help-10

[timid silo]

right

ABC = 90

[junior granite]

and we just verified that ABC =

yeah'

Required answer = sin(ABD) - cos(DBC)
implies sin(ABD) - cos(90-ABD)
implies sin(ABD) - sin(ABD)

[timid silo]

oh

so it is 0

[junior granite]

finally

are in UG programme?

[timid silo]

no

wait what is ug?

im taking A levels

and next month I have sat exam

[junior granite]

undergraduate

okok

[timid silo]

no im still at school

anyways

thanks

[molten stirrup]

aw i failed :(

[junior granite]

your profile just says undergraduate so that's why

[junior granite]

what?

[molten stirrup]

ill make up next time -)

[junior granite]

not failed

[timid silo]

bet bet

[molten stirrup]

i met him someitmes lol

[timid silo]

77 u majoring math?

[junior granite]

bruh just completed schools a few months ago

now preparing for university entrance exam

[timid silo]

damn goodluck bro

.close

[molten stirrup]

slay 💀

[obtuse pebble]

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[marble lark]

Hello

[dark stirrup]

The heads? I don't think I'm familiar with that term

[dark stirrup]

Ah

I think the average of the three points should give you the center iirc

[marble lark]

$\text{Midpoint of AB}$
$D = (\frac{1 + 1}{2}, \frac{-1 + 3}{2})$

same for others?

i mean create another midpoint for Ac (E) and get midpoint of DE?

[junior granite]

What does "passing by the heads" mean?

[warm shale]

Avicenna

[marble lark]

it means like in the image

[winter scaffold]

I think it means the vertices of triangle

[junior granite]

ah okok

[winter scaffold]

no that is for the centroid

[junior granite]

so I think if you assume the coordinates of m being (h,k)
then the distance from m to all points A, B and C will be equal

[winter scaffold]

I think we have to find the circumcenter of triangle

[marble lark]

Yes i think so

[winter scaffold]

yea

[junior granite]

like mA=mB=mC

[marble lark]

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[marble lark]

.help

[junior granite]

.help?

[obtuse pebble]

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[marble lark]

nah its ok i found a lesson

[marble lark]

.solve

[marble lark]

.close

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[timid silo]

noo

sad

[marble lark]

?

.close

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[tranquil girder]

is equal to 1/2. then what is x? i want to find this answer without using calculus

[whole saddle]

f(x)

[tranquil girder]

[junior granite]

!occupied

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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).

[whole saddle]

sory

[junior granite]

if $\frac{1}{2}=\sqrt{x}^{\sqrt{x}}^{\sqrt{x...}}$
$$
$\implies$ $\frac{1}{2}=\sqrt{x}^{\frac{1}{2}}$

wtf

wait

[tranquil girder]

[warm shale]

77²
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[junior granite]

probably makes sense right?

[tranquil girder]

yeah

[tranquil girder]

is answer 1/16 then?

[junior granite]

yeah I think it is correct

[tranquil girder]

ok

thx man

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[dim terrace]

I got the right answer for 5 but I’m unsure how to best leave all my work so it’s clear what my logic is

[dim terrace]

Like how do I write it out other than just doing it

[stoic yacht]

technically i feel like if you've identified the right coefficients for the combination you could just write it the way that you have with no other work

[upper shuttle]

are u doing q5? i suggest u write yours u's and v's a bit more distinctly

[dim terrace]

Yes question 5 and sorry I write sloppy on my iPad

I write better on pen and paper

[stoic yacht]

if you wanted to show some sort of work for how you originally found the coefficients, solve the system

1 1 | -2
1 -2 | 7

[dim terrace]

Hmm

So like

I guess it’s sort of just like I can see the answer. But for some reason even solving it I’m sort of unsure why something goes somewhere

No problem with gauss Jordan

Just the idea of c1 and c2 being the same thing as x1 and x2 here

Like I’d be inclined to write the vectors as columns within the matrix you sent rather than horizontally

As rows

But I guess that just me being slow cause the logic is the x of both vectors u and v should equal -2

So they should all be written as one equation

In other words as a row

[still wraith]

-2i + 7j = p(1i + 1j) +/- r(1i - 2j) , try taking p or r as some values and then u might get the answer

[dim terrace]

A question when it comes to question four is it OK if I use Cramers rule but sort of combined with the idea that we can find the determinant of a 3 x 3 matrix by adding the first two columns to the end of the matrix and then using the arrow rule?

So I use Kramers rule as far as replacing each column with the answer column or the constants let’s say, but to actually find the determinants each time I’m using the trick where you add the first two columns at the end of the matrix

[still wraith]

cramers rulee , and then for x it is delta 1 / delta and so onn for y and z

[dim terrace]

Sorry if there’s typing mistakes, I’m using talk to text

[still wraith]

lemme solvee

waitt

[dim terrace]

Yeah, I know the formula

But I mean to actually find my determinants. I’m using the trick where you can just rewrite the first two columns after the third column when it’s for a 3 x 3 matrix which in this case it would be, and then I’m using this trick to find each of the determinants, which I’ll then need to use to actually find or isolate the unknowns

[still wraith]

ya u can add the rows and columns and u can do it so that the process gets easierr

[still wraith]

ya yaa we need to replace one row for every variablee

like delta 1 , delta 2, delta 3

[dim terrace]

Would be 1 w3

[dim terrace]

1, 2, 3

[still wraith]

ya

[dim terrace]

Yeah ok got it thank youuuu

[still wraith]

welcome

[dim terrace]

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[runic notch]

@opaque dome

[obtuse pebble]

@runic notch Has your question been resolved?

[opaque dome]

You start from -1 <-e^-x < 0

[obtuse pebble]

@runic notch Has your question been resolved?

[timid silo]

https://drive.google.com/drive/folders/1JU03uDBDajZ2pApgFdwVkzrtlK7MN4-j?usp=drive_link

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[obtuse pebble]

@radiant hornet Has your question been resolved?

[pastel gyro]

Suppose that when the person is a distance $x$ from the spotlight, the height of the shadow is $y$ and the person is moving with velocity 2 ft/s to the right. We have $\frac{y}{40} = \frac{5}{x}$, so we get $y = \frac{200}{x}$. Differentiating both sides w.r.t $t$ (time), we get $\dot{y} = -\frac{200}{x^2} \left(\frac{dx}{dt}\right) = -\frac{400}{x^2}$, where $x$ is the position relative to the spotlight. Can you continue now?

[warm shale]

PowerUp

[pastel gyro]

Well, yes but x isn't fixed here. First, try to find the equation describing the rate at which the height changes since the rate of change of y is not constant, and only then calculate the speed when the person is 10ft away from the wall.

yes

I didn't follow your method very well but if understand correctly, you differentiated a and y with respect to time, but in your case both a and y are constants so the derivatives should've been zero (the reason they're constant is because you explicitly defined the distance the person is from the wall from the very start).

It doesn't matter. The speed is constant, and the difference is just what your origin is. In my calculation, I considered the origin to be the spotlight, but you can also consider the origin to be the wall (nothing will change except a change of sign. But in the end, you're asked to calculate the speed so direction doesn't matter).

Well, x + z = 40 so you can just substitute x = 40 - z and now you have z instead of x.

It would basically be $\frac{y}{40} = \frac{5}{40 - z}$ which simplifies to $y = \frac{200}{40 - z}$, and now just differentiate w.r.t t on both sides. You will get $\frac{dy}{dt} = \frac{400}{(40 - z)^2}$. Now substitute the appropriate numbers.

[warm shale]

PowerUp

[pastel gyro]

yes, but make sure to make the signs consistent. When they ask for speed or distance or scalar quantities, the sign doesn't matter. But if they ask for vector quantities (like velocity; anything with direction) the sign may matter. But in this question they're asking for speed so it doesn't matter.

Here the height is constant (the flashlight is placed at the top), but in the previous example we didn't really put any constraint on the height (it was constantly changing, the spotlight is placed on the ground 40ft away from the wall) so the situations are different.

Np 👍

[obtuse pebble]

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[dry pebble]

I need to state the local max and min of this function and justify it with reference to the sign of IROC

[dry pebble]

I can't find the first derivative because we haven't learned it in my summer school, we can only use two very close xvalues and plug them into the formula f(x2)-f(x1)/x2-x1

[obtuse pebble]

@dry pebble Has your question been resolved?

[dry pebble]

<@&286206848099549185>

[winter scaffold]

If that's the case then I guess you can solve it by First principle

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.reopen

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✅

[dry pebble]

I'm not allowed to use differentiation either

[obtuse pebble]

@dry pebble Has your question been resolved?

[dark stirrup]

Have you tried this?

[dry pebble]

Yea thats what im doing rn

[dark stirrup]

min and max local to what?

[dry pebble]

The question just asks "State the Local Max and Local Min. Justify your answer with a reference to the graph of this function and the sign of IROC."

And the function is h(x)=(1/6(cosx))+(1/3)(logx)+2

So im just gonna find the local max and min closest to the origin

Because I dont know how else to do this question

The graph's y value gets larger at every peak and it goes indefinitely

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.reopen

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✅

[dark stirrup]

Yeah local needs to be relative to some neighborhood. The problem has failed you

[dry pebble]

Yea I figured lol

Well thanks for your help

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[plain nebula]

whats the difference when doing X~ and Z~

[gilded needle]

just different names for random variables

[plain nebula]

so same method

i dont really understand the difference between N~ and Z~

[gilded needle]

^

[plain nebula]

yea ones called normal and the others called z value

i dont understand the difference between the two

[gilded needle]

no they're both normal

that's what N(mu, sigma^2) means

normal with mean mu and variance sigma^2

in the first one, X is a normal rv with mean 50 and variance 0.8^2
in the second one, Z is a normal rv with mean 0 and variance 1

[obtuse pebble]

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[polar fossil]

somewhat

ok i mean this seems simple enough

just have to remember what the symbols mean

what i would recommend is to pick some w

like "cat" or something

[open spoke]

{e, cat,catcat,...

[polar fossil]

sure yeah

can you make a turing machine that only moves to the right that recognizes that?

[open spoke]

oh shit

cant i just make like

a cycle

with the print state being the start state

[polar fossil]

do you mean accepting state? but yes

[open spoke]

i thought enumerator only has print states?

[polar fossil]

oh right enumerator not decider

but yes it sounds like that will work

[open spoke]

sonds good

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[fervent escarp]

can someone walk me through solving this problem:

[limber quartz]

Looks like u solved it

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[native grail]

helloo

[native grail]

i dont understand part b

about the height

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[heady turtle]

Why

[gilded needle]

what's the context? what tools do you have available?

fourier series etc?

[heady turtle]

I just want to know why this is equal to pi^2/32

I can go learn if it needs the tools which idk

But i don't even know what tool it used

[gilded needle]

well there are at least two methods, residue theorem (complex analysis) or fourier series
you could take a look at the answers here to see what's involved: https://math.stackexchange.com/questions/359667/sum-sum-n-0-infty-frac-1n2n13

afaik there's no simple method that doesn't use some machinery that requires work to develop

[heady turtle]

Tysm.

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[edgy needle]

Hiii I get confused by these worded questions

For question 9

Is it 7000=4000x1.03^n or

7000=4000x1.03^(n-1)

?

[warm sparrow]

I think the first

Ye definitely the first one

[edgy needle]

Why,

[warm sparrow]

Well

[edgy needle]

Bc the formula for term in a geometric sequence

Is tn=ar^(n-1)

[warm sparrow]

Uhh

[edgy needle]

Is it with the wording?

If it says after what year will the population reach 7000

Is it then n-1?

[warm sparrow]

Ye its wording but now your getting me to question myself so let me look it over again

[opaque dome]

Actually if they were saying the domain of n like N or N* it wouldnt be ambigous

[edgy needle]

Wat

[warm sparrow]

No I'm sure it just n and then ofcourse+ 1984 cause the 4000 is in that year

[opaque dome]

If P_0 is 4000 or P_1 is 4000

[warm sparrow]

P_0 is 4000 thats how the question is asked

[opaque dome]

Ok so this is just power n no ?

[edgy needle]

How do u know it’s not P1

[warm sparrow]

Exactly thats what im saying

[opaque dome]

So all good

[edgy needle]

How do u know its not P1

But p0

[opaque dome]

For me, they would have precise it if it was P_1

I hope at least

[edgy needle]

Cant it be both

I got n=18.93

So 1980+ 18.93

So maybe that is end of 1998

Or if i put n-1 its

19.93

So if i add 19.93 i get 1999.93

So maybe thats early 1999

[opaque dome]

Its either 0 or 1

[edgy needle]

Weird question

[old dagger]

U can test it by subbing the value into the eqn tho

[ancient drift]

should be ^n ig

Sub n=0 should give you 4000

So it can't be n-1

[edgy needle]

In test if i dont have time do i always need to sub it in

To check

Wait

Thats easy

Ok thx :P

[ancient drift]

Yea

Logically at year 0 the population is the same

So that's a good way to reason it out fast ig

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[eternal thistle]

Why do we assume the hessian to be indefinite if there are v,w such that Hv^2 < 0 and Hw^2>0

[eternal thistle]

And not if there is some v different than zero such that Hv^2 =0

[kind hawk]

why are you writing it like that

v^2 makes no sense

its just a def to call it that

it v^tHv >= 0 always and sometimes v^t H v=0, then it is called positive semidefinite

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[gloomy vector]

given triangle ABC such that AC=BC, assume P is a point in the excircle of AB such that it lies in the minor arc of AB, D is a point on BP such that PB is perpedicular to CD, prove that PA+PB=2PD

[gloomy vector]

ignore that extra line

my teacher said trig isnt allowed if its used somehow btw

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[ancient wedge]

During a conference, there are 1000 delegates which sits in a circle, each of the delegates choose between his two neighbours(one of the left and one of the right) to look at their tables, now suppose all the delegates who don't have anybody looking at theit tables are encircled, what is the largest possible delegates that will encircled?

[ancient wedge]

How does one find the number of encircled people?

[obtuse pebble]

@ancient wedge Has your question been resolved?

[ancient wedge]

<@&286206848099549185>

[rocky nymph]

This is very similar to The poked and unpoked baby problem in evan chen's paper: https://web.evanchen.cc/handouts/ProbabilisticMethod/ProbabilisticMethod.pdf

Look at sector 2.3

Just that in the paper evan chen looks for the expected value, not the largest value

[ancient wedge]

Oh, even the hmmt one finds the expected value

Smh

[rocky nymph]

sorry if i cannot provide an answer as im busy but maybe the paper can help with a way of finding one

[ancient wedge]

It's fineee

[rocky nymph]

ig you can see that for each delegate with an empty table, there are 2 tables with atleast 1 visitor

[ancient wedge]

Since 1000 is divisible by 4, could it be that 1000/4 = 250?

[rocky nymph]

idk tbh

[ancient wedge]

So 1/4th chance of each neighbours being missed

Evan chen said that E|x1 + x2 + x3 + x4... x1000| then E|Xn| = 1/4, then 1000*1/4 = 250

Can anyone confirms that this meant that the largest value is 250 or am I tripping

I don't think they are similar though

[rocky nymph]

by this diagram you see that for every 2 empty tables, theres min 4 tables that where visited

,rotate

[rocky nymph]

you can use this fact to show what is the number of max unvisited tables

[ancient wedge]

I think one could find the maximum when half the circle would look is the same direction, diverging in one guy where two people on his left and right look at his table

Can't prove it though

[rocky nymph]

unvisited + visited = 1000
2unvisited = 4visited
and then solve for unvisited. (i think??)

[ancient wedge]

Oh wait no

That's not true

[rocky nymph]

but in that case there are only 2 unvisited tables for the half circle (so 4 in total) and that would be minimizing not maximising

[ancient wedge]

Yuh

I found a case where for 4 tables, there could be 2

[last temple]

what is photosynthesis?

[ancient wedge]

Is this true?

[rocky nymph]

we want to maximise the amount of unvisited tables though, there will be a case where for x unvisited we have y visited. but by trying different combinations to minimize y and maximise x, i got 1x = 2y

you could mess around more and see if you find something even better, maybe 1x = 1y would be ideal but im not sure its possible

[ancient wedge]

So by that, there could be 500 non visited, we have 500 visited?

Wait huh

[ancient wedge]

X = 2y

[rocky nymph]

if 1x = 1y then yes we would have 500 non visited and 500visited, but its impossible to construct such a situation. The best i found was 1x = 2y (for every unvisited, there are 2 visited)

[ancient wedge]

250 750?

I'm fried rn

[rocky nymph]

for every one unvisited table, 2 will be visited. So:
x(unvisited) + y(visited) = 1000
x = 2y

x + 2x = 1000
3x = 1000
x = 333.333...
But x is an integer, is x = 333 or 334? uhhhhh idfk lol

[ancient wedge]

333

Ahhhhh

[rocky nymph]

lol

[ancient wedge]

It's a repeat of 0 1 2 0 1 2

WAIT

OMG

Wait no

It's so weird why i'm thinking of base 3

[rocky nymph]

0 2 1, 0 2 1, the issue is that these are 3 numbers that repeat, so they dont repeat fully over 1000, will the last number be 0 or 2?

ofcourse 0,1 and 2 being the number of visitors

[ancient wedge]

If 0 2 1 0 2 1 0 2 1, the ending would be 1 right

So if a 100th guy was added

*1000

On would just make it 0220?

Or no

[rocky nymph]

it isnt 1 and thats the issue, cause 1000 doesnt divide 3

[ancient wedge]

I mean in the pattern

For 999

0 2 1 0 2 1 0 2 1.... 0 2 1 and you connect them

And another guy, it would be adjacent to the last 1 visitor guy and the first 0 visitor guy

For maximum, he would just go with the guy with only 1 visitor

Instead of ruining it by visiting the guy that had 0 visitor

[rocky nymph]

hm wait

maybe there is a way to have 500 visited and 500 not visited

[ancient wedge]

Making it look like, 0 2 1 0 2 1 ... 0 2 2 0, then it starts again to 0 2 1

Hmmmm

How

[ancient wedge]

Interesting

1000 is divisible by 8

Its gotta be 02200220

[rocky nymph]

the pattern is closed after only 4 circles, so you just need to check that 1000 is divisible by 4. and it is. so this pattern repeats perfectly, and thus we have 500 visited, and 500 unvisited

[ancient wedge]

OH YEAH

It's by patterns of 4

[rocky nymph]

yep

or even pattern of 2 thats rotated 180deg every time

is 500 correct?

[ancient wedge]

Likely

Is there a greater than 500 case?

I don't think there is

[rocky nymph]

i doubt

[ancient wedge]

0 2 2 0 is the best scenario tbh

There can't be 0 3 3 0

[rocky nymph]

i mean 0 3 3 0 wouldnt change the answer, but its impossible cause the nunber is based on the which neighbours go there and it can be max 2

a better than 500 case would suggest that we have a 0 0 0 which is impossible but i have no way to prove this, just intuition

[ancient wedge]

0 0 0 is impossible because the dude in the middle has to visit someone adjacent

So 0 2 2 0 is the best scenario

[rocky nymph]

yep but i mean that idk how to prove that it will cause a 0 0 0

[rocky nymph]

i think so ye

[ancient wedge]

The expected value is 250

Then was is the supposed pattern though

What is the "most average"

Nvm

THANKS

.close

[obtuse pebble]

Channel closed

Closed by @ancient wedge

Use .reopen if this was a mistake.

[rocky nymph]

oh sorry i was away from the computer for a sec, yes the expected value is 250, like stated in evan chen's paper, but the maximum possible value would be 500

[obtuse pebble]

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[midnight void]

yo

[daring cairn]

someone pls help me w measurements gr 10

i need help finding sa for rectangular prisms,cylinders,and cone

[midnight void]

make ur own channel bum

[daring cairn]

how

[midnight void]

look at #❓how-to-get-help

can someone help me with this q

idk what to do

[obtuse pebble]

@midnight void Has your question been resolved?

[midnight void]

no

[obtuse pebble]

@midnight void Has your question been resolved?

[midnight void]

Can someone pls help me with part a

I just need the predator equation or how to find it

[obtuse pebble]

@midnight void Has your question been resolved?

[spiral void]

What’s the length of a prey cycle

[midnight void]

90t

so 90 years

i tried doing it,
p(t) = 20sin (90t - 90 degrees) + 60

is that wrong?

[spiral void]

I haven’t done trig in a long time

Let me try to Desmos it

[spiral void]

The period of sin(t) would be 2pi right

So sin(90t) would be 2pi/90

It’s phase shift

But yea

[midnight void]

i haven't learnt radians yet

[spiral void]

Hm

Just use pi=180 degrees

[midnight void]

pi/2?

so 20sin (90t - pi/2) + 60

[spiral void]

Hm

[spiral void]

The period is this

So a quarter of the period would be pi/180

Let me check that

[spiral void]

Does that work

[midnight void]

nop

wait let me try adding ur suggestion i forgot

even with urs its js a straight line

[spiral void]

Yea

Why doesn’t yours work

[midnight void]

it gives me this

[spiral void]

zoom into it

[midnight void]

same equation

[spiral void]

yours works

phase shift by pi/180

so the maximum is 80

miniumum is 40

so midline is 60

[midnight void]

i have to graph both on paper for part b

wouldnt that be rllyt hard

also rq what wud the points be 😭

-2,0 for first right

but what wud second one be

[spiral void]

divid it

[midnight void]

wud it be 2,-4?

[spiral void]

divide the polynomial

yea

[midnight void]

okok

[spiral void]

no

x=2 is undefined

because denominator is x-2

so you're dividing it by 0

[midnight void]

so 2,0?

[spiral void]

yea idk why they told you to graph it

[spiral void]

no it's not defined

there's a hole at x=2

[midnight void]

so i should just write undefined?

[spiral void]

yep

[midnight void]

ok

[spiral void]

any more help

?

[midnight void]

yeah

lol sry

r u good with desmos cuz i also have a question abt that

[spiral void]

not sure

just ask anyways

[midnight void]

wait lemme reset it

[spiral void]

what do you need help with

[midnight void]

oh shit i forgot to look at discord sorry

also this rq

its moving its a gif

thats yes right?

[spiral void]

not sure but I think so

[spiral void]

sin(x) has period of 360 degrees

what do you do to make the period 3x

[midnight void]

wym?

to make it 1080 its 3x

oh like the a value i think

[spiral void]

Have you learned about transformations of functions

[midnight void]

yeah i js forgot

[spiral void]

like af(bx)+c

ok so b is horizontal compression

[midnight void]

ye

[spiral void]

since you want the period to be 1080 degrees, you want to stretch it by a factor of 3

so b=1/3

what is a btw

[spiral void]

in here

[midnight void]

amplitude

?

[spiral void]

oh

alright

is it set

or can you change it

[midnight void]

thats the information im given

and i have to find the equation

its set

[spiral void]

ok

what did you try so far

[midnight void]

uh

1 sec

let me try

what is B

oh

nvm

now i js need the c and the d

[spiral void]

so does that work

ok

try playing around with it on desmos

[midnight void]

It's like a very flat sin function

[spiral void]

show what you have

[midnight void]

wrong one

[spiral void]

you can click radians

I think

try that

[midnight void]

wym

[spiral void]

nvm

click the toolbar

oop

this

and try radians

[midnight void]

oh

is there any vertical or horizontal shift?

[spiral void]

oh it's a sine function

I thought it could be any kind of trig function

ok so

plug in the point that's given

0,11/4

[midnight void]

where

[midnight void]

yeah but where wud i plug it in

for x and y?

[spiral void]

yea

for x

[midnight void]

it gave me a flat line

and nothing if i replace the y

[spiral void]

you have y= 3/4 (sin(x/3+c))+d

so y =11/4

x=0

what's the maximum point btw

[midnight void]

this

no?

[spiral void]

oh

what

oh

bruh

ok

so maximum point of sin(x) occurs at x=180 degrees

so sin(x/3+c) = 180

and since x=0

c=180 degrees

[midnight void]

that?

i put 3.14 cuz thats 180 degrees in radian

but ima change it all to degrees

[spiral void]

alr

click the toolbar

do you want to use radians or degrees

[midnight void]

degrees

[spiral void]

ok

click the toolbar and click degrees

[midnight void]

ok but i need to change the values now

[spiral void]

ok

so you have c right

now you just need to find vertical translation

11/4= 3/4(sin(180 degrees)+d

solve for d

[midnight void]

11/3

[spiral void]

what

[midnight void]

wait

[spiral void]

oh like d=11/3?

[midnight void]

yea

[spiral void]

11/4=3/4 (sin180 degrees)+d

what's sin 180 degrees

[midnight void]

0?

[spiral void]

mb

yea it is

wait ok

so the c value isn't 180 degrees

it's 90 degrees

because sin(90 degrees) =1

so that's the max

so 11/4=3/4 (sin(90 degrees) + d

solve for d

[midnight void]

ok

2

[spiral void]

yep

that's the function

put everything together

[midnight void]

l

like this is fine right?

[spiral void]

the expression inside sin() is 90 when x = 0

[midnight void]

?

do i gotta change smt

[spiral void]

yea

when x=0

sin(1/3(x+c)) = 1

solve for c

[midnight void]

icl idk how to

[spiral void]

sin(1/3(x+c))=1

when is sin(z)=1

[midnight void]

uh

90

?

[spiral void]

yea

so 1/3(x+c)=90

and x=0

solve for c

[midnight void]

270?

[spiral void]

yea

that's the answer

[midnight void]

wait so what do i change

[spiral void]

c=270

c=270

[midnight void]

so this is good?

[spiral void]

yea

[midnight void]

do u know how to make a moveable point on desmos

i need it so that the moveable point follows the red line

[spiral void]

yep

replace the x with like

a letter that is not x

so like

idk

t

and make a label for that

[midnight void]

now is js a straight line tho

oh wait i think i got it

[spiral void]

k

[midnight void]

should i change the 30 to radians

cuz my teacher had it set to radians alrdy n i changed it to degrees

[spiral void]

if you want

js use pi radian = 180 degrees

[midnight void]

ok wait i got the c value, -2

ima do cos for this one

y = a cos k (x-d) + c

nvm i got it all except for d

@spiral void

[spiral void]

substitute the value for a point

[midnight void]

for d 300 works

but 120 also works

ohh

[spiral void]

ofc

[midnight void]

its cuz i remove 180-

[spiral void]

yea

[midnight void]

a period

yeahhh

okok

did i solve that right

oh its 90 to the right isntit?

nvm it is 30

[midnight void]

ive been trying for 15 minutes i cant find an answer

.-.

[obtuse pebble]

@midnight void Has your question been resolved?

[spiral void]

Hi

Try sm values maybe

[obtuse pebble]

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[obtuse pebble]

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[gaunt helm]

Find exact value of;

[gaunt helm]

I’ve found cosine in the arc

I got 3/5

then idk how to go on

[high lily]

consider half and/or double angle identities

[obtuse pebble]

@gaunt helm Has your question been resolved?

[obtuse pebble]

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• After 15 minutes, feel free to ping <@&286206848099549185>.
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[true plume]

the bottom shape is a nonagon and the total interior angle is 1260

and i know all the angles except v and w so i know v + w = 141

also i tried doing that but i just ended up with v + w = 141 again

kinda stuck not too sure what to do rn

<@&286206848099549185>

[green bluff]

@true plume

[rich roost]

i think its more clear if you draw the triangles better here

[true plume]

basically like

the angle above the 61º is 90-61

so the top triangle in the left square has angles 61º, 90º, and 29º

the angle above the 68º is 180-68º

and then by the same method u can solve the angles in the triangle of the middle square

and u can express the angles of all the other triangles in terms of v and w

until you get v + w = 141

not sure what to do after that

[obtuse pebble]

@true plume Has your question been resolved?

[rich roost]

yeah sorry i thought i saw something but it wasnt quite right, not sure

[obtuse pebble]

@true plume Has your question been resolved?

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[gaunt helm]

I need help proving this

[tepid yoke]

What’s on the denominator, the second term?

[gaunt helm]

tangent(x/2)

[obtuse pebble]

@gaunt helm Has your question been resolved?

[obtuse pebble]

@gaunt helm Has your question been resolved?

[sick quiver]

The RHS is sec2x right?

[gaunt helm]

Sin

[sick quiver]

Ah ok

Try making the bottom half cosx by half angle formula

And if you're still stuck, ask away, I have the solution with me

[gaunt helm]

Try and make the denominator

Cosx?

by half angle formula

or wdym by bottom half

@sick quiver

[sick quiver]

Ya denominator

[gaunt helm]

Like this?

I tried squaring but I don’t think im getting anywhere 😔

[sick quiver]

Oho wait

Solve with this

[gaunt helm]

I am so confused

[gaunt helm]

.close

[obtuse pebble]

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[honest whale]

Hello! I need help proving that the minimum number of vertices of a triangulation satisfies the following estimate: (file)

This problem deals with the topic "Pontryagin-Kuratovsky graphs", 𝜋(𝑀)
is the Euler characteristic of the surface M.

[honest whale]

𝜋(𝑀)=𝑜(𝑀)−𝑠(𝑀)+𝑓(𝑀)

Where:

o(M) = number of vertices of triangles

s(M) = number of edges of triangles

f(M) = - number of triangles

The triangulation is the division of a surface into curvilinear triangles in such a way that any pair of triangles intersect either at a vertex, along an edge, or do not intersect.

[obtuse pebble]

@honest whale Has your question been resolved?

[obtuse pebble]

@honest whale Has your question been resolved?

[obtuse pebble]

@honest whale Has your question been resolved?

[obtuse pebble]

@honest whale Has your question been resolved?

[obtuse pebble]

@honest whale Has your question been resolved?

[obtuse pebble]

@honest whale Has your question been resolved?

[full rose]

This seems to come from a quadratic

$x^2-7x+6$

[warm shale]

ever

[full rose]

minus 1 and minus 6 works

[honest whale]

I didn’t really get of what part are you talking about, and I need to prove it, but I don’t really know how

[obtuse pebble]

@honest whale Has your question been resolved?

[weary reef]

The right hand side of the inequality is one solution to the quadratic equation $x^2 - 7x + 6\pi(M) = 0$

[warm shale]

StrangeQuarkAL

[obtuse pebble]

@honest whale Has your question been resolved?

[timid silo]

does anyone nee help

[buoyant cape]

Sorry, idk anything about triangulation or anything

But this pic looks like...

A root of a quadratic equation

And the equation is ig...

x^2 - 7x + 8pi(M) = 0

nvm me if this is totally unrelated, but this is what clicked in my mind

[honest whale]

Yeah actually it is, but I don’t know what to do after…

[buoyant cape]

Sorry dude, I can't help in this topic

<@&286206848099549185>

[timid silo]

yeah

Who needs help?

[buoyant cape]

@honest whale needs help

[worthy marten]

any dude wants help?

[tawny canyon]

YES

VERY MUCH!

[honest whale]

This is the problem

[buoyant cape]

<@&286206848099549185>

[timid silo]

hi

[buoyant cape]

This

The question is of @honest whale

[timid silo]

sorry wrong channel apparently

[buoyant cape]

Oh

[trim flare]

https://tenor.com/view/young-sheldon-spock-long-live-and-prosper-star-trek-sheldon-cooper-gif-15844681

[timber juniper]

Na

[trim flare]

na for nasty?

na for not attanded?

na for nationalization?

na for non-authorized?

what does na mean?

[buoyant cape]

na for nasal

[wicked gust]

Na for sodium?, NA for not available?

[cinder kestrel]

north america

[obtuse pebble]

@honest whale Has your question been resolved?

[obtuse pebble]

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[severe moat]

can someone show me what to do from here

[severe moat]

I have the original equation

and the derivatives

how do i solve alpha and beta

Derivative one

Non derivative one

not sure where to go

Do i maje anthing the subject and then recalculate?

[obtuse pebble]

@severe moat Has your question been resolved?

[lost tree]

What is the original question

[obtuse pebble]

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[rose ferry]

Hey I plotted this but got it wrong

because its + pi doesnt that mean it starts before 0?

cause - pi would move forward and + pi would move back

[plain stag]

"starts" doesn't really make much sense in the context of sin

unless you're only supposed to plot on a particular domain

[rose ferry]

?

[rose ferry]

ohhh i know what you mean

i was just showing one period before 0

.close

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

Wew long time

[worthy cargo]

U GOT A QUESTION CHIEF?

[dusk widget]

do you have a question?

[timid silo]

Ofc

What does it mean by this look

"If sides then angles"

[versed stratus]

Typo?

[junior granite]

what's the headline of the list?

[timid silo]

It's like in almost every proof of this section

Lemme show full proof

I understand the whole thing

And how it got there

But what is if sides then angles

Cause never knew that was a legitimate statement ngl lol

[polar fossil]

it's shorthand for "if the side lengths are equal, the corresponding angle measures are equal"

[junior granite]

ig, it means that if the opposite sides of these angles are equal then the angles are equal too

[timid silo]

Elaborate

🖖🙏

[polar fossil]

with triangle ABC, if AB = AC then <ABC = <ACB

or maybe it's easier to say if AB = AC then <C = <B

those angles being the ones opposite the sides

[timid silo]

Oooh

[timid silo]

Yeah I mean generally you use the middle term for angles right?

[timid silo]

These sort of reminds me of the interior remote angles of a triangles

Idk if I'm on the right track for that tho

Do yall suggest any video for this

[obtuse pebble]

@timid silo Has your question been resolved?

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[wild mountain]

No clue on how to start this question
help is very appreciated 🙏

[median dome]

Do you know what the determinant represents in a linear transformation?

[wild mountain]

uhhhhh

the image of i and j values?

[craggy tundra]

no that's the columns of the matrix

determinant is the area of the parallelogram

[wild mountain]

oh

so projection is involved...

[craggy tundra]

ok wait why is your unit square [0,1] [0,1]

[wild mountain]

good question

this is a practice question

[craggy tundra]

is that a typo

oh

[craggy tundra]

errr no i dont think so

[wild mountain]

oh then im lost

[craggy tundra]

im pretty sure you literally just evaluate the area of your parallelogram

which looks to be 3*6

[wild mountain]

i was thinking just 3*6

i need a new lecturer

thank you

.close

[obtuse pebble]

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[obtuse pebble]

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[heady turtle]

how to calculate this one

[obtuse pebble]

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[heady turtle]

<@&286206848099549185>

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[restive gorge]

Can you parameterize the region D?

[heady turtle]

parameterize? it's 1/4 circle with radius 2

[restive gorge]

You want integrate over D

Is f(x) defined or any function?

You can basically use polar coordinates

[heady turtle]

hmmmm

how?

[restive gorge]

you substitute

x = rcosθ
y = rsinθ

then dσ = dydx = r dr dθ

[heady turtle]

Just out of curiousuty, we didn't see the form of x^2+y^2, why do you want to use polar

[restive gorge]

Because the region is a half circle

you can stay on the cartesian plane also if you wan to

0 to 2
0 to sqrt(2²-x²)

[heady turtle]

ooh

[heady turtle]

f>0, that's all we know

this is a really weird form so i dont even know where to start

[restive gorge]

This should be up there in your first msg

Why are you hiding stuff

[heady turtle]

ooh i didnt hide stuff, f>0 bc it's under the root😭

[restive gorge]

lol

I mean f(x) = |...| then f(x) = 0 would be the only thing not allowed

[heady turtle]

hmm not quite understand but ok, so is there any possible to calculate this stuff?

cuz we dont have any expression for f

[restive gorge]

Yea okay

[heady turtle]

?

we can?

[restive gorge]

Maybe [sqrt(f(x)) - sqrt(f(y))] / [sqrt(f(x)) - sqrt(f(y)) ] maybe multiplying by this helps

Maybe there is a clever substitution, like the numerator

[heady turtle]

wait

hey

i found a property but idk how to use it

i found that this intergration, we can change x and y, and it will still be the same

[restive gorge]

oh wow nice property

You found that out?

[heady turtle]

ye but how to use it

[restive gorge]

tbh doesnt seem much of a help

is this calc 1 btw?

[heady turtle]

hmm idk cal 123 but i guess it might be cal2 or 3?

[restive gorge]

Maybe Aslan knows our friend and helper

[heady turtle]

.close

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[upbeat oracle]

Any idea?

[dense imp]

so since you're shown the graph of f(x-4), for what value of x-4 does y = 1?

then you can solve for x using x - 4 = ?

[upbeat oracle]

ahh got it

0

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[lone bobcat]

guys what does it mean
if the range is on the same or opposite side?
ah
the range is centered on -3 in the second case, so you have positive and negative
but in the first case both are to the left of -3
but why is -3 the number of interest here?, and why (-4,-2) doesnt work?

[plucky rivet]

Thats not how minus sign works @lone bobcat

-lnx = ln(1/x)

lna + lnb = ln(ab)

lna - lnb = lna + ln(1/b) = ln(a/b)

[lone bobcat]

how did they get -2ln(2)?

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[crisp marten]

Hello
Can somebody help me with this? I don't know how we got to the red rectangle part

[obtuse pebble]

@crisp marten Has your question been resolved?

[plucky rivet]

Limit comparasion test

Compared these two series given by taking limit of their general terms after dividing them to one another

Since limit is not zero nor infinity, these two series have the same character

Yo initial value being n=3 makes this question way easier ngl

Otherwise its not easy to show that 1/(nln(n)) diverges

Actually nvm still hard

@crisp marten do you know the integral test?

[crisp marten]

Yes

Thank you