help-27

[sand dove]

help us choose a divisor of 2520

[soft parrot]

a wah

[sand dove]

what are you confused by?

[dry geyser]

(divisor = possible factor)

[sand dove]

I'll keep on explaining this in the meantimme

yeah ok to choose a factor of 2520

[soft parrot]

ye

[sand dove]

that factor also has a prime factorization right?

it's gonna look like 2^a * 3^b * 5^c * 7^d * 11^e * ...

[soft parrot]

uhhh

uHh$hhH

[sand dove]

let's first get something out of the way

can there be any other primes than 2,3,5,7 in the prime factorization?

for a factor of 2520

[soft parrot]

idk

uhhh

uHHG

[sand dove]

if there was another prime in the factorization, say 13

that would mean 13 is a factor of a factor of 2520

is that possible?

[devout snow]

@soft parrot Has your question been resolved?

[soft parrot]

yeye

[devout snow]

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[upbeat pawn]

me again

[upbeat pawn]

bro wtf is this

row 1

ok nvm

.close

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[quaint citrus]

@pliant plover whatve u tried

[pliant plover]

im jsut stuck on plugging 3 in for the third function

when i put undefined onto the answer portal it says its wrong

[quaint citrus]

right, u dont put undefined

u put the places where the function is undefined

x = 3 would be an example

wait a sec

[pliant plover]

so do i use limits then?

[quaint citrus]

nvmnd

x = 3 isnt an example

take a look at the bounds of the piecewise

[pliant plover]

yeah 1/2 works but 3 doesn't

[quaint citrus]

wdym by 'works'

[pliant plover]

continuous

[quaint citrus]

but the function is continuous at x = 3

[pliant plover]

it is?

[quaint citrus]

yes

look at the functions of the piecewise

3 functions

the second function is defined from (0.5,3]

x=3 is part of the second function, not the third

[pliant plover]

continuous means no holes vertical symptotes or jumps

in this case there would be a jump on x=3

[quaint citrus]

o shoot

🙈

[pliant plover]

wait a minute

nvm

your right

[quaint citrus]

hold on lemme plot this in desmos

[pliant plover]

your right in a wrong way

because lim x->3 √x+1-2/x^2-9 is 1/24

thank you

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[abstract yew]

A constant force of magnitude F newtons accelerates a particle of mass 2 kg in a straight line from rest to 12m/s over a distance of 16m. What is F

[abstract yew]

How do I get acceleration from the displacement and velocity constant not a function

I think I may be having a mind blank someone help pls

[placid minnow]

what do you think are the kinematic equations you need to start with?

actually even before that

write down a list of all that you are given

and all that you need to find

it sounds dumb but holy hot damn does it make your life so much easier lol

[abstract yew]

F=ma @placid minnow ik

When v is 0 x is 0 when v is 12 x is 16

[placid minnow]

thats

well

alright maybe i shouldve been more clear

first have you learned:

v² = u² + 2as

where:
v = final velocity

u = initial velocity

a = acceleration

s = displacement

F = force

m = mass

[placid minnow]

also this is how you should list things out when you do a problem

except with the actually values or a ? if you dont know it/are trying to find it

[abstract yew]

I haven’t seen that formula maybe not in my syllabus

[vital hinge]

i remember my highschool physics teacher would dock marks if we didnt lay out the question as

• given + looking to find
• potentially useful equations
• work
• final answer

sort of harsh but very useful practice to have

[placid minnow]

to be fair thats what you shouldve done anyways

[vital hinge]

100%

[placid minnow]

that is concerning to say the least

[abstract yew]

Nah this is ext 1 most of it is easy to me

Since I do ext 2 but I just haven’t come across that formula

So assuming it’s old syallabus

[placid minnow]

i dont think this is possible without this equation or like any other similar equation

[abstract yew]

I don’t do physics either

Yea ok thanks

[placid minnow]

do you have like

different notation

cause i cant use fancy letters which is why its like normal letters

[abstract yew]

Nope I think in ext 1 it’s only a= (1/2v^2)d/dx

And in ext 2 it’s vdv/dx and dv/dt

[placid minnow]

ap physics or normal cant remember if derivatives are in normal

im confused because if you only know this much

and none of it like

relates at all

does he want you to just search it up or sum

[vital hinge]

no derivatives were in my highschool physics if that means anything

[placid minnow]

must be ap then

maybe he gave you enough info to derive the equation? ¯_(ツ)_/¯

[devout snow]

@abstract yew Has your question been resolved?

[devout snow]

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[inner ibex]

how would i solve it

[lost laurel]

which question?

[inner ibex]

5a

[lost laurel]

You've solved it, haven't you?

[inner ibex]

it says evaluate

so i need to have it in a simpler form

[lost laurel]

cos(π/3) is known

find cos(π/8) from cos(π/4) now

[inner ibex]

oh ok omg

[inner ibex]

wait wat

how is this known

[lost laurel]

cos(60deg)

[inner ibex]

ohhh oi forgot

wait but pi/8?

[lost laurel]

$cos(2x)=2cos^2(x)-1$

[woven radish]

A dense set

[devout snow]

@inner ibex Has your question been resolved?

[inner ibex]

nvm i did it wrong.

[devout snow]

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[buoyant escarp]

Whats the formula for solving this?

[upbeat pawn]

Log

[buoyant escarp]

https://tenor.com/view/elmo-stare-sesame-street-rocco-death-stare-gif-24438342

right...

[upbeat pawn]

It's stated thr lol..

[fossil locust]

take the logarithm of both sides (it doesn't matter which base you use)

then there's a rule to simplify $\log(a^b)$

[woven radish]

south's secret twin brother

[buoyant escarp]

sadfdwshfkjwml

grr annoying sibling

would this be how? ...

[fossil locust]

that's a different kind of question

[fossil locust]

search up log rules so that you can do this step

[fossil locust]

yeah, okay after you take the logarithm of both sides, what do you get?

[buoyant escarp]

wait what oh right

so uh

log_5 = 12log

hang on,

[fossil locust]

yeah the question doesn't want you to use log base 5 actually

just normal log

[fossil locust]

though this would be a perfectly valid method

[buoyant escarp]

log(5^(4x) = log12

[fossil locust]

cool, and then use rule 3 on your sheet

$k \log m = \log (m^k)$

[woven radish]

south's secret twin brother

[fossil locust]

ah if you know change of base you get $4x = \frac{\log 12}{\log 5}$, same thing

[woven radish]

south's secret twin brother

[buoyant escarp]

hm

dont think it wants this thro

lol

wait

is it this?

....

[fossil locust]

yeah so $x = \frac{\log 12}{4 \log 5}$

[woven radish]

south's secret twin brother

[fossil locust]

just divide by 4 so the 4 goes in the denominator

[fossil locust]

this would be 4 * log(12)/log(5) actually

[buoyant escarp]

oh

thank you.

.close

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[tender fractal]

https://forms.gle/223xkJPcFVoWeXmT8

[tender fractal]

huys

please fiil this

[limpid remnant]

i dont think thats what these channels are for lmao

[vital hinge]

different channel please this is for people who need help with math

[fossil locust]

.close

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[untold pivot]

Im very stuck, im not sure how to proceed

[untold pivot]

A friend of mine told me to show that (c/p)=1 but im not sure how and where this would follow from

[untold pivot]

and oops typo on 2nd set of equations, it should equate to 1*

[devout snow]

@untold pivot Has your question been resolved?

[untold pivot]

@fervent swallow

<@&286206848099549185>

[untold pivot]

<@&286206848099549185>

[full cloak]

what is that triple line thing?

remainder?

[untold pivot]

where

[full cloak]

i prob cant help you with this lol, dont know my termonologies

gl

[devout snow]

@untold pivot Has your question been resolved?

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[tulip stirrup]

What is the first thing you need to do when integrating this?

[timid nest]

apply double angle formula?

[tulip stirrup]

this?

[formal latch]

Nvm correct

Continue

[tulip stirrup]

umm

what to do next

[formal latch]

1 sec

Simplify the denominator

[tulip stirrup]

2(1 - sin^2(x))?

[formal latch]

Yes

[tulip stirrup]

then

oh

[formal latch]

You can write that as cos^2 x

And use substitution

[tulip stirrup]

okay let me try

[formal latch]

Split the integral

[tulip stirrup]

is this looking good?

[formal latch]

Yes

Don't forget dx

From there you can use integration by parts and u sub

[tulip stirrup]

ohh

okay

I think I can do it from now

thanks @formal latch

[formal latch]

Np

[tulip stirrup]

oh wait

that's sin 2x/cos^2x

[formal latch]

Which one

[tulip stirrup]

the right integral

[formal latch]

Yes you can also do that

But why?

[tulip stirrup]

no I meant I cant change the earlier form to sec x tan x

[formal latch]

This is a form easier to integrate

Also there's a shortcut to solve this

[tulip stirrup]

oh

[formal latch]

Let me know if you're finding it difficult to do it that way

[tulip stirrup]

I can change sin 2x to 2 sin x cos x right?

[formal latch]

Yeah sure

[tulip stirrup]

okay I can definitely solve this

[formal latch]

K

[tulip stirrup]

I finally got it

e^x tan x

[devout snow]

@tulip stirrup Has your question been resolved?

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[sharp thunder]

Hello I have a question regarding the first part of the integral

How can we manage to pull out a 1/2 from the z / (z^2 +1) ?

ohhh

could we also split that part ?

so we get z / z^2 + z/1

So we get 1/z + z and then take the integral of this?

integral of 1/z is ln(z)

or where does the 1/2 come from

[small raptor]

It seems like he just did a trick to make life easier

He times by half outside the integral and times by 2 inside

[sharp thunder]

but could we also split it ?

ill use 2 instead

wait

wait wtff

Man I dont understand

how do i do it without that trick ?

[small raptor]

No clue

I don’t do these integrals lol

I just know what they are

[sharp thunder]

okey

[sharp thunder]

So we do another substiution

So we get x/x which is one if we substitute out u = 2u

Or I substitute out that to be

v

Like that

but i dont underastand the second substituion

u / v = 1?

[wooden ravine]

v = u^2+1
dv/du = 2u

[sharp thunder]

ye but then dv is du / 2v

that is that 1/2v part

Like that

wtf is this man

[sharp thunder]

ohhhh ye

I understand

so the u / v * 1/2u

the u cancel

I pull out the 1/2 * the integral of 1/v

[wooden ravine]

Yes

[sharp thunder]

jesus

I had v

thats why they didnt cancel

so dumb

.close

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[restive river]

As X approaches infinity we have the first to equal to 0 and the second term arctan to be pi/2 if you are only considering the principal values

Multiply the numerator and denominator with 1/x^2

And apply limit

[wooden ravine]

Isn't it becuase when x approaches -inf arctan approaches -pi/2 but isn't -pi/2?

So it's larger than -pi/2

[restive river]

The limit both ways is 0

for the first term

as Cnidarian said, (sqrt(3)/x^2 + 1/x) / (1/x^2 + 1)

|arctan(x)| != pi/2 for any real number

infinity is not a real number

consider this

x > -y => x+y > 0

if z>0 then x + y + z > 0

[devout snow]

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[restive river]

He didn't let me finish!

so (sqrt(3) + x ) / (1+x^2) > 0 when x > -sqrt(3)

arctan(-sqrt(3)) = -pi/3

so we can prove the inequality holds at -sqrt(3)

[devout snow]

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[still echo]

I am SO confused. I put 115 but it wasn't the answer. I thought if they were parallel like that they had the same angle? Corresponding Angle Theorem or something?

[restive river]

that is for these two

[still echo]

Oh

So is it 180-115

[still echo]

Awesome tysm

:D

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[void knot]

how can I understand this intuitively

[fiery marten]

The intuition is that when the function can be both positive and negative, it "compensates" positive regions and it's "easier" to converge. However, if you substitute negative regions with positive ones, and it still converges, then it surely converged before that

Of course this is not a proof, it's just how I see it

A proper proof simply formalises this point of view

[void knot]

you mean like if we turn the negative regions all into positive ones？

[fiery marten]

yes

[void knot]

Yea now I think I understand this proof, tysm

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[restive river]

Prove that 2 * 7^n + 3 * 5^n - 5 is divisible by 24 for all n -> N.
I am stuck at proving for n = k+1 (assumption is n = k true)
let it be true for n = k
then 2 * 7^n + 3 * 5^n - 5 is divisible by 24
then 7^n/12 + 5^n/8 - 5/24 is an integer
Now consider the expression for n = n+1 (lol)
S_(n+1) = 2 * 7 * 7^n + 3 * 5 * 5^n - 5
14 * 7^n + 15 * 5^n - 5
Divide this by 24.
7[7^(n)/12] + 5[5^(n)/8] - 5/24 is now to be proved to be an integer.
if 7^n/12 + 5^n/8 - 5/24 is an integer (by our induction hypothesis)

[brittle inlet]

Could you post a screenshot or something?

[thin basin]

Do you know about mod?

Like 7 = 1 mod 3

[polar chasm]

is mod required?

[thin basin]

No but it can reduce the eqn

Like 7x+5 = 2x mod 5

So now you just gotta prove 2x

[polar chasm]

it wont do much here

[thin basin]

It would

[polar chasm]

anyway, the fraction thing is certainly not gonna lead anywhere

avoid fractions

14 * 7^n + 15 * 5^n - 5
you need this to be divisible by 24

2 * 7^n + 3 * 5^n - 5
and you know that this is divisible by 24

[thin basin]

2*7^n + 3*5^n - 5 = 0 mod 24

14*7^n + 15*5^n - 5 = (12*7^n + 12*5^n) mod 24

[polar chasm]

you dont need modulo for this

[thin basin]

I guess

Take 12 common inside the brackets is even

So it is divisible by 24

[devout snow]

@restive river Has your question been resolved?

[restive river]

im back

[restive river]

?

mod 24 should be inside brackets

idk how to proceed

[restive river]

I have not heard of congruence modulo.

[thin basin]

Oh

Just think of it this way

2*7^n + 3*5^n - 5 is divisible by 24

So for 14*7^n + 15*5^n - 5 to be divisible,
You only have to prove 12*7^n + 12*5^n is divisible

(just subtracted the 2 eq)

[restive river]

I think I am basically done.

The original equation is of the form 24m.
12(7^n + 5^n) = 12 * even = 24p
Their addition is divisible, therefore, by 24.

You are a pro

thanks

.close

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[thin basin]

Yup

[thin basin]

Hmm

. close

Lmao

.close

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[knotty plinth]

Can't seem to figure out if I should distribute the A throughout it or factor out the (x-a) ones first?

[twilit comet]

try plugging in specific values to find the coeffs

for example, i would plug in "0" to find A as the other terms all reduce to zero

then we get 1 = A(-1)(-2)(-5)

@knotty plinth hope this helps

[devout snow]

@knotty plinth Has your question been resolved?

[twilit comet]

@knotty plinth could you at least give me a response?

i mean the nerve

[knotty plinth]

sry. I'm current trying this out

[twilit comet]

you

[knotty plinth]

Me

[twilit comet]

really don't need to write it out

notice that 0 is a root of all the other polynomials except for the first

also -10 not 10

[knotty plinth]

-1 times -2 = 2 tho?

[twilit comet]

but

2 times -5 = -10?

[knotty plinth]

I completely forgot about that, my bad.

Does suck that B,C, and D are gonna take a minute tho since I can't just cancel everything else out 😓

[twilit comet]

why not

for B try x = 1

[knotty plinth]

Ok is see now, thx

.close

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[cinder plover]

Did I do 42 correct?

[spiral crag]

I havent done this type of q before but yeah it looks right

[devout snow]

@cinder plover Has your question been resolved?

[devout snow]

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[deft grotto]

I’m not sure how this is wrong?

[winter patrol]

can be simplified further

[deft grotto]

The correct answer says it’s 8/3

[restive river]

12*4

[brisk panther]

12 = 4 * 3

[winter patrol]

use sqrt(stuff you want to root)
/ is read as division

[brisk panther]

I saw that

Mr. Hollywood

[winter patrol]

also you missed the root symbol there

just realised that 4sqrt(12) appeared twice in the image, recropped to make it clearer which one i was referring to

[deft grotto]

Okay

I still don’t get how it equals to 8sqrt3

[brisk panther]

sqrt(12) = sqrt(4*3)

[winter patrol]

apply the same principle you do to get from
sqrt(48) → 2sqrt(12)

to the
sqrt(12) you now have

[deft grotto]

Okay I think I got it thanks

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[orchid pike]

this is zero correct?

for p < 1

[acoustic leaf]

as long as p > 0

[orchid pike]

Ok

can you explain why the series is divergent

series of 1/n^p as n -> infinity

and p < 1

[acoustic leaf]

you can use the integral comparison test

[orchid pike]

Ok gotcha

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[cursive rover]

Sorry just a question
X^-p-1
/
X^-p

How would I show the exponent algebraically sums to x^-1

[devout snow]

Please don't occupy multiple help channels.

[cursive rover]

I just know it by expanding x^-p x^-1 and then canceling the ^-p with the bottom ^-p

[devout snow]

@cursive rover Has your question been resolved?

[stiff thicket]

@cursive rover

didn't you just solve it then?

you have (x^(-p - 1)) / (x^-p)

by exponent laws, (x^(-p - 1)) = x^-p * x^-1

so now just cancel x^-p on top and bottom, and you're left with x^-1

[cursive rover]

Yeah but

How do you do it like

All in one

X^(the exponents) simplifies to the answer

@stiff thicket

If instead of writing it in fraction form I'd write it all in one line and then simplify

How do I show that

[stiff thicket]

oh i see

so we have x^-p as our denominator

that's equivalent to x^p, by exponent rules

so now, in our numerator, we have: x^-p * x^-1 * x^p

so we can collect, and by exponent rules, we get: x^(-p - 1 + p)

well, -p + p is just 0, so we're left with x^-1

[cursive rover]

Oh right thanks

[stiff thicket]

np

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[winged quarry]

if i need my answer in 3 significant figures, then if there would be any decimals before the actual answer, would those decimal also be to 3 significant figures of to 5 significant figures?

[restive river]

your figure starts with the first non zero digit

[winged quarry]

im sorry i dont understand

[restive river]

0.0005067 and your number would be 0.000506

[winged quarry]

thank u

[restive river]

np

[smoky nimbus]

It would be 0.000507 because rounding rules

[winged quarry]

would it because the last digit is higher than 5?

[smoky nimbus]

Yes

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[knotty plinth]

I'm trying to figure out why this doesn't work?

[supple knot]

Why do you think it should

[knotty plinth]

Kinda assumed this is how it worked cuz 1/x = x^-1, thought the 1 from 1/x was part ofx^-1

[thorny narwhal]

$x^{-2} = \frac{1}{x^2}$

[woven radish]

somehybrid

[thorny narwhal]

$x^{-y} = \frac{1}{x^y}$

[woven radish]

somehybrid

[thorny narwhal]

so basically $-\frac{x^{-2}}{2}$ turns into $-\frac{\frac{1}{x^2}}{2}$, which further simplifies into $-\frac{2}{x^2}$

[woven radish]

somehybrid

[thorny narwhal]

so it doesnt work bc you forgot the negative sign

[knotty plinth]

Oh

[knotty plinth]

Are we allowed to ask multiple different questions in these?

[thorny narwhal]

... probably?

[knotty plinth]

Cool, is this correct? I'm studying for midterms and this question isn't in the answer key cuz its all odds and this is an even question

[devout snow]

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[knotty plinth]

Just checking if this ss correct

[trail eagle]

This is wrong. You can't just use the power rule here.

Either use trig substitution or use the fact that this integrand has a known primitive, arcsin(x)

[knotty plinth]

K

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[knotty plinth]

@oak widget pls ban

[solid hull]

<@&268886789983436800>

[dapper storm]

no fkn way wtf

[modest dagger]

For future ref if you need to ping mods ping the actual mod role like gizmic did. Pinging the modnail acct won't ping anybody.

[devout snow]

@knotty plinth Has your question been resolved?

[knotty plinth]

Ah, sry will remember next timw

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[lunar void]

I got 1692pi/5 but it isn't right

[lunar void]

nvm I figured it out

.close

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[still rune]

Can anyone verify this question?

[uncut crow]

you should include the earlier parts of the question too

[timid nest]

we have no clue about how many animals are there

[still rune]

Oops yes sorry!!

[uncut crow]

yep i agree

[still rune]

Okay awesome thank you!

[uncut crow]

"at least one of each species" is a weird way to say exactly one of each loll

[still rune]

Maybe we had to make that connection on our own.

But yeah I see what you are saying lol

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[quartz linden]

Could someone please help me with the problem in the attached image?

[quartz linden]

This is the work for my problem

What did I do wrong? How can I get the correct y_p”?

[acoustic leaf]

if the function you would normally guess is a solution to the homogeneous equation, you should multiply your initial guess by t

[quartz linden]

Could you please give me an explanation of the derivatives in the attached image?

How are those derivatives correct?

Where did the +Acos(t)+Bsin(t) come from in the first derivative?

[acoustic leaf]

product rule

[quartz linden]

yeah I just realized that lol

Also

Why multiply by t?

[acoustic leaf]

due to the product rule, your derivatives will look like:
t*(the derivative of your original guess) + (a new function)
since your original guess was in the homogeneous solution, the part involving t will cancel itself out and hopefully leave you with something you can work with

[devout snow]

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[pseudo rampart]

PLS WHEN DO WE USE THESE FORMULAS MY EXAM IS IN 32 MINS

[olive jasper]

It all depends on question
If question is something like , find value of
2sin²theta+1+cos2theta
You can use the formula 6

[pseudo rampart]

SO I USE THIS TO VERIFY A VALUE

[wooden ravine]

U can use it to simplify and make it easier to solve

[pseudo rampart]

OKAY TYSMMM

!close

[olive jasper]

.close

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[haughty sedge]

Hello

[haughty sedge]

This is my question

C

I want to know if am solving it right or nit

Not*

?

[supple knot]

plug your x=2 into the equation for y to get a number and plug both numbers to see if they satisfy the original equations

[haughty sedge]

Sup riemann can u help

Ok but is my solving way right?

[modern seal]

Looks good to me

But you don't have a y

[haughty sedge]

I do

4y

[modern seal]

And you can follow this to check your final solutions

[haughty sedge]

Ok can u help me in this

[modern seal]

To 'solve' a system of linear equations is to provide a fixed real number for each of x,y,... and so on

[haughty sedge]

Number 3

It says u have to find answer

Points*

And put them on this square

Idk name in english

[modern seal]

(0,0) is the center of the graph

[haughty sedge]

Ik

[modern seal]

(1,0) is the point 1 unit to the right of (0,0)

You're solving for x and y that satisfy both equations

[haughty sedge]

Ik

[modern seal]

Then do it

[haughty sedge]

Uh

Ok.

Thank you ig

.close

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[haughty sedge]

.reopen

[devout snow]

✅

[haughty sedge]

BAC angle is 78 degree

Whats the angel/degree of ABD?

And how do i get it

[wooden ravine]

Angle cdb is same with?

[haughty sedge]

Idk

I have an ibt exam next tmr

So i need to know this

[haughty sedge]

Cab?

[wooden ravine]

Yes cuz this is a parallelogram

[haughty sedge]

What that mean

[haughty sedge]

Yes

متوازي الاضلاع we call it

Anyways

Complete pls

[wooden ravine]

So what's the sum of all angles of any square

[haughty sedge]

360 i believe

[wooden ravine]

Yes

[haughty sedge]

/4?

[wooden ravine]

We know that two of them is both 76

[haughty sedge]

How

[wooden ravine]

I mean 78

[haughty sedge]

How tho

[wooden ravine]

It's given

[haughty sedge]

It says bac is 78

So 3 angels not 2

Angles

[wooden ravine]

So cab and cdb are both 78

[wooden ravine]

Cuz it's a parallelogram

[haughty sedge]

Bro 🥲

BAC
A's angle is 78 cuz he said BAC angle is 78 ye?

Cuz the letter in middle is the angle

Right?

So a is 78 and d is 78

And c and b are unknows

[wooden ravine]

Yes

[haughty sedge]

So x or y or any thing

[wooden ravine]

But we know that c and d are same

C and v

B

[haughty sedge]

Yes

And a and d

[wooden ravine]

N all of them add up to 360

[haughty sedge]

Ye

[wooden ravine]

So we can make an expression for this

[haughty sedge]

Uh

78 + 78 + x + x = 360?

I think?

[wooden ravine]

Yes

[haughty sedge]

Or maybe

2(78 + x )?

= 360

[wooden ravine]

And then what should u do

[haughty sedge]

2 x 78

And 2 times x

So 156 + 2x = 360

Then 360-156

2x=204 i think

Then /2

So ABD is 102

[wooden ravine]

Correct

[haughty sedge]

Sigma

Nvm

Ty for hel0

Help

[wooden ravine]

Good luck

[haughty sedge]

Ty

.close

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[lavish sigil]

I need to find the mle of $\theta$ for a random sample from a population $X$ where $f_X(x) = \frac{1}{2}$ and $\abs{x - \theta} < c$

[woven radish]

jewels!

[lavish sigil]

I don't know how you'd do it since the likelihood function would just be 2^(-n) where n is the sample size

[supple knot]

show how you got your likelihood

[lavish sigil]

Well $L(\theta) = \prod_{i = 1}^n f_X(x_i) = \frac{1}{2} \times \frac{1}{2} \times \cdots \frac{1}{2} = \frac{1}{2^n}$

[woven radish]

jewels!

[supple knot]

there should be an associated domain

[lavish sigil]

yeah that's where theta resides

but how do I connect that to the likelihood function

[supple knot]

Find the domain of L(theta)

[lavish sigil]

hmm

I can say that $\theta - c \leq \min {X_i }$ and $\theta + c \geq \max{X_i}$, so $\theta \in [\max{X_i} - c, \min{X_i} + c]$

@supple knot is that right?

[supple knot]

well c should probably be somewhere in there

[woven radish]

jewels!

[lavish sigil]

mb I have a habit of subbing out arbitrary constants

[supple knot]

yea, i trust you did your inequality algebra correctly

[lavish sigil]

I trust me too

But how do I get the mle from this

[supple knot]

check which endpoint keeps your theta in your interval |x - theta| < c for all datapoints

[lavish sigil]

not sure I understand what you mean sorry

[lavish sigil]

also I think those should be strict inequalities mb

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[hushed sage]

helo

[hushed sage]

anybody

help pls

/end

.close

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[neon folio]

how do i describe the positions of the graph to one another

g(x)=(x=0→f(x))∧(x!=0→−f(x))

is this enough?

[devout snow]

@neon folio Has your question been resolved?

[neon folio]

can i say that the graphs have a y-axis symmetry?

.close

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[silver blade]

It feels intuitive that if there is a minus sign, that the parallel displacement is negative, but it's positive. Can someone explain it in a way that makes my brain say "ahaa!"

[silver blade]

I understand that it's a zero point

[fossil locust]

oh just consider the functions y = x and y = x - 3 for example

y = x has a root at x = 0
y = x - 3 has a root at x = 3

[silver blade]

But why is it going upwards instead of downards

[fossil locust]

hence y = x - 3 is shifted 3 units to the right

so you just shift the black curve pi/9 radians to the right
and you get the green curve

[silver blade]

Ok, so I basically start by thinking how the sinus curve looks like

then I think of shifting it pi/9 to the right

and the scenarios to the left is if it's cosnius, right?

nvm, it's not

I think I got it, thank you!

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[eager stone]

i think we need to give infinity and -infinity to x values but im not exactly sure how that works

[frosty portal]

what does horizontal aysmpnote

mean

[frosty portal]

doesnt every function have a horizontal asympnote then

[eager stone]

no, for example linear functions

x+2=y

also brother im the one with questions 😭

[solid osprey]

hmm im thinking k cant be greater than 2 cause if its like a third degree polynomial or higher then it would become like a linear, quadratic, ect right?

like say k=3, you can manage to divide an x for a linear function

eh idk

ik its cheating but playing in desmos confirms it

[eager stone]

wouldnt anything bigger than 3 work than

oh cant be greater than 2?

[solid osprey]

if its bigger then 3 it would become a polynomial right?

[eager stone]

oh true i think

[solid osprey]

here, maybe it can give you some ideas :p

[eager stone]

is it all even numbers

i cant have infinite answers..

[solid osprey]

by cheating its 0 1 2 btw

why even numbers?

[eager stone]

doesnt like 8 and 10 have horizontal asymptotes too according to the video

[solid osprey]

where

[eager stone]

oh damn mixed it with min value my bad

[solid osprey]

man i shouldnt even help you i dont think im at a high enough level lmao :p

[eager stone]

its fine ty at least i have the right values to speculate over now lol :D

and yeah i think i get it you were right

.close

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[winter yacht]

Each different letter in this addition problem stands for a different digit. A letter stands for the same digit everywhere it appears. Find the value of TEST. HE+SET+THE = TEST

[winter yacht]

Each different letter in this addition problem stands for a different digit. A letter stands for the same digit everywhere it appears. Find the value of TEST. HE+SET+THE = TEST

<@&286206848099549185>

[devout snow]

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.

[sage burrow]

is the point in TEST.HE a decimal point?

[devout snow]

@winter yacht Has your question been resolved?

[solid osprey]

i dont think si

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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[last apex]

Tom is three times as old as Jerry, and in six years, Tom's age will be twice what Jerry's age was four years ago. How old are Tom and Jerry now?

[last apex]

is there no solution to this problem?

how can jerry's age be -14

[static swallow]

ok

let x be the age of tom

let y the age of jerry

you get two equations

[last apex]

ok

then

[static swallow]

do you know how o solve a system of two unknown ?

[last apex]

x = 3y

yea?

but it's not a system of equations though

[static swallow]

yes

and the second one ?

[last apex]

then in 6 years, tom will be twice what jerry is 4years ago

so

jerry's age 4 years ago is y - 4

[static swallow]

nah

[last apex]

what

[static swallow]

write down what the second proposition means

with x and y

[last apex]

huh

so basically

[static swallow]

what does it mean with x and y that in six years, Tom's age will be twice what Jerry's age was four years ago

[last apex]

ok

heres my solution

x = 3y

then in 6 years

so

3y + 6

thats the age of tom

[static swallow]

nah

[last apex]

tom's age will be twice of jerry four years ago

wdym nah

[static swallow]

write x+6 = 2(y-4)

[last apex]

yeah

but x is 3y?

[static swallow]

yep

so now replace x with y

[last apex]

so 3y + 6 = 2y - 8

[static swallow]

uh no with 3y

yeah

[last apex]

then just solve like a normal linear equation

so

[static swallow]

and it makes no gyat damn sense right

what do you get for y ?

[last apex]

3y - 2y = -8 -6

[static swallow]

yeah

-14

[last apex]

yeah

but why is jerry -14 years old bro

[static swallow]

so now multiply by three

[static swallow]

idk prob an issue with the question

jerry is -14 and Tom is -42

[last apex]

makes sense

[static swallow]

yeah

ask yo teacha

[last apex]

what kind of homework

thx yo

[static swallow]

be cool and tell yo teacher that he cant write exercises

[static swallow]

np

[last apex]

aight

.close

[devout snow]

Channel closed

Closed by @last apex

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[quaint apex]

could i get some help on factorising f(x) completely, ive found a and b. a being 7 and b being 1

[devout snow]

@quaint apex Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[vivid topaz]

hello

[vivid topaz]

In the figure below, the end of vector c and the point of application of vector d are at the midpoint of segment QR. Express c and d in terms of a and b.

need help for this

answer are this

[hollow pulsar]

are u allowed to add anything on the figure?

@vivid topaz

[vivid topaz]

idk

[hollow pulsar]

welp thats unfortunate

i guess we find the hard way

[vivid topaz]

there is probably easy way

[hollow pulsar]

i found how to get C

so

in that triangle

can u express the vector c?

using that triangle

[vivid topaz]

idk

[hollow pulsar]

any idea on the relation of chasles?

[vivid topaz]

ah

i know

its like PR=PQ+QR

[hollow pulsar]

how about u express vector QR not vector PR

cause thats what we need

[vivid topaz]

yes

[hollow pulsar]

what would it be

[vivid topaz]

u mean starting by QR= ?

[hollow pulsar]

yes yes

[vivid topaz]

QR=PR+PQ

[hollow pulsar]

wait no

do vector RQ not vector QR

vectors have certain directions

[hollow pulsar]

its QP not PQ btw

u switched letters

which is not allowed in vectors

[vivid topaz]

the first letter is where the arrow goes

?

if its this its RQ=QP+RP

[hollow pulsar]

thats wrong

its PR not RP

[vivid topaz]

why its RQ then

[hollow pulsar]

hope this makes it clearer

use this to reanswer

[vivid topaz]

RQ=RP+PQ

[hollow pulsar]

yes

now substitute a and b

[vivid topaz]

why u said its PR not RP

[hollow pulsar]

i realise i wrote the wrong vector

[vivid topaz]

yeah

[hollow pulsar]

i apologise, sorry

[vivid topaz]

i realised also

np

[hollow pulsar]

so?

[vivid topaz]

wait

RQ=a+b

[hollow pulsar]

not right

u have to always notice the directions

b represents vectoe PR not RP

u have to do smt abt the sign of b to obtain the other direction of vector PR

[vivid topaz]

RQ=a-b

[hollow pulsar]

yes

gj

[vivid topaz]

so d=a-b/2

[hollow pulsar]

u just did the same mistake

focus on the direction

[vivid topaz]

-d

d=-a+b/2

[hollow pulsar]

good

Which vector did we wanna find again

[vivid topaz]

c

[hollow pulsar]

and d as well i suppose

well we found d

do yk that (-a + b)/2 can be written as 1/2 (b - a)?

[vivid topaz]

yes

[hollow pulsar]

so thats d for u

time to find c

focus on that triangle i circled

can u express c from that triangle using relation of chasles?

[vivid topaz]

we only have PQ how i can do that

[hollow pulsar]

actually why do we need that triangle im stupid

We found d

U can find c using relation of chasles in that triangle with vectors bcd

[vivid topaz]

c=b+d ?

[hollow pulsar]

as usual

directions please

[vivid topaz]

-c=-b+d

like that ?

[hollow pulsar]

why did u add a negative sign behind c

[vivid topaz]

idk

[hollow pulsar]

heres a formula of vectors to keep in mind

For any points M and N

MN = -NM

is this understandable or not

[vivid topaz]

its not the same with a b c

[hollow pulsar]

yes in this case u have just one letter to name the vector

which is why

focus on where the arrow is heading

[vivid topaz]

c is heading to down

[hollow pulsar]

if u wanna talk abt the vector that is opposite direction

add -

[vivid topaz]

but here how i can know who is in the oppositie direction

[hollow pulsar]

look

vector d is heading right yes?

[vivid topaz]

yes

[hollow pulsar]

if i wanna talk about that same vector but heading the opposite direction

we call it -d

take vector b for example

its the vector heading from point P to point R

what if i wanna talk about the vector heading from point R to point P? Which is the opposite direction

thats -b

does that help a bit

[vivid topaz]

i still dont understand

[hollow pulsar]

would this help?

[vivid topaz]

i know this

but it doesnt help for chasles

[hollow pulsar]

yes it does