 + 2333.

x^5 is greater than x^4 and x^2

idk if thats a shit answer but

[shadow dagger]

as in i'd tell them that

since x is bigger than 10, x^5 has to be bigger than 10x^4

and since x^2 is bigger than 100, 7x^4 is bigger than 700x^2

and since x^2 is still bigger than 100, 695x^2 is bigger than 69500

[misty magnet]

see that makes sense

[shadow dagger]

and then you just have to write this up formally

[misty magnet]

but i don't know what language i need to use for thus

that's my main issue

[shadow dagger]

just write it

[misty magnet]

like i agree fundamentally with what you're saying

but how do i write this in the proof syntax

what definitions can i use to help me articulate this

[shadow dagger]

just don't worry about it?

[misty magnet]

idk my professor said it has to be written in the proof syntax

so that's the frustrating part

also i'm working off of these definitions

and although they help sometimes

they feel lacking

[shadow dagger]

like a proof is not "i'll write down a list of n definitions and then use random symbols no one understands to come to a conclusion"

[shadow dagger]

your just turning ur watertight argument here into something more readable by mathematicians

so i'd say

[misty magnet]

but then why does my professor want me to use all this syntax to describe these proofs

😦

[shadow dagger]

Let $x \geq 10$. Then
\begin{align*}
x^5 &\geq 10x^4 \
&= 3x^4 + 7x^4 \
&\geq 3x^4 + 700x^2 \
&= 3x^4 + 5x^2 + 695x^2 \
&\geq 3x^4 + 5x^2 + 69500 \
&\geq 3x^4 + 5x^2 + 2333
\end{align*}

[misty magnet]

wait where did 7 come from

ugh i'm losing it

[shadow dagger]

ok idk how to format this correctly in latex bot

[shadow dagger]

i think ur probably misunderstanding ur professor

[misty magnet]

potentially

i feel stupid

i don't know why it makes sense when i see it but then i can't write it

[shadow dagger]

that would be sufficient as a proof

i've written it up by hand cus idk how to make latex look nice

[warm shale]

LY

[misty magnet]

okay nice thank you

so

you split 10x^4 into it's two parts

[shadow dagger]

yes

[misty magnet]

and then you further split up 7x^4 to be 700^2

[shadow dagger]

so often when we first have a problem we first try to figure out how you solve it/how to prove it

[misty magnet]

yeah

[shadow dagger]

then once you've found ur main argument you then want to convert it into a proof

you might use some 'backwards-logic' when you try to figure out how ur meant to solve it (happens a lot with inequalities)

but a proof almost always reads forwards

[misty magnet]

how did you get 695 if i can ask

[shadow dagger]

we wanted a 5x^2

[misty magnet]

i know i'm learning slowly so please be patient with me but

right

okay i remember now

[shadow dagger]

so split the 700x^2 into 5x^2 + 695x^2

[misty magnet]

ah i got it

so you just purely worked backwards

you just took the 10x^4 statement and kept splitting it

showing that it's just smaller than x^5 the entire time

do i have that right?

[shadow dagger]

ig you could see it that way?

but ultimately however you see how to solve the problem first you then just write it up in the most logical way

[misty magnet]

ugh

is proof writing always hard when starting

because this fucking sucks

[shadow dagger]

yeah so like with the qs here, once u've figured out what y has to be, i'd start by saying "fix x, then let y = whatever", and show the relation is satisfied

[shadow dagger]

i don't think it's meant to be

solving the problem should be the hard part, not turning that into a proof

[misty magnet]

for a lot of these proofs

it feels like you can look at them and automatically be like

[shadow dagger]

for the first few where it's just like "this is obvious" then yeah

[misty magnet]

"okay i know why thats true or not true"

but that's not satisfying to write in a course focused on proof writing

also

[shadow dagger]

i don't really like those as exercises if you haven't been given the axioms for the reals

[misty magnet]

it doesn't help that i have this course BEFORE logic

[misty magnet]

so to recap what you did

you split up our statement into it's base parts

and showed that it's still greater than the sentence on the right

no matter how much you slice it up

[misty magnet]

Another easier one I tried

[shadow dagger]

yeah that's fine

a few minor comments would be:

• you have ur in symbol the wrong way round lol

also depending on how much detail they want, i think writing 6n+10 = 2(3n+5), and saying that 3n+5 is obviously an integer is sufficient

[misty magnet]

Yeah probably don’t need to go that in depth

I attempted this one too but

Idk about it

[shadow dagger]

what is the question?

[misty magnet]

If a is divisible by c and b is divisible by d then ab is divisible by cd

[shadow dagger]

oh ok

[shadow dagger]

yeah again, i think ur writing the question here for ur own sake

but for the proof u hand in, i wouldn't

or if u did, i'd make it quite clear where your proof begins

[shadow dagger]

yeah i think overall it's fine

i'd personally like to have a conclusion at the end i.e. so ab is a multiple of cd or smth like that

but a lot of ppl don't so it's fine

[misty magnet]

So maybe what I just need is a lot of practice

a lot of grinding through direct proof exercises

[obtuse pebble]

@misty magnet Has your question been resolved?

[obtuse pebble]

Channel closed

Closed by @misty magnet

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.

[heady turtle]

Let ( D_t = {(x, y) \mid \sin t \leq x^2 + y^2 \leq t, 0 < t < 1} ), find the limit

[ I = \lim_{t \to 0^+} \frac{\iint_{D_t} \left[e^{(x^2 + y^2)^2} - 1\right] dx , dy}{(\tan^2 t - \sin^2 t) t}. ]

[warm shale]

miyo

[fossil crag]

!status

[obtuse pebble]

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

@heady turtle Has your question been resolved?

[heady turtle]

1

[fossil crag]

have you tried changing to polar coordinates

wait it is

[warm shale]

miyo

[heady turtle]

That's all I've done so far. Even If I have considered changing to polar, it still lead me nowhere

[fossil crag]

alright, now you have to approximate e^(r^4)

[heady turtle]

approximate e^(r^4)..?How?

[fossil crag]

yeah

taylor series

[heady turtle]

ooh

but

Can we use approximation in the intergration? Will the result still be accuarte?

[fossil crag]

well you can put in the whole power series if you want, but at some point there are some terms that will just go to 0

putting e^(r^4) - 1 = r^4 + O(r^8) might be enough

now it's all about finding equivalents

how do you know the limit is 0?

no...

you can't say the numerator is equivalent to 0

if your numerator is equivalent to 0 then you didn't have enough precision

[warm shale]

miyo

[heady turtle]

then what's wrong with this solution

[fossil crag]

the numerator

if t is equivalent to sin(t) for example

is it alright to say t - sin(t) is equivalent to 0?

[heady turtle]

ooh wait, I need to use atylor one more time?

[fossil crag]

yeah

or a^3 - b^3

oh and

you sure tan^2 - sin^2 is t^3/2 approximately?

how is t^3 even showing up in the approximation you did?

here's how I would do it: (unspoil only if you are really stuck).
for the denominator: ||tan^2t - sin^2t = (tant-sint)(tant+sint).||
||Using tant = t+t^3/3 + O(t^5) and sint = t - t^3/6 + O(t^5), we get tant+sint = 2t+O(t^3) and tant-sint = t^3/2 + O(t^5)||
||so tan^2t - sin^2t = t^4 + O(t^6) thus the denominator is equivalent to t^5.||
for the numerator:
||factor 1/6 out. then t^3 - sin^3t = (t-sint)(t^2+tsint + sin^2t).||
||t - sin(t) = t^3/6 + O(t^5) and t^2+tsint + sin^2t = 3t^2 + O(t^4) thus t^3 - sin^3t = t^5/2 + O(t^7), thus the numerator is equivalent to t^5/2.||

[warm shale]

miyo

[heady turtle]

pi/6

Thank you

.close

[obtuse pebble]

Channel closed

Closed by @heady turtle

Use .reopen if this was a mistake.

[obtuse pebble]

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 shuttle]

If X0is the path-component of a space X containing the basepoint x0, show that the inclusion X0 to X induces an isomorphism π1(X0, x0)→π1(X, x0).

[upper shuttle]

im not sure how to do this but isnt this not an isomorphism? if we take X0 to be a point and X to be S1 isnt this false?

[bronze mica]

Then X0 isn't a path component of X

[upper shuttle]

how is path connected component defined?

i thought it just means a subspace that isnt disconnected

eg like two distinct points

[bronze mica]

The path component containing x0 will be the largest subset of X that is path connected, and contains x0

In general the path connected components of a space are a partition into such biggest sets

[upper shuttle]

:0

haha thanks

i got it now

[bronze mica]

So e.g. if you have two disjoint circles, each is a path connected component

[upper shuttle]

yep

[bronze mica]

(And one of them contains the base point)

[upper shuttle]

thanks

.close

[obtuse pebble]

Channel closed

Closed by @upper shuttle

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[fathom light]

Divide both side by x^-1/3
Divide both side by y^-2/3

x^a/x^b = x^(a-b) hope you are aware of that

Ohhh my bad

Minus is invisible

x^-1/3 I meant

@fading zodiac ^^ I thought it's x^1/3 , didn't see the minus

(x^-1/3)/(x^-1/3)

What will be result

(x^2/3)/(x^-1/3)
What will be result?

We will see y one after a bit

Let's complete the x one first

[fathom light]

^^

Correct, can you rewrite the equation now again

1/3 * y^1/3 = 1/15 * x * y^-2/3

[fathom light]

Now what I asked in 2nd line?

No let's do your way then

1/3 = 1/15 * x * y^-1

This is what you are at right?

a^-1 = 1/a

No

1/3 = 1/15 * x * 1/y

This is what you have

Then you will have y/3 not 1/3y

Ohhh, I mean you need to write in a different way
1/3 * y or (1/3)y

If you write 1/3y

People will think as 1/(3y)

No problem

[obtuse pebble]

Channel closed

Closed by @fading zodiac

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[kindred geode]

There's a big giveaway, 200 people join, 5 are the winners.
Me and my friends squad up and we form a group of 14 people.
What's the probability of one of us getting chosen?
What if we are 22?

[fathom light]

One of you 2 ?or one of your 14 people squad?

[kindred geode]

At least 1 out of the 14 people squad and 1 out of the 22 people squad

[fathom light]

2 questions right?1st total is 14, second total is 22

[kindred geode]

yes

[fathom light]

So find out the probability when none of you wins

Then 1- none of you win probability

[kindred geode]

1 - 2.68?

[fathom light]

This is not probability

Probability can never be greater than 1

As far as I remember

[kindred geode]

so 0.268 then

[fathom light]

How are you finding that value?

You are using some tool?

[kindred geode]

no

i just thought

[fathom light]

Then? What formula you are using

[ionic oar]

its a percentage

[fathom light]

I know

I can see the sign

[kindred geode]

The following formula is used to calculate the chances of winning:

CW=(TW/TP)∗100
Variables:

CW is the chance of winning (%)
TW is the total number of winners
TP is the total number of participants

[ionic oar]

oh okay

[fathom light]

You can't use percentage here , you need to use combination formula

Do you know that?

[kindred geode]

Nope

[fathom light]

@ionic oar can we solve it using percentage? I know only combination way

[ionic oar]

i also only know the combination way sadly

[fathom light]

This is finding percentage formula

You want probability or percentage @kindred geode

[kindred geode]

Well whichever since it's the same

[fathom light]

Emmm it's not same 😅

[kindred geode]

I don't mean the number

[fathom light]

Probability is uncertain, percentage is certain

[kindred geode]

oh

yeah i know nothing about this stuff

[fathom light]

Well lets try to learn probability

Total people= 200
Your squad= 14

No of winners = 5

[ionic oar]

you should know, whats the formula for the chance of choosing 3 balls from a box of 10?

[kindred geode]

3:10*100

[fathom light]

No it's percentage of number of balls
Like question is there are 3 balls in 10 items , what is percentage of balls

[kindred geode]

30%?

[fathom light]

I am not asking question 😅, I am explaining the question for whatever you wrote

Not what copter has asked

[rough pelican]

hy

[fathom light]

Choosing 3 balls from 10 is not same as percentage of 3 balls from 10 items

[obtuse pebble]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[kindred geode]

Yeah

[fathom light]

Your main question is about choosing , not about percentage

[kindred geode]

right

[fathom light]

So if you want me to help you I can, or if you want to study the choosing things first that's ok as well

You need to be aware of something called permutations and combinations

And it's formulas

[kindred geode]

If you can help me that'd be great

[fathom light]

Alright

Do you know factorial @kindred geode 2!, 3! Etc?

[kindred geode]

yes

[fathom light]

Total people= 200
Your squad= 14
No of winners = 5
Your question is You need to find probability that atleast one of you 15 guys win the giveaway

[kindred geode]

1x2x3x4...

[fathom light]

Now if you want to choose r things from total n things , you can find that using formula
ncr = n!/((n-r)! * r!)

This is the formula for combination or selecting items

[kindred geode]

what is c?

[fathom light]

c is called combination

[kindred geode]

okay

[fathom light]

Understood this much @kindred geode ?

[kindred geode]

And what does the result mean?

ohhh wait

[fathom light]

It doesn't mean anything ,there are factorials involved

[kindred geode]

nvm okay

[fathom light]

Now if I ask you , I want to choose 3 balls from 6 items , can you tell me answer

[kindred geode]

20

[fathom light]

Correct

Now back to our question

Total people= 200
Your squad= 14
No of winners = 5
Your question is You need to find probability that atleast one of you 15 guys win the giveaway

If you want to choose 5 people out of 200, what will be the value @kindred geode

[kindred geode]

wait

[fathom light]

No need to find value , just tell me in that ncr form

[fathom light]

Well lets keep it 200c5 for now

[kindred geode]

okay

[fathom light]

Now how many people are not in your squad?

[kindred geode]

14

[fathom light]

Nooo

Not in

[kindred geode]

ohh

186

[fathom light]

Correct so if no one of you 14 wins , that means 5 people will be winning from those 186 people right?

[kindred geode]

Yes

[fathom light]

So how do you choose 5 people from 186?

[kindred geode]

186c5?

[fathom light]

Great

So
Probability of none of you winning= probability of winning all 5 from those 186 people

[kindred geode]

okay

[fathom light]

Now probability of winning all 5 from those 186 = choosing all 5 from 186/ choosing 5 people from total 200 people

Probability= desired outcome/ total outcome

This is formula of probability

[kindred geode]

okay

so 186c5/200c5?

[fathom light]

Yep

That's the probability of none of your teammates winning

[kindred geode]

okay

[fathom light]

So atleast one of your teammates winning probability = 1- none of your teammates probability of winning

[kindred geode]

oops

1-0.028=0.972

[fathom light]

Yeah should be alright, it's a big calculation

[kindred geode]

That's so high tho

[fathom light]

Yeah it should have been lower

Because less people less probability

[kindred geode]

hmm

[kindred geode]

nvm I forgot the ! at the end

1-0.69= 0.31

well thank you

learned something new

.close

[obtuse pebble]

Channel closed

Closed by @kindred geode

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[obtuse pebble]

@spring prawn Has your question been resolved?

[obtuse pebble]

@spring prawn Has your question been resolved?

[fathom light]

<@&286206848099549185>

[pliant nacelle]

first you have draw a triangle fulfilling those terms

[spring prawn]

i did

but i dont know how to prove it

[pliant nacelle]

so angle b=2 angle c will be simplified to b=2c, let's not take angle to count

and bicest means to divide into equal partd

that means you can place point D on BC so that angle A will be cut in half

then you can reconstruction with a new triangle with d being its new hyponuese

[spring prawn]

ye

after tht

after i constructed idk what to do

does D bisect BC tho?

[pliant nacelle]

idk, i failed my maths, so idk why I'm even giving you the answer, but i don't thing that would be important to your answe

or you can use the angle bisector theorem

@spring prawn Just use angle bisector theorem and plug in the angles and you will get the answr

[spring prawn]

...

[pliant nacelle]

i got that ${\frac{AB}{AC}}={\frac{BD}{DC}$

[warm shale]

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

[pliant nacelle]

and this should be correct

and then ${AB}({DC})={AC}({BD})$

[warm shale]

justinyap

[pliant nacelle]

then substitute ${AB}+{BD}$ into ${AC}$ and you will get $${AC}={AB}+{BD}$$

[warm shale]

justinyap

[pliant nacelle]

@spring prawn

[spring prawn]

how can we substitute ab + bd = ac

how angle bisector theorem says the ratio

[pliant nacelle]

it was at the question

[wintry swift]

i would try to express all angles in terms of angle at c. then i would try sine rule add addition-theorems for sin.

[spring prawn]

me no understandingg

aaaa

im so bad at this

[pliant nacelle]

all the stuff at the front are just describing the triangle

you need to solve the given question and not the triangle

[spring prawn]

i dont know how to approach these questions

like everytime i try to solve it but i dont get the approach

[pliant nacelle]

and you can also prove that the given information equals 180° because it's the interior of the triangle

[spring prawn]

how????

🙁

[pliant nacelle]

Wait, ill need to find the angle symbol unicode for this

${∠A}={180°}-{∠B}-{∠C}={180°}-{2θ}-{θ}$

[wintry swift]

have you tried this?

[pliant nacelle]

no

@spring prawn

∠A=180°-∠B-∠C=180°-2θ-θ,this is how you can express it

so basically, -∠B-∠C=-2θ-θ

[spring prawn]

right

then how do u prove ac = ab + bd

[pliant nacelle]

use the law of sins and find out

[spring prawn]

but this is 10th grade math in india

we didnt learn lawn of sins yet

how did we get this q

[pliant nacelle]

but it's more advanced, i would rather use the angle bisector theorem

you can see that ∠A will be cut in half therefore turning to A/2+A/2

[spring prawn]

how will this help tho

[pliant nacelle]

you see that (BD/DC)=(AB/AC)

[spring prawn]

this only gives ratio

[pliant nacelle]

that's all you need to solve it

[spring prawn]

hoiwww

[pliant nacelle]

the rest of the stuff are just describing the triangle

[spring prawn]

.....

ill try

brb

[obtuse pebble]

@spring prawn Has your question been resolved?

[obtuse pebble]

@spring prawn Has your question been resolved?

[pliant nacelle]

@spring prawn how long are you going to be holding this channel for?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[shadow lava]

has this this last sentence been worded correctly?

I did not buy a lottery ticket this week, or either I bought a lottery ticket this week, and I won the million dollar jackpot.

vs.

Either I did not buy a lottery ticket this week, or I bought a lottery ticket this week, and I won the million dollar jackpot.

both mean exactly the same thing in discrete maths?

Note: the only difference is placement of the word "either"

[obtuse pebble]

@shadow lava Has your question been resolved?

[drifting badger]

I agree that it is badly worded

Is the original answer key in English, or has it been translated?

Because the grammar would make sense in, for example, my language, so I'm assuming it also could in another one. But in English I don't see how it would make sense

[obtuse pebble]

@shadow lava Has your question been resolved?

[shadow lava]

technically its correct tho?

https://tenor.com/view/me-leaving-english-still-not-knowing-what-tf-a-adverb-is-me-leaving-english-still-not-knowing-what-the-fuck-a-adverb-is-what-is-an-adverb-me-leavng-school-not-knowing-what-a-adverb-is-gif-26853999

[obtuse pebble]

@shadow lava Has your question been resolved?

[obtuse pebble]

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.

[dark orchid]

The graph is confusing me

[midnight parcel]

try to zoom out

that might make more sense

[dark orchid]

oh. Ok

oh i see now

[midnight parcel]

its very big

that's why its hard to see

[dark orchid]

thanks!

yeah

[midnight parcel]

np

[dark orchid]

:)

[obtuse pebble]

@dark orchid Has your question been resolved?

Channel closed

Closed by @dark orchid

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[bitter terrace]

I got my other problem but now im confused on this one

[bitter terrace]

this is what I thought of

the only way that I could think of to relate the derivative and its original function is using the limit definition

since we haven't learned integrals yet in C

[tardy epoch]

Can you use Laurent expansion

[fast cliff]

haha dude i did this in 2nd grade XD

[tardy epoch]

Can you leave

[bitter terrace]

no we can't we haven't learned that

[fast cliff]

just take the triple domain expansion

[bitter terrace]

the only thing we really learned so far are limits, Cauchy-Reimann equations, the complex derivative and analyticy

and basic operations on C

[fast cliff]

probably the domain expansion tbh

[tardy epoch]

Stay in your channel

[tardy epoch]

What did you learn about analytic functions

[bitter terrace]

we just learned that a function is analytic if the cauchy-reimann equation is satisfied and analytic function at z0 is continously differentiable at z0

we also learned about the polar and exponential form

[fast cliff]

No one is helping rn so im helping others out

[bitter terrace]

of the complex numbers

[fast cliff]

branshi pls help me

i am only on linear algebra

[tardy epoch]

<@&268886789983436800> spammer

[bitter terrace]

maybe I can use the cauchy reimann equation here

is f'(0) = 0

[dapper bloom]

Don't troll or spam in the help channels.

[fast cliff]

Spam??

@dapper bloom false report

warn him

[bitter terrace]

then u_x + iv_x = 0

so u_x = 0 and v_x = 0

umm not sure where I would go from there though

[dapper bloom]

Okay, last warning. Stop trolling/spamming in the help channels. :^)

[fast cliff]

I am not spamming 😭😭

My bad tho ig

I’m a long time member bro won’t happen again 🙏🙏🙏

[oak escarp]

this kind of comment isn't helpful and neither are vague instructions, if you have nothing of value to add please don't mess with channels where people are already helping

[fast cliff]

Okay but I wasn’t being unreasonable why am I on my last warning

Can’t catch a break 😔

[bitter terrace]

ill just open up a different channel

.close

[obtuse pebble]

Channel closed

Closed by @bitter terrace

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

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

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

[boreal spade]

How do I simplify this?

In tbe middle

I suck wt simplifying w fractions

[dim burrow]

19 + what

is that written

[boreal spade]

?

Oh

19+h

[dim burrow]

solve the nr as a separate entity

take lcm

[boreal spade]

would lcm here be

19+h+7? I’m not sure

[dim burrow]

nothing is common multiply them in the dr

and do 19 -(19+h) in the nr

send the dr to below

[boreal spade]

so multiply all by 19 - 19+ h

so it moves to the denominator

[blazing folio]

Hi

[boreal spade]

hi

can you Save Me

[blazing folio]

What’s up

[boreal spade]

im very very bad at

simplifying complex fractions

[blazing folio]

Dawg

I want help

[boreal spade]

oh

[blazing folio]

Ion know how to do this

I’m sorry

[boreal spade]

all g

@analog vault can someone help me out

[bright tundra]

It's hard to read

[boreal spade]

1/19+h - 1/19

/ 7 + h - 7

[bright tundra]

Are you trying to find the difference quotient?

[boreal spade]

just to simplify

[bright tundra]

Just take an LCM

Wait someone already said that

[bright tundra]

What did you do for the LCM step

[dim burrow]

how yall doing functions without algebra on here

[bright tundra]

Well I did my algebra. Doesn't mean everyone would be strong at it

[boreal spade]

ok i think i got it, my mistake in lcm was i thought lcm could be (h+19)-19 but it should just be (h+19)19

[bright tundra]

Yes

[boreal spade]

i multiply that to everything on top

cancel out what i can

-h on the numerator so entire expression is -

then i multiply all by h to get rid of denom

[fathom light]

@boreal spade where are you stuck?

[boreal spade]

im not anymore i got the answer, although its just the entire process of simplifying fractions rlly gets me

[fathom light]

Got it, it happens. That's why better to solve numerator and denominator separately

Then put them together

[obtuse pebble]

@boreal spade Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[opaque galleon]

can someone tell me why area of infinitesimally thin ring is 2 pi r dr

[opaque galleon]

can u show me how to get it

[polar fossil]

if you take a ribbon and wrap it around a pole

the length of the ribbon is 2πr

and the thickness is dr

so the shadow of the pole is now slightly bigger, by 2πr * dr units

[opaque galleon]

oh okay ty

i thought it was 2 pi dr at first

[obtuse pebble]

@opaque galleon Has your question been resolved?

[obtuse pebble]

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.

[steel lagoon]

anybody know how to do this?

[steel lagoon]

I'm taking calculus this term so i'm trying to reinforce the basics of algebra/precal

[fiery sinew]

here the coefficient of x of both eqn is the same

when coefficient is the same we just straightly minus them or plus them if they are diff sign

here just minus

[frigid prawn]

out of curiosity, what software is that?

[steel lagoon]

yea but what are these answer choices, i dont understand what the questions are asking, do they want me to solve for x?

[steel lagoon]

mathmatize

[frigid prawn]

they want u to get rid of x

[fiery sinew]

they want u to make a new eqn without x, just y and constant

[steel lagoon]

so what happens to the x?

usually i rearrange the equation for whatever i want to find

[fiery sinew]

yeah it is actually the same but it is faster to + or - two equation

[steel lagoon]

do i just go

2x+y = -2
2x+y+2= 0
y+2= -2x
y+2/-2 = x

[frigid prawn]

nah that's not the goal here

your goal is to get rid of x

2x + y = -2
2x + 3y = -1

[steel lagoon]

sorry im confused

[frigid prawn]

you're not trying to isolate x

[steel lagoon]

how do you get rid of a variable

[frigid prawn]

substitution or note that x - x = 0

[steel lagoon]

so just subtract the equations?

[frigid prawn]

that's the intention (of the question)

[steel lagoon]

yea it worked thanks

[steel lagoon]

and if i want to solve it

do i isolate

[frigid prawn]

easier if u don't

just subtract, then isolate y, substitute y back to get x

probably easiest?

[obtuse pebble]

@steel lagoon Has your question been resolved?

[obtuse pebble]

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.

[warm tide]

How to simplify this further

[obtuse pebble]

@warm tide Has your question been resolved?

[obtuse pebble]

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.

[obtuse pebble]

@heady turtle Has your question been resolved?

[obtuse pebble]

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.

[manic cloak]

Can someone explain to me why the graph is like this given the equations

[ember frost]

because b is a freely moving variable

and it dictates how "high or low" the graph is

[warm shale]

Lingrod67

[timid silo]

!occupied

[obtuse pebble]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[crystal marsh]

sorry

[ember frost]

to be more technical, x^2 + b is a class of functions

[manic cloak]

uhm what is "size of opening and direction?"

[manic cloak]

Wdym b

[ember frost]

in your work you wrote $F(x) = x^2 + b$ no?

[ember frost]

or is my eye deceiving me

[obtuse pebble]

@manic cloak Has your question been resolved?

[obtuse pebble]

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.

[wide oxide]

hello

[wide oxide]

how to approach no.5

[pulsar tendon]

With sequences

(And the fact that Q is dense in R)

[wide oxide]

Can you tell me how to start with the steps

[pulsar tendon]

(Density) If you take a real number x, there exists a sequence of rational numbers qn converging to x

I will not give anything more, because it would give you the answer

What can you say about f and g with regards to qn ?

[wide oxide]

there exists sequence of rational number f and g which converges to a limit point say a

Like this?

[pulsar tendon]

I really don't understand

f and g are functions

(fixed functions)

[wide oxide]

ok

[pulsar tendon]

But what about f(qn) and g(qn) ?

[wide oxide]

sorry never seen this can you tell me

[pulsar tendon]

f is a function

You can evaluate it on numbers

In particular, on the elements qn of your sequence converging to x

These elements are rational, by assumption

What can you say about f(qn) ?

[wide oxide]

then it will converge to f(x) where x is the limit point of sequence qn

[pulsar tendon]

Exact

And if you look at g(qn) ?

[pulsar tendon]

Keep this in mind

[wide oxide]

it will also converge to f(x) or else it wont be equal

[pulsar tendon]

Can you explain a little bit more

[wide oxide]

as it is given that f(x)=g(x) that means for same x we get same output of x hence for sequence also f(qn)=g(qn) I will also get same output and it must have same limit point or the sequence will be different

[pulsar tendon]

Exact, but you go slightly to fast

as it is given that f(x)=g(x)
Only if x is rational, which is not assumed here (we took a "random" real number x)

And you want to show that then, it is also true if x is not rational

So, why is this f(qn)=g(qn) true ?

[wide oxide]

okay so do ween need to show that at every irrational number f and g are continuous.
So we take a sequence of irrational number (existence of which is ensured by density of irrational number) that converge to a rational number. then we show that both f and g are continuous at the point of convergence and by def are equal at rational points??

is this the way?

@pulsar tendon thanks

[pulsar tendon]

No, that f and g are equals at every irrational numbers

We already know they are everywhere continuous

But that's approximately the way, yes

[pulsar tendon]

And you want to prove that f(x) = g(x) for all real (and, in particular, irrational) number x

So, if you adapt your procedure to take account of this mistake (which is linked to the understanding of what is asked, read carefully the question), you will be right !

[obtuse pebble]

@wide oxide Has your question been resolved?

[wide oxide]

Thanks a lot @pulsar tendon

.close

[obtuse pebble]

Channel closed

Closed by @wide oxide

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.

[zinc dock]

how do you check if the triangle has a right angle

these are scalar products btw

and wouldnt it mean that the a) would have 2 right angles

[restive gorge]

deutsch

[zinc dock]

yea

[restive gorge]

Und was hast du probiert

Ich empfehle Skizzen

[zinc dock]

ich hab einfach a mal b und dann b mal c und dann c mal a

um zu schauen ob 0 rauskommt

[timid silo]

Na aber du musst die Seiten miteinander multiplizieren, d.h. Die Ecken voneinander abziehen

[timid silo]

Also bei a) z.B. sind A-B, B-C und C-A die Vektoren, die den Seiten entsprechen

[restive gorge]

Ist nur ein Beispiel

[timid silo]

Ansonsten past dein Ansatz, einfach multiplizieren (Skalarprodukt) und schauen ob 0 rauskommt

[zinc dock]

also ich muss zuerst die vektoren bestimmen und dann sie miteinander multiplizieren?

[timid silo]

Ja siehe Zeichnung von @bacc

[restive gorge]

Die Punkte/Ecken kann man als Vektoren fassen, und je nach dem welche Seite des Dreieckes man will z.B. die Grüne, da würde grüner Vektor = a - b sein

[timid silo]

Die Seiten in blau rot und grün sind jeweils eine Diffrenz aus den Ecken

[zinc dock]

nicht b - a?

[restive gorge]

Und ich wollte auch guten Morgen sagen btw

[restive gorge]

Beides geht

[zinc dock]

guten morgen lol

[zinc dock]

ok

danke ihr beiden

[restive gorge]

der Unterschied zwischem b - a und a - b ist dass der eine Vektor entgegengesetzt zeigt

Ender aber nichts ander Lage

[zinc dock]

achso ok

👍

.close

[obtuse pebble]

Channel closed

Closed by @zinc dock

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.

[dim burrow]

since the speed is decreasing

[dim burrow]

doesnt that mean that the smaller velocity disc was rotating in opposite manner

isnt that wrong here the conservation of angular momentum?

signs i mean

[north cradle]

Could you show the original problem

[dim burrow]

.

[hearty kettle]

I believe they are rotating in the same direction, it is just when two shafts rotating at different speeds are connected they must, in the end, rotate at one conjoined speed. Think of it as the second wheel speeding up the first one, instead of the first one slowing down the second.

If you want a better way to imagine it, imagine it in relative motion. Let's say one wheel is at rest compared to another which is rotating at (300 - 160) 140 rev/minute. If you connect the two the second one will try to rotate the first, and bring them to a common speed. However since it has transferred some energy to the second mass to make it move, it will lose some angular speed itself.

[obtuse pebble]

@dim burrow Has your question been resolved?

[dim burrow]

Hmm

what sucks is they didnt teach much about coefficient of restitution in rotational bodies

[hearty kettle]

yeah you mostly have to wing it

you're doing JEE?

[dim burrow]

hmm

.close

[obtuse pebble]

Channel closed

Closed by @dim burrow

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.

[lavish sand]

Can someone check this for me. Is it right way to solve this problem. When i use calculator it shows way more different approach but the answer is same

[restive gorge]

Sieht gut aus

but wait I wanna share a nice theorem

[lavish sand]

Is it valid if i write this on exam.

Thanks 🙏🏾

[restive gorge]

one note

$$\lim_{x\to a} f(x) + g(x) = \lim_{x\to a} f(x) + \lim_{x\to a} g(x)$$ is only applicable if you know that the limit exists, otherwise this can go wrong really quickly.

[warm shale]

bacc

[lavish sand]

Really how can i check it.

[restive gorge]

I was just mentioning it as side note

[restive gorge]

You can tell here that the limit exists, so that's okay what you did

https://groups.uni-paderborn.de/reiss/AnalyseBuch/Analysis/EigenschaftenVonFunktionen/grenzwertregeln.html?i=index

Aber sonst top gemacht!

[lavish sand]

When i use calculator it says for example 1/x approaches to 0 etc.

Is there table of some rules are like these

That is can memorize.

[restive gorge]

Manchmal wird gesagt, "Zeigen Sie, dass der Grenzwert existiert." Wenn er also existieren soll, kann man annehmen, dass er es tut, und man verwendet diese Regeln.

Not that I know of

[lavish sand]

Ach so.

[restive gorge]

https://www.onlinemathe.de/mathe/inhalt/Wichtige-Grenzwerte

Google mal wichtige Grenzwerte

[lavish sand]

Danke schön

.close

[obtuse pebble]

Channel closed

Closed by @lavish sand

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[lusty sorrel]

how can i divide 84.78 by pi?

[brazen gorge]

with a calculator

[vale pelican]

it depends on what you want out of life

[brazen gorge]

,calc 84.78 / pi

[warm shale]

Result:

26.986312150662

[brazen gorge]

[obtuse pebble]

@lusty sorrel Has your question been resolved?

Channel closed

Closed by @lusty sorrel

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.

[glossy ridge]

idrk what the question is asking, and the steps to answer it properly. can someone help me?

[high lily]

y value = f(x value)

e.g. for the first question
f(4),
look at at the graph where the x-coordinate is 4
f(4) will be the y-coordinate of that point

[glossy ridge]

so 3?

[high lily]

yes

[glossy ridge]

ok tysm

.close

[obtuse pebble]

Channel closed

Closed by @glossy ridge

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[near monolith]

Would this be (-inf,+inf) for the decreasing?

[near monolith]

Or would it be a hole at the-3

[sonic ruin]

That would be my take as well.

[sonic ruin]

And no holes for that x value.

[near monolith]

Ok thank you

.close

[obtuse pebble]

Channel closed

Closed by @near monolith

Use .reopen if this was a mistake.

[sonic ruin]

Or perhaps you mean an inflection point?

[sonic ruin]

I am not sure, though.

I currently lack self~confidence.

[near monolith]

.reopen

[obtuse pebble]

✅

[near monolith]

Oh then I will get another opinion

<@&286206848099549185>

[void quartz]

yes

[sonic ruin]

It's an inflection point, not a hole.

[void quartz]

you would exclude the -3 only if you were asked to find the interval/intervals for which the function is strictly decreasing

decreasing <= 0

strictly decreasing < 0

[sonic ruin]

I personally strongly doubt that.

[void quartz]

i dunno, this is how i was taught this 😛

anyways, no other reason to remove -3

[near monolith]

Ok thank you @sonic ruin and @void quartz

.close

[obtuse pebble]

Channel closed

Closed by @near monolith

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[full zealot]

How do i go further

<@&286206848099549185>

[tardy epoch]

!15m

[obtuse pebble]

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.

[full zealot]

It's been an hour

I posted it in another channel but it was closed

[zenith raft]

according to my watch it had been 0 minutes

[full zealot]

#help-19

[zenith raft]

my watch doesn't lie

[full zealot]

Well it was timed out there but yeah

[full zealot]

From this channel's pov

From mine its been an hour😭

Can you tell me what to do next😭

[full zealot]

.

[zenith raft]

sorry i was never any good with integrals

[full zealot]

I just need someone who can simplify that trig expression

[obtuse pebble]

@full zealot Has your question been resolved?

[tardy epoch]

,tex .prod2sum

[warm shale]

pizzanator

[tardy epoch]

Try using that

[obtuse pebble]

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.

[inland breach]

t stands for the time in hours.
So basically a ship started at t 0 and it took him 3 hours to get to t 3 (13|4) now I need a formula for it.

t 0 (1|-2)
t 0,5 (3|-1)
t 1 (5|0)
t 1,5 (7|1)
t 2 (9|2)
t 2,5 (11|3)
t 3 (13|4)

[inland breach]

Can anyone help me with that ?

(x|y)

Nvm

I got it

[obtuse pebble]

@inland breach Has your question been resolved?

[obtuse pebble]

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.

[elfin plover]

Where’d I go wrong here?

[elfin plover]

original problem: 8^(-x/3)=4

1/(8^(x/3)) = 4

((8x)^(2/3))/8x = 4

(8x)^(2/3) = 32x

[frigid prawn]

uh, just get a common base

[elfin plover]

64x^2 = 32768x^3

[brazen gorge]

x is in the power, not the base

[elfin plover]

Ohhhh

it was my bad handwriting

thanks

i couldn’t tell that the x was an exponent

[elfin plover]

got it, i see now that that’s a better approach

[obtuse pebble]

@elfin plover Has your question been resolved?

[elfin plover]

yes dawg

[obtuse pebble]

Channel closed

Closed by @elfin plover

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.

[grand basin]

Im having issues with how to build the second integral, I don’t know if I need to add or sub tract stuff considering it’s not flush with the x or y axis

[grand basin]

.close

[obtuse pebble]

Channel closed

Closed by @grand basin

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[faint socket]

is my answer equivalent ?

red answer is the answer

blue is my work

[hexed gull]

sure

remember cos(A) = cos(-A)

[faint socket]

ah yes cheers

!close

.close

[obtuse pebble]

Channel closed

Closed by @faint socket

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.

[static pebble]

how do I find the integral of sqrt (9-x)^2 ?

[tardy epoch]

That's not the equation

The power is only on x

f(x) is the equation of a circle

[obtuse pebble]

@static pebble Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[sinful falcon]

Can someone explained how 2 turns to 0?

[sudden zinc]

When you take the derivative of a constant, it becomes zero

[quiet wadi]

In between the second and third line, you take the derivative.

[sudden zinc]

So in this case, when you take the derivative of y, you use the power rule to take the derivative of all the terms containing x and the constant term becomes zero.

[sinful falcon]

Even

Negative

?

[quiet wadi]

A constant is a constant

[sudden zinc]

Negative constants also go to zero, yes (think of it as -0 is still 0)

[sinful falcon]

I see, I was confused what to do with the 12, did I do this right?

[quiet wadi]

I mean, think of the graph of a constant function for any constant. It's a flat line, no matter how where vertically that line is.

Those all have zero "change" in them, so the derivative is zero

[sudden zinc]

The 12 part is right, but the derivative of 3x is just 3 , and the rest is correct

[sinful falcon]

Just 3? How come I thought x^-1 is 1/x no?

[sudden zinc]

Basically you’re going from x^1 to x^0

Which is 1

[quiet wadi]

yes, x^-1 is 1/x, but that's not relevant here

[sinful falcon]

Oh

[sudden zinc]

So it’s 3*x^0 = 3

[sinful falcon]

So just

I see

Thank u

.close

[obtuse pebble]

Channel closed

Closed by @sinful falcon

Use .reopen if this was a mistake.

[sinful falcon]

.reopen

[obtuse pebble]

✅

[sinful falcon]

Can I just leave this as my answer? It feels incomplete

Uhhh

[sudden zinc]

Did the question say to differentiate with respect to t or x?

Or just take the derivative

[sinful falcon]

Just to differentiate the function

[sudden zinc]

Ok then you have to do d/dt of that function, so just differentiate normally but with t as the variable instead of x

[sinful falcon]

Ah ok

Thanks

Is my answer right though?

Cause that felt too easy

[sudden zinc]

The first part is fine, but the e^3 term doesn’t contain any t so it is constant and therefore 0

[sinful falcon]

So it’s just 3t^2

[sudden zinc]

Yes. Any term that doesn’t contain your variable is constant and goes to 0

[sinful falcon]

What about ln(5)

Constant still?

[sudden zinc]

Yes

[sinful falcon]

Or like logs

[sudden zinc]

Yes, because they are just a number if you actually evaluate them, and they don’t depend on your variable

[sinful falcon]

I see

[sudden zinc]

It’s really just if a term doesn’t contain the variable it is constant

[sinful falcon]

.close

[obtuse pebble]

Channel closed

Closed by @sinful falcon

Use .reopen if this was a mistake.

[sinful falcon]

,calc x^-2

[warm shale]

The following error occured while calculating:
Error: Undefined symbol x

[sinful falcon]

,diff of x^-2

,w diff of x^-2

.reopen

[obtuse pebble]

✅

[sinful falcon]

How do I differentiate the -3x^-2?

[modern onyx]

D/dx(x^n) = n*x^n-1

[modern onyx]

Differentiate x^-3 or -3x^-2

[sinful falcon]

I meant x^-3 I just don’t know where to go from -3x^-2

Oh wait

I added

It

[modern onyx]

Yea

[sinful falcon]

That’s why it looked wrong

Yea

.close

[obtuse pebble]

Channel closed

Closed by @sinful falcon

Use .reopen if this was a mistake.

[sinful falcon]

I’m gonna reopen because I’m dumb

.deopen

.reopen

[obtuse pebble]

✅

[sinful falcon]

Number 14 how do I do this? I’m just kinda confused on it a little on how to go from here

[modern onyx]

1/x = x^-1

So u can rewrite #14 as

at^-2 + bt^-4

Then that should be pretty easy to differentiate

[sinful falcon]

I’m still kinda confused sorry

[modern onyx]

Yk how

If u have a^-b

That can be rewritten as 1/a^b

[bold bane]

$\frac{a}{b} = a\cdot b^{-1}$

[warm shale]

Kookiemon

[sinful falcon]

Oh yea ok

[sinful falcon]

<@&286206848099549185> can anyone further explain this

[tardy epoch]

,tex .exp rules

[warm shale]

pizzanator

[tardy epoch]

3rd row

[sinful falcon]

I see but the numbers are different on numerator and denominator

[tardy epoch]

Second row them

The second row is just a special case of the third row

With x=0

[sinful falcon]

So 1/t^-1/2 is t^1/2

[sinful falcon]

.close

[obtuse pebble]

Channel closed

Closed by @sinful falcon

Use .reopen if this was a mistake.

[sinful falcon]

.reopen

[obtuse pebble]

✅

[sinful falcon]

Uh can someone help me number 14, am I doing something wrong? Or

[modern onyx]

This is the rewritten form of the original equation

Now apply the power rule

[sinful falcon]

-2at^-3 - 4bt^-5

is that my answer

.close

[obtuse pebble]

Channel closed

Closed by @sinful falcon

Use .reopen if this was a mistake.

[sinful falcon]

Hey guys I’m stuck again (sorry)

.reopen

[obtuse pebble]

✅

[sinful falcon]

Problem 21 I’m not sure what to do with this

[modern onyx]

Rewrite the radical function as x^-1/3

U should get

3e^x + 4(x)^-1/3

[modern onyx]

And then derive this

[sinful falcon]

So I not do anything to the 3e^x

Do I not

,diff of 4piR^2

,w diff of 4piR^2

[warm shale]

Results provided by WolframAlpha

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

Requested by light945850

[sinful falcon]

.close

[obtuse pebble]

Channel closed

Closed by @sinful falcon

Use .reopen if this was a mistake.

[modern onyx]

Well cause the derivative of 3e^x is just the same thing

[sinful falcon]

.reopen

[obtuse pebble]

✅

[sinful falcon]

23, I’m kinda confused on how to do this

[versed pier]

well if you divide

you get 3x + x^2

[subtle sinew]

The 1/x doesn't become + x^-1

[sinful falcon]

Oh

[subtle sinew]

Do you see how to do it now?

[sinful falcon]

Yes

[sinful falcon]

Could uh I get help on number 25 though (sorry)

[subtle sinew]

Where are you stuck?

[sinful falcon]

I’m not sure how to continue

[subtle sinew]

I mean that's a valid answer

[sinful falcon]

Just

That

?

Ok

[subtle sinew]

Yes

Unless your teacher wants you to simplify

[sinful falcon]

It just says differentiate the function

[subtle sinew]

Yes but does your teacher want you to simplify?

[sinful falcon]

I don’t recall

Should I just incase

Is problem 28 just the original function

,w diff of e^r + r^e

[warm shale]

Results provided by WolframAlpha

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

Requested by light945850

[sinful falcon]

I don’t know what that even means

[subtle sinew]

You did integral not derivative

[sinful falcon]

Oh

I don’t know how to do derivative

[sinful falcon]

But is my question right

Or statement

[subtle sinew]

Not quite

[sinful falcon]

How would I solve a question like this then?

[subtle sinew]

If you had e^x + x^e, would you be able to do it?

I just swapped the r's with x's

[sinful falcon]

Wouldn’t that mean they are differentiated of each other

[subtle sinew]

How would you take the derivative of e^x?

[sinful falcon]

By using the same function

E^x

[subtle sinew]

What about x^e?