help-23

[split kayak]

B becomes the "1" here
And we want to know what percentage the blue region takes in B

[primal onyx]

Got it

[split kayak]

Once you got that explanation, you probably can make sense of this formula

[primal onyx]

Sorry if wrong but imma try

So 0,015 devided through 0,03?

[split kayak]

almost

[primal onyx]

0,025*0,03 devided through 0,03?

[split kayak]

Nope. going back to the diagram

We know its divided like this

We know that the 3% is only B, and 1.5% is A and B

So B is different from 3%

[primal onyx]

hmmm

[split kayak]

Do you know what B is then?

[primal onyx]

1,5?

[split kayak]

Remember that B is the circle on the right in its entirity

Which, based on how we divided it, left us with two regions

[primal onyx]

4,5?

[split kayak]

yep

B is the sum of the red and green section

A∩B is the green part

now, what would you get at the end then?

Which, these are the same as we drew here

[primal onyx]

0,015/0,045

[split kayak]

yep

which is just 1/3
aka 33.33%

[primal onyx]

Perfect thanks

.close

[safe radish]

Channel closed

Closed by @primal onyx

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[vagrant ice]

a quick and dirty way is to draw a line between (0, 3) and (4, 0) and then find the area of that triangle

[cursive tiger]

what do you mean? how would that work

[vagrant ice]

you want around the same shaded area inside the triangle as the unshaded area

so that they would cancel each other out

[cursive tiger]

ohhhhhhh

lemme try it

it worked tyy

Its D

.close

[safe radish]

Channel closed

Closed by @cursive tiger

Use .reopen if this was a mistake.

[vagrant ice]

in fact there's more white area inside the triangle than the shaded area

[cursive tiger]

yes

[vagrant ice]

that tells you the area is even less than 6

I found the area using calculus and it's around 4.97

no worries!

[cursive tiger]

ohhh this isnt thta advanced so i think its jus estimated but tyy!

[vagrant ice]

yeah you would never need to do that

I just checked since I know how to find the exact area

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[vast shard]

hi can someone help please

[vast shard]

i dont undertsand

@visual kraken hi are you able to help lol

[plucky elk]

!noping

[safe radish]

Please do not ping individual helpers unprompted.

[vast shard]

and why did you ping me then

[plucky elk]

To let you know not to ping individual helpers

[vast shard]

well that was unprompted

[plucky elk]

This prompted

[vast shard]

<@&286206848099549185>

[safe radish]

@vast shard Has your question been resolved?

[vast shard]

<@&286206848099549185>

[safe radish]

@vast shard Has your question been resolved?

[limber leaf]

https://cdn.discordapp.com/attachments/1419791471061635204/1434796932286648320/attachment.gif

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[mossy urchin]

i keep getting the wrong answer for this

[rare briar]

Could you show your work?

[mossy urchin]

2x-1+2x+5x+6x-2+4x-1+3x > 29

[rare briar]

How did you find this side?

[mossy urchin]

6x-2 - 2x -1

[rare briar]

Make sure to put parentheses

6x-2-(2x-1)

[mossy urchin]

(6x-2) - (2x-1) yes

Ohh

well then

6x - 2 - 2x + 1

-4x - 1

[rare briar]

-4x?

[mossy urchin]

6x - 2x

Oh oops

4x - 1

[rare briar]

Yup

[mossy urchin]

[rare briar]

Everything else seemed to be good

[mossy urchin]

im getting -2

+2 to 29 makes 31

i need 33

[rare briar]

Well, you calculated 4x-1

And you seem to have put 4x+1 instead

[mossy urchin]

Ah

got -4

thanks!

.close

[safe radish]

Channel closed

Closed by @mossy urchin

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[primal onyx]

How does 4. Work?

[mossy lotus]

it looks to me that whatever is written on the page is wrong. Like 90/360 = 1/4 and not 1/3. but other than that the idea used looks okay

there are 5 ways of how many C's you can land upon rotating the wheel 4 times, which are: 0 times, 1 time, ... , 4 times landing on C

so, when you are asked about at most 3 times C, that means you need to count the cases for (0 + 1 + 2 + 3) times landing on C

which is equivalent to saying not landing 4 times on C

coz P(E) = 1 - P(not E) for an event E

[safe radish]

@primal onyx Has your question been resolved?

[primal onyx]

I dont quite get what u mean with this

[mossy lotus]

you can split the situation into a total of 5 different cases like I said herer, do you agree on this or not?

[primal onyx]

Yup that i get

[mossy lotus]

lets call each of that E0, E1 and so on

so what you want is P(E0 + E1 + E2 +E3) right?

[primal onyx]

Yup

[mossy lotus]

and P(E0) + P(E1) + ... + P(E4) = 1

[primal onyx]

Mhm

[mossy lotus]

now, since E0, E1 etc are mutually independent, you can say P(E0 + E1 + E2 +E3) = P(E0) + P(E1) + P(E2) + P(E3)

[mossy lotus]

and from this, you can directly substitute P(E0) + P(E1) + P(E2) + P(E3) as 1 - P(E4)

[primal onyx]

Mhhhh i see now

So now i would do 1- 90/360^4 ?

[mossy lotus]

yea

1- (90/360)^4

[primal onyx]

so in words all other outcomes- the outcome that it lands 4 times in a row

[mossy lotus]

I'd write it like this

where E is E0+E1+E2+E3 for this problem by earlier notation and not E is E4

[primal onyx]

Got it

Thank you

Could you help me with 8 and 9 aswell?

[mossy lotus]

well, what you said for 8 is very vague, and strictly speaking, makes no sense coz its either incomplete or wrong

3rd quartile is where 75% of the data lies below the value and 25% above it

so what was probably expected was something like 75% people finished the race in under [Q3] minutes

You said in 7 that q3 is 56, but it looks like its between 50 and 55, so more likely value for that would be 53 min

[primal onyx]

Mhmm

And 9. u can say its judt say it doesnt state the participant amount right?

[mossy lotus]

oh nvm, it looks like the values in the box plot are from the table in 6 I think?

so you need to take (56+59)/2 as the 3rd quartile I guess? but then the box plot looks like its wrong

can you confirm if the table and plot are related?

Oh Im dumb, they arent

nvm

[primal onyx]

I think not because min and max are also different no?

[mossy lotus]

yea, I just noticed that

Im an idiot

[primal onyx]

all good shaha

[mossy lotus]

yea, so for 9, you have written something quite irrelevant to whats being asked

you need to determine the total number of participants

but nothing in the box plot say anything about the frequency

so you have no clue of knowing about the size of the population represented by the plot

the plot only indicates the quantities which are independent of population size

[primal onyx]

Okey perfect got it

Thank you

.close

[safe radish]

Channel closed

Closed by @primal onyx

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[opaque fern]

For a linear, time-invariant system characterised by a frequency response $H(j\omega)$, consider the input $x(t)=\sin(\omega t)$. Is it correct that the corresponding steady-state output is the sinusoid
[
y_{\t{ss}}(t) = \abs{H(j\omega)}\6\sin{\omega t + \6\arg{H(j\omega)}}?
]
In other words, does an LTI system map a single-frequency sinusoid to another sinusoid of the same frequency but with amplitude scaled by the magnitude of the transfer function with a phase shift corresponding to its argument?

[opaque fern]

no original question or whatever, this just came up from some independent work im doing

I feel like this makes sense because complex exponentials are eigenfunctions of LTI systems

[safe radish]

@opaque fern Has your question been resolved?

[safe radish]

@opaque fern Has your question been resolved?

[safe radish]

@opaque fern Has your question been resolved?

[safe radish]

@opaque fern Has your question been resolved?

[lean otter]

Yeah, you have the right idea

Since complex exponentials are just eigenfunctions of LTI systems you can then write

[
x(t) = \sin(\omega t) = \Im{ e^{j\omega t} }
]

oops not sure how the bot works here. not familiar with texit

[warm warren]

$LaTeX in here$

[flat frigate]

Annie Maqionde

[lean otter]

but yeah from there the steady state response comes out as

$y_{\text{ss}}(t) = |H(j\omega)| \sin!\big( \omega t + \arg H(j\omega) \big)$

[flat frigate]

Solstyx

[safe radish]

@opaque fern Has your question been resolved?

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[lean otter]

Why is 0!=1? My teacher won't explain lol

[edgy breach]

what is x! in terms of x-1?

[broken folio]

Mostly because it works nice in formulas I think

[lean otter]

I'm sorry I don't really understand

[loud wren]

How many ways can you arrange zero objects?

[edgy breach]

x! = x(x-1)!

[lean otter]

Oh

OH

[edgy breach]

because to get to the next factorial its the same as multiplying all the numbers up to x-1 and also x

[loud wren]

We hath summoned a cult with this question

[broken folio]

Also this yeah

[cedar widget]

start with one approach at a time

[empty gyro]

This definition isn't helpful because you can equally argue 0!=0x(-1)!

[edgy breach]

i love how as soon as 0! is mentioned the entire server pools in here wanting to brag about their knowledge which is futile since clearly its not a brag lol

[opaque fern]

"Intuitive" explanation, expanding on the above:

4! = 24
3! = 6 (divide 4! by 4)
2! = 2 (divide 3! by 3)
1! = 1 (divide 2! by 2)
0! = 1 (divide 1! By 1)

[lean otter]

Thank you so much everyone!

I shall close this mini cult now

.close

[safe radish]

Channel closed

Closed by @alpine juniper

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[peak lake]

hi i need help

[peak lake]

I want to verify if I am right for the answer I got

[astral glacier]

Well what's the answer you got

[peak lake]

I got

AE = 2DB - CE

[astral glacier]

Show your work

Or your thought process

[peak lake]

is it right though

then i can show

[astral glacier]

Show first, I wanna see how you arrived at this conclusion

[peak lake]

il send a photo

here

[astral glacier]

Go ahead

[peak lake]

oh shi

mb

[astral glacier]

Yup

That's correct

[peak lake]

okay thanks

I also want to check if I got this right

[astral glacier]

Sure send your working

[peak lake]

I got

5/4 AB

[astral glacier]

Working my guy

[peak lake]

oh i got u

one sec

@astral glacier heres the pic

[astral glacier]

Oh shit sorry got busy in another channel

[peak lake]

nah ur good

dw

preciate the help

[astral glacier]

That image is nearly unreadable lol

[peak lake]

LMFAO

I got 5/4

[astral glacier]

But I think it's correct

[peak lake]

AB

[astral glacier]

After a lot of eye strain

[peak lake]

LOL

wait leme

resend

[daring river]

😭

Thats W handwriting man

[peak lake]

is dis better

[astral glacier]

It's the lighting, not the handwriting

But yea looks good like I said

[peak lake]

okay thanks

[daring river]

The handwriting is up and down.

[peak lake]

ur name is sk

[daring river]

ur name is k4sh

[peak lake]

ik its hard n ur pfp is pink

bro this is my channel

stop

for part 1 I got

220 km / h east

and part b i got

205km/h east

[astral glacier]

a is correct

B feels wrong

[peak lake]

oh shi

i meant

225

[astral glacier]

Yup

[peak lake]

yo how u so fast

holy

guy knows the answers right away

[astral glacier]

Lmao

[peak lake]

how do you though holy

[astral glacier]

Lots of time

[peak lake]

yeah

make sense

wait ima send 2 more

to check

@astral glacier

[safe radish]

@peak lake Has your question been resolved?

[rancid lion]

you can square the whole thing if you want

[brisk coral]

Ok

[rancid lion]

or notice that $\frac {1}{|\vec{u}|} \cdot \vec{u}$ is just vector u but scaled so that it has length 1

[flat frigate]

Carbonara

[peak lake]

@astral glacier

[rancid lion]

What's your answer here

[peak lake]

square root 2

is that right

[rancid lion]

it is

[peak lake]

@astral glacier hey

can u verify

[safe radish]

@peak lake Has your question been resolved?

Channel closed

Closed by @peak lake

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[astral glacier]

. Oops got busy, sorry!

[untold rover]

hey i wanted to know if there was an easy and fast way to memorize this trigonometric formulas, like the hexagon for basic and pitagoric functoins... i have a live or die algebra test in 1 week and if i dont pass it i will be kicked out of my career, usually i would spend hours to study with no problem but i also have 4 more topics to go :c

[plucky elk]

#study-discussion

But probably just do a lot of problems using them

[untold rover]

right

[proven lintel]

Guys I need help I've been doing this problem since the morning I can not figure ut out at all I've watched so many videos I can't do anything

I have tried 46.918 dividing, multiplying everything it won't work and I'm about to give up

<@&286206848099549185>

[empty forge]

get ur own channel lol

just copy and paste your question onto a unoccupied help channel

[proven lintel]

How do I do that please help me

Okay thank you

[empty forge]

this lol

[fierce sand]

Do u have the equation for the function

[proven lintel]

Nope it doesn't give one I'm assuming it's y=(x-2) or y=x^2 thats how I got the first one

[fallow thicket]

open a new channel

[fierce sand]

And does it tells u the area of each rectangle and exact sections under the finitions

Function

@proven lintel

[proven lintel]

No nothing everything is there thats all they give and it also let's you move the n around from 1 to 50

Im struggling to make a channel I dont see the option

[fierce sand]

Well then that is easy

Subtract the exact area by the given max difference

And test which n is closest but bigger then this

[fallow cairn]

Under Math Help (Available), send a message into any #help-X channel, such as #help-20 (currently available.) You can review this in #❓how-to-get-help

[fierce sand]

Like the sum of areas for that number of n

@proven lintel

Done

[proven lintel]

I made a channel can you please explain more

[fierce sand]

Which one

[proven lintel]

Help 6

[safe radish]

@untold rover Has your question been resolved?

Channel closed

Closed by @untold rover

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[valid mauve]

Hi

[valid mauve]

I need to show the theorem above, using the following*

I need to turn f(x) into a monic polynomial, but I'm not sure how to write it "formally"

[lean otter]

x^n+a1x^n-1+a2x^n-2+...+an-1

[valid mauve]

what?

[lean otter]

F(x).

[lean otter]

That is a "formal" monic polynomial.

[rustic goblet]

I'm confused, why can't you just take g_1 and h_1 as g and h respectively?

[valid mauve]

Well, I meant I need to re-write f(x) as a monic polynomial to use this. As far as I know, f(x) could not be monic at first

[rustic goblet]

ah, because g and h may not be monic

[valid mauve]

Yes

g and h could have their leading coefficents as "a" and "a^{-1}", so f would still be monic but g and h not

[rustic goblet]

well, the coefficients must live in Z, so the only options for their coefficients are 1 and -1

[valid mauve]

g and h are in Q[x]

[rustic goblet]

use the theorem to get g_1 and h_1 in Z[x]

[valid mauve]

but f should be monic first, to use the theorem I need to re-write f as a monic polynomial, because it could be not, so can't use the statement

[rustic goblet]

the theorem doesn't assume that f is monic, wdym?

[valid mauve]

I already proved this also

[rustic goblet]

you are also given that f is monic

[valid mauve]

This is what I need to prove

[rustic goblet]

oh, it's the other way around

[valid mauve]

My bad, I might have not been clear

[lean otter]

Wait if f is monic, then g and h have to be monic right?

[rustic goblet]

x^2 = 5x * 0.2x

[lean otter]

But we need to prove for integers coefficients?

[rustic goblet]

x^2 = -x * x

[safe radish]

@valid mauve Has your question been resolved?

[valid mauve]

nop because they are in Q

[safe radish]

@valid mauve Has your question been resolved?

Channel closed

Closed by @valid mauve

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[neat sail]

What's the difference between hill climb algorithm and gradient descent

[safe radish]

@neat sail Has your question been resolved?

Channel closed

Closed by @neat sail

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[loud cedar]

Wut is equation of a circle

[ornate wyvern]

x^2+y^2+2gx+2fy+c=0

(general eqn)

here centre is (-g,-f), radius is sqrt(g^2+f^2-c)

also there exists another eqn: (x-h)^2+(y-k)^2=r^2 where (h,k) is centre, r is radius

[worn pollen]

Basically you would have to convert the equation of circles in perfect square format

[loud cedar]

The wut

Perfect square format?

[ornate wyvern]

yes

[ornate wyvern]

like this here

[safe radish]

@loud cedar Has your question been resolved?

[ornate wyvern]

@loud cedar ?

[loud cedar]

Waittt

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[hoary seal]

how do we sketch this

[safe radish]

@hoary seal Has your question been resolved?

[fierce nimbus]

do u know how to sketch sine graphs

u just do the normal sine graph but phase shift it by a unit of 1

[hoary seal]

yep

[hoary seal]

I’m not familiar with unit of 1

I’m more familiar when it has pi in it

[fierce nimbus]

ur units is just numbers its not in pi anymore

[hoary seal]

How will I know the intervals

[fierce nimbus]

oh wait im ngl i forgot about this

i dont wanna bs u either sorry bro 😔

[austere goblet]

pi is just a number like anything else, with a value of ~3.141

so if you can do pi, you can do 1

it won't be a clean shift; the graph at x = 0 will be some height below the x-axis, yet not quite at its peak

alternatively, build intuition via desmos

[hoary seal]

Hm ok

so something like this?

[vivid bison]

Not quite

[vivid bison]

First sketch sinx (intersections with x-axis should be kπ where k is an integer)

Then shift that graph to the left by 1 unit

[hoary seal]

how much is 1 radian

btw for this question, Im not sure why I got this wrong?

[burnt notch]

Exactly the number 1

If instead you're referring to the angles in degrees, 1 rad is approximately 57°

[kindred dagger]

If you're talking about how to convert from radian to degrees - its 360° for the full circle which is equivalent to 2Pi. Using the direct proportion you get the result @burnt notch has stated of roughly about 57°.

[hoary seal]

im talking about tthe value of 1 radian

is it equal to 1?

example, e is 2.7

what about 1 R

[kindred dagger]

A Radian isn't a number - it's a unit, just like degrees

[hoary seal]

oh. alright

[hoary seal]

ive been actually struggling this problem since forever it would be nice if I could solve this soon haha

[hoary seal]

x-axis should be kπ where k is an integer)

i dontu nderstan this phrase

understand*

[kindred dagger]

Do you know how the normal sinus function looks like?

[hoary seal]

yeah

It starts from the origin

[kindred dagger]

Ok so there are different parameters when it comes to these functions

[vivid bison]

sinx should intersect with x-axis at x=[...-2π, -π, 0, π, 2π...]

[kindred dagger]

a*sin(b*x+c)+d is the form we're looking for

a is the amplitude
b is stretching or compressing the function
c is moving your function sideways
d is moving your function up/down

In your case a and b are 1, d is 0 so except for c all parameters are just like in the classic sinus function (c≠0 here). What you've now gotta do is check how changing c affects the function

[hoary seal]

but c is also 1

[kindred dagger]

Yep sorry, obviously meant d and c should be 0 in normal function

[hoary seal]

and c is 1 in our case

correct?

[kindred dagger]

Yup

So exactly thats the difference to the sin(x) function

[hoary seal]

everything is the same except the c

parameter

hence (x+1) in its argument

[kindred dagger]

Yes

[hoary seal]

I dont wanna graph it on desmos but will after getting the answer

[kindred dagger]

Alright yeah - so do you know how the +1 affects it now?

[hoary seal]

it shifts the function by 1

so we need to move back by 1

[kindred dagger]

Yes

[hoary seal]

im just confused with how I am supposed to get the intervals

the period is 2 pi -1 right?

[kindred dagger]

Oh don't take 1 2 3, use 1pi 2 pi 3 pi, etc. - makes your life much easier

No, the period stays the same

[hoary seal]

why?

[kindred dagger]

Because c only shifts the graph to the left/right

Only b changes the period

[hoary seal]

ohhh ok

[hoary seal]

why do we use pi? our argument wasnt in terms of pi

unlike most examples

[kindred dagger]

Because the sine function is generally periodic with 2pi

Sin of something usually generally assumes that the argument is in radians

[hoary seal]

wdym

[kindred dagger]

Remember when you did the geometrical interpretation of sin/cos/tan on the unit circle?

Theoretically speaking you could also write your x-axis as 3,14... 6,28... yet that won't be very neat so just write pi instead. Just like remember always when you use trigonometric functions to use pi on the x axis - really makes your life easier...

[hoary seal]

geometrical interpretation?

do you mean using the trig unit circle

[kindred dagger]

I suppose (sorry I'm not English)

[hoary seal]

All good

Could u check my answer to this

[hoary seal]

^

[kindred dagger]

You've calculated the extrema as pi/6 and 7pi/6, and calculated that pi/6 has to be a maximum and 7pi/6 has to be a minimum. Since the question asks for the value, I'd still calculate the corresponding y-value of the minimum though.

[hoary seal]

like this?

[burnt notch]

Yes exactly

[hoary seal]

nvm it supposed to be -1

I got the answer

[burnt notch]

Pay attention that cos(7π/6) is -√3/2

[safe radish]

@hoary seal Has your question been resolved?

[hoary seal]

.close

[safe radish]

Channel closed

Closed by @hoary seal

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[edgy osprey]

I have to show this using basic rules of absolute values: I tried but I am stuck. can someone help me out?

[vagrant ice]

well, $|xy + 2| = |\frac{x^3 y + xy^3 + 2x^2 + 2y^2}{x^2 + y^2}|$

[flat frigate]

south

[vagrant ice]

hmm it's not true that the left-hand side is <= |xy + 2| actually

[edgy osprey]

so the task is wrong? 😄

[vagrant ice]

the inequality is correct

I don't know how to do it though

[edgy osprey]

🙁

[vagrant ice]

the easiest way to do it would be to consider two cases

xy > 0 and xy < 0

for instance, xy > 0 includes the case when both x and y are positive, so you can drop all the absolute values

but when both x and y are negative, x^3 y = x^2 * (xy) is still positive, and everything is also positive, so again you can drop all the negative absolute values

now if xy < 0, you have -xy > 0, so it's the same all over again

replace $y \mapsto -y$ then you can drop all the absolute value signs

[flat frigate]

south

[vagrant ice]

I figured it out

[safe radish]

@edgy osprey Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[spark stump]

I need help in this
if gcd(x,y)=a
And lcm(x,y)=b
Solve for x,y in N

[warm warren]

What have you tried?

[spark stump]

I start with
ab=xy
And x=x'a , y=y'a
So gcd(x',y')=1
And b =ax'y'

So x'y'=b/a

I don't have any idea after this

[safe radish]

@spark stump Has your question been resolved?

[alpine shell]

You can try to find where x and y are compared to a and b first

Can you compare x and y to a and b in any way?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[lean otter]

How to think that

[lean otter]

[crystal palm]

i would rewrite the sqrt as powers
also eliminate the fraction and write all as powers
then use power rules to combine

[lean otter]

Is it hard maths problem or not

[empty forge]

no^2

[limpid lodge]

depends on your level....

[lean otter]

im amiddle school student

[limpid lodge]

mth root of x can be written as x^(1/m)..do yk tht

[lean otter]

Yes

[limpid lodge]

have you applied tht here?

[lean otter]

Not yet

[limpid lodge]

what r u waiting for TT

[safe radish]

@lean otter Has your question been resolved?

Channel closed

Closed by @muted skiff

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[umbral sand]

Ignore my writing

[umbral sand]

<@&286206848099549185>

Hi i got an exam tmrw

Appreciate if someone can help

[low echo]

You're gonna integrate that equation

with the limits 0 and the

[umbral sand]

Yea that's the issue I tried a lot I'm making a mistake while integrating

[low echo]

value of x at the point where it crosses the x axis

[umbral sand]

Can you integrate it if possible and send working, limits are 3 and 0

[low echo]

you can find that through the equasion

my pluging in y as 0

[low echo]

Can't rn

[umbral sand]

Nono ik the values

But I'm doing the integration wrong

[low echo]

Was just explaining

[low echo]

Alright

[umbral sand]

Is this formula correct? @low echo

[low echo]

I haven't learned that yet

So I'm not sure

[umbral sand]

Oh

[low echo]

Alright so I can't help with integrating it right now because I have to go so bye

[umbral sand]

Bye

Anyone can help I got an exam in 9 hours

Limits are 3 and 0 for the question, the only issue is in integrating

[strange needle]

distribute the 3-x to both and break the integral apart to get
3int(e^(-x/3)dx) - int(xe^(-x/3)dx)

now solve each integral
first one would be 3(-3e^(-x/3)) = -9e^(-x/3) due to u substituion of -x/3 (u = -x/3 and du = -1/3 dx)

second one required IBP so
let u = x
dv = e^(-x/3) dx
du = dv
v = -3e^(-x/3)
integrate using uv - int(vdu) to get -3xe^(-x/3) - 9e^(-x/3)

now combine both integrals to get 3xe^(-x/3)
plug in ur bounds of 0 and 3 and bam u get ur answer

[strange needle]

no
for an integral (udv) u can use integration by parts to make it vu - int(vdu)

[umbral sand]

I see

Let me solve it 5 mins and I'll get back to u

[umbral sand]

The answer is wrong can you identify my mistake

[strange needle]

uh ok so u made a mistake at the very start
since theres no anti product rule, u distibute those 2 (3-x) and (e^-x/3) by FOIL or just multiply the second by 3 and -x so u get integral of 3e^-x/3 - xe^-x/3

using that and the property of integrals, separate them into 2 separate integrals cuz subtraction and subtract them and integrate each one individually

[strange needle]

heres how to do that

and yeah

[umbral sand]

I don't geet wym by distribute

If possible can you solve on pen and paper

[strange needle]

multiply 3-x and e^-x/3 by each other

[strange needle]

sorry im travelling so i dont really have one with me rn i can try to use a whiteboard online hold up

[umbral sand]

Ohh

Bro ur actually goated

[umbral sand]

Oh and I just integrate that?

Damn

[strange needle]

yeah

[umbral sand]

I'm sorry I'm a bit slo

What's wrong here

Oh i have to integrate X too

[strange needle]

heres how u integrate them

[umbral sand]

I'm so cooked man

I'm gonna fail tomorrow

[strange needle]

ur good bro

js lock in

[umbral sand]

I'm gonna not waste time on integrals

Bro I cant solve this partial fraction

I reckon it's easy but idk what I'm on

[strange needle]

i have to go somewhere so i cant help rn so rip mb

[umbral sand]

Thank you for your help mann

[safe radish]

@umbral sand Has your question been resolved?

[frozen wedge]

i believe you can split this up into the following, hope im not wrong lol

(2x^2+7x+8/(1+x)(2+x)^2) = A/(1+x) + B/(2+x) + (Cx+D)/(2+x)^26

[umbral sand]

Yeah bro I solved it

I forgot about that xoncept

[low echo]

^26???

[frozen wedge]

obviously meant ^2 mate

use your brain

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[warped lark]

exercice 1 part I 1) b-

how i show that |f(x)| < or = to 1/2

[fathom adder]

You can start from inequality and see what happen

[warped lark]

yeah i did this

[fathom adder]

Or start from (|x| - 1)² >= 0

[warped lark]

wait i am gonna show you what i found

i did error

on the top its -x^2 -1 not -x^2 +1

oh wait i can factorise

yeah i found |f(x)| < or = to 1/2

[fathom adder]

Why equal

[warped lark]

wait i am gonna screen you what i did

@fathom adder is this corret

[fathom adder]

,rccw

[fathom adder]

Its not, rather use inequality and stay with it

[warped lark]

okk

like this?

[fathom adder]

,rccw

[warped lark]

x²+1 is always positi

[fathom adder]

Yes

Mb

[warped lark]

after this i have to show that 1/2 is the maximal value of f

[fathom adder]

You know for all x in R |f(x)| <= 1/2

Is it reached ?

[warped lark]

yes

[fathom adder]

At x = ?

[warped lark]

1

[fathom adder]

So what can you say

[fathom adder]

Also its not saying it is a maximal, its asking an open question here

[warped lark]

oh so i have just to say for x=1 : f(1)=1/2

[fathom adder]

And that for all x its bounded by 1/2

Can't go higher and is reached makes it a maximal

[warped lark]

okk thank you

[fathom adder]

Reached is important, else its not maximal

Anyway you good for the other questions ?

[warped lark]

i am gonna ask you if need help i didnt chek them yet

[safe radish]

@warped lark Has your question been resolved?

Channel closed

Closed by @warped lark

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[warped lark]

i need help again

[warped lark]

@fathom adder

exercice 1 part 1 3)

i dont know how do do this

i found this

i know that the maximum value of f is 1/2, and f is decreasing on [1, +∞)

[stray holly]

I cant read french could you type in the particular question?

[warped lark]

Deduce that for all strictly positive real numbers a and b, we have

@stray holly

[stray holly]

which function f are we talking about in the previous thing you said?

[warped lark]

f(x)=x/(x²+1)

[stray holly]

aah I see, that's cool, but you need its reciprical if you want to go about it that way for this problem. define $g(x) = \frac {1} {f(x)} = \frac{x^2 + 1}{x}$ which indeed $g$ is increasing, so wherenver $x \ge \sqrt 2$, $g(x) \ge g(\sqrt 2)$

[flat frigate]

PinkPurpleBlue

[warped lark]

idk

cause the question is saying deduce

from what i found before

[stray holly]

I see, well do the following deduction, if f(x) is decreasing as you said, prove that 1/f(x) is increasing and use that to solve the inequality.

[warped lark]

can i define g(x)=1/x and then use g o f?

[stray holly]

sure if you havr already shown that whenever f is decreasing, g after f is increasing then absoltuely

[safe radish]

@warped lark Has your question been resolved?

Channel closed

Closed by @warped lark

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[flat frigate]

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

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[visual pine]

I am trying to compute a logistic regression for a presentation, https://www.desmos.com/calculator/6cljbzhogs. My only issue is that my s curve seems very off when I plot for y = 0 or 1 goal or no goal of a shot and x = to xG (probability of a goal)

[visual pine]

.close

[safe radish]

Channel closed

Closed by @visual pine

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[astral glacier]

Is there an easy way to implement a function that deals with comparisons and operations with infinity? Essentially I am trying to do interval analysis on the integer variables in a program and if a value ever goes past, say, 50, I wanna assign it to infinity. Similarly if a value goes beyond -50, I wanna assign it to -infinity.

The problem comes up with the fact that I wanna still do the usual binary and unary arithmetic operations on this. My current thought is some kinda operator overloading but I am not sure if that is too much work.

[astral glacier]

Please tag if replying!

<@&286206848099549185> I know this is a coding problem but welp
I know how to do it, it's just that I wanna know what the best way to do it is

[wary python]

hi Xavier

[astral glacier]

Hullo alsx

[wary python]

what language do you use for this?

c?

py?

[astral glacier]

Java currently

[wary python]

yeah mb idk java xddd

[astral glacier]

A dynamically typed language would have made this somewhat easier to deal with

Currently anything I do looks like Integer.toString(Integer.parseInt(x)+Integer.parseInt(y))

Ig this is a good lesson in why you dont ignore parts of the requirements when you start working lmao

Now I gotta patchwork this to include inf

.close

[safe radish]

Channel closed

Closed by @astral glacier

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[viral cave]

i need help on c and d

[viral cave]

i feel like the rate probably isnt 218%

oh nvm i get it now oops

.close

[safe radish]

Channel closed

Closed by @viral cave

Use .reopen if this was a mistake.

[rustic goblet]

r is the annual interest rate, not monthly :p

so you should be multiplying by 4 instead of 48 and then dividing your answer of r by 12, but it seems you got it

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[hasty marsh]

can i write it as integrate 2x + integrate root 25 - x^2 where there is a bracket

[thin bridge]

the brackets are here to make the integrand more clear

not really necessary here
so you can still split using the linear/sum rule

[hasty marsh]

ok

thank u

.close

[safe radish]

Channel closed

Closed by @hasty marsh

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[surreal vapor]

Can anyone help (I know that this can be solved by assigning 2 variables, but our class doesn't teach them in the curriculum)

[surreal vapor]

(Btw, this is the question that is supposed to cover our understanding of Oxyz and 3D space, not really about calculus)

[left gyro]

theres a standard way you can solve this

taking a look at this, you only need to focus on three sides
the red one, the yellow one, and the blue one, right

[surreal vapor]

You mean like flaten the sides right?

I mean i tried flaten it out like this

Normally connecting A to B is enough to solve the problem

But that is only if the speed in the same at all point

[left gyro]

oh I didnt read that part, nvm

sorry about that

[surreal vapor]

Thats what make this one hard

[surreal vapor]

Np

All classmate of mine either skipped this one or use the multi variable method.

I'm not rll sure how to do this without using them

[left igloo]

Not sure if this is correct way, but what if you extended edge of yellow side by x4/3?

[left igloo]

So here, instead of 3 below yellow, you would have 4

[surreal vapor]

It can be done of not the the lines between the yellow and the blue side

As that side has to be constant

[left gyro]

Im going to say thats not correct but there might be a version of this that could work

Id have to test it first

halfasd you can go explain it while I make this

[surreal vapor]

Okat

So the problem from ur question is to translate the sides to make the flat plane

....

Im not sure who just deleted the message but I'm gonna continue explaining if anyone has questions

[zealous tundra]

no i don't need explanation

i was just saying wouldn't it be easier doing it by parts

[surreal vapor]

The problem that this is a min-max problem

And it requres 2 varible if u do it by part

And we didnt cover that in our class yet

[pure agate]

You only need one variable.

[surreal vapor]

Can u elaborate

[pure agate]

As you noted, the entire shape can be flattened out into a 2D surface. What one needs to infer is that the intersection at which the path crosses between the red and yellow surface is variable.

It's not necessarily a straight line.

[left gyro]

going to point out that A is locked in place, and only the yellow face has the slower speed

[zealous tundra]

the smallest path can be going to p

and then diagonal?

[left gyro]

no

[pure agate]

So you basically have three distances which you need to determine. Because point I is variable, that means all three distance equations can be written in terms of point I.

[left igloo]

Why did you assume that from I to B is straight line?

[surreal vapor]

Not really, since the path way in the yellow side can differ the line in the blue side

It can be a zigzag line

[surreal vapor]

Like this

[pure agate]

Happy now? 🙂

[left gyro]

hold on

@surreal vapor are you allowed calculus?

the single-variable version

[surreal vapor]

Yes

[left gyro]

what??

you can just do the multivariable solution then

just do the single-variable one twice

you first have I be constant then solve for where J is

then you vary I and solve for where the minimum distance is

however there seems to be a shortcut for this problem and I dont see how I can prove it

[surreal vapor]

This question is a short response type so shortcut are alr

What' ur shortcut?

[left gyro]

itll be proven if you do this step first

[surreal vapor]

Hang on lemme write it down

[mossy lotus]

||you could cheese it with a fermat's principle/refraction of light kinda thing||

[surreal vapor]

@left gyro

[left gyro]

ok thats not what I asked for

oh I see nvm Im blind

wheres your bmin formula?

[surreal vapor]

I use calculator for that

[left gyro]

bro

if youre gonna use a calculator, why didnt you just use it to solve the problem

like how did you use the calculator

[surreal vapor]

... Mine have a feature to find local minimum with respect to a singular variable

Lemme dif that then

[left gyro]

ok now that youre just using the calculator

do you see how to solve the problem

look at the t mins youre getting at various a

wait

shouldnt you be dividing by 4 and 3?

why are you dividing by 0.4 and 0.5?

[surreal vapor]

0,4 and 0,3 (opps)

On this casw mutiple the time formula by 10 fix that

The time it takes would be 10 times

[left gyro]

or just remove the 0, in the denominators

anyways its still proportional

[left gyro]

you can still see where the t mins are decreasing towards

you can also see where the b mins are heading towards too

[surreal vapor]

It should be when a and b both heading towards 0

[left gyro]

yea

[surreal vapor]

Yeah i think t get that now

Tysm

[left gyro]

np

btw

are you allowed that calculator for this question

because if you are, thats what Im assuming the fastest way you couldve approached it
just test out values to get a good sense since its not like youre gonna get the multivariable tools any time soon

[surreal vapor]

Yes (our test allows for calculator, but ours have funtion limitations)

[wild bough]

Was it 2.5

secs

[surreal vapor]

1.9

[wild bough]

NOT EVKW CLOSE

idk man i felt I did it somewhat right

But

Hmm

[left gyro]

for the record, theres no critical points in this problem

[wild bough]

:0

[left gyro]

oh btw, what were you thinking in mind for this

[surreal vapor]

Also curious about thus

*this

[mossy lotus]

oh its just that according to kookiemons diagram here, you would have AI and JB parallel to eachother, and the angles would be known too, from snell's law, coz this is exactly that kind of a situation

[left gyro]

they are not parallel

snell's law does not work for these kinds of cases

3 is too slow

[mossy lotus]

ahh, icic

well, if you did set up snells law, you would end up seeing that there is no solution in that case

[left gyro]

theres also the case that if red and blue were parallel, that would just force green to be parallel too

[mossy lotus]

and arrive at this

[left gyro]

and also that its entering and exiting the 3 medium at different sides

instead of at parallel sides

[mossy lotus]

what happens at the ends is not useful at all tbh, you dont need to care about that

[left gyro]

wdym AI and JB are parallel?? do you know what kind of shape that makes?

[mossy lotus]

the yellow region and blue region are the two media and thats all that matters

[left gyro]

??????????

are you aware the red and blue region are the same medium?

[mossy lotus]

yes, they are the same coz speed is 4dm/s in both

[left gyro]

are you still legit saying AI and JB are parallel?

[mossy lotus]

yes...

[left gyro]

tell me

consider we dont use fermat's principle at all here

[left gyro]

draw me AI and JB being parallel

just show me an example

then after that, Ill show you a different example of what snell's law would actually presumably do

if you want, you can consider as a variant of the problem where the speed is not 3 but instead 4 - epsilon for some epsilon you know about

(epsilon assumed to be rather small)

[mossy lotus]

something like this is what I'm visualizing

[left gyro]

now look at this

and then followed by this

,rcw

[mossy lotus]

ahh, i see what you mean

[left gyro]

what were you even thinking??

theyre not PARALLEL

[mossy lotus]

yea, i realize it now

mb

[left gyro]

it could be instead doing something like this

or something like this

that does mean you do need to put in a whole lot of work just to solve and find theres no solution

now given HAD gets to use a calculator...

other than that though this would be a real clean solution and it wouldve been the best

[surreal vapor]

Wait... is there a situation of extremely small epsilon where the time would be smaller than a=b=0

[left gyro]

consider if you had a version where the yellow side doesnt slow down at all

if you move epsilon slightly,

youd expect the light path to only change slightly too

and so itll pick a time that still crosses the yellow region at nonzero a, b

so yes theres a situation of (probably not even that small) epsilon where the time would be smaller a = b = 0

Im making something to test this out rn

[safe radish]

@surreal vapor Has your question been resolved?

[surreal vapor]

@left gyro t have attempt to plug it into 3d like this file

a,b,t in respect as x,y,z

From what i can see... it did not have much effect on the time

So ...

Yeah

Problem solved

I'm gonna close this chat then

[left gyro]

wait

didnt you already know that from me telling you

I thought you were waiting for my version that solves for it given the epsilon

[surreal vapor]

Yeah i was going to wait on that

What's ur though then

[left gyro]

my what

[left gyro]

@surreal vapor ok Im starting to realize why they allow you a calculator for this one

calculus or snell's law, you get a system of equations:

you have to solve for X, Y here
where -3 < X < 0 and 0 < Y < 2

[safe radish]

@surreal vapor Has your question been resolved?

[left gyro]

almost there

[left gyro]

by this point it doesnt seem possible to even reduce this to one variable
I did find a more direct equation for X and Y

a = -X, b = Y

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[left gyro]

.reopen

[safe radish]

✅ Original question: #help-23 message

[safe radish]

@surreal vapor Has your question been resolved?

[left gyro]

ok for now, you move the green point to where the red and blue curves intersect, and that is where the solution is
https://www.desmos.com/calculator/qjwnt991f5

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[somber lagoon]

H

[ember socket]

?

[safe radish]

@somber lagoon Has your question been resolved?

[magic junco]

.solved

[safe radish]

Channel closed

Closed by @magic junco

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[jolly sail]

this is my work, what I do wrong??

[zealous tundra]

seems correct to me?

wait did u fill in those values?

[jolly sail]

broo but its wrong here, telling me to check integrand and dA

[zealous tundra]

no

i thought those values were given wait

[jolly sail]

nope its my answer 😅

[zealous tundra]

u need the area btw thme

why did u write 5 dr dtheta?

[jolly sail]

what

[zealous tundra]

the area will be z2 - z1

[jolly sail]

whats the problem with 5 dr dtheta

[zealous tundra]

because u need the area between them

[jolly sail]

um so ur suggesting me to do 5 dtheta dr?

aint that the same

[zealous tundra]

$root(50 - r) - r$

[flat frigate]

vie

[zealous tundra]

didnt work

[zealous tundra]

what is z2 - z1?

[jolly sail]

z2 as in the one with roots and the z1 = r?

[zealous tundra]

yes

[jolly sail]

root(50-r^2) - r

[zealous tundra]

yes

so u need to integrate this region

[jolly sail]

hmmm so ur saying I integrate z2, then substract z1?

[zealous tundra]

no

[zealous tundra]

integrate this

[jolly sail]

oh thats the new function f(x,y) for the integrand?

I mean f(r,theta)

[zealous tundra]

write it down

i dont understand the wording

[jolly sail]

.rotate

nvm idk how to rotate

[zealous tundra]

why the 5?

[jolly sail]

oh cuz converting rectangular to polar we must have r dr dtheta

[ember socket]

,rccw

[jolly sail]

oh ok ill remember that

[jolly sail]

helpp this question, the pic below this one is my work, what I do wrongg

oh shoot my drawing was wrong

I double checked with desmos 😅 , it is an ice cream cone shaped

pls hold, ill recompute

nvm I cant do it

HELPPP

<@&286206848099549185>

[zealous tundra]

u just need to remove the 5

[jolly sail]

I already did and its wrong

actually I changed the dA part to rdr dtheta instead

[jolly sail]

nvm its correct

I put the r in the wrong box

wait wait but

I dont get why its top-bottom tho

[safe radish]

@jolly sail Has your question been resolved?

[jolly sail]

@zealous tundra I get it now, ty sir 🫡

.solved

[safe radish]

Channel closed

Closed by @jolly sail

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[unborn hedge]

In Partial Fraction Decomposition

[unborn hedge]

Why is the 2nd denominator (x-1)²?

Why isn't it (x-1) ?

The factors of the denominator are (x-1)² (3x+1), so why aren't the denominators on the right (x-1), (x-1) and (3x+1)?

[vagrant ice]

having (x - 1) twice doesn't make sense

[floral yew]

there is a rule in partial fractions if (x-b)^n is to be broken down (in denominator ) then you have to write the partial fraction as A/(x-b) + B/(x-b)^2 + C/(x-b)^3 + ..... + K/(x-b)^n

[vagrant ice]

you can think of it coming from $\frac{Bx + C}{(x - 1)^2}$

say, $\frac{2x + 3}{(x - 1)^2} = \frac{2(x - 1) + 5}{(x - 1)^2} = \frac{2}{x - 1} + \frac{5}{(x - 1)^2}$

[flat frigate]

south

[vagrant ice]

the principle is that deg numerator + 1 = deg denominator

[unborn hedge]

So if the factors were
(x-1)³ (3x+1),
would the denominators on the right be (x-1)³, (x-1)², (x-1) and (3x+1)?

[vagrant ice]

yep!

[floral yew]

you need to write each fraction with the exponential numbers increasing from 1 to n in the partial fraction in this case its (x-1)^2 so it will be decomposed as A/(x-1) + B/(x-1)^2

[unborn hedge]

Okay, thank you! ☺️

.close

[safe radish]

Channel closed

Closed by @unborn hedge

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[topaz furnace]

so uhm question a, i calculated the limit is -4/0, i donno what should i do next

[verbal cloud]

Are you sure

[topaz furnace]

yes

divide by n³ and i got lim = -4/0

i havent learnt about const/0 yet

[fathom pasture]

well

thats not possible

[topaz furnace]

oh, all the questions in this exercise are like this, const/0

[lean otter]

a or d?

[quasi timber]

division by zero is not defined

[lean otter]

You mean const/infinity?

Cuz the question is that.

[rancid lion]

okay lemme ask you this

so after the division the numerator tends to -4

[fast tapir]

Hey

[rancid lion]

what does the denominator tends to?

0+ or 0-?

[topaz furnace]

a

[lean otter]

Divide both the numerator and denominator with n^3.

[floral yew]

its inf/inf form tho

[lean otter]

Then find the lim of both.