help-23

[rough matrix]

oh wait it is

wait lemme see

ill send

wait then isnt 2(x^5) to functions since 2 is on its own a functino

ik its not but i dont get the logic

[weary hearth]

!status

[safe radish]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

@rough matrix 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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

Channel closed

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

[small ether]

nxbar-y ??

What's the correct process?

<@&286206848099549185>

[true veldt]

easiest way to do this kind of problem is to remember that the average is just the sum of n arbitrary numbers, all divided by n
So, you can write $\overline{x}\cdot n=a + \overline{y}\cdot (n-1)$, where $a$ is just the n-th term

[flat frigate]

sentinel

[true veldt]

all that equation is saying, is that the sum of all the numbers is equal to the sum of all the numbers except the last number, plus the last number

[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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[true veldt]

Like, if $\overline{x}=\frac{1+2+3+4}{4}$, and $\overline{y}=\frac{1+2+3}{3}$, then you know that:

$\overline{x}\cdot 4=1+2+3+4$, and $\overline{y}\cdot 3=1+2+3$

[flat frigate]

sentinel

[true veldt]

@small ether

[small ether]

Thanks.

[true veldt]

do you understand my thought process and how to get to the solution from there ?

[small ether]

Yes.

[true veldt]

awesome, ill just close the channel then

[small ether]

Yeah.

[true veldt]

.close

[safe radish]

Channel closed

Closed by @true veldt

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[steep magnet]

I dont understand what I did wrong, these are the same no?

My answer and the answer they wanted...

What is 'not necessary'?

[safe radish]

@steep magnet Has your question been resolved?

[edgy isle]

seems correct, only thing weird is to have a negative inside the root, even if it's an odd degree

[steep magnet]

Ah ok, maybe thats it

Thank you!

❤️

.close

[safe radish]

Channel closed

Closed by @steep magnet

Use .reopen if this was a mistake.

[steep magnet]

HI CHARTBIT ❤️ ❤️

HI ADONIS ❤️ ❤️

[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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[blazing knoll]

How do I find R?

[austere cypress]

what does the question says?

[blazing knoll]

The figure on the side shows the straight line x/8 + y/4 = 1 and the point Q drawn on a Cartesian plane. Find the value
(a) M,
(b) N,
(c) R,

Mb forgot to translate

[austere cypress]

Q(4, r) is the point in the graph where x = 4 and y = r. You can plug in x = 4 in the given formula for the line and find the value of y (which is r)

[blazing knoll]

So y=-1/2(4) + 4
y=-2+4
y=2

Ight tq

.close

[safe radish]

Channel closed

Closed by @blazing knoll

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[burnt grail]

for 8a, if i make gravity negative, then time is negative

[burnt grail]

is everything just meant to be positive?

cus someone helped me yesterday with this question and said i want to make the velocityu positive, gravity should be negative

[hard crest]

there is a solution with negative t, but is that the only one?

[burnt grail]

well t is cubed so yes

[hard crest]

I will say I don't understand how you got t³

[burnt grail]

multiply t on both sides

[hard crest]

I feel like your algebra is severely lacking

how did t get in the denominator in the first place

[burnt grail]

oh wait

what am i doing

[hard crest]

try to make sure not to confuse t and +

[burnt grail]

oppsie

yea ma fault

[hard crest]

put a hook on your t if it helps

[burnt grail]

oh u just make it into a quadratic

4.9t^2-14.7t+49=0

correct?

[hard crest]

yes it is a quadratic equation in t, however check your signs

oh wait yeah your signs are right

[burnt grail]

alrlr

erm im getting math error

[hard crest]

hmmmmm

[hard crest]

hey question

[burnt grail]

is this correct?

[hard crest]

where did that 49 come from

[burnt grail]

49m above the gorund

displacement

s = ut + 1/2at^2 rght

[hard crest]

right... what's the displacement of the wheel, from the start to the end? in words

[burnt grail]

the wheel is 49m from the start vertically?

[hard crest]

in which direction

[burnt grail]

up

[hard crest]

really? the wheel ends 49m above where it started?

[crystal palm]

Should be
49+14.7t-4.9t^2=0

Here 49 is the wheels starting position

[hard crest]

Martin...

[burnt grail]

ohhhhh

[hard crest]

remember what I said about keeping things consistent

[burnt grail]

mhm

[hard crest]

the Wheel's displacement is down, so negative

[crystal palm]

Oops sry

[burnt grail]

yep

[hard crest]

(this is why I was asking about signs, I knew something looked weird but wasn't sure what)

[burnt grail]

so in other words the actual equation is 4.9t^2-14.7t-49=0

[hard crest]

yep

[burnt grail]

alrlr

ight

ok yea now i got it

we get t = -2, and 5

but t cant be negative

so it must be 5

[hard crest]

yep

[burnt grail]

alr thank u man

[hard crest]

https://tenor.com/view/lotr-eowyn-i-am-no-man-gif-5386334

[burnt grail]

but how do i do b now

[burnt grail]

oops

sorry

[hard crest]

well, you have the height as a function of time

and it's a quadratic

alternatively you could use potential and kinetic energy

[burnt grail]

iii dont know how to do that

so instead of solving for t in the quadratic

we solve for s or?

[hard crest]

what class is this

what have you studied about quadratic functions and parabolas

[burnt grail]

tutoring

a lot

im not good at physics tho so idk what to do

[hard crest]

ok well.... h(t) = 4.9t² - 14.7t - 49

what's the peak of this parabola

[burnt grail]

5

t = 5

oh and then we just plug it into t

so 4.9(5)^2 - 14.7(5) - 49

[hard crest]

,calc 4.95^2-14.75-49

[flat frigate]

Result:

1.4210854715202e-14

[hard crest]

that is 0

the parabola peaks at height 0?

[burnt grail]

if t = 5 and t = -2

we have to try both values right?

and 5 alreayd doesn't work

since it's 0

[hard crest]

what do you think the peak of a parabola is

[burnt grail]

the vertx

oh shit

[hard crest]

yes

pay attention to the words I am saying

not what you think I am saying

[burnt grail]

ight mb

[hard crest]

that also applies for the words on the page

[burnt grail]

-b/2a = 14.7/9.8 correct?

which is 1.5

so the wheel reaches a maximm height of 60.0m

to 3 sig figs

[dusty yew]

You guys talking about physics? Mind if I join?

[burnt grail]

sure

im struggling rn

so if u wanna help, be my guest

[dusty yew]

Which one?

a/b/c?

[burnt grail]

i just did b

to which i got 60.0m

to 3 sig figs

[hard crest]

remember where we put zero

or you already did that

[burnt grail]

wait wdym

so i got 60.025

but to 3 sig figs

so it becomes 60.0m

[dusty yew]

Yea its correct

Its goes 11.025 m higher

[hard crest]

just thinking about the fact that we started at 49 but yeah it's already accounted for

[dusty yew]

so max elevation is 60.025

[burnt grail]

can u guys confirm that the next answer to the next question is 37.3ms-1

or is it -37.3?

since it's going downwards

[hard crest]

speed is absolute

[dusty yew]

You take the magnitude

[burnt grail]

oh so just 37.3

but in this case i can just solve for velocity but state that it can only be larger than 0?

uh oh

what did i do

[dusty yew]

What values did you plug in

[burnt grail]

i did v^2 = 14.7^2 + 2(-9.8)(-60)

[dusty yew]

Mb mb

I put 60.025 instead of 61.025

TwT

Silly me

Your answer is correct

[burnt grail]

so 37.3ms-1

so yk how this question asks to calcualte speed

why cant we calculate the actual speed (like distance/time) instead of calculating final velocity?

[dusty yew]

Erm

You put 60 in the last term

[burnt grail]

is it not 60?

[dusty yew]

Its -49

The initial position is y = 49

The final position is y = 0

[burnt grail]

but i thought we were using the max height

of the wheel

[dusty yew]

So displacement = 0-49

[dusty yew]

You can do that too, but in that case the initial velocity will be 0

[burnt grail]

why

[dusty yew]

The velocity of an object becomes 0 at maximum height

Thats why it cant go any higher

Does that make sense?

[burnt grail]

oh yes

oh bc in this case then we consider that it starts from 60m

[dusty yew]

Shouldnt you use 60.03 instead?

That would produce a more accurate result

Or just 60.025

[burnt grail]

i mean sure

37.31

37.32*

barely a change

[dusty yew]

v^2 = 0 + 2 x (-9.8) x (0-60.025)

34.3 m/s :3

[burnt grail]

oh if u do my equation but instead of -60, u put -49

u get the same

ahhh

[dusty yew]

Yeah

Same result, no matter how you approach the problem

Btw you asked me about calculating the actual speed

You need differentiation for calculating instantenous velocity/acceleration

I dont know about it much TwT its not taught in 10th grade

[burnt grail]

so when they say speed here, they just mean velocity

but instead of giving direction, we just give magnitude

[dusty yew]

No, speed is the magnitude of velocity

Velocity is a vector quantity

Whereas speed is a scalar

Speed doesnt have any direction

[burnt grail]

yea

ight

[hard crest]

we want the speed exactly when it hits the ground, not the average speed starting at the top

[burnt grail]

oh so that basically means we want the final velocity when it hits the ground right

[hard crest]

yeah

[burnt grail]

ight

[hard crest]

which we then ceremoniously strip of its directional information leaving only a quantity

[burnt grail]

gotcha

[dusty yew]

Yes, technically

[dusty yew]

Oh he meant average speed! I thought he was talking about instantaneous velocity 🙂

[burnt grail]

how should i do 9c

[burnt grail]

yes

[hard crest]

wait why does the stuntman end up going faster than the bus at the end...?

[burnt grail]

tbh idk

ig bc he has to jump into it

so he needs to run faster

[hard crest]

yeah but once he's jumped into it shouldn't his velocity be the same as the bus?

[burnt grail]

not sure

i can ask my teacher if this question's correct

if it doesnt make sense

[hard crest]

first one is wrong

[burnt grail]

oh it's 3 seconds right

well between 2 and 4 seconds

[hard crest]

looks like a little over two... maybe use algebra to solve that

[burnt grail]

isn't a and c like almost the same?

cus if he reaches the same speed as the bus

oh wait nvm

then c would be 4 seconds

[hard crest]

erm maybe? your stuntman is moving with constant acceleration

so he's x(t) = 1/2 at²

and the bus is moving with constant velocity

so it's b(t) = vt

at what point do those intersect?

[dusty yew]

x = vt = 1/2 at^2
t = 2v/a

So its gonna be 6.4 s

[burnt grail]

i dont get this

so what's x(t)

[dusty yew]

Its the position (x) of the stuntman as a function of time (t)

[burnt grail]

oh so at some point in time, he is in x position

[dusty yew]

Yep

[burnt grail]

ok

[dusty yew]

you can assume the initial point to be x = 0

[burnt grail]

yep

[dusty yew]

And the point they meet is x

So for the stuntmant :

x = 1/2 at^2 (as he starts from rest)

And the bus is going at a constant velocity

Hence, x = vt

Does that make sense?

[burnt grail]

oh yea

[dusty yew]

1/2 at^2 = vt

You can just cancel out the t (as it cant be 0)

It will make the calculations easier

[burnt grail]

wiat so what's the velocity

i got t = 2v/a right

a is 2.5

[dusty yew]

Its 8

[burnt grail]

v is 8?

[dusty yew]

Yea

Its in the graph

[burnt grail]

ight

is d 8m

[dusty yew]

Umm, d? Displacement?

[burnt grail]

no for part d

[dusty yew]

Ohh alright

Its just vt or 1/2 at^2

t is 6.4

[burnt grail]

i did 1/2at^2

[dusty yew]

1/2 x 2.5 x (6.4)^2

51.2 m

[burnt grail]

oh shit

i forogt the squared

.close

[safe radish]

Channel closed

Closed by @burnt grail

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[lean otter]

I had asked this question on 12 September, 2024.

Note: This is not a very simple question.

[digital sparrow]

diagram pls

[lean otter]

Inradius of triangle EHF = that of HFG = 5 units

Inradius of EFG = 6 units

Angle F = 90 deg

Find FH.

<@&286206848099549185>

20 minutes passed just like that

I need to go now.

.close

[safe radish]

Channel closed

Closed by @woven vine

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[brazen parrot]

what does the gradient rerpesent

[digital sparrow]

try to represent this in terms of y and x

then compare with y = mx + c
m will be the slope

[brazen parrot]

is h the slope..

planks constant?

[digital sparrow]

yupp

[brazen parrot]

oh ok

than ku

do u know about photoelectric stuff?

cus i kind of struggle wit hit

[digital sparrow]

i do

[brazen parrot]

when u increase the intensity of the light are u increasing the amount of electrons emitted per unit time

[digital sparrow]

yess

[brazen parrot]

and what about frequency of the light

if its frequency is lower than the threshold frequency it doesnt emit anything?

[digital sparrow]

correct

[brazen parrot]

what is a "stopping potential"?

[digital sparrow]

think about it like this
you go to buy a chocolate

[brazen parrot]

yes

[digital sparrow]

the tax is constant and 5 coins

if you have 4 coins you cant buy the chocolate

[brazen parrot]

oh

okok

[digital sparrow]

if you have 10 coins you can buy a choclate worth 5 coins

[brazen parrot]

does this relate back to emission spectra i learnt in chemistry?

where electrons get enough energy to be promoted into higher energy levels

[digital sparrow]

that is quantization of energy levels

[brazen parrot]

oh

[digital sparrow]

its like one chocolate is 10 coins

then next is 20 coins

no in between

[brazen parrot]

ok

[digital sparrow]

and if you have 15 coins you cant buy any of those

[digital sparrow]

stopping potential is just work function

fancier name lol

[brazen parrot]

oh wtf

[digital sparrow]

like till how much can it stop the electron from leaving

[brazen parrot]

how come E equals all these equations

[digital sparrow]

E = hf

do you get this?

[brazen parrot]

hf is energy of the incident ray?

[digital sparrow]

yup

[brazen parrot]

yea

[digital sparrow]

hf = phi + E_k

[brazen parrot]

whats pho

phi in the equation

[digital sparrow]

its written in the pic

[brazen parrot]

oh

is ek the energy that is lost

[digital sparrow]

nope

[brazen parrot]

oh

how come incident ray = phi + ek

[digital sparrow]

what is phi?

[brazen parrot]

idk

ok way

wait

so e =hf

hf=e

hf= phi + ek

[digital sparrow]

yup

but what is phi?

and what is ek?

hmm

[brazen parrot]

r u sure ek is not the enerfy released

OH i said lost

[silk portal]

Can I get help

Please

[brazen parrot]

#❓how-to-get-help

so phi is probably the work function

[digital sparrow]

correct

[digital sparrow]

it is

oh lol

[brazen parrot]

and rearranging that u get ek = hf - w

[digital sparrow]

E_k is the kinetic energy gaines

[brazen parrot]

phi

[silk portal]

I'm struggling with intersects

[brazen parrot]

u cant forget maximum 😡😡

[safe radish]

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

[brazen parrot]

ok thank u

i have a test on this on monday is it ok if i dm u for help tmr?

bcoz its 12 am rn

[digital sparrow]

that is why we write 1/2 m v^2 instead of E_K

[brazen parrot]

ohh

[digital sparrow]

monday as in next week?

[brazen parrot]

yes

[digital sparrow]

ohh sure

[brazen parrot]

ok thank u so much

im kind of doing bad in physics

[digital sparrow]

i dont know if ill be online tmrw tho

so yeah

[brazen parrot]

oh its ok

we have all of this week lol

[digital sparrow]

kk good luck for your test

[brazen parrot]

thx have a good day

.close

[safe radish]

Channel closed

Closed by @brazen parrot

Use .reopen if this was a mistake.

[digital sparrow]

[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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[lean otter]

hello

[lean otter]

So im modelling this bottle

This one and the purple dots i used a quadratic equation to model it

[sinful glen]

,rotate

[lean otter]

But i decided ill use an exponential function instead since ive only been using quadratic equations to model this bottle which I feel like wouldnt help me

In the scoringn process

So a person did help me and he founded an exponential equation here

But im confused how he got it

[deep rapids]

wow real life application of quadratic?

[lean otter]

2.57449-1.3269810^{-7}(3.0137199999999)^{x} is what they got

[lean otter]

lol

Those are my points

And i input two points from this into the exponential equation

And its totally wrong so idk what im doing wrong

<@&286206848099549185>

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

@lean otter 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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[lilac hatch]

Hello! I'm having a little bit of trouble with the following problem:

Using the form of the definition of a integral using right endpoints, evaluate the integral of (5x + 2) from 0 to three with respect to x.

So far my attempts have gone something like this:

/ n
| (5x + 2) dx = lim E (5xi + 2) (3/n)
/ n -> inf i = 1

[smoky nacelle]

waiting

[lilac hatch]

Sorry, I'm just typing my work out if that's alright.

[smoky nacelle]

yeah yeah i mean im waiting

lmao

[weary hearth]

imatheq exists if you are having trouble writing math

[smoky nacelle]

$\LaTeX$ ftw

[flat frigate]

Percy

[smoky nacelle]

you'll have to learn it eventually.

i mean unless you're a highschooler just trying to survive ig

[weary hearth]

no you won’t

not if you avoid math

[smoky nacelle]

most stem related fields yes you will

[smoky nacelle]

dunno if you'd take calc if you're avoiding it but yeah fair

[weary hearth]

you won’t need latex if you avoid stem

[smoky nacelle]

i can't read this at all sorry

do you mean you wrote the integral $\int^3_0 (5x+2) dx$ and are now confused or

[flat frigate]

Percy

[lilac hatch]

Sorry about that! I'm typing it all up in iMathEQ as we speak.

[smoky nacelle]

/nbr just genuinely no clue what that says

[smoky nacelle]

Okay

[smoky nacelle]

holy hell you're doing riemann sums?

if you don't need to do it that way i'd suggest avoiding it

[lilac hatch]

I am required to do it this way in this case, otherwise I'd definitely just take the easy route.

Basically, I've tried using the def of the integral (i.e., the right equation) to find the integral, but for whatever reason after multiple tries I am consistently ending up with 45/2 as my answer, which is, according to the textbook, false.

[smoky nacelle]

,wolf integral (5x+2) from 0 to 3

yeah hm

[weary hearth]

cant even use the bot lmao

you flipped the bounds

[flat frigate]

Results provided by WolframAlpha

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

Requested by percykel

[smoky nacelle]

it doesn't matter shush

but okay be happy

[weary hearth]

are you going to do the riemann sum to verify his answer?

[smoky nacelle]

i'd check his solution

[lilac hatch]

If it helps any, here's my exact step-by-step thought process for how I got to 45/2

The "(3/5)"s are meant to be (3/n)s

@smoky nacelle I don't mean to bother or rush you, but are you still there?

[safe radish]

@lilac hatch Has your question been resolved?

[lilac hatch]

<@&286206848099549185>

My apologies if I am making some mistake in using the @ Helpers ping.

[uneven pawn]

Can you send a screenshot of this instead of the pictures? It's a bit hard to read

[lilac hatch]

Of course!

Give me just a second to type it out again since my internet funked up. Sorry to make you wait!

[uneven pawn]

np

[lilac hatch]

The question essentially asks one to, using the information in the integral equation in the top left-hand corner of the first image, find the value of that integral equation using the definition of the integral/riemann sums.

[uneven pawn]

How are you going from 5xi+2 to 15i/n +2?

What even is x actually

[lilac hatch]

Because xi, if we are using right endpoints, is equal to a+i * change in x, or delta x, so xi is in this case 0 + i * 3/n, which, multiplied by 5, is 15i/n.

[lilac hatch]

The value of the ith interval.

[uneven pawn]

Ahh, you mean $x_i$, and you're saying $x_i=0+\dfrac{3i}n$

[flat frigate]

Zayden

[lilac hatch]

Yes, basically. Sorry for the confusion.

[uneven pawn]

k

In step 3 to 4, you can't pull 3/n out of the limit

You can pull it out of the sum however

[lilac hatch]

Fair enough. Is that because it isn't technically a constant?

[uneven pawn]

Yeah

$$\lim_{n\to\infty}\frac3n\sum_{i=1}^{n}\left(\dfrac{15i}n+2\right)$$

And then you can break the sum into two sums, one with the i terms, and one with just the 2

[flat frigate]

Zayden

[lilac hatch]

Could you also simply make i = n^2 + n / 2, or nada?

[uneven pawn]

See, i is basically a dummy variable

It's a shorthand for, add all these things from 1 to n

But once you break the sums, you can do a bit of simplification that'll make life simpler

[uneven pawn]

This is the right idea, but you'll have to get to a place where you can use it

[uneven pawn]

What happens when you break this into two sums and simplify?

[lilac hatch]

Hmmm...let me see real quick.

Okay, thus far this is what I have come up with:

[uneven pawn]

I'd advise against putting 3/n back into the sum, that's just extra work. And you can't do the i to n^2/2 + n/2 thing, because that isn't true

I'd do

$$\sum_{i=1}^n\left(\dfrac{15i}n+2\right)=\left(\sum_{i=1}^n\dfrac{15i}n\right)+\left(\sum_{i=1}^n2\right)$$

[flat frigate]

Zayden

[uneven pawn]

Ignore the limit and 3/n for now

[uneven pawn]

Then you can take 15/n out of the first sum, and since there's no i in the second sum it's equal to 2n

[lilac hatch]

I'm sorry, I'm not quite following. What do you mean by this? Why could I not do (15((n^2+n)/(2)))/(n)?

[uneven pawn]

You're trying to use that i = n^2/2 + n/2, right?

[lilac hatch]

Yes.

[uneven pawn]

Could you explain what this means in english

[lilac hatch]

The summation of i is equal to n (the number of intervals, or iterations) squared plus n, all divided by 2.

[uneven pawn]

Yeah, basically what you're saying is that $\sum_{i=1}^n(i)=\dfrac{n(n+1)}2$

[flat frigate]

Zayden

[uneven pawn]

Which is very different from i=n(n+1)/2

[lilac hatch]

But is not n(n+1)/2 simplified equal to n^2 + n / 2?

[uneven pawn]

Yeah, that's fine

What i mean is

The sum of the i values being equal to that

Is different from a single i value being equal to that

When i write a summation, the value of i is already decided - it's gonna take, one by one, the values from the subscript to the superscript

If I say $\sum_{i=1}^9f(i)=100$, what I mean is $f(1)+f(2)+f(3)+\dots+f(9)=100$

[flat frigate]

Zayden

[uneven pawn]

i is forced to take the values 1 through 9

It cannot do anything else

In this case you're saying that $\sum_{i=1}^n(i)=\dfrac{n(n+1)}2$, which is true, but to use it you can't just subsitute $n(n+1)/2$ into $i$

[flat frigate]

Zayden

[uneven pawn]

What you must instead do

[uneven pawn]

Is take the first sum

Take 15/n common

To get

$$\left(\sum_{i=1}^n\dfrac{15i}n\right)=\dfrac{15}n\left(\sum_{i=1}^ni\right)$$

[flat frigate]

Zayden

[uneven pawn]

And now you can substitute the thing inside the bracket for n(n+1)/2

[lilac hatch]

Doesn't that end up giving us the exact same thing?

[uneven pawn]

You cannot have the sum there at the end

If you're using the fact that the sum of all i is something, then you must have added all the terms

[lilac hatch]

So because we have 15i/n, and the n in the denominator, for instance, is not accounted for, we cannot say that 15n^2+15n/n?

[uneven pawn]

Think of it like $$\begin{align}\sum_{i=1}^n\dfrac{15i}n&=\dfrac{15\times1}n+\dfrac{15\times2}n+\dots+\dfrac{15\times n}n\&=\dfrac{15}n(1+2+\dots+n)\&=\dfrac{15}n\dfrac{n(n+1)}2\end{align}$$

[flat frigate]

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

[uneven pawn]

See how there's no summation symbol at the end

The only mistake you're making is that you somehow add the terms while still leaving the sum symbol there

[lilac hatch]

I'm sorry, I'm not quite following, are you saying that when I substituted n^2+n/2 for i, and solved from there, I missed the fact that that technically solves the summation?

[uneven pawn]

I'm saying that you can't substite it with i, you have to substitute it with the whole sum

the sum of i from 1 to n

It's these two things that are equal, not the i inside the sum

[lilac hatch]

Ohhhhhhhhhhhhh

So, ergo:

?

[uneven pawn]

Yupp

You have to add 2n tho, given the fact that sum of 2 from 1 to n is 2n

Wait a sec

You did that

Yeahh, 57/2 seems correct

[lilac hatch]

Could you also reach the same answer via distributing the (3/n) when doing the sum of the summations, or is that violating some law that I'm not aware of?

[uneven pawn]

You'd reach the same answer, it'd just take more calculation

[lilac hatch]

Ah, I see.

That about answers my question. I was working on this for what felt like forever on my own, so thank you for your time, help, and being a lifesaver!

I hope you have a wonderful day!

[uneven pawn]

Thanks, you too

[lilac hatch]

.close

[safe radish]

Channel closed

Closed by @lilac hatch

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[verbal trout]

R these correct? I have a question for Q#2

[safe radish]

@verbal trout Has your question been resolved?

[tardy mango]

You can check these yourself in #bots

,w maximize 2x^3-18x^2+48x-1 for 0 \leq x \leq 3

[flat frigate]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon

[tardy mango]

,w (1/3)x^3-4x^2+12x+1 decreasing

[flat frigate]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon

[tardy mango]

\leq is < and \geq is > btw

[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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[thick zealot]

How to find the C value in a Sinusoidal Function? As I got the D, A, & B but the graph won't work still?

[lean otter]

Can you post the question? 'A', 'B', 'C', and 'D' aren't used the same way universally for trig functions.

[thick zealot]

D= 5, A = 6, B = 1 and idk C

0?

[lean otter]

Is your B value correct? I agree with your values for A and D

If two consecutive mins are at 3 and 13, then the period is 10. So the B value would be 2pi/10 = pi/5

[safe radish]

@thick zealot Has your question been resolved?

Channel closed

Closed by @thick zealot

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[lean otter]

i need help w these questions!! the solutions are so unclear to me, should i send them also?

[quiet plume]

Do you understand why those statements are true intuitively?

[lean otter]

yes!! the first one makes sense to me, but not sure how to show it

[quiet plume]

Yeah it'll be helpful to know what you're finding unclear

[lean otter]

one sec

i dont get this n0(epsilon) bit

like is it a function

so baffed

[quiet plume]

It's just trying to make it explicitly clear that n0 depends on the value of epsilon you'er given

[lean otter]

oo okay, then is H their 'epsilon' for sn

[quiet plume]

H is from the definition of a limit tending to infinity

The first line of the answer gives that definition

[lean otter]

ohhhhh

its seperate from the convergent one

[quiet plume]

Yes

[lean otter]

i seeeee

okay, i understand the first one now

the second i just dont get where the set comes from

is it the terms in the sequence?? whats the point of saying min when the minimum is 1

[quiet plume]

The set is the set of terms in the sequence.
H=1 is arbitrary here. The idea is that because the limit tends to infinity, at some term n0 and after, the terms of the sequence are all above 1

But that means that there is only finitely many terms before right?

So we can bundle up the terms of the sequence into two parts : the terms after n0, which we know are bigger than 1, and the terms before n0, which we don't know much about, except for the fact that there are only finitely many of those (namely s1, s2, s3, ..., s_(n0 -1))

Since there is only finitely many of them, then this finite set has a minimum, but we have to add 1 because the rest of the sequence is at least 1

[lean otter]

i get the finite terms before n0 now, and the fact that it would have a min, but i still dont get the 1 bit

[quiet plume]

$\underbrace{s_1, s_2, s_3, s_4, \ldots, s_{n_0 - 1},}{\text{exactly $n_0 -1$ of those}} \underbrace{s{n_0} ,s_{n_0 + 1} ,s_{n_0 + 2} \ldots}_{\text{all $\ge 1$}$

[flat frigate]

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

[quiet plume]

Well you want to find a lower bound for all the terms of the sequence

[lean otter]

i see i see

this makrs srnse

TAHNK YOU SM

saved my life

.close

[safe radish]

Channel closed

Closed by @astral nebula

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[maiden mountain]

@solar hazel we argued with prof today and we convinced him its 19c4 kudos to you!

is it fine if we reiterate how did we come up with 19c4? i kind of forgot how we did it, because i had a friend who explained it in a different way and was easier to understand.

you could technically squish all those rectangles together to get an actual rectangle and then count the rights and ups from there, then suppose all of them are r, well you need 4 ups so you choose 4 of those 19 to be ups and that'll acount to every scenario

1b is correct,

1c) he said to count the number of ways to go through c from the top, and then the bottom, and then count the number of ways you can get to C directly

13^15 - (13^136^2 + 13^137^2)

well i think we messed it up a little bit.

its not 6^2 because if you look, the one on C is 5 not 6

[solar hazel]

can’t respond rn but i will be back later

[maiden mountain]

if we do it the way we did it earlier for 1c,

13^13 cuz other columns are fine
now the options for the ones below are 5 not 6

to enter the column of C itself the column before gives you 5 options, and then after you are on the C column, you have 6

and i think for it its 7^2

i want to try and do it directly though

so we have to count the number of ways it can be crossed from above ,and then the numbers of ways it can be crossed from below and then directly cossed

<@&286206848099549185> can anybody help me count the number of ways of the line coming from a to cross C from above, below and directly?

it comes down to the column before and on C i believe and for the other columns they can be represented as 13^13 since for every column there are 13 options

[safe radish]

@maiden mountain Has your question been resolved?

[maiden mountain]

<@&286206848099549185> any idea? im trying to think of how to represent this rn

[maiden mountain]

this specifically

7 places above C you can come down from, 5 you can come up from

and then 1 you can come directly to?

[maiden mountain]

<@&286206848099549185> anyone?

if we can do 1c now we'll be free, let me tell you what i think,

prof said we have to count the num of ways we cross C, from above, below and horizontally,

heres what i think, if we consider the ones from above c,

we have 7 places we could go down from then after we cross c, we are left with 6 places where the line can proceed to the right from since it cant revisit itself,

and for the below one, we have 5 places, and after we have 7 to proceed from,

now for directly i have no idea how id count this because is it just 1?
heres a way ive looked at it aswell

<@&286206848099549185>

[maiden mountain]

<@&286206848099549185> pls anyone

[maiden mountain]

<@&286206848099549185> any clue?

i could reexplain

[maiden mountain]

might have figured it out

,calc 13^13 * 7 * 6 + 13^13 * 5 * 7 + 13^14

[flat frigate]

Result:

2.7258759593303e+16

[maiden mountain]

i think i have figured it out

.close

[safe radish]

Channel closed

Closed by @maiden mountain

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[rough mango]

the formula of Surface Area Measurement Nets and Rectangular Prisms. If a small box on the top of big box

[sick mason]

how do i write a proof for congruence in geometry, im lost i dont know what to do please help

[rough mango]

Anyone online?

[safe radish]

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

[rough mango]

Anyone?

[safe radish]

@rough mango Has your question been resolved?

[safe radish]

@rough mango 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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[tardy copper]

Is the max opperator something I can multiply both sides of the equation with and it would stay the same?

[austere cypress]

what do you mean

[plucky elk]

You don't multiply operators. You apply them

[safe radish]

@tardy copper 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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[supple monolith]

Hi, would you mind helping me understand this? I have trouble understand the behavior of f(x)! isn't it a composition function actually?
Need some hint.
Thanks.

[safe radish]

@supple monolith Has your question been resolved?

[supple monolith]

I found both B, and C as empty set, sicnc here is my conclusion:
for a set T, the power set of T, cannot be subset of T, so B is empty.
And T cannot be subset of power-set of T, but a member, so C is empty too.
Did I get it right?
That f(x) definition is so confusing, I substituted it with P(x), and I don't know what am I doing rn!

[supple monolith]

[left willow]

I'll use < sign for subset
Let X be a set st, f(X)<X
Then B<X
Which implies f(B)<f(X)<X
Thus f(B)<X
Now take the intersection over all X in A st f(X)<X
We get f(B)< n X= B (from def)
So f(B)<B

Thus B is the minimal element

@supple monolith

[supple monolith]

Thank you, what does the "minimal element" mean?

[left willow]

Smallest set under subset order st f(X)<X

[supple monolith]

The f(x) returns the power-set of given set X, and in B it states that f(B) which is power-set of B is subset of B, how could it be possible? isn't an empty set?

[left willow]

No what

f is a map which maps a subset of A to another subset of A

[supple monolith]

Sorry, a little confusing, so let say A={1,2,3,4}, and B={1,2}, then what's the result of f(B)?

[left willow]

Idk what f is here, but it will be a subset of A

f:A->B
elements of A are mapped to elements of B
Elements of P(A) are subsets of A

[supple monolith]

The f is defined as f:P(C) -> P(C), I just think I can substitute f(x) with P(x) then?

[left willow]

No why

[supple monolith]

Great, so let say f(A) = P(A), now in B it states that P(X) is subset of X, how could it be possible?!

[supple monolith]

IDK , if I just understand that f(x), I win.

[left willow]

Thats not possible since P(A) is not an element of P(A)

f(P(A)) would be P(A) if f was a surjection

[supple monolith]

Let say we have A={1,2,3,4}, and T={1,2}.
In B, it states, power-set of T which is {{1},{2},0,{1,2}} is a subset of T, so it's not possible, then B must be empty then? for any given subset of A, or still I'm reading it wrong?!

[left willow]

Why would P(T) be a subset of T?

[supple monolith]

It's the condition were given in definition in B.

[left willow]

No

It says f(B)=B

[supple monolith]

I'm talking about the B itself, not f(B), if I prove B is empty, the rest is obvious. For now, I like to know, what does B look like for let sy A={1,2,3,4} ?

[safe radish]

@supple monolith Has your question been resolved?

[left willow]

How can you comment on B without knowing f

say f maps every to A, except {1,2,3}
And map that to {1,2}

[safe radish]

@supple monolith 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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[tardy lark]

Where does the 2a_2 come from ?

[pine horizon]

put n=0

[tardy lark]

Where ?

Omg

Nvm

I was looking at the upper right side

thanks

.close

[safe radish]

Channel closed

Closed by @tardy 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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[plain shore]

What do u uhh.. do here?

Couldn't even get the diagram

[digital sparrow]

@plain shore do you know how to calculate the mirro image of a point about a line?

[plain shore]

yeah

[digital sparrow]

let a point on the parabola be (t^2, 2t)
find its mirror image about the given line

[plain shore]

ohh like uhh focal chord or something do we need that

[digital sparrow]

i dont think we need the focal chord?

[plain shore]

oh yeah mb

I just am not able to visualize the diagram tho, I can work out the calc

where does C even lie

on the parabola?

or inside

HEH?/

[digital sparrow]

C is a locus

not a point

[plain shore]

oh

a locus of a point

[digital sparrow]

yup

[plain shore]

but like what does "Tangent to C from (2,3)" mean like I don't see a how a tangent could touch C from (2,3)

[digital sparrow]

its tangent to C at (2,1)

not 2,3

[plain shore]

yeah 2,1 my bad

[digital sparrow]

lets go step by step

[plain shore]

okay

[digital sparrow]

draw the parabloa y^2 = 4x

[plain shore]

alright

[digital sparrow]

and now y=x

does 2,1 lie on any one of them?

[plain shore]

hmm uhh no

[digital sparrow]

correct

now take any arbitary point on that parabola

[plain shore]

at^2 and 2at?

[digital sparrow]

yup

[plain shore]

okay which would just be uhh t^2 and 2t cuz a=1

[digital sparrow]

correct

now find its mirror image about the line y=x

[plain shore]

okay

oh (2t,t^2)?

[digital sparrow]

correct

so what will be the locus of C?

[plain shore]

2t,t^2

wait

no that's parametric points

I don't even have like a slope tho

how can I calc locus

[digital sparrow]

let h = 2t, k = t^2

[plain shore]

oof okay

[digital sparrow]

now find the relation between h and k

that will be the locus

lol

[plain shore]

what relation is between h and k hmm

T-T all I know is the perpendicular distance from (h,k) to y=x and (k,h) to y=x is same

[digital sparrow]

hint: try to eliminate t

[plain shore]

and HMM (k,h) satisfies the parabola

so uhh as y^2 = 4x,
h^2=4k

[digital sparrow]

correctt

now replace h by x and k by y

[plain shore]

okay so x^2 - 4y =0

[digital sparrow]

correct this is C

[plain shore]

okay what do we do now

[digital sparrow]

now do you know how to find its tangent?

[plain shore]

Tangent of P(2,1) or C

[digital sparrow]

tangent of C at the point (2 , 1)

[plain shore]

we can't use two-point form can we

[digital sparrow]

do you know how to find the tangent to a parabola?

[plain shore]

ik the general equation is y=mx+a/m

[digital sparrow]

it is good

but thats for y^2 = 4ax

this is x^2 = 4ay

[plain shore]

ohh wait there's that yy1 thingy

yy1=2a(x+x1) for parabola at a point right

for y^2=4ax

[plain shore]

ohh

right

xx1=2a(y+y1) then

[digital sparrow]

yup use that

[digital sparrow]

correct

now what is x1 and y1?

[plain shore]

firstly we have his

[plain shore]

2,1

[digital sparrow]

put it

[plain shore]

uhh brain not braining wait

2x-4y=0?

[digital sparrow]

how?

i dont think so

[plain shore]

oh we were supposed to sub in this

[digital sparrow]

lmao

[plain shore]

2x=2y+2 then
x-y=1

ahhhhhhhhhhhhhh

thankss

[digital sparrow]

lesgoo

!done

[safe radish]

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

[plain shore]

.close

[safe radish]

Channel closed

Closed by @plain shore

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[odd folio]

How do I do thos

[digital sparrow]

!img

[safe radish]

Please post images (such as PNGs or JPGs) of the question rather than other filetypes such as PDFs which have to be downloaded. Non-image downloads can potentially contain viruses or other security risks.

[lean otter]

Wait, isn't it directly viewable?

[odd folio]

What

[safe radish]

@odd folio Has your question been resolved?

[safe radish]

@odd folio 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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[lean otter]

There are two magnitudes A and B such that they satisfy the following relations:

A DP B when B ≥ 20
A^2 IP B when B ≥ 20
If when A=9, B=10, find the value of A when B=45.

[lean otter]

A√B/B = k, B ≥ 20

[lapis shadow]

What are dp and ip

[safe radish]

@lean otter 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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[buoyant oar]

Hey

[buoyant oar]

Is this integration correct?

[gilded vault]

could you show us the integration?

[buoyant oar]

Ya just a sec

[gilded vault]

yes its correct

[buoyant oar]

Can you elaborate using u-substitution

[gilded vault]

We use u=x^3+1

and get that du=3x^2dx

Thus, the integral of x^2dx/sqrt(x^3+1) is the same as the integral of 1/3sqrt(x^3+1)du

which is the integral of 1/3sqrt(u) du

[ocean crypt]

You can also use the chain rule

[gilded vault]

chain rule is for derivatives, but we are integrating here?

[ocean crypt]

I mean this one

[gilded vault]

sure ig

[buoyant oar]

Thanks

[safe radish]

@buoyant oar Has your question been resolved?

Channel closed

Closed by @buoyant oar

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[dire fjord]

@empty gyro lets continue the discussion rn if you arent busy

[dire fjord]

if you are then we can do this later

[empty gyro]

I am busy at this moment. But i am acknowledging that i saw this and will return in perhaps an hour or so

[dire fjord]

np take your time

[dire fjord]

I will close this channel and whenever you are ready dm me

.close

[safe radish]

Channel closed

Closed by @dire fjord

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[steep magnet]

They both factorize to give this

Sub in -2 and you get 0 in the denominator

So it DNE, no?

[quiet plume]

The arrow is downwards so it's from the right isn't it

It does blow up to infinity, so maybe they want that?

[steep magnet]

Can you explain sry?

I vaugly remember how to do these but not really

Im so out of practice 😅

[quiet plume]

The limit at -2 does not exist, but the limit from the right goes up to infinity.
Depending on what you learned, this might count as the limit "existing" from the right

So maybe try to input infinity as the answer

[steep magnet]

Why does it exist / got up to infinity from the right

It was the correct answer btw

But I still dont understand it really

[quiet plume]

If you input -2, it's true that you get (something nonzero) / 0.
This is an indicator that you have an asymptote over there, but you can still determine the direction in which the function is going from the left or from the right.

If you take 1/x for instance, the limit towards 0 from the left is -infinity and the limit towards 0 from the right is +infinity

To see this more algebraically, you can use the notation $-2^+$ to signify you're going at it from the right, so it's just a little bit more than -2.

If you plug that inside your function, you get $$\frac{(-2^+ + 7) (-2^+ - 9)}{(-2^+ - 2)(-2^+ + 2)} = \frac{5 \cdot -11}{-4 \cdot 0^+}$$

[flat frigate]

Azyrashacorki

[quiet plume]

So it might look a bit daunting, but really all it's saying is that if you approach from the right, then x + 2 should be slightly positive (that's why there is a 0^+ popping out there).

We know that this expression will be really large (the limit is either +inifnity or -infinity), but now we have the signs, so we can decide which it will be

So here, the numerator is negative and the denominator is also negative, so the whole function will be positive, thus it has to be +infinity

[steep magnet]

I think I get it but I need to reread this a few times first 😅

Ok yes I think I get it now

I just tried an example and got it right haha

The maths is actually very simple lol

But thank you so much you explained it really really well

Youre a great teacher!!

❤️

.close

[safe radish]

Channel closed

Closed by @steep magnet

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[slow mesa]

Hey guys, I need help with this:

"you must calculate on a hat with a volume of exactly 2000 cm^3.
You must optimize material consumption. this means the surface area must be as small as possible
The hat you need to optimize is a combination of a cylinder and the top is a cone as shown in the sketch below

a) What dimensions must this hat have in order to minimize the surface area, and how large will the surface area be.
it is about finding the heights of the cylinder and the cone of which the hat consists, so that the surface area is minimized."

[obtuse plover]

are u familiar with lagrange multipliers

@slow mesa

[slow mesa]

No

[obtuse plover]

what class is this for

[slow mesa]

calculus

[pale lily]

looks like a optimization problem

calc 1

[gilded vault]

ok so first of all how can we characterize this shape

we have a radius, the height of the cylinder, and the height of the cone, right?

[slow mesa]

yes,

I already have the radius, which is 8.75 cm

[gilded vault]

is this given in the problem?

[slow mesa]

Basically yes and no. I had to calculate it in the start of another task that looks like this one. This was multiple assignments, it has nothing to do with the other calculations for the other connected tasks, so the only thing given here is the radius

[gilded vault]

oh ok

so this is a much easier optimization problem then

so can you express the volume in terms of the h_l (cylinder height) and h_c (cone height)?

[slow mesa]

yes

So do I have to use the formula for these two shapes?

[gilded vault]

yes

[slow mesa]

ok, then what do I do with it?

I have been told for optimization that I first had to create a function then differentiate the function and then set it equal to 0

[gilded vault]

we aren't at that step yet

[slow mesa]

ah, ok

[gilded vault]

we are still creating the function

what is the volume in terms of h_l and h_c

it is pi*r^2(h_l+h_c/3) right?

[slow mesa]

yes

[gilded vault]

so we have that 2000=pi*r^2(h_l+h_c/3) right?

[slow mesa]

yes

[gilded vault]

im going to rewrite this as 2000/(pi*r^2)=h_l+h_c/3

moreover I will call 2000/(pi*r^2)=c, so i don't have to type it all out every time

so now, can you tell me the surface area of the cone-cylinder complex in terms of r, h_l, and h_c?

[slow mesa]

the formula or..?

[gilded vault]

yeah

[slow mesa]

In all together?

[gilded vault]

yeah so the surface area of the party hat

[slow mesa]

the surface area of a cone is:
A= pi*r(r+sqrt h^2+r^2)

[gilded vault]

yes

but

but i think you mean (l+sqrt h^2+r^2)?

[slow mesa]

oh, yeah yeah that is it

[gilded vault]

yes so we have that l+h/3=c

and we have that A=pi*r(l+sqrt h^2+r^2) right?

[slow mesa]

I'm sorry, but what happened to the other terms in this one?:
2000/(pi*r^2)=h_l+h_c/3

(just so I understand correctly

[gilded vault]

i abbreviated 2000/(pi*r^2) as c

we will plug it back in

[slow mesa]

so that was the formula for the cylinder or was that for the whole shape...?

[gilded vault]

the whole shape

also you seem to be using h_l as l and h_c as h in your writing

so we can use that notation

[slow mesa]

ok

[gilded vault]

so we now substitute l with c-h/3

and we get A=pi*r(c-h/3+sqrt(h^2+r^2))

[slow mesa]

is there a specific reason for it?

[gilded vault]

because we want A to be in terms of one variable

so that we can differentiate it

and now we have our function we need to differentiate

[slow mesa]

how do I differentiate a function like that?

do I just use the normal rules of differentiation.... or?

And does it mean I have to calculate the other values before differentiating this, right?

[gilded vault]

yes

[gilded vault]

the other variables are constants tho right?

you can just keep it in terms of them

[slow mesa]

shouldn't it be?

[gilded vault]

yes r and c are constants

[slow mesa]

why is r constant?

[gilded vault]

you stated that we knew the radius right?

[slow mesa]

Right

[gilded vault]

yeah, so r is the radius?

and since we knew it, its a constant?

[slow mesa]

oh, yeah, just trying to understand what we're doing

Right

[gilded vault]

okay so can you differentiate it?

[slow mesa]

Do I plug in the radius as it's value or just the letter?

[gilded vault]

i would not plug it in until later

just treat it as a constant

[slow mesa]

ok, I will try

What rules do I use?
does it have any specific rules?

[gilded vault]

product rule and chain rule

i gtg tho

[slow mesa]

ok

thanks

[safe radish]

@slow mesa Has your question been resolved?

[slow mesa]

I have differentiated the function:
A=pi*r(c-h/3+sqrt(h^2+r^2))

And I got :