help-36

[main mirage]

y = 5 - x^2

What's the value of b?

[gentle zephyr]

5

[main mirage]

mmm not quite

Rememebr our quadratic is in the form

y = ax^2 + bx + c

And what we have right now is y = 5 - x^2

What is the number attached to just x? (Is there a number attached to x?)

Btw I have to go now unfortunately

[gentle zephyr]

0

[gentle zephyr]

no

[main mirage]

The reason why I am always stressing for you to graph it is because I strongly believe that being able to graph a function allows you to better understand what is going on.

This is especially important when you get to evaluating double and triple integrals, because it is almost impossible to evaluate integrals without actually seeing the region you are integrating.

Once you draw all four equations together on the same axis, you want to find the region enclosed by all of them to get the region A.

Based on the image, that also tells you where the pairwise intersections are.

[gentle zephyr]

yes

[gentle zephyr]

is it?

[main mirage]

Idk how you can evaluate multiple integrals without knowing what the regions are

Well I mean the actual evaluation is probably simple but

Setting up the integrals (arguably the most important part of evaluating an integral) definitely requires that you know what you are looking at

Anyway I'll leave this here as a crosscheck: But, once you figure out the points of intersections, you can substitute them into the original function to get three test values.

[gentle zephyr]

can you come later

or are you going to leave me alone and helpless

[main mirage]

Sure! If you still need help, I should be on later today

[gentle zephyr]

OK. because everyone insists on parametrization and I an going insane dude

[main mirage]

I have a feeling your help channel will still be on by the time Im next free, so ill show up then

[main mirage]

😭

[gentle zephyr]

oki

I'll be waiting for u mate

[main mirage]

We're not saying this because we want to, we are saying this because it makes the problem significantly easier 😭

[main mirage]

Anyways GL!

[final saddle]

@gentle zephyr Has your question been resolved?

[final saddle]

@gentle zephyr Has your question been resolved?

[final saddle]

@gentle zephyr Has your question been resolved?

[main mirage]

@gentle zephyr did you manage to make some progress :D

[gentle zephyr]

im hardstuck

[main mirage]

Oof

[main mirage]

Give me a moment to prepare. Show me what you've got so far

[gentle zephyr]

i got stuck at the pairwise intersections step

[main mirage]

Hmmmm okay

So, back to what I said earlier,

We have the four constraints: x = 0, x = sqrt(5), y = 0 and y = 5 - x^2

Using these four constraints, we can graph the region that these constraints represent - that's pretty much what we were doing awhile ago.

https://media.discordapp.net/attachments/908076393198419988/1444858228251955220/SPOILER_image0.jpg?ex=692e3c95&is=692ceb15&hm=ba6672494799e0033750455befdb06b974130e12917a618703372e049cd119c1&=&format=webp&width=432&height=751

This is what you had awhile ago, and now I asked you to graph the parabola:
y = 5 - x^2

You told me that the vertex occurs at x = 0, so the vertex of this parabola is (0, 5)

How would you draw this parabola then, given this piece of information?

[glossy zephyr]

damn we still on this one, ill still insist on the method i explained twice
@gentle zephyr

[final saddle]

@gentle zephyr Has your question been resolved?

[gentle zephyr]

yeah we stopped here

[gentle zephyr]

yep

[gentle zephyr]

igts just an upside down parabola (sad face parabola) where we are moved by 5 upwards the y axis

[gentle zephyr]

what is your method

that at the boundaries we parametrize?

[glossy zephyr]

yea, and using the gradient

[gentle zephyr]

why not lagrange multipliers

[glossy zephyr]

cause i dont know how to use them

[gentle zephyr]

well its hears more complicated than what it really is, but we can do it with parametrization and change the multivariable problem to a single variable problem

[glossy zephyr]

Have you already found A?

[gentle zephyr]

but A is given

is a compact region

[glossy zephyr]

Yes, i know, but like, can you figure out how it looks just based on the bounds

aka, can you find the corresponding curves for boundaries

[gentle zephyr]

the boundaries of the region are 0 = x
x = sqrt(5)

0 = y

5-x^2 = y

@glossy zephyr

[glossy zephyr]

yeah, and what about parametrization

[gentle zephyr]

dunno

[glossy zephyr]

also just for myself

parametrizations are of the form c(t) = (x(t) , y(t)) here

We have 3 distinct bounds

so we will have 3 curves

Youll prob want to draw the figure so we cant work it out.

[gentle zephyr]

4

[glossy zephyr]

nope, just 3

I dont mean the bounds for the xy coordinates

i mean the bounds of the area (frontier)

[gentle zephyr]

care to elaborate

[glossy zephyr]

Again, have you found how the area A looks?

[gentle zephyr]

is not needed

to know how this shit looks

[glossy zephyr]

no, not really, but it seems it will help

[gentle zephyr]

we just want max f inside this region and min f inside this region

[gentle zephyr]

it is hard to draw the region by hand

[glossy zephyr]

tbh its pretty easy, just for the sake of reference

0<x<sqrt5 forms a stripe that stretches infinitely up and down

from 0 to sqrt5

and 0<y<5-x^2 is the region defined from the inside of a parabola up to y = 0.

for them both to be satisfied, you have to take the intersection of both

[gentle zephyr]

no idea

[glossy zephyr]

the blue area

A looks like this

[steep nest]

A is all the points x,y in R^2 where x is inbetween 0 and root 5, and y is between 0 and 5-x^2

[glossy zephyr]

now you should be able why we can define the frontier as three curves

two of them are "curves" which simply satisfy a straight line following the x and y axis

the other follows y = 5-x^2

For the inside, you just use the gradient of the scalar function

for the boundaries you define:
c1, c2, c3 as functions of t and plug it in in your original function

all of them will have polynomial order, once you do that, derive with respect to t, and find the values of f'(t) = 0 for all of them

• the corners

• you can apply the following principle

[final saddle]

@gentle zephyr Has your question been resolved?

[lament vale]

Renato I thought you understood Lagrange multipliers yesterday

You could at least try trusting your knowledge from yesterday and make some progress

[hot hornet]

hm maybe renato doesn't have a good conceptual understanding of them yet?

[tribal gazelle]

dose any body do physics here ???

[lament vale]

I assume so, but trying is always worth a shot, especially when the steps of a solution of a completely analogous problem are easy to find on this very server

Afterall, how does one learn without trying their current abilities?

There should be a feedback loop

[gentle zephyr]

the idea was that there is multiple restrictions now, not just 2

but the idea we discussed should still hold?

[gentle zephyr]

like should be still the same procedure with the exception we take the pairwise intersections and add those points as potential candidates

[lament vale]

yep

[lament vale]

absolutely

[gentle zephyr]

the issue is. we have 4 restrictions now

[lament vale]

Well, anyways

[lament vale]

Judging from this image the 4th restriction does nothing, so basically 3 restrictions

And only 3 corners

[gentle zephyr]

how?

[gentle zephyr]

why cant I use the 4 restrictions even though one is redundant

[lament vale]

Sure, use all 4 of them

[gentle zephyr]

0 = x
x = √5
0 = y
y = 5 - x^2

[gentle zephyr]

I get weird stuff when I intersect first with second

[lament vale]

That's because they do not intersect

[gentle zephyr]

like, 0 = √5

ok

candidates = {(0,0), (0,5), (√5,0)}

this is all the points I got from the intersections

and of course all this points are inside the region

[gentle zephyr]

so do I need to apply lagrange multipliers 4 times?

I already found the candidates from the intersections

then I pressume would need to find the critical points unrestricted and see which ones fall inside the region

[gentle zephyr]

and then apply lagrange multipliers 4 times with each of these

g1: 0 = x
g2: 0 = √5 - x
g3: 0 = y
g4: 0 = 5 - x^2 - y

[lament vale]

correct

[gentle zephyr]

L1 = (x-1)(x-y) + λx

L1 = x^2 -xy -x + y + λx

L1x = 2x -y - 1 + λ

L1y = -x + 1

L1λ = x

2x -y - 1 + λ = 0
-x + 1 = 0
x = 0

@lament vale are you seeing this? I get 1 = 0

[lament vale]

Okay, so this system has no solutions

Proceed with the next lagrangian

[gentle zephyr]

wtf is going onnn

and you guys want me to do this by myself without any help whatsoever

like if I were Albert Einstein

[lament vale]

Bro is it your first time seeing a system with no solutions?

[gentle zephyr]

no, but is off putting seeing something like this in my second exercise with lagrange

L2 = x^2 -xy -x + y + λ(√5-x)
L2 = x^2 -xy -x + y + λ√5-λx
L2x = 2x - y - 1 - λ
L2y = -x + 1
L2λ = √5 - x

0 = 2x - y - 1 - λ
0 = -x + 1
0 = √5 - x

[gentle zephyr]

I get √5 = 1

L3 = x^2 -xy -x + y + λy

L3x = 2x - y - 1

L3y = -x + 1 + λ

L3λ = y

0= 2x - y - 1

0 = -x + 1 + λ

0 = y

x = 1/2

one possible candidate is (1/2, 0)

candidates = {(0,0), (0,5), (√5,0), (1/2,0)}

L4 = x^2 -xy -x + y + λ(5-x^2-y)

L4 = x^2 -xy -x + y + 5λ - λx^2 - λy

L4x = 2x - y - 1 - 2xλ

L4y = -x + 1 - λ

L4λ = 5 - x^2 - y

0= 2x - y - 1 - 2xλ

0 = -x + 1 - λ

0 = 5 - x^2 - y

λ = 1 - x
2xλ = 2x - y - 1
λ = (2x-y-1)/(2x)
1- x = (2x-y-1)/(2x)
2x - 2x^2 = 2x - y - 1

0=2x^2 - y - 1

y = 2x^2 - 1

y = 5 - x^2

5 - x^2 = 2x^2 - 1

6 = 3x^2

2 = x^2

x = ± √2

y = 3

so two possible candidates is (√2, 3) ,(-√2, 3)

f(x,y) = x^2 -xy -x + y

fx = 2x - y - 1

fy = - x + 1

(x,y) = (1,1) is another candidate

[gentle zephyr]

.close

[final saddle]

Channel closed

Closed by @gentle zephyr

Use .reopen if this was a mistake.

[gentle zephyr]

at the end my TA said parametrization is easier and preferred

I am a stupid ass

trying to use lagrange when we could always use parametrization

[glossy zephyr]

You should prob practice parametrizing the boundaries areas on its own totally beyond the fact of looking for maxima and minima

[gentle zephyr]

wdym?

you mean like the borders of the region

[glossy zephyr]

being able to find the curves (pametrized curves that is) that make up the border

[gentle zephyr]

yeah fair enough

well I still dunno if I like it

like, we needed to use a lot of trigonometry for this exercise he was showing me

and find the angle of some points in the xy plane

I will share it here when I get home

like we were parametrizing this exercise he was showing me and he was struggling in the middle of it

some prof came and show him how to get unstuck

then we did it with lagrange and it was way shorter and simpler

no geometry whatsoever

he still prefers parametrization because it turns into a single variable problem

but when we had to parametrize an ellipse the parametrization becomes trigonometric functions

and in some point or another we had to find some angles

so that was nasty and difficult in my opinion

in the case of lagrange for the ellipse we had a three unknowns three equations system

we solved it in a couple of steps and we found the same points that we found when parameteizing the ellipse but without all that trigonometric jazz

[hot hornet]

Yeah this is a big reason why Lagrange multipliers are helpful

[final saddle]

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.

[latent dragon]

What have you tried and what are you stuck on?

[onyx canyon]

Im stuck on whether when you times the whole equation by 5

do you still use the same denominator

or also times by 5

[latent dragon]

You should start by subtracting both sides by 7/6

[latent dragon]

How come you want to × both sides by 5?

[onyx canyon]

because i was solving a question similar to this and the equations times the equation by 5

like this

[latent dragon]

,rotate

[latent dragon]

You don’t always × everything by 5.

that was just an example.

[onyx canyon]

oh

so then how do i do it

[latent dragon]

In problems like these, you should start by removing any constants in the left hand side

$9m+\frac76=4$

[soft zealot]

𝙸𝚗𝚏𝚒𝚗𝚒𝚞𝚖³

[fossil kiln]

u could times by 6 tho to remove the fraction

[latent dragon]

Sure, but you’d also have to × 6 in 9m too

and that just makes things longer than necessary

Anyway, @onyx canyon, subtract 7/6 from both sides

[onyx canyon]

okay\

[latent dragon]

Which gets you?

[onyx canyon]

i dont get it because theres no like terms in 9m

so

[fossil kiln]

YYeah but iif she really wants to multiply the eqn lol

[latent dragon]

$9m+\frac76-\frac76=4-\frac76$

[soft zealot]

𝙸𝚗𝚏𝚒𝚗𝚒𝚞𝚖³

[latent dragon]

The +7/6-7/6 cancel out

To just leave you with 9m

[latent dragon]

You should belooking at the constant 7/6 in the left hand side right now

[onyx canyon]

ohh

so then its just 9m = 4 - 7/6?

[latent dragon]

correct.

and then let’s turn 4 - 7/6 into one fraction.

@onyx canyon know how to do that?

[onyx canyon]

uhh

4/1 - 7/6

and then find common denominator

and then times 4/1 by 6 to get the same denominator

[latent dragon]

✅

[onyx canyon]

24/6 - 7/6

[latent dragon]

Which would get you?

[onyx canyon]

17/6

[latent dragon]

yep!

$9m=\frac{17}6$

[soft zealot]

𝙸𝚗𝚏𝚒𝚗𝚒𝚞𝚖³

[latent dragon]

what can we do here to get 𝑚 all alone?

[onyx canyon]

divided by 9

[latent dragon]

Correct. Divide both sides by 9

$\frac{9m}{9}=\frac{\frac{17}{6}}{9}$

[soft zealot]

𝙸𝚗𝚏𝚒𝚗𝚒𝚞𝚖³

[latent dragon]

notice the 9/9 in the left hand side. What can we do to it to get rid of it?

[onyx canyon]

9 and 9 would cancel each other out

and then that leaves m

[latent dragon]

correct.

[onyx canyon]

alone

[latent dragon]

$m=\frac{\frac{17}6}{9}$

[soft zealot]

𝙸𝚗𝚏𝚒𝚗𝚒𝚞𝚖³

[latent dragon]

you can simplify this further. Do you know how?

[onyx canyon]

well we cant really simplify 17/6

[latent dragon]

But you can simplify the entire fraction

[onyx canyon]

maybe find lcd between 6 and 9?

[latent dragon]

$\frac{\frac{17}{6}}{9}=\frac{17}{9\times6}$

[soft zealot]

𝙸𝚗𝚏𝚒𝚗𝚒𝚞𝚖³

[latent dragon]

you can bring the six down

[onyx canyon]

ohh

17/54

[latent dragon]

[onyx canyon]

and that cant be simplified

so m = 17/54

[latent dragon]

correct!

[onyx canyon]

oh thank youu

[latent dragon]

if you want to plug it back into check that’s always a good idea.

[onyx canyon]

okay!

[latent dragon]

if your question has been answered you may close the channel with .close

[onyx canyon]

.close

[final saddle]

Channel closed

Closed by @onyx canyon

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.

[pearl leaf]

for this equation, how do you calculate the uncertainty of r?

[pearl leaf]

given that you have delta v, delta I

[vital crag]

Use chain rule to find dr

https://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_(Apex)/12%3A_Functions_of_Several_Variables/12.04%3A_Differentiability_and_the_Total_Differential

[final saddle]

@pearl leaf Has your question been resolved?

[final saddle]

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.

[dreamy moon]

hi can someone look at what went wrong? Idk why they got 3-e

[final saddle]

@dreamy moon Has your question been resolved?

[dreamy moon]

how is it e-0?

[loud sundial]

What is 0 times 1

[dreamy moon]

0

[loud sundial]

good

$1 \cdot e^1-0=e-0$

[soft zealot]

Civil Service Pigeon

[dreamy moon]

Omg

I suddenly switched the order for evaluating an integral

oops..

[loud sundial]

rip

[final saddle]

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

[final saddle]

@dreamy moon Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[final saddle]

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.

[fathom imp]

Wouldn’t the x centroid of the second rectangle with dimensions 270 and 30 be, 240+15=255

[fathom imp]

Nvm

It would be 240-15 right

[chilly pollen]

Yes

[fathom imp]

And the Y centroid would be half of 270

[chilly pollen]

+30 to it

[gritty drift]

assuming the first rectangle contains the base of the second, yes.

[fathom imp]

I cut the first rectangle into 240 and 30

So I’m taking the 30 base of the second rectangle

So would it be half of 270, or do I still add 30

[chilly pollen]

Yes you add 30 to get the coordinate

[gritty drift]

the centroid is a positional value, you still need to add 30

[chilly pollen]

Same thing we did with x

[fathom imp]

Alright

I see

.close

.close

[final saddle]

Channel closed

Closed by @fathom imp

Use .reopen if this was a mistake.

[fathom imp]

.reopen

[final saddle]

✅ Original question: #help-36 message

[fathom imp]

So I tried this problem

I made a big rectangle minus 2 right triangles

Rectangle having dimensions of 120 and 150

[winter lava]

you should subtract three triangles

[fathom imp]

Oh I didn’t see that triangle

Is there a diff method or should I continue with this

Btw

For my triangle on the top left corner

I have dimensions 60 for base and 75 for height

My x centroid being b/3=20

And my y centroid being 75+H/3= 100

Is that correct

[winter lava]

why do you need the centroid?

[fathom imp]

The question asks to find the centroid of the entire shape

[winter lava]

oh

[fathom imp]

So I’m using the method where you find area, centroids, centroid times area, then use the formula to find x and y centroids

[fathom imp]

So would these forms be correct

[tepid salmon]

I would do three shapes, one rectangle from x = 0 to 60, y = 0 to 75. then a large triangle across the top, and finally one smaller one on the right

[fathom imp]

Yeah I just changed it to that

I made this

Now my question is, for the triangle 1 that’s on the top, left face, would the x centroid be 20 and y be 75 + H/3= 100

I feel like the x centroid should be 2/3 of base

[tepid salmon]

the x centroid for triangle 1 should be 40

if the triangle was this orientation x would be b/3, since it is flipped, x is b-b/3 which is 60-60/3 = 40

your intuition is right

[fathom imp]

Hmmmm

If that triangle was flipped

Upside down

Then the height would be 2/3 h right

Also

For triangle 2

Would it be 60+ b/3

[tepid salmon]

I mean if the triangle was flipped along the y, then it would be in the orientation of triangle 1 in the picture earlier

[fathom imp]

My x centroid is coming out wrong

It’s coming out to be 56

[final saddle]

@fathom imp Has your question been resolved?

[final saddle]

@fathom imp Has your question been resolved?

[final saddle]

@fathom imp Has your question been resolved?

[fathom imp]

.close

[final saddle]

Channel closed

Closed by @fathom imp

Use .reopen if this was a mistake.

[final saddle]

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.

[languid cobalt]

u_4 = 13
s_10 = 55
u_1 + u_2 + u_3 .... u_10 = 55
9(u_1) + 37d = 55

thats as far as i got

[sullen tundra]

d€N?

[languid cobalt]

?

[sullen tundra]

Is d in N

The natural numbers

[languid cobalt]

didnt specify i assume its R|

real numbers

[sullen tundra]

K

And u_1 is in Q ?

[languid cobalt]

yes

[sullen tundra]

K

If both were real there will be an infinite number of solutions but I supose there is only one

Cuz it's THE

Well idk what a common difference is

[languid cobalt]

u_2 - u_1 = d

[sullen tundra]

Oh

[languid cobalt]

the common difference is the pattern of the sequence

ex: 3, 7, 11, 15
d would be 4

[sullen tundra]

So it adds up every time?

Yea ok

Why 9(u_1) tho?

Isn't it 10?

And 40d

[languid cobalt]

yep nvm ur right

[sullen tundra]

So like u_1 +4d=5.5

[languid cobalt]

yes

so u_2 = 5.5/4

[sullen tundra]

And u_1+3d is 13

[languid cobalt]

yes

[sullen tundra]

Yea

But with that u can find d

d=55-13=42

And u_1=55-4d=55-4×42=55-168=-113

[languid cobalt]

u_4 = u_2 + 2d

we have u_4 and u_2 and we can find d

[sullen tundra]

Yea

[languid cobalt]

ok thx

.close

[final saddle]

Channel closed

Closed by @languid cobalt

Use .reopen if this was a mistake.

[final saddle]

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 pilot]

may smn help me learn for my next math argument cus i got really lost pls😭
from wht i undestood the arguments sholud be "differential equations, homogeneous" "Beurnoulli"
here an example ig

[vital crag]

Do you have the original problem statement

Translate it to english if you want responses sooner

[spark pilot]

im scared i might am not understanding wha u jus said

tho i think the thing on top is the start ya

id need smn to explain me the argument thats just an example😓

<@&286206848099549185> ?😭

oh sorry i jus saw i need to wait 15 mins well 10 mins ok😓

[vital crag]

What is there to explain exactly

You need to ask a specific question of what you want to know

[spark pilot]

id like to know if smn would like to get in a call w me or overall make me understand differential n homogenous equations

[vital crag]

Well getting someone to hop on a call with you is unlikely

[whole verge]

Why not ? It's ridiculous, why isn't there voice channels in this server 😕

[spark pilot]

idk i jus hope to uderstand how to make the passages for me to understand

[spark pilot]

u sure u wouldn call pls?

[spark pilot]

kinda right ngl😓

[spark pilot]

<@&286206848099549185> ?😭😭😭😭😭😭😭😭

[final saddle]

@spark pilot Has your question been resolved?

[sharp parrot]

Let $y=tx\implies\frac{dy}{dx}=\frac{d}{dx}\left[tx\right]=t'x+t$ given these re-write the original ode in terms of $t$ and $t'$

[soft zealot]

fred172

[sharp parrot]

here t is a function of x

[spark pilot]

oh

hummm so?

r u starting from the basics?

[sharp parrot]

yup

[spark pilot]

oh thx

wait would u be willing to get in a call n explain all to me would be easier for both i think pls?

[sharp parrot]

I'm afraid I can only help you with in chat

[spark pilot]

oh why are u busy?

[sharp parrot]

do you have any doubts about the method shown above?

[spark pilot]

hummm ya i don really understand it

i don get how it works

but i don think that thing is tooo needed

watch

I think i need to understand these first

I kinda do but not all n not all the way n i lack of examples

(The pics need to load)😓

@sharp parrot

[sharp parrot]

yup

[spark pilot]

can u help me understand them?

like can u explain them please😭

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[spark pilot]

.reopen

[final saddle]

✅ Original question: #help-36 message

[sharp parrot]

\begin{itemize}
\end{itemize}

[soft zealot]

fred172
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[spark pilot]

i ll wait

[sharp parrot]

1. Rember how $\frac{d}{dx}\left[A\right]=0$ where A is a constant, when you perform integration we need to write +C when the integral is indefinite

[soft zealot]

fred172

[spark pilot]

so it becomes

where "A" can be any number?

[sharp parrot]

yes

[spark pilot]

ok

[sharp parrot]

This page is just a list of rules for integrals

[spark pilot]

ya ik

mh ya i should be knowing all abt that one page

r you sure u cant call cause this could be so long like this😓

[sharp parrot]

sorry I must go

[spark pilot]

omg😭 its ok fred thx

[spark pilot]

<@&286206848099549185> sorry smn else who can help me thx😓

smn who can call would be FANTASTIC

[final saddle]

@spark pilot Has your question been resolved?

[final saddle]

@spark pilot Has your question been resolved?

[untold grove]

Which textbook are you using on your ODEs course?

[spark pilot]

may u tell me why u ask that cause idk the answer n what ODEs is so if its really needed maybe i get informed abt it

@untold grove

[untold grove]

ordinary differential equations

you said you're strugling to understand non homogeneous differential equations

@spark pilot

[spark pilot]

ahhhhh well i don use the textbook because our teacher doesn use it and its hard to understand what it says seeing what he says

tho i might tell u

oh its italian tho

[untold grove]

Well, if you need help with your exercises, you need to clarify it

[spark pilot]

its italian tho

[untold grove]

which topics are you strugling the most?

[spark pilot]

integrals differential n homogenous equations

(bornoulli)

[untold grove]

do you already know integration?

[spark pilot]

name of my textbook: Matematica.verde 5

[spark pilot]

a bit ig

[spark pilot]

id need to restudy this

it should be easy i didn understand sum stuff last time but i understood the most i should learn it fast

would u be avaible to call (that would be fantastic istg😭)

u can even tell me ya in 2 hours or so

[untold grove]

maybe, the problem is that it's almost 10 P.M. in here

[spark pilot]

2 am at my place ahah (im so done😭 ) humm so cant u rn?

[untold grove]

just a minute

[spark pilot]

omg thx

thx bro really

@untold grove the goat🙏🙏🙏

[untold grove]

ready?

[spark pilot]

YAP

[untold grove]

I tried calling you

@spark pilot

[spark pilot]

oh i send u a friend req

[final saddle]

@spark pilot Has your question been resolved?

[final saddle]

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.

[craggy plank]

2 6 7 10 8 2

I'd like my work checked

[hasty mist]

Share your work here lil blud

[craggy plank]

not necessary at all, it's pretty simple and I just need someone to check if I'm fumbling anything dumb

[glossy zephyr]

yeah, the sequence is correct.

[craggy plank]

Appreciate it

love ya

.close

[final saddle]

Channel closed

Closed by @craggy plank

Use .reopen if this was a mistake.

[final saddle]

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.

[gentle zephyr]

when is this zero?

for what theta

-25sin -100sin -120co

[severe canyon]

First of all, simplify the similar terms

Then I'd suggest to change signs as well

[icy current]

$-25\sin(2\theta) -100\sin(2\theta) -120\cos(\theta) = 0$

I would start by simplifying $\sin(2\theta)$

[soft zealot]

@icy current

[final saddle]

@gentle zephyr Has your question been resolved?

Channel closed

Closed by @gentle zephyr

Use .reopen if this was a mistake.

[final saddle]

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.

[jagged flare]

what does it mean with resting on the inside and outside? i dont get the definition of r_i and r_o

[pliant shore]

something like this

[jagged flare]

uh whar

[pliant shore]

the torus is inside the sphere for r_i

but the sphere is contained within the torus for r_o

[jagged flare]

isnt the torus bigger than the sphere

how can it be inside the sphere

[candid pulsar]

like

• donut inside and at the bottom of a spherical shell
• donut on the top of a spherical shell

[jagged flare]

ohh wait hold on im silly the torus is smaller than the sphere

[candid pulsar]

yes

[jagged flare]

ok ok i think i get it now

so like, if we take the vertical cross section it would look like this?

[candid pulsar]

yeah

[jagged flare]

oo ok i see

ill close this for now, im gonna try it

thanks guys!

.solved

[final saddle]

Channel closed

Closed by @jagged flare

Use .reopen if this was a mistake.

[final saddle]

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.

[warm python]

I need help with G/H

I'm thinking {i+<H>}+<H>

[worldly mesa]

(i + <20>) + H

[warm python]

yes

oops

[warm python]

that's it ,right

or can this be simplified further

[worldly mesa]

not really

but third iso tells you this is isomorphic to Z/4Z

[warm python]

third isomorphism theorm?

[worldly mesa]

yes

[warm python]

i'll read that soon

tq

.close

[final saddle]

Channel closed

Closed by @warm python

Use .reopen if this was a mistake.

[final saddle]

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.

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.

[worldly spruce]

[final saddle]

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.

[indigo swan]

,rotate

[indigo swan]

Which one is right?

[tired walrus]

the first

[indigo swan]

The top one i presume

[indigo swan]

Is it the same with logarithmims?

[tired walrus]

yes

[indigo swan]

Okay thanks ann

[tired walrus]

when you apply a function to both sides of an equation it goes on the very outside

[indigo swan]

Are there any other functions id be applying instead of these 2

As a high school student

[tired walrus]

square root

or like ^2, ^3, whatever. raise both sides to some power

[indigo swan]

Okay thanks

.close

[final saddle]

Channel closed

Closed by @indigo swan

Use .reopen if this was a mistake.

[final saddle]

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.

[compact ocean]

13 c

Idk how to solve it at all

[abstract zodiac]

Damn

Might be able to if you send the problem in english

[compact ocean]

It’s in English

Look inside the bracket

Yo?

Heyeyeyeyey?

HII?

[spark swan]

is it 9th grade circles?

[compact ocean]

Yup

[spark swan]

nice

what theorems about arcs do you recall?

[compact ocean]

Do yo how to solve?

[spark swan]

yes

my internet's acting up sorry if i disappear suddenly

[compact ocean]

Man

We haven’t leant any

Of arc theorems

[spark swan]

why're they making you solve this then? 😭

[compact ocean]

Well

They call it out theorem

In our exam

It’s of 2 mks

[spark swan]

wdym

[compact ocean]

Meaning

It won’t be taught

You’ve to solve it by using brain

[spark swan]

you'll have to use the theorems, try going over them

[compact ocean]

Alright then

.close

[final saddle]

Channel closed

Closed by @compact ocean

Use .reopen if this was a mistake.

[spark swan]

hold on i'll guide you through this one

[compact ocean]

Ye?

.reopen

[final saddle]

✅ Original question: #help-36 message

[spark swan]

im not sure how to motivate this

what properties of isosceles trapeziums do you know?

[compact ocean]

Idk any

😂

[spark swan]

oh 💔

well for this one, the one you need is the fact that their diagonals are equal

[compact ocean]

Well

[spark swan]

then you can show that it is either an isosceles trap, rectangle or square

[compact ocean]

Oh

Yes

I’ll try it

I’ll dm you

at morning

It’s 22:33 rn

[spark swan]

you'll need this
pulled it from https://ncert.nic.in/textbook/pdf/iemh109.pdf

[compact ocean]

In my country

[spark swan]

alright

[compact ocean]

Yo

I know this

I know inscribed angle and central angle standing on the same arc are equal

And inscribed angles standing on same arc are equal

But idk how to relate it with this question

[spark swan]

dw you only need the fact that equal arcs means equal chords

[compact ocean]

Ohhh

So equal arcs have equal length of chords?

[spark swan]

yep

[compact ocean]

Okay

Then I can easily solve it

I’ll dm you in the morning

I’ll sleep for now

Bye!

Thanks

.close

[final saddle]

Channel closed

Closed by @compact ocean

Use .reopen if this was a mistake.

[spark swan]

good night

[spark swan]

👍

[final saddle]

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.

[whole halo]

using this proof from the lecture notes, does that mean the eigenvalues of T* are conj(the eigenvalues of T)?

[opaque ember]

ya

[whole halo]

.close thanks

[final saddle]

Channel closed

Closed by @whole halo

Use .reopen if this was a mistake.

[final saddle]

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.

[manic leaf]

isnt it clearly positive definite?

like

if we have an eigenvalue of 0 then isnt det A = 0?

[tired walrus]

what is Delta_k(A)

[manic leaf]

ig that doesnt make this statement wrong but we could make it stronger

uhh

[tired walrus]

is it the determinant of the k by k top left submatrix

[manic leaf]

yes

correct

[tired walrus]

in that case these guys are only required to be >0 up to n-1

not up to n

[manic leaf]

yes

but if det A >= 1

[tired walrus]

ah hold up. ah...

[manic leaf]

and product of eigenvlaues are equal to determinant

[tired walrus]

[manic leaf]

isnt lambdan >= 1/lambda_1 * ... * lambda_{n-1}?

[tired walrus]

okay hm i think i am too tired to answer this confidently

[manic leaf]

so it has to be positive

ig that still would make it positive semidefinite

tho

[final saddle]

@manic leaf Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[final saddle]

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.

[vital kelp]

what are some good eample of isomorphic rings ?
Zero divisors ?

[steady locust]

huh why did it get deleted

[vital kelp]

idk man the bot is dumb

[winter lava]

i think you already said this, but Z_rs is isomorphic to Z_r x Z_s when gcd(r,s)=1

[steady locust]

if you have two isomorphic rings R and S then M_n(R) is isomorphic to M_n(S)

[vital kelp]

Great thanks

more ?

[steady locust]

R x {0} is isomorphic to R

[vital kelp]

nice

more ?

[steady locust]

there are trivial examples with renamed variables, e.g. R[x] is isomorphic to R[y]

[vital kelp]

you think in a trivial course like intro to discrete math they'll count this as an example ?

[steady locust]

i dont think discrete math would cover rings at all?

[vital kelp]

My course does

Just a trivial introduction

so we can move onto to finite fields

[steady locust]

wait what have you gone over then?

cause that would tell you what examples they might use

[vital kelp]

I mean not much just modular counting

[steady locust]

yeah you will probably just need to know integers mod n and CRT

[vital kelp]

yea

[steady locust]

maybe something super trivial like R isomorphic to R x {0}, but nothing beyond that

[vital kelp]

would it be possible to define some ring of functions ?

Maybe a ring of idk continous functions frmo [0,1] --> R

oh wait not closed under composition

ring of continous functions from R --> R

?

[steady locust]

yeah

[vital kelp]

wait i don't think she'll accept this but ig i can just be a prick and say

R x R x {0} is isomorphic R x R

C x {0} is isomorophic to C

C x C x {0} is isomorphic to C

[steady locust]

if a question is open ended and asks for isomorphic rings use integers mod n

[steady locust]

thats a pretty crazy discrete math class tho

[vital kelp]

fr ? it's the most trivial class i've taken

I studied hard for 10 hours and I went from being 2 weeks behind to 2 weeks ahead

[steady locust]

are you in europe?

[vital kelp]

yea

[steady locust]

"discrete math" might mean smth different to you because here discrete math is a very introductory class for 1st year students

just begins to cover proofs, sets, etc.

well that might be true for you as well looking at it

[vital kelp]

it's 2nd year here

[steady locust]

its just rings and fields that is unique now that i look at it

everything else is standard

[vital kelp]

yea fields and rings is 1.5 lectures, is not much

[steady locust]

in a US institution you would only be introduced to rings and fields in an abstract algebra class

discrete math is more for computer science

[vital kelp]

yea that's why i wish i took this course before abstract algebra lol

would've made my life quite a lot easier

[winter lava]

i think it's a problem if you allow functions with zeros

[vital kelp]

then forget it

[winter lava]

the multiplicative identity is f(x) = 1, right?
and if you have a function with a zero like g(x) = x, then g doesn't have a multiplicative inverse

[vital kelp]

hmm

[steady locust]

its not a field

but it is a ring

C(R,R) is a ring

[winter lava]

oh yeah we don't need a multiplicative inverse

idk what C(R,R) is

[vital kelp]

set of continous functions from R to R

[steady locust]

@vital kelp actually this gives you another good example of isomorphic rings

if R isomorphic to S, then the ring of functions from R -> R is isomorphic to the ring of functions from S -> S

[vital kelp]

That jives

[steady locust]

continuity is not necessary, by the way

[vital kelp]

yea i just realized since ring is pretty weak in terms of conditions

[steady locust]

plus to define continuity you would need a topological ring

[vital kelp]

[winter lava]

huh?

[steady locust]

https://en.wikipedia.org/wiki/Topological_ring

[winter lava]

but they define continuous functions in calculus

[steady locust]

for an arbitary ring R, not R as in the reals

[vital kelp]

right becaouse you need some sort of norm

[steady locust]

and topology is all about continuous maps

generalized

[final saddle]

@vital kelp Has your question been resolved?

[final saddle]

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.

[dusky idol]

With S(x) = x²-5x+25/2

[steady locust]

can you translate

[dusky idol]

Okk

Wait 2 sec

A) Deduce the factorization of S(x) - 75/8 and its sign.

B) Find the values ​​of x such that S(x) ≤ 75/8.

[dusky idol]

.

[steady locust]

so first you find what S(x) - 75/8 is, right?

x^2 - 5x + 25/2 - 75/8

[dusky idol]

Yes

??

[steady locust]

what did you get?

x^2 - 5x + 25/8 right?

[dusky idol]

x²-5x+50/16

[steady locust]

50/16 = 25/8

then, you factor that

[dusky idol]

Okk

And after this i dont now

[dusky idol]

Pls do this

[steady locust]

B)?

you can do

S(x) <= 75/8

->

S(x) - 75/8 <= 0

and you already know what S(x) - 75/8 is

@dusky idol ?

[dusky idol]

Yes i know

But the sign no

[steady locust]

so you have

x^2 - 5x + 25/8 <= 0

[dusky idol]

.

[steady locust]

same thing

[dusky idol]

Yes

[steady locust]

and you know roots of that?

$\frac{10 \pm 5\sqrt{2}}{4}$

[soft zealot]

c2b7

[dusky idol]

Tes

[steady locust]

do you know how to find when it <= 0

since you have the roots

[dusky idol]

Yes

[final saddle]

@dusky idol Has your question been resolved?

[final saddle]

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.

[dusky idol]

Yes

[atomic moon]

Tu connais la règle pour le signe d'un polynome du second degré avec deux racines ?

[half raptor]

.close

Ahhhhhhhhhhhhhhhh

You can’t close other help channels now?????

[atomic moon]

Sounds fair doesn't it ?

I think it was always the case

[worldly spruce]

.close

[final saddle]

Channel closed

Closed by @worldly spruce

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.

[fervent eagle]

a. In a group of 2000 people must at least 5 have the same birthday?

b. What is the number that must share a birthday?

c. What is the minimum number for 5 people to share a birthday?

I'm not sure how you would exactly get the answer for part b? Nor am I sure if I'm doing part a and c correctly? Am I correct in using 365 for my k (group) to get my b? Because if they share a same birthday, that means they have to share 1/365 days of the year? Thank you.

[vital crag]

do you know pigeonhol principl

[fervent eagle]

Very roughly, that's what I was trying to apply but don't know how. Basically if you have n + 1 items, but it has to fit into n groups, then at least 1 of them will always have 2, right?

[vital crag]

right apply that to needing 5 people to share a birthday

oh which part is b) you didn't label it in your question

[fervent eagle]

What is the number that must share a birthday?

Sorry, my bad.

[vital crag]

yea instead of 5 people sharing a birthday, it's 2000 balls sharing the same 365 boxes

[fervent eagle]

I see, give me a minute, I'm just trying to understand this. So could we say instead of 2000 'balls', we basically are trying to fit in 365 + 1 items into 365 boxes?

[vital crag]

something like that. from pigeonhole you get that 366 people, two must share one birthday

[fervent eagle]

Ah I see.

[vital crag]

repeat for 365 * 2 + 1, 365 * 3 + 1, etc.

[fervent eagle]

I'm sorry, I'm a but confused as to why we're repeating?

We're repeating until all the items run out?

[severe hawk]

The pigeonhole principle states that if you have n places to put stuff, and you have more than n items, at least one has to share places with another.
Example. If you have 4 boxes, and you have 5 items, you'd put the first 4 items in a different box each, but now all boxes are filled. So the fifth item needs to go into an occupied box

in your example, you have 365 "boxes", which are each of the days. So if you have more than 365 people, at least two are forced to have the same birthday. You'd repeat this after having each "box" with one person, to have each "box" with two people, and so on

does that help?

[fervent eagle]

Again, sorry if I'm slow, I do get this part I think, and I see what you're saying with the second part, the books shows it too that way. But I guess would that mean it's 365 * number of boxes + 1 = 2000? Am I correct?

[severe hawk]

it's not an equality, it's an inequality

[fervent eagle]

Ah I see, that's why you'd do ceiling.

[severe hawk]

if you have 365, they each fit in one day. So they are not forced to share.
if you have from 366 to 365*2, they fit with only pairs sharing. There's no forcing of 3 ppl to share.

[fervent eagle]

Ah ok. And same with 365*3.

[severe hawk]

so every 365, or fraction, you need another "slot" in each "box"

and that's why the ceiling

so they are basically asking, is 2000 smaller, or bigger than 365*5?

[fervent eagle]

Oh I see, sorry, give me a minute. I'm gonna write this down as a note.

[severe hawk]

if 2000 is larger, they wont fit, so they need to share
if 2000 is smaller, you have enough "boxes", so they dont need to share

[fervent eagle]

Yes, 2000 is bigger than 365*5.

So you would at least need 6 boxes?

But wouldn't that be the answer to part a, not necessarily part b?

a. In a group of 2000 people must at least 5 have the same birthday?

b. What is the number that must share a birthday?

c. What is the minimum number for 5 people to share a birthday?

Wait wait, I think I see.

If there has to at least be 6 'boxes', that means at 5 must share a birthday.

Right? Again, sorry if I'm still not getting it.

Wait, no, in this case it would be 4?

[plucky rover]

c is slightly unclear tbh. Is it asking what's the minimum size of the group for 5 people to always share a birthday or what's the minimum size of the group for 5 people to possibly share a birthday

Looks like they mean the first

[fervent eagle]

I don't know, that's just what the question says. 😐

[plucky rover]

Okay idk what has been done so far but

[fervent eagle]

But unless 'm wrong, wouldn't it be that there has to be at least 6 people to share the same birthday?

[plucky rover]

See each day as a box and each person as a ball

If there's more than 365 people, at least one of the boxes must have one more than one ball

That's two people sharing a birthday

[fervent eagle]

Here, I'll just show you what I've done, not sure this is right or not either, I'm stuck on b mainly

[fervent eagle]

Yes.

[plucky rover]

The answer to the first is just "yes" lol

But yea 1 looks good

[fervent eagle]

Ok, nevermind, I'm a dumbass.

[plucky rover]

And 2 is what you've done

[plucky rover]

No, you were gonna need to do it anyway for 2

[fervent eagle]

Wait, I'm sorry, I'm confused, how is it 5 and not 6? Won't you divide 2000/365 and find the ceiling?

[plucky rover]

Do 5 people share a birthday? Yes
How many people share a birthday? At least 6

[plucky rover]

You would yes

[fervent eagle]

OH MY GOD I'M DUMB

I don't know how I got the arithmetic wrong

[plucky rover]

What

What 400

[fervent eagle]

Wait, it's 2000/365, right?

No, sorry, nevermind.

I tried checking it again and used 2000/5 instead of 2000/365. But this is what I got for 2000/365 and got 5.47..., if you take the ceiling, it would be 6? So shouldn't it at least be 6?

[plucky rover]

...slow down you're panicking

[plucky rover]

Yes

The answer to a is yes

[fervent eagle]

Ah ok.

[plucky rover]

The answer to b is 6

You are correct

,calc 2000/365

[soft zealot]

Result:

5.4794520547945

[plucky rover]

Your answer to c is correct as well

365 * (5-1) + 1

[fervent eagle]

Ok, sorry.

[plucky rover]

Don't be

Now are you confused about why these work

[fervent eagle]

rubs temples I'm really bad at this.

Yes.

[plucky rover]

Cool

[fervent eagle]

I thought a would be 6, not 5.

[plucky rover]

A isn't asking for a number mate

It's a yes no question

If 6 people share a birthday, 5 people also share a birthday

[fervent eagle]

Ah, admittedly my reading comprehension sucks.

[plucky rover]

Just ignore one of those people

[fervent eagle]

🤦

That makes sense.

[plucky rover]

Lmao issok

[fervent eagle]

Yea no, the sentence makes sense now.

[plucky rover]

Cool what about the others

[fervent eagle]

Just to make sure, for the third one, I was reading in the book, and you're finding the converse to answer c, right? Just to make sure I'm applying this correctly.

[plucky rover]

Not sure what you mean by converse

But what you've done is correct

If you have n boxes and you want to ensure at least one of them has more than k balls

You need at least n(k-1) + 1 balls

[fervent eagle]

This is what it says. So yea, from what you're saying I am doing the right thing.

[fervent eagle]

Alright, thanks a lot. I think I get it, so I'm actually doing the right thing, but my reading comprehension sucked so I misunderstood the first part of the question. Have a good day/night. + 1 is the extra pidgeon, n is the amount of pidgeons, and k - 1 (from your version) is maximum pidgeons per hole.

.close

[final saddle]

Channel closed

Closed by @fervent eagle

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.

[novel nexus]

i need to find supremum and infimum of Z, how do i do that? i see that on the bottom it's (n-20)^2+something but i dont know what to do next

[rocky tusk]

well no

have you tried anything really?

other than vertex form

[novel nexus]

i mean i could just guess as in find such n that (n-20)^2 ~ 30 and just check since it's just natural numbers

[rocky tusk]

ok so for the first one you have (n - 20)^2 - 30 so clearly this will have a negative inf and positive sup yea?

[rocky tusk]

but yes that is the idea

[novel nexus]

right, 1/6 sup and -1/5 inf

i guess i'm tired

thanks you

.close

[final saddle]

Channel closed

Closed by @novel nexus

Use .reopen if this was a mistake.

[final saddle]

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.

[severe robin]

How do I continue this proof, I work with the LHS and that results in using the ih to replace lhs with (k+1)^2

[winter lava]

$\sum_{i=0}^{k+1}(2i+1)=((k+1)+1)^2$

[soft zealot]

Axe

[winter lava]

did you get this?

you said you were working with the LHS, so maybe you did something like this?

$\sum_{i=0}^{k+1}(2i+1)=\sum_{i=0}^{k}(2i+1) + (2(k+1)+1)$

[soft zealot]

Axe

[severe robin]

wait honestly I'm just not sure hopw to get that last part

I know it'sm the last term, I'm unsure how I can know that myself?

[winter lava]

oh you substitute $i=k+1$ into $2i+1$

[soft zealot]

Axe

[winter lava]

you use $i=k+1$ because that's the upper limit of the sum

[soft zealot]

Axe

[severe robin]

OHH

thank you you're a life saver I see what it means now

I'll continue solving it knowing this

thank you!

[winter lava]

you're welcome

[severe robin]

.done

oh

.close

[final saddle]

Channel closed

Closed by @severe robin

Use .reopen if this was a mistake.

[final saddle]

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 rivet]

yo can anyone show me how to solve this question

[peak rivet]

i js want the answer my teacher taught me i forgot

[spiral narwhal]

Draw a right triangle

[peak rivet]

ok

[final saddle]

@peak rivet Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.