help-10

[odd talon]

hi please may someone help me with this i dont understand simple interest and everytime i read it i get more confused

[timid silo]

are you familiar with linear functions

[odd talon]

no

[timid silo]

okay are you familiar with y = mx +b

[odd talon]

no

im like really really bad at math

[timid silo]

okay sure let's do a more intuitive approach i guess

[odd talon]

idk what that word means but ok

[timid silo]

okay actually, me explaining an entire concept to you will not end up well for your understanding. Do you prefer if I linked you some resources to watch from first?

[odd talon]

ok that sounds good

[timid silo]

https://www.khanacademy.org/math/in-in-class-7th-math-cbse/x939d838e80cf9307:comparing-quantities/x939d838e80cf9307:simple-interest/v/intro-to-simple-interest-comparing-quantities-class-7-india-math-khan-academy

watch this

then follow up with the rest of the sections on the left

[odd talon]

THANK YOU🤍

[obtuse pebble]

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[vernal atlas]

Hello, if I have lim of x->inf (2^-n), should I have it at the end 1/inf and this will equal 0?

[knotty crow]

x -> inf and 2^(-n) ?

not x there?

[vernal atlas]

Sorry, x is n

[knotty crow]

2^(-n) = 1/2^n

1/2^(inf) is infinitely small, hence result is 0

[vernal atlas]

Is there a process for passing 2^(-n) to 1/2^n? I'm confused when the exponent is a variable

[knotty crow]

law of exponents

[vernal atlas]

Oh oh, got it 100%, thanks for the help :))

.close

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[dawn nest]

I have to draw the graph of 45 √p and √p right?

[alpine raven]

what do they mean by parent function ?

[dawn nest]

f(x) = √x?

I guess

[obtuse pebble]

@dawn nest Has your question been resolved?

[dawn nest]

uhm

<@&286206848099549185>

[obtuse pebble]

@dawn nest Has your question been resolved?

[outer cave]

Yes

[obtuse pebble]

@dawn nest Has your question been resolved?

[dawn nest]

ah alright, and do these graphs look correct (I know it' impossible to make it super accurate by ykk)

y axis -> scale of 5
x axis -> scale of 1

for 45 √p

and for √p, y axis -> scale of 0.5, and x axis -> scale of 1

[obtuse pebble]

@dawn nest Has your question been resolved?

[dawn nest]

<@&286206848099549185>

[tardy epoch]

try using graphing software to plot both

,w plot y = sqrt(x), y=45sqrt(x) for 0 < x < 200

[warm shale]

Results provided by WolframAlpha

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

Requested by riemann#2529

[obtuse pebble]

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[acoustic sun]

Hi guys, I have this related rates problem, and I am honestly stuck on what to do from here. I understand I am supposed to use a law of trig but I really am just completely stuck 😭 any help would be great

[acoustic sun]

rotated pic

[jolly ginkgo]

but we don't know the initial position of the plane so how are we going to know about 1 minute later

[acoustic sun]

I tried looking up an answer for it, I found a chegg answer for it, however I tried understanding it and I really am unsure, this is the diagram they provided.
they also used the law of cosines to solve this, but I do not understand where they got the 135 degrees. I also do not understand how this diagram represents the situation

[jolly ginkgo]

the airplane is said to be climbing but I don't see how this is a correct representation of the situation

[acoustic sun]

<@&286206848099549185>

This is the rest of their reasoning, but I do not understand this at all, wondering if anyone can just help me understand what exactly is happening

[obtuse pebble]

@acoustic sun Has your question been resolved?

[acoustic sun]

That chegg thing is wrong btw, still figuring out the problem

any help would be appreciated, think I got the right diagram this time

[rich plume]

The plane is going downwards?

[acoustic sun]

No upwards, drew it as flying from right to left my bad

[acoustic sun]

<@&286206848099549185>

[rich plume]

Is this diagram correct?

[obtuse pebble]

@acoustic sun Has your question been resolved?

[obtuse pebble]

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[timid silo]

x and y are full numbers tho

[timid silo]

like 1 2 3 4 5 -1 -2 -3 -4 -5

x^3-y^3=217

[jolly ginkgo]

factorize

[timid silo]

(x-y)(x^2+xy+y^2)

and 217=1×217=7×31

[jolly ginkgo]

ok good

[rough stratus]

X=6, y=-1

$217 = 216 + 1 = 216 -(-1) = 6^3 - (-1)^3$

[warm shale]

ThickduckPlayz

[rough stratus]

Therefore, $x=6, y=-1$

[warm shale]

ThickduckPlayz

[rough stratus]

@timid silo

[obtuse pebble]

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[toxic shuttle]

How many "points" are there in a unit square and what exactly are points?

[toxic shuttle]

Trying to work through this example: https://i.imgur.com/QTAGQwz.png

if we turn the unit square into a plane then (0.1, 0.1) is a point but isn't (0.0001, 0.0001) also a point?

ok I don't think I need to answer that question to work on the problem but I still want the answer to the question if anybody knows

[obtuse pebble]

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[midnight elm]

did i do this right?

[timid silo]

I don’t remember the molar masses on the top of my head, but this dimensional analysis looks correct

[midnight elm]

thanks!

.close

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[timid silo]

How do I use chain rule here?

[timid silo]

I tried bt I'm not sure

Or we use other formulas?

I'm doin partial differentiation

This is the question

I did the frst order now I'm doin chain rule

[timid silo]

n got dis

x1^2+4x2-4x1x2^2/(x1^2-4x2)^2

[pine sail]

$x_1^2-4x_2 - (x_1-2x_2^2)(2x_1)$ should be your numerator

[warm shale]

What the hell am I doing here?

[pine sail]

And you have something else. So yeah.

[obtuse pebble]

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[fast rover]

can someone explain this question to me? I tried using VSEPR theory and used a trigonal bipyramidal structure to get bond angles of 120 and 90, but my professor said the bond angles needed to be evenly spaced out/the same. this is for a linear algebra class btw.

[obtuse pebble]

@fast rover Has your question been resolved?

[fast rover]

<@&286206848099549185>

[obtuse pebble]

@fast rover Has your question been resolved?

[obtuse pebble]

@fast rover Has your question been resolved?

[hidden garnet]

This rather seems like a Group Theory application than a Linear Algebra thing to me but I digress

You have to consider the rotation and flip symmetry of a tetrahedron

[fast rover]

could you possibly expand on that? I am still pretty confused 😅

[hidden garnet]

Actually you know what

I now understand why it was in a Linear Algebra class

Consider

The carbon atom to be in the origin of R^3

That is, (0,0,0)

And let the hydrogens be in (1,1,1), (-1, 1, -1), and (1, -1, -1) and (-1, -1, 1)

You can use the dot products to find the angle

This is a regular tetrahedron also

This works because all bonds are C-H bonds, and sp^3 hybridized, hence all are in equal length

[fast rover]

yeah that makes sense, but i thought the problem is asking about 5 hydrogens around a central carbon

[hidden garnet]

CH5

Unfortunately that's impossible

[fast rover]

yeahhhh idk its so weird 😂

[fast rover]

i guess its like asking to consider a hypothetical molecule and somehow using properties of vectors or like dot products and stuff to calculate an angle

but still

its pretty weird

[hidden garnet]

I mean for that you kinda need to know the shapes

If you know shape you know angle

[obtuse pebble]

@fast rover Has your question been resolved?

[mighty geyser]

i think start by guessing the angle (it's a nice number)

then next it's to prove you can do no better than that

so you place the first two down at that angle, then you have very limited space for the other 3, then apply some geometric pigeonhole

[obtuse pebble]

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[subtle warren]

Vector question, Hi does anyone know the properties of cross product for this question, because I'm not sure about how to go about it

[obtuse pebble]

@subtle warren Has your question been resolved?

[forest sinew]

can i suggest #linear-algebra

im surprised more people havent jumped on this question

you might try looking at a proof first though

https://www.youtube.com/watch?v=jmDzoaLTCG8

[obtuse pebble]

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[golden gorge]

why are they subtracting 4?

[golden gorge]

also why are they subtracting 1 from this equation

oh

nvm

.close

[obtuse pebble]

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[golden gorge]

.reopen

[obtuse pebble]

✅

[golden gorge]

nvm

didn't figure it out

[obtuse pebble]

@golden gorge Has your question been resolved?

[tardy epoch]

,tex .cts

[warm shale]

riemann

[golden gorge]

hmm

i think I got it

maybe

ok

thanks]

.close

[obtuse pebble]

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[timid silo]

how many numbers from 1 to 9 we can form, the number must be used only once a. divisible by 9? b. second fourth and 6th digits are all even c. the sum of the first 4 digits equal the sum of the 4 last digits

[timid silo]

how do we do this

what formula do we use and why please

explaining is enough no need to solve anything i just feel a little stuck

[ashen cosmos]

All a b and c are the same case or separate cases?

[timid silo]

im really sorry for not making it clear but they are seperate cases so explaining a single one is enough if they are all solved using the same method

[ashen cosmos]

You know the divisibility rule of 9?

[timid silo]

the sum of digits must be divisible by 9 right?

[ashen cosmos]

Digital sum of digits must be 0 or 9

Yeah same thing

[timid silo]

nice

[ashen cosmos]

So

[timid silo]

yes ?

[ashen cosmos]

The way you’ve typed this out is kinda hard for me to understand your question, do you have any image of the question or did you type out the exact question on the chat

Wait no I think I get it

First you could see how many a digit numbers are divisible by 9

Which is 2

Then for 2 digit numbers, make pairs of singular digits that are divisible by 9

[timid silo]

yes i do i'll try to translate it more accurately

[ashen cosmos]

Like 18, 81, 27, 72 etc

[timid silo]

oh nice

[timid silo]

yes

[ashen cosmos]

But I guess manual counting would be too long

[timid silo]

waiitt i think i get this

[steel marsh]

Yeah I think there’s a way to generalize the permutations of numbers

[ashen cosmos]

Yeah I was think the same thing

Wait I might need a paper and pencil I’ll see how I can make permutations

Ok I get this

I think

[timid silo]

yep there is since we were meant to in this unit but idk how though

[ashen cosmos]

Just going off a hunch

[timid silo]

thank you so much ele!

[ashen cosmos]

I haven’t done anything yet I’m still thinking 😭

No need to thank me rn

[timid silo]

i'll try to translate the question accurately to make it more clear

[ashen cosmos]

Wait is it in another language?

[timid silo]

it was in arabic i only tried to explain the question in english

[ashen cosmos]

Ahh I see

I get the question so don’t bother

Are there any options or anything?

[timid silo]

so the question is how many 9 digit numbers can be made from the digits 1 to 9

the cases are

the number is divisible by 9 ... second forth and sixth digits are even... the sum of the first four numbers is equal to the sum of the last 4 numbers. what i know is that we are meant to do combinations and permutations

[ashen cosmos]

Wait is it just 9 digit numbers??

Or any digit numbers?

[timid silo]

yes and the number has to be used only once

[ashen cosmos]

So the answer for a is 9!

[timid silo]

9

oh really?

[steel marsh]

Wait are you sure?

[ashen cosmos]

Yeah

Wait lemme show my solution on the paper cause I’m bad at explaining

[steel marsh]

Okay

My first thought was 8! but idk

[timid silo]

can you explain why please cause i find this lesson a bit confusing

[steel marsh]

9!/9

[ashen cosmos]

No because the digit 9 can come on any place value of the number

[timid silo]

right so 9 factorial bc we can arrange 9 numbers in many different orders so we just multiply the numbers together?

[ashen cosmos]

Does this make any sense or have I committed the big dum dum

The main gist is that we are trying to make groups of 2 individual numbers whose sum is 9, which is (1,8)(8,1)(2,7)(7,2) etc

So we can see that if we add all numbers from 1 to 9 we get a multiple of 9, agreed?

[timid silo]

this is cool its all clear now! i think im starting to get this now

[ashen cosmos]

So we just need to see how many ways the digits 1,2,3,4,5,6,7,8,9 can be arranged

Which is 9!

[steel marsh]

But aren’t the total permutations 9! numbers?

Then you’d need only the ones that are divisible by 9, which you can get by 9!/9 right?

That’s my thought process for 8!

[ashen cosmos]

For the second part you need to think, by first making that 9 dashes I made and then putting how many possibilities can come in the digits, and as soon as you pick a number from the subset, you can’t count it again if that makes any amount of sense

[ashen cosmos]

Yeah and all permutations of digits from 1 to 9 are divisible by 9 are they not? I could be overlooking something simple

[timid silo]

may i ask why did we have to make groups of 2 individual numbers when we're arranging 9 different numbers? sorry i can ask the dumbest questions in order to understand eventually

[steel marsh]

Would something as simple as 21 be a valid permutation and not divisible by 9?

[ashen cosmos]

No no that was my subconscious talking. Like what I meant was to make it clear that all digits from 1 to 9 when added are divisible by 9

Like it’s a subconscious method I’ve developed by solving questions and stuff

[timid silo]

OHHHH

[ashen cosmos]

Could you rephrase that cause I didn’t get what you said

[ashen cosmos]

Yeahh, you could use this method of making 9 dashes and using logic to see what works for the other parts

[ashen cosmos]

Does the second part only have 2nd 4th and 6th only or 8th also cause usually questions be like that sometimes

[timid silo]

ur right plss it has 8th too

[ashen cosmos]

Hah ok

So you could do like

[timid silo]

yep developing a method is so cool i think i understand this now

[ashen cosmos]

For the second digit, there can be 4 even numbers, for the fourth it will be 3 even numbers and so on and then adjust the odd numbers as well

[timid silo]

5 over 9 for the ones that have odds then

yesss

ok this is getting more clear the more u explain it i think im starting to grasp this

[ashen cosmos]

So it would be 5443322

No discord be doing the ugly

Let me type that again

[timid silo]

lmaoo

[ashen cosmos]

Damn does mobile not have those fancy ascii characters

Just assume x is multiply sign

Then the answer I think would be

5x4x4x3x3x2x2

I could be wrong

But from what I think

[timid silo]

wait so what u did was taking the odd numbers seperating them from the even digits and reducing the possibilities ?

then multiplying them together

[ashen cosmos]

I’ll show you the image

[timid silo]

like this?

[ashen cosmos]

Basically if you could put 5 digits in the first place, and couldn’t repeat the digits, there would be only 4 to put on the other place and so on

[timid silo]

nicee

[ashen cosmos]

Did you get it?

Btw which grade question is this? I’m curious lol

[timid silo]

i did !

[timid silo]

im 16, grade 11th

[ashen cosmos]

Nice!! For the third part, try to think using logic instead of formulas or smth

Visualise the situation and how it could fit in

[ashen cosmos]

Nice, I turn 16 this year too but I’m one year behind and I’m in 10th this year

[timid silo]

thank you ele i really appreciate it also nice pfp lmao

[ashen cosmos]

But I did study PnC from my brothers textbook so I’m aware of basic permutations

[ashen cosmos]

You too :D
Is that you?

[timid silo]

ur actually so cool mashallah

yesss it is

[ashen cosmos]

I just like math very much but thanks :>

It’s pretty late so I can’t help you with the third part right now, if you need any help in the future you can ask me

[timid silo]

i like math too but i struggle with it sometimes but ur actually so good at explaining cause i watched like 4 vids and couldnt understand until u explained it to me

[timid silo]

ok ele i'll keep that in mind, good night!

[ashen cosmos]

I could explain the third part tomorrow morning or after coming from school tomorrow

[ashen cosmos]

Byeee

Man I got so distracted by higher level math that I didn’t finish my homework </3

[timid silo]

if u want to then im down

[ashen cosmos]

Ig this help channel has served its purpose so may I close it?

[timid silo]

math can be fun yet distracting

[timid silo]

yes

byee

[ashen cosmos]

.close

[timid silo]

.close

[ashen cosmos]

Ah I can’t close it since I don’t open it 🤡

[obtuse pebble]

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[deep barn]

help pls

whats angle c

[trim portal]

whats sum of all angles in that shape?

[deep barn]

what does sum mean

hablo espanol

[timid silo]

adding the values together means sum

[deep barn]

Ok

[trim portal]

what's green+purple+orange+blue?

[deep barn]

uhh

how i work out blue

[royal basin]

suma

you don't need to know the blue angle by itself

[timid silo]

the sum of angles in all shapes with 4 angles is always 360

[deep barn]

oh

[trim portal]

Using that you can find the blue angle, and using that you can find the red angle

64+130+129+blue=360

[deep barn]

323

is all the angles labled

added together

what i do next

[trim portal]

so 323+blue=360

subtract 323 from both sides

[deep barn]

oh

so it would be

37?

[trim portal]

yep

[deep barn]

yay

is that the anlge of C

angle

[trim portal]

no you found the blue angle

[deep barn]

oh

[trim portal]

do you know how to find the C?

[deep barn]

so i now take that away from 180

[trim portal]

yep

180-37

[deep barn]

143?

[trim portal]

yep

C=143°

[deep barn]

thanks

how about this one

[ashen cosmos]

Do you know what the small square in the angle means?

The angle below m, has a square symbol

[deep barn]

no

[ashen cosmos]

It means that the angle is right angled, meaning it’s value is 90

Now would you be able to find the angle diagonal to m? After that I think you would be able to do the question

[deep barn]

whats this

[obtuse pebble]

@deep barn Has your question been resolved?

[obtuse pebble]

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[void fable]

I've got a problem I've spent an hour on and just cant find the answer, would be great if someone could help me.

A ball is dropped from a window 30m above the ground. Half a second later, another ball is projecter vertically upwards, directly below the window. The balls collide when they are 15m above the ground. Find the initial velocity of the second ball.

[torpid token]

!status

[obtuse pebble]

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

[void fable]

3

[torpid token]

Tell me about it

[void fable]

so I know its just basic SUVAT stuff, but I'm not really sure where I'm going wrong

I know the answer is 17.4 but I can never get it no matter what i do

[torpid token]

Well, have you tried making a function for the position of each ball?

As a function of time

[void fable]

I know thats not what we're meant to do

its just using the normal 5 SUVAT equations

[torpid token]

I mean it pretty much still is

[void fable]

how would you do that then?

still new to this so ive got no idea how to di it

[torpid token]

Just try finding the position of each ball as a function of time

And maybe graph them both in the same plot

Then you will probably find the answer

[void fable]

alr thanks

[timid silo]

you have to use
$\Delta y = \frac{1}{2}gt^2$

[warm shale]

hannibal

[obtuse pebble]

@void fable Has your question been resolved?

[timid silo]

I got 18.3 with g = 10

Each ball uses a different time.

1. calculate the time it takes for ball 1 to fall 15m.
2. the time it takes the second ball to reach 15m is that time, minus 0.5 seconds
3. use y = vt - 0.5gt^2 to find initial velocity

[obtuse pebble]

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[hard hill]

hi, how can I get phi in this case? I don't know L and I have tried with sin() but I can not get rid of the L, how could I get rid of the L?

[grizzled shore]

You don’t need L

[hard hill]

yes, yes, and how can I cross it?

[grizzled shore]

Show your work

Show me what you’ve tried

[hard hill]

I have tried sin(phi) = opposite/hipotenusa but I get sin(phi) = L/4L and I can not cross L, I think I am searching for a trigonometric function that let me do 4L/L for crossing L but I don't know which one

[grizzled shore]

What do you mean you cannot cross L

[hard hill]

like L/4L is not 4 no? instead 4L/L is 4 right?

[grizzled shore]

What’s $\frac{L}{4L}$

[warm shale]

Frosst

[hard hill]

sin() no?

[grizzled shore]

Not that

Can you simplify it further

[hard hill]

haaa is this 4 · (L/L)?

[grizzled shore]

Yes

[hard hill]

so much thanks

[grizzled shore]

No

Wait

It’s not

What is $\frac{10}{40}$

[warm shale]

Frosst

[hard hill]

(2 · 5)/(2^3·5) I think

[grizzled shore]

Not what I’m asking

[grizzled shore]

Can you simplify this fraction

[hard hill]

yes, 1/4

[grizzled shore]

Ok

What is $\frac{1\cdot 10}{4\cdot 10}$

[warm shale]

Frosst

[hard hill]

1/4 no?

[grizzled shore]

Ok

What is $\frac{1\cdot L}{4\cdot L}$

[warm shale]

Frosst

[hard hill]

1/4

[grizzled shore]

What is $\frac{L}{4L}$

[warm shale]

Frosst

[hard hill]

1/4?

[grizzled shore]

What is $\sin{\Phi}$

[warm shale]

Frosst

[hard hill]

1/4

[grizzled shore]

There you go

What’s phi then

[hard hill]

14.48 I think

[grizzled shore]

,calc asin(1/4)

[warm shale]

Result:

0.25268025514208

[grizzled shore]

,calc asin(deg(0.25))

[warm shale]

The following error occured while calculating:
Error: Undefined function deg

[grizzled shore]

First off

How did you get 14

Arcsin is only defined from -1 to 1

[hard hill]

I mean like 14.48 degrees

[grizzled shore]

Degrees

,w convert arcsin(0.25) to degrees

[warm shale]

Results provided by WolframAlpha

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

Requested by Frosst#1111

[grizzled shore]

Ok good

[hard hill]

thank you, but one more think sorry

I think once my teacher had done like a/a·b -> (a/a) · b this is not right then?

[grizzled shore]

Brackets are important

I didn’t say this earlier but

[grizzled shore]

I have tried sin(phi) = opposite/hipotenusa but I get sin(phi) = L/(4L) and I can not cross L, I think I am searching for a trigonometric function that let me do 4L/L for crossing L but I don't know which one

You should’ve had brackets there

[hard hill]

why?

[grizzled shore]

Because

$a(ab)^{-1}\neq a(a)^{-1}b$

[warm shale]

Frosst

[grizzled shore]

First one is $\frac{a}{ab}$

[warm shale]

Frosst

[grizzled shore]

Second one is $\frac{a}{a}\cdot b$

[warm shale]

Frosst

[hard hill]

haaa, the second one is (a·b)/a no?

[grizzled shore]

Yes

Or ab/a

Or ba/a

We read left to right

If you want to put things under a division line you better bracket what’s under to be unambiguous

But on paper you can write it underneath the line so it’s fine

[hard hill]

okey, so much thanks really 😀

[grizzled shore]

Np 👍

[hard hill]

.close

[obtuse pebble]

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[deep barn]

whats the answer

is it B??

<@&286206848099549185>

PLEASE

HELPME

[frigid prism]

!nosols

[obtuse pebble]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

@deep barn Has your question been resolved?

[obtuse pebble]

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[sour granite]

Is it even possible to find A(k) given

[obtuse pebble]

@sour granite Has your question been resolved?

[tardy epoch]

write sine in terms of complex exponentials then fourier/inverse fourier transform

[obtuse pebble]

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[sour granite]

Not sure that works tho cuz its gives both, I tried multiplying by sin(xr) and integrating to get delta(k-x) which kinda works

[sour granite]

Then ofc my result is wrong anyways but at least im close enough

[tardy epoch]

what do you mean "wrong but close enough" ?

[sour granite]

I got an answer.. which is better than just blank lol

[tardy epoch]

alright? do you still have questions?

[sour granite]

Nah i give up lol

Look at how well my answer (green) agrees with the initial condition

[tardy epoch]

do .close if you're done

[sour granite]

Oki

.close

[obtuse pebble]

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[manic karma]

So I actually know how to graph this which is all I'm asked to do here, but I was wondering if there was a way to find an explicit equation for such a function

[wise talon]

if you have the graph maybe

it will probably be piecewise

[high lily]

depends on what you chose to draw

there are many possible solutions,
not realistic to get equations for some of them

[manic karma]

ooh right, makes sense

is there some polynomial or trig function that would work

[wise talon]

uh

are you trying to avoid graphing it

i dont think any polynomial will work

because theyre continuous on R

[obtuse pebble]

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[tepid urchin]

https://tenor.com/view/huh-rabbit-cute-gif-15676652

[warm canopy]

open a new channel this one is going to die soon

[tepid urchin]

oh my

how tragic

.close

[warm canopy]

[obtuse pebble]

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[fallow granite]

Hi

[fallow granite]

Anyone how I would go about doing this

[tacit gate]

first second both?

[fallow granite]

Any of them

Which ever is easier

It’s practice for test

Just need to understand how it’s done

[tacit gate]

well did you try anything?

[fallow granite]

Well for the first i multiples 20 and 10

For the area of the rectangle

[tacit gate]

okay

[fallow granite]

And half of that is 100

Which is area of triangle

[tacit gate]

right

[fallow granite]

But those half circles idk

[tacit gate]

what can you say about the circles

what you need to find the area of a circle?

[fallow granite]

2 pi r

[tacit gate]

okay we only need radius

[fallow granite]

Radius?

[tacit gate]

can we locate a radius with what we are given?

[fallow granite]

It’s 10

[tacit gate]

that's not the radius

that's the diameter

[fallow granite]

5

[tacit gate]

2*radius is diamter

okay perfect

now you have areas of the circles

of the rectangle and triange

what else can you do

[fallow granite]

Subtract?

[tacit gate]

which one

[fallow granite]

Rectangle minus circle

Actually idk

[tacit gate]

so let's see the triangle

[fallow granite]

Yea

[tacit gate]

inside it

there's a circle missing a small part

[fallow granite]

Yea

[tacit gate]

and then it's a small part without the big circle

[fallow granite]

One is missing a smal part and the other is missing a big part

[tacit gate]

problem specified the two circles are congruent (the same)

giving us the hint that what is missing on the first circle

is present on the small part

[fallow granite]

Ok

[tacit gate]

so the answer to the first problem would just be Area of triangle - area of the circle

[fallow granite]

100 - 10pi?

[tacit gate]

yes

[fallow granite]

wait is area 2pir

2 pi r or pi r^2

[tacit gate]

you handle the equations\

just make sense of the problem

[fallow granite]

yea but which one is it

i mean i already got the area of triangle

100 - 78.54

21.46

@tacit gate

[obtuse pebble]

@fallow granite Has your question been resolved?

[tacit gate]

pi r^2

[fallow granite]

so its 100 - 78.54 = 21.46

[tacit gate]

if you did your calcs right it is

[fallow granite]

can u check it fo rme

for me

i double checked and it looked good

i dont have a calc on me rn

[obtuse pebble]

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[stable pulsar]

y'all, I'm struggling to draw accurate phase portraits for non linear systems. For example, for part c we get the gradient system [x',y'] = [ycosx, sinx], which when we linearize has non hyperbolic eigenvalues at the equilibrium points, so we can't use those as reference for the behavior of the solution

[stable pulsar]

am I meant to actually solve the system [x',y'] = [ycosx, sinx]? I'm not sure where I'd start on that

or is there something I'm missing

[obtuse pebble]

@stable pulsar Has your question been resolved?

[stable pulsar]

@ruby fulcrum

[tacit gate]

damn this is first time seeing a problem like this

[obtuse pebble]

@stable pulsar Has your question been resolved?

[obtuse pebble]

@stable pulsar Has your question been resolved?

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[untold bone]

How would you double derive equation x^2 - 2xy + 2y^2 + 5 = 10x

[untold bone]

That’s the equation of the curve, the question asks for the tangent at the point P(1,2), which I found was y=2x

Which means y’ is 2

But for y’’, I got 6/5 when the solutions say it’s -5/3

[obtuse pebble]

@untold bone Has your question been resolved?

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[inland talon]

Can someone explain what f^-1 (x) does to the function and the asymptope

[winged aspen]

f^-1 is the inverse function. So the whole graph is basically flipped on the y=x line

[inland talon]

The y axis?

[winged aspen]

no y=x line

its a diagonal

[inland talon]

Ok

[winged aspen]

the easy way to understand it is that any x value becomes y and any y value becomes x

[inland talon]

Ok

But the asymptote doesnt change

It stays the same

[winged aspen]

how to find the inverse function? Swap the x and y value and solve for y
Domain and Range swap

[winged aspen]

if your flipping the whole graph

[inland talon]

Yes

[winged aspen]

the asymptote would flip as well

[inland talon]

So an asymptote of 4 becomes neg 4

Or just stays 4

[winged aspen]

y=4 asymptote?

it would become x=4 asymptote

[inland talon]

X=4

Becomes y=4

[winged aspen]

then itll be y=4

[inland talon]

Ok

[winged aspen]

yeah you just swap it

[inland talon]

Thx

.close

[obtuse pebble]

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[teal horizon]

i am lost on this

[teal horizon]

where do i even start

.close

[obtuse pebble]

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[timid silo]

Anyone know why the last part is wrong?

[obtuse pebble]

Please don't occupy multiple help channels.

[hollow portal]

pretty sure this is -x/32

[timid silo]

wait why would it be -x/32?

[hollow portal]

$\frac{1}{64}(-\frac{4x}{2})= \frac{1}{64}(-2x)=\frac{-2x}{64}$

whoops

[warm shale]

ℕαv

[timid silo]

oh ok

.close

[obtuse pebble]

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[native briar]

how ?

[native briar]

I wonder that is this shape

.close

[obtuse pebble]

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[frail rapids]

I will send my attempt gimme a sec

Not sure where i went wrong

it doesnt line up with the answers

[royal basin]

everything is fine until this step

[frail rapids]

omg yes

im a dummy

thanks

.close

[obtuse pebble]

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[frail rapids]

not really sure what to start

[jolly ginkgo]

what is x and y intercept

[frail rapids]

hmm, how would I use the length of the line and the gradient to find those intercept points of (P, Q)

[jolly ginkgo]

you don't need to

just put x=0 and get y intercept and vice versa

you will get a relation between x,y,P,Q too

[frail rapids]

ahhhhh

I seee

so i got $y=-b and x=a$

[jolly ginkgo]

don't use the bot

[warm shale]

MathematicsPractice

[frail rapids]

lol ok

sorry just trying it out recently

[jolly ginkgo]

so P and Q are x and y intercepts respectively too according to question

[frail rapids]

yep

[jolly ginkgo]

P=a , Q==-b

so the points are P(a,0) and Q(0,-b)

now find the slope

[frail rapids]

k

-b over a

which equals 5/2 ahhhh

so the length of the line thing is useless?

[jolly ginkgo]

why?

how can you say values of a and b by just 5/2

[frail rapids]

because the slope of PQ is equal to the slope of (a,0) and (0,b)

which is equal to 5/2

so -b would equal to 5

and a would equal to 2

im probably wrong sorry

[jolly ginkgo]

certainly*

[frail rapids]

lolol

.close

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[sleek marsh]

Is there any way to deal with $\int^{2\pi}_0\frac{f'(nt)}{f(nt)}dt$

[warm shale]

Orthonormal

[sleek marsh]

If we know $f$ is piecewise smooth

[warm shale]

Orthonormal

[jolly ginkgo]

If g(t) = f(nt) then g'(t)= n f'(nt)

So the integration will give us log(f(2pi n)-f(0))/n

[sleek marsh]

.close

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[candid cloak]

Can someone give me a step-by-step solution to this integral?

[candid cloak]

I’ve tried by parts and substitution but I’m stuck

[obtuse pebble]

@candid cloak Has your question been resolved?

[obtuse pebble]

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[glacial ravine]

hi i need help on question 28

[glacial ravine]

i dont know where to start

pls help'

[timid silo]

uh do you know the ratios of the sides in a 30-60-90 degree triangle?

[tawny nacelle]

So, it's basically trigonometry.

Have you learnt that?

[glacial ravine]

yes i figured out the top angle is 30

[glacial ravine]

yes

[royal shard]

so you know sin cos and tan?

[glacial ravine]

my teacher is saying we have to use the unit circle or something

[glacial ravine]

yes

[tawny nacelle]

Then you know that if we're working with the opposite side and the hypotenuse, we can just use sin.

[glacial ravine]

so far all ive wirtten is x = 9/sin60

[tawny nacelle]

Yup.

[glacial ravine]

the answer page says its 6sqrt3

[tawny nacelle]

It is.

[tawny nacelle]

Plug this into a calculator.

You'll see it's 6 sqrt3.

[glacial ravine]

how do i get to 6 sqrt3

[royal shard]

60° and 30° are special
sin(30°)=0.5, cos(60°)=0.5

from here on we can see (via pythagoras) what sin(60°) and cos(30°) must be

[tawny nacelle]

Calculator...

Unless you wanna multiply by sin by hand...

[timid silo]

you don't need a calculator to find out sin 60

[tawny nacelle]

What-

Ok you take over.

[royal shard]

sin(60)^2+cos(60)^2=1
sin(60)=sqrt(1-cos(60)^2)
sin(60)=sqrt(1-0.25)=sqrt(3/4)
sin(60)=sqrt(3)/2

[glacial ravine]

ya i learnt how to solve these today

[glacial ravine]

ty

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[unkempt quartz]

hello

[unkempt quartz]

i need help

its about functions with restricted domain

ping me if ur available.

[glacial ravine]

omg i did that a month ago it was hell on earth

[unkempt quartz]

lol

[glacial ravine]

can u use a calculator for this question

[unkempt quartz]

not too sure

someeeeeeonee help

[glacial ravine]

do u have a class pad

idk how to solve that ngl but i think it would help if you graph it on desmos or something

[unkempt quartz]

oops i got it

u just sub h1 with the metres and make t=0

okk some1 close this or something idk

[obtuse pebble]

@unkempt quartz Has your question been resolved?

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[little tinsel]

The values of a for which the following equation is satisfied
$\sqrt[6]{a^3^0}=a^5$

[warm shale]

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

[little tinsel]

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[hot dawn]

does the direction that you draw the arrows matter in a commutative diagram?

i.e. could I draw the anticlockwise version instead?

Also, in a commutative diagram, what is meant by "commutes"?

is it commutativity of elements in the traditional sense? i.e. a * b = b * a

or simply that the consequtively applied linear maps $\tau$, then $\Theta$ is indeed equivalent to $\Theta\circ\tau$

[warm shale]

normalAtmosphericPa=101,325

[warm canopy]

The circular arrow can go in any direction its just shorthand for "commutes" which in this case is that the two different ways you can go from W to F^n are in fact the same

[hot dawn]

Thank you!

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[hot dawn]

What is $[\Theta]_{\mathcal{A},\mathcal{B}}$?

[warm shale]

normalAtmosphericPa=101,325

[hot dawn]

normally, I see square brackets representing a coordinate vector with one subscript denoting the basis

but here $\Theta$ is a matrix representaiton of a linear transformation

[warm shale]

normalAtmosphericPa=101,325

[warm canopy]

Presumably it's denoting the matrix that represents the linear map Θ with respect to the bases A and B

[hot dawn]

I don't get the wrt bases A and B part

[warm canopy]

You have to choose bases for the domain and codomain of a linear map before you can represent it by a matrix

[hot dawn]

yeah

uh

by analogy

say I have a ixj matrix over R

i.e. $[a_{ij}]$

[warm shale]

normalAtmosphericPa=101,325

[hot dawn]

so I know it's dimensions in that notation

do A and B play a similar role in that notatoin

[hot dawn]

here

[warm canopy]

A and B are just lists of vectors so not really sure what you mean

[hot dawn]

is the ordering flipped?

i.e., it's written in the order AB

like which one denotes the comain and domain

for A and B respectively

[warm canopy]

I'm not sure what you're asking still

A is a basis for the domain of Θ

[hot dawn]

ok

thank you!

I guess I will need to just do practice problems and slowly memorise/ internalise the definitions lol

[warm canopy]

Yeah you definitely need to know definitions of things before you try and understand theorems and proofs

O/w you'll have no hope

Like trying to read a book in a language you don't know

[hot dawn]

yeah but my professor is trying to make be prove things 2 seconds after she introduces the fat definitions

:/

we're proving this

[warm canopy]

Unfortunate side effect of teaching with limited time:(

Oh well witj that context A and B do look "flipped"

They will have some point defined whay the subscript notation means

[hot dawn]

so a bit of computation before proof writing?

[warm canopy]

Well at the very least knowing the definitions and notation

[hot dawn]

yeah that's what I mean

i.e. learning the defintions and notation through doing a few problems

unless you mean rote memorising them before moving onto proofs?

writing them out on paper a few times

[hot dawn]

Do the parenthesis (r,c) denote a specific entry of the matrix?

aren't indiv. entries of a matrix normally written in the notation $(a_{ij})$?

[warm shale]

normalAtmosphericPa=101,325

[warm canopy]

Sure but you can use whatever letters you want

[hot dawn]

so are ordered pairs fine too?

[obtuse pebble]

@hot dawn Has your question been resolved?

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[timid silo]

Differentiation of x^-1

[timid silo]

Will the minus com down with the power

-1x^-1?

Or -1x^1

Or 1x^-1

[viral blade]

it will

remember you have to subtract one from the exponent too

[timid silo]

Oh yes

One more wait

Can u do partial differential?

I got one problem I'm not sure how to do it

[viral blade]

yeah

[timid silo]

1st order partial diff , 2nd partial diff order and 2nd cross partial diff order the system goes lyk this

The question is y=...

[viral blade]

,rotate

[viral blade]

the full answer isn't included

[timid silo]

U mean i will show ma answer?

[viral blade]

I assumed that's what you'd intended

[timid silo]

Tho i didnt did the cross partial part since it was hefty calculation and also i was not sure

I will send

The pages cam out reverse check the last pic it starts from there

Tho i only need to know if my steps are correct

Then i can proceed with cross partial

[viral blade]

ngl I don't have the the energy to go over 4 pages of work

[timid silo]

Ahh

No need of calculation

Jst tell me how to proceed

To second order

[viral blade]

,w derivative of (x-2y^2)/(x^2-4y) wrt x

[warm shale]

Results provided by WolframAlpha

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

Requested by monikanicity#0205

[timid silo]

Yea dis cam out correct

Bt now how to proceed to the next step

Second order same diff?

Bt there is power on the deno

So it's complicated🫡

[viral blade]

you need second partial with respect to x?

[timid silo]

Yea if possible

It's gonna be too much calculation

So i need a shortcut

So i used the chain rule

Bt then I'm not sure again

On 2nd pic

I sended

[viral blade]

I think you need quotient rule still

you can still square the denominator

(x_1^2-4_2)^4

[timid silo]

Ahh i see

[viral blade]

then the rest is annoying calculation

[timid silo]

Bt wat abt the numerator

[timid silo]

Yes

[viral blade]

well you'll have to do u'v-uv'

[timid silo]

Bt i didnt thought abt dis oof bt too much

Still on the numerator part

Any other shortcuts to proceed tho?

If u can share

[viral blade]

I don't think there are any

[timid silo]

Ahhh i wont do dis then bt thanks for the deno part dat didn't cam in ma mind

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[viral blade]

np

[obtuse pebble]

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[eternal raft]

Can I get help with this question?

[jolly ginkgo]

First find the bounds of integration

[eternal raft]

I used spherical polar coordinates relation

[jolly ginkgo]

Yes that's good

[eternal raft]

But I'm not sure what the limit should be considered for that particular integration

[jolly ginkgo]

I may be able to find them but idk if I'll be able to explain

[eternal raft]

ah okay

thats the concept im struggling with

[jolly ginkgo]

0 to pi/2 for both theta and phi

[eternal raft]

to what angle do i take the limit

[eternal raft]

is it calculated in some manner or the quadrant is considered?

[jolly ginkgo]

You have the final answer to this problem?

[jolly ginkgo]

Yeqh

I have some questions that you can try for this

They are polar questions but tricky ones

[eternal raft]

yeah its pi/2 ( 5/3 - pi/2)

[eternal raft]

oh that would be helpful i think :D

[jolly ginkgo]

Here limit of r will be some function of theta and phi too

Oh no it won't be since when x²+y²+z² is constant so r will be constant

[eternal raft]

i mean i consider limit of r to be 0 and 1 because thats what the value of r is taken

yeah

[jolly ginkgo]

0 to 1 will be right

I'll show you those questions

Try this integration with limits I gave and see if you get anything

[eternal raft]

im struggling with angles because in some questions its taken 2pi and pi

okay i'll try

[jolly ginkgo]

That's when it's a whole sphere

V

[eternal raft]

so in this we just consider only first quadrant?

[jolly ginkgo]

Yes

[timid silo]

help 🥺

[eternal raft]

if its okay can u explain if is there a criteria to follow or is it taken from the equation?

[timid silo]

urgent 🥺

[eternal raft]

u should use the available help channels dats when bot can pin message

[timid silo]

Umm?

[jolly ginkgo]

Like the V given in this question is in 1st quadrant so imagine I rotate the positive axis by 90° and then that 1/4th circle by 90° then we get the first quadrant sphere which is V

[timid silo]

sorry new to this server 😭

[eternal raft]

available ones

[timid silo]

Oh okay

[viral blade]

what's the thing on the bottom right say?

[jolly ginkgo]

Check these problems inessa

[eternal raft]

wait which one

[jolly ginkgo]

From 1 to 13 with answers

Once you try these you may get comfortable with conversion of bounds

[eternal raft]

oh okay okay i'll give them a try!

[jolly ginkgo]

You have to do this graphically

Or it will be too tricky

[jolly ginkgo]

First solve your integral

[jolly ginkgo]

This is what I said for your question

Ping me for any update

[eternal raft]

okay okay

[eternal raft]

So like whats the difference in previous and this question because in this one the value is taken to pi and 2pi?

[jolly ginkgo]

Ok so here x²+y²+z²=<1 is a whole sphere right

So if I have a unit radius on positive x axis

I rotate it by 2pi on xy plane

I'll get a whole circle

Then if I rotate that circle by pi I get a sphere in 3d

2pi and pi swipes a whole sphere

First 2pi to swipe a line to get a circle then pi swiping circle to get sphere

[eternal raft]

oh yeah i understood the concept of why we use it! but like how did u identify if its a full sphere or just one quadrant? because equation is same in both questions

[jolly ginkgo]

In first question they gave x>0 , y>0 , z>0 so V lies in 1st quad

[eternal raft]

Oh! okay! okay okay now i get it!