help-19

[odd edge]

@dapper ginkgo Has your question been resolved?

[odd edge]

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.

@royal palm Has your question been resolved?

[odd edge]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[odd edge]

Available help channel!

Send your question here to claim the channel.

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

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

[novel venture]

Shouldnt this be e

[mystic saffron]

,w sum n = 0 to inf 1/(n - 69)!

[clever fjord]

Results provided by WolframAlpha

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

Requested by alison_burg3r5

[mystic saffron]

Yeah Wolfram Alpha gives 0 for some reason

why do you think this should evaluate to e?

I feel like the answer should be undefined

cause if you think about it

n = 0 --> (0 - 69)!

and that doesn even exist!

[static totem]

it's lieke dividing by 0

[mystic saffron]

mate are you sure it says 0 - 69?

cause all values from n = 0 all the way to n = 68 would evaluate to negative values

and we know that factorials of negative values aren't really a thing

also if you want this to evaluate to e

I think the following would make more sense

$$\sum_{n = 69}^\infty \frac{1}{(n -69)!} = e$$

[clever fjord]

Edmund Cloudsley (Hello CHAT)

[mystic saffron]

since this is just the taylor series expansion of 1 over n factorial

,w sum n = 69 to inf 1/(n - 69)!

[clever fjord]

Results provided by WolframAlpha

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

Requested by alison_burg3r5

[mystic saffron]

voila!

This worked

yeah

[mystic saffron]

I tried this expression on my calculator

and it evaluated to undefined lol

[odd edge]

@novel venture Has your question been resolved?

[odd edge]

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.

[minor minnow]

Hi i need help with this

[odd edge]

@minor minnow Has your question been resolved?

[minor minnow]

<@&286206848099549185>

[odd edge]

@minor minnow Has your question been resolved?

[odd edge]

@minor minnow Has your question been resolved?

[minor minnow]

<@&286206848099549185>

[strange glacier]

binomial theorem ?

[deep mason]

next time 👍 thanjks

[odd edge]

@minor minnow Has your question been resolved?

[weary hamlet]

@minor minnow

do u have it

cuz im almost done

@minor minnow

[odd edge]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[odd edge]

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.

[errant timber]

might just be me or is there something wrong with this problem?

[buoyant ocean]

Which color curve is f(x) and which color curve is f'(x)?

Once you can identify which one is f'(x), then consider what the slope at f'(1) must be

That will then tell you what f''(-1) has to be

[errant timber]

i'd assume that blue is the original and red is the derivative

[buoyant ocean]

Correct, now look at f'(-1) on the red curve

What is the slope there? (this will tell you what f''(-1) must be)

[errant timber]

0

[buoyant ocean]

Yes

So notice how f'(-1) is below the x-axis, so it has to be negative

And then we have that f''(-1) is equal to 0

So what is bigger, 0 or some negative number?

[errant timber]

its f''(1)

not -1

[buoyant ocean]

Ah my mistake

[errant timber]

all good

[buoyant ocean]

The answer is still the same regardless

:)

[errant timber]

it's concave since it's past the inflection point at ~.5 it's going to be a positive number

which means that the second derivative at x coordinate 1 would be bigger

[odd edge]

@errant timber Has your question been resolved?

Channel closed

Closed by @errant timber

Use .reopen if this was a mistake.

[odd edge]

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.

Channel closed

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

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.

[opal temple]

given T : V -> V, where V is a fin. dim. vector space. prove that if m_T(0) != 0 then there exists a polynomial f in F[x] s.t. f(T) = -1

[opal temple]

(m_T is the minimal polynomial for T)

[odd edge]

@opal temple Has your question been resolved?

[opal temple]

@rancid moat

oops sorry

<@&286206848099549185>

.close

[odd edge]

Channel closed

Closed by @opal temple

Use .reopen if this was a mistake.

[odd edge]

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 plover]

2+1

[quasi sparrow]

Close

.close

[odd edge]

Channel closed

Closed by @quasi sparrow

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.

[rich bridge]

I am given the curve (x^2+y^2)^2=16(y^2-x^2) and using the maplesoft math program I need to find all the points on this line where the slope of the tangent line is equal to 4, anyone have any idea what I can do to find this?

[rich bridge]

this is what I've done so far

[odd edge]

@rich bridge Has your question been resolved?

[odd edge]

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.

[analog elm]

Hi!

I am here for some experienced advise.

Context:
Out of my carelessness and stupidity i ignored mathematics since 7th and 8th grade.
Studied only to just pass out the exams and move to the next grade.

Problem:
I am beginning to realize that i could have done good to build a solid foundation to learn better things.
Out of my fair bit of regrets, one is that i did not pursue mathematics and effectively build my foundations.

I am 28 now and am willing to put in the work to go back and start from the basics if need be and build back to the top.

What would be the best way to do so?

Dilemma:
"Options Paralysis"
What is the best online service that helps a person like myself?
I've been told Brilliant helps but i just want to get experienced advise from a community such as yourself.

Kindly extend me the courtesy of leading me down the right path.

Thank you for the time!

-GEDD

[hasty dome]

Hello. Khan Academy is an excellent way of learning math from elementary school up until the first years of university. Click on Explore in the upper left corner of https://www.khanacademy.org/.

Brilliant is also good, but it's not free.

[analog elm]

Hi Chai, thank you for writing back to me.

I will explore Khan Academy.

In terms of ease of understanding and the quality of articulation (from teacher or course to student).

Which of them are considered the best?

[hasty dome]

I don't know which would be best. Khan Academy has video lectures and practice quizzes. Brilliant has animations and stuff like that.

Khan Academy is free. Brilliant charges past the first few lessons in a topic.

I haven't paid for Brilliant, so I don't know which is better.

You can pick a subject and try it in both places and go with the style you like better.

Oh, Khan Academy is more like regular school.

Brilliant has a nice wiki.

https://brilliant.org/wiki/best/

If you're still unsure, I'd recommend Khan Academy.

[analog elm]

I will definetly take your advise on the approach of comparing classes for specific topic and go from there.

Thank you so much for the time Chai

[hasty dome]

You're welcome.

[analog elm]

I appreciate your input

I hope you have a wonderful day!

Take care!

[hasty dome]

You too.

[analog elm]

.close

[odd edge]

Channel closed

Closed by @analog elm

Use .reopen if this was a mistake.

[odd edge]

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.

[forest yoke]

Hi guys , i have a doubt in "limits"

[forest yoke]

This is the question , and my answer

I got the answer as -pi

But the correct answer is +pi

And i dont know what is my mistake could some one help me find my error? Please !

[leaden karma]

pi*cos^2(x) doesn't go to 0 as x goes to 0

So that limit is wrong

[forest yoke]

Ohhh so only if
The entire pi*cos²x goes to zero could i use that rule?

[forest yoke]

Is that correct?

@leaden karma

[leaden karma]

Yes

[forest yoke]

So if in the question it was given lim x---> 1

Then i could have used the rule?

[leaden karma]

No

cos(1) is not 0

[forest yoke]

Sorry i meant pi/2

[leaden karma]

Well yes

But you wouldn't need to do anything for that

Because it's not an indeterminate form

You can just substitute the values

[forest yoke]

Yeah

[forest yoke]

True true

I get it now

Tysm

[leaden karma]

Also you cant use l'hopital's rule for a limit if it's not indeterminate

So that step is wrong anyways

[forest yoke]

One sec

If

X--->0 then pi*cos²x

[forest yoke]

Would just be pi

And then

Sin pi is 0

[leaden karma]

Yes

[forest yoke]

So dosent that make sin tend towards 0?

[leaden karma]

It does

[forest yoke]

So if it tends to zero why cant i use the rule?

[leaden karma]

Here i was talking about the limit where you used l'hopital's rule

[forest yoke]

That i get

[forest yoke]

Im talking about this

[leaden karma]

You can use it on the initial limit

[leaden karma]

You said it yourself, pi*cos^2(x) tends to pi

[leaden karma]

So the limit I circled here goes to pi/0

Which is not indeterminate

[forest yoke]

Ohhh i see

So what would be the correct way to solve this sum?

[leaden karma]

(This whole limit is wrong anyway because of that wrong step you took initially, but I'm just pointing out that even if it were correct using l'hopital's rule is not right)

[leaden karma]

Well

You can use l'hopital's rule on the initial limit

[leaden karma]

Looks good

[leaden karma]

Correct

[forest yoke]

So this is correct?

[forest yoke]

Alr

Ummm just one more thing

I didnt quite understand

[leaden karma]

An alternate way is to write $\sin(\pi\cos^2 x)=\sin(\pi-\pi\cos^2 x)=\sin(\pi(1-\cos^2 x))=\sin(\pi\sin^2 x)$

[clever fjord]

kheerii

[forest yoke]

What went wrong in my 1st step

[forest yoke]

Yeah this is what my teacher did

But i wasnt satysfyied

Because i didnt know what went wrong with my way

[leaden karma]

The result you were using is that $\lim_{x\to 0}\frac{\sin x}{x}=1$, and you applied it to thr limit $\lim_{x\to 0}\frac{\sin(\pi\cos^2 x)}{\pi\cos^2 x}$

[clever fjord]

kheerii

[forest yoke]

Correct thats what i did

[leaden karma]

But this only works if what you're replacing x with (in this case pi*cos^2(x)) also tends to the same value (in this case, 0)

[forest yoke]

Wait so if im getting this right

I can only use that rule
When after substiting x's value the limit becomes 0/0?

Please cirrect me if im wrong

[leaden karma]

Yeah

There are a few more caveats relating to continuity but this is good enough for now

[forest yoke]

And in the case of the question after substituing the value of x
We were getting 0/pi and not 0/0 therefore using the rule wasnt correct

[forest yoke]

I see

[leaden karma]

$\lim_{x\to a}f(g(x))=\lim_{u\to b}f(u)$, where $b=\lim_{x\to a}g(x)$

[clever fjord]

kheerii

[leaden karma]

Yes

[forest yoke]

This is?

[leaden karma]

In particular for this to hold f(x) has to be continuous at x=b

[leaden karma]

It's the same rule we just talked about

[forest yoke]

I see

[leaden karma]

Let f(x)=sinx/x and g(x)=pi*cos^2(x)

[forest yoke]

I see

i get what my mistake was now

It was the incorrect use of the rule as it wasnt indeterminate form

Tysm

Once agaim

[leaden karma]

Yes

[forest yoke]

Ill close the forum now

Ty

.close

[odd edge]

Channel closed

Closed by @forest yoke

Use .reopen if this was a mistake.

[odd edge]

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.

[grim wedge]

wat to do

[narrow crypt]

Binomial

Theorem

For two first terms

[mystic saffron]

https://tenor.com/view/major-modern-general-the-pirates-of-penzance-pirates-gif-14709947

[grim wedge]

what does it mean by non zero terms coz i did that

[nimble blaze]

if the expansion ended up as something like
$$3 + \underbrace{\gray{0x}}_{0 \text{term}} + 14x^2 + 15x^3$$
they'd want: $3 + 14x^2$

[clever fjord]

ℝαμOmeganato5

[grim wedge]

ohhhhhhhhhhhhhhhhhh ty that is a sick way to present it

do u mind guding me through this question please?

for a do i just

do

8C5 x (2)^3 x (ax)^5

[nimble blaze]

=3402x^5
also don't use x for multiplication

[grim wedge]

shall i use dot

[nimble blaze]

for text use * (put spaces on both sides it to stop discord from italicising stuff)

[grim wedge]

448a^5 = 3402

or 448a^5x^5 = 3402x^5

made a silly mistake but my final equation ^

[nimble blaze]

yeh

[grim wedge]

so a = 3/2

what next?

[nimble blaze]

that's part a) done

[grim wedge]

yep

do u mind doing a worked solution? i can give u the ms if youd like

[nimble blaze]

solution for what

[grim wedge]

b

[nimble blaze]

start by identifying which terms you want in the expansion of (2+3x/2)^8

1 * what power of x and hence which term results in a constant
1/x^4 * what power of x and hence which term results in a constant

[odd edge]

@grim wedge Has your question been resolved?

[odd edge]

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.

[zenith jasper]

whats the mark scheme dong in the second M1?

t = 4.205-4.22/ that part

[mystic saffron]

bros defo from the uk

lolz

is that hypothesis testing?

[zenith jasper]

no i'm from hong kong

[zenith jasper]

yes

but that is a levels

[mystic saffron]

ahh cool cool~

[zenith jasper]

yeah

i guess

idk what is going on in the question tho

[mystic saffron]

umm lets see~

[zenith jasper]

thx

[mystic saffron]

so thats normal distribution right?!

do u know the formula for it?~

[zenith jasper]

should be, it says the runs are normally distributed

[zenith jasper]

wdym?

[mystic saffron]

so 4.205 is mean right?!

[zenith jasper]

yep

[mystic saffron]

tbh i just use a calculator lolz

[zenith jasper]

no i mean

i dont get this part

[warped urchin]

do you know how to do t-tests?

[zenith jasper]

uhh

only heard of them

im self studying this sorry

[warped urchin]

respect

[zenith jasper]

i have to memorize this formula?

[warped urchin]

so notice how there is only two hypotheses here i.e the one where she hasnt improved and the one where she has

[zenith jasper]

yep

[warped urchin]

yea you basically need to memorize this formula

[zenith jasper]

damn :(

[warped urchin]

to conduct this test you need to know a few things

[zenith jasper]

whyd the sign of t change btw

[zenith jasper]

yeah?

[warped urchin]

which sign?

[zenith jasper]

-1.44 to 1.44

[warped urchin]

its cause the sample mean is less

$$ t = \frac{\bar{x} - \mu_0}{\frac{s}{\sqrt{n}}} $$

[clever fjord]

Banana Steeler

[warped urchin]

this is what the formula for t-tests is

[zenith jasper]

nono i mean uh

why did it turn from

**-**1.44 to 1.44

emphasis on the - sign

[zenith jasper]

oh yeah i just looked this up, will keep this in mind

[warped urchin]

i dont exactly know why british people are weird cause the calculation does result in negative

maybe its a typo??

actually i doubt it

[zenith jasper]

how would you do it then?

leave it as negative, and compare with tabular value?

nah but when i use my calculator to inverse student t, i get -1.833

[warped urchin]

and since -1.44 is greater than -1.833

what does this mean

[zenith jasper]

um

within critical value?

accept H_0

[warped urchin]

yup

its the null hypothesis

thats it

[zenith jasper]

oh

i have a question though

is the critical region only bounded by one critical value

or two

[warped urchin]

its a one tailed test so its just 1

[zenith jasper]

how do we know it must be greater than critical value to accept H0

[warped urchin]

you just need to know to assume when in a one tailed test when the t statistic is greater than the critical value to accept the null hypothesis

[zenith jasper]

like just a fact?

[warped urchin]

yea

[zenith jasper]

oo i see

[zenith jasper]

thx for ur help!

i get it now

.close

[odd edge]

Channel closed

Closed by @zenith jasper

Use .reopen if this was a mistake.

[odd edge]

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.

[candid star]

Based on the mean and standard deviation of the ratings, what is the likely range for the number of customers who will give the highest rating (5 - Strongly Agree) for:
a. Quality of service, in order to maintain a 80% probability of success?
b. Timeliness of response, in order to maintain a 85% probability of success?

[warped glacier]

what is the mean and sd

send the original question pls

[steep python]

Yo how to do 6th question

[warped glacier]

!help

[odd edge]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[candid star]

i dont get the question were supposed to use binomial distribution here and from what i calculated on the tables i got a
A.
mean = 80
sd = 4

B
mean = 85
sd = 3.5707

[candid star]

this is the entire question ;-;

[warped glacier]

also what do you mean by likely range

I assume the question wants a confidence interval

[candid star]

THAT IS MY PROBLEM LIKE LEGIT

[warped glacier]

is this the 95% confidence interval

[candid star]

i dont get it why is saying likely range

[warped glacier]

yeah that's not a proper statistics term

don't use it

[candid star]

the percent is the probability of default thingy

[candid star]

the thing is i didnt. thats the question given in my case study...

[warped glacier]

what class is this for?

[candid star]

math in the modern world....

[warped glacier]

ah goddamnit just calculate the 95% confidence interval then

so that's (mean - 1.96 sd, mean + 1.96 sd)

[candid star]

i tried asking my prof about it and i didnt even get her explanation

she said how many scores of 5? do you need to maintain a 80% and 85% probability of success

something like that

[warped glacier]

sounds like your teacher is bad at stats

jesus

[candid star]

on GOD IM DOOMED

[warped glacier]

that's just restating the question

[candid star]

this case study is doomed from the start the question itself is faulty

.close

[odd edge]

Channel closed

Closed by @candid star

Use .reopen if this was a mistake.

[odd edge]

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.

[arctic spoke]

hi i need the formula for this because i cannot find it online, once you give me the formula could you give me a step by step tutorial pls? this is for my exam pls help

[arctic spoke]

also ping me when you have the formula because im gonna be doing something

[south turtle]

whats the formula for the circumference of a circle?

[arctic spoke]

circumference = \pi x diameter

or

circumference = 2 x \pi x radius

act like the /pi thing is the pi symbol pls

[south turtle]

Okay so we have half a circle, so instead of pi*diameter what must we do

just to get the curved part

For example if the full circumference for a circle was 10, how long would the curved bit for a half a circle be?

[arctic spoke]

5

for like half the circle you mean?

[south turtle]

Yes

[arctic spoke]

yeah 5 then

[south turtle]

So instead of pi*diameter we do?

[arctic spoke]

pi*radius?

[south turtle]

yes

[arctic spoke]

ohhhh

[south turtle]

or pi*diameter / 2

which is the same as pi*radius

[arctic spoke]

is / division btw? im new so idk

[south turtle]

so do that then dont forget to add the 94

[south turtle]

yes

[arctic spoke]

alr ty

[south turtle]

.

because its also a part of the perimeter

[arctic spoke]

so like at the end after i finish the formula

i + 94?

[south turtle]

yes

[arctic spoke]

alr tysm

your an absolute legend thank you

🙏

.close

[odd edge]

Channel closed

Closed by @arctic spoke

Use .reopen if this was a mistake.

[odd edge]

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.

[royal frost]

Hi

[royal frost]

I use this rule for finding 2nd order y_p part for variation of parameters

Can we expand it to apply to any u_i??

Chatgpt gave me this. Does this mathematically apply to any y^(n) derivative?

<@&286206848099549185>

Am pinging early cuz this is the 2nd day I post this question yet I didn't get an answer

[odd edge]

@royal frost Has your question been resolved?

[royal frost]

://

[echo ginkgo]

here's a page that shows you how variation of parameters can be generalized http://mathonline.wikidot.com/the-method-of-variation-of-parameters-for-higher-order-nonho @royal frost

[echo ginkgo]

I doubt that's correct, that y_j(i)/a_n seems extremely odd

it might be just some rewriting I don't see tbf

[untold vessel]

well the perimeter of that will be 2r which is d/2 and since u know the d u can use it there. then the arc part is just half of the normal cicumference so its js pi r

[odd edge]

@royal frost Has your question been resolved?

[odd edge]

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.

[swift sky]

1. The square of an even number is even.

2. The square of 6 is an even number.

Therefore, 6 is an even number.

Can i make the following conclusion from the premises above?

[swift sky]

the truth value doesnt matter, it's a question about reasoning

[crisp wadi]

No, it looks like you are assuming the converse of the first statement

[tepid pelican]

1. horses have four legs
2. I have something with four legs

Therefore the something is a horse

this is essentially what youre doing

[swift sky]

yes exactly

i thought so too

thanks!

.close

[odd edge]

Channel closed

Closed by @swift sky

Use .reopen if this was a mistake.

[steady tide]

horses have four limbs, i also have four limbs, thus i am a horse

🐴

[odd edge]

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.

[severe shell]

Problem Statement: How many even three-digit numbers with distinct digits can be formed using the digits from 0 to 9?

Answer according to the textbook: 328

My doubt: According to my calculations, it would be 243. See my reasoning:

1st digit: can be numbers 1 to 9. Therefore, 9 possibilities.

2nd digit: can be numbers 0 to 9. But it needs to be different from the 1st digit, so it results in 9 possibilities.

3rd digit: can be 0, 2, 4, 6, or 8. However, it must be different from the 1st and 2nd digits. Therefore, 3 possibilities.

Total: 9 * 9 * 3 = 243

Where am I making a mistake?"

[signal oar]

3rd digit: can be 0, 2, 4, 6, or 8. However, it must be different from the 1st and 2nd digits. Therefore, 3 possibilities

This is surely not correct

[severe shell]

I know. But I cannot get to a better reasoning for this step. How would you formulate this step?

[clear current]

Are you sure it’s 328

Cause I’m getting 360

[low locust]

if the first two numbers are for example 1 and 5, then for the last one you have all options 0,2,4,6,8

[severe shell]

It's 328 according to the textbook

[low locust]

you have to account for what the first two digits actually are

[narrow crypt]

Split into two cases: 0 is used last, 0 is not used last

I did that way and got 328

[clear current]

Oh yea that’s where I went wrong 0 can’t be first digit

[narrow crypt]

Should i post solution or

[severe shell]

By doing so, I get 328 too. But I want to find the number of possible outcomes for each digit. So I can do (possibilities for digit 1) * (possibilities for digit 2) * (possibilities for digit 3). If I manage to find the values for each digit, this should solve the problem as well

[clear current]

It’s easier if you think about the possibilities for digit 3 first

[narrow crypt]

I see

[clear current]

And then the possibilities for digit 1 and 2 after

[odd edge]

@severe shell Has your question been resolved?

[odd edge]

@severe shell Has your question been resolved?

[odd edge]

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.

[undone crater]

guys! I 'd like some help with a problem i've been stuck on for a while now,i'll tell what i did and the key insights i had while trying to solve and i'd like like it if someone can guide through solving it

[undone crater]

anywho

we have u a digonalisable isomorphisme

and an automorphism named phi_u_(f) that associate to each morphism of L(E) ; ufu^-1

and we want to prove that phi_u is diagonalisable as well (so that phi(f) is diagonalisable for every f in L(E) :this is actually wrong , phi_u can be diagonalisable even if there exist f such as phi_u(f) isn't)

now the first thing this made me recall are the similitude classes of an endomorphism and matrix

and i thought that maybe tackling it in its matrix version would sound better

but at the same time i noticed that there were no information given about eigenvalues or eigenvectors of u or phi(i'll refer to phi_u_ from now on as phi)

this made me give up on that path, and chose instead to tackle the problem using only the fact that there exist a base made of eigenvectors of u and in which the matrix of u is diagonal or in another way that we can write E as the direct sum of a fininite number of eigenspaces associated to their respective eigenvalues

[fickle silo]

I don't see how this is true, what if u = id and f is not diagonalizable? Then ufu^-1 = f

[undone crater]

so the problem was wrong? honestly i am relieved , i had a hunch but never thought of proving it wrong

but what if we suppose that u is different than id

or maybe the hypothesis was wrong and we should suppose that f is diagonalisable

in this case we get the result immediately which is weird ,so i guess they didn't want the question to be , if f is diagonalisable then phi(f) is also diagonalisable

so i guess we should search for another condition on u

oh wait , in any case if f isn't diagonalisable then ufu^-1 isn't since they are similar

but what we're trying to do is to see if phi_u is diagonalisable

and not every individual phi_u_(f)

so like the automorphisme that associate to every endomorphisme its conjugate

yeah i think i get it

so the vectors that we are actually searching for are in L(E)

a natural base for this space is the base (e(i,j)), that gives to every vector x , ej*(x)ei where ej* is a vector of the duale base and ei is a vector of the base of E

then if we apply phi_u to the this base's vectors(that are morphisms)

we get if u is diagonalisable and we have a base made of its eigenvectors let's sau (v1......vn) associated with its eigenvalues (a1....an)

that for every k u^-1(vk)=1/ak vk

by applying an endomorphism of our base to this

we get if j=k that e(i,j)(1/ak vk)=1/ak vk

and in other cases it's 0

then we apply u

and we get that phi_u_(eij)= ai/aj vi

and by doing this for all the base guys we get that phi-u is in fact diagonalisable and that its eigenvalues are ai/aj

i think that this is it

[odd edge]

@undone crater Has your question been resolved?

[undone crater]

!close

.close

[odd edge]

Channel closed

Closed by @undone crater

Use .reopen if this was a mistake.

[odd edge]

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.

[dusk moon]

I don't understand what it's trying to say. Isn't g_a here the definition of the heavy side function

[stone cipher]

no, the heaviside function is 0 for negative numbers and 1 for positive numbers

this is 0 if t is >= and 1 if t < a

[sinful grove]

Same but shifted

Oh

[stone cipher]

(and flipped)

[dusk moon]

From my notes u_a(t) = 0 if t<a and 1 if t≥a

[stone cipher]

ok

u_a(t) = 0 if t<a and 1 if t≥a
g_a(t) = 1 if t<a and 0 if t≥a

see the difference?

[dusk moon]

I guess I see the difference if I draw the picture but how would I relate the two

[sinful grove]

You want to make 0 map to 1 and vice versa, so essentially flipping them. Now simply doing -g_a is not enough, do you see it?

[dusk moon]

Would the negative make it reflect to x axis

Similar to x^2 and -x^2

[sinful grove]

Yes, oh and to be more specific do this with u_a

Since you want to express g_a in terms of u_a

[sinful grove]

But this is not enough of course, do you see how to fix it? Hint add a number

[dusk moon]

dont know if I drawed it correctly but this what I think it looks like

[sinful grove]

Yes but why did you stop drawing suddenly the part on the left of a?

The domain does not change

[dusk moon]

i dont get what youre trying to say

[sinful grove]

You left a big hole

[dusk moon]

oh yeah thats my bad

[sinful grove]

Ah

In any case apart from that, yes that’s correct

Now compare this to g_a

What is the difference?

[dusk moon]

Not sure if I have this right but the left side should go up 1?

[sinful grove]

What’s left side?

[dusk moon]

This line

[sinful grove]

So you’re saying that after this adjustment you want to keep the right side negative?

Draw g_a first is my suggestion

[dusk moon]

The right side should be on the x axis I think

[sinful grove]

Indeed

So you want the left side to move up by 1 and the same for the right side

What does this amount to doing?

[dusk moon]

Maybe -u_a(t)+1 to get left side up 1 unit but I don't know if it affects both sides

[sinful grove]

Correct!

+1 would of course affect each side

You’re offsetting everything by 1 upwards

[dusk moon]

But from a to the right side the distance between them wouldn't you be assuming it's 1?

[sinful grove]

Hm?

What distance exactly?

[sinful grove]

You’re not assuming it’s 1

Why do you think that?

It is 1 by construction

[dusk moon]

Or maybe could I think of the distance as -1 so when I add the 1 to -u_a (t) you get 0 which is why is why it lands on x axis

[sinful grove]

When you say the word distance you’re implicitly talking about something that is non-negative, so if you don’t mean distance don’t say that as that is confusing

[sinful grove]

Yea as u_a(t) = 1 when t >= a

Then -u_a(t) = -1 when t>= a

Add 1

1-1 = 0

[dusk moon]

I mean adding the 1 makes logical sense but I just can't say for sure it shifts to x axis perfectly

[sinful grove]

?

Why can’t you say for sure?

[sinful grove]

When you drew this

Did you forget the y-values?

[dusk moon]

Like the right side looks like the line y=-1 just restricted

[sinful grove]

So how did you even draw it?

Why not label the y-values

That way, when you multiply by -1

It’s not really surprising why you have that it’s exactly the line y = -1

On the the right side

[dusk moon]

Maybe I just forgot to add the y values

[sinful grove]

[dusk moon]

But other than that everything made sense

[odd edge]

@dusk moon Has your question been resolved?

Channel closed

Closed by @dusk moon

Use .reopen if this was a mistake.

[odd edge]

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.

[mint lance]

I’m reading Elementary Functional Analysis By Charles Swartz and I got stuck after reading a commentary after theorem 5.12. They state the map Pk projects an element x from a Hilbert space H to other element y in a closed, convex subset of H, denoted by K. Because of theorem 5.12 I know y is unique, and they also explain that Pk is uniformly continuous on H. The thing is, in previous chapters they state a linear bounded operator is continuous. My teacher also explained that for linear operators, boundedness and continuity are equivalent concepts. So my question is, could the map Pk be a linear bounded operator? I suspect it’s not linear since K is only a closed and convex subset, so either of the linearity properties might fail, but what about boundedness? In class we have only worked with linear, bounded operators, could the the operator be non linear but bounded? If so, how could I prove it? Maybe Lipschitz condition?

[odd edge]

@mint lance Has your question been resolved?

[amber walrus]

🗿

[echo ginkgo]

in general it's not bounded either

take this super simple example in R
say K = [1,2], it's non-empty, closed and convex
all the elements of K have norm >=1, therefore ||P_K(x)|| >= 1 for all x in R

and ||P_K(x)||/||x|| >= 1/||x||

so if ||x|| goes to 0, this ratio blows up to infinity

of course here I chose on purpose a K which doesn't contain 0, that's the main problem

if it does contain 0, the projection map is prolly bounded

[mint lance]

Oh I see, and that makes sense because my teacher said that to prove a linear operator is continuous, it was enough to prove its continuous at 0, but since its not linear, we can’t be sure it’s continuous at 0, and the example depicts it. I had doubts because in class we defined boundedness concepts only for linear operators, but since K is not necessarily a subspace of H, The definition of linear operator doesn’t apply. (We defined in class linear operator T: X->Y and X, Y are vectorial spaces).

.close

[odd edge]

Channel closed

Closed by @mint lance

Use .reopen if this was a mistake.

[odd edge]

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.

[steady tide]

how would i do (c)?

[steady tide]

dimU = 3, so i just need to find a W such that dimW = 2

but not sure where should i start

[lone elbow]

Can you

Use the orthogonal complement of U

Or I might me tripping

[steady tide]

err, what is that

[lone elbow]

Forget it then

[steady tide]

for reference, this is what i have only learned so far

[lone elbow]

I mean is just the vector space with all the vectors orthogonal to U

Should be dim 2 and should not intersect U

But idk

[odd edge]

@steady tide Has your question been resolved?

[lone elbow]

Or you can use the extended basis from b) to get the two vectors from W

If you managed to extend a basis of U to a basis of R5 and dim(U)=3 there you have two linearly independent vectors

From the definition of direct sum, U n W ={0} only trivial intersection

What are you confused about?

[steady tide]

mainly on how to start constructing such subspace

if it helps, this was my work on (a) and (b)

[lone elbow]

W = <(0,0,0,1,0),(0,0,0,0,1)>

[steady tide]

wouldnt it be <(0, 1, 0, 0, 0), (0, 0, 0, 1, 0)>?

[lone elbow]

No no wait mb

[lone elbow]

Yeah sorry

[steady tide]

ah i see now

so maybe something like

${(0, x, 0, y, 0)\in\mathbb R^5}$

[steady tide]

would work?

[lone elbow]

Yeah since W =<(0, 1, 0, 0, 0), (0, 0, 0, 1, 0)>

a(0,1,0,0,0)+b(0,0,0,1,0) = (0,a,0,b,0) with a,b in R

We can check if they only intersect trivially but since they form a basis of R5 alongside the vectors from U idk if necessary

[steady tide]

alright, thanks

.close

[odd edge]

Channel closed

Closed by @steady tide

Use .reopen if this was a mistake.

[odd edge]

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.

[jagged lantern]

can i get help on question 9?

[jagged lantern]

it’s just below question 8

[odd edge]

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

[jagged lantern]

1

all i’m understanding from this question is that the longer base is 30cm

[pastel steeple]

uh you mean the 3 equally split parts are each 10 cm?

[jagged lantern]

why is that

?

[pastel steeple]

it says the long sheet of metal is bent to form that shape

and theres congruency markers on each section

[jagged lantern]

but how do i know which dimension is which

30cm??

[pastel steeple]

wdym

it says the long sheet of metal is 30 cm

if it was divided into 3 equal lengths then each one would have to be 10 cm?

[jagged lantern]

wouldnt that be the longer base at the top?

[pastel steeple]

that doesnt look bent does it

and it says open gutter

im assuming the top is actually open

[jagged lantern]

i honestly wouldnt have known those 3 are equal to 30 altogether

it doesnt click in my head

[pastel steeple]

if you still arent convinced if the top was 30 cm then there can only be one angle where the 3 bottom sections are congruent

anyways do you know how to write the area of one of those triangles on the side given the angle and side length

[jagged lantern]

would their base and height be 10cosx and 10sinx?

[pastel steeple]

hmmmmmm i believe so

[jagged lantern]

so it’s 0.5(10sinx * 10cosx)

which is just 50sinxcosx

[pastel steeple]

there's 2 triangles

[jagged lantern]

oh so

100sinxcosx for the two right?

[pastel steeple]

i think so

the rectangle in the middle should be easy right

[jagged lantern]

it’s 100cm^2

wait no

100sinx

[pastel steeple]

is it sin or cos

sin is opposite of the angle

cos is adjacent to the angle

[jagged lantern]

so 100cosx

[golden marten]

sin = o/h cos = a/h

[pastel steeple]

what is the area now

[jagged lantern]

100cosx + 100cosxsinx

which is

100cosx(1 + sinx)

[pastel steeple]

[jagged lantern]

i’m not a fan of trigonometry 😩

bear with me

there’s a second part to the question

idk if it’s visible on the image

[pastel steeple]

its cut off

it looks more like a calculus problem than a trig problem anyways

[jagged lantern]

lemme resend and try on my own

that part b

[pastel steeple]

yeah yeah

i dont think its hard if you got the fundamentos of calculus

[chilly ravine]

That's incredibly easy if you did physics

[chilly ravine]

Wait Q9 or 8?

[jagged lantern]

question 9

[chilly ravine]

Where's part a

[chilly ravine]

You did part a already?

What's the answer

[jagged lantern]

yez

[jagged lantern]

^

[chilly ravine]

I meant like the calculations since it already gives the answer in the question lol but whatevs

[jagged lantern]

ohh

[chilly ravine]

Differentiate, find Q, differentiate and show that it is max, then plug in Q into A

[jagged lantern]

a little above

[chilly ravine]

That's it

[jagged lantern]

there’s some working out

[chilly ravine]

I'm guessing you don't know how to differentiate?

[jagged lantern]

i do know how to

i found the answer

[chilly ravine]

Ah okay cool

[jagged lantern]

i differentiated, equated to 0, found values for theta, then differentiated again and plugged in each value to see which one is a max

the angle is pi/6

[chilly ravine]

Yeah then you plug in Q=π/6 in your A area equation

[jagged lantern]

very simplified, but yes

these questions allow calculators

thanks again for the help guys

.close

[odd edge]

Channel closed

Closed by @jagged lantern

Use .reopen if this was a mistake.

[odd edge]

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.

[median bane]

m

[median bane]

A 310 000 kg meteor is heading directly towards a space shuttle at 35 m/s. It is pushed for a period of 45 seconds after which its velocity is 27 m/s and it has veered 22° from its original course.
a) Find the impulse given to the meteor (magnitude and direction).

for this question i need help finding the angle

so far i found Pi, Pfx and Pfy

itd just be tan-1 (pfy/pfx) right

[vale vortex]

Nice pencil

[median bane]

ty man

do yk how to do it

[vale vortex]

I could def figure it out but I’m going to bed ngl

[median bane]

bro

[vale vortex]

If your desperate I could ask ai if u can’t rq

[median bane]

like chatgpt?

i did

[vale vortex]

Did it help

[median bane]

no 💀

useless for physics

[vale vortex]

Which model did u ask ?

[median bane]

i got it srry

new one

[vale vortex]

👍

[fringe bough]

definitely don't use gpt lol

[median bane]

i was overthinking bc my friends got diff answers but i think its just this

[vale vortex]

That’s what gpt said

lol

[median bane]

fr

ty real one

[vale vortex]

Might as well send this since I asked

[median bane]

what is ts 💀

its 22 right

[chilly ravine]

Chat GPT

[vale vortex]

Idk

But

[mystic saffron]

I also got -45 for the angle.

[vale vortex]

Type shit

[median bane]

cooked

[chilly ravine]

Would've been so much easier if you just drew a diagram

[mystic saffron]

Impulse in x direction = Mass * (27 cos 22 - 35)

Impulse in y direction = Mass * (27 sin 22)

[odd edge]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[vale vortex]

Idk who sent that but u should read some context 🙄

[median bane]

i see

thatd also change the 4.4e6 Ns too

[mystic saffron]

No, I agree with 4.4e6 for the magnitude

[median bane]

so everythings right i just have to replcae my Pfx?

[median bane]

oh

[mystic saffron]

Yea, and once you do the inverse tan you should get approx. -45 for the angle

[median bane]

how is it still 4.4e6

like if i do pythagorean wouldnt the hyp be diff now

[mystic saffron]

I did the Pythagorean theorem with the x and y component

Computations here: https://www.desmos.com/calculator/npviddedao

[median bane]

fr

ty

[mystic saffron]

Actually the angle should be -45 + 180 since the x-vector is pointing left and the y-vector is pointing up

[median bane]

yea -45 or 135

im writing it as (W45N)

alr ty i appreciate it alot fr

.close

[odd edge]

Channel closed

Closed by @median bane

Use .reopen if this was a mistake.

[odd edge]

Available help channel!

Send your question here to claim the channel.

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

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

[delicate sinew]

why is it not sqrt(4k-2/5)

[odd edge]

@delicate sinew Has your question been resolved?

Channel closed

Closed by @delicate sinew

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.

[mystic saffron]

<@&286206848099549185>

[hearty crest]

use unit circle

[mystic saffron]

What's that?

[west hull]

It’s a circle with radius 1

[autumn bolt]

do you know the basic sine and cosine values?

[west hull]

Where points on the circle are found (cosx,sinx) for (x,y)

[mystic saffron]

Like this?

[autumn bolt]

yes

[mystic saffron]

No..

[autumn bolt]

okk

you need just 5 for now

sin 0 is 0

[mystic saffron]

okie

[autumn bolt]

$\sin(\frac{\pi}{6})$ is $\frac{1}{2}$\\
$\sin(\frac{\pi}{3})$ is $\frac{\sqrt{3}}{2}$\\
and $\sin(\frac{\pi}{2})$ is $1$\\

[mystic saffron]

https://tenor.com/view/anime-spy-x-family-dizzy-anya-cute-gif-25812281

[mystic saffron]

okay that's better

[autumn bolt]

you can convert pi to 180 degrees too

sin 30 degrees is 1/2

[west hull]

Why list out values when you can teach how to find them from the unit circle

[autumn bolt]

the op doesnt know the beginning values though

and the unit circle is for angles like 7pi/6

[west hull]

The unit circle is for any of the values on it

[autumn bolt]

thats true

but you need to know the primary values first

[west hull]

And where do those come from

[autumn bolt]

from triangles

the unit circle is another representation

[west hull]

From waves

Just teach her how to fish. You waste her time giving her fish

[mystic saffron]

https://tenor.com/view/anime-confusion-what-gif-19368852

[mystic saffron]

How about we begin with an example on how this work TwT

[autumn bolt]

ok then say what you want to now

it feels like the same thing to me but well see

[mystic saffron]

Can weeeee pleasee begin with an example on how will I solve it

The first question asks for sin^-1(√3 / 2),

Another way of asking is, "What angle, if I took the sine of it, would return √3 / 2?"

On your unit circle, values for sine are shown in the y-coordinates

Which two angles have a y-coordinate of √3/2?

Q1 30 degrees

[inland rover]

is sin(30)=\sqrt(3)/2?

[mystic saffron]

What

Not quite. We're doing the inverse sine, so we are looking for where the **y-coordinate **is equal to √3 / 2

Note that I have marked the two angles that have a y-coordinate of √3 / 2.

Which two angles are those?

Q1

Sorry you might not know quadrants

On the right hehe

NO WAIT

On the left

because sin-1

[tacit wasp]

What??

[tacit wasp]

Just answer this

[mystic saffron]

How do I mention angles...

The various locations on the unit circle have an angle marked like so

Oh

NO

120 degrees

Both 60 degrees and 120 degrees are correct

[steep mantle]

isnt sin^-1(x) {-pi/2<=x<=pi/2}

[mystic saffron]

but it's sin-1

[tacit wasp]

Yep, therefore which one do you choose between 60° and 120° ?

[mystic saffron]

120

<@&286206848099549185>

[odd edge]

@mystic saffron Has your question been resolved?

[mystic saffron]

<@&286206848099549185>

[tacit haven]

?

[mystic saffron]

Math

[tacit haven]

what are you stuck on

wait werent you on like exponents a few weeks ago

[mystic saffron]

yeah

time move on so fast

anyways

idk how to solve this

<@&286206848099549185>

Come on

Anyone??

It's been so long

[tacit haven]

arcsinx is "sin of what angle is x"

[signal crown]

where are you stuck

[south turtle]

You've pinged helpers like 5 times

[mystic saffron]

I had a timer and everything man

It's insane

I even tally how much times people ignore

[signal crown]

🚶‍♂️‍➡️

[tacit haven]

.

[mystic saffron]

Okay so uhhh

[tacit haven]

have you learnt inverse functions

[mystic saffron]

This is like everyday thing, Activity before discussion

[south turtle]

"If your question has not been answered for a minimum of 15 minutes, you may use the helpers tag once. Do not abuse this ping."

[mystic saffron]

So I have no idea

[tacit haven]

oh

[mystic saffron]

I timed it

15 mins on the clock

[tacit haven]

sin(x) = y implies x = arcsin(y)

[south turtle]

Im not sure whether that means you can ping helpers every 15 mins or just once every time you open a help channel

[mystic saffron]

I ping helpers every 15 mins

[signal crown]

just let it slide

[mystic saffron]

" After 15 minutes, feel free to ping <@&286206848099549185>."

So I can do it every after 15 mins

oops.

[mystic saffron]

I don't get it

[south turtle]

Whatever its fine

[mystic saffron]

YIPPE

[signal crown]

the basics of inverse function

arcsin is the inverse of sin

[mystic saffron]

Okie

So x in reverse is y?

[signal crown]

now for the second time, where are u stuck

[signal crown]

no, not like that

[mystic saffron]

well.. I wasn't stuck on it it's just tha every answer I did was wrong

[signal crown]

when we are talking about inverse, we are talking about application

[signal crown]

ah

[mystic saffron]

Okie

So i guess Im stuck on answering the question-

[signal crown]

for example : f(x) = y, means that x = f^{-1} (y)

[forest yoke]

Hi

Lets look at the first question

Which sbould helo with some basics

Of inverse functions

[mystic saffron]

Yes please

[forest yoke]

The question says

[mystic saffron]

So x will be negative?

[signal crown]

no

[forest yoke]

Sin-(root of 3/2)

Now this question is fairly straight forward

You must know the trignometry table

We know sin 60 degrees is root 3/2

[signal crown]

work in radian

[mystic saffron]

yes

[forest yoke]

There fore the answer to the first question is 60 degrees

[forest yoke]

Ok

60 degrees is pi/3

Do you know how to convert from degrees to radians?

[mystic saffron]

pi/180

[forest yoke]

Correct

So now the second question has 2 functions

The first function being cos

[mystic saffron]

WAIT

[forest yoke]

And then the second being arc sin

[mystic saffron]

How did the first question got answered??-

[forest yoke]

Yes?

[signal crown]

the answer is pi/3

do you know how inverse function works ?

$\left(f \circ f^{-1} \right)(x) = f(f^{-1}(x)) = x$

[mystic saffron]

No

[clever fjord]

Herels

[signal crown]

ok, do you know what a function or an application is ?

[mystic saffron]

I don't get it

[mystic saffron]

no...

[signal crown]

things will get complicated...

[forest yoke]

Lol

Its ok

Look inverse usually means opposite right?

[tacit haven]

wait why are you studying inverse functions then😭

[signal crown]

welp how would I define a fonction

[mystic saffron]

Idk! Ask the teacher

[signal crown]

which grade are you

[mystic saffron]

11

[signal crown]

grade 11 and doesnt know about function

hmmm

thats weird

[tacit haven]

a function is basically doing some operation on something, like f(x) = x^2, f(y) = sin(y), f(z) = z!

[mystic saffron]

IM SO SORRY I'M DUMB

[mystic saffron]

Please don't ever judge me like that ever again

[tacit haven]

teacher is probably trying to make the class catch up quickly

[signal crown]

not your fault, maybe the fault of your teacher

[signal crown]

i'm not judging

[mystic saffron]

I did study that when I was Grade 5

so yeah maybe a recap

[tacit haven]

^

[mystic saffron]

I just forgot

[tacit haven]

a function can also be constant

[mystic saffron]

and reverse function is something like... f(-1) x?

[signal crown]

a fonction is like a map sending a value from a set to an another set

the inverse is doing the reverse

[tacit haven]

for example suppose f(x) = x^2, then the inverse of f(x) is sqrt(x)

[mystic saffron]

I don't get it

[forest yoke]

So what is a function?

Lets look at some real life examples

Look at a mixture grinder : its function is to grind and mix stuff

You put in fruits and other stuff and the mixture grinds evrything and gives u juice

Now in math terms let the grinder be the "function"
The fruits be the "input"
And the juice be the "output"

There fore a function has an input and an out put

Now you cant put a huge water melon in a grinder can you?

Same way you camt put EVERYTHING in a function

A function has some thing called " domain" and " range"

Now wth is domain and range????

So if you look at the muxture

It has a size limit of fruits and stuff u can put in it

We call that domain

In a function

And in a mixture the only out put u can get are juices
You can think of the different types of juices the grinder can make as " range" of the mixture

Do you understand a bit?

We usually denote a function as f(x)

If you dont ubserstand lemme know

[mystic saffron]

So if I put it in an inverse function

the domain will be the juics

while the ranges are the diferent types of fruits?

[forest yoke]

Ummm well kot exacy

Exactly

Lets just assume

The mixture was the function
So lets just call inverse function the "inverse grinder"

In the inverse grinder you would hypothetically but in juices as the input

And you would get fruits

As the out put

The domain of the "inverse grinder" would be " only juices"

And the range of the inverse grinder would be " fruits"

[forest yoke]

So yeah

Ur rigjt

My bad

[mystic saffron]

What

[forest yoke]

Ur right

The domain will he the juices

And the range will be fruits

U get?

[mystic saffron]

Okay

[forest yoke]

Now try applying that same logic to the first question

Where the function is sin inverse

[mystic saffron]

uhhh

[forest yoke]

And the in put is root 3/2

We need to find the output

Now what you should ask your self is :
What value of sin gives me root3/2

And we know sin pi/3 = root 3/2

[mystic saffron]

Now I'm confused

[forest yoke]

Is ok happens

Did you understand what a function is?

[mystic saffron]

Yeah

[forest yoke]

Do you understand what an inverse function is?

[mystic saffron]

Yes

[forest yoke]

Good job

Now

Lets look at the first question

The first question has an inverse function in it

The inverse function is
" sin^-1 "

That power of -1 indicates its an inverse function

You get?

[mystic saffron]

Yeah

[forest yoke]

Now lets forget about that inverse function