precalculus

[hushed ember]

so the following is not an equal polynomial>??

[hard hornet]

you're solving for a and b for now

a+b = 0
3b - 2a = 5

the x terms are equal to the x terms

the non x terms are equal to the non x terms

so you have two equations now

[hushed ember]

ohh

b=5/4

[hard hornet]

uh no

check your math again

[hushed ember]

a=0-b

ohh +2b haha

b=1 haha

[hard hornet]

yup

[hushed ember]

wait how do i find c

da hell

[hard hornet]

there is no c

in the first equation

can't find something that doesn't exist at all lol

[hushed ember]

ahh ok

im gonna try do c now

question c*

[hard hornet]

ye go for it

lmk if u have any more questions

[tropic crown]

for (3/7)^x

as x approaches infinity

[rocky bison]

As a limit?

[tropic crown]

7^infinity climbs faster than 3^infinity

[willow bear]

yes as a limit

[tropic crown]

so it converges to 0

right?

[willow bear]

kinda

[tropic crown]

is that an okay way of thinking

thingas

[rocky bison]

A better way is to keep the fraction

[willow bear]

but a more honest-to-goodness way of thinking of this is that $\frac37 < 1$

[obsidian monolith]

Ann:

[tropic crown]

thank you ^3^

[willow bear]

that wasn't funny, @wraith idol

[wraith idol]

ok

[frozen needle]

[serene heath]

[viscid thistle]

Hey guys!

Quick question.

It's about matrices

[royal gull]

[zinc briar]

I wanna do pre-calculus after i'm done with my current studies (I mastered pre-algebra, algebra basics, and most of algebra 1 so far), I'm gonna take algebra 2/high school geometry/trignometry and master them as well, however will I need more than this for pre-calculus, like math analysis as well? https://i.imgur.com/9f8LklB.png

I just need to know if covering these topics is sufficient information to be considered as calculus ready.

[short sorrel]

that just sounds like a "precalc" class

like, i'm pretty sure "math analysis" is just what your school calls precalc.

the curriculum lines up pretty exactly

and yes, that's definitely enough for calculus

[viscid thistle]

How do you transform polygons using matrices?

Not the transformation part. But, the matrix multiplication part.

Like, I always get the answer wrong because I would have put the wrong coordinates into the matrix.

It would be much appreciated if anyone can help me explained the matrix multiplication part for transformation.

[zinc briar]

So even if I don't take math analysis which is considered "Algebra 3" i'll be ready for calculus? @short sorrel

[short sorrel]

no, i'd imagine your calculus class will expect you to have it

"calculus" and "precalculus" are different things

precalc comes before calc, generally

[zinc briar]

Hmm

That's a lot for me to study, so I need math analysis as well..

Challenge accepted.

[short sorrel]

again, i'm pretty sure "math analysis" is just what your school calls precalculus

the term isnt really standardized

but it covers the exact same material

[zinc briar]

I'm going to University I don't think they'll make me learn pre calculus.

[short sorrel]

behaviour of common functions and limits

[zinc briar]

I mean they'll help me with pre calculus*

So I gotta educate myself on this ffirst.

Facepalm, I mean I don't think my university will help me with precalculus so yeah.

[viscid thistle]

Anyone?

[charred hull]

?

[viscid thistle]

@viscid thistle don't ask to ask

and as it's about matrices #linear-algebra is probably a better place to ask your question

Oh...okay.

[viscid thistle]

This is the question.

Wrong sub server.

[wraith idol]

Algebra 3

Hmmmmmm

Idk what to say about that

[charred hull]

@wraith idol dw they already helped them in #linear-algebra

'less you're talkin about something else

[wraith idol]

Yeah I'm talking about the previous image

@charred hull

"Whereas Math Analysis, which some instructors sometimes call Algebra 3"

It just sounds a bit funny to me

[charred hull]

oh

yeah

there's a lot of strange things with that statement

[deft fox]

5. How is the quotient rule for logarithms derived from the product rule and the power rule?
6. How does the interest rate affect the present and future values of an annuity?

help

pl0x

please

help

[charred hull]

if you're dividing to get a/b

you can rewrite that to become a * (b^-1)

@deft fox

[deft fox]

i found the answer from someone else, but this also helps too since the answer i found is alot of reading

thx

[charred hull]

np

[shrewd urchin]

$|R|^2=2F^2+2F^2(cos^2(\theta/2)) \implies F/3=2Fcos(\theta/2) \implies \theta/2=\cos^{-1}(\frac{1}{6})$

[willow bear]

what did you even do there

how did the first $\implies$ happen

[shrewd urchin]

?

[obsidian monolith]

Ann:

[shrewd urchin]

i took positive sqaure root of both side

wait woops

[willow bear]

yeah you fucked up there

you don't need to square-root anything here

the equation is linear in cos(θ)

[obsidian monolith]

Krishna (An average mathy):

[willow bear]

ok that's

correct

as in

you get the right answer

[shrewd urchin]

NO

[willow bear]

even if it's not quite in the same form as any of the options

but the angle IS equal to $2 \arccos(1/6)$

[obsidian monolith]

Ann:

[shrewd urchin]

hmmm

but optiosn

[willow bear]

hint: what is $\cos(2 \arccos(1/6))$?

[obsidian monolith]

Ann:

[willow bear]

answering this question will help you select the right answer option

[shrewd urchin]

i dont have calculator

also dont now how to manipulate inverse trig

anyways

answer is the first

i didnt makee the sub that 1+cosx=2cos^2x/2

Help please

[shrewd urchin]

<@&286206848099549185>

[hard hornet]

draw a apicture

seriously

[charred hull]

if they move 30(sqrt(2)) southwest

just think of it as a triangle

a right triangle with a diagonal of 30 sqrt(2)

[hard hornet]

DRAW IT FIRST

[charred hull]

yeah actually

draw it

[hard hornet]

i refuse to help anyone that doesn't put in the same effort

[shrewd urchin]

$30\sqrt{2}-10\sqrt{13}$

[obsidian monolith]

Krishna (An average mathy):

[charred hull]

it's a lot easier to understand visually than me explaining through words

[shrewd urchin]

So the answer is $30\sqrt{2}-10\sqrt{13}$

[obsidian monolith]

Krishna (An average mathy):

[charred hull]

just draw it out

[shrewd urchin]

Indeed like 3 diagrams

I draw(

**(

[charred hull]

then show them, please

[charred hull]

do you know what a 45-45-90 triangle is

[shrewd urchin]

🤔

[charred hull]

break the southwest portion up into its x and y components

[shrewd urchin]

Ok

Xcompo is 30m+x and ycompo is 20m

[charred hull]

[shrewd urchin]

Let me figure out what's the x

[charred hull]

stop right there

again

take the information

that it is south-west

meaning it has a bearing of 45 degrees from south

meaning it forms a right triangle

[shrewd urchin]

.yup

[charred hull]

with 2 45 degree angles

meaning that the legs of said right triangle are equal

in fact, just reverse pythagoreas

[shrewd urchin]

[charred hull]

????

a^2 + b^2 = c^2

you have c

and you know a = b

[shrewd urchin]

The sw displacement is more then the hypo of the tri u talk abouy

[charred hull]

the south west displacement is the hypotenuse of the triangle i'm referring to

[shrewd urchin]

Yes correct

[charred hull]

i'm giving you the method with which you can find the x and y components of the southwest displacement

>The sw displacement is more then the hypo of the tri u talk abouy

how is the southwest displacement more than the hypotenuse if it is the hypotenuse

[shrewd urchin]

https://cdn.discordapp.com/attachments/363224154469826562/606751848765849601/19_Q_5_005.png

[uncut mulch]

did you split the 30sqrt(2) SW into its x,y components?

[charred hull]

i've spent 20 minutes trying to get them to, for some reason they completely refuse

[hard hornet]

dude don't expect the answer jesus christ

colorado did a nice job helping you

[shrewd urchin]

If I want answer I would better go for a Google search

[royal gull]

just draw it on a plane, then try to divide it in triangles maybe and use pythagorean theorem

[prisma marten]

Reee is so cringe

[shrewd urchin]

No U

[deft phoenix]

Q 49

[pale kettle]

What have you tried

[deft phoenix]

See I know how to do it but the problem is. I can't factorise 6x²+5x+4

[willow bear]

well its discriminant is negative

[deft phoenix]

Yeah then is q wrong

[willow bear]

it definitely looks like none of the answer options fit!

so i guess yes

[deft phoenix]

Okay

[viscid thistle]

how can i solve this recurrence f(n)=n*sqrt(1+f(n+1))

[visual canyon]

Looks like cancer but I guess doable

f(0) = 0 obv

I would presume maybe rearrange to have what f(n+1) is on outside just to make it look better

So we’d have (f(n)/n)^2 - 1 = f(n+1)

[viscid thistle]

right...

[visual canyon]

So f(1) if I’m not mistaken is -1

Wait no

[viscid thistle]

it's f(1)=sqrt(1+f(2))

[visual canyon]

Yes ok I guess I can rearrange just not for n = 0

Hmm

Maybe difference of squares hmmmm

Is this for ur precalc class? Lol

[viscid thistle]

no im still in high school it's for smth esle

[visual canyon]

Oh ok

1 sec I’ll try it with paper

@viscid thistle couple of questions

A. am i finding the explicit formula and B. is it for integer values n>0 or is it anything

[viscid thistle]

if an explicit formula is possible to derive then yes and if it's for any n even better.If it's easier to assume that n>0 then that's also cool

[visual canyon]

well

If i dont assume n>0 i track into imaginary territory

[viscid thistle]

the n>0

then

sure

[visual canyon]

what is this problem for lol

[viscid thistle]

i'm trying to solve this: sqrt(1+2sqrt(1+3sqrt(1+4*sqrt(...)))) to infinity

[visual canyon]

oh

so ur trying to figure out the value of that?

[viscid thistle]

yeah i've tried different things but nothing worked just approximations

converging approximations i think at least

but with no discernible pattern so they're useless

[visual canyon]

k one sec

[heady jewel]

@viscid thistle

its uhm very difficult rather congested in finding a number = to that expression

throught the expression

think of how each and every number can be represented in surd form

[rugged ice]

The sum of a positive arithmetic infinite series is infinity, right?

[rocky bison]

wat

It might be

Might not be

Oh arithmetic

skipped a very key word there

I guess so

[short sorrel]

its divergent, yes.

[rugged ice]

According to my teacher, it isn't

[short sorrel]

are you sure you heard them correctly?

[rocky bison]

Ask for an example

[rugged ice]

The following statement is false. Rewrite the statement to make it true.

The sum of the infinite series 3 + 4 + 5 + 6 + … is LaTeX: \infty ∞ . (This symbol is infinity.)

[short sorrel]

I mean, saying "the sum is infinity" is being... imprecise with wording

[rocky bison]

Rewrite?

what

lmao

[short sorrel]

I'd say "the series is divergent"

you cant really define summation of an infinite divergent series, so assigning a value like "infinity" is being informal

[rocky bison]

Maybe that's what they want?

Saying something like that equals infty is questionable

Maybe they want it written in sigma notation

[short sorrel]

that seems unlikely.

[rocky bison]

True

I can't think of anything else though

[short sorrel]

I'm pretty sure they just want you to say it's divergent

[rugged ice]

What are explicit and recursive formulas?

[rocky bison]

Explicit

Is the nth term

So the formula is defined in terms of n, the term number

Recursive means it's defined in terms of itself

i.e.

[rugged ice]

Can you give an example of recursive?

[rocky bison]

,$ f_{n+1}=f_n+1

[obsidian monolith]

Pseudo:

[rocky bison]

that's a very simple example

[rugged ice]

I still don’t quite understand

[rocky bison]

So we say f_0 = 1 or smth

[rugged ice]

So you set the equation up to be equal to itself?

[rocky bison]

No

The n+1th term

is the nth term +1

Like f_0 = 1

We want f_2

Now

,$ f_2=f_1+1

[obsidian monolith]

Pseudo:

[rocky bison]

We don't know f_1

We need f_1

,$ f_1=f_0+1

[obsidian monolith]

Pseudo:

[rocky bison]

We know f_0=1

So

,$ f_1=1+1\f_2=f_1+1\f_2=2+1

[obsidian monolith]

Pseudo:

[short sorrel]

why are we notating it as f_1 and f_2

instead of the conventional f(1) and f(2)

[rocky bison]

Idk just picked a letter

I was always taught it as a_n

[short sorrel]

thats... weird

but ok

[rocky bison]

I just picked f for consistency here

EItherway it's irrelevant tbh

The point is nth term can be an expression of previous term(s)

[rugged ice]

So basically

Adding the common difference to the nth term is a way of writing it?

[rocky bison]

It might not be a common difference

This is a very simple example of recursion

[rugged ice]

That isn’t what I asked

[rocky bison]

,$ f(n)=\sum_{i=0}^{n-1}f(i)

[obsidian monolith]

Pseudo:

[rocky bison]

This could be another example of recursion

Which doesn't have a common difference

[rugged ice]

I’m doing an example with common difference

[rocky bison]

Then yes

[rugged ice]

Thank you

[rocky bison]

But it doesn't have to be

[rugged ice]

So this sequence doesn't have a common ratio or a common difference, it's going up in increments of odd numbers 3, 5, 7....

How would I find the equation for that if there was one?

The sequence starts on four

Got it

[shrewd urchin]

Any hints?

[blazing parrot]

draw a diagram

make a equation and take one from the question and solve simultaneously

[shrewd urchin]

Done thanks

[unreal monolith]

hi

[heady jewel]

hi lmao

[unreal monolith]

hi honey

@heady jewel how do u do honey?

[serene heath]

[unreal monolith]

help

[severe verge]

.

[unreal monolith]

hi honey

how may i help u? guys hi help me please

[severe verge]

ur pretty close to getting banned

[unreal monolith]

hi wood how might i help u

honey listen, math is live thing like phisys

[severe verge]

k

[shrewd urchin]

LOl

[heady jewel]

"wood"

lmfaooo he just called you wood

[dry pawn]

What prerequesties do you need to do well in calculus

From precalc

[hard hornet]

trigonometry

uhhh

and tons of algebra

conics

[charred hull]

trig doesnt really come into play for a while tho imo

the ability to graph, visualize graphs

that's p good as a skill

[hard hornet]

^

[subtle mason]

I think you just need calculus

[charred hull]

i actually. am not sure what goes into calc from precalc. and not sure what goes into calc from alg 2

@subtle masonnah you dont do any calculus in calc

[subtle mason]

Sorry I meant precalculus

[hard hornet]

precalculus is just a lot of preparation before calculus

lots of algebra, trig, conics, main part is graphing

[charred hull]

the main point is just a bit of mathematical maturity being developed, but there's not exactly a direct application for some of the skills

[subtle mason]

Really?

I’m only a sophomore in high school so I’m only in precalculus right now

[charred hull]

oh wait. exponents and logarithms

[hard hornet]

thats a part i forgot too ^

polynomials

[charred hull]

a little bit of an understanding of limits

zeroes of a graph

[hard hornet]

understanding limits is the start of calculus i think

zeros of graph sounds like precalc

[charred hull]

true

thinking about it, there's a decent amount that's necessary from precalc

it's just hard remembering it now

[subtle mason]

People say the concept of limits is difficult but I think it’s really simple

[pale kettle]

r/iamverysmart

[limber bone]

look whos talking lol

[pale kettle]

@subtle mason do you know the actually definition of limits

[karmic topaz]

https://ncatlab.org/nlab/show/limit

[subtle mason]

Yes

It is where f(x) approaches as x approaches something

[karmic topaz]

so no

you dont

[limber bone]

most people worry about the real rigorous definition

the epsilon-delta definition

[grizzled orchid]

Kek

[pale kettle]

I don't think you know what a definition is

[grizzled orchid]

He's like 15 so its probably fine

[subtle mason]

I know what it means but I can’t word for word recite a definition

[grizzled orchid]

You don't know what it means

Trust me

Actual definition is very different from what you learn in a precalc class

[charred hull]

it means whatever you want it to mean

[subtle mason]

So the precalc definition is different from the real definition?

[grizzled orchid]

Yes

[charred hull]

yes

[pale kettle]

https://en.wikipedia.org/wiki/(ε,_δ)-definition_of_limit#Precise_statement_for_real_valued_functions

[grizzled orchid]

Do you know what delta and epsilon are?

[pale kettle]

What you learn in precalc is not a definition

It's just an intuitive idea of what a limit is

[valid flint]

precalc doesnt really define a limit, it gives an intuitive explanation

[grizzled orchid]

Yeah

[subtle mason]

Stupid precalc

[charred hull]

precalc doesnt really define anything

[grizzled orchid]

It gives you enough to apply to certain well behaved cases

[pale kettle]

you wouldn't be able to understand the definition so

[subtle mason]

Bruh I can’t wait for real ap calculus

[grizzled orchid]

Not enough to understand it properly

Lel

Ap calc bc is not rigorous either

[valid flint]

wait until analysis tbh

[grizzled orchid]

Or read spivak or smth

[subtle mason]

But it’s better than precalculous

[valid flint]

or some good college calculus

[grizzled orchid]

Both are meme tier

[charred hull]

college calc doesnt rly get that rigorous depending on your path tho @valid flint

[grizzled orchid]

In terms of rigor

[charred hull]

i took engi calc so basically: no rigor

[grizzled orchid]

Kek

RIP colo

[charred hull]

now i have to make up for it

[grizzled orchid]

Maybe in another life you could have escaped your fate

[charred hull]

no regerts

[valid flint]

well yeah, which is why i specified good. physics calc usually not too rigorous either

[grizzled orchid]

[valid flint]

see i am making up for my lack of rigorous calc with analysis lol

[grizzled orchid]

@subtle mason are you planning on majoring in math

[subtle mason]

Yes

[charred hull]

in another life idve paid more attention to my capstone timeline and be done by my 3rd year of uni

smh

[grizzled orchid]

Hmmm

You'll probably learn the rigorous definition in like

2nd year

Depending on how early you take calculus

[charred hull]

1st year uni lol

[grizzled orchid]

Lel

[subtle mason]

Or I can go to Wikipedia and learn it now

[grizzled orchid]

Kek

[charred hull]

math majors prolly do analysis around then

[grizzled orchid]

That's not learning

[charred hull]

@subtle mason it wont translate well

[valid flint]

umm buy a book instead aeion

like spivak or smth

[grizzled orchid]

buying books

[charred hull]

yeah

[grizzled orchid]

Steal pdfa

*pdfs

[charred hull]

baby rudin works

but i recommend

[grizzled orchid]

Baby rudin before knowing any calc

[charred hull]

that you finish precalc first

[valid flint]

baby rudins pcool, i just constructed the reals from it and i am happy due to it lol

[charred hull]

if you havent finished precalc

it's going to be like squeezing blood from a stone

[grizzled orchid]

[charred hull]

actually, it's probably closer to squeezing from a beet, you will get a result that seems to be correct but most likely is not

[grizzled orchid]

Kek

[subtle mason]

I will eat the spivak book to absorb the knowledge and learn it

[grizzled orchid]

All the math you have done so far is just skirting around actual mathematics

[subtle mason]

I know

[grizzled orchid]

Learn precalc first

[pale kettle]

You should always stop saying shit like "People say the concept of limits is difficult but I think it’s really simple"

[charred hull]

will probably be just as effective as reading it rn without precalculus maturity

[subtle mason]

I can’t wait until later math

[valid flint]

i mean if we are being honest how much of precalc do you really need in calc

[subtle mason]

Well now I know the precalculus definition is different

[valid flint]

i have always thought that calc and precalc hybrid class would be better than wasting a year on precalc

[charred hull]

@valid flint as mentioned before, understanding what limits are

imo it's just to develop mathematical maturity tho

[pale kettle]

Comparing yourself to others like that is just an asshole thing to do

[charred hull]

being able to visualize graphs somewhat familiarly

[subtle mason]

I thought the precalculus definition was the actual definition and the precalculus definition is simple and that’s why it’s simpler than I thought

[grizzled orchid]

Is there any mathematical maturity in precalc

[subtle mason]

This is a bruh moment

[grizzled orchid]

Precalc level induction kek

[subtle mason]

No there isn’t

[valid flint]

hmm i thought visualizing graph was an algebra ii thing, but tb fair i am not really all that familiar with algebra ii/precalc

[charred hull]

precal does like

polynomial shit a gud amount

finding zeroes of graphs

curvature of graphs

[grizzled orchid]

I thought that was alg II

[charred hull]

they're p much the same

[valid flint]

yeah i thought those were alg ii too

[charred hull]

hm

what the fuck is precalc

what do they even do

[subtle mason]

It is algebra II but I’m pretty sure there’s a fair amount of it in precalculus

[valid flint]

from what i hear precalc is trig identity spam

[charred hull]

o wait

[subtle mason]

Precalculus is supposed to be preparing you for calculus

[charred hull]

exponents n logs

that's. important overall

[valid flint]

hmm still would imagine alg ii for that

if those are not in alg ii, then what is taught in alg ii lol

[charred hull]

me too, but they kinda bleed together in my head

[subtle mason]

Can we rename precalculus so that it’s now named algebra iii

[charred hull]

they feel like the same course to me, but like. whatever it is, finish it before trying to do analysis

didnt someone have that as a class

[valid flint]

i think, alg ii and precalc should either be combined, or calc and precalc should be combined, or combinations thereof

[charred hull]

yeah some people call math analysis algebra 3 for some reason

which i think means they should be shot

[valid flint]

lol analysis algebra iii, why

[charred hull]

@valid flint there's a bit of complex numbers that pops up and idk how long that takes to explain to kids

as well as polar coords

[valid flint]

thats fair. although highschool complex number is like 5 minutes of content tbh

[charred hull]

it is

but highschool kids are notoriously difficult to teach

[valid flint]

and in my opinion, they should wait until taylor series is taught before teaching eulers identity

yeah that is true i guess

[charred hull]

nah just teach em stuff before they can properly comprehend it

teach em riemmann sums before even teaching em addition

[valid flint]

lol highscools pmuch like that

[charred hull]

lol the precalc "mathematical induction"

the "proofs" you get in geometry

altho it's like. an okay ish way to teach mathematical logic ig

[valid flint]

those geometry proofs were stupid. didnt all of them like use similarity

i dont know why they dont have a mathmetical logic class

like it doesnt really have prereqs

[charred hull]

not enough school funding

[grizzled orchid]

I thought all of that was in alg II

[valid flint]

and it is super useful

[charred hull]

plain and simple, schools dont have the money most likely

esp bc it goes for math degrees, which isnt engineering so it gets tossed to the wayside

schools already struggle to get students to precalculus before uni in the US

[grizzled orchid]

The first unit of a geo class should just be extra fast formal logix

Logic

[charred hull]

logix

[grizzled orchid]

Logix

[valid flint]

well i would argue mathmetical logic is important in many fields, even if it isnt explicitly helping.

[grizzled orchid]

The rad version of formal logic

[charred hull]

not sure about that

engineering doesnt rly use it tbh

just aboos the work of actual mathematicians

[valid flint]

like just thinking of statements by logical connectives is very useful for critical thinking imo

[charred hull]

true

[grizzled orchid]

Engineers that admit their inferiority are allowed to live as clowns in the coming revolution

[charred hull]

i mean, that's the whole reason that cs has discrete maths

and also the reason that discrete maths is considered a weeder class lol

[valid flint]

lol

[hasty geode]

if you talk about ee, it relies heavily on calculus , algebra and probability

[deft fox]

i need help ;w;

A bicyclist races on a bicycle with 13​-inch-radius wheels. When she is traveling at a speed of 43 ​ft/sec, how many revolutions per minute are her wheels​ making?

[charred hull]

what have you tried so far?

@deft fox

[deft fox]

i found it out so its ok lol

[charred hull]

o

[pale bison]

Pearson SOCKS!

[viscid thistle]

A sample of 4 million bacteria increases by 25​% each hour. How long does it take for the sample to reach 24 ​million?

having difficulty with this question, how would I set this up in the formula

[pale kettle]

Well okay, how much would you have after one hour

[viscid thistle]

5m?

I have the formula 24(t)=4(1.25)^t
would I have to divide the 4 first?

[pale kettle]

what do you mean by 24(t)?

[viscid thistle]

for exponential growth formula

or is it P(t)=4(1.25)^t

[pale kettle]

That one is correct

[viscid thistle]

how would I go on about solving for t

[uncut mulch]

P(t) is a function. you can't swap in the 24 like that.

[viscid thistle]

divide the 4 right?

[uncut mulch]

your need to find t when P(t) = 24

[viscid thistle]

ah I got it thanks guys for the help

[viscid thistle]

Can u solve the bacteria problem using geometric sequence?

[limber bone]

sure

[hushed ember]

can anyone help me with part ii

[sour plinth]

well first $A(x) = (x-4)(x+1)$

[obsidian monolith]

187:

[sour plinth]

$\therefore M(4) = M(-1) = 0$

[obsidian monolith]

187:

[hushed ember]

wait where did m4 come from

im confused

[sour plinth]

do you know the factor theorem?

@hushed ember

[hushed ember]

what is that

if you explain i might know what it is

[sour plinth]

actually nevermind u dont need it, i didnt see the question above

i didn't know they were connected

ok so using ur result from part (i)

uh

$x^4-5x^3-6x^2+4x-8=(x^2-2x-8)(x^2-3x-4)-28x-40$

[obsidian monolith]

187:

[sour plinth]

what we can do is move the -28x-40 to the other side

$x^4-5x^3-6x^2+32x+32=(x^2-2x-8)(x^2-3x-4)$

[obsidian monolith]

187:

[hushed ember]

OHHH

so thats what it meant

alright

yeah the wording was really weird i didnt understand it

but i get how u did it thanks

[sour plinth]

👍

[tropic crown]

can someone help me with the intermediate steps

of this function?

it kinda seems like they used the quotient rule

but it looks a little weird to me

[tardy abyss]

yeah it is

quotient rule

[uncut mulch]

product rule was also being applied in the same step

[tardy abyss]

yea

[uncut mulch]

last step was just factorisation

[tropic crown]

okay, i see, thanks!

[shrewd urchin]

Show that vector $\vec{a}=2i+5j-6k$ and $\vec{b}=i+5/2j-3k$ are parallel.

[obsidian monolith]

Krishna (An average mathy):

[shrewd urchin]

i know that both are parallel as $\vec{a}=2\vec{b}$

[obsidian monolith]

Krishna (An average mathy):

[shrewd urchin]

assume i is a unit vector along +X and j along +Y

Is here a better way to show this/

?

[blazing parrot]

from what i learnt just $\vec{a}=k\vec{b}$ where k is a scalar

[obsidian monolith]

Not Chezstick:

[shrewd urchin]

Ok .

[glass cradle]

Hi guys. Are there anyone who can give me arithmetic and geometric sequence problems in which i will solve? :")

[willow bear]

if you want i can try to generate some problems of that sort for you

[glass cradle]

Yes please thanksss

[willow bear]

how many do you want

[glass cradle]

Atleast 5-10?

[willow bear]

ok

[glass cradle]

Thankss!!

[heady jewel]

what difficulty level

lol

[glass cradle]

On a scale of 1-10, 8

[willow bear]

alright i got one, more coming soon i guess

[01] An arithmetic progression consists of 20 terms. Its sum is equal to thrice the value of the 5th term, and its last term is equal to -2 times the first term. Find the 11th term in the progression.

[glass cradle]

Thanks

[willow bear]

[02] A sequence of four numbers is such that the first three are in AP and the last three are in GP. The sum of the first and last numbers is 2 more than the sum of the second and third numbers. If the first number is increased by 5/2, the entire sequence becomes a GP. Find the four numbers.

02 may be a bit over the top in its difficulty but it should be solvable unless i messed this up

[glass cradle]

Ok ill try

[willow bear]

[03] A nonconstant geometric progression consisting only of positive numbers is such that its 4th, 10th and 13th terms are in AP. The 10th term of the progression is 1. Find the floor of the 49th term.

coming up with these as we speak, btw, so these aren't arranged by difficulty

[glass cradle]

Thanks

[willow bear]

[04] Three distinct numbers are in AP. Switch the last two numbers and the AP becomes a GP. Find the step of the AP.

this one's a bit easier than the other three

i'd say the difficulty ranking is approximately 01 < 04 < 03 < 02

[glass cradle]

Thank u

[heady jewel]

have you solved any yet?

[glass cradle]

Number 1is 53?

[willow bear]

that doesn't match the answer i had for it, can you show your work?

[glass cradle]

Im so bad lol

[willow bear]

a_5 = a_1 + 4d = 5
a_20 = a_1 + 19d = 125

where did you get those 5 and 125 from?

[glass cradle]

The 5th term and i cube it

[willow bear]

why are you cubing the fifth term?

i did not say that the 5th term was equal to 5, nor did i say that the last term was equal to the cube of the fifth.

you seem to be making some stuff up that has no relevance to the problem i wrote

[glass cradle]

so how do i know their values

[willow bear]

you don't, nor do you need to

[glass cradle]

Can i see yours?

[willow bear]

i mean... no, because that'd give away the answer, and i'm not doing that

try again

[glass cradle]

Okay ill try again

[mystic dagger]

need help finding angle

i know the triangle adds up to 180 but forgot the other rules

[short sorrel]

if the triangle adds up to 180

then whats the missing angle of the triangle?

[frozen needle]

x is 180° minus the 3rd angle of the triangle

[mystic dagger]

so 180 - 31

[short sorrel]

yes

[mystic dagger]

ok thank you i havent practiced in awhile so this helps a lot

[short sorrel]

after all, a full circle is 360 degrees, right? and this is half a full circle

half of 360 is 180

so x + the missing angle of the triangle should add up to 180

[mystic dagger]

wow at first i thought the horizontal line was 360 but that statement really helped to clear the confusion

[icy current]

its okay

[mystic dagger]

for this problem i have the equations, 1st worker=x , 2nd worker= y, x + y = 235, x times 20 + y times 15= 4100

am i on the right track?

<@&286206848099549185>

[proud raven]

yea, id define x and y a little better

but right track

[mystic dagger]

@proud raven how would i go about this

in which way could i define it better? would i be able to start to solve or do i need to define more?

[proud raven]

no you can start

use substitution

its better to define precisely so when you get a number as an answer you know what it means

i.e. x= hourly rate for this worker $/hr

go ok?

[mystic dagger]

ok got it thank you

[tame wedge]

Can someone help explain what exactly this set is describing I’m having a hard time getting my head around it!

[limber bone]

x is an element of the rational numbers such that 3 times that number is an element of the integers

1/3 for example

1/3 is an element of the rational numbers

and 3(1/3) is an element of the integers

got it? @tame wedge

[tame wedge]

Oh okay so B only contains x that satisfies both of these

[limber bone]

y

that | means such that

so x is an element of q such that 3(x) is an element of z

Q* Z*

[tame wedge]

Would it mean the same thing if it were written the other way around?

[limber bone]

lets try

x is an element of Z such that 3x is an element of Q

so you want an integer

which 3 times that integer gives a fraction

is that possible

?

[tame wedge]

Definitely not

[limber bone]

got it?

[tame wedge]

Yeah, I actually do yeah thanks !

[willow bear]

@limber bone ummmmmm no

no

${ x \in \bbZ \mid 3x \in \bbQ}$ isn't empty as mo2men seemed to suggest, @tame wedge

[obsidian monolith]

Ann:

[willow bear]

because Q isn't the set of "fractions"

it's the set of RATIONAL NUMBERS

which contains the integers

every integer is also a rational number

[grizzled orchid]

kek

i

why would that be empty

[willow bear]

scroll up

no seriously

this is a pretty fucking serious fuckup on mo2men's part and i want to make sure it's set straight

[grizzled orchid]

Q is the set of numbers that are 1/q in lowest terms is

interesting

[limber bone]

uh ohh

[echo plaza]

wat

[limber bone]

sorry

[echo plaza]

[limber bone]

fuck bad mistake

[willow bear]

{x in Z | 3x in Q} is actually the same thing as Z

bc 3 times an integer is again an integer, and hence a rational number too

[limber bone]

@tame wedge

yes ty abn

ann

sorry

[grizzled orchid]

ye

its

kinda dumb tbh?

[limber bone]

ye

[grizzled orchid]

there's no reason to include the condition 3x in Q there

[limber bone]

sorry guys

[willow bear]

scroll up sloth

[limber bone]

original question was the converse

what a fuck up

[rare galleon]

This is an example of people self-studying and don’t know what they are talking about @limber bone . But hey, it’s a mistake and he will@learn from it

[tame wedge]

Thanks for the help guys, I understand the mistake all is well!

[shrewd urchin]

Consider example A is it wrong ?

[willow bear]

example what

there are examples 9, 10 and 11

which one are you talking about

(also, φ for empty set? yuck)

[shrewd urchin]

Example 11 @willow bear

[willow bear]

ok then what do you mean by "is it wrong"

[shrewd urchin]

Yes that phi is for null set or empty set

[willow bear]

yeah ok phi is not meant for that. the empty set has its own symbol. but whatever

[shrewd urchin]

Read the example 11

[willow bear]

the solution?

the solution is perfectly valid, though the last sentence is weird

[shrewd urchin]

How?

[willow bear]

how what

[shrewd urchin]

Is A={1} is an element of Of B and B is an subset of C then why not A Subset of C

[willow bear]

if A were a subset of C, then every element of A would also be in C

do you agree

[shrewd urchin]

Yes

[willow bear]

the only element of A is 1

therefore, if A were a subset of C, then 1 ∈ C

do you agree

[shrewd urchin]

Yes It is

[willow bear]

1 ∉ C

[shrewd urchin]

C={1,2,3}

[willow bear]

no

C is not {1, 2, 3}

C is {{1}, 2, 3}

1 is not the same thing as {1}

[shrewd urchin]

🤔

[willow bear]

what

[shrewd urchin]

And A={1}

[willow bear]

yes

[shrewd urchin]

C={{1},2,3}

[willow bear]

yes

[shrewd urchin]

A is contained in C

??

[willow bear]

A is an ELEMENT of C.

but is not a SUBSET of C.

[shrewd urchin]

A Subset C means all elements of A are contained in C .

[willow bear]

no

it means all elements of A are ELEMENTS of C

[shrewd urchin]

Yes

[willow bear]

"contained" is usually reserved for subsets, not elements

[shrewd urchin]

Yes

A is in C

A is an element of C

But A is not a subset of C

[willow bear]

yes

exactly

[shrewd urchin]

A is an singleton set all elements A are in C then why not A Subset C . I am confused

What's the difference between {1} and 1?

Donno

@faint mason do you know?

What you asked

[faint mason]

Oh

[shrewd urchin]

???

What's the difference between {1} and 1?

[faint mason]

I don't know anything about sets really, but I'd assume 1 is the element of 1. Whereas {1} is the set containing the single element 1.

C contains a set containing 1, but it doesn't contain 1 itself.

Someone more knowledgeable in this topic please correct me if I'm wrong.

[shrewd urchin]

Finally gotcha

[faint mason]

It seems intuitive that way.

[shrewd urchin]

Q.3: Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?
(i) {3, 4} ⊂ A , (ii) {3, 4} ∈ A, (iii) {{3, 4}} ⊂ A
(iv) 1 ∈ A, (v) 1 ⊂ A, (vi) {1, 2, 5} ⊂ A
(vii) {1, 2, 5} ∈ A, (viii) {1, 2, 3} ⊂ A, (ix) φ ∈ A
(x) φ ⊂ A, (xi) {φ} ⊂ A

[willow bear]

phi used for empty set 🤢

i think it'd be helpful if each of those 11 statements were on its own line js

[shrewd urchin]

1 is not correct as 3,4 is not an element of A

[willow bear]

do you mean to say that neither 3 nor 4 are elements of A

(you're right, but your wording needs work)

[shrewd urchin]

yes both 3 and 4 are not element of A

2nd is true as {3,4} are elemnt of the A

[willow bear]

is

{3,4} is one object

that happens to be a set

[shrewd urchin]

ok

[willow bear]

\begin{enumerate}
\item $ { 3, 4 } \subset A$
\item $ {3, 4 } \in A$
\item $ {{3,4}} \subset A$
\item $1 \in A$
\item $1 \subset A$
\item ${1,2,5} \subset A$
\item ${1,2,5} \in A$
\item ${1, 2, 3} \subset A$
\item $\varnothing \in A$
\item $\varnothing \subset A$
\item ${\varnothing} \subset A$
\end{enumerate}

crap

[shrewd urchin]

??

[obsidian monolith]

Ann:

[willow bear]

there

just wrote all those statements the problem provides

[shrewd urchin]

3 is true as {3,4] is an elmen tof A

TYPING on laptop is frustrating

4 is true

Confused about 5

[willow bear]

5 is nonsensical because 1 isn't a set.

[shrewd urchin]

yes so 5 is wrong too lol

6 is true

7 is not true

8 is not true

Confused abou 9 and 10

[short sorrel]

that symbol is the empty set - ie, {}

is the set {} in A?

[shrewd urchin]

my textbooks state that {} is subset of all set

[short sorrel]

right

thats not what i asked, though

[shrewd urchin]

no its not

[short sorrel]

right

[shrewd urchin]

so9 iis wrong

10 is true

[short sorrel]

correct

[shrewd urchin]

why do wesay that {} is subset of all sets

[short sorrel]

if a set X is a subset of a set Y

then every element of X is also in Y

the empty set has no elements

so by default, every element it does have is in every set

since it... has none

[shrewd urchin]

ok

[short sorrel]

there is no element in {} that is not in A

since {} has no elements

so it must be a subset

[shrewd urchin]

but the null set is contained in set a

A*

[short sorrel]

?

it's a subset

its not a member

[shrewd urchin]

THATS WHAT I AM SAYING

[short sorrel]

then why the "but"

whatever

can you do 11?

[shrewd urchin]

yes

[short sorrel]

(its comparable to #1 and #3)

[shrewd urchin]

its false

[short sorrel]

yep, since the empty set is not an element of A

so if the empty set is an element of this set, it cant be a subset of A

[shrewd urchin]

@short sorrel the 3 is wrong says the answer key

[short sorrel]

that's... weird. 3 should be correct.

[shrewd urchin]

are you sure?

@willow bear is 3 correct or incoorect

[willow bear]

3 is true

[shrewd urchin]

i misread the answer key

yes

[shrewd urchin]

If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15}and D = {15, 17}; find
(i) A ∩ B (ii) B ∩ C (iii) A ∩ C ∩ D
(iv) A ∩ C (v) B ∩ D (vi) A ∩ (B ∪ C)
(vii) A ∩ D (viii) A ∩ (B ∪ D) (ix) ( A ∩ B ) ∩ ( B ∪ C )
(x) ( A ∪ D) ∩ ( B ∪ C)

I misread the answer key again

[viscid thistle]

How is this difficult?

[hybrid charm]

🙀

[viscid thistle]

I mean, $A \cap B = {7, 9, 11}$ is kinda child's play.

[obsidian monolith]

Rajarshi:

[serene heath]

sorry bossman

[tidal sequoia]

I must be dumb, but I have a question thats

"Which points are the same as (5,64 degrees)?"

[royal gull]

[tidal sequoia]

So I thought of just going with coterminal angles so like (5,424) and (5,-296)

but the answer also includes (-5, 244) and (-5,-116)

to which I dont understand the latter answers

[viscid thistle]

Yeah, this is the one. This ought to make it easier.

@shrewd urchin use this one to solve it.

@tidal sequoia
(2.1918557339453875, 4.493970231495835)
This point, I think.

I mean, (5, 64 degrees) is in Polar coordinates, right?

[tidal sequoia]

oh ok

I was just confused because polar coordinates tend to do radian measurements so I forgot derp

thx

[viscid thistle]

Glad to be useful.

[tidal sequoia]

What do polar graphs do that make them special?

Like whats the usefulness of them

[hybrid charm]

useful in exams

[grizzled orchid]

it helps to model things like, well, coordinates for navigation

that aren't served well by an Cartesian coord system

[tidal sequoia]

so it's just an alternative model to something that can already be modeled, but it's just more user-friendly for the application(s)?

[grizzled orchid]

kinda

[bold maple]

In the equation above, a, b, c, and d are constants. Which of the following is a factor of ax^5+bx^2+cx+d if the equation has roots 2, 5, and −7 ?

How would I do this?

I dont know how to facotr

[short sorrel]

a root is a zero of a polynomial, right?

a value that makes it equal to 0

[bold maple]

yes

[short sorrel]

when we factor a polynomial, we break it into a form that shows its roots

for example, a root of 2 means the polynomial is 0 when x = 2

so if we have the factor (x - 2)

this corresponds to a root of 2

since when x = 2, (2 - 2) = 0, so our polynomial is multiplied by 0

and anything multiplied by 0... is 0

so let's try and reverse-engineer our polynomial with this knowledge

it has roots of 2, 5, and -7

these correspond to the factors (x - 2)(x - 5)(x + 7)

can you see why?

[bold maple]

yes

(2-2) = 0 and (5-5) = 0

@short sorrel Would that be all I have to do? just find the opposite of the root given?

[short sorrel]

that lets you find the factors we know

are any of those choices?

and yeah, you "find the opposite"

[bold maple]

2,-2,5, and -7 are all the choices i have for my answers

[short sorrel]

more precisely, you rearrange the equation:
x = 2
x = 5
x = -7
for 0

[bold maple]

Would -2 be the answer since its the only one that +/- my root or 2, would be 0?

[short sorrel]

not quite, in that case

(x - 2) is a factor, but we dont know whether is a factor yet

can you expand (x-2)(x-5)(x+7) into a polynomial?

[bold maple]

I honestly don't know how to

Im in im1 trying to get ahead \

[short sorrel]

hold on

is the phrasing you gave the exact phrasing of the question?

[bold maple]

ax5+bx2+cx+d=0
In the equation above, a, b, c, and d are constants. Which of the following is a factor of ax5+bx2+cx+d if the equation has roots 2, 5, and −7 ?

thats the exact wording

[short sorrel]

and the answers just look like

a. 2
b. -2
c. 5
d. 7

or whatever?

[bold maple]

A
x+2
B
x−2
C
x+5
D
x−7

[short sorrel]

ah, ok, taht clears it up

yeah, it's x - 2 then

[bold maple]

ok thank you

[short sorrel]

a root of 2 corresponds to the factor (x - 2)

because a root makes a polynomial equal to 0

and if we input 2 into (x-2), we get (2-2) = 0

anything multiplied by 0 is 0 (remember, a factor is something you multiply by)

so when we have a root of 2, we have a factor of x - 2

again, we can think of this as rearranging x = 2 to be equal to 0

x = 2
subtract 2 from both sides
x - 2 = 0

[bold maple]

ok thank you

Which of the following expressions is equivalent to x2−5x+1 / x−2

can anyone help me?

A
x−7+15/x-2
B
x−7−13/x-2
C
x−3+ 7/x-2
D
x−3− 5/ x-2

<@&286206848099549185>

[wraith idol]

Eh close enough

[proud raven]

are they asking you to split the fraction its hard to tell

oh

[bold maple]

im not sure

[proud raven]

its polynomial division my man

[bold maple]

yes

[wraith idol]

Oh

That makes so much more sense

[bold maple]

wait long division?

[wraith idol]

Parentheses are your friends —Ann

[proud raven]

yea but with variable expressions instead of numbers

[bold maple]

oh

[proud raven]

its essentially the exact same process except with variables

so if you have a good grasp

[bold maple]

I understand division

thank you

[proud raven]

the part that remains a fraction is just the remainder

[bold maple]

I didnt know what it wanted

Thought I was dumber then I am already

[bold maple]

If u(x)=7x^2+19x−27 and v(x)=7x^2−8x−9, then the function w(x)=u(x)−v(x) must be divisible by which of the following?

A. 2
B. 6
C. 9
D. 12

<@&286206848099549185>

[wraith idol]

Omg

!15m

[jolly silo]

is this pre calc?

[wraith idol]

[jolly silo]

doesnt look pre calc

[wraith idol]

Why bot not working

[bold maple]

think im3

not sure though

I dont understand what to do since 7 is an integer which can not be divisable

[charred hull]

@wraith idol bot only works for questions channels

[proud raven]

where does w(x) come from

[bold maple]

am i not allowed to ping from start?

im not sure

thats how the question was worded

[proud raven]

you have to wait 15 minutes

[bold maple]

oh ok

[proud raven]

that is how the question is worded

[charred hull]

read #❓how-to-get-help

[bold maple]

i copy and pasted the exact wording

[proud raven]

i feel like if you examine how to get to w(x) youll see the question is easier than you think

[charred hull]

find u(x)-v(x)

it's completely doable, there shouldnt be a 7x^2 in w(x)

[wraith idol]

@charred hull 1) the bot isn’t even online, 2) the sentence there means you can only tag helpers if you’re in #❓how-to-get-help

[charred hull]

o shit speyr down

[wraith idol]

@fossil crown

Wait it is here

Weird

It’s not in the bots list

[charred hull]

speyr doesnt work anywhere else