help-0

[alpine sable]

Like it takes up more space

[stuck plinth]

but most of the times professors will ask

"is it bigger or smaller"

and i cant tell wtf they mean

[trim current]

Want to use the mindset of a smarter person, would that be correct as well

?

Just checking my work, last work of the school year ahha

[woeful pulsar]

that's just confusing now

like -100 is smaller than -1 by the < ordering of the reals

[trim current]

?

[alpine sable]

Like it depends on what you mean

[woeful pulsar]

I'll probably just say "negative numbers of bigger absolute value"

[charred flint]

use screenshots dawg

[alpine sable]

In value -100 is smaller

In space -100 is bigger

[trim current]

Wdym

[stuck plinth]

nono thats less confusing

[charred flint]

your laptop has a screenshot key

[stuck plinth]

a bigger negative number is -100 relative to -1

[charred flint]

click that then ctrl+v into discord

[stuck plinth]

but if the professor doesnt say "negative" and just asks "whats the bigger number"

then am i retarded for not knowing wtf they mean?

[alpine sable]

Then it means larger as in value

[stuck plinth]

or are they being too vague

mm

so then itd be smaller

[alpine sable]

Yes

[charred flint]

yea in value is the standard

[stuck plinth]

but

the problem is

i am sure there are professors who dont use this "standard"

[charred flint]

to be specific to what you want you'd say "the magnitude of -100 is bigger"

[stuck plinth]

yeah but this is multiple choice and you cant say that

[woeful pulsar]

by what is bigger, they probably intend you to compare by <
if they say anything about magnitude, then you can do that

[stuck plinth]

alright

[alpine sable]

If not assume value

[stuck plinth]

ill go with that

yeah

alright thanks guys

🍻

[woeful pulsar]

how did you get 1/128

[stuck plinth]

@alpine sable ty @charred flint ty @woeful pulsar ty

[alpine sable]

You're welcome

[jade coral]

ok, so about finding the inverse of an absolute value

how do i go about doing that?

[charred flint]

bigboom can you post the full question again, it really depends on the wording

|x| doesn't have an inverse for all numbers though, since it fails the horizontal line test

[woeful pulsar]

it was up here

[charred flint]

that X->X doesn't mean anything

[jade coral]

here is the entire question.
Let X denote the set of real numbers. Compute the inverse of the function 𝑓:𝑋→𝑋 if it exists. 𝑓 (𝑥)=|𝑥|−2

I realize i left the first line out of the original

[woeful pulsar]

what is X?

[pseudo summit]

is pythagoras theorem just a simplification of the law of cosines? Or like, one of them derived from the other?

[charred flint]

oh well I'm sure the question means real numbers so there's no inverse

[jade coral]

why would that be?

[charred flint]

like |x|-2 is V-shaped so there are multiple points with the same y-value

so the function sends multiple x values to the same y value

[jade coral]

ah

that makes a lot of sense

[charred flint]

an inverse would try to send the y values back to x values, but it would have multiple x to choose from

[jade coral]

that helps me a ton. Now im off to learn how to prove by mathematical induction in the next 12 minutes XD

thanks a bunch

[trim current]

2 to the 7th

Did I do something wrong maybe?

[woeful pulsar]

but why plug in n=-6

[trim current]

Because the 8th value is -6 so I just want to make sure that i did it alright

[trim current]

-6 is what it is equal to

[woeful pulsar]

oh wait

n=8

whoops there was not enough resolution to see that (in discord)

[trim current]

Oh, so is my answer correct then?

[trim current]

My b lol

[woeful pulsar]

the presentation can be improved tho

[trim current]

Yeah my b lol

[woeful pulsar]

like don't write $\cdot128=\cdot128$

[ocean seal]

811ττερραlE

[trim current]

How should I change that

[pseudo summit]

so, the law of cosines is based in pythagoras theorem?

[trim current]

Like times 128/1?

[woeful pulsar]

well you can just implicitly do it and then state the value of a

however, don't use a to both refer to the first term and the function that gives each term

[trim current]

Bro hold up what did u say XD

my mind is dumb rn

[woeful pulsar]

you used -6=a(1/128) to use a to mean the first term

but you wrote a(n)=...

don't use the same symbol for two different things

[trim current]

Ohh so like for the second part where I show the equation

[trim current]

Wait im confused

So this is what I got, what should I change? @woeful pulsar

[pseudo summit]

[sacred flax]

Can someone tell me whats wrong or if there is nothing wrong

[woeful pulsar]

don't write $\cdot\frac{128}{1}=\cdot\frac{128}{1}$

[ocean seal]

811ττερραlE

[woeful pulsar]

like yeah they are probably the same

but just show the next step after applying that transofmration

[trim current]

Should I delete it then?

Or just put one of them instead?

[woeful pulsar]

just show what you get after you put the same thing on both sides

if you really want to write it you can say "multiplying both sides by 128" explicitly in words

[trim current]

Ohh like this

[woeful pulsar]

yeah, now the next issue is you use a both as a number and a function

[trim current]

Where at and how should I change it?

[woeful pulsar]

just use two different letters

like f(n) for the function

or just a_n

$a_n=...$

[ocean seal]

811ττερραlE

[trim current]

I can't do this on the thing I'm pasting it on so I have to put like a()

[trim current]

A(n) is the worse part

Otherwise I would use that

[woeful pulsar]

A(n) might be better tho, otherwise you are using the same letter for two different things

[trim current]

Yeah, thanks bro

One more question I think haha

Blurry asf

[trim current]

How does that look? @woeful pulsar

[woeful pulsar]

well you made a calculation error I think

for the final answer

[trim current]

Oh,

[woeful pulsar]

not sure about the other box, I think they expect just numbers in the formula

but idk

[trim current]

Oh

So what part did I get wrong then?

Like what would the final answer be? Let me try to figure it out then

[woeful pulsar]

the calculation

[trim current]

Would it then be 9207 instead of 9027?

[woeful pulsar]

yeah that looks reasonable

[trim current]

@woeful pulsar something like this looks reasonable?

[cosmic stream]

Can I have help with this? I don’t know how to do it

[woeful pulsar]

the idea's there, the correct answer's there, tho I'm not sure what to put in the box when they ask for formula

[woeful pulsar]

what identities do you know about binomial coefficients that can simplify the problem? do you understand the question?

[cosmic stream]

I have no idea how to do it

[woeful pulsar]

n choose n-2 can be simplified

so that it's easier to work with

[cosmic stream]

o choose-2?

[woeful pulsar]

wait how

[cosmic stream]

I’m just guessing I know how to do this with factorials

But not like this

[neon sonnet]

Guys please i need help

I need help with a study guide

I have a quiz on monday and i need to study

Can someone help me understand

[trim current]

Ty sm bro, ima eat then I need to check some other stuff 🤣

@woeful pulsar

[woeful pulsar]

hmm then maybe try it with factorial definition of binomial coefficents

see what cancels out and see what's left

[cosmic stream]

How do I find that?

[woeful pulsar]

just write $\frac{n!}{(n-2)!2!}=66$ and cancel out everything that's common, see what's left

[ocean seal]

811ττερραlE

[cosmic stream]

I can do it from here

I just didn’t know how to get that

I got 12

N=12

@woeful pulsar

[woeful pulsar]

basically apply the factorial definition of binomial coefficients

[alpine sable]

I have a question

Is “selecting a group of students to go on the New York trip”a permutations or combinations?

[cosmic stream]

I don’t know what that means D:

[woeful pulsar]

remember that ${a\choose b}=\frac{a!}{(a-b)!b!}$

[ocean seal]

811ττερραlE

[cosmic stream]

Oh ok

I didn’t know about this formula thank you!

How do I do this?

The first one has 2 cards possible

2nd one has 48 cards possible

3rd one has 17 cards possible

4th one has 16 cards possible

[trim current]

I'm back @woeful pulsar haha

Now time to check other things let me pull it up

[alpine sable]

@cosmic stream There are 52 cards in the deck

There are 4 suits

So there are how many black 7s?

[cosmic stream]

2

[alpine sable]

Yes

So put that over the amount of cards in the deck

Then simplify

[cosmic stream]

Oh just regular probability

[alpine sable]

Yes

[cosmic stream]

I over thought this lol

Thanks!

[alpine sable]

Yw

[trim current]

Would this be correct m

[vivid sinew]

yea

i got same

[trim current]

You got the same for my answer?

[vivid sinew]

yes

[trim current]

Just wana make sure u are not talking abt anyone else haha!

[vivid sinew]

ok lit

could someone help me for my problem

[alpine sable]

So take the amount of letters that could be used as the first letter

Multiply that by 26

Then by 26 again

Then there are 10 possible digits

So multiply by 10 3 times

[trim current]

26 times 10 times 10 times 10

Most likely would equal the answer if I'm correct

[vivid sinew]

how about y or z?

[trim current]

@woeful pulsar idk if ur on but what would u get for this?

Or anyone in general. What would u guys get for it, m

?

[woeful pulsar]

not the first option

because when you plug in k=1 it doesn't give 3

[vivid sinew]

could u look if mine is right

[trim current]

Yeah I was thinking the same thing

[alpine sable]

Hey Boi1da

[woeful pulsar]

check the other options by plugging in k=1 and see if it gives you the same numbers

[alpine sable]

Do 2 x 26 x 26 x 10 x 10 x 10

[vivid sinew]

why would u multiply by 2?

@alpine sable

[trim current]

I got the third one

[woeful pulsar]

^

[alpine sable]

Because y or z is 2 letters

[trim current]

Yessir

[vivid sinew]

oh ok

@alpine sable

it says 3 letters

so wouldnt it be 26^3

[alpine sable]

I just read it it is worded strangely

[vivid sinew]

ik

[alpine sable]

Do 2 x 25 x 24 x 10 x 10 x 10

[vivid sinew]

why 25 and 24

bro

there are like 10 other places to ask

[trim current]

Wdym?

Oh my b srry

[vivid sinew]

its ok

[trim current]

I'll delete this and post it somewhere else my b bro

[vivid sinew]

its ok

@alpine sable

why 252421010*10

25x24x2x10x10x10

here question

[cosmic stream]

Can someone help me with this?

[cosmic stream]

<@&286206848099549185>

[full canopy]

i mean since the bride and groom must be in the middle they can be excluded temporarily. Just looking at how to arrange the other 6 people the answer is 6! , then you double that since there are 2 cases for the bride and groom, the one where the bride is on the left and the one where the groom is on the left. so 6! * 2 is 1440.

I could be misinterpreting the question tho

[cosmic stream]

Oh ok ty!

But if 2 groomsmen are next to each other it’s the same if they swap places right? @full canopy

[tight locust]

think about it like this

3 bridesmaids : A, B, C

Bride and Groom: E, F

groomsmen: G, H, I

now make a group:

A, B, C, (E,F), G, H, I

there's only 7 objects

so 7!

but you must multiply that by the number of permutations of the group

so actually 7! * 2!

,w 7! * 2

[ocean seal]

Results provided by WolframAlpha

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

Requested by EndTimes#8053

[tight locust]

wait nvm it is 6! * 2

because bride and groom are always in the middle

[golden birch]

Guys are you using this channel?

[mystic sinew]

2 * 1 0
0 2 1

why is this not 2
0

[vivid sinew]

??

[mystic sinew]

it's 2 0 times the matrix 2 1 times the matrix and 0 0 times the matrix and 0 1 times the matrix right

[glass lichen]

$\begin{bmatrix}1&0\2&1\end{bmatrix}\begin{bmatrix}2\0\end{bmatrix}=\begin{bmatrix}2\4\end{bmatrix}$

[ocean seal]

Mosh

[glass lichen]

since it's 2[1,2]

[mystic sinew]

why is 2 0 not on the left?

[glass lichen]

cause 2x1 then 2x2 dont commute

[mystic sinew]

$\begin{bmatrix}2&0\0&0\end{bmatrix} =\begin{bmatrix}2\0\end{bmatrix}

[glass lichen]

also when we define a linear transform (operator in this case) $T:V\to W$, we can equivalently consider the co-ordinate vector concept of everything by defining $T[v]=(T)_{\beta}^{\alpha}v$ for respect to some V basis $\beta$ and W basis $\alpha$

[mystic sinew]

wince x + y = x + y + 0z

[ocean seal]

Mosh

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

[mystic sinew]

you can commute 2 0
0 0 with it tho

[glass lichen]

you cant do a 2x1 times a 2x2

[mystic sinew]

and that's the same as 2
0

[glass lichen]

it's not

a 2x2 isnt a 2x1 matrix

[mystic sinew]

2 is just the same as a linear equation where 2x right

[glass lichen]

what??

[mystic sinew]

and 2x + 0 z = 2x

that's how we were thought matrices that they are systems of linear equations

[glass lichen]

yeah you add the 0 coefficients when doing Gauss Jordan

[mystic sinew]

what

I don't know what that is

[glass lichen]

but that doesnt mean you willy-knilly add 0's and pretend like they're the same things

a matrix is an object by itself

[mystic sinew]

I don't know what you're talking about bro I am doing HS math

[glass lichen]

I mean you suggested that $\begin{bmatrix}2\0\end{bmatrix}=\begin{bmatrix}2&0\0&0\end{bmatrix}$ which is just false

[ocean seal]

Mosh

[mystic sinew]

I derived that since we were taugh that matrices correspond to a system of linear equations and that you can write pic attached as
y= 2a + 0b
y = 0a + 0b

is that not correct?

that's how I've been thinking about them

[glass lichen]

those arent equations

yeah a=y/2 is the solution to that system

[mystic sinew]

I never said anything about a= y/2

[glass lichen]

you asked me what the solution to y=2a is

a=y/2

[mystic sinew]

I asked you if matrices correspond to a system of linear equations

[glass lichen]

they do

Ax=b is a system of linear equations

[mystic sinew]

then if it corresponds with 2a + 0b and 2a + 0b = 2a + 0b + 0c

[glass lichen]

sure if you want to add variables that dont exist

[mystic sinew]

a variable corresponds to a collumn right

and the coefficient to the thing in the collumn

therefore there's a new column in the matrix with thing inside that's 0

[glass lichen]

ok sure

[mystic sinew]

so this is true?

[glass lichen]

no

[mystic sinew]

where was my logic wrong

[glass lichen]

cause matrices by themselves are not systems of equations, since it's not augmented with a constants vector

$Ax=b \iff [A|b]$

[ocean seal]

Mosh

[mystic sinew]

what's that notation?

what's a constants vector

[woeful pulsar]

it's an augmented matrix

[mystic sinew]

what's an augmented matrix?

[woeful pulsar]

basically the notation smooshes the matrix and the vector together

so that they form one matrix

[glass lichen]

the 3x3 matrix is the co-efficient matrix the 3x1 vector is the constant vector

[final crag]

Could I use a program to graph my matrix btw?

[final crag]

do you know?

[glass lichen]

"graph a matrix"

[final crag]

i made a transitive closure matrix

but im not sure how to graph that

[glass lichen]

beyond my scope of LinAl

[final crag]

could i use that?

https://graphonline.ru/en/create_graph_by_matrix

<@&286206848099549185>

[wary stream]

What matrix question did you have?

[final crag]

i have a transitive closure matrix

from a graph

but im not sure how to graph it

been stuck on this forever now

[woeful pulsar]

yeah I think it's something like that

so you have 0 and 1s in your matrix?

[final crag]

yeah

[muted raft]

Adjacency matrix

[final crag]

just straight 0 and 1s

[woeful pulsar]

yeah, then treat it as an adjacency matrix

[timid wedge]

could someone explain this to me

I am a little confused in the wording

[woeful pulsar]

how many roots can a degree 6 polynomial have

real roots

[timid wedge]

6 right

[woeful pulsar]

not sure if you should count multiplicity tho

well it can have up to 6 real roots

do you count repeated roots?

[timid wedge]

yeah

like (x-2)^2?

[woeful pulsar]

yeah

[timid wedge]

yea

but im confused on what it is trying to ask me

haha

[woeful pulsar]

how would you make a graph with fewer than 6 real roots

[timid wedge]

make it not intersect the x axis?

[woeful pulsar]

okay that's 0 real roots

how can it look like?

[timid wedge]

like this right?

@woeful pulsar

[woeful pulsar]

yeah but might want to draw it smoother

that's one possible general shape for 0

[timid wedge]

well yes this was a rough sketch

[woeful pulsar]

can you try making 2?

or 1?

[timid wedge]

yea

would it be this?

[woeful pulsar]

actually the diagram on the right

has a root with multiplicity 2

[timid wedge]

oh how would you make it 1?

[woeful pulsar]

is it possible?

[timid wedge]

mmmmm

let me check

i dont think so

[coral pagoda]

One way is to make it so the graph never touches the x-axis

So something like x^6+1 has all complex roots

[timid wedge]

ooohhh ok thank you

[crystal quest]

can someone help me?

[crystal quest]

is it neither or perpendicular ?

[gilded quarry]

can i have some help with this question E7+A7

(btw its hexadecimals

[woeful pulsar]

use your standard addition algorithm

[wary stream]

Honestly I would convert to decimal, add, then convert back to hexa

[woeful pulsar]

start from units digit

[gilded quarry]

ok thx for the tip

[drowsy scroll]

What is the answer here
$2y^{3}-2y^{3}$

[ocean seal]

BP

[woeful pulsar]

??

[drowsy scroll]

Just $y^{3}$?

[ocean seal]

BP

[woeful pulsar]

like are you supposed to simplify this?

what's X-X

[drowsy scroll]

0

idk

[woeful pulsar]

yeah

you are subtracting something from itself

[timid wedge]

hi again :D i need help solving for X

pls

[ionic jewel]

why are you solving for x

not sure it's actually possible

[timid wedge]

idk thats what my teacher wants us to do

[woeful pulsar]

it's a quartic here

it's possible

there are closed form solutions

in radicals

[ionic jewel]

maybe they want you to simplify?

oh

my bad then

math I don't know

[woeful pulsar]

but it's not usually taught

[timid wedge]

its end of yr things

next week is my last week so hes making it the most painful as possible :/

[woeful pulsar]

are you sure you are supposed to solve for x

[ionic jewel]

you can factor out an (x-2) and an (x+3), that's probably what they want

[woeful pulsar]

x in terms of y?

[timid wedge]

he just typoed the equation

this is the correct equation

[ionic jewel]

you do not have to solve for x in terms of y

[timid wedge]

oh just with 0 sry

just x

[ionic jewel]

you need to do B before C

did you do B?

[timid wedge]

I did b

yeah

[ionic jewel]

what intercepts did you get?

[timid wedge]

-3,2

[ionic jewel]

yes

so you know the factored form of the equation had an (x-2)(x+3)

so you can divide your polynomial by those to get the rest

[timid wedge]

ohh ok

[ionic jewel]

it'll leave you with a quadratic that has imaginary solutions

[shrewd sable]

Complex, not imaginary

[timid wedge]

wouldnt it be (x-2)^2+(x+3)^2?

[ionic jewel]

no

[ionic jewel]

doesn't that make them imaginary

[timid wedge]

^^

[ionic jewel]

or does that only mean scalars of i

[shrewd sable]

No, if they were imaginary they wouldn't have a real component

[ionic jewel]

ah i see

[normal lance]

Tell something about vector

[ionic jewel]

no idea where this came from but it's not right

[timid wedge]

because wouldnt this graph be 2nd degree?

the graph is confusing me

because it looks like its 2nd degree

[ionic jewel]

it's not

[crystal quest]

Is it okay if the slope is -x/3 like this?

[timid wedge]

why not just for clarification

im a little confused on that

[ionic jewel]

because it has an x^4 in the equation

[timid wedge]

yes but lets say that they didnt give me the equation

and only this grapoh

how would I know that its degree 4

[ionic jewel]

then guessing quadratic is reasonable

[timid wedge]

oh lol

[ionic jewel]

although if you plot all 4 points given i don't think you can fit a quadratic to them

eg intercepts and vertex

[timid wedge]

I see

well thank you for the help! :p

[alpine sable]

Not really sure what to do

The letter on the very right is a D

[normal lance]

Teke the radius

[alpine sable]

I don't know that yet

I need to find it

[normal lance]

Make another with radius OF OD OA OC then see it

[alpine sable]

Gotcha

Would I use pythag to find it?

[sage rapids]

OE=2 and radius= 2√5

[alpine sable]

Thank you

[timid wedge]

@ionic jewel last question

so would I didvide the equation by both x intercepts?

[timid wedge]

so both?

[ionic jewel]

yes, you can try to manually factor it (its all integers iirc) or do synthetic/long division

[timid wedge]

for the synthetic

would I first divide by (x-2) first?

or both?

[ionic jewel]

i forgot how synthetic division works ngl

[timid wedge]

lol its ok

[ionic jewel]

but i think you can only do one linear factor at a time

[timid wedge]

ok so one at a time?

[ionic jewel]

or do both if you know how

you can multiply them together and do both with long division

it ends up like

$$y=(x-2)(x+3)(x^2-2x+8)$$

[ocean seal]

bunny

[ionic jewel]

then use quadratic equation on that last part to find the complex roots

[plush zephyr]

not able to solve my homework :(

need to find its roots 👀

[ionic jewel]

heres a hint

$$a^{\log_a(b)} = b$$

[ocean seal]

bunny

[ionic jewel]

@plush zephyr

[plush zephyr]

hmm

[ionic jewel]

assumign its log base 2 of (x^2) and not (log base 2 of x)^2

[plush zephyr]

then

ughm

so x^2?

x^2 - 3x - 4 = 0

roots are 4 and - 1

👀 thanks @ionic jewel

@ionic jewel help again :(

[strong furnace]

what have you tried ?

[plush zephyr]

a lot

these are a bit confusing so can't/not able to answer

but the rest I've found out

and also this is the last question of my math homework 👀

[strong furnace]

notice how the missing term from the power is 1/log(a) for a^(something)

[plush zephyr]

nvm I've found an optional so can leave this 👀

uhuh..

[strong furnace]

does that mean I should continue or are you confused

[plush zephyr]

I'll get to confused maybe later :)

[strong furnace]

so continue?

[plush zephyr]

⛔

Thanks anyways

[echo spire]

I do get stuck around here

If I substitute them into the formula

It is giving me nothing

Exercise 5 I need to prove that cos(a+b) = that formula.

[timid wedge]

is this correct?

[strong furnace]

it is

[timid wedge]

ty man

[frigid moon]

Question and answer is boxed. I don't understand why 1 and 0 are included, to me, those points aren't "in" the box

I see that as a point "on" the cube, but not a point "in" the cube. I feel like there is a distinction that the author isnt considering

[remote heron]

in seems synonymous to on here

either way its included in the inequality so whatever word you need to use to convince yourself

[frigid moon]

Well I don't see how it would be included if we take the literal meaning of the word is "in," is my point

But I think it might be a waste of time bogging myself down in these questions, I just have to understand everything correctly when im implementing this in the real world

I think thats what you meant by your last comment though

[cosmic chasm]

I have about an hour to submit this HW question, could anyone offer some guidance?

[vivid kayak]

We are given the demand equation: 𝑃 = 82 − 2𝑄𝐷
and the supply equation: : 𝑃 = 10 + 4𝑄𝑆

(a) Show that the equilibrium price and quantity are P=58, Q=12.
(b) Use the integration method to show that the Consumer Surplus is 144 when the market is
at equilibrium

Ignore A and go to B

Basically at P=58 and Q=12 CS= 144

The upper triangles area

[proud burrow]

George your answer

[vivid kayak]

ignore my qn

i got it

[lofty peak]

could someone help with this assignment😩

[quartz tusk]

Hello, I need help to understand how scientific notation are written .

[vale wigeon]

what do you mean?

the format of scientific notation is ±(mantissa) * 10^(exponent), where the exponent is an integer and the mantissa is a real number between 1 and 10

does this answer your question? @quartz tusk

[quartz tusk]

@vale wigeon thanks for replying I didn't get the ping.

So what I didn't understand was that when people write it in scientific notation thye use different formats

Like 25.85 x 10^2

[vale wigeon]

are you talking about the "e" stuff?

[quartz tusk]

Now someone will use 2.585x10^3

I don't get why they are different

[quartz tusk]

Yeah that one too

[vale wigeon]

25.85 * 10^2 and 2.585 * 10^3 are the same

[quartz tusk]

Numerically they are same but I don't know which one is correct notation

Are there any standard for it?

[vale wigeon]

formally, scientific notation requires the mantissa to be between 1 and 10

as i mentioned earlier

[quartz tusk]

Mantissa ?

The number before decimal ?

[vale wigeon]

the number before the power of ten

like, in 5.48374 * 10^-5, the mantissa is 5.48374

[quartz tusk]

I see

Also what is precision ?

[vale wigeon]

an indication of how close a measured or calculated quantity is to the true value

or equivalently (ish), the number of correct decimal places in the mantissa

[quartz tusk]

Can you simplify a but more ?

[vale wigeon]

here's an approximation of pi with precision 10^-1: 3.1

here's an approximation of pi with precision 10^-8: 3.14159265

[quartz tusk]

When you say precision is 10^-8

[vale wigeon]

i mean that the value i give is within 10^-8 of the true value

[quartz tusk]

I.e 8 decimal points ?

[vale wigeon]

8 decimal places yes

[rich veldt]

Can some

one e

help me

the question asking Solution set

adn they are the opitons

[vale wigeon]

have you made any progress so far?

there is a thing you can do to this system of equations which will greatly simplify it

[deep field]

If we look at the options it’ll be even easier

[vale wigeon]

yeah but you do not need to look at the options

[rich veldt]

frankly idk how to solve

so..

can someone explain how to solve this question

[ionic jewel]

i haven't solved it but a common denominator of xy looks pretty fantastic

[rich veldt]

can you try to solve pls

[vale wigeon]

we will not do this problem for you

[rich veldt]

i need learn the how to solve like this question

but idk how to solve

[quaint trout]

First thing to notice is that x, y and xy cannot be 0. So you can multiply both sides of the equation by xy.

[vale wigeon]

however, as bunny suggested, you might want to multiply both sides by xy in the first equation as a first step.

[quaint trout]

Start there and show what you get

[rich veldt]

at aleast show me the progges

[ionic jewel]

what's a prog

[quaint trout]

I assume he means process

[rich veldt]

next?

[quaint trout]

That was good

Now you can isolate x in the first equation

To get x equal to an expression in terms of y

Then substitute that expression into the second equation

That gives you a quadratic with only y which you can solve

[rich veldt]

i guess -6,-1 ??

[quaint trout]

What is that supposed to be?

The solutions to y or a solution (x,y)?

[rich veldt]

(x,y)= (-6,-1)

[quaint trout]

That is a solution yeah, but if you did what I said

You would have gotten two answers for y

I think

Nvm, that's right.

[sly stream]

how is the laplace of "2(t-1)u(t-1)" equal to 2e^-1/s^2

why is it not

2[2/s^2 - 2/s]e^-s

[spare fern]

$\mathfrak{L} {u(t-c)g(t)}=e^{-cs}\mathfrak{L} {g(t+c)}$

[ocean seal]

The Godfather

[sly stream]

oh okay i have to change the 2(t-1) to 2(t+1-1)

makes sense

ty

[autumn herald]

what's the reason for vector AB divided by the length of vector AB being put equal to cos(v) and sin(v)

i thought it maybe could've been due to the basic relation we know of cos(v)^2+sin(v)^2 being put equal to 1, and vector AB divided by the length of vector AB has the length 1

but i just dont get why it's put as cos(v) and sin(v) solely, and not cos(v)^2 and sin(v)^2

hahaha i hope it makes sense ahhh

[woeful pulsar]

...

we don't just give answers here

[lone heart]

From

#❓how-to-get-help

Rule 7

When asking for help, do not insist on getting just the answer; we are here to help you learn, not cheat. Likewise, if you are providing help to others, try your best to explain and elaborate instead of simply giving away the answer.

[woeful pulsar]

since you have the remainder if you subtract the remainder from the polynomial you will get a polynomial that is divisible by x^2-2x+k

you can still run the polynomial division algorithm

and see what happens, the remainder should be 0

[limber sierra]

integral of √(hl²-h³).dh
how to solve this?

[rigid smelt]

what is l?

a function of h?

[limber sierra]

i tried....but integral of such forms hadn't been taught and for a derivation...i need to solve this

its constant

irrespective of l

h*

[rigid smelt]

so $\sqrt(h \cdot l^2 - h^3)$ correct?

[ocean seal]

waler

[limber sierra]

yeah i meant this

[rigid smelt]

just nvm that

[jagged imp]

braces instead of parentheses for less ugly sqrt

[rigid smelt]

i really need some sleep

yeah

hmm i guess you can trig sub

[limber sierra]

yeah i thought that...but maybe only if there was integral of l²-h²

here it seems hard

and btw i am currently not in need of methods...i need to know the result just....i saw in net the answer.. couldn't understand what it meant

lemme forward

wth it means? its so .... :/

[rigid smelt]

hmm im not familiar with that function either

[jagged imp]

its the "hypergeometric function"

[rigid smelt]

probably some non-elementary

[jagged imp]

are you sure you have this problem copied down correctly

[limber sierra]

i came to integrate this while deriving a Physics formula

[jagged imp]

this integral can't be expressed in terms of elementary functions according to WA

[limber sierra]

😓

[jagged imp]

this is what wa outputs

[limber sierra]

i dont think it will be ok explaining that question here :'/

not understanding those semi columns and all

[rigid smelt]

does this formula look anything like that at all?

[limber sierra]

maybe i should just leave

[limber sierra]

i believe i am close

[rigid smelt]

hmm

[limber sierra]

its gonna look like that...the constants and dimensions have done their jobs

anyways thanks...maybe i should look for other approaches 🤔...i was going for a long one intentionally

[chilly garden]

help ;-;

[chilly garden]

hey icepingu, the channel is occupied

[jade harness]

oh sorry

let me delete

[chilly garden]

sorry to bother you!

thanks :)

[jade harness]

nah all g

[chilly garden]

<@&286206848099549185>

[jagged imp]

goodbye e4... hello c4.
cant help someone like you sorry

jk, what issue are you facing?

[chilly garden]

xD

[chilly garden]

i proved the above for n = k

but i have no idea how to begin proving for n = k + 1

[jagged imp]

I can get you started if you don't know where to start

I'm gonna take photos since i'm not putting that into latex

,rotate

ah give us a sec

[chilly garden]

👍

@jagged imp i got the following

idk where to go from here though

[jagged imp]

yeah i was gonna show you that but i wanted to figure out how to proceed from there

i may have bitten off more than i can chew

no, matrix multiplication doesn't commute

but this channel is taken

[chilly garden]

yeah this is wack

[jagged imp]

fuck me no its not

[chilly garden]

lmfao

[jagged imp]

Yeah I'm at a bit of a loss here. maybe some double angle bullshit with stuff you got from compound angle?

oh wait yeah it is wrong sorry, should be sin(4ntheta)cos(4n)+cos(4ntheta)sin(4n) right?

or other way around

idek sorry I'm tired

[chilly garden]

its fine

idk i might grapple with this a bit longer

[oak anchor]

Hello!

I have this question

And here’s the solution from the book

Notice the line I marked with "?" says that "P(2) = 0".
Why is that? As far as I understand, the remainder of P(2) is 0, not P(2) itself...

[gray isle]

factor theorem and remainder theorem

[warped carbon]

can someone help me for this aleks thingy?

[gray isle]

consider the quotient remainder form of a polynomial

[alpine sable]

Find out the length of all sides and use heron's formula

[gray isle]

P(x) = D(x)Q(x) + R(x)

[warped carbon]

thanks

[oak anchor]

So P(2) = D(2)Q(2) + R(2), and I know that the remainder is 0, so R(2) = 0

Hmm

[gray isle]

yes, (since D(2) = 0)

[oak anchor]

@gray isle Sorry I got confused again... How do you know that D(2) is 0?

[gray isle]

what's your divisor here?

and what happens to that divisor at x=2

[oak anchor]

One moment please, I'd like to think about it for a bit

Thank you for pointing me in the right direction

[river vector]

ugly ppl are good at math

[glossy nymph]

How dare u

[gray isle]

<@&268886789983436800> questionable posts and potential age issue.

[oak anchor]

I realized I don't know exactly what B(X) and Q(X) mean so I am going to research this a bit more...

I mean, how do I find them from the equation in the question

[river vector]

im sorry Makarov for my inconvenience, but penis poop

[oak anchor]

Maybe after I understand the answer will become clear to me

[fading zephyr]

@river vector please don't post low quality content here. if you want to share random stuff, #chill is better suited

[gray isle]

whats B

consider looking up quotient remainder form of a polynomial

consider having a polynomial P(x)
and a divisor (x-a), (which I previously represented using D(x))
P(x) = (x-a)Q(x) + R(x)
P(a) = (a - a)Q(a) + R(a)
P(a) = R(a)

[chilly garden]

ramonov ;-;

help with trig ;-;

no one can solve this

and i cri

[timid flint]

Hi im wondering if anyone know what minimum deduction is?

[oak anchor]

@gray isle Makes sense?

I've realized my mistake. I learned the polynomial remainder theorem wrong.

I thought that, P(x) / x - a = a, not the remainder of P(x) / x - a

I also completed the next exercise correctly, I am so happy 🙂

Thank you very much!!!

[mossy mulch]

can someone please help me solve this

[alpine sable]

try writing 1.5+sqrt 2 in the form a^2+b^2+2ab

[mossy mulch]

(1+sqrt 2)squared/2?

i cant solve after that

[alpine sable]

Hi

Try factorising itm

[hidden horizon]

take 1.5+root2 as some K and try to factorise it

let x = the expression

complete the square

[mossy mulch]

hey guys i got the answer

[hidden horizon]

did u complete the square ?

[mossy mulch]

nah, i did it some other way

[hidden horizon]

pls tell how u did would like to know

[mossy mulch]

wait

the lighting is bad but here u go

[hidden horizon]

damn thanks !

[ocean seal]

Looit

[analog patio]

If I have a finite dimensional vectorspace, for example $\Q^2$ and I take a vector, for example $v$, how can I find a corresponding vector in the dual space?

[ocean seal]

Rassilon

[analog patio]

Eg. can I just tilt the vector on the side?

Oh, sorry, is this channel occupied?

[timid flint]

f(x)=0,11x3 −2,31x2 +13,44x+81,3 , 0≤x≤12 Determine the slope of the straight line passing through the points (0, f (0)) and (12, f (12)).

Does anyone know HOW to svolve this one?

[sly mantle]

@analog patio wdym corresponding vector

[analog patio]

What does wdym mean?

[vale wigeon]

it means "what do you mean"

[analog patio]

Thats what I mean

Like, I know that there is a dual basis in a dual space and if the basis is orthogonal the dual basis consists of the dot product with the corresponding basis

[normal lance]

Can you please evaluate by taking a and b as non zero constant

[analog patio]

And you could informaly visualize this (in finite dimensional case) by just tilting the vector on its side

[normal lance]

34and 36

[analog patio]

excuse me?

[analog patio]

even so it is a totally different operation and doesnt have anything to do with tilting any vectors onto theirs side

So if I want to flip a vector on its side, what operation does this corespond to in the dual space? @sly mantle

[buoyant vale]

could someone help with this

idk what it means by the coefficient of x in that for one

like surely there are multiple

[oak chasm]

@buoyant vale The x coefficient is the coefficient of x to the first power.

[buoyant vale]

wdym by the first power? as in for both brackets the first x terms?

[oak chasm]

@buoyant vale When you expand that and combine like terms, you'll have a term with x to the first power.

It'll have a coefficient.

[hidden horizon]

Hey can someone help pls :
Two sides of a regular polygon with n sides , when extended meet at an angle of 28 degree . What is smallest possible value of n ?
i tried angle chasing but i didnt get idea

[oak chasm]

@hidden horizon Sorry, channel is busy.

[buoyant vale]

nah its ok im done now

thank you for the help

i got it

[oak chasm]

No problem.

@hidden horizon Do you know the formula for the interior angle of a regular polygon?

[hidden horizon]

yeah , its ((n-2)180)/n

[oak chasm]

OK, assuming I understand the question, you can set that equal to 28.

[hidden horizon]

how do u say so confidently ?

coz answer is 28

ohhh i got it

tysm for helping

[harsh swallow]

holy shit i found the answer

[sly mantle]

@analog patio by flipping i assume you mean transpose when writing vectors as their coords in the standard basis. formally vectors in Q^2* are NOT row vectors but DO have row vector representations. if B is an orthonormal basis of Q^2, transposing the vectors in B gives the row vector representation of B’s dual basis in terms of the dual basis of the standard basis of Q^2. if B ISN’T orthonormal then this doesn’t hold

[abstract goblet]

I have to integrate it, but should i consider "tg" as a constant or does it stand for some other attribute ?

[shell widget]

its the tangent function

tan

tan(sqrt(x))/sqrt(x)

[abstract goblet]

sorry i didn't understand

og i got it

thanks

[visual fulcrum]

pairs of angles

[solar tapir]

For 5, show that angles LMN and NMC are congruent

Same for 6 with angles LMN and DML

[visual fulcrum]

ok thanks

[buoyant vale]

struggling with all of this

the answer written out or something would be greatly helpful

[fading jay]

,w integrate sqrt(8x)*dx from 1 to a

[ocean seal]

Results provided by WolframAlpha

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

Requested by Panavia Tornado#1576

[alpine sable]

what's the xá€' axis

[frail lagoon]

in probability

what does P({a1, a2}) = 1/2 signify ?

is the probability of a1 and a2 happening at the same time or what is it?

[gusty scaffold]

if that is 1/2 means the both values must be equal, use this hint

[frail lagoon]

1/2 is just an example value

so P(a1) = P(a2) ?

[gusty scaffold]

No, sorry here the values of a1 and a2 are same but here they become 1/4

1/4+1/4 = 1/2

here, there is no plus. but the value is equal since the result is 1 per 2

[frail lagoon]

so the notation P({x, y, z}) means P(x) + P(y) + P(z) ?

P({x, y, z}) = 3 * value

?

[gusty scaffold]

No, in probability, we can not use + and - but i used that to signify that the values must be same since the answer is same. No, you can not plus them

just P(x) P(y) P(z)

[frail lagoon]

what is the meaning of the notation

so times ?

[gusty scaffold]

means there is a value called P then the x,y,z is changing accroding to a constant pattern

[storm solar]

Please help me understand this

I don't get it and it is due sunday

[sick radish]

Is Chat occupied?

[muted raft]

#help-4 is not in use

[sick radish]

Can y’all help me

[fading rover]

In #help-4 we can help you

[sick radish]

Oh Alr thx

[rocky dock]

can someone help me w/ something simple

how do you convert a time like this into hours and minutes

it took 3.24 hours

or 0.89 hours

nevermind

i found a video on youtube

?

t = 5.24 hrs

jeff: t-1
kirk: t
together: 4 hrs.

[buoyant vale]

idk what to do

[gleaming bronze]

ok

so let 4a + 199 = x (just so easier to type)

7tan(x) = 8 sin(x)

tan(x) = sin(x)/cos(x)

7sin(x)/cos(x) = 8 sin(x)

divide both sides by sin(x)

7/cos(x) = 8

7/8 = cos(x)

x = arccos(7/8)

4a + 199 = arccos(7/8)

a = (arccos(7/8) - 199)/4

dont have calculator

but that is answer ^

and then i think check other solutions

to determine if its the smallest

[gloomy lintel]

Don’t divide by sin x because it could possibly be 0

That’s not good practice

[clear crescent]

Hello

[gleaming bronze]

you're right! Didnt even consider that! how would you do it?

[gloomy lintel]

7 sinx = 8 sinx cos x
8 sin x cos x - 7sinx =0
Sin x( 8cosx -7)=0

So sin x is 0 or 8 cos x -7 =0

So then you can find alpha from there

[gleaming bronze]

got it!

[buoyant vale]

i get you up to this point but when i put it in my calculator i get -42

ish

how do i find the other solutions for this?

[gloomy lintel]

Use the graph of sin and cos x to get the other solutions of x, and then rearrange to get alpha

You can use a cast diagram if you want but I’ve never used them personally bc I always found them unnecessarily confusing

[gleaming bronze]

Can you not add 2kπ?

[gloomy lintel]

No bc for eg,

Excuse the crappy drawing lol, but the white horizontal line is y = 7/8 and the green graph is y = cos x

So yeah we add on integer multiplies of 2pi

But we also have solutions due to the symmetry of the graph

For eg the one before a full cycle comes from the 2pi - the inital answer

But then we have one after that which is the inital plus 2pi

[buoyant vale]

so i find the solution for x (4a -199) that is the lowest positive ?

as in when put into that gives me the lowest posutuve value

[gloomy lintel]

Yeah and alpha>0

[buoyant vale]

thank you

[light ermine]

Could someone help me understand why this is wrong?

[alpine sable]

how did you get zero?

[gleaming bronze]

denominator is zero?

[light ermine]

Because of it being divided by 4x, so it’d be divided by 0

Should 0 not be in there?

[gloomy lintel]

You cannot divide by 0

[alpine sable]

so you mean dividing by 0 will give 0?

[light ermine]

I thought I’d have to add it since it couldn’t be divided

[gloomy lintel]

That’s impossible, that’s the one thing you can’t do in maths

[alpine sable]

dividing by 0 will give you answers that tend to infinity. you can chop up and apple into infinite pieces of nothingness

so no, 0 is a wrong answer

[light ermine]

Alright thanks

[storm solar]

Any chats free?

[alpine sable]

this one's free i think

[steep steeple]

does anyone know how to solve this, step by step?

i am kind of confused

[teal orbit]

Hey everyone! I'm posting this again. I'm a PHD lawyer in corporate sector, I've recently found that I can't solve equation that is written on the photo. I've forgot how to do basic math, I would like to ask you a favor (Which I'll return back), can someone solve this simple Quadratic System Equation?
x^2+y=29
x+y^2=21

So far, I'm stuck on Y^4-42y^2+y+412=0 <= can't get past it.

[alpine sable]

My teammates says the answer is C. but i think it's A. what do you think?

[knotty sleet]

Hi George, is your question solving over real numbers or just integers?

[muted raft]

None of the lines are passing through correct points ???

On the image on the left

[teal orbit]

English is my third language so I'm sorry for not knowing definitions. This is a quadratic system equation, and as I've calculated (roughly, myself) x=5 y=4 so It's about numbers I guess?

[mental skiff]

can anyone help with this?

[knotty sleet]

Oh that's ok😄

You can subtract the second equation from the first and use difference of squares to factorise

But you've factorised it by inspection which of course is perfectly fine

[alpine sable]

Sorry i forgot to mention its the one of the right im trying to solve. the first graph i just because i wasnt sure what perpendicular in englsih meant exactly. (i assume its opposite of paralel) - The math question is a bit weird. because i have 4 options. (a, b, c, d) but they mention a line that is only described as "the linen that passes through (0,5) and (1, 3) so i was wondering if im suppose to draw a line myself from those points.

[muted raft]

Well clearly it cannot be c)

[knotty sleet]

But it's the intersection of two parabolas if you graph it which means it can have upto 4 solutions

[muted raft]

Since when x=3, y is not 1

[muted raft]

So yes, your original answer a) is indeed correct

[knotty sleet]

I suppose what you've done is the best method

Factorise out the 4, then there are various systematic ways in which you can solve the cubic

[steep steeple]

anyone know this one

[muted raft]

move 2x to the other side and then complete the square.

You should find your vertex from that after

[alpine sable]

Thnaks a ton 🙂

[vestal ore]

Could someone explain why x=3 in this case, it seems really simple but i cant get my head around it

[rustic hatch]

how do u find an angle in law of sines

?

[vestal ore]

sinA/a = SinB/b

?

[rustic hatch]

wdym?

[rustic hatch]

and then what do i do

?

[alpine sable]

can someone explain this please the vid is not helping
https://cdn.discordapp.com/attachments/830987746897559582/845732642518335518/unknown.png
watched it like 4 times and i still dont get it
its the last skill i gotta learn before getting 100% in the math curriculum

[wary stream]

You can create a system of equations

[remote heron]

you need to identify the number of things you don't know, and then that number of equations from the given information

[wary stream]

One equation involving the distance and one with time

[remote heron]

its an almost useless generalization, but in normal problems they usually take the form of: unknown 1 + unknown 2 sum to some known quantity, and then unknown 1 times some constant plus unknown 2 times sum constant sums to some other known quantity

x+y=c

ax+by=d

almost useless but still

[tiny trout]

Hi, I'm doing this exercise, but idk how can I start :(
Any suggestion?

[wary stream]

Can you translate that for us?

[tiny trout]

Let f:[a,b] -> R a derivative function. F is a primitive of f in [a,b]. Without using integration by parts proof that:

[alpine sable]

Hello, I have a quick question if anyone uses octave

How do I set format to rational numbers?

[wary stream]

Like the answers?

I think "format rat" (without the quotes) does that

[warped frost]

I think just

rat (number)

also does it

[alpine sable]

Can anyone help me with vectors

[wary stream]

You would have to apply that to every solution, format rat is one and done and all the answers will be radical

[alpine sable]

Strange, it doesn't work?

Oh, nvm it does

Thank you so much!

[mighty fern]

Yo guys this kinda a stupid question but is 0.0945 a rational number?

[knotty sleet]

yes

[warped frost]

If you can express it as a quotient of two integers, then it's a rational number. The first thing I'd try to do is account for the division by 100, so that you have $\dfrac{9.45}{100}$

[ocean seal]

TiredPatzer

[warped frost]

You can probably figure out how to write 9.45 as a quotient of integers as well, so it's probably a rational number.

[wary stream]

Interesting you used dfrac instead of just frac, what's the difference?

[warped frost]

I think the latex bot here has no difference with its output, but "dfrac" is a composition of "\displaystyle \frac", which gives you a larger display of the notation

Think of it as the difference between in-line notation (smaller format) and the ones centered on display in textbooks

[dim spear]

hey can someone help me

[fair crater]

I don't see a difference in #latex-testing

[warped frost]

Yeah, that's what I figured with this bot - you'd notice a difference in a local latex environment or something like Overleaf. I think it just has the displaystyle formatting turned on by default

I just write it out of habit

[fair crater]

Wait there is a difference lol see #latex-testing now

[warped frost]

Oh, yeah I see. Yeah, that's it!

[frigid moon]

I have a question: How many corners does a cube have in 4 dimensions? How many 3d faces?

My question is about the second part, I dont see how a face can be 3d. Faces by definition are 2d

[warped frost]

16. To understand why, recall how you draw a cube by connecting the vertices (corners) of two squares. You would draw a projection of a 4-dimensional cube in the same way with two 3-dimensional cubes. You can even generalize that to n-dimensional cubes.