help-19

[sterile blaze]

there is no second one

[woeful rivet]

sorry my teacher just threw this at us 😭

[sterile blaze]

is there another question?

[woeful rivet]

wait what i got one line

[woeful rivet]

no like hes just making us research how complex numbers change or smt

[sterile blaze]

oh how the curve varies as u change a and b?

[woeful rivet]

but i cant find anything

[woeful rivet]

i think as n changes

oh nvm a and b

how does it change

[sterile blaze]

what happens is, depending on a and b u get some magnitude

the trivial case would be b being 0 and its a real number in which case

if a is 0, we still get 0

[woeful rivet]

my friend did this is she right?

[sterile blaze]

if a is between 0 and 1 it goes to 0 as n increases

[woeful rivet]

how is she getting these intricate patterns

[sterile blaze]

what she got is a spiral but for discrete values

aka a spiral but we only take integer valued points

we get a smooth spiral when we take in all decimal values

[sterile blaze]

as i was saying, if a is 1, z would remain at 1

if a is more than 1 z goes to infinity as n increases

now if a is negative or b is non zero, we can look at the magnitude of z

if the magnitude is 1 as we vary n, we stay on the unit circle. if the magnitude is >1 the spiral goes outwards as n increases. if mag<1 spiral goes inwards

[woeful rivet]

ohh

ok so i just take a ton of examples?

[woeful rivet]

how come some of hers dont look like spirals tho

[sterile blaze]

um

exactly as i said it

[woeful rivet]

oh

so is using de moivres theorem better for this research task?

[sterile blaze]

try graphing y=x^2

u get a curve right?

[woeful rivet]

yes

[sterile blaze]

however if u plot the graph for only discrete values of x and connect them with a line

u get an approximation of the graph

[woeful rivet]

what does discrete values mean?

[sterile blaze]

that is similar to what she got

countable?

[woeful rivet]

oh

[sterile blaze]

in this case just take it as integer values

[woeful rivet]

discrete = countable numbers?

real numbers?

or integers

[sterile blaze]

countable and real numbers are distinct

[woeful rivet]

oh whats discrete then?

[sterile blaze]

just take it as, less values

in this case it would be for integer values

[sterile blaze]

less points plotted before connecting

[woeful rivet]

o

[woeful rivet]

wait so i can only plot 1 line?

i cant plot anymore?

[sterile blaze]

the spiral is when u have a lot a lot of points. so its smooth instead of with distinct edges

[woeful rivet]

oh

how can i plot my existing dots?

[sterile blaze]

vary the t in the menu

[sterile blaze]

if u want to plot only the dots, then do as u did before where u entered in each value separately

[woeful rivet]

omgg

[sterile blaze]

i would recommend you put in the spiral instead though

[sterile blaze]

u got the idea of how it works now?

[woeful rivet]

im pretty sure

is it ok if i dm u if i need some help with it?

[sterile blaze]

id rather u not

[woeful rivet]

oh

can i ping you here instead? :p

[sterile blaze]

i might not respond but sure

all the best

[woeful rivet]

i dont get this step

why do we take the i out?

cause i = y?

[sterile blaze]

when graphing complex numbers we denote one axis to be the real axis and the other to be the imaginary axis

so a point z=a+bi would be on the point, (a, b)

[woeful rivet]

am i saying this right

[sterile blaze]

no..

[woeful rivet]

...

[sterile blaze]

u dont have to mention the y axis anywhere really

u can call it the real and imaginary axis and not mention that

just mention that z^n is |z|^n cis(n theta)

[woeful rivet]

whats cis

[cursive field]

cos theta + **i ** sin theta

[sterile blaze]

cis theta is what ren said

[odd edge]

@woeful rivet Has your question been resolved?

[wispy quail]

Sa

[odd edge]

@woeful rivet Has your question been resolved?

[woeful rivet]

hey are u still here..

[sterile blaze]

just ask ur question

[odd edge]

@woeful rivet Has your question been resolved?

[low vigil]

hey guys i need help... how would you find the nth derivative of sqrt x

[odd edge]

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[viral copper]

i diserve to be in the secret club

[viral copper]

ngl

mods

[onyx cloak]

what

[viral copper]

me in secret club ong

i am an obsidion pillar

[summer river]

I believe you

[viral copper]

i diserve to have a graduate voice

huh

oh

i didnt open dis

idk how to open channels

💀

[summer river]

".close"

[cursive field]

.close

[odd edge]

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[onyx cloak]

!help its a help channel

[cursive field]

this is not the place to ask such questions

[odd edge]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[cursive field]

#discussion

[summer river]

it's all g no harm done @viral copper have a good day

[viral copper]

how did i open a channel

[summer river]

j next time

[viral copper]

thx u 2

[cursive field]

you posted a message here

[viral copper]

bru

[cursive field]

yeah lol

[viral copper]

💀 mb id dint know

[summer river]

it's all g have a good day bro

[cursive field]

go to #discussion or smth

idk

[viral copper]

ight thx

[summer river]

#discussion

[onyx cloak]

if u message in any channel in the math-help category u open a help channel

[viral copper]

ight thx

.close

[onyx cloak]

its already closed

[viral copper]

oh

[summer river]

(stop talking here)

[vernal yacht]

So cute

[odd edge]

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[livid storm]

I have X C U C M, with the closure of X in U (subspace topology) compact, M hausdorff. I want to show that the closure of X in M is the same as the closure of X in U

[livid storm]

I know that the closure of X in U is closed in M, because M is hausdorff

So the closure in M of the closure of X in U is the closure of X in U

I cant get to the closure of X in M being the same as the closure of X in U

[odd edge]

@livid storm Has your question been resolved?

[livid storm]

<@&286206848099549185>

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@livid storm Has your question been resolved?

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[elder wasp]

That should just be $\frac{\lambda^ke^{-\lambda}}{k!} = \frac{12^{10}e^{-12}}{10!}$

[nocturne belfry]

[clever fjord]

Pen

[elder wasp]

which gives 0.104

[nocturne belfry]

[elder wasp]

but the book states it's 0.0859

Jan, this keeps happening when I deal with large factorials or exponents and I am often unsure of whether I am wrong

[nocturne belfry]

,w PDF[PoissonDistribution[12],10]

[clever fjord]

Results provided by WolframAlpha

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

Requested by janniku

[elder wasp]

Yeah

[nocturne belfry]

,calc 2985984/12!

[clever fjord]

Result:

0.0062337662337662

[nocturne belfry]

book looks like a mistake

[elder wasp]

wow

[nocturne belfry]

could go through the parameters swapping k for lambda

to find out what they did wrong

[elder wasp]

There has been 3 word problems before this that were also wrong in the book

I had to verify with my teacher that I was solving them correctly

[nocturne belfry]

if its a well knowner book

you can check for errata

do you know the name of the book

[elder wasp]

Yes

I am not sure what errata is

STOKASTIK Sannolikhetsteori och statistikteori med tillämpningar.

[nocturne belfry]

its a collection of errors in a book that is usually published electronically after a book is released

[elder wasp]

Oh, that would be a life saver!

[nocturne belfry]

i dont see anything through

maybe because its ... finnish

?

idk

maybe theres a different word in finnish

[elder wasp]

Doesn't seem to be one

It's Swedish xD

[nocturne belfry]

damn i was close

also called rattelser

[elder wasp]

Can't find one, tried erratta, rättelser and "tryckfel" which I think is the closest translation

nope

[nocturne belfry]

sorry fren

have to trust yourself, then

[elder wasp]

Welp

I had to ask here when it comes down to word problems cause maybe the logic is wrong

Guess I'll just trust myself when it comes to simple evaluations like this

[nocturne belfry]

depending on the question

[elder wasp]

Thanks Jan for clarifying that I am not delusional

[nocturne belfry]

like, if its probability then monte carlo can be really helpful

but thats a pretty small subset of problems

ive had to do it before lol

anyways, np

[elder wasp]

❤️

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[elder wasp]

"Lina estimates that she gets 1.6 emails per hour and estimates that this is true throughout the day. If $\lambda = 1.6t$, where t is the time in hour, what is the probability of her getting more than 3 emails an hour? You may view it as a Poisson distrubution"

[elder wasp]

If I am not mistaken, one could view this as the complement to getting exactly 3,2, 1 and 0 emails an hour

[clever fjord]

Pen

[elder wasp]

If M = mail per hour, $P(M > 3) = 1 - FM(3) = 1- \sum_{k=0}^{k=3}{\frac{1.6^ke^{-1.6}}{k!}}$

[clever fjord]

Pen

[elder wasp]

The correct answer is 0.0782

Wow, nvm

That was stupid of me, I missed a decimal point when using my calculator

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[weak wharf]

angle AOC + angle BOC = 180 degrees
AOC/BOC = 2/7
Find BOC, AOC

[weak wharf]

NVM FOUND ANSWER

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[spare hill]

Hi, is this answer not (x+3)/(x+4)?

[spare hill]

Not sure why my tutor says that my answer is "not quite"

[zinc glacier]

maybe you need to specify y != 5 and x != -4

[spare hill]

there isn't factorial in this question wdym

[zinc glacier]

im not exactly sure whats not quite about this

oh i mean != as not equal

[spare hill]

Oh, here is what I wrote

I must have mixed up the variables

maybe that is why it is not quite 💀

wait i did not though?

[zinc glacier]

you forgot a comma i guess?

[spare hill]

😭

[spare hill]

Not sure, maybe that is it

my answer is correct though?

[zinc glacier]

seems right to me

[spare hill]

ok then, thank you for your help!

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[elder totem]

hello, i am studying combinatorics and i am lost with permutations and combinations. so classic example of arranging "words", it's n!/r1!r2!...rk! where r are repetitions, but then if i look online it just says n^r

[elder totem]

so for example this question:
1. We have 7 identical balls that differ only in color: 1 red, 3 blue, 1 green, and 2 yellow. In how many ways can we arrange them in a row?
this is using permutations with repetitions
2. In the box, there are identical balls of 4 different colors (at least 7 of each color). In how many ways can we choose 7 balls?
this is using combinations with repetitions

so my questions is what is n^r used for :D

the only thing i can think of is if we have sets X = {x1, x2, ..., xn} && Y = {y1, y2, ..., 2m} the number of functions f : X -> Y will be m^n

[wanton bison]

Say you wanna create password out of 5 letters, where you choose from the alphabet (26 letters).
Since each password is unique and you are allowed to take the same letter multiple times, you would use n^k.
Sine we choose n = 26 and pull k = 5 times there would be 26^5 combinations.

[elder totem]

sure yeah

follow up, for permutations with repetitions, sometimes it just becomes combinations like AAABBB make a 2 letter word it will be 6!/3!3! = 6C3

guessing thats just a special case when it just happens to fit into the binomial coefficient

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[quasi sparrow]

What are x and y

[mystic saffron]

We have to find sin theta - cos theta in terms of x and y

[elfin zodiac]

Set then equal to t

Sin(theta)/x = t

[mystic saffron]

Ooooooh

[elfin zodiac]

That way u will have sin(theta) = tx and cos(theta) = ty

[mystic saffron]

then how do we eliminate t?

sin theta - cos theta = t(x-y)

[elfin zodiac]

Use Pythagorean

Sin^2 + cos^2

=(tx)^2 + (ty)^2

[mystic saffron]

👍 yep

Oh

Can we do (a-b)²

[elfin zodiac]

How?

[mystic saffron]

Sin² theta+ cos²theta - 2sin(theta)cos(theta)

[elfin zodiac]

No

Not ()^2

[mystic saffron]

Then sqrt this expression

[elfin zodiac]

Sin^2(theta) + cos^2(theta)

The left side u know it’s 1

[elfin zodiac]

1 =

[mystic saffron]

X² + y² = 1/t²

?

[elfin zodiac]

Better the other way

t^2 = 1/(x^2+y^2)

[mystic saffron]

Why tho

[mystic saffron]

I recognise this as the equation of a circle with radius 1/t

[fluid tundra]

note sin(theta) / cos(theta) = tan(theta) = x/y

[mystic saffron]

Why this way

[elfin zodiac]

Because

[wanton bison]

x/y?

[fluid tundra]

well that is what the problem says

[elfin zodiac]

Now u have sin - cos = t(x-y)

[elfin zodiac]

And sub t with

[mystic saffron]

Ohhhhh

You're right

[elfin zodiac]

Remember to apply sqrt

To get t

[mystic saffron]

Yes now I can do

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[fluid tundra]

it immediately follows sin(theta) = x/sqrt(x^2 + y^2); cos(theta) = y/sqrt(x^2 + y^2)

& problem is done

except ± which would be necessary to include in ans ig

[mystic saffron]

Yea a triangle with perpendicular= x and base = y

[elfin zodiac]

Are you sure about this?

[elfin zodiac]

.

[mystic saffron]

?

[elfin zodiac]

Dont worry about that

[mystic saffron]

Oh alr

[fluid tundra]

no restriction on the possible values of theta, x, and y except them being reals is implicit, so yes

[odd edge]

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[mystic saffron]

how do i show this converges/diverges?

i wanted to compare it to 6^k / k!

but i dont know

because the ratio test doesent work

it screams comparison test to me

but here is the thing

$\dfrac{6^k + k}{k!+4} > \dfrac{6^k}{k!}$

[clever fjord]

Derivative

[mystic saffron]

and 6^k / k! diverges by ratio test

so the other diverges as well

is this good?

[forest sky]

does it?

[mystic saffron]

it converges

sorry

but isnt this true here? $\dfrac{6^k + k}{k!+4} > \dfrac{6^k}{k!}$

[clever fjord]

Derivative

[mystic saffron]

let me check

ah its false

nvm then

[forest sky]

one thing you can do is split it into two series and show they both converge individually

[mystic saffron]

ah i see

thats true

[odd edge]

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[minor juniper]

Hi math fellows, I need a help to understand the "proof of variance of a discrete uniform(p)"
I'm reading https://www.probabilisticworld.com/mean-variance-discrete-uniform-distributions/
I just cannot understand how to come up with equation(4)? I mean I think I don't understand the algebra behind it.
Any hint is appreciated

[odd edge]

@minor juniper Has your question been resolved?

[minor juniper]

I think I found the solution, I have to study "Sum of Squares of n Natural Numbers" now, like: https://www.cuemath.com/algebra/sum-of-squares/

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[feral igloo]

Im not sure if Im doing this correctly,

[feral igloo]

am i supposed to get decimals when i divide by 48?

[odd edge]

@feral igloo Has your question been resolved?

[feral igloo]

?

[quasi sparrow]

Yes

[feral igloo]

ok

hm.

[feral igloo]

Im not how to do this...

next step is to factor it,

but ah

hm.

im making 3.667-1.5 which is 2.167

And,

I cant seem to remember, whichterm was the one that is the product and which was the sum

i think b is the one that gets added while c is *

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[fierce pollen]

You should subtract 48 from both sides and not divide by 48 on both sides

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[pearl quiver]

Help

[pearl quiver]

It's Algebra 1

I need to know if I'm doing it right because I don't understand how to do it

[woven atlas]

what are u stuck on

[pearl quiver]

The postive/negative thing, idk what it's asking

[woven atlas]

the question is asking you the range where the output of the function is greater than 0 for positive and less than 0 for negative

[pearl quiver]

Huh?

The range is the y and the domain is the x?

[woven atlas]

yes

[pearl quiver]

Ok so that means -5>0, -5<0

Yeah?

[odd edge]

@pearl quiver Has your question been resolved?

[odd edge]

@pearl quiver Has your question been resolved?

[feral igloo]

oh. No wonder. I had solved a similar problem like this by doing that. Does subtracting or adding always work for this then?

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[solid spear]

How do I go from the red line to the yellow line ?

<@&286206848099549185>

[somber jackal]

i'm unfamiliar with the material but it looks like we're just breaking up the fraction? $\frac{a-b}{x}=\frac{a}{x}-\frac{b}{x}$

[clever fjord]

b

[solid spear]

Where did the "v" go ?

<@&286206848099549185> anyone ?

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[signal perch]

How do I do R(x) the revenue

[signal perch]

I'm guessing this is like an exponential equation right?

For r(x)

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[hollow bear]

hi guys I need help

[odd edge]

@hollow bear Has your question been resolved?

[odd edge]

@hollow bear Has your question been resolved?

[odd edge]

@hollow bear Has your question been resolved?

[odd edge]

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[untold tide]

Find g(b) and g’(b) where g(x) is the inverse of f(x)=(x^2+5x)^1-2, where b=6

[amber schooner]

what is f(x)?

$(x^2+5x) - 2$

?

[clever fjord]

knief

[untold tide]

<@&286206848099549185>

[limber glade]

is this f(x)?

[keen hearth]

Do i miss something because its basicly x^2+5x-2 so its in general function which you can find (x^2+5x) - 2=0 via delta

[amber schooner]

that’s what i was asking lol

they wrote ^1-2

which was confusing

[limber glade]

yeah but they disappeared

[amber schooner]

yup

[untold tide]

The exponent is 1/2

Does this help?

<@&286206848099549185>

.closed

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as this action is irreversible, and this channel may abruptly lock.

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[barren lake]

idk if this is the right method or what to do enxt

[dense moth]

Bro

You are given two eqns two variables

[barren lake]

do u js solve it the usual way

[dense moth]

Now we can solve using direct formula

Or

We can do some manipulation

Like we can multiply the first eqn with (1+i) the second with (1-i) and then subtract them to get w

[barren lake]

yea

alr thatll do probs

ty

.close

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[slender haven]

any idea on how does this logic work? i never understood it

[slender haven]

never understood the theoretical concept/logic of this certain topic

[sly crane]

the function is defined differently for different values of x

like you have a graph but that's different in certain parts and different in others

that graph can't be defined by one function throughout

but can be broken in parts which can be defined

so we define it that way

[slender haven]

so in the question i asked it was 2 functions joined to make single function, so does it mean that a function can have more than 2 functions joined into one to form a graph being different from in each part of the line?

[sly crane]

wdym in each part of the line?

also those definitions are only valid for some certain values of x

they have a fixed domain

[slender haven]

i mean the graph line

[sly crane]

i don't think i really understand what's being asked here

but the point is that we are using different definitions to define one function

i think someone else will be able to explain this better

[slender haven]

can we use more than 2 definitions in 1 function?

[sly crane]

sure

here in the above example

there were 2 definitions used

[slender haven]

i said more than 2

[sly crane]

it can be more

yea

ofc

[slender haven]

i think i got it

[sly crane]

as much as necessary

function changes it's behaviour on certain intervals

that's why we use this arrangement

it can change multiple times

so we will have to use it accordingly

[slender haven]

thanks

i'll prolly try some problems on it and to get a better understanding of it

.close

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[amber schooner]

recall that $x^a \cdot x^b = x^{a+b}$

[clever fjord]

knief

[amber schooner]

and $(ab)^c = a^c \cdot b^c$

[clever fjord]

knief

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[scenic lodge]

<@&268886789983436800>

[pastel dew]

lol

[pastel dew]

this is not a physics server

[scenic lodge]

<@&268886789983436800>

[fresh shard]

What?

What is going on

[scenic lodge]

this kid is being a dick for no reason

[fresh shard]

ok well let's chill for a sec

[pastel dew]

WHAT?

[fresh shard]

This is a pretty basic math problem. Does it involve physics? Yes. That is not an issue though

[scenic lodge]

y are you even commenting if you dont know what youre talking abt or even trying to help?

this server you can ask physics questions

[pastel dew]

yeah whatever, I m going to help someone with a real math question

[scenic lodge]

so if you want to complain about it you should write the mods a lletter

[fresh shard]

This is not helpful. If you want the role, I suggest not being rude to people asking for math help in the math server.

[scenic lodge]

totally irrelevant not deserved either

[pastel dew]

stay calm pls

[fresh shard]

Let's refocus on the question.

[scenic lodge]

great

it is a 3 part question

i need help with the last part

for this part i got 36.76

is that correct?

.close

[odd edge]

Channel closed

Closed by @scenic lodge

Use .reopen if this was a mistake.

[fresh shard]

why did you close the channel

[scenic lodge]

.reopen

[odd edge]

✅

[fresh shard]

I'm not offering to help, but just wait patiently and someone will eventually help you

[scenic lodge]

@fresh shard this guy is dm'ing me now

[fresh shard]

Send a screenshot to @pseudo vessel

[scenic lodge]

its not bad but without context it wont make sense.. but ill send it.. he's just doing it to harass me at this point @fresh shard

[pastel dew]

what a big deal wakamole ... I just missed clikc

i am sorry ...i didn t mean to click you

[fresh shard]

[pastel dew]

wakamole think about you question instead

[scenic lodge]

you sent me a messgaE 'lol' as your first messgae you obviously meant to click me, please just leave me alone. ty.

[fresh shard]

I suggest just blocking eachother

[scenic lodge]

great

im going to close this

.close

[odd edge]

Channel closed

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[odd edge]

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[low compass]

Bit lost here in terms of where to begin ?

[wicked kestrel]

Begin by recalling what result the squeeze theorem tells you

[low compass]

this is what it is from our textbook

.close

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[turbid drift]

I'm thinking it's a conjunction but what if it's a disjunction

I'm not sure.

[amber schooner]

no sir

[turbid drift]

So it's a conjunction

[amber schooner]

neither

[turbid drift]

Huyh???

Is it a flow proof? lol

im kidding

[amber schooner]

nope

[turbid drift]

wait\

yeah I got no idea

[amber schooner]

do conjunctions have hypotheses and conclusions?

[turbid drift]

It doesn't say in my book

But I can't find a word that has iut

[amber schooner]

how do i do this without just telling you lol

[turbid drift]

wait

is it a conditional statement

[amber schooner]

what has a hypothesis and conclusion

yes

[turbid drift]

Boom shackalacka

[amber schooner]

https://tenor.com/view/boomer-dhakslaka-gif-8910204572677111429

tough bro

[turbid drift]

It's a take home test

so

im locked in

she said we can cheat

[amber schooner]

<@&268886789983436800>

[turbid drift]

HUHJ

ITS A TAKE HOME TEST

[amber schooner]

alright

did she?

open internet

[turbid drift]

on my momma

YES

[amber schooner]

i fw the pfp heavy

hard bro

[turbid drift]

omg

thanks so much!!!

yk...

I might need

a little more help later on

MIGHT

[amber schooner]

doubt it

you’re killing it man

only took you a few tries to get conditional statement

this test has no idea what’s coming

[turbid drift]

boo ya ka ching!!!

im loicked in

loked*

l;okced*

locked*

[turbid drift]

hey bud

How do I know if it's inductive reasoning or a conjecture

[amber schooner]

from reading your notes

[turbid drift]

ok smart guy

you wanna see the notes?

it says they're the same thing pal;

sooooo

nvm its a proof

im smart

[turbid drift]

alr bud

I finished my vocab test

BOOM SHAKALACKA

I GOT A 40% @amber schooner

[amber schooner]

awesome job

open notes quiz

still gets a 40

setting records

[turbid drift]

40/100 🔥🔥🔥

[amber schooner]

crazy work brother

[turbid drift]

Wel listen

I thought

If I did it without using my nktes

Notes

She’d give me extra credit

You know what I mean?

[amber schooner]

or you could’ve just used your notes and or internet to get a 100

which you did

but you didn’t get a 100

[turbid drift]

Nope

I mean

My grade will go up

I have a 8%

Let’s gooo

[odd edge]

@turbid drift Has your question been resolved?

[odd edge]

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[thin bluff]

How do I draw this?

[hidden trench]

what math is this

[thin bluff]

Geometry

[hidden trench]

i mean grade

[thin bluff]

11th

[hidden trench]

ngl look like smth i learned in tech design class

[thin bluff]

Can u help?

[hidden trench]

can i try

[thin bluff]

Sure

[hidden trench]

what is compass used for?

thats weird

[thin bluff]

To draw arcs or circles

[hidden trench]

oh u mean the thing draw circles

[thin bluff]

Yee

I think I got it

Thanks for trying tho 🙂

.close

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[desert panther]

i don’t know how to start this

[true minnow]

when is a piecewise function continuous?

assuming that your function is continuous, you can rearrange the requirements for continuity to get values for c
you want values for c that support all requirements

[desert panther]

ok i got it

.close

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[vagrant pawn]

I had a question regarding satisfiability.

Lets say we have something like this (P∨Q∨R)∧(¬P∨¬Q∨¬R) and we want to see whether it is satisfiable or not.

When checking for satisfiability we assign truth values to the variables. In the case that we assign it like this P = Q = R = TRUE, this compound proposition is unsatisfiable, because in the second part, all of the variables are negated which means that entire side is false, and we have an "AND" operator in the middle.

My question is when checking for satisfiability can we assign different truth values to the variables, or do the variables HAVE to have the same truth values.

For example: P = FALSE, Q = TRUE, R = FALSE. In this case, the (PvQvR) part would be true, and so would the (¬P∨¬Q∨¬R), which would also mean the entire proposition is true because we have an "AND" sign in the middle.
Im a bit confused because I was going through a youtube video online, and they only tried one combination of truth values so I wasn't sure if all of the variables need the same truth value, or if we can have different truth values.

[vagrant pawn]

I asked this question yesterday in here and got a response, but my TA is telling me that this is wrong and I am so confused.

my TA said this

No matter which variables you assign the T or F values to
The outcome to the above equation isnt gonna be satisfiable
This was pretty clear as the second set of brackets comtain negations of values of the first bracket so logically its gonna be

1 AND 0 or T AND False

Which isnt gonna satisfy it

@gleaming turtle , i saw you answered when i put it in yesterday, what do you think?

[odd edge]

@vagrant pawn Has your question been resolved?

[static totem]

anythgin except TTT and FFF satisfies the formula

like you said

[odd edge]

@vagrant pawn Has your question been resolved?

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[pearl quiver]

What does this mean?

[wicked kestrel]

what does what mean?

[pearl quiver]

Im supposed to solve for x but idk how to

[wicked kestrel]

could you solve it if it was an equality?

[pearl quiver]

What?

[wicked kestrel]

could you solve the equation 7+9x-9=7x-10?

[pearl quiver]

Yeah

You do the constants first

-2+9x=7x-10?

[wicked kestrel]

keep going

[pearl quiver]

8+9x=7x

What now?

[wicked kestrel]

i asked if you knew how to solve it and you said yes

[pearl quiver]

Idk 8th grade is hard bro

[wicked kestrel]

https://www.khanacademy.org/test-prep/praxis-math/praxis-math-lessons/praxis-math-algebra/a/gtp--praxis-math--article--linear-equations--lesson

[pearl quiver]

No its, 9x=7x-8

cuz you add 2 to both sides

You subtract the 7x, so its 2x=-8

Divide to get x alone

x=-4

How do you type it on the inequailty?

[wicked kestrel]

we're getting there

solving linear inequalities is almost exactly the same as solving linear equations

the only difference being, when you divide by a negative number when solving an inequality, the direction of the inequality flips

[pearl quiver]

x>-4

yeah?

[wicked kestrel]

so first, the inequality in the question is $\leq$ so your final answer should involve $\leq \text{ or } \geq$

[clever fjord]

Steakanator

[wicked kestrel]

not >

second, make sure you're 100% sure about which direction it's facing

[pearl quiver]

So its this?

[wicked kestrel]

can you justify why you use >= instead of the <= given in the question?

[pearl quiver]

Cause the thing turned negative?

[wicked kestrel]

what thing?

[pearl quiver]

The solution for x?

[wicked kestrel]

please read this again

[pearl quiver]

Cause you divided by a negative number!! 🤯

[wicked kestrel]

at what point did you divide by a negative number in your solution?

[pearl quiver]

Cause -8/2=-4???

Does it stay the same?

No

So its this?

Thank you guys

.close

[odd edge]

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[cunning parrot]

for what value of n is the given expression arithmetic mean of a and b

[cunning parrot]

<@&286206848099549185>

[odd edge]

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[brazen bough]

this just gives me y' + (6t-3y+12)/(-2t+y-4) = 0

idk what to do with that giant fraction

[narrow crypt]

i suppose

move to right side

and factor?

[brazen bough]

how do I factor with two variables

[narrow crypt]

$(6t - 3y + 12) = -3(2t + y - 4)$

[clever fjord]

Average Calc Student

[brazen bough]

0_0 you're right

yeah that makes it much easier lmao

@narrow crypt if dy/dt = 3, does that mean the integral is 3t

it seems you dont even have to do seperable equation stuff

[narrow crypt]

ye

i suppose + C too?

to give general solution

[brazen bough]

yeah

alright, thx

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[wispy turtle]

Hi, I just wanted to make sure my answer is correct!

[wispy turtle]

Here’s my work

[wild hull]

hi

[wispy turtle]

I would also like if someone could explain whether it’ll be a or e and the logic behind it because I am a bit lost on how you’d know if it’ll be -8 from the left or right

But I do think it has to be a or e

[wispy turtle]

Hello!

[wild hull]

?

[wispy turtle]

what’s wrong

[wild hull]

Just put the value of x

[wispy turtle]

I did

I got -8

[wild hull]

4- means the value is 3.999999999

4+ means the value is 4.0000000000001

[wild hull]

so what's wrong

[wispy turtle]

Yea that part makes sense but

[sonic nova]

Between 3.9 and 4

What does f do

[wispy turtle]

I’m just not sure if it would approach -8 from the left or right

[sonic nova]

This is how you start

Does it increase?

Decrease?

As you approach 4 from left

[wispy turtle]

Decreases

[sonic nova]

So then inside g

The number is going from higher number to lower number

You're approaching from a place greater than 8

Because as x goes to 4 from left,

f(x) approaches 8 from a place greater than 8

i.e. from the direction of positive things

[wispy turtle]

Ahhh I see. Thank you. You do mean -8 though, right ?

[sonic nova]

Yea sorry xD

-8

[wispy turtle]

Haha okay thank you sm!!

[sonic nova]

Whatever the key number was

Ye

Yw!

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[lavish chasm]

X^(2y+1)/X^(2y-1) simplification

[lavish chasm]

<@&286206848099549185>

.close

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[alpine hawk]

Why did you close?

Got the answer?

[lavish chasm]

i forgot to distribute the negative sign

thats all

[alpine hawk]

Okk

X^2 will the be answer right?

[lavish chasm]

yep

.close

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[valid mauve]

How do I solve this problem without plugging in numbers?
gcd(a! ; b!) + lcm(a! ; b!) = 7
a +b = ?
0 < a < b

[short egret]

this isn't that bad for plugging in numbers but if you don't want to... recall that if a<b then the gcf(a!,b!) = a! and lcm (a!,b!) = b!

so basically the problem is just find a and b such that a! + b! = 7

[valid mauve]

i did this

but how can i solve a! + b! = 7?

[onyx cloak]

by plugging numbers

[short egret]

you know they have to be positive integers lol

its not bad at all

1+6=7
2+5=7
3+4=7

only one works

[valid mauve]

i thought its wrong

Thanks.

.close

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[umbral cove]

Can someone help me with this one t hank you

[tulip dew]

the graph of the inverse is reflected over the line y=x

[umbral cove]

..?

lets use easier example

[umbral cove]

i see

but for the graph relation that is shown

its like

not the same i feel like

cause its not a straight line

[onyx cloak]

still the same logic

[tulip dew]

yes

one way you can start is by looking at a point on the existing graph and swapping the x and y coordinate

[umbral cove]

this one would be the right one?

This one has -2,0 as well though

[onyx cloak]

now check for another point

[umbral cove]

Looks about right

so the third option is the answer

Can you help me with this one next perhaps

[onyx cloak]

what is an inverse function

[umbral cove]

the inverse of an f(x)

[onyx cloak]

no i mean

what happens when u inverse a function

[umbral cove]

undoes a function

[mystic saffron]

..

he s talking in terms of range

[umbral cove]

shit idk thats why im asking for help

[onyx cloak]

if f(x) gives you 2 when u input 1

[umbral cove]

i am so lost in this subject. Ive never struggled at math so much

[onyx cloak]

then inverse of this function will give 1 when u input 2

basically domain and range swaps

[umbral cove]

Okay, so if the range is 17 and the domain is 3 the domain will now become 17 and the range 3

[onyx cloak]

yes

[umbral cove]

Okay

so could we use the same logic in this one

[mystic saffron]

ye

[umbral cove]

wait im still tryna figure it out hold up

ok let me do it

[onyx cloak]

wait

its asking for domain of g(x)

u can do that directly

[umbral cove]

so that its inverse is a function?

what does that mean

[onyx cloak]

domain of g(x) so that g^-1(x) is a function, not a relation

[umbral cove]

ok

[onyx cloak]

basically

the inverse of that will be of the form y^2 = x

and this isnt a function

so what its asking is domain of g(x) such that its inverse would be a function

[umbral cove]

holy am i lost

i used to go to school in french

and i dont know any of these words

it was even different letters

[onyx cloak]

[umbral cove]

😭 so sorry

[onyx cloak]

the answer is both A and B

why?

[umbral cove]

why would be great

i am here to learn

[onyx cloak]

if u didnt restrict the domain then it would be this, as u can see the inverse is not a function

[umbral cove]

ngl

i still dont get it 😭 wtf

[onyx cloak]

do you know the requirement of a function

[umbral cove]

kinda

[onyx cloak]

tell me what is it

[umbral cove]

ik any input produces only one output

thats all ik and remember

[onyx cloak]

yes

[umbral cove]

from my days in school

[onyx cloak]

so here

tell me if the white one is a function or not

[umbral cove]

its has no output no>

^*

?*

[onyx cloak]

what

it has output

infact 2 for every input

[umbral cove]

fawk idk what im looking at bro

i never been so lost

like im looking at this one and im so lost

ive tried recreating that on this

but it makes no sense

how come one has a y and one has two Xs

[onyx cloak]

what?

[umbral cove]

the first one i sent

has y = 3(x-1)^2-27

whilst the second

doesnt have a y

for what

[onyx cloak]

what

it has a y

[umbral cove]

where

[onyx cloak]

y = 3(x-1)^2 - 27

^ right here

[umbral cove]

https://cdn.discordapp.com/attachments/903463355619110912/1285489746574835752/image.png?ex=66ea751e&is=66e9239e&hm=fb1d6a7a45131586af9e5697f99ef93d033cd05ec16ddf8ae158c7d42d571cda&

talking bout this one

this what i did and got lost

[onyx cloak]

the f(x) isnt x

its y

[umbral cove]

like wtf am i even doing with my life rn

[onyx cloak]

f(x) is the output when u input x in the function f

[umbral cove]

ohhh fax

i remember that

so

i got it all wrong here

one sec

lemme restrat

holy shit did i do some bullshit

so what did i do wrong here

[onyx cloak]

how did y+3 become y+9

[umbral cove]

oh wait

does the ^2

become the square root^

?*

[onyx cloak]

$(y+3)^2$ -> $\sqrt{(y+3)^2}$ -> $y+3$

[clever fjord]

Astar777

[umbral cove]

okkk

i see

so this one would be the answer

[onyx cloak]

why is that 3 positive

$y+3 = 0$ -> $y=-3$

[clever fjord]

Astar777

[umbral cove]

ohh

makes much more sense now

thanks alot for ur help

i will go and study more on this subject

cause wow was i confused

[onyx cloak]

!done

[odd edge]

If you are done with this channel, please mark your problem as solved by typing .close

[umbral cove]

.close

[odd edge]

Channel closed

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Available help channel!

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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.

[mystic saffron]

How do I do this?

[fervent hawk]

what have you tried?

[mystic saffron]

I just tried shuffling things around to form other trig ratios but nothing worked

[fervent hawk]

ah see, that means back to the start

my first thought is to sub u=tan(x)

that's makes us a nice expression

[fluid tundra]

divide numerator and denominator by some power of cos(u)

[mystic saffron]

I tried that too

[fervent hawk]

oh, what did you get

[mystic saffron]

I got it I think

Man I am struggling with integrals so much

I have another I need to integrate

Integrate ( sin-1 (cosx))

Haven’t got a clue

[steady arch]

sin-1(cosx)?

[dusky cairn]

u=sin^2x simplifies this integral

[mystic saffron]

Yes

[mystic saffron]

What hinted you to try that

[brave gale]

arcsinx+arccosx=pi/2

[steady arch]

do you mind using the bot to represent that im a little confused

idk hjow to use the bot

[dusky cairn]

Whoops that doesn’t work the dx part is on the denominator

[mystic saffron]

$cos^{-1} (sin x) $

[steady arch]

got it

[steady arch]

yeah i get it 1 sec

[brave gale]

$\arccos\left(\sin x\right)$

[clever fjord]

BlazeKunal

[brave gale]

use this

[steady arch]

change sin to cos using pi/2

[mystic saffron]

Yes

[steady arch]

this is making my butt ache so bad i had an exam on integration yesterday

[mystic saffron]

How do I proceed after?

[brave gale]

multiply secx^4 in numerator and denominator

[steady arch]

already tried so, i get (sec^2x)^2

and tanx in the denom

[brave gale]

take one sec^2x for substitution

and expand the other

1+tanx^2

[steady arch]

OH SHIT

thanks dude

[brave gale]

u'll get something like pi/2-arcsin(sinx)

[mystic saffron]

What do I do after?

[brave gale]

then it really depends on limits