help-4

[stark wedge]

you put a ^2 on the term 3x when it wasn't supposed to be there at all, and by the looks of it you would've gotten 2x^2 + 3x + 2 = 0

[deft condor]

xD i fixed it

what else did i do wrong

[deft condor]

ty

[stark wedge]

nothing by the looks of it

2x^2 + 3x + 2 = 0 is correct, now solve for x

[deft condor]

😭

[stark wedge]

??

[deft condor]

okie

[stark wedge]

what's the issue

[deft condor]

nooo

nothiong dont worry

imma close

thank you Ann

.close

[vale dock]

Channel closed

Closed by @deft condor

Use .reopen if this was a mistake.

[waxen quest]

Just use Photomath

Or faith

[hearty belfry]

photomath?

[waxen quest]

Ye

helps with problems

and can help also

With explaining

[stark wedge]

!nogpt

[vale dock]

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).

[stark wedge]

(photomath is like marginally better ig)

(but it can rot your brain from overuse)

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[surreal rivet]

Question 1

[hearty belfry]

could you provide a translation?

!status

[vale dock]

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

[hearty belfry]

this as well

[tawny moon]

also, do show what you've tried

[surreal rivet]

Let be the function with domain , defined by

h(x) = 1 + \frac{x}{2} + 4^{-x}

a) Show that the point belongs to the graph of the function .

[stark wedge]

Let h be a function with domain R given by h(x) = 1 + x/2 + 4^-x.

a) Show that the point P(0,2) belongs to the graph of h.

b) On the graph of h there exists a unique point whose y-coordinate exceeds half of the x-coordinate by 3 units. By using only analytical methods, find the coordinates of this point.

[surreal rivet]

Idk where to start

[stark wedge]

i think it's this but im not 100% on the translation of b)

[surreal rivet]

Ts

[stark wedge]

do you want a) or b) or both

[surreal rivet]

Its ts

[stark wedge]

what does the word metade mean btw

[surreal rivet]

.

[surreal rivet]

Half

[stark wedge]

btw idk who wrote $4^{-x} = \log_4(-x)$ but it's wrong

[rocky lotus]

Ann

[stark wedge]

oh half.

[surreal rivet]

Not me......haha

I am so dumb

[stark wedge]

do you want a) or b) or both

[surreal rivet]

A

[stark wedge]

a) is just to verify h(0)=2

[surreal rivet]

Ohhhh

[surreal rivet]

I thought it was y=2

So h(x) would be 2

[stark wedge]

no you overthought it

(x,y) belongs to the graph of f means f(x)=y, no more no less no sideways

[surreal rivet]

But still how do i do 4^-x

[surreal rivet]

.

[stark wedge]

what do you mean by "do"

are you able to insert x=0 into 4^(-x)?

[surreal rivet]

No,the question has an equation

Ohhh

Sorry

I think i understand ,i am gonna post here what i think it is

[stark wedge]

a) is just to verify h(0)=2
that means you need to calculate h(0) and you should get 2 as the answer

[surreal rivet]

Btw idk what is 0/2

[stark wedge]

what's half of 0

[surreal rivet]

0

?

[stark wedge]

so you do know

[surreal rivet]

Oh

[stark wedge]

i threw your own question right back at you and suddenly you knew the answer how did that work

[river shale]

,rccw

[surreal rivet]

Magic

Also can you help me with b?

[stark wedge]

y-coordinate exceeds half of the x-coordinate by 3 units.
can you write this as an equation using the letters x and y

[surreal rivet]

Idk

Where to start

[stark wedge]

can you write "half of x" in symbols

[surreal rivet]

Guess thats it

[river shale]

,rccw

[surreal rivet]

.close

[vale dock]

Channel closed

Closed by @surreal rivet

Use .reopen if this was a mistake.

[vale dock]

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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>.
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• 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.

[drowsy atlas]

How did they get -1?

[tawny moon]

from the function statement, y = 2x - 1

[drowsy atlas]

OH

im stupid

ty

[tawny moon]

nah it happens haha

!done

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@drowsy atlas Has your question been resolved?

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Channel closed

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[vale dock]

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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.

[dull river]

<@&286206848099549185> kindly help with this one

[dull river]

Here i have to prove that angle FDA= angle EDA

And AD is perpendicular to BC. E and F are AC and AB respectively such that AD,BE and CF are concurrent.

Kindly help me on this one

<@&286206848099549185>

[tidal swift]

!15m

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

@dull river Has your question been resolved?

[vale dock]

@dull river Has your question been resolved?

[dull river]

Plz help, im stuck on this one for 2 days 🥹

[hazy frost]

hi

uh, so you got to prove ∠FDA = ∠EDA

I mean, the concurrency of AD, BE, CF means is a triple cevians meeting at the point P

so, since AD is still an altitude

it imposes the geometric relation between E and F

so, you can use Ceva's theorem in lenght form

[late cypress]

ping me after you find the solution tho pls

[vale dock]

@dull river Has your question been resolved?

[candid bolt]

lol i remember posting this question here

construnt a line parallel to BC through A

then use/prove some ratios ( angle bisector theorem), similarities...

ceva's

@dull river

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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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[ionic sequoia]

Help

[glass kelp]

i need somebody help

[ionic sequoia]

Deriving the Formula for the Volume of a Pyramid
We know from geometry that the formula for the volume of a pyramid is V=13Ah. If the pyramid has a square base, this becomes V=13a2h, where a denotes the length of one side of the base. We are going to use the slicing method to derive this formula.

[ionic sequoia]

what's up?

[glass kelp]

oh dear

[ V = \frac{1}{3}Ah]

[rocky lotus]

k

[ionic sequoia]

Yes? What do you have to do?

[glass kelp]

by "slicing method"

do u mean integration

[ionic sequoia]

yes

[glass kelp]

cool

use a linear eq

wait

are we proving this for any base

or js square base

[ionic sequoia]

Square base

[glass kelp]

cool

so what have u found out abt each slice

[glass kelp]

i say modelling each slice perpendicular to the x-axis is quite nice using this

[ionic sequoia]

idk

[glass kelp]

ok

so

[ionic sequoia]

It's on the x-axis

[glass kelp]

This is the main idea

The area of each cross section can be calculated by squaring the y-value of the linear eq representing the line from (0,a) to (h,0)

Do u agree with this?

@ionic sequoia

[ionic sequoia]

oh okay

[ionic sequoia]

We square to get the area of each slice?

[glass kelp]

What do u think

[ionic sequoia]

$\frac{1}{3}a^2h$

[rocky lotus]

Andy

[glass kelp]

Ye

So have u found the formula for the linear equation

[ionic sequoia]

Is this linear algebra?

[glass kelp]

No

😭

[glass kelp]

.

[ionic sequoia]

No

[glass kelp]

It passes through (0,a) and (0,h)

[clear path]

hi guys !

[ionic sequoia]

hi

[clear path]

how are you I'm new here

[ionic sequoia]

maybe r = (xh/a)^2

[ionic sequoia]

good!

[clear path]

you are the first person who answers me

[ionic sequoia]

heh

[clear path]

yeah

[glass kelp]

${y = -\frac{h}{a}(x) + a}$

[rocky lotus]

k

[glass kelp]

do u know how i got this

[ionic sequoia]

what is this sorcery

[clear path]

but what about here ?

[ionic sequoia]

probably not

[glass kelp]

${y - y_0 = m(x-x_0)}$

[rocky lotus]

k

[ionic sequoia]

There are various channels

check them out

this is a one-to-one help channel lol

[clear path]

i very love maths cuz i'm study computer engineering !

[ionic sequoia]

nice

[glass kelp]

interesting

[ionic sequoia]

https://tenor.com/view/of-course-gif-21373815

[clear path]

specially ML/AI engineering

[glass kelp]

now

[ionic sequoia]

I think so

[glass kelp]

[ V = \int_0^h \left(-\frac{h}{a}x + a\right)^2 \dd x]

[rocky lotus]

k

[glass kelp]

this is the volume for the pyramid then

[clear path]

so i let you continue and i'll come next !

[ionic sequoia]

Wait, why the tangent slope formula?

[ionic sequoia]

sure, cya

#computing-software

[clear path]

thanks

[glass kelp]

hmm

somethings off

[ionic sequoia]

Can you recap what we were trying to do?

[glass kelp]

prove that ${V = \frac{1}{3}a^2 h}$

[glass kelp]

this is wrong lol

[ionic sequoia]

oh

This is a proof?

idk what's going on

[rocky lotus]

k

[glass kelp]

ye

[ionic sequoia]

idk how I am alive

[glass kelp]

..

[ionic sequoia]

maybe dividing a by h, then multiplying that by x and then square all of it

$(\frac{ax}{h})^2$

[glass kelp]

[ m = \frac{a-0}{0-h} = -\frac{a}{h}]

[rocky lotus]

k

Andy

[glass kelp]

so

From the slope-point formula $y - y_0 = m(x-x_0),$ ${y - y_0 = -\frac{a}{h}(x-x_0)}$. Pick ${(x_0,y_0) = (h,0)}$ for convenience, ${y - 0 = -\frac{a}{h}(x-h)}$.

[rocky lotus]

k

[ionic sequoia]

maybe the rate of change at every slice helps?

[glass kelp]

?

why tho

[ionic sequoia]

the average rate of change*

[glass kelp]

no need

[glass kelp]

do u understand this tho

this is the correct eq now

[ionic sequoia]

What does the slope have to do with this

[glass kelp]

do u recall the slope-point formula

from pre-calc

[ionic sequoia]

I learned algebra, trigonometry, pre-calc and calculus all at once; yes

[glass kelp]

ok

[ionic sequoia]

just the basics of trig tho

[glass kelp]

so u should be familar with ${y-y_0 = m(x-x_0)}$

[rocky lotus]

k

[midnight pier]

ok now learn calc 3

[ionic sequoia]

sure

[glass kelp]

u kinda need strong foundation of pre-calc and calc..

[ionic sequoia]

Let me understand this application

[ionic sequoia]

yes

[ionic sequoia]

But why the slope

WHY

how does it apply here

[glass kelp]

.

so that u can find the line y

[ionic sequoia]

oh

[glass kelp]

cuz we've discussed how ${V = \int_0^h y^2 \dd x}$ where ${y}$ is the eq of the line

[rocky lotus]

k

[ionic sequoia]

I didn't know you're trying to do then

[glass kelp]

ok

at which part are u confused abt

[ionic sequoia]

How do we get each slice?

[glass kelp]

.

[ionic sequoia]

there's some writing in there

what does it say

[glass kelp]

integrate along this

in general, do u know how to do volume using cross sectiosn

[ionic sequoia]

so we were trying to find the length of y?

[ionic sequoia]

yes

[glass kelp]

yes

cuz the length of y squared is the area of each cross section, no?

[ionic sequoia]

we know the height of the pyramid

[ionic sequoia]

yes

We only get half of the pyramid with y...

[glass kelp]

how so

[ionic sequoia]

It is evenly distributed between the negative and positive parts

so whatever y gives us is just half of it?

[glass kelp]

make sense

so given side a

it should be

[glass kelp]

from (0, a/2) to (h,0)

regardless, we will do some multiplication

so the thing cancels out anyway

but the diagram is faulty, yes, my apologies

[ionic sequoia]

a is the radius?

[glass kelp]

the side of the square base,yes

ok

lemme update the diagram

the area of each cross section is henceforth given by ${(2y)^2}$. Now using ${m = \frac{0-\frac{a}{2}}{h-0} = -\frac{a}{2h}}$. So, we will be doing
[ \int_0^h \left(\cancel{2} \cdot - \frac{a}{\cancel{2}h} (x-h)\right)^2 \dd x = \int_0^h \left(-\frac{a}{h}(x-h) \right)^2\dd x]

[rocky lotus]

k

[glass kelp]

i hope this clarify the diagramatic issue

now

@ionic sequoia do u agree with this

[ionic sequoia]

no

[glass kelp]

why

[ionic sequoia]

I don't even know

[glass kelp]

..

[ionic sequoia]

wait

That reminds me of the slope

It's decreasing

we already have the formula for the area

we just prove it by integrating the slope

but why is it squared

[glass kelp]

how do u find area of a square

[ionic sequoia]

squaring the area

[glass kelp]

i beg ur pardon? T_T

[ionic sequoia]

squaring a side of itself

[glass kelp]

ye

now whats each side of the square

[ionic sequoia]

a

a represents a side of the square, I think

[glass kelp]

thats only for the cross section at the base

whats the side of the square for cross section elsewhere

why the slope

what

have u done volume for cross sections b4

genuienly

[ionic sequoia]

no

[ionic sequoia]

yes

[ionic sequoia]

I misread your question

[glass kelp]

so whats each side of the square

[ionic sequoia]

i don't know

I am gonna use proportions instead

[glass kelp]

https://youtu.be/qMXPnfx2MQM?si=gPEy1gJz4QFBr6VK

[ionic sequoia]

I hate yt videos

Okay, thanks @glass kelp

[vale dock]

@ionic sequoia Has your question been resolved?

Channel closed

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[vale dock]

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• 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>.
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[hardy flicker]

hi

[hardy flicker]

1. Induction and the Binomial Theorem
2. Limits
3. Tangents and Normals
4. Inverse Function
5. Optimization Problems
6. Graph Plotting
7. Taylor Polynomials

i have exam and i wonder which part i should start with the easiet of them

and focus on mainly to able to pass the exam

[hearty belfry]

I mean I'm not sure since we don't really have much context with what the exam will be like

[hardy flicker]

i can show u

[hearty belfry]

Best just to go through each topic thoroughly

[hardy flicker]

the issue is i have the exam in 10 days

and i have other exams so i need to make sure to pass the exam

[hearty belfry]

I'd focus on the topics that you are weak on the most

[neat locust]

spend ~1hr per day focusing on one topic

[hardy flicker]

and put the most hours for the easier part then the hard part

[neat locust]

Go through old homeworks to see where you struggled

[hardy flicker]

it was 2 years ago i did this test

so i dont remeber quite anything tbh

[neat locust]

why are you taking the test now?

Do you have any old homeworks to look through?

[hardy flicker]

cuase i have it still

[neat locust]

have what still?

[hardy flicker]

i need to pass it

havent passed the exam yet

[neat locust]

Do you have any old homeworks?

[hardy flicker]

no

i have just good pages

[neat locust]

good pages?

[hardy flicker]

yea with the formula and more

[neat locust]

did you ever do any homework? Is this a class?

[hardy flicker]

yea i did but i dont have the homework with me atm

went back to my parents house lol

[neat locust]

dang. You better try to get it back if you can. It's really good for study

but, we'll work without it

spend today reviewing each topic for ~10min, and spend ~10-15min doing 2-4 problems per section

See where you do fine and where you struggle

[hardy flicker]

well i know where i struggle for example

on limits i have the issue where i have not learned all the rules

[neat locust]

what rules do you know?

[hardy flicker]

like this one for example

i need also learn it without líHÙpitals rules

[neat locust]

$\lim_{x\to0}\frac{\sin x}{x}$ is one of the limits you should just know. But, you can always cheat it with l'hopital

[rocky lotus]

SWR

[hardy flicker]

well i have write it down sin x /x is always going to be 1

[neat locust]

L'hopital's rule: If $\lim_{x\to a} f(x)=0$ and $\lim_{x\to a} g(x) =0$, and $f$ and $g$ are differentiable at $x=a$, then
$$\lim_{x\to a}\frac{f(x)}{g(x)}=\lim_{x\to a}\frac{f'(x)}{g'(x)}$$

[rocky lotus]

SWR

[hardy flicker]

i cant use the rule...

[neat locust]

wdym?

[hardy flicker]

is not allowed

for the exam

[frozen ledge]

provided the limit of f’/g’ exists

[neat locust]

Then you want to use the identity $\lim_{x\to 0}\frac{\sin x}{x}=1$

[hardy flicker]

yea i know that part

[frozen ledge]

lmao

🤣

nice wink bro

[rocky lotus]

SWR

[frozen ledge]

f and g being differentiable isn’t sufficient

[hardy flicker]

i have also wrote down a few other rules

but long away from all the rules i need to know

but i wanna just know what to focus on mainly

cuase some of them are a bit easier then the rest

[neat locust]

That's up to you to decide.

We don't know what's easy for you

[trim harbor]

Damn man when's the exam lol

[neat locust]

I still recommend this ^

[hardy flicker]

i can show u but the issue its on swedish xD

[hearty belfry]

they said in ten days

[hardy flicker]

here u go

[trim harbor]

Well then you have enough time to revise each part I would say

[trim harbor]

This is a great way to find out which part you struggle with

[hardy flicker]

the issue is i have 3 other exams also xD

beside this one

[neat locust]

we can't really help you beyond this. There's no magic trick to getting more hours out of a day

You just need to start

[hardy flicker]

yea ik thx but idk where to start tbh

[trim harbor]

I mean I would say limits are quite easy when you get them

And you get the least points in the exam for them

[neat locust]

I can recommend you where, but you need to actually listen

[trim harbor]

But they have a lot of uses

[hardy flicker]

okay

[trim harbor]

And Taylor's polynomials are templated tasks in my opinion

[hardy flicker]

from what i have seen from the past

exams

is the first question

is easy

and the limits are also easy but i just need to focus learning all the rules

asap

and Tangents and Normals is easy in my opinion but i have to revisit it

[hearty belfry]

Do they teach you lhopitals rule as well?

[hardy flicker]

no

its not allowed for the exam

[hearty belfry]

that's weird

[hardy flicker]

yea otherwise it would be much easier with it

[hearty belfry]

Ngl that's mean of them 😭

[neat locust]

I think for the sinx/x limits, it's not allowed

[trim harbor]

My exam in this area was also like that 😞

[neat locust]

which makes sense, because l'hopital requires derivative, and derivative of sin uses the sinx/x identity

[trim harbor]

They taught us l'hospital and on the exam it said "without l'hospitals rule solve..."

[hearty belfry]

That makes sense, you'd use squeeze theorem for that

[hardy flicker]

u study in sweden?

[trim harbor]

Nope

Croatia

[hardy flicker]

ahh okay

[trim harbor]

But math professors are mean everywhere I guess 😭

[hardy flicker]

is there somewhere where i can find all the rules?

for limit?

[trim harbor]

I can look at old posts my professors gave

Maybe I have a list

[hardy flicker]

okay would be rly kind of u

[trim harbor]

Hm i can't find any rules except this one

Wait

I mean it's important but not much lol

[hearty belfry]

I mean some limits are just rearranging them into a form that allows you to use other known limits such as 1/x = 0 when x approaches infinity

[trim harbor]

I also have my old exam in limits if you don't mind the Croatian

[hardy flicker]

yea thx have it written down

[hardy flicker]

yea the one u see in the exam the question 2 a) is pretty easy but b) and c) are the ones i struggle with

[hardy flicker]

and this

[trim harbor]

The last one is derivatives but the first one is limits and second can we solved using limits

[hardy flicker]

yea thx will look in to it

[trim harbor]

The b type is the easiest

[hardy flicker]

rly?

[trim harbor]

If 1 is a root in both equations

[hardy flicker]

would u able to name b and c what kinda type they are i mean which rule i need to know?

[trim harbor]

You just factorise both as (x-1)(...something...) and cancel x-1

And then plug in 1

If there's no problems then just plug in 1

[hardy flicker]

i have seen others like the b where they have used Polynomial long division to solve it

[trim harbor]

In c you could use a substitution I guess

Or notice the expression in the numerator is a quadratic with ln(x) instead of x

And you can sub z=ln(x) and solve it like b

[trim harbor]

Yes yes that's a common way to solve it also

And important later on

Also decomposition into partial fractions if you learned that already

[hardy flicker]

yea

i have learned it

[trim harbor]

Cuz you get easier expression and can use the rule that lim(a±b) is lim(a) ± lim(b) if both limits exist

[hardy flicker]

wait is it easier to solve with decomposition into partial fractions?

[trim harbor]

To me it is

Unless the limits don't exist

Then you just wasted time lol

[hardy flicker]

i thought in some cases

u needed to use both

[trim harbor]

Yes cuz of the rules of decomposition into partial fractions

[hardy flicker]

but that a other exam i refering to tho

[trim harbor]

b

$lim(\frac{6}{(x-2)(x+2)} - \frac{3}{x(x-2)})$

[rocky lotus]

ka.

[trim harbor]

And now make it one fraction

And again think like the other examples

This is an example of the decomposition into partial fractions being a waste of time since both limits don't exist lol

So put it back to one fraction

Try to sub/divide/cancel out blablabla

Just anything you can

To get rid of the x-2

[hardy flicker]

so u mean decomposition into partial fractions is not optimal here ?

[trim harbor]

That's the point of all limit problems
Just try anything to eliminate the "problem" lol

[hearty belfry]

you can type your limits like this $\lim_{x \to 2}$

[rocky lotus]

឵឵MxRgD

[trim harbor]

Nope cuz then you would get infinity - infinity which is undefined

[hardy flicker]

uhh i see

i feel cooked ngl lol

so much to take in with the rules

[trim harbor]

Yeaaah I mean I can't really comfort you here

[native plinth]

If you're struggling with the limits thing

[trim harbor]

You kinda have to know what you are allowed to do and what you aren't in which situation

I found it very helpful to learn the theory behind it first like understanding the theorems

[native plinth]

At the basic stage(that is, assuming you won't have to do anything like rewriting limits as riemann sums, etc), and without l'hopital's rule, it usually boils down to one of two things

[hardy flicker]

well i have learned the other maths just look in the past exams and yt to learn the rules and more

[native plinth]

1: Adding/multiplying one in a convenient form
2: bounding the limit and using the ordering of R(the "sandwich" rule)

[trim harbor]

Ah yes I forgot the sandwich rule !!

I usually use it when I'm ready to give up on the limit lol

That's the last resort for me

[native plinth]

I don't like resorting to it much either since you need to have the right idea(i.e come up with the correct bounds) but it's helped me some times

[native plinth]

(that being said, I'm.not the biggest fan of calculus in general)

[hardy flicker]

so if i learn this 2 i would be able to complete the question from a b c?

[hardy flicker]

same i rly enjoyed linear algebra

[native plinth]

I guess? But 1 is extremely general

What a "convenient form of writing 1" is depends heavily on the question

[trim harbor]

I mean I survived calculus by doing the most exercises I can and seeing the most situations possible

And then you start thinking in that way

[trim harbor]

Yessss

I am a demonstrator in linear algebra at my college

I don't know if you have that in Sweden??

[native plinth]

I'm gonna have to retake calculus 💀 , and an annual subject at that

[trim harbor]

But basically I'm in love with it

[trim harbor]

Oh no

[native plinth]

Changed universities and I didn't manage to get them to recognize calculus, so I'll have to go through it again

[hardy flicker]

ngl i am just doing the exams lol

[native plinth]

💀

[trim harbor]

I'm so glad I got rid of it

The professor was a little bitch as well

Good luck soldier 🫡

[native plinth]

I mean, that usually works if all you want is a passing grade(and if your subject isn't too proof heavy of course)

[midnight pier]

💀

[hardy flicker]

well i have realized it does not matter so much if u just pass the exam or u get 20/20

[native plinth]

Hopefully I'll be free of it soon(though after this one I have a differential calculus and an integral calculus subject to get through💀)

[native plinth]

Depends on what you want to do, but most of the time it's the same yeah

[hardy flicker]

so yea aiming to just passing and put the hours in league

[midnight pier]

league of legends ?

[trim harbor]

What other exams do you have?

[hardy flicker]

xD yes

[native plinth]

💀

[hardy flicker]

2 economy exam

and python exam

[midnight pier]

i am pretty sure the further you go in studying the harder exams will become . Year 1 is pretty easy , but I guess year 2 will be tuff unless i will put more hours into studying

[hearty belfry]

good luck with them

[trim harbor]

Good luck man

[hardy flicker]

well i am in third year xD

[hardy flicker]

its a easy one

but the issue it devided

in 2 parts

the first part is the coding which is rly easy

but the second part is theory

[trim harbor]

What are you studying? Economy?

[hardy flicker]

which i failed both times xD

[hardy flicker]

its called engineering in industriell economy and management

[trim harbor]

Oho

Sounds cool

[midnight pier]

same thing btw

both have E

[native plinth]

Depends on the person, some find year 1 unsurmountable because they started with a wrong idea of what it would be

[hardy flicker]

in sweden?

[trim harbor]

I was just confused why you had linear algebra and economy in the same uni

[native plinth]

And then sort of get used to it and do better

[native plinth]

I mean, fairly sure econ majors have to take some linear algebra

Nothing crazy, up to eigenvalues iirc, but some

[midnight pier]

true,but in general exams contain less complex material or just less material, even with 70 % of understanding you can get a decent grade

[hardy flicker]

uhh its a big uni lol

[midnight pier]

idk I am not from sweden

[native plinth]

I guess, I dread the calculus subject I'm gonna take though, and it's a first year one

[midnight pier]

true

[hardy flicker]

hmm weird where u from then?

[trim harbor]

I guess matrices can be useful but I don't think they need isomorphism theorems lol

[hardy flicker]

cuase i havent heard this beside in sweden

[native plinth]

Have a bunch of friends of higher years saying it's their lowest grade

[native plinth]

Isn't that abstract algebra, though? Don't remember covering isomorphism theorems on linear

[trim harbor]

Oh my

Idk

I am studying like just math

[native plinth]

Since, y'know, the isomorphisms between finite vector spaces are simply invertible linear transformations

[trim harbor]

My college is literally called math lol

[midnight pier]

i have physics modules and they are objectively easiest one to get a good grade because 2nd part of the exam is done from home , but material itself is harder then most of my math modules

[native plinth]

And that's essentially all you cover in linear algebra

[trim harbor]

Nd I had linear algebra where we covered basically everything

[native plinth]

Yeah, I'm also majoring in mathematics

But don't your subjects have names like these?

[trim harbor]

From groups to isomorphism theorems to vector spaces to unitaran operators etcetc

[native plinth]

So you covered groups, rings, ideals, quotients and the such too?

[trim harbor]

Nope, I already noticed that when I research something in English everything has a different name lol

[trim harbor]

Yeah all of that

That was the start of linear algebra in Croatia

[midnight pier]

i had introduction to special relativity but no linear algebra ((((((((((((((

[hardy flicker]

well we had all the calulus and linear algebra

and pyhics also

[native plinth]

That's a weird subject then

Generally, you take linear algebra in first year which covers finite vector spaces, linear transformations, quotient spaces, some affine geometry, diagonalizations, etc

And then you take a dedicated subject on groups, rings, algebras, fields and the rest on second year

[trim harbor]

It's Croatian but it says groups, mapping groups, ring body field...

[trim harbor]

Ahh that was the second part of LA1 and some LA2

[native plinth]

I mean, we technically do have an introduction to those concepts at the start of the subject, but it's really basic

Have you covered cyclic, normal and quotient groups, divisibility and all that?

[trim harbor]

Yes all of that

I mean you need that for the isomorphism theorem

[midnight pier]

idk i am pretty sure i will have some linear algebra in my 2nd year but in first it was primarily set theory,calculus,and analysis,kynematics , oscilattions ,special relativity,introduction to quantum theory and differential equations

[trim harbor]

But Croatia is weird

Since what you call calculus, integral calculus etc

Is all in a subject we call mathematical analysis

[hardy flicker]

hmm cool but which direction of economy are u studying?

is it more for b2b or ?

[midnight pier]

i am doing theoretical physics

[hardy flicker]

uhhh thought u study the same thing as me lol

[trim harbor]

Linear algebra has a huge application in quantum physics so you muuust have it imo

[native plinth]

Geez

[native plinth]

Analysis and calculus are different, analysis is a more rigorous treatment of the subject, the integral and differential calculus subjects I mentioned before are actual analysis(we cover lebesgue, measurings and measure spaces, r's topology, etc, which is kinda just mentioned in the first year subject)

[native plinth]

I'm curious, which isomorphism theorem are you talking about?

[trim harbor]

Ohhh okay okay fair

[native plinth]

Also just noticed I somehow got the helpful role

[trim harbor]

Wait I'll find the exact thing from my college presentations

[midnight pier]

idk maybe, but i am pretty sure whe havent had module that was called linear algebra.I had algebra and further algebra so maybe it was a linear algebra idk ?

[native plinth]

Also, set theory? I'm fairly sure you guys don't really need set theory

I mean, i'm self studying it and it's hellishly abstract

[midnight pier]

it was introduction to set theory, but we will more of it in year 2

[native plinth]

Don't see how you'd use it in physics

[midnight pier]

yeah it is pretty lame

[native plinth]

Oh, so just basic intersection and union stuff

[native plinth]

Nah, wdym, it's lit

Hard as nothing else I've tried, but it's really interesting

[trim harbor]

Oooo I have that next year

[midnight pier]

it is hard

[trim harbor]

I hear it's quite hard from older students

[native plinth]

I only remember the last one, which iirc had to do with the canonical projection

[midnight pier]

introduction was lame but generalised version is pretty cool

[native plinth]

But I've quite forgotten it, don't know much about abstract algebra tbh

[midnight pier]

I want to main in math , physics is hella cryptic

[native plinth]

What are you gonna cover? Fairly sure I'll be able to tell what anything there is about

[native plinth]

Math is even more cryptic though

[trim harbor]

Ooooo thank you, I'll go check for a min

[midnight pier]

i don't remember anything from my exams (i had 2 months ago) despite doing well in them

[midnight pier]

english is not my first language so i have more problem with physics

than math

[native plinth]

My case is not really that, it's just that I literally have not taken the subject 💀

[hearty belfry]

physics can be tough with there diagrams

[native plinth]

I only know what I've coincidentally read online/covered somewhere else

[midnight pier]

true

[hearty belfry]

I remember struggling how to resolve forces

[native plinth]

Math will eventually become full fledged essay writing, though

English is not my first language either, but you'll get used to it

[midnight pier]

yes but not right now, i still like physics but only theoretical part of it

[midnight pier]

me too

[native plinth]

I'm gonna be taking physics this year too

I'll essentially be taking everything I do NOT want to take: physics, statistics, calculus, probability...

[trim harbor]

This is what I'll be learning in set theory in a few months

This all sounds like stuff I already learned tbh

[midnight pier]

i hate probability but i had to catch up with it ,cause it would be weird to learn everything except easiest module

[hardy flicker]

nah its fun ngl

[native plinth]

Arithmetic of cardinal bro

The translation kinda wacky ngl

[hardy flicker]

i learned gambling is rly bad that way xD

when its comes to %

[native plinth]

If you know how ordinals kinda work you should be fine

Looks like it's not axiomatic

[trim harbor]

I just put it into a random photo translator 💀💀

[midnight pier]

i had probability and statistics ,they are very similar but i dislike 1 but not the other somehow

[native plinth]

Snd you won't be covering cofinality, filters, Aoc or stuff like that, from what I'm reading here

[trim harbor]

It could be axiomatic

[midnight pier]

its 50/50 you either win or no

[trim harbor]

I mean I expect it to be

[hardy flicker]

same it was both in a 1

[trim harbor]

Also these explanations don't really go in depth

[hardy flicker]

nah we went deeper

btw are u guys paying to go in uni?

[hearty belfry]

Btw, the channel is meant to be closed and if you wanna discuss, you should move onto #serious-discussion (discussion1 is pretty fast) and #chill.

[hardy flicker]

^

.close

[vale dock]

Channel closed

Closed by @hardy flicker

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[native plinth]

Which year are you on?

(actually should probably leave this channel before I occupy it)

[vale dock]

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[tawny musk]

What conditions does a topos need to satisfy for the equality $\neg \forall x, p(x) = \exists x, \neg p(x)$ to hold internally?

[rocky lotus]

alt_to_alt

[vale dock]

@tawny musk Has your question been resolved?

[hardy coral]

Isn't that De Morgan's law for predicate logic?

Not sure what you mean by topos but to me this always holds true

[native plinth]

As far as I know a topos is a type of category with some relation to logic

[hardy coral]

Maybe https://discord.com/channels/268882317391429632/497227343337881640 then?

[tawny musk]

dyk what intuitoinistic logic is? a topos is a model for that

generally, only a limited version of the de morgan rules hold in intuitionistic logic

[cloud shadow]

help doesn't feel like the most suitable place to ask for help on topoi lol

[tawny musk]

alr

.close

[vale dock]

Channel closed

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[hardy coral]

Wouldn't this cover your question?
https://en.wikipedia.org/wiki/Intuitionistic_logic#Existential_vs._universal_quantification

.reopen

[vale dock]

✅

[hardy coral]

Perhaps this too: https://math.stackexchange.com/questions/120187/do-de-morgans-laws-hold-in-propositional-intuitionistic-logic

@tawny musk

[cloud shadow]

You found things good job!

[hardy coral]

Anyway, good luck

.close

[vale dock]

Channel closed

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[tawny musk]

That covers the converse of my question but I dont think so

[hardy coral]

Probably just ask in https://discord.com/channels/268882317391429632/497227343337881640 then

[vale dock]

Available help channel!

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[thorn maple]

When I solve for example sin = 0, I was taught that the general formula is x = 2nπ + θ or 2nπ + π - θ. But the book not only takes one solution but it also removes the 2. The book's solution is x = nπ. This happens to other solutions as well can anybody explain?

[dark pewter]

Your general formula for sin(x) = 0 would yield x = 2npi or x = 2npi + pi = pi(2n + 1). These solutions are the even or odd multiples of pi, or in other terms just any multiple of pi, which can be written just as n pi.

So both work, but n pi is a shorter way to write it

[red tulip]

because sin(0) is 0 and so is sin(pi), its the only case where its the same every pi radians

[thorn maple]

So why does the book put the two? Do I not miss anything?.. again, the book says x = 2npi + θ or 2npi + (pi -θ), k belongs to Z. Anyway ty for your time

[red tulip]

because its only for 0

[thorn maple]

Oh that's why we don't take the 2?

[red tulip]

yes

if it were sinx = sqrt3 then it would be every 2pi because if you add pi radians you have -sin(pi/3) instead

[thorn maple]

Is 0 a special case? Are there any other special cases? I was just studying functions, tan = sin/cos where cos ≠ 0 and yeah I was confused where did the 2 go

[red tulip]

think about it

[thorn maple]

For example i found x = 2npi ± pi/2 but the book merely said pi + pi/2 without the negative case

[red tulip]

the sin of an angle is the y coordinate on the unit circle

[thorn maple]

Yes

[red tulip]

if the y coordinate is 0 it can be on the opposite sides of the circle

which is adding pi radians

its not the same for any other value

if cos(x) is 0 its the same thing but its down the y axis instead of the x axis

[thorn maple]

What about this? Pi/2 and - pi/2 doesn't end up in the same place right?..

Oh so it's just abt the value of cos?

And since they are opposite we don't care?

[thorn maple]

Like because same cos? For p/2 and 3p/2?

Sorry for bothering you

[red tulip]

was this the same question

[thorn maple]

Yes abt this

[dark pewter]

Again, x = 2npi +- pi/2 and x = npi + pi/2 are esentially the same solutions, just written differently

[red tulip]

what was the exact question

[dark pewter]

you can try a few values of n to convince yourself

[thorn maple]

So because it is the same every pi turns it doesn't matter.

Either it's negative or positive

[thorn maple]

Dw I bothered you enough. I got it ty both

[dark pewter]

here because the angle is pi/2 it just so ends up we can rewrite it nicer as x = npi + pi/2

[thorn maple]

Oh I fucking got the sin one I feel so stupid 😭

I really am stupid. I should take example values instead of watching yt videos

I got what you mean written better

[dark pewter]

Nah you're not, math can be confusing sometimes

[thorn maple]

Ty still

[vale dock]

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[gray patrol]

how can I learn how to expand those type of questions ?

[hearty belfry]

which question?

some of them you can't expand like the one with the square root in demoniator

because there aren't any brackets

[gray patrol]

@hearty belfry

ok most of them

[hearty belfry]

alright let's start with (3x-2)(4-x) then

do you know the FOIL method?

notice how we times them together for each letter

[gray patrol]

oh yes that's clear

the image shows the FOIL in easy way

[hearty belfry]

alright could you try to apply it with (3x-2)(4-x)

[gray patrol]

ok

[hearty belfry]

show your working out btw

[gray patrol]

step 1

[hearty belfry]

It should be 4-x

not 4+x

[gray patrol]

yah that's true

my bad

[hearty belfry]

although you don't really need to put them into that form either, it just saves time

[lament spoke]

You can expand the one with the square root as you need it to solve the integral

[gray patrol]

GOOGOGGOOGOGOGOGOOGOGOGOG

missed you

<3

[lament spoke]

$x^{2}/x^{1/2} - 2/x^{1/2}$

[hearty belfry]

should be -2x btw

[lament spoke]

Me too

[gray patrol]

but it is -2 * -x ?

[rocky lotus]

NotGogo495

[hearty belfry]

oh what

nvm

that's right, I got confused with myself as well

[gray patrol]

am i right ?

[hearty belfry]

you are right

[gray patrol]

its ok it happens

and now 12x should be 14x right ?

[hearty belfry]

yeah the -2(4+x) fiddled me up when it should be -2(4-x)

[hearty belfry]

yeah

[gray patrol]

but why not 10x becase we are moving it to the other side ?

[hearty belfry]

because we're not doing a subtraction of 12x - 2x

we're doing 12x + 2x

[hearty belfry]

Does that count as expansion?

I always thought of expansion for brackets

[lament spoke]

It may be called a transformation rather than expansion

But it’s needed to solve the integral

[hearty belfry]

Yeah I get what you mean

[hearty belfry]

I don't think transformation is the right word for that

[lament spoke]

After that you get $x^{3/2} - 2x^{-1/2}$

[hearty belfry]

I guess I'd just say splitting the fraction

[rocky lotus]

NotGogo495

[lament spoke]

Yeah could be

English is not my native language so I’m not that familiar with the terminology

[hearty belfry]

no worries

[lament spoke]

And when you integrate it you should get $2x^{5/2}/5 - 4x^{1/2}$

[hearty belfry]

yeah, although the original question doesn't look like it's asking for integration

[rocky lotus]

NotGogo495

[hearty belfry]

they asked for how to expand

[lament spoke]

Yeah I know but he showed me the questions yesterday

They’re on definite integrals

[hearty belfry]

Right i see

[lament spoke]

Now I don’t know the values given so that’s as far as I can help with the question

And it’s 3 am local time so I’ll be heading to bed soon

[hearty belfry]

lol it's 1am for me

[lament spoke]

British?

[hearty belfry]

yeah

[lament spoke]

I saw a few brits talking about the bmo (I thought it was the Balkan math Olympiad but they meant the British one)

And I know we have a 2 hour time difference

Bmo also sounds like the adventure time character lol

[hearty belfry]

there's two of them you do. One for BMO1 which is a qualifer for BMO2. And then once you done BMO2, you can join the team for the IMO

[lament spoke]

Ohh yeah makes sense

We also have an Olympiad, though we call it National so - NMO. We have 3 rounds. But there are also three other competitions called the Autumn, Winter and Spring Tournament. You sum up the points from the NMO3 + Autumn + Winter + Spring to get the IMO team

There may be some other type of qualification but I haven’t reached that level so I’m not sure

I hope this year I can do

[hearty belfry]

you can look into #competition-math

where you can posts competition problems that you might need help with, or I guess talk about competition math in general

[lament spoke]

I will try it when I go over such questions, thanks

But rn I’m studying by a book I found online

Problem-Solving Strategies by Engel

[hearty belfry]

Nice

[lament spoke]

Did we answer all questions?

[hearty belfry]

I mean OP doesn't seem to be here lol

[lament spoke]

I think the remaining ones were just the formula (a+b)^2 = a^2 + 2ab + b^2

[hearty belfry]

yeah

[lament spoke]

Well, imma head to bed so if there are some other questions I’ll have a look at them tomorrow

Goodnight

[hearty belfry]

gn

[gray patrol]

ohh sorry guys just had a call from my mother

@lament spoke

still here ?

[lament spoke]

Yup

[gray patrol]

is it ok if you teach me how to solve this one tomorrow ?

[lament spoke]

Yeah no problem

[gray patrol]

thx alot <3

[lament spoke]

Of course

[gray patrol]

@hearty belfry

what about this one ?

[hearty belfry]

there isn't anything to expand for that one

[gray patrol]

so how can we solve this one ?

[gray patrol]

i think there is smth we should do about it before starting to solve it

do you have any idea about how to solve it ?

[gray patrol]

i meen this ?

[hearty belfry]

what are you solving it for?

could you show the full image

[gray patrol]

@hearty belfry

[hearty belfry]

that one is doing the integral $\int_{1}^{a}\frac{2}{x\sqrt{x}}dx=3$

[rocky lotus]

឵឵MxRgD

[hearty belfry]

and solving for a

[vale dock]

@gray patrol Has your question been resolved?

[vale dock]

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[plucky flicker]

can anyone explain how to do these kinds of questions? (this wasnt talked about in the notes but it was in the test practice 😭 )

[ivory valley]

Are you familiar with the washer method?

[plucky flicker]

nope

whats that

[ivory valley]

It's an integral formula that lets you compute the volume of a rotated solid

[plucky flicker]

ohh

alr thanks ill check out some videos on google

[ivory valley]

yeah i think that's best

https://www.youtube.com/watch?v=rfSRfWSX3vc

[vale dock]

@plucky flicker Has your question been resolved?

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[humble flicker]

have i done 2a correctly so far? if so, how do i simplify it further

[glass kelp]

Looks good

,w d/dx arccos(e^-x)

[rocky lotus]

Results provided by WolframAlpha

Click here to refine your query online
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Requested by nuclearinteraction

[glass kelp]

👍

[humble flicker]

hm

bc for the solutions they put that

and idk if they’ve done smth else

[glass kelp]

Conjugate w/ e^x

They did that

But I don’t think it’s necessary /:P

[humble flicker]

oh right

do yk with differentiation how simplified u need to be

[glass kelp]

Depends on ur instructor lol

[humble flicker]

mm alr

thanks for the help

.close

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[humble flicker]

how do i prove question 1

[stark wedge]

well your derivative is correct, now write it all in terms of sin and cos and then simplify

[low frigate]

you don't even need to reduce to all sin and cos, you can use the pythagorean identity for $tan^2x$ in the denominator and it nicely cancels out with the numerator

[rocky lotus]

cytos

[humble flicker]

oh ur right it does

[low frigate]

also the derivative technically ☝️🤓 isn't constant because it's undefined when $x=\frac{\pi}{2}+\pi n, n\in\mathbb{Z}$

[humble flicker]

how would u prove that

[stark wedge]

\in not \epsilon

[rocky lotus]

cytos

[stark wedge]

also a function can be constant without its domain being $\bR$

[rocky lotus]

Ann

[stark wedge]

technical objection overruled

[humble flicker]

lol

.close

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[spark herald]

Number 17 and 19

[spark herald]

Help please

[stark wedge]

ok do you know your SOH-CAH-TOA

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@spark herald Has your question been resolved?

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[onyx peak]

I don’t understand where we get the “bounds” for the range of arc sin and arc cos. Why is it 0 to pi and -pi/2 to pi/2? I get that it is to prevent and infinite number of answers, but why those specific bounds? It seems like they are just random numbers. Can someone please explain?

[stark wedge]

mostly convenience tbh

these ranges contain 0

thus the outputs will be as "small" as they could be

[onyx peak]

Can you please give an example? A lot of my unit circle knowledge is corrupted sadly

[stark wedge]

and for positive values of x, you get angles in the first quadrant

e.g. arcsin(1/sqrt(2)) = pi/4

and arccos(1/2) = pi/3

[onyx peak]

The way I’m thinking is that for sin it corresponds to y, so anything in Q1 and Q2 is above y so it’s makes sense why sin is positive there, so then why does arcsin go from Q1 and Q4? Does ASTC not apply for inverse functions?

[stark wedge]

you want to be able to calculate the arcsin of a number between -1 and 0, yes?

[onyx peak]

Original Q

[stark wedge]

would have liked to see that earlier.

[onyx peak]

Sorry

[stark wedge]

so what's troubling you here

[onyx peak]

I got to simplifying to 7pi/5

Now idk what to do and how to first find the exact cos of that

Without calculator

And then from there find the arccos

And confused since arccos is 0,pi but this coordinate is not

[stark wedge]

you don't need to

also im gonna slightly abuse terminology here and say 7pi/5 is an angle not a coordinate

and yes you're right it's out of range

btw you should never drop the brackets

[onyx peak]

[0,pi]

[stark wedge]

you should always write intervals like [a,b] or (a,b) or (a,b] or [a,b) depending on which ends are closed

yes

you can subtract another 2pi so that cos(7pi/5) = cos(-3pi/5) and then use the fact that cos is even

[onyx peak]

Wdym cos is even?

[stark wedge]

do you know what an even function is?

[onyx peak]

No 😭😭

[stark wedge]

we say that a function f is even if it satisfies f(-x) = f(x)

i.e. its graph is symmetric across the y-axis

cosine is one of these functions

[onyx peak]

Meaning sin will be odd?

[stark wedge]

sine is indeed odd but i would expect you dont know what an odd function is either?

[onyx peak]

Nope

[stark wedge]

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

anyway point is cos(-3pi/5) = cos(3pi/5)

[onyx peak]

Because both will either be on the left or right side? (Either q1 and q4 or q2 and q3)

Or is that wrong way to think of it?

[stark wedge]

yeah i'd say it is wrong and/or bad

[onyx peak]

Where could this thinking fail? In this particular case -3pi/5 and 3pi/5 are both in q2 and q3

[stark wedge]

not sure if i have the energy to explain how to think about it better rn sorry

[onyx peak]

All good, thanks for your efforts

[vale dock]

@onyx peak Has your question been resolved?

[vale dock]

@onyx peak Has your question been resolved?

[tiny torrent]

what do you need help with @onyx peak

[onyx peak]

^

[onyx peak]

Confused on even odd

[onyx peak]

I’m saying this but I was told it’s not the right way to think about this

[lyric sundial]

The only thing you need to know is that arccos outputs an angle between 0 and π, whereas arcsin outputs an angle between -π/2 and π/2

[onyx peak]

So I’m overthinking the “why” part?

[lyric sundial]

Yes

The why is that you need the function to be invertible, hence bijective

[lyric sundial]

And this can be done by considering cos(x) with x between 0 and π, and sin(x) with x between -π/2 and π/2

[onyx peak]

Will I need to know that for calc I and II?

[lyric sundial]

I don't know what those cover honestly

[tiny torrent]

as long as you know the restricted domain you’ll be fine for calc 1 and 2

[lyric sundial]

But if they go over limit, integrals and derivatives then yes

[tiny torrent]

you dont really need to know the why

[onyx peak]

Those are all def there

[tiny torrent]

you’ll probably revisit the why in a course like discrete math

[lyric sundial]

I think it helps remembering though

[tiny torrent]

yeah thats true

[lyric sundial]

But apart from this, trig is very important (at least the fundamentals)

[onyx peak]

But I can’t remember if I don’t even know the basic why. Like I have no idea what this means

[lyric sundial]

You don't know what invertible means?

[onyx peak]

Bijective

[tiny torrent]

bijective means your function is one to one and onto

to have a inverse a function needs to be one to one

[onyx peak]

Wdym one to one

[tiny torrent]

cos is not one to one on its full domain since it is periodic

one to one means that for every value in your domain there is one corresponding y value

for example

x^2 is not one to one

because there are two x values that gives the same y value

-2, and 2

both give 4

this can’t happen for one to one function

every x value needs to have a unique y value

since cos and sin is periodic there are multiple values in its domain that gives the same y value

[onyx peak]

Ah so sin and tan are also not one to one then?

[tiny torrent]

ye

because sin(0) and sin(2pi) give the same y value

same with cos

do you know what it means for something to be a function?

[onyx peak]

Never learned that term “one to one”

Each input needs 1 output

[tiny torrent]

right

the reason we can’t have an inverse if our function isn’t one to one is because when you take the inverse you now have an input that gives two outputs

[onyx peak]

So to solve this mathematicians decided to just limit the range?

[tiny torrent]

limit the domain of cos yeah