help-27

[woven radish]

bacc

[faint gorge]

What happens now for a = 4 and a = -4

[lament schooner]

if i a = 4 then its just 0-0

if a=-4

then

z=1?

[faint gorge]

good

[faint gorge]

no

what happens with (a-4)(a+4)

if a = -4

[lament schooner]

oh sorry i meant

0= -8

[faint gorge]

yes

so

[lament schooner]

therefoer inconsisntent

if a = -4

[faint gorge]

my grammar is also inconsitent

you mean no solutions

for a = -4

[lament schooner]

yes

[faint gorge]

ok

[lament schooner]

but all other a would

haev a solution so

i sit still infinte?

[faint gorge]

whaaat

[lament schooner]

like what i meant is

if only a = -4

is inconsistent

determine the values of a for which the system
has no solutions, exactly one solution, or infinitely many solutions.

whcih would this system correspond to

[faint gorge]

to all

it depends on a as we just found out

.

[faint gorge]

for a = 4 infinite solutions

[lament schooner]

oh

nvm i overthought

ty

[faint gorge]

and for a = -4 no solution

[lament schooner]

sm!

[faint gorge]

sm what

[lament schooner]

tysm!*

[faint gorge]

😂 😭

[lament schooner]

https://tenor.com/view/monkey-gif-18890916

[devout snow]

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[lament schooner]

well the timing

[devout snow]

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[agile violet]

1)a) pls

[flat stratus]

!status

[devout snow]

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

@agile violet Has your question been resolved?

[devout snow]

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[marsh forge]

this is law of sines

angle angle side

i decided to solve for my a

but im getting 25

instead of 27

idk how to do the tool itself but i did sin122.7/a = sin34.4/17.3

i think i've did something wrong but i cant figure out what i've did wrong

[agile elbow]

send the full question

[safe knoll]

17.3 :c

b = 18.3

[marsh forge]

oh shit

one sec

[agile elbow]

oh there it is

[marsh forge]

yea sorry its two seperate pictures

i've got it now i just plugged in the wrong number

[marsh forge]

thank you

since i've gotten my a i'm wondering how could i get my c when im not given the angle or side

would i do 180- angles?

ok 22.9 = y

ty both ive solved the problem

.close

[devout snow]

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[mossy turret]

what's P(a<= X <= b)
can I not split it into the difference of the cumulative function at b and a, given that b>a ?

[faint gorge]

,, \mathbb{P}(a \leq X \leq b) = \mathbb{P}(X \leq b) - \mathbb{P}(X \leq a)

[woven radish]

bacc

[mossy turret]

i don't think this holds though
see, the proof of this says that we're basically taking the union of the intervals,
so when taking their probabilities, we made sure they were disjoint, now they won't be disjoint anymore and I've got an additional term to figure out what to do with, I am just not sure if this is what I am thinking it is, $P(X=a) + F_x(b) - F_x(a)$ where $F_x$ is the cumulative distribution function of random variable X

[woven radish]

Quiet

[mossy turret]

or....
am i supposed to take the limit?

[faint gorge]

how is this related to your original question? Can you post what you are actually trying to do

[mossy turret]

I am splitting the mass function given on a range into its cdf, which is exactly what i did above
i am trying to do just this only?

[faint gorge]

If you draw a number line it should be clear why it holds

[mossy turret]

we need a more rigourous proof than that

[faint gorge]

no

it's common sense

[mossy turret]

we take the union of disjoint events, which we define on the line
that's why, when taking the probability, it introduces the additional term of intersection of your event sets.
that's what got me confused here

[woven radish]

Quiet

Quiet

Quiet

[mossy turret]

check here

the main problem is, this equation may not hold discrete random variables

[mossy turret]

this one ^

[faint gorge]

it doesn't

I assumed a continuous distribution

because then it's negligible

[mossy turret]

obviously

[faint gorge]

but you are right for discrete

[mossy turret]

so,
do i take the limit or add that extra term?

[faint gorge]

idk

[devout snow]

@mossy turret Has your question been resolved?

[devout snow]

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[earnest canyon]

can anyone explain unit circles and radians?

[earnest canyon]

sin (x) = -1/2 where o<= x <= 2pie

how do i figure out the quadrents

[mossy turret]

in 0 to 2pi,
sin function only takes negative values for 3rd and 4th quadrant

this is the standard table

[frosty gyro]

There’s also an abbreviation called CAST

Yea that

[earnest canyon]

yeah i think i got that figured out

[frosty gyro]

Which tells which functions are positive in 4th 1st 2nd 3rd quadrants

[warm breach]

A = all
S = sin & cosec
T = tan & cot
C = cos and sec

all +ve^

[earnest canyon]

im confused where you get x+x/6=7x/6 from

[mossy turret]

I was taught
"After School To College" for the positve values of the functions
A - first quadrant
S - second quadrant
T- third quadrant
C -fourth quadrant

[mossy turret]

what?

can you send the full question

[earnest canyon]

isnt that how u figure it out

[mossy turret]

oh i see what you're doing

[woven radish]

Quiet

[mossy turret]

@earnest canyon if there is any doubt, then let me know

[earnest canyon]

that makes me confused 😭

[mossy turret]

which part did you get stuck at?

[earnest canyon]

so x is in the neg quadrent

but where do u get pie/6 from?

[mossy turret]

its a standard value for sin function
there's a small list of values it is assumed every student knows

[earnest canyon]

can you send me the list?

[mossy turret]

some people also learn the values for 15 and 18 degress, but this is the bare minimum one should know

i am hoping you are aware of radian to degree conversion right?

[earnest canyon]

its like pie/180

summ like that right

so

[mossy turret]

yea
you multiply by that for degree to radian
and for radian to degree, its the inverse of that

[earnest canyon]

so30* would be pie over 6

[mossy turret]

yeah

[earnest canyon]

oh duh

thats what i was getting confused about ig

[mossy turret]

are you clear on why we wrote $\sin(\pi +x) = - \sin(x)$?

[woven radish]

Quiet

[earnest canyon]

nah

canu explain it pls

[mossy turret]

its cause after 180 (which is $\pi$), we get negative values for the $\sin$ function, that's why.
Also, have a look at the graph of the sine function, it makes this whole thing a lot easier to notice.

[woven radish]

Quiet

[earnest canyon]

thats what ivebeen loocking at

[mossy turret]

that's fine
but personally when I was introduced to this
the wave thingy was the first thing that got through my head lol

[earnest canyon]

yeah i learnt that too

i have another question

how come she wrote 4 instead of 2?

[mossy turret]

can you observe from this that there is another value of x for which sin(x) gives the same value?
think you can figure that out?

[woven radish]

Quiet

[earnest canyon]

like pie/2, 1 and 3pie/2,-1?

[mossy turret]

not quite
we want sin(x) to give -0.5 again

let me know if this gets confusing, I'll break it down more for you

[earnest canyon]

yeah it apears further down the graph

idk the number though

[mossy turret]

try to think about it visually for now
interval length is pretty important here
we added $\pi/6$ to the $\pi$ and got to that place
how can we cover that same distance again, if so, what's a good starting point for that

[woven radish]

Quiet

[earnest canyon]

dawg im so confused

[mossy turret]

this might help

[woven radish]

Quiet

[earnest canyon]

what do the blue and yellow mean?

if we are talking about the -0.5 and matching it on the other side

it wouldnt reach 2pie right

[woven radish]

Quiet

[mossy turret]

yes it wouldn't, because we want to stop at -0.5

[earnest canyon]

hang on

so i get like pie/4 pie/6 and pie/3

but like

how do i get the small numbers

like 7pie/6 or summ

[mossy turret]

first off, that's a number greater than pi, not smaller
so you would get it in another quadrant
basically, your sine wave is divided into 4 quadrants just like you did with the circle.

and these quadrants are exactly the same as you made them in the circle

[woven radish]

Quiet

[earnest canyon]

okay

and if i didnt have a graphing calc what would i do?

would i just have to memorise it?

[mossy turret]

make that in your notebook
with practice, you'll be able to do that in your head super quick

i'll just suggest to solve more problems, that'll show you more interesting things

[earnest canyon]

damn alrigh

ill do my best

[mossy turret]

good that's the spirit

[devout snow]

@earnest canyon Has your question been resolved?

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[mossy turret]

this

[mossy turret]

reopening cuz it got closed

[crude wasp]

i mean it seemed like ur problem is basically resolved up there

but if ur worried about X being discrete

[mossy turret]

its anything but resolved 😭

[crude wasp]

then P(X <= b) - P(X < a)

that solves ur issue with P(X = a)

[mossy turret]

okay wait
let me ask
are you familiar with this?
i mean
lke
really familiar that you can help me out 🥺

cuz i have something to ask and i don't want to like, get ditched after a while
cuz i do have to leave for meal

[crude wasp]

depends on what u ask me

[mossy turret]

but i've been stuck on this for so long,ugh
its just so frustrating

[mossy turret]

okay give me a second

[crude wasp]

but like doesn't this resolve ur issue?

[mossy turret]

this issue issued a lot more issues

Help me complete this table please
I couldn't help but think of more permutations while I was waiting for a reply @crude wasp

I can't even convince myself that what I wrote is correct or not

[crude wasp]

i mean we've split it into continuous and discrete but like

[mossy turret]

but?

[crude wasp]

you can just have a 'continuous' r.v. that's like P(X=a) is non-zero for particular values of a

yeah what u've done with the limits is fine

[crude wasp]

what u've written for continuous can also just work for discrete too

[mossy turret]

so all 8 entries use the same formula?

when does it get different?

[crude wasp]

yeah

[woven radish]

Quiet

[mossy turret]

i don't think so
imo
i am not sure
check this out

https://math.stackexchange.com/questions/4555678/what-is-mathbbp-lefta-x-mathbin-colorred-b-right-for-a-discrete

[crude wasp]

in that case u can just take the limit as x -> b- and as x -> a- (separately)

[mossy turret]

for continuous, they said limit stuff
for discrete, i definitely would have to sub/add something....

[crude wasp]

it's exactly as we've said

[mossy turret]

yeah but what about others...
also this won't hold for discrete
there's like some specific value we have to exclude

[crude wasp]

"this works for any random variable X, regardless of if it's continuous, discrete or neither"

[mossy turret]

what?
there isn't?

[crude wasp]

from the stackoverflow thing u sent me

[crude wasp]

the limit excludes it

[mossy turret]

what...

[crude wasp]

you can prove it via events and like all ur measure theory stuff

i kinda cba rn but i could do if u want me to

[mossy turret]

oh..

[crude wasp]

basically

[mossy turret]

well.. uh
idk
what to say...
ig..
i got it?

[woven radish]

Quiet

[woven radish]

Quiet

[crude wasp]

oh yeah mb lol

[mossy turret]

sigh
i got it
okay so, that works for the continuous one
what about the discrete ones

you sure it won't change?

[crude wasp]

wait hang on let me properly think about ur 4 cases

[woven radish]

Quiet

[crude wasp]

that will be ur answer to all 4 cases, holds for all r.v. X

obviously if you had a discrete r.v., i'd advise against actually using these formulas to compute stuff

cus P(X < a) = P(X <= a) - P(X = a) which is much easier to compute than lim x-> a- P(X <= x)

[mossy turret]

yeah exactly
that's what i thought

so.. I was right then...
imo
kind of..
vaguely...

i'll take 50% of the W
you did good job clarifying that continuity part
much thanks to you

[crude wasp]

nw lol

basically overall i'd advise against trying to memorise n different formulas and use logicto work out what the formula should be

(obviously if it asks you to prove it then you need to do ur stuff with events)

[mossy turret]

yeah
my track player was just stuck trying to digest this part
aside from this, question solving was a breeze in the sea

[crude wasp]

then remember that P(X < a) = P(X <= a) - P(X = a) is easy to compute for discrete r.v.

or alternatively, P(X < a) = lim x-> a- P(X <= x)

[mossy turret]

yup
got it now
bows head in thanks

take care

.close

[devout snow]

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[crude wasp]

nw!

[devout snow]

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[summer knoll]

guys i’m cooked

[summer knoll]

can someone help me with b?

i don’t even know where to start

[radiant anvil]

is b the top right question?

[summer knoll]

yup

bro like what even is that

wait are we fraction busting or something like that

[radiant anvil]

I have not heard of fraction busting

you could start by multiplying both sides by 25

[summer knoll]

even the 0.8x too?

I ended up with this

[winter patrol]

its more efficient to cancel common factors (that's the whole point of using the lcm the denominators)
rather than multiply to the numerator directly

[summer knoll]

like when u multiple the numerator solve the fraction?

[snow raptor]

I will tell you a good step

from original equation

[summer knoll]

i think i did this right

[snow raptor]

add 0.8x on both sides

[snow raptor]

yes correct

[summer knoll]

okay bet lemme try ur way too

cause i have a test tomorrow i want this to be easy

[snow raptor]

0.8 = 8/10

[snow raptor]

then add both x terms

[summer knoll]

Like this?

(2/5x)

[snow raptor]

ye

convert 0.8 to fraction

[summer knoll]

how?

[snow raptor]

8/10

[summer knoll]

ohh

okay i got 8/10 now

[snow raptor]

add 2 to both sides

[snow raptor]

you will get +0.8x

bc in original equation its in RHS (negative)

[summer knoll]

what is rhs?

[agile elbow]

Right hand side

[summer knoll]

ohh

[snow raptor]

Right side of equation

[summer knoll]

ohh the 8/10 is positive??

my bad 😭

[snow raptor]

then solve for x

[summer knoll]

like that?

[snow raptor]

yes

[summer knoll]

okay now what

[snow raptor]

add the terms in rhs

[summer knoll]

like -13/25 from both sides

?

[snow raptor]

no I mean add 13/25 and 2 in rhs

don't take the terms to lhs

[summer knoll]

ohhhh

okay one second bag work

okay i got 63/25

[snow raptor]

now multiply both sides by 5/6

basically dividing both sides by 6/5

[summer knoll]

like cross multiply?

[agile elbow]

No that's a different thing

[summer knoll]

period ended in yall free time can yall show me how to multiply by 5/6 😭😭

[snow raptor]

cross multiplication of fractions

[agile elbow]

Alaska is telling you to remove 6/5 by dividing both sides by 6/5

[agile elbow]

I messed up fr

[snow raptor]

yep

[agile elbow]

@summer knoll do you understand it ?

[agile elbow]

When you are dividing a fraction from something, you have to multiply the reciprocal of the same fraction to it. that's how it's done @summer knoll

[snow raptor]

this is how I remember it, but you can remember by KFC which is Keep, Flip Change

[agile elbow]

Never thought KFC will be used in maths

[snow raptor]

KCF or KFC

[agile elbow]

At my time, it was confusing to me ,so I remembered it as flip.

[agile elbow]

Understandable

[summer knoll]

sorry i just got to my next class

[agile elbow]

3 best ways have been shown here

[summer knoll]

lemme read this

okay i get it when i get my notebooks

[summer knoll]

ill plug the fraction into this and send yall the answer

yall can close ticket

[snow raptor]

only you can close it

bc you asked the question

[summer knoll]

oh how do i close it

/close

[agile elbow]

You have to type .close

[devout snow]

@summer knoll Has your question been resolved?

[devout snow]

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[devout snow]

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[wary rain]

How did they get the 2 there when completing the square?

[wary rain]

I thought when you complete the square it just puts a - 1 on the outside? shouldnt it be a 1?

[torn vessel]

it would be a 1, but it get's multiplied by that 2 they factored out in the step above

[wary rain]

so like

it becomes x^2 + 2(y - 1) -1 = 0

where does the 2 that gets factored out go?

[torn vessel]

2(y^2 -2y + 1 - 1) = 2(y^2 - 2y + 1) - 2

[wary rain]

interesting, I dont really get it but im gonna try and watch a yt video, thanks

.close

[devout snow]

Channel closed

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[versed ice]

wrong screenshot

[olive snow]

Well two planes are parralel if their normal vector are colinear and they don't have a common point

[frank siren]

how do u do this

[versed ice]

Brother

[olive snow]

So you would have $(2,2,-4) = \lambda(2,a,b)$

[woven radish]

YakuBros

[olive snow]

!occupied

[devout snow]

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).

[versed ice]

what is lambda here

[frank siren]

no one’s helping me

i had to come

[versed ice]

you asked your question less than 10 minutes ago

[olive snow]

The coefficient of proportionnality/colinezrity

[olive snow]

You can't come up to someone else channel

To ask for help

[versed ice]

oh yeah

[frank siren]

no one helping me mb gng

[olive snow]

Not a reason to ask help in others channel

[versed ice]

thanks yaku bros

.close

[devout snow]

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[olive snow]

Pretty forward after indeed, you're welcome

[devout snow]

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[ancient valve]

Am I correct? How do I do this

[devout snow]

@ancient valve Has your question been resolved?

[devout snow]

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[terse granite]

how do i do this

do the logs cancel

so y^2=x^3

so y=x^3/2

[faint gorge]

ye

but then

your last step is wrong

[terse granite]

?

[faint gorge]

it's y^2 not 2y

you take the square root on both sides

[terse granite]

did i not do y62

[wicked turtle]

probably intended to be x^(3/2)

[faint gorge]

oh

[terse granite]

yh

mb

[faint gorge]

makes sense

mb

[terse granite]

i always forget brackets

.close

[devout snow]

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[rustic pecan]

f(x)=-3(x+1)^2+5
How would i graph it?
(this is gonna be a series of questions so, to anyone willing to answer them, bless your heart)

[next crystal]

yes, start with the most fundamental function you can see, then try graph transformation

[rustic pecan]

how do i do that..?

[next crystal]

can i post an image here? like typing will be hectic

[rustic pecan]

yeah of course

[next crystal]

Sry for the orientation

[rustic pecan]

no worries

😁

my apologies, is this an f?

[devout snow]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[next crystal]

Oh noo, it 'i' in a circle

Like, first point

[next crystal]

Alright

[rustic pecan]

it makes sense now

thank you!!

[rustic pecan]

it was an explanation ❤️

how would i find f(-7) using this graph?

what would be f(-7) anyway?

never mind

[next crystal]

Just put -7 in eqn

[rustic pecan]

figured it out

[rustic pecan]

thank you tho!

[devout snow]

@rustic pecan Has your question been resolved?

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[raw hearth]

i can simplify it to

well the inside to

36

so then its

lim_x-->2(36) = 36

did i do that right

[tender wren]

Limit of a sum is the sum of limits

[raw hearth]

?

[tender wren]

And then apply definition of continuity

[raw hearth]

and that would be

i forgot what applying the definition of continuity means

[tender wren]

$$ \lim_{x\to a} f(x) = f(a) $$

Damn

[raw hearth]

i get what you tried

x-->a

[vocal cypress]

Put a space between to and a

[woven radish]

Anurag.[UdayS]

[tender wren]

Thx

[raw hearth]

so like

what do i do with lim_x-->2(36) = 36

$$ \lim_{x\to 2} 36 = 36 $$

[woven radish]

Devil Wears Prada

[raw hearth]

this is what i simplified it to

from the original function

help

[tender wren]

How does the inside simplify to 36

You can't skip all steps right

[raw hearth]

g(x) = 6

so i substituted

?

but it says g(2) = 6

um

[tender wren]

Right

[raw hearth]

omg

what do i do then

can i make it

wiat idk

[tender wren]

What exactly did you substitute

[raw hearth]

its not possible to do what i did ignore it

i now want to know what is possible

is there a limit law i can use?

[tender wren]

Apply theorems of limits

Assuming you know them

[raw hearth]

which one would work here

i dont know them very well

[tender wren]

Well,

https://youtu.be/1GnxvuzAabQ?si=VUz_w8CoYb0VfCuD

5 mins of your time

[raw hearth]

ok

[raw hearth]

well i watched it and now im stuck

$$ 3\lim_{x\to 2} f(x) + \lim_{x\to 2} f(x) \cross \lim_{x\to 2} g(x)= 36 $$

bruh

how to do multiplication sign in texit

[tender wren]

$$ \cross $$

[woven radish]

Anurag.[UdayS]

[tender wren]

Backslash

[woven radish]

Devil Wears Prada

[tender wren]

Correct

[raw hearth]

ok so i got this now

can i make it

[tender wren]

Now use the definition of continuity

[tender wren]

^

[raw hearth]

$$ 4\lim_{x\to 2} f(x) $$

[woven radish]

Devil Wears Prada

[tender wren]

This is true if and only if fx is continuous

[raw hearth]

oh i dont know that yet

oohhh

$$ 3\lim_{x\to 2} f(x) = f(2) $$

[woven radish]

Devil Wears Prada

[raw hearth]

$$ 3\lim_{x\to 2} f(x) = f(2) + \lim_{x\to 2} f(x) = f(2) \cross \lim_{x\to 2} g(x) = g(2) $$

[woven radish]

Devil Wears Prada

[raw hearth]

$$ g(2) = 6 $$

[woven radish]

Devil Wears Prada

[raw hearth]

so

$$ 3\lim_{x\to 2} f(x) + \lim_{x\to 2} f(x) \cross 6 = 36$$

[tender wren]

Put _ after lim

[raw hearth]

where my 6

[tender wren]

Right

[woven radish]

Devil Wears Prada

[raw hearth]

idk what i can do now

oh maybe move over the 6

[tender wren]

No...

[raw hearth]

oh

[tender wren]

Do you see some linear equation like stuff or

[raw hearth]

what

oh wait

not really

[tender wren]

Do you see the limit thing is the exact same

[raw hearth]

3x + x times 6?

[tender wren]

Don't call it x. Call something else

Like y

But the idea is right

[raw hearth]

ummm

$$ 3\lim_{x\to 2} f(x) + \lim_{x\to 2} f(x) \cross 6 = 36$$

[woven radish]

Devil Wears Prada

[raw hearth]

but like what do i do from here

[raw hearth]

3f(x) + f(x)

?

x 6

oh wait

3f(2) + f(2)

x 6

[tender wren]

Are you aware of the BODMAS or PEDMAS rule from Middle school?

Don't forget that one, it's a handy one

[raw hearth]

yes i gotta multiply

so

$$ 9f(2) = 36 $$

[woven radish]

Devil Wears Prada

[tender wren]

Yeah there you go

Solved

[raw hearth]

nice

$$ f(2) = 4 $$

[woven radish]

Devil Wears Prada

[raw hearth]

thx

/close

.close

[devout snow]

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[devout snow]

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[kindred kernel]

you're on the right track, but i want to ask you

you have n copies of x, correct

[ocean trench]

yep !

[kindred kernel]

and you also have the sum of numbers from 0 to n-1

[ocean trench]

yep

[kindred kernel]

wait i thiknk i see what went wrong lol

you used the wrong formula for the sum of the integers

[ocean trench]

OH

[kindred kernel]

waiaait

no hold on

it's the right bound for n-1

one moment

okay i've got the formula but let me make a

quick derivation for it

and see where you went wrong for it

yeah?

because your idea isnt far off

[kindred kernel]

okay so, let's go back to the original series idea

we have x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5)

right

so

we can say that this is

$\sum_{b=x}^{x+n} b$

[woven radish]

Serphic

[kindred kernel]

pelase tell me this rendered please

oh my god it worked

where x is the integer we started with, and n is the number of integers we want to go by

example, if we started from 5 and went to 11, x would be 5 and n would be 6

we can then separate this into two series

$\sum_{b=0} ^{x+n} b - \sum_{b=0}^{x-1} b$

aand that didnt render 😔

[woven radish]

Serphic

[kindred kernel]

and then you can easily simplify it from there

let me

see

where your method went wrong tho

because it LOOKS like it should be equally as valid

[ocean trench]

i feel as it looks logically equivilant but its not

😭

[kindred kernel]

i may have found out where it went wrong

yep i think i found it

wait 😭 im losing it

no it does work whar

[visual hazel]

does this statement work for even n?

[ocean trench]

n is only a odd integer

im proving wether the sum of every n consecutive integers is always divisible
by n or not

[visual hazel]

should've stated that

[ocean trench]

my bad dawg i thought it was written down buy its above a)

so it works ? 😭

[kindred kernel]

so this was the result i got

now to test when it's divisible 😔

ignore the dummy variables

[visual hazel]

then just let n = 2k + 1

[kindred kernel]

okay so that was a pain in the ass

but it does work out

[devout snow]

@ocean trench Has your question been resolved?

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[ocean trench]

thank you for checking for me !!!!

[devout snow]

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[frozen rover]

anyone can help me solve this mc question thanks

[solid osprey]

could you find the length of each side of the square?

[frozen rover]

yep

[frozen rover]

but i cant find the radius of the circle

[solid osprey]

me too :p im guessing yhetrs some pythagoras thing you can do

[frozen rover]

ive tried to use properties of tangent

[solid osprey]

something you might be able to do is to is to let A be like a coordinate or something

[frozen rover]

but the prob is it isn't coord

I let the center point, drawing lines AC, center to everypoint a b and c

[solid osprey]

yeah its not but as a last result you can probably use it

ill just shut up now :p

[frozen rover]

<@&286206848099549185>

[solid osprey]

if you can get AB and BC, you can do this almost instantly, not sure how tho :(

[sonic badge]

what math are you in?

[frozen rover]

this

[sonic badge]

geometry?

[frozen rover]

ya

I need to find the radius of the circle

so as to find the area of the circle

oh ye thanks

[solid osprey]

no?

[visual hazel]

nah its a lot longer than 7

[sonic badge]

oh shi mb

[frozen rover]

ill send it out again

still cant solve it

I tried to connect lines ac and cg

and also let m being the cente of the circle

connecting lines am, bm and cm

[devout snow]

@frozen rover Has your question been resolved?

[devout snow]

@frozen rover Has your question been resolved?

[cobalt plinth]

reminder use the question's key words such as : tangent
It'll rlly help

y = mx ± a √[1+ m2].

[frozen rover]

thanks

[devout snow]

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[devout snow]

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[unborn cedar]

how do i figure these problems ou

[unborn cedar]

out

[devout snow]

@unborn cedar Has your question been resolved?

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[honest furnace]

can someone please help me understand how exactly a derivative works?

[light niche]

https://youtu.be/N2PpRnFqnqY?si=xhEVjNgpGGeVmsQ8

[honest furnace]

im using this online tracing animation for desmos and its saying the yellow line is the derivative of the quadratic? But then what is the dashed line??

i thought the derivative was the equation of the dashed line

[honest furnace]

yeah i thought that this video was saying that the dashed line is supposed to be the derivative

[light niche]

The yellow line is the derivative at that point

You can see the blue line aligns with the yellow line at one point

[honest furnace]

yes

[light niche]

The yellow line represents the value of the derivative

Look at how the indicators on the yellow line move and align with the the one on the blue

[honest furnace]

Okay

[light niche]

I think someone else could explain it better

[honest furnace]

Im just puzzled on why he keeps saying instantaneous rate of change if the legitimate instantaneous rate of change somehow isnt actually the derivative

[light niche]

It is

The value is the derivative at that point tbh. The function that gives the value is kinda also but the value exactly is the derivative

At the point

[honest furnace]

What do you mean?

[light niche]

The derivative is the value of the rate of change at that instant

[static charm]

The blue line is the tangent line - which is also the derivative for any given x

[honest furnace]

okay

[light niche]

So if you have a function that plots values from x1 to xn the derivative is the value of rate of change at one of those points for that point

[honest furnace]

if this is the case why do derivative equations get so bizarre and convoluted later on

why would a point to another point not be anything other than a straight line

[static charm]

When you take the original function F(x) and find the derivative function F'(x), you can plug in any value of x into F'(x) to find what the slope of the tangent line at that point of F(x) is. The trick is finding the derivative function F'(x) so you can find the instantaneous rate of change for any value instead of trying to draw tangent lines

[honest furnace]

hmmmm

okay i see

[restive river]

i need help

what is anti derivative of dx

[honest furnace]

you’re not supposed to ask for help in a channel thats being used

[static charm]

@restive river im new here but i think you should try #❓how-to-get-help

[restive river]

where should I ask for help

[static charm]

Since it's a fast and easy one. What does dx mean? Derivative of x (or change in x). So what is the anti-derivative of the first derivative of x?

[devout snow]

@honest furnace Has your question been resolved?

[hollow dune]

yo

can anyone help me

[devout snow]

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[wooden hinge]

so uh i have a problem
The question ask "If there are 4 boy and 4 girl and they are arrange in a row, how many way to arrange them so that the boy are not next to each other" my answer is 69120 and it seem so wrong to me

my working is
girl: 4!
boy: 4! x 5P4
2(4!)x5P4

[static charm]

what is 5p4?

[wooden hinge]

nPr

basically permutations

[static charm]

ahh, okay sorry it's been a while since i've seen that form

[ornate cave]

Isnt it like 4×4×3×3×2×2×1×1

[static charm]

well, i'm not entirely sure how to solve it using npr. i would do something intuitive like this.

they must be arranged in either BGBGBGBG or GBGBGBGB. so then if you have 4! permutations for the boys BBBB and 4! permutations for the girls GGGG, you have 4!*4! and then you multiply by 2 again since there are two arrangements BGBGBGBG and GBGBGBGB

leaving 2*4!*4! as my answer. i think im right here

[ornate cave]

I think 4!×4!×2

[static charm]

oh wait but the girls can be next to each other... so you could have BGGBGBGB

corrected the original logic, thank you

[wooden hinge]

that doesnt work though

cause it can be BBGGBBGG if u just 2(4!)

[static charm]

that's why its 4!*4!

not 2*4!

[static charm]

however we still have these cases with 2 girls together

[wooden hinge]

ya i know 4! for boy and girl each

but the boy and the girl will be together

wait

shhould i use 5C4

or 5P4

[flat stratus]

5P i think

cuz combinations there would be 1 total combo which is 4 boys and 4 girls

[static charm]

P, because nPr is for when arrangement matters

[wooden hinge]

yep i found the answer

[static charm]

oh but wait, npr doesn't fit here because since you're using all of the elements of the set

[wooden hinge]

4!x4!x5C4= 2880

this is my 2nd answer

i think this is the correct one

[static charm]

why 5c4?

that's just 5

[wooden hinge]

cause if u arrange the 4 girl

it will be G G G G

so the boy can fit into
G_G_G_G

bruh discord

[static charm]

but dont you have 8 elements instead of 5

[wooden hinge]

let me rewrite hold on

[flat stratus]

pretty sure it's alternating of boys and girls

[wooden hinge]

• G - G - G - G -

[flat stratus]

so it's 4! * 4! and then * 2 cuz it can be BGBGBGBG or GBGBGBGB

[static charm]

there are 3 more

[wooden hinge]

the dash mean the boy can fit into the 5 slot

[flat stratus]

3 more?

[wooden hinge]

siince we only need to choose 4 so 5C4

[static charm]

BGGBGBGB BGBGGBGB and BGBGBGGB

[flat stratus]

oh yea trur

i forgor the girls can go next togtehte

[wooden hinge]

arrangement of choosing slot dont matter so i use 5C4

[flat stratus]

yea 5C4 is more mathematical

[static charm]

it does matter tho, because there are 4!*4! permutations for each of the 5 arrangements

[wooden hinge]

let me think

[flat stratus]

cuz BGBGBGB and another G can go into 5 spots

well 5C4 is sus actually

[static charm]

B1 G1 B2 G2 B3 G3 B4 G4
B4 G1 B2 G2 B3 G3 B1 G4
for example are different arrangements of the same BGBGBGBG ordering

[flat stratus]

i think it's 8C5 - the amount of times boys are together is the mathematical way but that takes too long

[wooden hinge]

i ma rethink my logic

u guys are confusing me lol

[static charm]

im pretty sure its 5*4!*4!

[wooden hinge]

i come up with the same thing

pretty sure thats the working

[static charm]

so you were right about 5c4 lol

[wooden hinge]

ya i guess

[static charm]

im just the silly one who doesnt know the notation

[flat stratus]

5C4 isn't like mathematically perfectly accurate but it works somehow

[static charm]

yeah i dont think its supposed to work out that way lol

[flat stratus]

cuz C says u can only put 1 girl into each space btw boys

but u have the extra 3 from a double - the 3 from 0 girls btw 1 of the boys = same thing

[wooden hinge]

so 5c4 is correct?

[flat stratus]

well, no

u got lucky

[wooden hinge]

i need an expert my brain is getting brainrotted

[agile elbow]

Take a break

[static charm]

I think I figured it out

4 positions for the girls, -x-x-x-x-
leaving 5 positions for the boys at the dashes. so, 4! arrangements for the girls and 5! arrangements for the boys since you can leave a - empty

so that's where your 5 is coming from. i didn't understand at first

[wooden hinge]

hm hm

wait so is my correct

[static charm]

i dont think you use npr/ncr at all because you aren't picking 4 boys from 20 boys, you just have to arrange 4 boys

[wooden hinge]

i use ncr to choose the 5 slot

[static charm]

oh wait im so sorry you're right

yeah because 5c4 winds up being 5!, not 4!

my mistake

[wooden hinge]

finally this question is solve

[static charm]

and now i understand how to use ncr properly 😆 thank you

[wooden hinge]

whoever invented this nc/pr pls never exist omfg

thx ya

[static charm]

haha good luck, hopefully this didnt mess you up too bad. i just got confused by the definitions and because i havent used it in a long time

[devout snow]

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[lament schooner]

is it normal im learning matrices and elementary row operations after gaussian elimination

[lament schooner]

cuz now im just confused why im seeing this

[earnest kite]

its literally just learning gaussian elimination again

except this time there are brackets around the numbers

[lament schooner]

https://tenor.com/view/jet-bean-killer-bean-ragdoll-ragdoll-fall-gif-23762382

okay ty

.close

[devout snow]

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[flat stratus]

!status

[devout snow]

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

@tardy hatch Has your question been resolved?

[tardy hatch]

1

help me

[flat stratus]

well 1st use ur index laws to put 64^21 into 2^n

so u can easily work with 2^stuff

then figure out the patterns of the triangles and squares

then find an equation that summarises the patterns

[devout snow]

@tardy hatch Has your question been resolved?

[devout snow]

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[glossy pilot]

can anyone help write the matrix for quintic polynomial regression

[devout snow]

@glossy pilot Has your question been resolved?

[devout snow]

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[opaque talon]

For b

Why do they sub 99

And not 99-1?

[winter patrol]

you have the equation for the nth term

you're interested in the 99th term
your n is 99

[opaque talon]

But the formula says a +(n-1)d

N -1

So it should be 98 ?

[winter patrol]

no

even if you were to use that formula
n is still 99
the value of n-1 is 98
n is n

[opaque talon]

Yeah but I should use 98

[winter patrol]

wdym

[opaque talon]

For that formula right?

[winter patrol]

no?

n is n

don't conflate n with n-1

you have the equation for the nth term
you're interested in the 99th term
your n is 99
doesn't really matter how your equation/formula is presented

[opaque talon]

Ok but un = a +(n-1)d

So a = 55

N-1 is 98

And d is 2

And then plug that all in

What’s wrong with that

[winter patrol]

the first term isn't 55

your equation isn't quite in the form
un = a +(n-1)d

[opaque talon]

Oh but 53 then?

I thought it was that at first

A =53

[winter patrol]

and d here is -2, not 2

[opaque talon]

Shit

Ah right

Yeah I just got the original method

Over complicating it

Thanks

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[glossy pilot]

No

[devout snow]

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[sharp obsidian]

Can someone help me solve this, but please don't use the second derivative test because I haven't learnt it yet

[robust berry]

Then just calculate critical points for first derivatives

Do you know how to use them?

[sharp obsidian]

Yes

Derive and then equal 0 right?

But then how do I decide whether it's a maximum or minimum?

Cus you get 2 answers for D

[robust berry]

Do you agree that at a maxima, the graph would first go above and then down

[sharp obsidian]

Yes

[robust berry]

And if a curve is going above that is increasing

What can u deduce about first derivative

[sharp obsidian]

Wdym? Like if the first derivative is positive, then a negative, it's a maxima?

[robust berry]

yes

at the critical point

if it goes from + to -ve its a maxima

and vice versa

[sharp obsidian]

But how do I find the gradient before the critical point?

[sharp obsidian]

I'm aware of the chart method but this isn't a whole number so it's confusing

[robust berry]

see

[robust berry]

consider this

when u equate f'(x)=0

u get this critical point

to the left of the critical point

slope that is first derivative is +ve

afterwards its -ve

and it would look like this for a minima

[sharp obsidian]

Yeah but how do I find in an equation whether the gradient is negative or positive before the critical point without a graph

[robust berry]

show me ur first derivative

[sharp obsidian]

So at f'(x)=0, D is either 0 or 4k/9

This is what I got based on the question

[robust berry]

yes

now at 0

plug any suitable value of x before and after 0

[robust berry]

greater than 0 but less than 4k<9

and then just evaluate if it would be +ve or -ve

no need to get the exact value

[sharp obsidian]

I have no idea what's less than 4k/9

[robust berry]

you know the wavy curve method?

for inequalities

[sharp obsidian]

I don't think I've heard of it

[robust berry]

https://www.youtube.com/watch?v=6Er_kP-XWwM

you can watch this or any other related to the topic

[sharp obsidian]

Can I just plug in any positive number into k to make it a whole number? As the question states that k is a positive constant

[robust berry]

you can do that too

[sharp obsidian]

Thank you

[robust berry]

and you can use k/9 2k/9

like that too

[robust berry]

still ill recommend this as itll help u greatly

[sharp obsidian]

Ok I'll watch that

One last question though

Do you think the answer is a whole number?

[robust berry]

it will depend on k

[sharp obsidian]

Ok thanks

Highly appreciate it

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[mild sorrel]

a + b + c + d = 47
a b c and d are positive integers

[mild sorrel]

find number of ways in which this can be done

[robust berry]

are they to be distinct?

[mild sorrel]

No, not necessarily

[restive river]

Hi

[robust berry]

theres a general formula then

n+r-1 C r-1

n is the required sum

[restive river]

I need help

:((

[mild sorrel]

#❓how-to-get-help

[robust berry]

r is the number of numbers like here 4 (abcd)

[mild sorrel]

canyou express it more clearly

ok got it

[restive river]

I need help

[mild sorrel]

hmm

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[abstract dock]

A company's balance sheet shows total assets of $500,000, total liabilities of $300,000, and equity of $200,000. Calculate the company's debt-to-equity ratio and provide a brief interpretation of the result.

[woven radish]

justinyap

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[abstract dock]

.close

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[granite arch]

I am supposed to use a poisson distribution right?

[topaz axle]

no

[granite arch]

what do i use

[topaz axle]

binomial

[granite arch]

thx

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[sturdy mango]

using obs i got this

[sturdy mango]

but when applying

when doing rhl rule

i am getting 0

where i am going wrong?

[stone stump]

what does the expression equal when for example x=2.1

[sturdy mango]

[2.1]+[-2.1]

[stone stump]

which is?

[sturdy mango]

2-3

=-1

but putting

[stone stump]

what about 2.01

[sturdy mango]

h->0 and

replacing x= 2+h

[restive river]

isn't [x] the integer part of x?

[sturdy mango]

u get diff or i did something wrong which i definitely did

greatest integer fn

so no [-2.xxx ]= -3

[restive river]

so this is floor function, ok, makes sense

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[floral lodge]

How should I view the following theorem?

[floral lodge]

"Let P be a measurement of Omega and A1 be an event where P(A1) > 0. Then, Q, for each event A, is defined as a measurement of Omega"

Is it even correct for me to view Q as some sort of function that depends on event A while A1 is a "constant" event?

[teal zodiac]

I think it could depend on what the actual question is asking you to do.

[floral lodge]

Shortly after this, they begin using this theorem to explain repeated conditional probability.

Translating from Swedish to English, please correct me if I am using the wrong terminology

[teal zodiac]

No part of this is saying that P(A1) = 0 means P(A) = 0. At most, you know they are not mutually exclusive.