help-23

[alpine hornet]

Damn

Okay so only tan and sin become negative in the front?

Cosine does not

Cosine becomes positive

Whatever that means😂 lmao

So it would be just sqt2/2?

Okay so

Hear me out

I somehow got that sec120 is 1/cos60 is 1/sqt3/2

[lusty ridge]

Is cos 60 not 2

1/2

[alpine hornet]

Correct.

Looking at my paper I noticed I put Soh-COh-Toa

Right. 1/2

[lusty ridge]

Also

Cos120 is -1/2

[alpine hornet]

Why

[lusty ridge]

Unit circle

Cos is the x co ordinate which is negative in q2

[alpine hornet]

Where did cos120 come from?

Oh. I changed it to sec(60) before flipping it over 1

[lusty ridge]

Yup

[alpine hornet]

So… now I’m confused again.

If it changes to cos(60) isn’t that positive?

How do I know if cosecant secant and cotangent are positive or negative?

Okay. I see, kinda.

So cos150 is cos30 is -sqt3 / 2?

Okay so..

Sec210

Is 1/cos30?

Which cos30 is sqt3/2

So… 1/sqt3/2

So my answer is… -1/sqt3/2 ?

Three fraction?

Why? How?

I gotcha

Wait it was sqt3/2

Confused again

Ugu math is weird

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[safe radish]

Please don't occupy multiple help channels.

[severe pond]

so if a polynomial has some zero x=a

then it has a factor (x-a)

and then when you have 4 factors

you can let x=0 and find any other constant multiples by setting =-108

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[severe ridge]

what's the expression for e?

is it s(6)?

[steel stag]

yes since it doesn't go backwards

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[severe ridge]

can someone check my math? I found the 2nd derivative to be a(t)=−t^2e^-t + 2e^-t

[hasty wagon]

should be wrong, lemme check

,w d²/dt² t²e^(-t)

[flat frigate]

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Requested by biscuityxd

[hasty wagon]

yea, it's incorrect

[severe ridge]

k ty

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[feral beacon]

ignore the bottom two lines, but how do i figure out the coefficients for the series, is it not as simple as plugging in n?

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[weary osprey]

how do I prove U(p) is cyclic ?

[weary osprey]

ie, it has a some primitive root modulo p

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[hushed oxide]

Im having trouble understanding how to arrive at the answer for number 14

I keep getting 1/8 alpha t^2

[steel stag]

how are you using the equations?

for the second part w will be alpha*t

[hushed oxide]

I used this to find delta theta

[steel stag]

oh I used the 1/2at^2 one let me see how this one goes

presumably this one is worse because it doesn't let you use the time data they give you

looks like it works when you do
a^2t^2=0+2aV
(1/2at)^2=a^2t^2+2aV

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[hushed oxide]

I DID IT

😭

Is this a valid method

I found omega and delta theta of the first “part” through integrating from 0 to t1

Then integrated from t1 to 2t1 and added the starting omega and delta thetas

This is a better photo

[steel stag]

nice, yea that's fine it's where all the equations came from anyways

[hushed oxide]

When i use the given equations, do i need to split it up into 2 parts?

If thats necessary i think thats where i got stuck

Not sure why i kept getting the wrong numbers

I plugged in the average acceleration from 0-2t for alpha. Is that wrong?

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[young summit]

I know the answer, but I don't know how to calculate it. answer is 0 2√3/9　 5

[lean otter]

consider the range of x

[iron topaz]

我是火星人

[iron topaz]

定数k決定数実数考慮

[dense vector]

wow Chinese

[iron topaz]

it's japanese

but yeah they the same pretty much

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[young summit]

cold you write equation and send me?, I don't know where I miss

sry

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[harsh sapphire]

unrelated but ur username is so fire

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[steep gust]

why is positive?

[frigid locust]

$$a^{-b} = \frac{1}{a^b}$$

[flat frigate]

JustToPro

[frigid locust]

and vice versa ,
$$a^{b} = \frac{1}{a^{-b}}$$

[flat frigate]

JustToPro

[steep gust]

oh i see thx

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[dense wadi]

how did the equation up turn into equation down

like where did the 9/pi^2 go

[copper kernel]

the -9/pi^2 C term got moved to the other side

so the left side would be (1+9/pi^2)C and then both sides were divided by (1+9/pi^2) to isolate C

[dense wadi]

otherside like

left side of the =?

[copper kernel]

yeah

[dense wadi]

wait where did the 1+

come from

[copper kernel]

$C+\frac{9}{\pi^2} C=\frac{e^{3x}}{\pi}\sin {(\pi x)} + \frac{3e^{3x}}{\pi^2}\cos{(\pi x)}$

[flat frigate]

Luke

[dense wadi]

okay im brain dead asf

tysm!

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[molten idol]

Hi, could you check my anwsers? I would say the first one and the last one are correct.

[frozen marlin]

yep

that's correct

!done

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.done

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[lean otter]

(\log_2(x^2+4x)=\log_2(5))

[flat frigate]

!

[lean otter]

i got the answer of x=-1 and x=5, but the answer is x=1 and x=-5, is it fine or is my answer considered wrong?

please ping me if anybody's helping.

isnt that x=5 or x+4=5 ==>x=1

[coarse jolt]

because technically I think the way you factored it is kinda off

If we have -5 + 1, that'll be -4

which would be x^2 - 4x

but we have +4x

so it shouldn't be factored into x - 5 but x + 5

$(x + 5) (x - 1) \rightarrow x^2 + 5x - x - 5 \rightarrow x^2 +4x - 5$

[flat frigate]

Kai

[lean otter]

sorry i need to go rn. gtta do smth irl. ill be back later and also dw ill read ur text later

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[lapis token]

Is this correct?( I’ll translate the task in a moment)

[lapis token]

It was not lol

I managed to find the mistake on my own tho

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[spare grotto]

can someone help me solve this? "The vectors e1 and e2 form a base in the plane. Two other vectors, {f1,f2}, are chosen as a new basis:
(f1 = 7e1 + 8e2, f2 = e1 + e2.)
a) Express the vectors e1,2 as LK of the new basis vectors.
b) Determine the components of the vector u = 5e1 − e2 the new basis.

[red spoke]

LK?

[spare grotto]

linear combination

[red spoke]

Fine

its not hard

you looking for a ez way to solve it?

[spare grotto]

yes sure

[red spoke]

then what is 7*f2

tell me

[spare grotto]

7e1 + 7e2

[red spoke]

7*f2-f1?

[spare grotto]

-e2

[red spoke]

then e2=f1-7*f2

right?

[spare grotto]

yes

[red spoke]

And try to figure out e1

by yourself

[spare grotto]

8/7?

[red spoke]

8/7?

where are f1 and f2?

[spare grotto]

e1 = 8f2 - f1

[red spoke]

Correct

Very good and now we can solve question2

[spare grotto]

okay b do i just put in e1 and e2

[red spoke]

yes

Express the vectors e1,2 as LK of the new basis vectors.

just like f1=Ae1+Be2

[spare grotto]

u = 47f2 - 6f1?

[red spoke]

e?

u = -42f2 + 6f1

maybe

[spare grotto]

why -42?

[red spoke]

e1 = 8f2 - f1 e2=f1-7*f2

[spare grotto]

i put in e1 and e2 and get u = 5(8f2 - f1) - (f1 -7f2)

then u = 40f2 - 5f1 - f1 + 7f2

[red spoke]

sorry my mistake

[spare grotto]

oh okay

[red spoke]

Thats fine

[spare grotto]

so thats the answer?

[red spoke]

yes

[spare grotto]

okay thank you

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[spice ore]

Hello, I am working on linear algebra, and I dont know how to approach this problem for finding the algebraic properties of dual maps.

[spice ore]

Should I try considering how the basis changes?

Just starting with a), how would I approach this

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[soft blade]

can someone help me go through the solution

[soft blade]

im kinda confused about the whole dP part

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[unique quiver]

Let $f : [0,\pi] \rightarrow \mathbb{R}$ be a continous function such that $f(\pi - x) = f(x) \forall x \in [0,\pi].$ \ Using integration by substitution, prove that \ $\int_{0}^{\pi} \ f(x),dx = 2\int_{0}^{\frac{\pi}{2}} \ f(x) ,dx$

[flat frigate]

Curry

[unique quiver]

on the left hand side I split the integral

$\int_{0}^{\pi} \ f(x) ,dx = \int_{0}^{\frac{\pi}{2}} \ f(x) ,dx + \int_{\frac{\pi}{2}}^{\pi} \ f(x),dx$

from there I used the substitution x = pi/2 - u

which gives me

$\int_{0}^{\pi} \ f(x),dx = 2\int_{0}^{\frac{\pi}{2}} \ f(\frac{\pi}{2} - x) ,dx$

[flat frigate]

Curry

[unique quiver]

but I am not sure where to go from here

[flat frigate]

Curry

[unique quiver]

this was how I split the integral

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[unique quiver]

<@&286206848099549185>

Apologies for the ping

I feel this is short and I am doing something very silly

Just came back to the problem again anything would be appreciated

[cobalt niche]

remember the f(x+a-b) formula?

[unique quiver]

yeah

oh wait

[unique quiver]

do I make another substitution again with what I have on the right hand side?

that would give the required result

[cobalt niche]

hold on im lost asw

[unique quiver]

I feel like I have defintely done something wrong

[cobalt niche]

im getting x-pi

instead of pi-x

[unique quiver]

as in the substituition to make?

[cobalt niche]

yh and idk why

[unique quiver]

hm

what have you done?

[cobalt niche]

shamelessly assume f(pi-x) = f(x - pi)

cause i cba

[unique quiver]

yeah that is a very bold assumption

It's better than nothing tho 😭

thank you

[cobalt niche]

i mean x is in [0, pi] so we might aswell

[unique quiver]

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[cobalt niche]

lets go boys we did it

[unique quiver]

😭

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[ocean tapir]

can someone help me w this

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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

[tardy mango]

Draw free body diagrams for both and use F=ma for both

[ocean tapir]

ok but can u define tension for me pls

i've had a hard time understanding what it really is

[tardy mango]

tension force comes from when you stretch smthn like a string or cable

[shrewd solar]

tension is not an independent force

[ocean tapir]

okay so what is ma + mg

do i have to apply it to find t

or smthn?

[shrewd solar]

ma + mg is m(a+g)

not sure if that the answer to your problem, that is just what ma+mg is

if you want better help with physics you could try the physics server

link in #old-network

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[oak violet]

i think its all correct but it seemed too easy..

[severe pond]

this is correct

[oak violet]

hm

im not surprised

my math checked out but like

it was deceptively simple yknow?

[severe pond]

yea probably just testing the notation

[oak violet]

thanks lol

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[fleet gull]

hey

[magic junco]

yes?

[fleet gull]

hey this is gonna seem kinda odd but i have a biology question

none of the bio chats are responding to me

[shrewd solar]

what biology question

[fleet gull]

one sec

idk if im doing the punnett square right tbh. None of the types of inhertaince seems to make sense in this problem

[last condor]

ITs right

[last condor]

is that Ap Bio 🗿

[fleet gull]

no its regular bio

its my worst class by far

[last condor]

oh my bad

[last condor]

Wait four years, because I'm starting college this year and majoring in biological science. Then I'll help you.

[fleet gull]

lol

thanks for trying ig

[last condor]

You can look up some videos on youtube

about that topic

[fleet gull]

alr thanks

[last condor]

np

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[void plaza]

This is what I did

Is f'(0)=0 when x=0 and f'(0)=17/2 otherwise?

When x approaches 0

[pliant egret]

f'(0) cant be 0 and 17/2 at the same time

you only showed that limit x->0 f'(0)=17/2

[void plaza]

If the limit x->0 of f'(x) is 17/2 does that not mean f'(0) is 17/2

[pliant egret]

the limit doesnt indicate value itself

[void plaza]

So how would I find the value of f'(0)

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[void plaza]

<@&286206848099549185>

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[steep vessel]

f'(0)=17/2
Usaly how you are supposed to do peice to show dirivitives you should do
Lim h->0+ (f(h)-f(h))/h
And lim h->0- (f(h)-f(0))/h
But if lim x->y+ f(x)=lim x->y- f(x) then lim x->y f(x) is possible

[void plaza]

So I need to show the limit approaching 0 from above is equal to the limit approaching 0 from below?

And both equal to 17/2

[safe radish]

@void plaza Has your question been resolved?

[safe radish]

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[mortal rampart]

Hi, I've been having trouble doing this question, heres a screenshot of the problem and an explanation of the same problem with different numbers from my professor.

[steel stag]

just from plugging into a computer maybecheck if it should be tan-1(-1/3) instead

[mortal rampart]

Sure

its still incorrect

<@&286206848099549185>

[safe radish]

@mortal rampart Has your question been resolved?

[safe radish]

@mortal rampart Has your question been resolved?

[mortal rampart]

<@&286206848099549185>

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@mortal rampart Has your question been resolved?

[safe radish]

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[tardy violet]

hello is there a fast way to do this

[fleet orbit]

do you know this formula :
floor(x/p) + floor(x/p^2) + floor(x/p^3) + ....

i forgot its name

[tardy violet]

nope no clue

[fleet orbit]

yeh its the formula

where p is a prime number

in this case its 2

[tardy violet]

whats x meant to represent

[fleet orbit]

10

[tardy violet]

wait the question is structured weird, it's meant to be "Find the largest power of 2 that is a divisor of 10!"

[fleet orbit]

yeh

[tardy violet]

oh

wait then wat does the floor mean

[fleet orbit]

it would be floor(10/2) + floor(10/4) + floor(10/8)

floor (1.2) = 1

for example

its int in python

( kinda different but yeh )

[tardy violet]

uh sorry i dont do coding

[fleet orbit]

its basically a number without the floating part

[tardy violet]

oh

[tardy violet]

wait but wudnt that go on forever

like when does it stop

[fleet orbit]

yeh but after some time

it would be 0

floor (10/16) = 0

and floor (10/32) = 0

and so on

[tardy violet]

isnt that 5/8 which is more than zero??

[terse lichen]

is the answer for i. 3..?

[fleet orbit]

yeh but its floor

[tardy violet]

its 8

[fleet orbit]

it removes the floating part

[tardy violet]

wait like the exponential part??

[fleet orbit]

floor(0.8) = 0

[tardy violet]

damn idk that notation

[terse lichen]

is it asking for the power

or the number

[tardy violet]

power

[terse lichen]

cause 2^3 = 8

[fleet orbit]

no

the decimal part

[tardy violet]

how is the decimal part floating

[fleet orbit]

mb it is called that in programming ...

[tardy violet]

oh😐😐

[terse lichen]

so 3 is an answer right..?

unless it wants powers of 2 be 1, 2, 4, 8, 16 and so on

[tardy violet]

wait wat it only says 8 is the answer for part i

like 2^8 is the answer

idk

[fleet orbit]

yeh it is

5 + 2 + 1 + 0 + 0 ... = 8

[tardy violet]

?!?!?! i still dont understand that floor notation

wait what is the formula meant to find

[terse lichen]

oh yeah 8 is the answer

[tardy violet]

pls help i dont understand 💀

[terse lichen]

because 10! = 10 * 9 * 8 * 7 * ... * 1

[tardy violet]

yea

[terse lichen]

then inside all those numbers, find the numbers that have 2 as a factor

so 10 is 2*5

that is 1

8 is 2^3

6 is 2*3

[fleet orbit]

lemme send you a link

[terse lichen]

then just multiply all those powers of two together

[fleet orbit]

https://mathcentral.quora.com/What-are-the-prime-factors-of-50-factorial

[terse lichen]

or add i should say, exponential laws

[tardy violet]

isnt that like 5+3+3

which is 11

wait

[terse lichen]

no

look at the powers

10 only has 2 to the first power right?

[tardy violet]

OHHHH

oops

[terse lichen]

because 10 = 2*5

[tardy violet]

alr thx

[terse lichen]

8 has 2 to the power of 3, so its 3

[tardy violet]

soz i read it as 10^5 oops

[terse lichen]

yeah then you just continue it like this

add the powers of 2 together

[tardy violet]

oh it is 8

ohhh okok i see thanks for helping guys

.close

[safe radish]

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[winter kernel]

Theory Help

[winter kernel]

f(x) = 2x^2 + 2x + 2

let a and b be the zeros

[frozen marlin]

so f(x) = 2(x+0.5)^2 + 0.5

right?

[winter kernel]

I apply quadratic formula and get +- for both a, b

[frozen marlin]

!show

[safe radish]

Show your work, and if possible, explain where you are stuck.

[winter kernel]

those are the factors

[winter kernel]

let me finish

when I multiply them together, I am getting

x^2+x+1

[frozen marlin]

ok wait before we start
i think it's worth mentioning that this doesn't have any real solutions?

[hidden mist]

are those roots even real

[frozen marlin]

no

that's my point

[hidden mist]

yeah thats what im talking abt

[frozen marlin]

you don't even need to solve to see that

[winter kernel]

they aren't

[hidden mist]

b^2-4ac is clearly less than 0

[winter kernel]

I get sqrt{-12}

[frozen marlin]

wow

[winter kernel]

in the 4ac

[frozen marlin]

bro

that's what we're SAYING

[winter kernel]

yes

[hidden mist]

ay chill

[frozen marlin]

?

this doesn't have any real roots

[winter kernel]

Why does it matter that they aren't real roots?

[frozen marlin]

try completing the square

you'll see why

[winter kernel]

and if they were real roots, would I get the complete f(x) back?

[frozen marlin]

i mean if u want x-intercepts on ur graph ur gonna need a graph in C^2 instead of R^2

[frozen marlin]

wat?

[winter kernel]

(x-a)(x-b) = f(x)

[frozen marlin]

yes

what

no-

what???

[winter kernel]

why not?

[frozen marlin]

okay wait wait wait

[hidden mist]

Completin the square

[frozen marlin]

(x - a)(x - b) is the factorized form

[hidden mist]

might help

[frozen marlin]

exactly my point

[winter kernel]

idk what that means?

[frozen marlin]

don't try to factorize this--it isn't possible

[hidden mist]

can u tell him what is completin gthe square-

[frozen marlin]

...

it's hard to explain

u try

[hidden mist]

thats why I told u

[frozen marlin]

xD

[winter kernel]

hold on I'm reading

[frozen marlin]

ok

[hidden mist]

wouldnt the x coefficient be root2 here then

[winter kernel]

it's basically representing ax^2+bx+c in the form a(x + h)^2 + k

yes?

where a, h, k are coefficients

[frozen marlin]

sort of yes

basically, yes

[winter kernel]

ok another question relating to it then

[frozen marlin]

like

x^2 + 6x - 7 = 0
can be turned into (x+3)^2 - 16 = 0

[frozen marlin]

fire away

[winter kernel]

where did the coefficients of h and k come from
a, I understand

[frozen marlin]

look at this example.

we know 6x is a term in (x+3)^2

BUT instead of 9, we have -7

that means we subtracted 16
so we do that

hope that helps

i gtg, sorry.

maybe snow can help

[hidden mist]

Ok we'll try

[frozen marlin]

ok ty

[terse lichen]

what was the original question here?

[hidden mist]

no tsure

[winter kernel]

scroll up and read :p

[hidden mist]

thats all I saw

so probably find a and v

b

[terse lichen]

idk man yall jumped from imaginary roots to factoring to completing the square

[hidden mist]

its imaginary

so theres no factorizing

[winter kernel]

you cant factorize imaginaries?

[winter kernel]

hold on I'll restate the question

[hidden mist]

I guess no???

[winter kernel]

hm, ok

[hidden mist]

how do u find roots

it will be going into complex numbers

[winter kernel]

Main question, I have this, this from the form of (x-a)(x-b) where a and b are zeros of f(x)=2x^2+2x+2

I got the value of a and b from the quadratic formula
However, when I do (x-a)(x-b) I get x^2+x+1 !=! f(x)
why?

@terse lichen

[terse lichen]

lemme simplify those roots and stuff brb

[winter kernel]

k

[hidden mist]

thats basically complex numbers-

[winter kernel]

exactly

[hidden mist]

ren and I thought u arent supposed to go into complex numbers

[winter kernel]

so they can't be factorized, but I'm multiplying them

[winter kernel]

would be best to avoid them yes

.close

[safe radish]

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[harsh olive]

fourteen identical objects is given to three people.

probability that one person misses out?

[harsh olive]

i got (3c2 * 15) / (16!/(14!*2))

or 3/8

[dense prism]

How did you arrive at this expression

[harsh olive]

i thought once you choose two people to split the objects between

it would be a 14 object between two people stars and bars question

so the numerator is that

[dense prism]

if you assign 0 objects to one of the chosen 2, then 2 people will be missing out, but it says ONE PERSON misses out

And what's the denominator

The objects are alike

And 14 in number

So the total ways should be number of ways to express 14 as a sum of 3 ordered whole numbers

[safe radish]

@harsh olive Has your question been resolved?

[harsh olive]

oh okay that was what i was missing

[harsh olive]

i dont get this tho

cos distributing 14 objects between 3 people is like arranging 2 identical separators between 14 identical objects

thats how i got 16!/(14!*2!) for total

[harsh olive]

so do i just subtract that in the numerator? so 3*15 - 3

[dense prism]

Yeah that is correct, earlier ig you had written something else

[dense prism]

Yeah you can do that

[harsh olive]

oh yeah i typed 4! instead of 14!

[dense prism]

Or just 3c2 * 13 the start

[dense prism]

Same thing

[harsh olive]

ok thanks

.close

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[covert talon]

hui

hi

[covert talon]

how do you find the equation of P(-7,3) and R(8,-12)

ik the gradient is -12-3
8--7

which is -1

but for the y intercept

do i use any point?

[thin bridge]

yes, using either is fine

[safe radish]

@covert talon Has your question been resolved?

[safe radish]

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[brave narwhal]

Can somebody tell me what could be wrong in here?

[brave narwhal]

I did check the answer in a math website and the answer is instead -42

a friend of mine did it like this, there's a slight difference which is when we did gauß method... idk what could possibly make it wrong in my calculation

<@&286206848099549185> Deutschsprachige Helfer:innen sind auch herzlich willkommen, wenn du mir auf Deutsch helfen möchtest ☺️

Sorry but i don't know how to read and/or implement that one😭

[brave narwhal]

yeah but here my friend did the exact same thing, the difference is only when he implemented gauß method to get more 0 inside the matrix, do you see the difference?

he said he didn't include -1...

[safe radish]

@brave narwhal Has your question been resolved?

[brave narwhal]

it is because our gauß is kinda twisted: he subtracted II other rows and I subtracted other rows with II

@young nexus sorry I think it was a misunderstanding, I noticed what you noticed but it was all because of this difference in the approach while doing gauß, it makes me confused. Yes I understood what's in the wikipedia page as well, my friend there, he didn't plan to multiply it with -1 in the first place that's why I'm confused, I'm sorry I think I might have made everything more confusing. You don't have to continue helping if you don't want to, I just wanna say this🙏

.close

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[brave narwhal]

@young nexus now I know why it seemed like so... he told me this, he multiplied 1 with -1 before he went with gauß, I didn't do that that's why I still need to multiply with -1 after I did gauß. Yes I understand everything.

I just wanted you to know I'm so sorry, thank you for your help

[safe radish]

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[ivory iron]

pls help

[dusk gate]

There has to be more information

Oh wait.. it's just a measurement problem.. bottom right

Got a ruler?

[safe radish]

@ivory iron Has your question been resolved?

[safe radish]

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[brazen parrot]

excuse me

[brazen parrot]

how do i do thsi

[stark stratus]

Factorials

Weirdly phrased

So theyre in a row with their colors? If thats the case then its 2+2+24

Which is 28

[brazen parrot]

without restriction

[stark stratus]

Oh well

8!

Plug into calculator

[brazen parrot]

wrong

[stark stratus]

Cause?

[brazen parrot]

the answer is 420

8! is 40320

[stark stratus]

Uhm

Ok

[brazen parrot]

uh...

[stark stratus]

Why is it 420?

[brazen parrot]

idk thats why im here

...

wait

i think ik

omggggggggggggg

OMGGGGGGGGGGG

I AM A GENIUSSSSSSSSSSSSSSSSSSSSSSSSSSS

[stark stratus]

Oh right lol

Damn im gonna need that for my exam too

Fuck

[brazen parrot]

this math sucks

bring me back to 7th grade algebra

[stark stratus]

That is worse

[brazen parrot]

NOOO I LOVE ALGEBRA

[stark stratus]

Geometry is so much better

[glass flame]

fym this the easier side 😭

[brazen parrot]

math got easier when they introduced letters

[brazen parrot]

no.

NO

[stark stratus]

Yeah

It is

[stark stratus]

Circles, kite, spirals, trig

[brazen parrot]

no I HAD TO DO PROOFS

[stark stratus]

Yikes

[brazen parrot]

proofs and circle theorems

[stark stratus]

Shit is easy bro. Thats the easiest part

[brazen parrot]

NO WTF

i like circle theorems

NOT PROOFS

[stark stratus]

We had like a whole true or false part, third of the exam

Proofs is easy if you know the theorems

[stark stratus]

Then proving

[brazen parrot]

no proofs are way harder

[stark stratus]

Then like an essay or whatever the fuck it was, then like drawings

Drawings are so fun

Well solving the arcs and angles i mean

[brazen parrot]

how is this easy

proofs

[stark stratus]

I cant draw for shit

[brazen parrot]

legit suffered in this test

😭

[stark stratus]

This shit is so easy? Contrapositives is just glorified english tests

[desert pasture]

doesn;t look too bad

[brazen parrot]

NOOOOOOOOOOOOOO

I WAS SUFFERING

WE ONLY HAD 25 MINUTES

[desert pasture]

ok, that sounds a bit messed up

[split fulcrum]

get an indian math student to sit it for you

ez

[brazen parrot]

FR

the indian kid in my class

IS A GENIUS

[split fulcrum]

lmao

[brazen parrot]

bro it is

thats the non calc section

[stark stratus]

Wtf you just reverse this shit

[brazen parrot]

the circle part is the calc section

[stark stratus]

If q is not equal to p, then p is not equal to q

How hard is that

Just do same shit

[brazen parrot]

ITS HARD WHEN U HAVE 25 MINUTES OK

i was sweating

[stark stratus]

If n is odd, then that weird equation im not typing out is even

Thats it

[split fulcrum]

knees weak palms are sweaty

[stark stratus]

ALl you gotta do is calm yo titties

[brazen parrot]

no

[stark stratus]

A is what i said
B is literally picking a random odd number then plugging it in

[brazen parrot]

the prove part

my hand started cramping

[stark stratus]

Yikes

Not that deep cuh

Bros hand started cramping

Its never that serious

[brazen parrot]

I WAS WRITING FAST

[split fulcrum]

sit ext 2 hsc fr

[brazen parrot]

nah

do not even

talk about HSC rn

idc LAST YR I HAD AN AVERAGE OF 99%

[stark stratus]

I mean honestly this shit is just

What level are you?

[brazen parrot]

AND THEN I GOT 68%

[stark stratus]

Bro

[brazen parrot]

im in 10th but im taking accel

[stark stratus]

This is accel for yall?

[brazen parrot]

no im only accel the class is normal

[stark stratus]

The fucking boys at the back of my class can answer this while wiping the shit from their ass

[brazen parrot]

bro im starting on vectors tmr and i havent even finished combinatorics

im gonna cry myself to sleep

[split fulcrum]

stop glazing

[brazen parrot]

and i have a physics test tomorrow

[split fulcrum]

nuclear lol

[stark stratus]

Im the boys at the back, i average a 98

[brazen parrot]

YES CHERNOBYL SH

[stark stratus]

Shoulda been 99

I had 1 mistake for the entirety of the quarter

ANd it was on a meaningless book activity

[brazen parrot]

the average for this test was 41 LOL

[split fulcrum]

blud said its ight

[stark stratus]

Lol the teachers remarks

[brazen parrot]

no thats mine

LOL

[stark stratus]

"Reflect on yourself" this shit is 10th grade math

[brazen parrot]

my friend got 10% i felt so bad

[stark stratus]

It is NEVER that serious

[brazen parrot]

YES IT IS SERIOUS

cuz what if it comes up in my exam

I WILL DIE

[split fulcrum]

its always serious everyhing is serious you die if you get things wrong its like squid game

their school is squid math

[brazen parrot]

my skl makes the tests hard on purpose though

so our school marks get scaled up

[stark stratus]

Bro is not in squid game

[brazen parrot]

when we do well on the exam

[split fulcrum]

million dollar prize

[stark stratus]

Btw thanks for that flag question, i need that shit

[brazen parrot]

nws man

[stark stratus]

Upcoming exam and i usually dont study for math exams but i get the feeling imma need to actually read some shit this time

Trillion fucking formulas

[split fulcrum]

if ur the boy at the back u dont need to study

[stark stratus]

Nah id win

[brazen parrot]

i cant wait for

calculus

apparently its way easier than all of this stuff

[desert pasture]

that's fun

it's hard

but fun

[brazen parrot]

naw they introduce it to us slowly

its easy this year

[desert pasture]

especially integral calculus

[brazen parrot]

next year it'll get hard

[split fulcrum]

and real analysis fftr

[brazen parrot]

its just questions like this lol

[desert pasture]

oh

[brazen parrot]

ok thx guys

i need to do more questions

or ill fail my next test

.close

[safe radish]

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[desert pasture]

I was expecting something like $\int \frac{\left(x+1\right)}{x\left(1+xe^x\right)}dx$

[flat frigate]

Why am. I here

[split fulcrum]

so ez just pfd fr

[desert pasture]

nah, there's a better way

notice xe^x's derivative is just (x+1)e^x

that's helpful

[split fulcrum]

then u sub ?

[desert pasture]

yeah

I think so

been a while since I did this

and too lazy to redo it right now

or even better ln(x)=y

[desert pasture]

yeah, try ln(x)=y

that works better

[split fulcrum]

where is lnx here?

[desert pasture]

not there

but

x=e^y, and e^x=e^(e^y)

try it

[safe radish]

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[lone arch]

"As part of the art activity, a cube-shaped tent should be built on the ground (at x = -3.4) within the sculpture. Determine an equation that can describe the edge length of this tent. Neglect the thickness of the edge structure" .

[lone arch]

My book says it's 2 * f(x) = sqrt(2) * (x - (-3.4))

Why is it not just 2 * f(x) = x - (-3.4)?

[lone arch]

TThe two ellipses here indicate the entire sculpture

[safe radish]

@lone arch Has your question been resolved?

[safe radish]

@lone arch Has your question been resolved?

[lone arch]

<@&286206848099549185>

[desert pasture]

why would a cube shaped tent have ellipeses ?

[safe radish]

@lone arch Has your question been resolved?

[lone arch]

It's just to visualize that we're in 3d

[safe radish]

@lone arch Has your question been resolved?

[safe radish]

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[compact solar]

Im not sure how to do this at all. I understand how theorem 12 works but not with 2 unkowns

[uneven tree]

hello

[compact solar]

Hey

[uneven tree]

I'm not sure what theorem 12 is

[compact solar]

This is what I learnt

[uneven tree]

Ok :)

.status

!status

[safe radish]

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

[uneven tree]

ok :)

which sides are proportional in our figure?

according to our theorem

[compact solar]

?

Not entirely sure what you mean?

[uneven tree]

our theorem says

$$\frac{|AD|}{|DB|} = \frac{|AE|}{|EC|}$$

[flat frigate]

dp

[uneven tree]

in our figure, what is the value for AD,DB,AE, and EC?

[compact solar]

It would be x over x+4 = 12 over 18

I assume

[uneven tree]

it would be

$$\frac{x}{x+4} = \frac{12}{18}$$

[flat frigate]

dp

[compact solar]

Yeah

[uneven tree]

Now we just have to solve for x :)

[compact solar]

Thats where Im lost

[uneven tree]

ok :)

we can multiply like this

$$18x = 12(x+4)$$

[flat frigate]

dp

[uneven tree]

we can multiply the right hand side

$$18x = 12x +4 $$

[flat frigate]

dp

[uneven tree]

And I assume you know where to go from here :)

[compact solar]

I understand how to get x from here. but how did you get to this point?

[uneven tree]

if we have $\frac{a}{b} = \frac{c}{d} \text{, then } ad = bc$

[flat frigate]

dp

[uneven tree]

we can prove it very easily

[compact solar]

Ohhhh cross multiply

I understand

[uneven tree]

Yeah :D

[compact solar]

Thanks man

[uneven tree]

np :)

[compact solar]

appreciate it so much

.close

[safe radish]

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Closed by @compact solar

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[safe radish]

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[oak violet]

did i get all the coords?

this one too

i think both are correct but i just want to check

[safe radish]

@oak violet Has your question been resolved?

[oak violet]

<@&286206848099549185>

[oak violet]

.close

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[lime hound]

I’m trying to practice for my exam next week and I am absolutely lost with chain rule/product rule/differentiating functions as a whole. On the homework I’ve been kind of guessing and getting it right but I want to know why I’m getting it right.

[tardy mango]

product rule: $$f'(x)=e^x \frac{d}{dx} \left[\sin(x^2) \right]+\sin(x^2) \frac{d}{dx} e^x$$

[flat frigate]

Civil Service Pigeon

[tardy mango]

do you see how I got this?

[lime hound]

I kinda just stare at the problem and don't know where to start

[tardy mango]

so yes or no?

[lime hound]

no

[tardy mango]

this is a product of two functions, namely e^x and sin(x^2)

so that's why we chose to use the product rule

better?

[lime hound]

I see I see

Yeah I can understand that

When would you want to use chain rule?

[tardy mango]

lol you actually use it here

so now we need to compute those two derivatives

of sin(x^2) and e^x to finish

Imma start with $\frac{d}{dx} e^x$ b/c that's easier

[flat frigate]

Civil Service Pigeon

[tardy mango]

what is this derivative?

[lime hound]

I have no idea

[tardy mango]

that's one of those common derivatives you just need to know

$\frac{d}{dx} e^x=e^x$

[flat frigate]

Civil Service Pigeon

[tardy mango]

you can prove it but I'l leave that to you to search up later if you want

$f'(x)=e^x \frac{d}{dx} \left[\sin(x^2) \right]+e^x \sin(x^2)$

[flat frigate]

Civil Service Pigeon

[tardy mango]

now we have this

now, for this derivative, we need to use chain rule

any idea of how you would set that up?

if you're not sure for this particular example, tell me what you know about setting up the chain rule in general

[lime hound]

I would use the derivative of sin no? and then put it to x^2cos(x^2)

[tardy mango]

close but no cigar

how did you set it up?

[lime hound]

on paper or how did I get there

[tardy mango]

how you got that

unless you want to write how you got it on paper and send it

whatever floats your boat

[lime hound]

in my notes I was given some derivatives for certain functions and I looked at a question I recently answered and got correct

it was just f(x)=sin(e^x) and the answer was e^xcos(e^x)

so I applied the same rule

[tardy mango]

yeah that's b/c the derivative of e^x is e^x

tell me what you know about setting up the chain rule in general

[lime hound]

the most I know is just some derivatives, I have trouble plugging everything in

[tardy mango]

composition of functions

does this sound familiar

[lime hound]

from precal yeah

[tardy mango]

do yk how it relates to the chain rule?

[lime hound]

I do not

[tardy mango]

https://tutorial.math.lamar.edu/classes/calci/chainrule.aspx

It'll be more helpful with lots of examples

so here you go

[lime hound]

Thank you so much

[safe radish]

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[tame zephyr]

is isomorphism basically just bijection??

cause surjective and injective

lollol

[sharp tundra]

Not quite, it also needs to preserve addition and scalar multiplication

Which is what linear transformations do. ie, any bijective function V to W is not necessary an isomorphism, but any bijective linear transformation V to W is an isomorphism.

[tame zephyr]

ahh ok

even this theorm lolol

reminds me of cardinalities..

how for countably infinite sets, they must have the same cardinality iff its bijection

[sharp tundra]

Right. Same cardinality does not, however, necessarily mean isomorphic vector spaces. For instance, R^2 and R both have the same cardinality, but as R-vector spaces, they are not isomorphic, since their dimensions are different.

[safe radish]

@tame zephyr Has your question been resolved?

[tame zephyr]

i'll stay here for a bit

[safe radish]

@tame zephyr Has your question been resolved?

[safe radish]

@tame zephyr Has your question been resolved?

[tame zephyr]

for c), if Ker(T) requires all constant polynomials and range(T) requires all zero constant terms...

you cant have a polynomial that satisfies both ker, and range...

so

thats ok right?

thats allowed because for i) which is not in range(T), that would just mean nullity = 3 and rank =0

<@&286206848099549185>

[tame zephyr]

what do you mean.. @junior smelt

[junior smelt]

(there is one exception, the zero polynomial but otherwise yea )

[junior smelt]

And well the nullity is 2, rank 1 here (e.g. x and x^2 are in the range of T, 1 is in the kernel of T)

[tame zephyr]

ahh yes

ok

thank you

[junior smelt]

(also respond to the bot just in case it closes the channel )

[tame zephyr]

and for nullity and rank you just find the dim of the basis

[junior smelt]

You can sure [of the kernel and image respectively]

[tame zephyr]

for T: V->W I can say range(T)=dimension of basis for W right.. (Im not sure if basis is the right word, but R^2 =2, 2 by 2 matrix=4, P_2=3) if V maps W(so all V(x) in W can be mapped by an x in V)

yes, i think so

[junior smelt]

The range is the dimension of the image of T, said image is a subspace of W (but needn't be all of W if T isn't surjective)

[tame zephyr]

linear algebra is giving me depression

[junior smelt]

Awwwww

[tame zephyr]

hahah no but in all seriousness,

i wont be messed with

so

lin alg better watch out hehe

[junior smelt]

Hehe