help-27

[sudden breach]

5%

So das 0.12 right

[hybrid pond]

what exactly do you mean

[sudden breach]

To use for the formula

Compund interest

Applications

[hybrid pond]

12% interest is not 0.12

its 1.12

unless you mean 1 + 0.12

[sudden breach]

I had to make a fraction

For this ex

[hybrid pond]

yeah

gimme a sec

ima work this out

[sudden breach]

It was 1000(1+ 0.12/1)^1(3)

And the result was 1404.93

[hybrid pond]

for which year?

[sudden breach]

This one was annually

[hybrid pond]

ok, i think i understand now

lets go back to the basics

the formula for comound interest is

p(1+r/n)^nt

p=initial value

[sudden breach]

Ye

[hybrid pond]

do you know what p in this case is

[sudden breach]

Yea 4000

[hybrid pond]

do you know what r is?

[sudden breach]

5/

5%

So would it become 0.5

[hybrid pond]

no

[sudden breach]

Or 0.05

[hybrid pond]

yeah

[sudden breach]

Alr das what i was wondering

Thx

[hybrid pond]

np

[sudden breach]

So the equation would be

Wait

[sudden breach]

For monthly

Wjat would i set it as

[hybrid pond]

what is your n value?

[sudden breach]

1

Isa chart

[hybrid pond]

nope

[sudden breach]

Theres multiple

[hybrid pond]

when is the interest being compounded?

[sudden breach]

It says monthly

[hybrid pond]

how many months are in a year

[sudden breach]

But like som months have more days than the other

12

[hybrid pond]

thats ur n

[sudden breach]

12

Oh

Oh right

Mb

[hybrid pond]

u good

[sudden breach]

So the equation is 4000(1+0.05/1)^12(12)

?

[hybrid pond]

not exactly

[sudden breach]

Dis where im confused on

[hybrid pond]

the interest value is wrong

remember n is applied in 2 places

[sudden breach]

Wym

Ohh

[hybrid pond]

your t value is also wrong

[sudden breach]

Wym

Isnt it always 1

[hybrid pond]

do you know what the t value is?

[sudden breach]

No

[hybrid pond]

its the (12) next to your n

t in this case is years

so it would just go as 1,2,3,4,...

[sudden breach]

So

It wouldnt be

4000(1+0.05/12

[hybrid pond]

no thats right so far

[sudden breach]

O

[hybrid pond]

just add the exponent

[sudden breach]

So the 1 is always there

Ok so

[hybrid pond]

yup

[hazy thicket]

hello anyone needs help?

[hybrid pond]

???

wrong thread gang

[hazy thicket]

oh sorry im new

[hybrid pond]

its alr

[sudden breach]

4000(1+0.05/12)^12(12)

Wait

[hazy thicket]

where do I help people

[sudden breach]

But we doin monthly

Its 12

[hybrid pond]

yeah

[sudden breach]

And u said the n is same

N is 12

[hybrid pond]

t is 1

[sudden breach]

So it is 12(12

[hybrid pond]

bcus we're doing years

[sudden breach]

How many years

[hybrid pond]

what ur doing rn would give you the value for 12 yrs

t is your input value

[sudden breach]

Oh

So the (12)

Becomes a 1?

[hybrid pond]

yup for the first value

[sudden breach]

So 4000(1+0.05/12)^12(1)

@hybrid pond

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[plush grail]

could someone explain part b

[plush grail]

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[rotund umbra]

A normal subgroup $N$ of a group $G$ has the property $\forall; g \in G .; gN = Ng$.
A left ideal $I$ of a ring $R$ has the property $\forall; x \in R .; xI \subset I$.
What is the reasoning behind the differences in these properties, when they are both necessary for the definition of quotients?

[woven radish]

Shuba

[rotund umbra]

By which I mean, why not define a left normal subgroup with $\forall; g \in G .; gN \subset N$, or are left and right normal subgroups the same?

[woven radish]

Shuba

[toxic grove]

If you define normal subgroups like that then there won't ever be any normal subgroups

1 is in every subgroup, so multiplying it by g for some g not in the subgroup will not get you a subset

[rotund umbra]

yeah, good point

[toxic grove]

*except the whole group

[rotund umbra]

So why not $\forall; g \in G .; gNg^{-1} \subset N$ for groups, and $\forall; x \in R .; xIx^{-1} \subset I$ for rings?

[woven radish]

Shuba

[rotund umbra]

There's clearly some subtlety between quotient groups and quotient rings I'm not seeing.

[toxic grove]

It's been a long time since I did any ring theory, but basically the reason is just that those are the required conditions for the quotient ring/group to make sense

The "group theory" structure in rings is in the addition

But the additive group of any ring is abelian so every subgroup is normal

Ring multiplication doesn't have inverses so the requirement for that to work over quotients is weaker

[rotund umbra]

well the group structure of a ring needs to be commutative

otherwise you have a semigroup

[toxic grove]

Well yes

But what I mean is that in a commutative group, every group is normal

[rotund umbra]

ahhhh because we don't have inverses. obvious now XD

[toxic grove]

Hence why you don't see that as a requirement for ideals

[inner anvil]

Why is your name depression 🙏

[rotund umbra]

Here's what's motivated the question. Suppose I have a quotient ring R/I where I remember R is a ring and I is an ideal. Suppose I also have the forgetful functor F which maps R/I to G/N where G is a group amd N is a normal subgroup. Why does F map I to N when their definitions are so different?

Or can I not in general construct such a functor?

[toxic grove]

No no you can do that

I'm fairly sure

When you do that though, multiplication gets forgotten entirely

[rotund umbra]

I'm fairly sure it's possible too

[toxic grove]

All you end up with is a subgroup of an abelian group

Which is normal

[rotund umbra]

because R/I is a ring, and G/N is a group, so just use the same forgetful functor that maps R to G to map I to N

[toxic grove]

It's pretty descriptive if you ask me

[rotund umbra]

yeah, good point

Or, put it another way, suppose I use a free functor from groups to rings. why would this map normal subgroups to ideals?

[toxic grove]

I'll be honest idk what that is so I can't answer that, I never did much category theory

[rotund umbra]

it's a functor that reveals additional structure. For example, I can construct a free functor from the set of integers less than 7 to the additive group of integers modulo 7 by revealing addition.

[toxic grove]

Ah okay

Then would you get free multiplication of some kind? or is it tailored to the specific group

Bc if it's the latter then if you take the additive group of gaussian integers, then the normal subgroup of real integers definitely wouldn't map to an ideal

Anyway long story short idk and I can't verify it either (but I would be a bit surprised)

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[lucid mason]

im kinda confused about the answer

Revenue = (850 + 100x) (50 - 10x)

r'(x) = -2000x - 3500

so x = -1.75

so shouldnt the new price ne $675 because price = 850 + 100(-1.75)

why is the answer still $850

or do they only care about increasing the price, so since nothing else works then it stays the same?

[lusty sapphire]

You have to consider discrete changes

[lucid mason]

?

oh

[lusty sapphire]

What is x btw?

[devout snow]

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[potent panther]

do i use u-subsitution or integrating by parts

[versed vault]

always try u sub first

what is going to be ur u

[potent panther]

-3x^2?

[versed vault]

ye

whats du equal to

[potent panther]

but the deriv of that is -6x

but

theres only x

[versed vault]

ye

[potent panther]

on the integral

[versed vault]

there is a cosntant

u csan throw constants

out of integrals

right

[potent panther]

ohh

yes

so like

u can make x into -6x

then just do 1/6 outside the int?

[versed vault]

-1/6

but ye

[potent panther]

o

then

🤔

[versed vault]

u have thgis right

[potent panther]

yes

[versed vault]

what is integal of e^udu

[potent panther]

e^u

[versed vault]

ye

Now just sub in u

u=-3x^2

[potent panther]

ooo

so its just -1/6 * e^-3x^2 + c?

[versed vault]

https://cdn.discordapp.com/attachments/1297365478347378769/1308892826167414885/IMG_0183.gif

Yes!!!!!

[potent panther]

YESSIR

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[hidden sapphire]

Can someone help me graph 1 a

ik i have an asymptote and x = 2

and y = 0

i just dont know how to plot the graph

[devout snow]

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[umbral maple]

im really confused

[spare crypt]

the vertical rectangle is in the middle basically, and it wants you to calculate the diagonal dotted length and set it equal to 1

[umbral maple]

alright, so im finding the dotted lines first?

[umbral maple]

so it would just be 1sqrt2 correct

oh nvm

the height isnt 1

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[turbid lance]

Can someone explain to me how this works

[acoustic leaf]

that limit is often taken as the definition of e

if you have an alternative definition then it can be shown to be equivalent

[sacred rampart]

it really depends on how u define e

[turbid lance]

wdym

[fathom flint]

@turbid lance show ur work

[sacred rampart]

as cloud said, if u take some other definitions, you can always show this property

[pseudo basin]

have you seen the number e before in your life at all

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[wanton hatch]

hi can someone explain to me how my teacher got here (in gr 11 functions if that helps)

[pseudo basin]

show original problem

[pseudo basin]

ok, and in this solution, which is the earliest step that doesn't make sense to you?

[wanton hatch]

the transition of 3 to 4 doesnt make sense to me

[pseudo basin]

they put everything on one side and collected like terms.

kinda skipping over the arithmetic of it all.

[wanton hatch]

ive tried solving it and got this

[wanton hatch]

i did that and got a different answer for 4

[pseudo basin]

this term should be 90x not 9x.

that and 2025 ≠ 2205.

[wanton hatch]

oh- thank you so much

[pseudo basin]

yeah arithmetic happens to the best of us

[wanton hatch]

thanks again!!

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[restive river]

I know how they managed to down the graph

I just dont understand how they got the roots

I know that the roots are equidistant from the midpoint and that they are +-b/2

But i dont understand how they go from that to getting the roots

.close

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[royal laurel]

I found calculating 36.9(2.301/0.301) a challenge

[pseudo basin]

,calc 36.9*2.301/0.301

[woven radish]

Result:

282.08272425249

[soft umbra]

Concise and neat

[royal laurel]

I will exhibit my process on vc

[soft umbra]

Not necessary at all

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[viral lynx]

The radius is 5 so C and D have the y coordinate of -3

If we sub in -1 into the circle formula we get the x coordinates for A and B

x^2 + (-1 - 2)^2 = 25

x^2 + 9 = 25

x^2 = 16

x = +-4

So the line on which M, B and D are all on has the slope (-1 - 2)=m(4 - 0)

-3 = 4m

m = -3/4

So the equation of the line is y = -3x/4 + 2

Sub in y = -3 to get the x coordinate of D

-3 = -3x/4 + 2

-20 = -3x

x = 20/3

So C is (-20/3, -3) and D is (-20/3, -3) and M is (0, 2)

Half the base is 20/3, the height is 5

(5)(20/3) = 100/3

Which is what they wanted 😅

Okkkk sorry hehe

.close

[twin spoke]

....

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[blissful igloo]

you gotta stop doing this man

[viral lynx]

😅

Its not on purpose

[devout snow]

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[night cypress]

need to draw this, please note that this is above my current maths level as i do not know conic sections

[night cypress]

a circle such that it is tangent to absicaa, ordinate and the bigger circle of radius 1

[devout snow]

@night cypress Has your question been resolved?

[blissful igloo]

so you want the equation of the hand made circle ?

[devout snow]

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[iron kindle]

!nogpt

[devout snow]

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

[regal berry]

I was wondering if I did anything wrong here

[regal berry]

funny how you would assume it is gpt:D

No it is not gpt

If you would like to see my work on paper sure but everyone here is yelling at me bec they can't understand my handwritting

[iron kindle]

is this not chatgpt font?

?

[regal berry]

Yk other apps use similar fonts right-

[solar goblet]

not all white math text on grey background is chatgpt

[regal berry]

fr

[iron kindle]

sure

[verbal vector]

just plug -4 into the original equation and see if you get 0 = 0

then you’re fine

[iron kindle]

much more likely its chatgpt than smth else though if you see it here

[regal berry]

right lemme try

[coral jay]

Cap. Chatgpt gets everything right at least if it till 9 grade. Gpt 3.5 was 50/50 but 4o much smarter

[verbal vector]

then you’re good

[regal berry]

I so hate when my book gets the answer wrong

Istg It makes me so scared that I did not understand the chapter lol

tysm

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[iron kindle]

where does the -4 come from btw?

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[winter patrol]

.first step was wrong

[halcyon rivet]

The question I have is that after applying f(x) once, you get a real number, so how can you apply it again

Because you can't find the determinant of a real number

f(x) outputs a real number and takes a matrix as its input so it cannot be nested into itself

[thin fern]

I think the determinant of a real number is just defined to be itself

[halcyon rivet]

Oh

Then the question makes sense

[halcyon rivet]

Hollow knight pfp

W

[lime plaza]

Isn't A'=a^-1?

[thin fern]

wait

No you're reconstructing A every time I think

[halcyon rivet]

What is A'?

Transpose?

[lime plaza]

yes

[thin fern]

$A_n = \begin{bmatrix}
1 & \tan(f^{n-1}(x)) \
-\tan(f^{n-1}(x)) & 1 \
\end{bmatrix}

[gray summit]

Oh, you are "dave the masked" lol. I used to think you are "dave them asked"

[thin fern]

no

[woven radish]

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

[thin fern]

yessir

[halcyon rivet]

A^T is adj(A)
Im not sure about A^-1

[halcyon rivet]

Then the question is worded improperly

If this is true

[pseudo basin]

yeah it is a bit scuffed

[halcyon rivet]

Thank you

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[restive river]

I need help on a trig question

[pure flower]

ok

!nohi

rop

[restive river]

I don’t understand how to do it

Here it is

[pure flower]

!da2a

[devout snow]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[restive river]

C

[pure flower]

!status

[devout snow]

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

[restive river]

I don’t know where to begin

At all

[pure flower]

what do you know about inv trig

[restive river]

Like the range and domain are flipped

And they are opposites

Not reciprocals

This is on the practice exam for midterm two so I need to understand how to solve these types of problems the exam is tomorrow

[pure flower]

that's a start

[restive river]

Okay

[pure flower]

can you find $\arccos(\cos(\frac{\pi}{2}))$

[woven radish]

Percy

[restive river]

No I can’t probably do where it is just the inverse and a number

[pure flower]

what does that mean

[twin spoke]

he meant he can find something like arccos(0) and all

I think

[restive river]

Like this

I can do this but not accurately I know the process

And it has to be in a boundary

-pi/2 and pi/2

[pure flower]

,rccw

[pure flower]

...what does the second line mean

do you mean that as something that follows

[restive river]

You put the inverse sin to the other side

And it become sin

And you can find sin 1/2 on the unit circle and the would equal your theta

[pure flower]

im so confused

okay

what's $\arccos \frac12$

[woven radish]

Percy

[restive river]

Pi/3 I think

[pure flower]

okay that's good

what's $\arccos(\cos(\frac{\pi}{3}))$ then

[woven radish]

Percy

[restive river]

I have no clue where to begin

[pure flower]

...what's cos pi/3

[restive river]

1/2

There the same question

[pure flower]

i dont see the issue

[restive river]

Okay I understand

You are going from theta to the point

Or no?

[pure flower]

the 'point' is a weird way to say 'the cosine' but yeah

[restive river]

But wouldn’t it just equal pi/3 again?

[pure flower]

anyway point is that $\arccos(\cos(\theta)) \equiv \theta; \forall \theta \in [0, \pi]$

,wolf domain of arccos

[woven radish]

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Requested by percykel

[pure flower]

yes

[restive river]

Okay going back to the original question

9pi/8

[woven radish]

Percy

[pure flower]

no just follow what im saying

[restive river]

So how can I use this?

What does it mean?

[pure flower]

it means what it says

what part do you not get

[restive river]

The stuff after the = sign

[pure flower]

there's an \equiv sign

but sure

that's 'for all theta in [0, pi] (the set of all reals between 0 and pi, inclusive)'

[restive river]

So how would I solve this one

[pure flower]

maybe follow what im saying first

[pure flower]

you dont just start solving shit on a topic you know nothing about

well

only very little about

[restive river]

Okay

[pure flower]

okay?

does it make senes

[restive river]

So the boundary is 0 to pi

No I don’t understand what you are trying to say

Arccos= what?

I understood how to the one before that

[restive river]

This one is easy

But the 9pi/8 is difficult

How can I start

Wait

Is it undefined????

Because it is bigger that pi

[pure flower]

holy shit slow down

[pure flower]

which part

[restive river]

The 0,pi

9pi/8 is greater than pi

It falls out of the boundary

[pure flower]

sure and thats irrelevant to what im saying

[restive river]

How can I find cos of 9pi/8

[pure flower]

stop skipping ahead

[restive river]

Then find arccos of that

[pure flower]

okay im just gonna assume you get the basic fact

[restive river]

Like we did before

Found cospi/3 then found arccos

[pure flower]

what's a way to express $\cos(\frac{9\pi}{8})$ as $\cos(\theta), \theta \in [0, \pi]$?

[restive river]

Like a degree?

[woven radish]

Percy

[pure flower]

...like a radian.

[restive river]

9pi/8 right?

That is what theta is

[pure flower]

no

[restive river]

How ?

Oh

Because it is bigger than pi

So how would you do it?

If it is greater than pi

I’m so lost

[pure flower]

trig, mostly

[restive river]

How?

If it is bigger than pi how can you make it less than pi

That doesn’t make sense

[pure flower]

as i said- trig, mostly

how are you doing inv trig while not knowing trig 101

fun fact, they're periodic

[restive river]

I don’t know

It doesn’t make sense

So how do I do trig on this type of problem

[fast rose]

One way is to learn properly step by step

[pure flower]

yes it totally does

,wolf cos(pi/2) - cos(pi/2 + 2pi)

[restive river]

How can you solve it if it is greater than pi

[fast rose]

For trig problems you should look up unit circle

[woven radish]

Results provided by WolframAlpha

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Requested by percykel

[pure flower]

would you look at that theyre periodic

how insane is that

[blissful igloo]

look at the graph of cosx

[pure flower]

yeah he's being really weird with the jumping ahead shit

[pure flower]

im gonna kms

[pure flower]

https://www.youtube.com/watch?v=yBw67Fb31Cs

come back here later

[pure flower]

you get points for trying

[pure flower]

watch this and come back later

you can ping me if you want

[restive river]

Okay

Thank you

[pure flower]

!done

[devout snow]

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

[pure flower]

hooboy

[restive river]

I’m back

@pure flower

[restive river]

Is this correct?

[pure flower]

it

super isnt

just watch the video

[restive river]

I found a way to do it

It is iii

[pure flower]

well

[restive river]

So how can I do these type of problems ?

[pure flower]

how you can do them is with a calculator i guess

[pure flower]

oh this

yeah youd have to learn stuff

[restive river]

Okay

I think I’m cooked

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[long prawn]

Can someone help with this question ? Part b) it says fund the area of the shaded region,, and this is what I’ve done so far I know there’s a mistake but this is my progress

[long prawn]

@ me when someone answers thank you !

[devout yarrow]

The integral ends at 1

[ancient dagger]

-1 to 1

Not 0

[long prawn]

oh yeah oki

Is that the only mistake or ?

[blissful igloo]

yeah

y= sqrt(x) dosent exist in -1 to 0

[long prawn]

It’s undefined at -1 but I just counted an absolute value in the radical

[blissful igloo]

so whats sqrt(-0.5)

[long prawn]

With the absolute value?

Inside the radical

[blissful igloo]

no

y=sqrt(x) dosent exist for x<0

so for -1 to 0 just integrate the line

[long prawn]

So it’s gonna be -1 to 0 g(x) and then from 0 to 1 g(x) - f(x) ?

[devout yarrow]

The line should be -1 to 1 and root x is 0 to 1

[long prawn]

Aha okay

[blissful igloo]

yeah

[long prawn]

Okay lemme solve it now

Is it correct now 😭

[blissful igloo]

should be

[long prawn]

Oki I checked both terms on photomath I think it’s correct

Is this correct too I js wanna know if my answers’ correct part a) & b)

The given stuff is next to number 3.

[devout snow]

@long prawn Has your question been resolved?

[lunar harbor]

This should be $\left[\frac{x^2}{2} \right]^{2}_{-1}-2(3)$

[woven radish]

Civil Service Pigeon

[lunar harbor]

The rule is $\int^{b}{a} f(x) \dd{x}=\int^{b}{c} f(x) \dd{x}+\int^{c}_{a} f(x) \dd{x}$

[woven radish]

Civil Service Pigeon

[lunar harbor]

Applying that here, $\int^{4}{2} f(x) \dd{x}=\int^{4}{-1} f(x) \dd{x}+\int^{-1}_{2} f(x) \dd{x}$

[woven radish]

Civil Service Pigeon

[long prawn]

Oh oki thank you

[long prawn]

So b) is gonna be -1?

[lunar harbor]

yes

[long prawn]

And a) -7/2? or

[lunar harbor]

no

[long prawn]

-9/2

[lunar harbor]

yeah

[long prawn]

Okay thank you

.close

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[devout snow]

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[devout snow]

@cerulean juniper Has your question been resolved?

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[queen ravine]

what does it mean if a matrix maps a vector from R^n to a vector in R^m

[pseudo basin]

....

it means exactly what is said?

!xy

[devout snow]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[graceful cosmos]

If you take your vector from R^n, and multiply it by the matrix, you get a vector from R^m

We consider this a function on that vector, and the matrix is "the mapper" here

[queen ravine]

does it mean that we have 3 linear equations with four variables. is the four dimensional vector being converted to 3d

like it goes from R^4 to R^3

you know what im sayin?

[warped field]

That Matrix is collapsing a dimension down

[queen ravine]

is that the official term for it?

[queen ravine]

so the vector goes from 4 dimensions to 3 ´?

as an example

[warped field]

Yes

If you look at a more intuitive case

Of Collapsing R^3 into R^2

We essentially take all vectors and "ignore" their z coordinate

[queen ravine]

why do we ignore their z-coordiantes?

[warped field]

So all vectors of form (a, b, c) will become (a, b)

No matter what c was

[warped field]

Because that's the nature of the transformation here

We are collapsing a dimension, a dimension eraser

[queen ravine]

what does it mean physically for the vector to undergo a dimensional collapse

like what are the applications of this

[warped field]

You can think of it as a projection

Like looking at 2d shadows of 3d objects

[queen ravine]

ooooh

okay that makes sense

thanks bro

.close

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[loud bluff]

where did I go wrong?

[raven leaf]

why don't you take a picture from directly above

,rotate

[loud bluff]

This one's clearer!

[raven leaf]

let's not plug numbers in

then call density $\rho$

[woven radish]

Xetrov

[loud bluff]

The formula for work is $\rho$Agddy

[woven radish]

Le

[loud bluff]

Right?

[raven leaf]

for each kg, it takes $mg(9-z)$ Joules to lift it out

[woven radish]

Xetrov

[raven leaf]

oh ok

cool, rho, A is area at that level, g is grav constant and what's d

[loud bluff]

I mean integrated from a to b of course

[raven leaf]

depth?

ya

[loud bluff]

Distance the slice is moved

I got 1-y for d in this problem

[raven leaf]

that's 9-y

[loud bluff]

How so?

[raven leaf]

because you have 8m from the height of the cone ya?

8+1

[loud bluff]

Yep but in the diagram I set the top of the cone to be at the center of the axis

was that wrong?

[raven leaf]

oh ok

so your ys take negative values

gotcha

then integrate

you'll need to relate your r to y though

[loud bluff]

The radius right? It's 5/8y right?

[raven leaf]

sounds about right, shifting y by a constant

[devout snow]

@loud bluff Has your question been resolved?

[devout snow]

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[restive river]

I need help with rig

[restive river]

I have a problem I can solve I don’t know the first step how to solve it

#71

[sly oyster]

Arcsin(y)= Q
So sinQ=y.
Now what is sin in terms of measurement of right angle triangle?

[restive river]

I need help on this question I don’t understand what to do

I have the question double angle

I did it but I don’t know what to do after

I have a midterm tomorrow so I have to lock in

[sly oyster]

You don't have to write tan(-5/2) . -5/2 is already the tan value you are using

[restive river]

Okay?

So how would approach this question to efficiently and accurately solve it

[woeful token]

U do if u wanna sub it into the double angle formula

[restive river]

Yeah I want to double angle

[sly oyster]

Make the pythagoras triangle. Write down its sides. Than write down sin, cos and tan of the angle . Use formulas like sin2x=2sinxcosx to find the required value

[restive river]

This doesn’t make any sense

[woeful token]

Ur given tanx = -5/2

if u want to get tan2x you need to use the tan2x identity where 2tanx/1 -tan^2x

sub in -5/2 as x you get 2(-5/2)/1-(-5/2)^2

[restive river]

Yeah I did that

[woeful token]

I think use pythag to find the missing values

[woeful token]

did u simplify that

[restive river]

How do I do that’s

That*

[woeful token]

are u working in radians or degrees

[restive river]

Radiant

[woeful token]

is it asking for the exact value

ok it is

[woeful token]

what ur doing is

tan(-5/2)

but tanx = -5/2

so rewrite it as:

2(-5/2)/1-(-5/2)^2

[restive river]

Like this?

[woeful token]

yes

Now u can simplify it

so tan2x = 20/21

[restive river]

How by plugging in the calculator

[woeful token]

Sure

[restive river]

That is not what I got

[woeful token]

its 2(-5/2)

[restive river]

This is what I got

Oh I did positive

[woeful token]

1 - (-5/2)^2 = -21/4

[restive river]

Yeah

[woeful token]

so -5 / (-21/4) = -20 / -21 = 20/21

so tan2x = 20/21

[restive river]

Yeah that makes sense

[woeful token]

and now you want to find sin2x and cos2x

because sin2x = Opp/Hyp, cos2x = Adj/Hyp and tan2x = Opp/Adj

therefore the opposite is 20 and adjacent is 21

therefore the hypotenuse is sqrt(20^2 + 21^2) = 29

so sin2x = 20/29 and cos2x = 21/29

[restive river]

I did it a different way

[woeful token]

what way

[restive river]

I did a harder way

[woeful token]

21 is not the value of the hyp though

tan2x = 20/21 therefore 20 is the opposite and 21 is the adjacent

to find out the hypotenuse you need to use Pythagoras

[woeful token]

SOH CAH TOA

[restive river]

Yeah that makes sense

My ta was trying to make me do to much

[devout snow]

@restive river Has your question been resolved?

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[queen ravine]

guys i know this matrix implies that there is no solution for the linear system of three equations. but my question is, since the (-2/3,1,6) can be thought of as a vector. does it mean that the vector does not exist, or that the planes do not intersect at the tip of the vector arrow?

[astral lodge]

no, it just means the planes never intersect

each equation describes a plane

[queen ravine]

so (-2/3,1,6) cant be thought of as a vector?

[astral lodge]

eh

for the purposes of finding intersections, no

[queen ravine]

but it is a vector no?

[astral lodge]

think about a line

[astral lodge]

eh

[astral lodge]

^

[queen ravine]

what does that mean🤣

[graceful cosmos]

When we write a matrix with a bar (I'm forgetting the name right now) we are asking "for what x does Ax = b?" Where A is the matrix to the left, and b is the vector to the right

You've correctly identified that there is no vector x that solves this

[queen ravine]

isnt x a vector then

oh

[graceful cosmos]

But b definitely exists

[queen ravine]

what does it mean for a vector to solve for the point of intersection of planes?

does it then mean, that there is no values of a,b,c that gives the vector (1,-2,5)

[graceful cosmos]

So you've written a matrix equation. I don't see anything about planes here.

These things do typically relate, but not enough such that I can guess what you're getting the matrix equation from

Oh I see, you're solving the solution of three planes

[queen ravine]

does that mean that vector (1,-2,5) does not exist on the planes?

[graceful cosmos]

When you solve this, you are getting the common intersection of all three planes.

This common intersection of all three planes needs not exist, though

[astral lodge]

no

did you read what i said 😭

[astral lodge]

it only implies this in the context you have

[queen ravine]

but b can be thought of as a vector though?

[astral lodge]

yes it can

again, context

[queen ravine]

well, what is the geometric significance of the vector b

there must be an explanation.

[astral lodge]

https://math.stackexchange.com/questions/1041079/what-does-solving-ax-b-mean

[queen ravine]

thanks, this was quite helpful

.close

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[viral pivot]

would the set 1. be transitive if you added (2,2)?

[sand dove]

no

there's (8,2) missing as well

[viral pivot]

ah i missed that thanks

can u explain how u came to that?

[wise scarab]

2R9, 9R8, but not 8R2

[devout snow]

@viral pivot Has your question been resolved?

[viral pivot]

where do u get 9R8 from?

[wise scarab]

oops, I acccidentally assumed the relation is symmetric

[viral pivot]

im thinking 8,9 -> 9,9 is satisfied becaus 8,8 and 9,9 are in the set

but 8,9 -> 9,2 is not valid because 8,2 is not in the set

i think this is kinda what you were saying if it were symmetric

not sure tho halp

[devout snow]

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[hollow crow]

How does tan(arcsinx) simplify when deriving?

[fierce ember]

use tan' = 1/cos² and cos²+sin² = 1 i think

[hollow crow]

Wait so would I still need to apply chain rule? 😭 I’m very confused by this question because I thought it was as easy as using the chain rule

[fierce ember]

yerp

you do the chain rule

and then simplify the tan'(arcsin(x)) using the circle relation

if you dont know the derivative of arcsin you can get it by doing the chain rule on sin(arcsin(x)) = x

[hollow crow]

HELP this is all i have so far😭😭 i figured that tan(arcsin(x)) is x/root(1-x^(2))
But i don’t know why😭

Ik I need to use quotient rule tho

[sharp kayak]

remember secant is cosine reciprocal not sine

[hollow crow]

OH yes you’re right. That was negligence on my half

[sharp kayak]

you can then simplify that to something without trig functions

[hollow crow]

Wait how so? I’m gonna be really honest, I don’t see it

[sharp kayak]

you have to think in terms of a right triangle

[fierce ember]

So you apply the chain rule and find 1/sqrt(1-x²)*1/cos²(arcsin(x))

what's a relation that you could use to get that cos to turn into a sin

[sharp kayak]

i mean

pretty sure can just simplify the cos^2(arcsin(x))

[fierce ember]

yea i'm asking her how 😭

[sharp kayak]

using triangle

no but like just

without identity

i mean same thing

nvm

[fierce ember]

Yea

[sharp kayak]

yeah ig identity easier in that case

[hollow crow]

Cuz I was thinking with Pythagorean identity it would be 1/1-sin^2(arcsinx) right

[sharp kayak]

yes

[fierce ember]

yes

sin(arcsin(x))² also simplifies

[hollow crow]

Wait so I can factor out that square?

[sharp kayak]

(inverse cancellation property)

[hollow crow]

So it’s x squared

[fierce ember]

it's not really factoring it out but yea

[hollow crow]

Idk what to call it😭 sin^2(x)=(sin(x))^2

[fierce ember]

yea it's just different notations 😭

[hollow crow]

ohh okay I am starting to get it this is what I have now

[fierce ember]

yea

[sharp kayak]

,rccw

[fierce ember]

you can get it into a simpler form by writing sqrt(x) as x^(1/2)

but otherwise its good

[hollow crow]

So it would simplify to 1/1-x?

[fierce ember]

no

[sharp kayak]

i mean you could do 1/(1-x^2)^(3/2) if you really want to

[fierce ember]

$\frac 1 {(1-x^2)^{\frac 12}} \frac 1 {1-x^2}$

[woven radish]

Azenx

[fierce ember]

and then what builder said

[hollow crow]

Ohh okay

Ohhhh okay I see

OHHH I get it

Omg

THANK YOU

Thank you azenx and builder🙏

[fierce ember]

👍🏻

[hollow crow]

Ok cool thank you

.close

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[restive river]

how do i create a graph with just the function?

[restive river]

and how do i find the asymptote and whether it is vertical or horizontal

[rustic jetty]

all exponential functions have a horizontal asymptote

[restive river]

would that mean all log functions have a vertical asymptote?

and also how would i extract points from that function?

[rustic jetty]

just plug in values for x and evaluate the function

[restive river]

oh ok

thanks

.close

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[oblique oyster]

Can someone explain why the bearing is N63E let me send the question

[oblique oyster]

pls excuse my shit handwriting

also oh i meant to swap the 750 and 375 in the top left part um

anyway

i thought the return would be S63E

[winter patrol]

you didn't draw you diagram correctly

the question says the plane flies south, but your diagram seems to indicate it flew north

[oblique oyster]

ohhhhhhhhhhhhhhhhhhhhhhhhhhhhhh well that would make a lot more sense

thanks

.close

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[wanton hatch]

can someone show how to solve this step by step

[winter patrol]

did yo make an attempt yet?

[wanton hatch]

i genuinely have no idea where to begin my brain is fried

[winter patrol]

start with drawing a diagram

[wanton hatch]

ok its a cube right

[winter patrol]

you should have two figures,

and no, not a cube

[wanton hatch]

but what about the open topped box?\

[winter patrol]

for your two diagrams
one of the original square with indication of squares being cut out
the other will be a square prism

start with first one

[wanton hatch]

like this?

[fossil locust]

yep, and now cut out all 4 corners

[fossil locust]

great, now imagine folding the 'flaps' up to make a box

4 flaps and a square base

[wanton hatch]

ohhh i get it

[winter patrol]

and put dashed lines on the fold lines

[fossil locust]

from the diagram you just drew, you can find the length, width, and height of the box in terms of x

[winter patrol]

with all these geo problems, always draw a diagram

[wanton hatch]

oh so it's
(x-5)^2

?

[winter patrol]

no

[wanton hatch]

oh

[fossil locust]

no, that's not the right length for the base

[winter patrol]

first

and put dashed lines on the fold lines
and use clear reasoning to get an expression for their length

[wanton hatch]

im lost are we talking abt the 5 by 5 squares or the bigger x by x one

[winter patrol]

neither

first
and put dashed lines on the fold lines
the lines along which you fold up the flaps to form your prism

draw those in

[wanton hatch]

sorry im bad at this

[winter patrol]

yes

[wanton hatch]

is this correct

[winter patrol]

why did you erase the 5s and the x

[wanton hatch]

i didnt

its a new thingy

[winter patrol]

and make a completely new diagram

w/e add dashed lines to the old diagram,
or put in the 5s and x for this one

[winter patrol]

now try determine the length of the dashed lines

clearly explain your reasoning as you do it

[wanton hatch]

they would be x-5 since the og length was x and 5cm was cut out from it

[winter patrol]

not quite

make sure you're looking at the diagram when calculating this

[wanton hatch]

oh its x-10

[winter patrol]

yes

[wanton hatch]

sorry i couldnt figure it out sooner

[fossil locust]

it's okay, that's why we're here!

to help you do things that you have the ability to do

[wanton hatch]

thank you!

so now to calc the volume it would be l* w *h
so it's
500 = (x-10)(x-10)(5)

i think?

[winter patrol]

yes

[wanton hatch]

should i use the quad formula now?

[fossil locust]

no don't expand!

I mean you could factorise after this

but you also could have just done $100 = (x - 10)^2$

[wanton hatch]

should i leave the 5 out?

[woven radish]

south

[fossil locust]

and 100 is a square number

(you can square root both sides if you know that x >= 0)

[wanton hatch]

ah im confused

[lime plaza]

So basically send the 5 to LHS

500/5 =(x-10)(x-10)

[wanton hatch]

oh

[lime plaza]

Then take square root since x>0

[wanton hatch]

so x=20?

[lime plaza]

yes

[wanton hatch]

oh

so the length of the og carboard would be 20 by 20

[fossil locust]

cool

[wanton hatch]

thank you all so much!!

[fossil locust]

no worries!

[wanton hatch]

https://tenor.com/view/cat-thank-you-gif-15118451686995476919

.close

[devout snow]

Channel closed

Closed by @wanton hatch

Use .reopen if this was a mistake.

[devout snow]

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.

[finite briar]

name the following

[finite briar]

(this is a question born completely out of my curiosity with IUPAC nomenclature)

my guess is 3-methyl,bromoethyl-5-methylhexanol

[final osprey]

this isnt math

[pseudo basin]

transparent background unreadable

also where you see a bromine at all? @finite briar

i see a poorly written barium

for my own sake...

univalent barium do be sus tho

[final osprey]

me thinks

[pseudo basin]

where are you people seeing any bromine...

[hollow ice]

where do yall see the ethyl on the Br chain? Its just Br attached to single methyl group

[final osprey]

oh right

[hollow ice]

the barium is Br

[pseudo basin]

HOW

[hollow ice]

bad handwriting

[pseudo basin]

it says Ba as far as i can read it

@finite briar get better handwriting

[hollow ice]

Honestly, that B is more eszett than B as well

[finite briar]

hello

[gray summit]

Probably it's in cursive

[finite briar]

its bromine

[final osprey]

wouldnt the chain with more substituents b considered as the main chain

[gray summit]

Seeing the stroke order helps

[pseudo basin]

how can you cursivize an r to look like a

[finite briar]

i am writing with a mouse

[pseudo basin]

in paint??

[finite briar]

yes

[pseudo basin]

you know it has a text tool right

[finite briar]

no???