help-10

[celest mantle]

thanks man

i kinda wanna do B before going to sleep

for B and number 1 would u have to do 2500 x 1.60 and then x 1/3

[fierce lagoon]

I mean I gtg

1/3 • 1.6(2500)

[celest mantle]

so what i said is still right?

its like 1333.333333

[fierce lagoon]

Yeah

[celest mantle]

cool cool well ye ima go sleep too, ty tho man gn cya

.close

[obtuse pebble]

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[gloomy valve]

what did you get for (a), whats the dim

and now notice in (b) it says for i > 1, that is v1 itself might not be in the span

so it could be that you only have m-1 linearly independent vectors

because it could be that w = 0 for example

[obtuse pebble]

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[wraith snow]

could someone explain what this is asking?

[obtuse pebble]

@wraith snow Has your question been resolved?

[zenith raft]

so for 1a, if a line passes through $(0,A_1)$ and $(1,A_2)$, then its slope is $\frac{A_2-A_1}{1-0} = A_2-A_1$, and its $y$-intercept is $A_1$. So the equation of the line is $y=(A_2-A_1)x+A_1$. Since $(2,A_3)$ is on the line, $y=(A_2-A_1)x+A_1$ must be true when $x=2$ and $y=A_3$. So $A_3=(A_2-A_1)\cdot2+A_1$

[warm shale]

layla💜

[wraith snow]

thank you so much!

[obtuse pebble]

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[winter fossil]

I haven't found area of a region with the stuff on the right for the value of X

is that just a fancy look for the bounds of X per equation

[cedar lichen]

Well, you have to integrate each part separately

[winter fossil]

Ohh do I add the integrations of both, usnig the bounds to the right?

[cedar lichen]

Yep

[winter fossil]

got it, ty again!

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[tender tinsel]

Can someone please help me with this question

[obtuse pebble]

Please don't occupy multiple help channels.

[tender tinsel]

I don't know where to start from

[tender tinsel]

my other channel is inactive with no response 😭

[nocturne minnow]

Then close it

[tender tinsel]

i still need help tho

with that question

[nocturne minnow]

Okay, so? You still don't open multiple channels, like the bot stated

[tender tinsel]

i just thought i'll wait on that and ask my other question in another channel

but if thats not allowed, i;'ll just send this there

.close

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[dawn quarry]

Khan is at a car dealership to buy two cards, one DMW and one plexus. The dealership currently has 20 DMW cars and 15 plexus cars. Of those cars, khan like 8 DMW and 5 plexi cars. What is probability that he buys a DMW and plexi car he likes?

[silver fox]

Uh how is he going about buying them random selection?

[worthy cargo]

yeah probably

[dawn quarry]

Original problem

I’m pretty sure I made mistakes typing the problem but idk

[silver fox]

Well 8/20 and 5/15 are the chances of each of the different things

If they are independent

What do we do

[dawn quarry]

Do we just multiply them

[silver fox]

Yes

[worthy cargo]

yes

[dawn quarry]

2/15

[worthy cargo]

yah

[dawn quarry]

ok thanks

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[obtuse pebble]

@hazy junco Has your question been resolved?

[obtuse pebble]

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[glacial jetty]

Just trying to understand what it means by where “x is negative”

I assumed it’s talking about the absolute value?

And if so, is f presumed to be the positive and q the negative?

[cedar lichen]

f(x) is the function for all x

q(x) is specifically when x < 0

[obtuse pebble]

@glacial jetty Has your question been resolved?

[glacial jetty]

Does all x include positive and negative?

I’m confused what to compare and how to simplify f(x) to compare to q

[cedar lichen]

All x includes all x yes

[glacial jetty]

So from that definition, they’re not the same, because q is just a subset of f isn’t it

[cedar lichen]

In a way, yes

But you still have to find q

[glacial jetty]

I found q

[cedar lichen]

Which is?

[glacial jetty]

-x^2-3

[cedar lichen]

Yep

[glacial jetty]

And I compare that to the original f?

Or do I simplify f

[cedar lichen]

You can't simplify f

Nor does the problem asks you to

All it asks is to find the domain of q and if q is the same as f

[glacial jetty]

So for f and q to be the same would w simplified have to be just be f

Sorry if my qs are redundant

I’m just trying to wrap this idea around my head

[cedar lichen]

.

You already concluded they aren't the same

The domain is different

[glacial jetty]

I see- thanks for your help

[obtuse pebble]

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[grand sable]

Whats wrong here ?

[obtuse pebble]

Please don't occupy multiple help channels.

[grand sable]

.close

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[timid silo]

what is 1 + 1

[minor anvil]

3

[timid silo]

thanks bro

.close

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[zenith raft]

I believe it's 2

[timid silo]

.close

meh

[zenith raft]

it's ok it will close

[obtuse pebble]

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[unborn epoch]

hey guys what is thedifference between a saddlepoint and point of inflection

[obtuse pebble]

@unborn epoch Has your question been resolved?

[obtuse pebble]

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[unborn epoch]

no

[unborn epoch]

diffeernce ebtween point of inflection and saddle point and how to find it in multivariable

[obtuse pebble]

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[obtuse pebble]

@unborn epoch Has your question been resolved?

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[cedar lichen]

Well, what fraction of the class has c grade?

[brave matrix]

So what are those 2 fractions added together?

[cedar lichen]

Since 2/3 have a and 1/5 have b

But what fraction

Out of the whole class

13/15 have a or b

What fraction is the rest?

If 2/15 of the class is 15 people, can you find how many people there are?

[timid silo]

ohhh i get it

[cedar lichen]

Well, let's say there's x people in the class

[timid silo]

bye

[cedar lichen]

And what's 2x/15 equal to?

[cedar lichen]

2 isn't equal to 15

Solve for x

?

Where'd you get 7.5

Yes, but you should round since you can't have half a person

👍

Should be

No answer is too big if it's right

[timid silo]

@viscid pollen what grade is this math for

just curious

LOL

damn

gr 9 smarter than gr 10 bye

LOL

rip

good luck

oh wow

then defintaleye good luck

definitely

i cant write or do math

meh

its ok

[obtuse pebble]

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[summer salmon]

can someone help me with c?

.close

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[minor dome]

is the quadratic formula still valid for factorizing even if it only a left hand side ie: 2x^2 + 8x + 20 as opposed to 2x^2 + 8x +20 = 0?

[potent dagger]

yes

[minor dome]

good

thats all

.close

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Please don't occupy multiple help channels.

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[coarse path]

what is 1+1

[coarse path]

nvm solved

.close

[obtuse pebble]

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[coarse path]

.close

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[keen trail]

How do I do 10 c)

Like,

I got (2!)⁴ x 4! x 2! / 40320(ofc)

Because, B G B G B G B G

Soo, 2! because it can be GB or BG

^4 because 4 of them

times with 4! because it changes position and 2! because it can also G B

actually, now that i think about it my calculation makes no sense(wrong ans)

Hey uh not to disrupt you but this channel is currently mine,

You may go to math help(available)

[timid silo]

hey sorry when I started writing it was unoccupied my bad!

[keen trail]

its cool

[obtuse pebble]

@keen trail Has your question been resolved?

[zenith raft]

I think the number of valid arrangements would be 2*4!*4! because they must be arranged in BGBGBGBG or GBGBGBGB and for each of those, there are 4! ways to arrange the girls and 4! ways to arrange the boys

[keen trail]

hmm

[drifting wraith]

i agree

[keen trail]

ah that makes sense

but how about 2!

[zenith raft]

what about it?

[keen trail]

Like, I get there are 4! ways to arrange the boys and 4! ways to arrange the girls

what effect does 2! do

[zenith raft]

4!*4! arrangements that look like BGBGBGBG, and 4!*4! arrangements that look like GBGBGBGB

for (4!*4!) + (4!*4!) total

which is 2*4!*4!

[keen trail]

ooh i see

I got it,

thanks

[zenith raft]

great!

[keen trail]

.close

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[timid silo]

There is a track with 2 hurdles.
1000 runners participate.
Only 50 runners finished the track race.
Unknown amount of runners passed the first hurdle.
Out of those only 40% passed the second hurdle and finished the track race.
How many runners passed the first hurdle?

[obtuse pebble]

@timid silo Has your question been resolved?

[proven zephyr]

Ok so

where are you stuck

and what have you tried

[timid silo]

40% of what number is 50 ?

2/5X=50
x=125

right?

[proven zephyr]

yes

yes

yes

yes

[timid silo]

.close

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[stable rain]

can we apply landaus big O to
sin(1/z) as z-> 0

[stable rain]

so taylor expansion of sin(1/z) is

1/z - 1/(3!z^3) + 1/(5!z^5) -...

normally if its z-> inf we can just use 1/z + 1/O(z^3) right

but idt we can do that here as they get bigger (as z -> 0)

is there some manipulation we can use

or we just cant use landaus notation here

[obtuse pebble]

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[stable rain]

.close

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[plush vigil]

How do I write tan^-1(-1/√3) in radians

[random depot]

• pi^2/1080 rad

[plush vigil]

Ok thanks

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[heady moss]

hello! shouldn't this inequality hold for negative real numbers as well?

[timid silo]

Yeah

But what is n here tho? Number of terms?

[wild swallow]

that much should be obvious

[severe monolith]

n can't be negative. You cant have anything but a natural number amount of terms

[wild swallow]

there it pretty explicitly lists out the a_blah sequence to be indexed from 1 to n

but there's also the GM and HM

and you want positive reals for those inequalities

[obtuse pebble]

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[obtuse pebble]

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[graceful pollen]

2x2 = -10

not 8

[obtuse pebble]

@steady frigate Has your question been resolved?

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[fallow ember]

Am I doing smth wrong here ?

[fallow ember]

Oh I think I c error

Can someone check my work pls

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[supple glade]

Can someone tell me how the base is equal to 2d? I know it's a physics question but my query is fairy mathematical and I'm banned in the physics server 💀

[obtuse pebble]

@supple glade Has your question been resolved?

[supple glade]

<@&286206848099549185>

[obtuse pebble]

@supple glade Has your question been resolved?

[supple glade]

.close

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[lofty thunder]

Hey I'm trying to understand why my professor's example shows the exponents being added instead of substracted as to the division exponent rule. Is it because of the parentheses?

[lofty thunder]

oh wait I screwed up actually

[clear fog]

yes it is because of the parenthesis. sicne it is m^x/m^y end result should be m^(x-y) where in this case x is 2 and y is -6

so m^2-(-6)

Parenthesis makes a lot of difference and oh my lord I have lost a lot of marks cause of it

[lofty thunder]

could you dumb that down lol

[random depot]

Make a^-8 to the denom using -ve exponent rule

[lofty thunder]

I messed up the calculation because of the signs, it seems he did subtracted

.close

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[timid silo]

hello can anyone help me here

[uneven palm]

[timid silo]

quadratic equation question

[uneven palm]

well.. let's see the question

[pine sail]

,rccw

[timid silo]

stuck man

pls help with this

there are two real and distinct roots

[pine sail]

Definitely not.

Wait it says 5 to infty not all x.

Basically now you shall make cases.

[timid silo]

so i did D is greater than equal to 0

[pine sail]

Why exactly?

[timid silo]

_b/4a < 5

[timid silo]

making all the cases to make one answer

[timid silo]

see

[pine sail]

If D >= 0 it means 2 distinct roots or 1 root

[timid silo]

you can see the graph right

[pine sail]

Yes but that's just one case

[timid silo]

yes right

[pine sail]

ok yeah let's deal with this one

You have to ensure your roots are less than or equal to 5, both of them.

[timid silo]

we get 3 graphs satisfying the condn

[timid silo]

how

[pine sail]

There are lots of tricks you could pull off.

Have you studied any such cases, which deal with roots' location?

[timid silo]

pls can you help me with the solution

like i dk what i am doing ... all frustrated

[timid silo]

yupp

there are 6 graphs

[pine sail]

If both roots are less than 5, what would you generally do?

Like apply a few conditions. What would those be?

[timid silo]

in which 3 of them satisfy the condition

[pine sail]

What graphs are you taking about

[pine sail]

Is that everything you've been taught?

[timid silo]

well there are few more pages

[pine sail]

Location of roots, good.

[timid silo]

thats all i think so is imp for the question

[pine sail]

Yes

Now you want the expression to be greater than 0 for all x greater than 5

The first thing you want to do is notice that for that to happen, the parabola must be facing upwards.

yes?

[timid silo]

yes i did it

all 3 cases

[pine sail]

What cases are you even talking about I don't see that in your work

[timid silo]

ok

[pine sail]

The one you posted above.

[timid silo]

if f(x)>0 and X is 5 to infinity so f(5)>0

[pine sail]

Not necessarily.

f(5) could very well be 0

[timid silo]

have u read the guestion

q*

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[rocky cosmos]

An integer is a prime if and only if it cannot be expressed as a product of two integers. An integer is a composite number if and only if it can be expressed as a product of two integers.

Express these definitions with explicit universal statements.

[brave oxide]

Can someone explain step by step how we get to the a(s)=lθ’’term by using the first formula, which is the acceleration in the x direction of a pendulum? Thanks in advance

[rocky cosmos]

@brave oxide Go to a different channel.

[brave oxide]

Sorry

[royal basin]

these "definitions" are incorrect as stated

[rocky cosmos]

Yeah, my teacher wants me to express them as stated, using symbols or what have you.

So starting with the prime.

[royal basin]

exactly as stated, paying no mind to the technical inaccuracy?

are you sure?

[rocky cosmos]

Yeah

[royal basin]

are you also sure that the technical inaccuracy was not introduced by you?

[rocky cosmos]

Yeah

We are meant to answer if it’s false or not

[royal basin]

did either one state something about the factors being greater than 1?

[rocky cosmos]

No

That’s why it was necessary false

[royal basin]

oh so you're meant to check if it's true...

should've said so

anyway

[rocky cosmos]

I already did that

My objective is to formalize it now

[royal basin]

$n \text{ is prime} \iff (\forall a, b \in \bZ)(ab \neq n)$

[warm shale]

Ann

[royal basin]

$n \text{ is composite} \iff (\exists a, b \in \bZ)(ab = n)$

simple as that rly

[warm shale]

Ann

[rocky cosmos]

So n is a composite if there exists a product of the integers a and b, and vice versa

But not for all integers a, and b. Because 0 don’t work :)?

[royal basin]

actually according to these defns all integers are composite

because n = n*1

[rocky cosmos]

Yes, could you clarify the definition of prime? Why do we write ab ≠ n?

[royal basin]

for any two integers a and b their product isn't n

that's what it means for n to be inexpressible as a product of two integers

[rocky cosmos]

Well couldn’t we say a prime number n is a product of 1 and n?

[royal basin]

and that's exactly the technical inaccuracy i brought up at the beginning!

[rocky cosmos]

Okay I see, thanks

.close

[obtuse pebble]

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[tropic beacon]

guys i need help in logarithm

[timid silo]

yes?

[versed cave]

[tropic beacon]

1st one

@timid silo

[versed cave]

Like this is really hard to tell what you did, but did you write 256 as 2⁶? Because 256 is 2⁸

[faint prism]

When doing algorithm, you kinda want the base same as the algorithm’s base.
So, $log4(256)$ should be $log4(4^4)$, instead of $log4(2^8)$.

And the right part, you wrote 1/2, which is a bit unclear. Write $\sqrt{2}^2}$ instead.

[warm shale]

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

[tropic beacon]

ohh

[tropic beacon]

i wrote 2^8 only

ans is 5

and mine is log 3 on the base 2

[faint prism]

Don’t skip writing the terms unless you are certain.

[tropic beacon]

no i didnt missed

[faint prism]

Second line, where’s the 2 other log2?

[tropic beacon]

😅 on actually i solved that term first and then the second

[faint prism]

Hmm, I dunno if this is a method that I haven’t learned. If so, I apologize.

[tropic beacon]

@faint prism

i mean you want it in this way ?

<@&286206848099549185>

[faint prism]

Actually, the last line should be: A=5, or add another line of A=5

[faint prism]

Also, this isn’t a whole term, it’s two terms.

I think this is the part where you got confused.

If it’s a whole term, there will be a parentheses including $(256+2log\sqrt{2}(2))$

[warm shale]

Potet

[tropic beacon]

ohh i thinks thats the mistake i made

i should not have added that

[faint prism]

👍

[obtuse pebble]

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[dry ember]

How do I know how much 1.15 percent is per? Is it per month? Per year?

[royal basin]

unless otherwise stated i'd assume it's per year

that's the default in finance

[worn swan]

it says semi annually

which is twice a year

[obtuse pebble]

@dry ember Has your question been resolved?

[obtuse pebble]

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[urban needle]

I need to find the intersection between the function f(x)= e^(x-1)-2 and g(x)=1-2x

[velvet spade]

what have you tried?

[vast wren]

at how many points do the graphs of those functions intersect

think about the graphs

[rigid pine]

I'd recommend simplifying f(x) = g(x) to get e^(x - 1) = 3 - 2x then you might see the solution by eye for nice round number x.

[urban needle]

I've set them equal to each other to get e^(x-1)-3+2x=0

[vast wren]

for x>1, we have to deal with e, right?

so what if we eliminated the constant?

[urban needle]

You'd have to set e^(x-1)= 3-2x

Then you get x-1= ln(3-2x)

[vast wren]

hint: make e^(x-1) equal to an integer

[vast wren]

you could go from there too

[vast wren]

but we have a much easier solution method

[urban needle]

Ok idk what it is lol

[vast wren]

e^0 = 1

[urban needle]

So input 1 for x on both sides?

[vast wren]

yep

and to check if there’s more than 1 solution

[vast wren]

.

one is an exponential function, and the other is a line with negative slope

[urban needle]

Yes

[vast wren]

so if you drew them on a coord plane

there’d only be how many points of intersection?

[urban needle]

But I need the value of the intersect

[vast wren]

exactly, one intersection point only

[urban needle]

Not how many there are

[vast wren]

thus x=1 is our only solution

[vast wren]

we already found tho, no?

for the ordinate, find f(1) or g(1)

[urban needle]

My calculator puts the intersectiong x-value around .266

I'm putting one is -1

Inputting**

[vast wren]

I’m fairly certain that’s the answer

[urban needle]

Ohh I see

I input the function wrong lmao

[vast wren]

it happens lol

[urban needle]

Racking my head over a dumb mistake

Thanks

[vast wren]

glad I could help

[urban needle]

.close

[vast wren]

yw

[obtuse pebble]

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[dry ember]

How do I know how much 1.15 percent is per? Is it per month? Per year?

[warm canopy]

semi-anually

thats twice a year

[obtuse pebble]

@dry ember Has your question been resolved?

[dry ember]

Yes but its compounded twice a year. Whats the rate of interest per?

[warm canopy]

1.15%

each time

[dry ember]

Are u sure? Thats the amount of compounding per year

[warm canopy]

well is there context you're not showing? bc as written it seems that you're compounding twice a year at 1.15% each time

[obtuse pebble]

@dry ember Has your question been resolved?

[obtuse pebble]

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[celest mantle]

can someone explain how it’s the red answer

[celest mantle]

,rotate

[kind hawk]

well 6955.65*1.15=7999

plus minus a bit of rounding

[celest mantle]

how would i work it out tho

[kind hawk]

divide 7999 by 1.15

[celest mantle]

oh

aight ty

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[marble hamlet]

I'm having trouble finding the bounds and setting this up using shells

[obtuse pebble]

@marble hamlet Has your question been resolved?

[covert otter]

I would integrate from y=0 to y=8

[obtuse pebble]

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[summer stone]

.close

[obtuse pebble]

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[drowsy stirrup]

is this closed? idk

<@&286206848099549185> i think this is meant to be closed coz i accidentally deleted a msg and it closed but the channel itself isnt closing

[obtuse pebble]

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[gray creek]

Hello I’m a little confused with b and c

[royal shard]

https://en.wikipedia.org/wiki/Classification_of_discontinuities

for c:
we know where the function is discontinous

therefore we can say where it is continous

example:

f is continous in

$[-6,-3)=-6\geq x>-3$

[gray creek]

How would it be 6? I thought the discontinuities were -3 and -1?

[gray creek]

I’m a little confused with this answer?

[warm shale]

~Martin

[obtuse pebble]

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[gray creek]

.close

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[zenith raft]

a_n must be less than 1 for all n greater than some N if a_n -> 0

so you can compare the series from N on

[full relic]

wait sorry idgi

[obtuse pebble]

@full relic Has your question been resolved?

[nocturne cloak]

By the definition of convergence of a series, there must be some N which for all n > N, a_n < 1

[zenith raft]

I wouldn't really say that's by the definition of convergence of a series

[zenith raft]

in more detail, it's more like: if $\sum_{n=1}^\infty a_n$ converges, then $\lim_{n\to\infty}a_n=0$ by whatever you call that theorem, and from that, there exists an $N$ such that $|a_n|=a_n<1$ for all $n> N$

[warm shale]

layla💜

[zenith raft]

intuitively, since a_n converges to 0, eventually the members need to be close to 0 (and we're choosing close to mean less than 1 away, but that's not specific to 1)

[zenith raft]

and more formally, if you write out what it means for a_n to converge to 0 in epsilon language, let epsilon = 1 and you'll get the second part of this

[obtuse pebble]

@full relic Has your question been resolved?

[full relic]

rightttt ok thank you sm :""

[zenith raft]

np!!

[full relic]

could you give me some hints for this? :o

i was thinking of using the same method but

a_n<1 so sqrt a_n< 1

[zenith raft]

the same approach will not work for that

[full relic]

bcos i wont be able to compare the two right

[zenith raft]

yea

my hint is... go a completely different route lol

[full relic]

since a_n converges to 0, its root will converge to 0 too..?

shucks i rlly have no clue

[zenith raft]

yea but that's not very useful information =/

can you give some examples of convergent series?

[full relic]

the p series

[zenith raft]

with p = ?

[full relic]

more than 1

OH

huh wait

but idk what a_n is

[zenith raft]

that's ok

just go with this for now

[full relic]

oki

so the p now will be divided by 2

the problem is i cant ensure that the power for sqrt a_n >1

[zenith raft]

that's getting somewhere

[zenith raft]

so what do you think the answer to this is?

[full relic]

inconclusive? HAHA

[zenith raft]

not the word I'd use but sounds like you got it lolll

[full relic]

oh fr?

i thought id have to give a solid answer

[zenith raft]

you seem pretty close to a solid answer if you don't have one already

[full relic]

ah!

thank u so much once again😭

[zenith raft]

yea np 🙂

I'll add that a "solid answer" could involve explicitly giving 2 sequences {a_n} and {b_n}, where sum sqrt(a_n) diverges and sum sqrt(b_n) converges

or just providing one that diverges and answering "not necessarily" could be fine too

and those sequences satisfy all the conditions in the problem

[full relic]

yep gotcha

[obtuse pebble]

@full relic Has your question been resolved?

[obtuse pebble]

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[smoky zenith]

is this correct?

[nocturne minnow]

Definitely not

Is the slope of that line positive or negative? And is the slope of your equation positive or negative?

[smoky zenith]

Is my work right?

[nocturne minnow]

You realize, [-5, 5] aren't given points, right?

That's the scale of the plot

[smoky zenith]

so if these are not point, how would i do it?

[nocturne minnow]

Find two points that are on the line and then do the same process you were doing

[smoky zenith]

but arnt the points that are given to me on the line too?

[nocturne minnow]

What points are given?

[nocturne minnow]

Those aren't points

They are the scale of the x and y axis

[smoky zenith]

oh

[nocturne minnow]

It's say the grid in the x direction goes from -5 to 5

Even if you thought they were points, does (-5, 5) fall on the line?

[smoky zenith]

maybe tbh but ya i see where your going

[nocturne minnow]

Are you sure that (-5, 5) is on the line?

[smoky zenith]

well i cant see it but i assume so but anyway
is this the right answer?
y=1/2x+1

[nocturne minnow]

Well, you can't assume because you can see it. All you do is move 5 units to the left, then 5 units up, so as I have asked, was (-5, 5) on the line given?

[smoky zenith]

I got it wrong but is the work right at least?

[nocturne minnow]

Those points aren't on the line either

[nocturne minnow]

You realize that coordinate isn't (-2, 1), right?

[smoky zenith]

but then where can i find the points?

[nocturne minnow]

I mean you picked points on the line, the values aren't proper

Like (-2, 1)

You went 1 unit down in the y direction, right?

[smoky zenith]

oh shit, ya i need some sleep

it should be (-2,-1)

[nocturne minnow]

Yes

[smoky zenith]

Welp thank you for dealing with me, Good night

.close

[obtuse pebble]

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[storm mortar]

i have a question about discrete math

[wild swallow]

no, A = {1, {1}}, P(A) = {{}, {1}, {{1}}, {1, {1}}}

[storm mortar]

i thought the definition of disjoint sets was that there were no common elements in between the two sets

how come your P(A) doesn't have the value 1 itself

what about just A = {1}

[wild swallow]

the elements of P(A) are sets

it does not contain 1

[storm mortar]

so no set (besides the empty set) can be disjoint with its own power set

[wild swallow]

no

[storm mortar]

or

[wild swallow]

sometimes it might be

sometimes it might not be

[storm mortar]

just sets with only numbers for example

like B = {2, 4, 5}

would be disjoint with its power set

[wild swallow]

well yes

[storm mortar]

what about the set C = {{}}

[wild swallow]

well P(C) would also have {}

[storm mortar]

so it wouldn't be disjoint

[wild swallow]

no

[storm mortar]

what about like

D = {{0}, {1}}

[wild swallow]

check it

list out P(D)

[storm mortar]

{{}, {{0}}, {{1}}, {{0}, {1}}}

is that right

[wild swallow]

seems fine

[storm mortar]

so it would be disjoint

seems like if the number of brackets stays constant it'll be disjoint?

[wild swallow]

what does that mean

[storm mortar]

idk i'm just trying to come up with a rule that makes sense for when they'll be disjoint

[wild swallow]

whenever A does not contain a subset of itself

[storm mortar]

ok that makes sense

P({0,P({0})})

what would be the elements of this set @wild swallow

it simplifies to P({0, {}, {0}}) = {{}, {{}}, {0}, {{0}}, and all the combinations?

[wild swallow]

P({0, P({0})) = P({0, {{}, {0}}}) = {{}, {0}, {{{}, {0}}}}, {0, {{}, {0}}}}

or in other words

P({0, P({0})}) = {{}, {0}, {P({0})}, {0, P({0})}}

[storm mortar]

does this contain all the combinations too

like shouldnt {{}} be a member

[wild swallow]

there are only two elements in {0, P({0})}

0 and P({0})

[storm mortar]

oh hmm

okay that makes sense

i was going into the other layers to make combinations but it's not needed

if you're taking the cartesian product of two different sets where one has size 1 and the other has size 2

do you treat it like a polynomial

like x(y + z) = xy + xz

vs

{0} x {0, {0}} = {(0, 0), (0, {0})}

@wild swallow

[wild swallow]

?

[storm mortar]

when distributing

[wild swallow]

i mean

the operation is the same in terms of what you do with the elements

but its not really polynomial multiplication per se

i guess thats the idea behind generating functions

[storm mortar]

ah

ok thanks for the help dude

[obtuse pebble]

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[silent imp]

https://gyazo.com/f00b1fa8d17d53a0e4f0431db6cb3827

[silent imp]

what am i doing wrong

oh nvm

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[obtuse pebble]

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[lean dock]

this is my working rn

idk wtf im doing as u cana probably tell

[warm shale]

ｇａｂｂｌｅｓ．

[obtuse pebble]

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[lean dock]

https://cdn.discordapp.com/attachments/903430332324405288/1018789916349579274/195407275337187328.png

.open

bruh

[obtuse pebble]

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[waxen patrol]

https://youtu.be/k-TDe0OP2XY?t=152 can someone explain this please? I dont get how 44 is put in b

[waxen patrol]

how is the one in yellow mark used instead of 4^2 = 16

[graceful pollen]

4^2 - 4(1)(-7)

[waxen patrol]

I do not get the video overall

[graceful pollen]

it's simplified

16 + 28

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

Question f: i need to find out what a, b, and x is. i have no clue how to do this my teacher didnt explain it in class

[compact prairie]

a is 50 degrees because they are alternate angles of parallel lines

a+90=50+90=140 degrees therefore the dot= 180-140=40 degrees

therefore b=90 degrees

oh wait the question specifies there congruent

[timid silo]

Yeah

[compact prairie]

yeah so x=11

the triangle has just been rotated 180 degrees

[timid silo]

Oh alr

Thanks

[obtuse pebble]

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[whole spruce]

Sin18deg.sin36=

[random ocean]

wdym

sin18*sin36?

[weary delta]

$sin(18^{\circ}) \cdot sin(36^{\circ})$ I guess

[warm shale]

Learath2

[random ocean]

in terms of what, or u need the value

[whole spruce]

The value

Yes it's sin 18 degrees*sin 36 degrees

[random ocean]

do uk how to calc sin18

without calculators

assume 18=x,
2x=90-3x, take sin both sides,
sin2x=cos3x, 2cosxsinx=4cos^3x-3cosx, 2sinx=4(1-sin^2x)-3, solve the quadratic and you'll get sinx ie sin18

( take the positive value from the quadratic formula cause sin18>0 )

[whole spruce]

Sorry to waste your time. It's actually sin 18 cos 36

[random ocean]

find cos36 from formula cos2x=1-2sin^2x

its alright

[whole spruce]

.close

[obtuse pebble]

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[random ocean]

ok

[obtuse pebble]

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[sage gorge]

hi

[sage gorge]

i have a ti 84

and i put in inverse cos ( -1)

and it just shows an error pls help

[devout sable]

Because arccos (-1) doesn’t exist

,w Domain of arccos

[sage gorge]

i put it in my computer calc and it comes up

[warm shale]

Results provided by WolframAlpha

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

Requested by Deep.#0001

[wild swallow]

it doesnt?

[devout sable]

Wait

[wild swallow]

LOL

[devout sable]

Hmm

[wild swallow]

i mean

-1 <= cos <= 1

maybe show what you entered into calculator?

[devout sable]

Maybe ur calculator was designed by me

[sage gorge]

its ok, if you cant fix the inverse thing, pls help with this question

[devout sable]

Whats (CF)

[sage gorge]

complex familiar

just the classification of the question

[devout sable]

Hmm

-1<=cosx<=1

So -1<=cos(2x)<=1

-2<=2cos(2x)<=2

So 0<=2cos(2x)+2<=4

So minimum at f(x) =0

2cos(2x) + 2 =0

Did you get what i did so far?

[sage gorge]

sure

i dont know what u do

[devout sable]

Now can you calculate then?

[sage gorge]

do u has steps 4 me to follwo cuz i stupid

[devout sable]

Which step, can you reply that

[wild swallow]

lol im not sure how relevant this is

[sage gorge]

from the start

[wild swallow]

we only care about the x-axis intercepts

[sage gorge]

what to do first then whats next

[wild swallow]

not what the minimum is

[devout sable]

Hmm wait

I read wrong

[sage gorge]

lol

[devout sable]

Maybe I should quit

[sage gorge]

no

pls hepl

[devout sable]

Touches x axis means y=0

So 2cos(2x) +2=0

Or 2cos(2x)=-2

Or cos(2x)=-1

Hmm minimum

In the question do they mean smallest positive?

[obtuse pebble]

@sage gorge Has your question been resolved?

[obtuse pebble]

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[agile robin]

Where I go wrong

[weary delta]

,w integral of (x^2 + 1)e^(-x)dx

[warm shale]

Results provided by WolframAlpha

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Requested by Learath2#2281

[weary delta]

Looks good to me and wolfram, just need to group it properly

[agile robin]

I’m thinking pull out an e^-x?

Out of all terms

[weary delta]

first of all get rid of the integral in the final line, it's just -e^(-x), then factor out an e^(-x)

I think that should be enough, if not you might have gotten a sign wrong somewhere, I skimmed over it so it's possible I missed one

Oh and for these there is something called the DI method, a shorthand way to do integration by parts over and over again, you might find it useful to learn

It comes in handy when you have to do more than 1 ibp in a row

[agile robin]

I’m close to the answer sign got messed up somewhere

[agile robin]

I heard of it, I’m gonna watch a video

[weary delta]

pull an - out aswell

Yeah, you did mess the sign up somewhere. Let me take another look see if I can spot it

You messed it up when plugging the integral on the very last line

,w simplify -(x^2 + 1)e^(-x) - 2xe^(-x) + 2(-e^(-x))

[warm shale]

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[obtuse pebble]

@agile robin Has your question been resolved?

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[agile robin]

3rd and 2nd line from bottom

[obtuse pebble]

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[empty oar]

CLAIM:If $\alpha_n \leq \beta_n$ Largest limit point of $\alpha_n $ $\leq$ largest limit point of $\beta_n$

PROOF: Let the largest limit point of $\beta_n$ be $L$. Since there are no limit points of $\beta_n$ above $L$, there are only finitely many $\beta_ns$ above $L+\epsilon$. Since $\alpha_n \leq \beta_n$ there are finitely many $\alpha_ns$ above $L+\epsilon$. Therefore, Largest limit point of $\alpha_n $ cannot exceed $L$

[warm shale]

Schrödinger's cat

[empty oar]

Is the proof okay?

[obtuse pebble]

@empty oar Has your question been resolved?

[empty oar]

<@&286206848099549185>

[obtuse pebble]

@empty oar Has your question been resolved?

[obtuse pebble]

@empty oar Has your question been resolved?

[restive ridge]

context?

[empty oar]

This is independently true...

[obtuse pebble]

@empty oar Has your question been resolved?

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[timid silo]

Hey guys

[timid silo]

How do I know if alpha is on the right or left side of the graph

<@&286206848099549185> sorry for ping

please

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

<@&286206848099549185> please this is a t distribution question with 19 degrees of freedom

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

[frosty spoke]

not sure what any of that means lol

what graph

so T has a t-distribution with 19 degrees of freedom

[obtuse pebble]

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[obtuse pebble]

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[drowsy girder]

$$x^3 - x^2(m + 2) + x(m + 1) - m \geq 0$$

[warm shale]

Pluton

[drowsy girder]

Idk how im supposed to solve a cubic inequality

Guessing by the fact that this is a problem from a competition and it should have a somewhat nice solution i should factor stuff. But idk what to factor

[timid silo]

help

1/2 , 5/6 , 7/6

recursive how do I solve

[drowsy girder]

#❓how-to-get-help

[timid silo]

ohhh wrong channel

mb

[drowsy girder]

<@&286206848099549185>

[obtuse pebble]

@drowsy girder Has your question been resolved?

[obtuse pebble]

@drowsy girder Has your question been resolved?

[drowsy girder]

Oh ye the question is to solve the inequality in terms of m

Idk why i forgot to add that

[drowsy girder]

I solved it

.close

[obtuse pebble]

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[mint atlas]

Is the domain d€R | d <= -8 and range v€R | d<=0?

[cedar lichen]

Explain your answer

[mint atlas]

Well you can’t have the square root of a negative number (not in this case) so -8 and above is what d can equal

[cedar lichen]

That's √(d) + 8, not √(d + 8)

Also, you wrote d ≤ -8

Aka, d less than or equal to 8

That's -8 and below

[mint atlas]

Sorry sorry 😭

[mint atlas]

I didn’t notice that

So in that case d>=0

[cedar lichen]

Yes

And the range?

[mint atlas]

Is it greater than or equal to -8?

[cedar lichen]

Why -8?

[mint atlas]

That’s a great question

In that case it’s greater than or equal to 8

[cedar lichen]

Yes

[mint atlas]

I see I just put the square root over the +8 which screwed it up

Thank you!!!

.close

[obtuse pebble]

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[swift pagoda]

Yo hello can someone help me with my homework?

[swift pagoda]

I don’t understand what to do

I’m behind because I just moved to a new school, so sorry if i seems stupid

[stable rain]

oh

u are suposed to plug values into the calculator?

[swift marsh]

No

[hard anvil]

Can anyone give me a equation

[swift marsh]

You can work these out directly

[hard anvil]

I wanna test my skills 🙂

[swift marsh]

Wrong channel

[swift pagoda]

No they didn’t give us a calculator

[stable rain]

yea lol, #❓how-to-get-help

[stable rain]

oh, i was assuming as u literally had a calculator in the image u sent us

wait or is that to enter values idk

[swift pagoda]

Oh no

[swift marsh]

I think that’s just for typesetting

Yea

[swift pagoda]

Yeah

[stable rain]

kinda weird to have square root in typesetting when they want decimal(i guess?) answers

and nth root lol

[swift marsh]

It’ll be an application-wide thing

[swift pagoda]

They do it for every question

[stable rain]

icic

but yea so

they want answers in decimal?

[swift pagoda]

Maybe idk

[swift marsh]

Go to #❓how-to-get-help as @stable rain said

Either would be accepted I’d imagine

Some make more sense in some cases

[hard anvil]

I go to #discussion

[swift marsh]

Sure

[stable rain]

i mean, fraction maybe as well, but like, probably at least not directly give the nth root lol

but generally the Q should specify

[swift marsh]

Yeah they wouldn’t accept that the point is just simplifying it as far as possible

[swift marsh]

I guess so

[stable rain]

o well @swift pagoda u there

[swift pagoda]

Yeah sorry

Was doing something

[swift pagoda]

Yo hello?

[stable rain]

so

did the question specify to give answer in decimal or fraction or anything

[swift pagoda]

Ni

No

Alr I did the problem but 1 is wrong

<@&286206848099549185>

[tidal hawk]

ummm

why is 1 wrong

cube rt 1 is 1

[cedar lichen]

Umm ackshually you forgot the other two roots 🤓

[tidal hawk]

HAHAHAH omg do u watch fuslie by any chance

[tidal hawk]

also what other 2 roots?

[cedar lichen]

Complex roots

[tidal hawk]

LMAO

nope idk complex stuff

[cedar lichen]

Nope 🤓

[tidal hawk]

awww u sounded like her HAHA

the ackshually

[swift pagoda]

I don’t mean the Question 1 lol, I meant like one out of them all is wrong

@marble ibex you gonna finish that sentence today?

[tidal hawk]

HAHAHA

[tidal hawk]

ohh then idk it seems fine to me

unless they want u to express in form of indices?

oh wait u said one out of everything wrong

huh but they’re all correct no?

[swift pagoda]

Yeah that’s what I thought

[tidal hawk]

oh wait

HAHAHHAA

I found it

cube rt of 64 isn’t 8