help-49

[subtle blaze]

Sort of like pinning it on X then rotating it a bit

Which side would coincide with DF?

[echo zodiac]

i cant understand the rotating stuff

[eager fjord]

CB..?

[subtle blaze]

Yup

And in terms of the congruency notches

[eager fjord]

yea it lines up

[subtle blaze]

They both have 3 notches

[eager fjord]

so its 3.6?

[subtle blaze]

So those are the “equal length” line segments in the diagram

Yep

[echo zodiac]

wait

[subtle blaze]

3.6

[eager fjord]

rigt

wait

bruh that was ... not hard lol

[echo zodiac]

im dumb they both are congruent

by SSS

i thought it was

tough

[eager fjord]

i forgot all that SSS SSA stuff a whole ago

while

[subtle blaze]

Nope it’s not hard just gotta read it through and process what the problem is!

[echo zodiac]

i got carried away by angle stuff

[echo zodiac]

SAS

or SSS

FOR SURE

[eager fjord]

but theres 3

[echo zodiac]

WHat is HL

[eager fjord]

hypot length

i think its that, ssa, sas

or ass

[echo zodiac]

YEH hl

also

[glossy ibex]

I think SAS, SSS, HL

[eager fjord]

yea

imma try that

wish me luck!!

[echo zodiac]

yeh yeh

[glossy ibex]

Vine boom

[echo zodiac]

is that ur postgraduate question

[eager fjord]

lol no

silly story actually

a friend made me bet that i hadnt forgoten basic geometry bc we are studying diff geo

so i guess i have to pay him now..

[glossy ibex]

Just get good and never forget anything, truly a skill issue

[echo zodiac]

i was like how tf a post graduate student is not able to solve 3-4 grade problems

[eager fjord]

so true

[eager fjord]

well technically its grade nine but i did geometry in 5th and algebra 1 in sixth

[eager fjord]

you know what they say us fancy math folk are good at symbols

but not numbers

[echo zodiac]

in india we get this in 4-

[eager fjord]

tee hee

[eager fjord]

bruh yall are so gifted

[glossy ibex]

Wish I lived there

[eager fjord]

(you should conquer america)

isint the education system on fire rn?

[echo zodiac]

my mother was a math teacher she did her post grad in math

and taught me math

[glossy ibex]

Oh checks out

[eager fjord]

wow

what field?

like what subfield fo math

[echo zodiac]

topolgy

[eager fjord]

wow!!!

[echo zodiac]

and some other feild

and u know what was the funny part

i was the smartest one

in math in my whole class

but got like 10%

of the marks in

test

and i was able to solve difficult

problem

ezly

[glossy ibex]

Blud got the Einstein myth type marks

[eager fjord]

yea

ask her if the unit circle is path connected

shell be impressed

[glossy ibex]

Time to google what in the world that means

[eager fjord]

or if every compact set necessarily closed

[eager fjord]

path connected means like no holes (gross simiplification)

[glossy ibex]

Ah

[echo zodiac]

what are u doing rn

[eager fjord]

in school?

[echo zodiac]

like carrer wise

[eager fjord]

im going to be an ai researcher at a SV corp after i do post grad

[echo zodiac]

post grad in what

[eager fjord]

you shold study math then come to America

[eager fjord]

differential geometry

with focus in Machine elarning

[echo zodiac]

brother i saw ur syllabus

it was

shit

like

what u study in high school

we study that

[eager fjord]

really?

thats shocking

ok quiz question;

[echo zodiac]

in grade 6-8

[eager fjord]

Is the domain of a function isomorphic to its graph?

5

4

3

2

1

fail tee hee

[eager fjord]

you may be thinking regular geoetry

this is multidimensional curved geometry

[glossy ibex]

Imma just go to sleep, goodnight you two

[eager fjord]

good night!!!

https://tenor.com/view/blåhaj-haj-mobil-weeeeee-speed-driving-gif-5591280404365460062

[echo zodiac]

i m cooked

[echo zodiac]

its good morning in here

[eager fjord]

where?

kya territory me rehthe hai

[midnight plank]

@eager fjord Has your question been resolved?

[midnight plank]

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[bleak pier]

What should I do next?

[twilit field]

The question is basically saying the determinant is more than 0, right?

[bleak pier]

Yes

[twilit field]

Hmm , am > gm perhaps

[bleak pier]

I see

Why it comes to mind?

[bleak pier]

t^3-3t+2>0

.close

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[prime salmon]

how do you solve this?

[midnight plank]

Please don't occupy multiple help channels.

[prime salmon]

helpp

aaaaaaaaaaaaaaaaaaa

[midnight plank]

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[wanton juniper]

a

[midnight plank]

Please don't occupy multiple help channels.

[wanton juniper]

this is the anwser key I dont get how they got anwsers

[unreal light]

angle AOB = 60 means triangle AOB is equilateral

Since AO = OB (radii)

[midnight plank]

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.

[wanton juniper]

sorry

[wanton juniper]

ok then

how do we get AB

[unreal light]

triangle AOB is equilateral

[hexed harness]

Since all angles are 60° , the opposite side of each angle is same length

[unreal light]

all sides equal

[wanton juniper]

well the angle is 60 and lenth is 6

[wanton juniper]

oh ok

[hexed harness]

Yes

[wanton juniper]

so how is that possible

[hexed harness]

In figure length of AO already given , which is 6

[wanton juniper]

yes

[hexed harness]

So ultimately length of each side of AOB is 6

[wanton juniper]

how tho

so the opposite is same?

[wanton juniper]

yo can u help me part b.

[unreal light]

BOC is a right isosceles triangle at O

[wanton juniper]

yes and BO is congruent to OC

[unreal light]

Use Pythagoras to find expression for BC

[wanton juniper]

but dont we need 2 lenths

[unreal light]

Yes

[wanton juniper]

How do we know what OC is?

[unreal light]

AO = BO = CO = DO = 6

It's a circle bro

[wanton juniper]

I see

I get it

[hexed harness]

Since we see all angles are same , so this is equilateral triangle, and length of AB is 6

[wanton juniper]

yea I see

since its a circle al radius = lenth

[hexed harness]

Yes

[wanton juniper]

yo

can u help me in this

[wanton juniper]

!

[unreal light]

Yes

[wanton juniper]

Do u know hwo to do this

[unreal light]

Yes

[wanton juniper]

Can u tell me how u did it step by step

[unreal light]

Boba did it for you

[wanton juniper]

Oh I see it

the paper

[wanton juniper]

yes

[hexed harness]

Is it clear

[wanton juniper]

I dont get still

what was the 1st step u did

[hexed harness]

See OP is the sum of radius of both circles

[wanton juniper]

oh I see then u did 10+5

I get it

[hexed harness]

Yes 👌

[wanton juniper]

ok lets do 16!

🙂

[hexed harness]

🙂‍↔️

[wanton juniper]

🙂

[wanton juniper]

u very good teacher

[hexed harness]

Thanks for your words 🙏😄

[wanton juniper]

Who can help me

[wanton juniper]

help me pls

I beg on my hands and knees

[hexed harness]

For 16 just wait a minute, it's almost finished

[wanton juniper]

kk!!!

[hexed harness]

Sending

[wanton juniper]

thanks!

[wanton juniper]

how u know TV and SR supplementry

[hexed harness]

In question it's given that TU and SR two different tangent lined and SR divides TU in two parts

[wanton juniper]

Oh I see

[hexed harness]

Check is it clear to you or not

[wanton juniper]

ok I am proccesing it

[hexed harness]

👌

[wanton juniper]

Ok I understand it!

Thank you soo much dude!

u were extremly helpfull

and helped me a lot

https://tenor.com/view/cat-gif-7898695231799564452

[hexed harness]

🙏 feeling blessed to help you

[wanton juniper]

ty I hope u have a great rest of ur day

[wanton juniper]

oh u also did the next 1

[hexed harness]

Yes 🤣

[wanton juniper]

Now number 17 is much more clear to me

TYSM

🙂

[hexed harness]

Hmmm good to hear this

[wanton juniper]

ok tysm and bye I gtg sleep

thanks a lot

bye!

[hexed harness]

Ohh good night 🤣

For me , it's a good evening 🤣🤣

Different time line 🫠

[midnight plank]

@wanton juniper Has your question been resolved?

[midnight plank]

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[bleak pier]

What will be the ratio of circumradius inradius and exradius of right angle triangle?

[bleak pier]

√2+1:1:x?

What will be x

[midnight plank]

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[bleak pier]

.close

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[midnight plank]

Please don't occupy multiple help channels.

[bleak pier]

Here need to find general solutions

B and d looks same

[nova yoke]

they are

another poorly formed question

[bleak pier]

🥲🥲

It looks [e-mail]

@nova yoke

,w √3secx+tanx=0 general solution

[grand pond]

Results provided by WolframAlpha

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

Requested by doctcieu

[bleak pier]

.close

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[slow moon]

help me for this please

like step for step

so far i’m here

i found the partial dericitives

i need to confirm if they are right

[tribal tartan]

looks good

[slow moon]

okay now imma try to find

lamda

now to neutralize?

[tribal tartan]

looks right

prob use the constraint now

solve for either x or y in terms of the other

[slow moon]

why can’t u just put it in the partial derivitve of lamda

like sub it in that one?

[tribal tartan]

yeah thats the same thing

you're using the lagragian function

the partial wrt to lambda is the same as the constraint

[slow moon]

oh okay, usually what is easier?

[tribal tartan]

theyre the same thing

the lagragian is a function thats specifically set up to contain all the information from lagrange multipliers

it just makes it easier to put into a computer

telling it to take the gradient and set it equal to the 0 vector

[slow moon]

oh okay

so i subbed it on

does this seem right

[tribal tartan]

the negative is outside the parenthesis

[slow moon]

oh

so it’s y= add or subtract 1/738

?

[tribal tartan]

yeah with the square root

[grand pond]

y0shi

[slow moon]

yass

okie i got it right

tysm

.close

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[slow moon]

this is where i am so far

is this correct so far

[tribal tartan]

mhm

simplify a bit then it should be pretty obvious where to go from there

[slow moon]

i’m ngl i have no idea how to equalize

what’s the process?

[tribal tartan]

we have $3xy^9=9y^7x^3$

[grand pond]

y0shi

[tribal tartan]

we can cancel out an x and a y^7 on both sides

[slow moon]

yeah

[tribal tartan]

so we'll have 3y^2=9x^2

[slow moon]

ohhh

[tribal tartan]

yeah and now you can use the constraint or partial wrt lambda

to solve for one of the variables

[slow moon]

this is enought to start subbing in?

[tribal tartan]

mhm

well maybe dividing out the 3

so like y^2=3x^2

you can sub that into the constraint

[slow moon]

like this?

[tribal tartan]

you forgot the 9 on the right hand side

[tribal tartan]

should be this

[tribal tartan]

then this

[tribal tartan]

works too

[slow moon]

leading to this?

[tribal tartan]

uhh no need for that

[slow moon]

oh ok

[tribal tartan]

remember that the constraint is x^2+y^2=1

you have y^2 in terms of x so

or x^2 in terms of y

[slow moon]

oh right

got this for y

[grand pond]

y0shi

[slow moon]

yeah

[grand pond]

y0shi

[tribal tartan]

and multiply by 3/4

[grand pond]

y0shi

[slow moon]

would this be right

i just kept going idk

[tribal tartan]

yeah y^2=3/4 and x^2=1/4

so you would have 4 solutions

since you can vary them

[slow moon]

we need f max

would this mean subbing in c^3y^9

[tribal tartan]

yeah so you would just test each point we got

until you find the one that gives you the maximum for f

if they all give you the same value, which it shouldn’t, you would have to pick some random point and compare it to our critical points

[slow moon]

like this?

and plug the posative in x^3y^9?

[tribal tartan]

okay so the 0.25 is x^2 not x

the 0.75 is also y^2 not y

[slow moon]

yeah

this is where i’m stifling

[tribal tartan]

so we would have $x=\pm\frac12$ and $y=\pm\sqrt{\frac34}$

[grand pond]

y0shi

[tribal tartan]

you plugged in 0.25 for x

plug these in instead

see how we have 4 possible points

we can have 1/2 and sqrt(3/4)

-1/2 and sqrt(3/4)

1/2 and -sqrt(3/4)

[slow moon]

like plug this in x^3y^9?

[tribal tartan]

and -1/2 and -sqrt(3/4)

yes

plug all the points i just listed into that

[slow moon]

like this?

[tribal tartan]

yep

[slow moon]

got this

would that be the awnser

[tribal tartan]

well we have to test all the other points too

[slow moon]

oh

damn

[tribal tartan]

$(\frac12,\sqrt{\frac34}),(-\frac12,\sqrt{\frac34}),(\frac12,-\sqrt{\frac34}),(-\frac12,-\sqrt{\frac34})$

[grand pond]

y0shi

[tribal tartan]

yeah all of those

[slow moon]

and then find the highest?

[tribal tartan]

mhm

that should be the max

tho these aren’t the only solutions actually

there are 4 others

but those will be 0 when we plug it into f

so we can ignore it since we aren’t looking for the min (those aren’t mins either actually)

[slow moon]

i think

like i just did it all

on photomath

the highest is 0.03425

and the lowest is the negative version of that

[tribal tartan]

alright that’ll be it then

that’s rounded i assume

since it should be irrational i’m pretty sure

[slow moon]

yass it’s correct

tysm

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[lofty beacon]

Solve the equation x^4 +
x^3 + x^2 + x + 1 = 0 in complex numbers.

[lofty beacon]

<@&286206848099549185>

[runic hamlet]

does 1+x+x^2+x^3+x^4 remind you of something?

[lofty beacon]

No

[runic hamlet]

what if I say the word geometric

[lofty beacon]

No ideas

[runic hamlet]

you havent heard of the geometric sum or geometric series?

[lofty beacon]

No

And how can this help to find complex roots?

[runic hamlet]

because it gives you a formula thats easier to work with

1+x+x^2+x^3+x^4=(x^5-1)/(x-1)

[lofty beacon]

Then the roots will be at the vertices of a regular 5-gon

Without a one

[midnight plank]

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[elfin fox]

Why does multiplying a matrix by an elementary matrix have the same effect as applying an elementary row operation onto the matrix?

[elfin fox]

I am looking for some intuition as to why this is true, rather than a proof.

[runic hamlet]

well just do the multiplication and see what effect it has on the entries of the result

[subtle blaze]

Because the act of “applying an elementary row operation” is actually just multiplying by a elementary matrix

[midnight plank]

@elfin fox Has your question been resolved?

[echo wharf]

I don't know if i can help any more than what has been stated but it might be worth thinking.
Suppose f(A) is some function f on matrix A.
Then, consider if f can be represented by some matrix B such that either f(A) is AB or BA.
Then, consider what function g which you can do to A such that there is no B such that g(A) is AB or BA.

[elfin fox]

Thanks I have to think about this

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[bleak pier]

Hints please

[bold beacon]

What is lim x->infinity x/(1+x)? different question but same idea

You can use a similar trick

[bleak pier]

Infinity/infinity

1/1

=1

@bold beacon

[bold beacon]

yep

[bleak pier]

1+1+1+1+.... divergent

[bold beacon]

yep

[bleak pier]

How did you find this example?

I meant what comes to mind

Can there be any other examples too?

[bold beacon]

When I heard the word divergent I was thinking something tending to infinity although that is not necessary

What about 1) does remind you of anything?

[bleak pier]

i am checking

n/(1+n+n^2)

by taking common n^2 demoninator

1/n...which is divergent

[bold beacon]

I was not thinking about that. If you divide by a_n you get sigma 1/(1/a_n +n). But this is just a shifted harmonic series

A harmonic series is always divergent

I am not 100% sure about my calculations. Will need to think about it

[bleak pier]

Yes

[bleak pier]

Yeah

Let me check second one

B will be convergent

1/n^2

By p test

[bold beacon]

sounds correct

[bleak pier]

Tq very much

.close

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[manic bison]

it seems simple but idk what to do

[unreal fjord]

Is R_f a range of that y?

[manic bison]

yea

[unreal fjord]

Ok... let's say we are working with real number, what is range of sqrt(x)?

[manic bison]

non negative numbers?

[unreal fjord]

yes

what about the range of sin(x)?

[manic bison]

from-1 to 1

[unreal fjord]

Now, think about it for a second. If I know that my x is between [-1,1] from the range of sin(x)... then what will be my range of sqrt(sin(x))?

or let say t = sin(x), what is the range of sqrt(t)

[manic bison]

uhhh

[unreal fjord]

but we know that t can only be in -1 to 1

[manic bison]

it will have some complex numbers ig

[manic bison]

yea

[unreal fjord]

so let's ignore things that is complex for now

let say we are dealing with real number

[manic bison]

yea

wait so

0 to 1?

[unreal fjord]

yes

[manic bison]

what about sin

(root x)

[unreal fjord]

same idea but now your input to sin(x) is from [0,inf)

(non-negative)

[manic bison]

still -1 to 1 right?

[unreal fjord]

yes

[manic bison]

tysm

.close

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[mighty zodiac]

29,30,31?

[midnight plank]

Please don't occupy multiple help channels.

[mighty zodiac]

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[wind oxide]

$$ 0 < x + \frac{1}{x} \leq 7, - 3 \sqrt{5} \leq x - \frac{1}{x} \leq 3 \sqrt{5}, x > 0 $$

[wind oxide]

range of $x^2 - \frac{1}{x^2}$?

[grand pond]

rak³en

rak³en

[jagged saffron]

where are these numbers coming from?

[bright shoal]

What

I have heard x+1/x>2

[wind oxide]

just a question

[midnight plank]

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[midnight magnet]

can someone help me out with this problem?

[midnight plank]

@midnight magnet Has your question been resolved?

[midnight plank]

@midnight magnet Has your question been resolved?

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@midnight magnet Has your question been resolved?

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[quaint whale]

<@&286206848099549185> can anyone pls explain to me when exactly we use a negative binomial distribution? It's very confusing for me.

[robust sphinx]

You flip a coin until heads appears k times

Crazy

I was literally reading about negative binomial 5 seconds ago

[raven abyss]

What

[quaint whale]

Woahh

So basically

[raven abyss]

!15min

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[quaint whale]

It gives us the probability of getting head k times, am I correct??

Or tails

Is it?

[robust sphinx]

Wait excuse me

let me type the formula

So

[quaint whale]

Okay

[robust sphinx]

P( X = K ) = (K-1) choose (n-1) * p^n * (1-p)^(k-n)

In the case of fliping coins p = 1/2

so similarly 1 - p is also 1/2

[quaint whale]

What does X= k random variable refer to?

I'm confused on that

[grim vector]

X= k is the probability that X = k, in binomial distribution

[robust sphinx]

The probability that it happends K times

[quaint whale]

What does 'it' means here?

[grim vector]

X is the random variable not k

[robust sphinx]

it means your random event

and p is its probability of happening once

You redo this event many times

[polar mortar]

in a binomial ditribution the random variable represents the number of 'successful' trials in a fixed number of tests.
negative binomial the random variable represents the number of tests needed to get a fixed number of 'successful' trials

[quaint whale]

So basically if we consider the case of a coin flip, X represents the no. of times a head occurs, right?

[quaint whale]

Oh I see

[quaint whale]

Wait

That definition does not match with the one Chris gave me

I'm so confused

[robust sphinx]

Where does it not match?

[quaint whale]

This seems completely different

[robust sphinx]

oh mb I think I misworded that

that might cause confusion

[quaint whale]

You said that it gives the probability that it occurs K times. The other person said that it gives us the probability that our preferred outcome is true after k number of times

[quaint whale]

Oh I see

[robust sphinx]

Whenever you heard the word negative in the name of a distribution

It means that it talks about the version of that distribution up until that number of times it happens

[quaint whale]

Got it! Thanks a lot!

[quaint whale]

Thanks to you to!!

[robust sphinx]

That's all i can help with. I am not the best with probability

[quaint whale]

.close

[robust sphinx]

I just literally had the formulai in front my eyes and you asked that question 5 seconds later xd

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[short ginkgo]

im confused

[short ginkgo]

.close

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[slate patio]

Determine an equation for a polynomial function with zeros -4 (order 4) and 2 (order 3)

[slate patio]

Does order mean to the power of? If so I have (x + 4)^4 * (x - 2)^3

[ruby imp]

Yes

[slate patio]

thank you

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[bleak pier]

In this question 14 my guess is A and B both incorrect

[bleak pier]

Reason is because U,V are linearly independent but U+V will be linearly dependent

[nova yoke]

what was your reasoning for A

[bleak pier]

Opps they are saying u+v and u-v

Yes true they will be linearly independent

Option B left only

I didn't read clearly option A

[nova yoke]

correct, can you prove it?

[bleak pier]

Yeah

2x+y=0
2x+3y=0

4x+4y=0

Now vector first and third are linearly dependent

[nova yoke]

sure

how do you relate that to A (or B)

[bleak pier]

Linearly independent

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[drifting root]

How do I prove collinear (part B)

[midnight plank]

@drifting root Has your question been resolved?

[drifting root]

<@&286206848099549185>

[summer terrace]

using what you found in question (a), try to show that the vector MC is a scaled version of the vector MP

[drifting root]

ah

[summer terrace]

i mean: MC = k . MP

[drifting root]

then theyre parqllel and therefore cause its joined together, the same line?

[summer terrace]

since both the vector start from M

[drifting root]

ok

thx

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[bright shoal]

Ok

Come

@bleak pier yo

[bleak pier]

[bright shoal]

Fr

do u know

sint^2

Is (1-cos2t)/2

And u know cos2t is what?

@bleak pier

[bleak pier]

Yeah i know it

Cos2t=cos^2t-sin^2t

1-2sin^2t

2cos^2t-1

In terms of tan

[bright shoal]

No

Yes in terms of tan

Put

@bleak pier

Now u have two equations in tam

[bleak pier]

1-tan^2t/1+tan^2t

[bright shoal]

Tan*

Yes

Two equation

Two variables

[bleak pier]

What?

[bright shoal]

Find theta and phi

[bleak pier]

Equation?

[bright shoal]

See u expressed sint/sinq to the whole power 2 in terms of tan

Right 👍

[bright shoal]

What

Bro

Yes

U checked it?

See

@bleak pier

U have tan t/tan q =3

Now I will not tell anything

Understand think how to use it

[bleak pier]

Bro

You only show the formula and I wrote

I am not understanding what you are trying to say

@bright shoal

[bright shoal]

See

[bleak pier]

Show

[bright shoal]

U wrote Sint/sinq in terms of tan

This is equal to 3 as given in the question

It's also given that tant/tanq =3

Now how can u use these both

Think

[grim vector]

Think like rodin

[bleak pier]

I got

[bright shoal]

Fr

He got it

Yes fr

[bleak pier]

Is this what you wanted?

.close

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[midnight plank]

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[bleak pier]

168 hints

[runic hamlet]

maybe write a variable instead of the number

[bleak pier]

Where?

[tribal tartan]

replace 100+75i with x

[bleak pier]

I see

[tribal tartan]

you should start to notice something

[bleak pier]

Complex number

x^n/n!

[tribal tartan]

mhm and what does that represent

[bleak pier]

x^n>n!?

Any number/n!

[runic hamlet]

that series should scream at you

"hey look I look very familiar"

[bleak pier]

Hang on

[grand pond]

y0shi

[tribal tartan]

beautiful series

[bleak pier]

I haven't seen series in sum forma

Let me put and then see

N=1,2,3

x+x^2/2!+x^3/3!

Expansion of e^x-1

Opps n=0

Then e^x

[tribal tartan]

yeah just e^x

[bleak pier]

Which is??

Comvergent?

I guess divergent because it tends to infinity

Ohh it is comvergent

Our x was a constant number

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[midnight plank]

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[cloud ice]

How do I prove this?

https://proofwiki.org/wiki/Sum_of_Cosines_of_Angles_in_Triangle/Proof

I saw similar variant online

But I'm not too sure if the question is right

Can someone verify?

[humble torrent]

First direct thought is just to test some values to check if you’re unsure

Also so according to proof wiki, they’re claiming then that

cosA + cosB + cosC = -cosA + cosB -cosC

If I haven’t missed anything

[sweet totem]

there is 8 stones that have different weight and there is scale where u can only put one stone each side . what is the least amount of weighing that will tell us which one is the heaviest and second heaviest stone

guys can u help me with this

[midnight plank]

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

[cloud ice]

Nvm. I did it

.close

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[vernal jungle]

how do i get the answer? and does anyone know the faster way of doing this? no 14

the most that i can come up with is to try to “reconvert” them

4:3 -> 16:12 for example

[vernal jungle]

4:3 ratio —> 24:16 ft

with the area of 24 ft; its base is 3 ft

16 ft area; 4/3 ft base

[atomic plume]

What is going on

[vernal jungle]

no 14

[gray prism]

bh/b'h' = 4/3, h/h' = 3/4 => b/b' = 16/9 smth like this?

[vernal jungle]

With the area of 2 triangles at a ratio of 4:3; its heights are in the ratio of 3:4

what is it’s base

[vernal jungle]

how’d u arrive at the answer

[gray prism]

h/h' * b/b' = 4/3, so b/b' must be 4/3 / (h/h') = 4/3 / (3/4) = 16/9

[vernal jungle]

area of triangle is (bh)/2

[gray prism]

yeah but since you're working with ratios, that cancels out

$\frac{bh/2}{b'h'/2}=\frac{bh}{b'h'}$

[grand pond]

π=√g

[vernal jungle]

how would it cancel out

[gray prism]

like that, you can always simplify fractions by multiplying the numerator and denominator by the same number (in this case multiply by 2)

[vernal jungle]

so is it gnna be

$\frac{\frac{bh(b’h’)}{2}}{\frac{b’h(bh)}{2}}$

[grand pond]

Maladroit

[vernal jungle]

something like this?

[gray prism]

I dont think so

How do you simplify the fraction $16/10$?

[grand pond]

π=√g

[vernal jungle]

common factor of 2

8/5

[gray prism]

Ok, so in this case, $\frac{bh}{2}$ and $\frac{b'h'}{2}$ have a common factor of $\frac12$, so their ratio simplifies as $$\frac{\frac{bh}{2}}{\frac{b'h'}{2}} = \frac{bh}{b'h'}$$

[grand pond]

π=√g

[vernal jungle]

mhm

[midnight plank]

@vernal jungle Has your question been resolved?

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[red sparrow]

hello, can somebody please help me understand (second paragraph) why the fact that A isn't bounded implies that the sequence (x_n) cannot have a convergent subsequence?

also, how can we assume that there exists a convergent sequence in A in the first place? (first line)

[junior flower]

every subsequence of (x_n) is not bounded

[junior flower]

that doesn't matter really but if A is nonempty, you could make a constant sequence

if A is empty then there are no sequences at all, but that's fine

[red sparrow]

every sequence (x_n) isn't bounded, hence every subsequence of (x_n) isn't bounded and therefore doesn't converge?

correct?

[junior flower]

well it's more than just that (x_n) isn't bounded

0, 1, 0, 2, 0, 3, 0, 4, ... isn't bounded but has a convergent subsequence

this property is important

[red sparrow]

i dont get it im sorry

A is unbounded, therefore for every n there exists some element x_n such that abs(x_n) >= n

how does this relate to sequences?

[junior flower]

(x_n) is not just an arbitrary sequence in A

[junior flower]

it's a particular one constructed with this property

[visual tiger]

if x_n_j converged to some x, then ||x_n_j|| would converge to ||x||, but it diverges to infinity

[midnight plank]

@red sparrow Has your question been resolved?

[red sparrow]

ok i think i get it now

[red sparrow]

can you explain please?

[midnight plank]

@red sparrow Has your question been resolved?

[midnight plank]

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[languid dagger]

I have tried setting $u=x+1$, and $u=x^{2}+2x-2$ to no avail. If I differentiate $(x^{2}+2x-2)^{\frac{1}{2}}$ getting $\frac{x+1}{\sqrt{x^{2}+2x-2}}$ which seems to be along the right lines I'm just not too sure how they relate.

[grand pond]

noah

[small jasper]

Trig sub

[languid dagger]

huh?

[small jasper]

Trigonometric substitution

Basically u substitution but with a trig function

After you do u=x+1, idt there’s rlly any way to compute the integral other than trig sub

[languid dagger]

I get that im just not too familiar with whipping trig out of nowhere

[small jasper]

Welp

There’s a first time for everything

https://tutorial.math.lamar.edu/classes/calcii/TrigSubstitutions.aspx

[languid dagger]

tyty

[zealous schooner]

You can just do this by observation

$\frac1{(x-1)\sqrt{(x-1)^2-3}}$

[grand pond]

kheerii

[zealous schooner]

This is the exact structure of an arcsec integral

[languid dagger]

ohh yeah that makes a little more sense

I assume what youve done under the root is completing the square

[small jasper]

(It’s derived by trig sub btw)

[zealous schooner]

Yes

[small jasper]

But yeah if you have it memorized then you can use it

Personally, I never memorised it

[zealous schooner]

I’d say it’s derived by the derivative of arcsec

[small jasper]

I’m talking abt if you don’t know all the inverse trig derivatives

And you don’t want to test all 6

This is mainly me being lazy lol

[zealous schooner]

Trig sub works here yeah

It’ll just lead to the exact same thing

[languid dagger]

for this exam at least, youre only given the derivatives of arcsin, arccos, arctan

[midnight plank]

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[languid dagger]

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[last slate]

Hello I need maths help

[last slate]

This statistics which is confusing me

Can someone please help me 🙂

<@&286206848099549185>

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[knotty otter]

can someone help

is b right

[abstract glen]

erm

no

consider the concavity of the graph is it facing up or down

and how it is shifted down and left

[knotty otter]

wait so if its not b it has to be c right?

[abstract glen]

idk if ur guessing or trying to work out the answer

[knotty otter]

i dont understand it im doing my best

and this is 100% a

im right

ik it is

@abstract glen

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[fading quarry]

how do i show this?

[cobalt gorge]

no horizontal asymptotes

[fading quarry]

how does that prove it?

[cobalt gorge]

it shows that there is no restrictions on the y value of the function

[shell basin]

you can find the horizontal asymptote you'll find its some line with a slope and you'll see there's no restrictions

by polynomial division

if you wish

[fading quarry]

ohh

yea thanks

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[bleak pier]

Any hints?

Is this a theorem?

[fathom knoll]

its cauchy integral theorem

answer is hence A

[bleak pier]

Hang on

Let me check into answer key

[fathom knoll]

ok

[midnight plank]

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[dreamy lynx]

I have done linear algebra and a first calculus course (one variable), what exiting math can I continue with?

[bold beacon]

exiting math?

Are looking for a math subject where you meet the prerequisites?

[dreamy lynx]

Yes

Some usefullness, some novelty, idk
I am far from cutting edge math but I want to find something to do
"Exiting", eh, thats somewhat subjective

[bold beacon]

You mean exciting. I think discrete maths is useful as it will give you core mathematical knowledge. The subject quality will depend on how it taught but Susanna E.P is a good reference.

[dreamy lynx]

I will look into it, thanks!

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[bleak pier]

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[last slate]

how do i solve dy/dx + (1/x)(tany) = (1/x^2)sinytany

[gaunt nimbus]

just

split the equation into terms of x and y

then integrate both sides

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[spice scroll]

question: find det(A)

[spice scroll]

solution:

let H_n = |A|

and then the solution (not in english) managed to find out:
$H_n = H_{n-1} - 6H_{n-2}$

what i DONT understand is they then proceeded to say "let:

and solved for lambda in order to represent H_n by n alone

why the use of lambda to the power of n all of a sudden?

[grand pond]

Ayanokoji (ALWAYS PING ME)

[midnight plank]

@spice scroll Has your question been resolved?

[runic hamlet]

thats a general approach to solve recurrences like this

[visual tiger]

when you have recurrence u_n+2 = au_n+1 + bu_n, you have three possible forms for u_n:

depending on the roots of the equation r^2 = ar + b

if both roots are real and distinct:

if you have a single root:

if you have two complex conjugated roots re^(ialpha) and re^(-ialpha):

[spice scroll]

can you explain also why then they made this step? the second (-6*...) should be lambda to the power of n-2 i think and not n-1

[visual tiger]

yes it's n-2

[spice scroll]

since intuitively according to this defintion thats what it should be

[twilit jetty]

I think you should screenshot all of the steps together

[spice scroll]

it's read right to left

[twilit jetty]

you dont take this line literally, its a awy to convert Hn into the appropriate equation that we're mentioning above for r

[spice scroll]

then why is lambdato the power of n defined with 2 power n-1?

[twilit jetty]

youre asking a lot of questions for a method that doesnt need them, do you also want to ask for why the method works?

[spice scroll]

but then also, why is lambda^0=1? since H_0 is clearly undefined

[twilit jetty]

lambda is nonzero

anything to the zeroth power is 1

[spice scroll]

in a sense i think it's a "just works" method?

[twilit jetty]

you can leave it as a "just works" method if you want

[spice scroll]

but H_0 itself, as in a matrix of 0x0, is undefined

[twilit jetty]

please

dont take this line literally

[spice scroll]

as in, this is the first time they showed this, and it's in a applied example

no explanation onto it

[spice scroll]

but we have to

[twilit jetty]

no youre not

Hn is not "literally lambda to the nth power"

that is a rule you use to write the characteristic equation

[spice scroll]

but thats the equality given here?

[twilit jetty]

.

[spice scroll]

i guess, i mean i can kind of see why

but i dont "agree" with it

[twilit jetty]

I dont either

now have you solved equations of the form y'' + ay' + by = 0 before

[spice scroll]

y'' and y' are derivates or polynomials of different powers?

[twilit jetty]

derivatives, not derivates

the ' symbol is "prime", it means "derivative of"

[spice scroll]

in general i havent done this in this class (linear algebra 1), and maybe not in high school either

but i can derivate twice and try if thats what you mean

[twilit jetty]

no

what do you think solving an equation like y'' + 3y' + 5y = 0 means?

[spice scroll]

yes that i learned when the lecturer used it once or twice for A -> A' (mutated)

[twilit jetty]

thats a different usage of the prime symbol

for calculus, ' is used to mean "derivative of"

[spice scroll]

i dont really know, but i could try doing it for something like y=x^2

[spice scroll]

yes i know, i had done that too in high school

[twilit jetty]

then you dont say youre taking the derivative of a matrix

[spice scroll]

we just started learning function in calc 1

[twilit jetty]

there are two separate definition for ' - your lecturer did not teach the calculus definition when they used A to A'

[spice scroll]

no no, i just meant thats the usage i've seen in this class with it, i understand the usage you mean

[twilit jetty]

youre solving the equation for a function y that would make this zero everywhere

so somehow theres a function out there where y'' + 3y' + 5y would completely simplify to just 0

for a simpler example, think of y' = y

[spice scroll]

yes im familiar with derivates, for example for y=x^2
the above expression is written as:
$y'' + 3y' + 5y = 0 \Rightarrow 2 + 6x + 5^2 = 0$

[grand pond]

Ayanokoji (ALWAYS PING ME)
Compile Error! Click the reaction for more information.
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[twilit jetty]

one of the solutions to this equation is "y = e^x"

youll notice there that solution is a function of x instead of just a number

youre trying to find functions y(x) that can fit y' = y

this is called a "differential equation", they get hard quickly

y'' + 3y' + 5y = 0 is a differential equation with a standard method

[spice scroll]

i dont understand this explanation completely

[twilit jetty]

you only asked to plug in y to see that it makes it zero somewhere

thats what you mean by "plugging in x^2 and solving for it"

yes?

[spice scroll]

yes so e^x, a contant, or something else i guess

[spice scroll]

yes

[twilit jetty]

we're not looking for a function that only fits y'' + 3y' + 5y = 0 some of the time

setting y = x^2 will mean y'' + 3y' + 5y = 0 will only be true for up to two values of x

thats not what we're looking for

we're solving for a kind of y that would fit y'' + 3y' + 5y = 0 every time