help-13

[plucky summit]

of inside the prenthesis?

[bold kernel]

i dont think so...

[plucky summit]

oh ok

the notiation looked familiar

[bold kernel]

just do this the same way you did 1 and 2

with tables

[plucky summit]

alright

and the top number is a?

or is the top number b

[bold kernel]

yes this is with antiderivatives but based on problems 1 and 2 im inclined to think they want an approximation with riemann sums

[bold kernel]

b

@plucky summit here is the problem stated in terms of the other two

[plucky summit]

so i can do 3-1/4?

and do a subinterval of 4?

ohhh okay

thank you

and i choose right or left endpoints

and i choose my subintervals

[bold kernel]

yes

ues

yes*

[plucky summit]

is this ok so far?

@bold kernel

subinterval of 4

[bold kernel]

yes

thats correct

[cedar kiln]

@plucky summit Has your question been resolved?

[cedar kiln]

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[languid sky]

.open

[languid sky]

Im really struggling with the min max problems

I cant seem to factor the equations correctly

it is always factoring problems that I struggle with the most

[shell lance]

You shouldn't need to factor for this equation

You just need to find the points where the partial derivatives are 0

[languid sky]

@shell lance when I find the derivative of f(x,y) I get 16y^3-2x

if in respect to y

in respect to x it is the same thing incept the variables swap places

[shell lance]

Right you shouldn't need to factor

You set both equal to zero and you can solve for x and y

[languid sky]

oh

[quartz frost]

i think you already had this

this is trivially 0 when x=y=0

[languid sky]

ik that one of the critical points is (0,0)

but there are two more

[shell lance]

Correct

[quartz frost]

this is how it looks

[shell lance]

We see that $8y^3=x$ and $8x^3 = y$

[wraith dagger]

hello2248

[shell lance]

Can you solve from there

[languid sky]

so u make the y = to 8x^3

then solve from there

[shell lance]

You go from $16y^3 - 2x = 0 \implies 16y^3 = 2x \implies 8y^3 = x$

[wraith dagger]

hello2248

[shell lance]

And the same with the other one

And yeah, plug it in

[languid sky]

Im struggling to factor this one too I ended up with 4096y^9-y

wait

nvm

yea idk Im cant figure this one out

arent we still factoring

[shell lance]

4096y^9 = y

y^8 = 1/4096

[languid sky]

oh that was thinking about doing

it just when I put it in mathway it said there were multiple answers

ngl Im getting mentally exhasted I been trying to finish 4 homeworks and a quiz I havent finished yet before midnight

[languid sky]

is that the minimum

wait that for y

[ocean badger]

This may help.

Close to the bottom the stationary point section.

Read finding stationary points and after finding one use the classifying portion to help determine if it is a max or min.

[languid sky]

I cant read it

it blurry

the resolution is low I guess

[ocean badger]

Uhh one sec

I’m on my phone

Better @languid sky

?

[languid sky]

yes

now I need to figure out what the question is asking for

cuz for some reason it is not a point

[ocean badger]

Let me work on yours specifically

[languid sky]

I figure it out

I just needed to put the critical points into the original equations

[ocean badger]

Okay

Nice job!

[languid sky]

ty

well I did get help from symbolab but the answer I got alined with the one in symbolab

[cedar kiln]

@languid sky Has your question been resolved?

[cedar kiln]

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[timid kindle]

Hi could someone explain this question

[timid kindle]

I thought it was 45x6

but the answer says c because each side is 45.5

[hallow elm]

no clue why the sides would be 45.5

[timid kindle]

does ! change anything

[hallow elm]

oh haha

if you look at the question

you can see little exclamation points next to 45

I'm sure it meant to say 45.5 but the 1/2 just didn't load

[timid kindle]

ohh

I converted it to docs

that must explain it

yeah this is the pdf

[hallow elm]

there you are

[timid kindle]

thanks lol

[hallow elm]

yep no worries1

[timid kindle]

.close

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[latent path]

Hi, so i know that if given 2 points s.t. (1,2) (3,5) it is a degree one polynomial. But if we're only given one point, say (2,3) is this a degree 0 polynomial? Or what would be the proper definition?

[vagrant orchid]

Yes, you can fit a 0-degree polynomial such that it goes through 1 point. The equation in your case would be y = 3, no x term.

btw, note that a polynomial through 3 points isn't necessarily a degree-2 polynomial

If it goes through (1, 2), (2, 4), (3, 6), then it's still degree 1 because a line can fit through those 3 points.

Also, you can have a higher degree polynomial (e.g. degree 100) fit through less number of points (e.g. 3 points).

[latent path]

weird my math textbook says if all x terms are distinct then it is a unique polynomial

[vagrant orchid]

It's still unique in that you cannot find a different polynomial with degree less than or equal to 2 that goes through 3 points.

…of degree (at most) d…

[latent path]

Sorry can you explain this?

[vagrant orchid]

Ok, do you understand that there's a line that goes through (1, 2), (2, 4), and (3, 6)?

[latent path]

yes

[vagrant orchid]

In this case, d = 2

[vagrant orchid]

and "Property 2" says that you cannot find a polynomial with degree ≤ 2 that goes through these 3 points other than y = 2x

[latent path]

But this has degree 1 as you stated before so it would break that property

[vagrant orchid]

1 ≤ 2

It's not saying the polynomial must be degree 2

It's saying the polynomial must be degree ≤ 2

[latent path]

oh i see thank you

can you help me out with one hw problem? Im not sure if I am understanding the question correctly and it relates to this

[vagrant orchid]

I'll have to go soon. Maybe someone else can help

[latent path]

ok thank you!

.close

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[crimson sedge]

I don’t know if I can do anything from here, not sure if I did smn wrong

[crimson sedge]

It’s correct

In the last step just replace theta with arcsin x and add the constant of integration

I haven’t learnt arcsin yet ;-;

Arcsin is inverse sin

Just notation for the sine inverse

Oh I’m silly

sin^-1(x) is arcsin(x)

[crimson sedge]

Not to be confused with cosecant

Cosecant is 1/(sin(x)

So this is the final answer?

Ignore the stuff above it aha

Yes it is the final answer

You could simplify the sin (2*theta) into 2sin(theta)cos(theta)

So it would become 2sin(arcsin x)cos(arcsin x)

Does sin(arcsin x) simplify into sin(x)?

Wait

X

I mean

[crimson sedge]

It simplifies into x

Because the sin and arcsin cancel out

Yeah yeah okii it’s a lil prettier that way :)

Thanks for the help

.close

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[crimson sedge]

How do I know what to substitute, I can’t find anything that works

[hallow elm]

you may need to use trig sub yeah

[crimson sedge]

ohhhh, alr lemme give it a try

[green belfry]

X= sec,^2

Yes that would work

U

[crimson sedge]

How about u=1-x

[crimson sedge]

So du=dx

[green belfry]

It would work with a trig sub aswell

[crimson sedge]

But u=1-x is simple

[green belfry]

Yes agreed

What a strange question

[green belfry]

Good spot

[crimson sedge]

Why?

[green belfry]

I would one hundred percent have done a trig substitution then used the reduction formula

And never have thought of the simpler method

[crimson sedge]

Yeah sometimes i tend to overcomplicate things

Is this right so far? If so I don’t know what to do next xd

I thought of u=1-x but discarded it bc it had u and x in the formula, could I get around that somehow

Oh and don’t mind when I integrated instead of differentiating in the top right xd

u= 1-x is a lot simpler though

[crimson sedge]

How did it have both u and x?

If you substitute u instead of 1-x, x * sqrt(1-x) becomes (-u+1)*sqrt(u)

Alr is this right?

calculator says yes, thanks for the help everybody!

.close

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[crimson sedge]

Calculator says 80/3 not sure where I went wrong

[gaunt hamlet]

The bounds aren't from 0 to 4 anymore

You forgot to change the bounds after making the u sub

[crimson sedge]

oh yeah its been a while aha

so would the new bounds be from 1 to 9?

[gaunt hamlet]

Yes

[crimson sedge]

alr i got it right thanks :D

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[shy night]

How to do the k , k+1 part

[dire geode]

Did you calculate the first 5 terms?

[shy night]

???

Why would you do that

[dire geode]

To find a pattern

[shy night]

Even after that how do you do the k and k+1 part

is that what k and k+1 if for

[dire geode]

Finding the pattern helps

[balmy apex]

show that $x_{n + 1} \geq x_n$

[shy night]

So you don’t have to calculate

[wraith dagger]

illuminator3

[balmy apex]

then that $x_1 > 2$

[wraith dagger]

illuminator3

[shy night]

How did you come up with that

[dire geode]

Maybe by this

[balmy apex]

induction step

[shy night]

Okok I try

Ty

[cedar kiln]

@shy night Has your question been resolved?

[cedar kiln]

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[livid fog]

Hello, Im confused on this

[rugged palm]

What exactly is confusing you? What have you tried?

[livid fog]

Well I know

an intercept has to do with the change

of negative to postive

[rugged palm]

Yes, or the other way around

So when does a change of sign happen in both the x and y values?

If you don't like to think it this way, the very last option is to graph the points

[livid fog]

I think it's the far left one

because

the sign change only happens once

because it cant have more than

only one y intercept

[rugged palm]

What's an intercept

[livid fog]

where it

insersects

at an axis

[rugged palm]

yes, you need two intercepts, one with x and one with y

[livid fog]

it only has one x intercept

which is

1,0

right

[rugged palm]

It doesn't matter what the intercept point is

[livid fog]

oh yea

[rugged palm]

So which one has both a x and y intercept

[livid fog]

thats only if

f(x)=logb(x) where b>1

[livid fog]

the middle one

[rugged palm]

yes

[livid fog]

ty

[rugged palm]

[livid fog]

that made alot more sense to me

[rugged palm]

If you have more questions feel free to ask, otherwise remember to .close the channel

[livid fog]

ok

.close

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[tropic oxide]

yeah

[inner yoke]

thanks

.close

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[crimson sedge]

guys

[crimson sedge]

i need help

[crimson sedge]

kek

[livid hound]

show work

[crimson sedge]

i havent done

can u tell fast plsssssssssssssss

my class is gonna start

or else my teacher will scold me

faast pls

[tropic oxide]

we don't give out answers here + we don't do other ppl's homework (or whatever) for them

[crimson sedge]

bruh

i just need one help

[livid hound]

so 32/99 was just a blind guess?
same with 707/333?

[crimson sedge]

no idk

i did some shitt

i got wrong

i aske dmy frnds

[livid hound]

show the shit you did

[crimson sedge]

they also got 707/333

[livid hound]

showing what you did allows us to gauge what level you're at and cater our explanations accordingly

doesn't matter if the work is wrong

[tropic oxide]

also it helps us see where you went wrong and address THAT instead of simply going "nope this is wrong"

[cedar kiln]

@icy cypress Has your question been resolved?

[cedar kiln]

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[swift anchor]

how do I do this

[tropic oxide]

the first step is to tell off your teacher for conflating "number" and "digit"

[swift anchor]

lol

[tropic oxide]

the second step is to realize that the odd digits which are immediately to the left of an even digit are all the nines except the last, and nothing else

[swift anchor]

that’s what I got confused about

but how do u know if it means digits instead of numbers

it could mean number

[tropic oxide]

what's a "number within a number" then

[swift anchor]

like 09 is to the left of 0

Wait

i just realized

i thought left was right my whole life

wait what does it mean odd number within this number

[tropic oxide]

as i said i think the author meant digits

[swift anchor]

yeah I think so too now

ok what next

is it just 9 times 2009

dosent that seem too simple

i think it means all odd numbers within the number 2009200920092009…

[crimson sedge]

it basically is that yeah

9 * 2009 - 1

[swift anchor]

,calculate 9*2009

[wraith dagger]

The following error occured while calculating:
Error: Undefined symbol ulate

[swift anchor]

,calculate 9 * 2009

[wraith dagger]

The following error occured while calculating:
Error: Undefined symbol ulate

[swift anchor]

18081

in the answers it says

18072

[crimson sedge]

all odd numbers except for the last one

because it isnt to the left of an even digit

Idk i think it should be 18080

[cedar kiln]

@swift anchor Has your question been resolved?

[cedar kiln]

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[flat elbow]

does this look good

it just feels wrong

for some reason

[crimson delta]

well the step from going p in {...} to (1,1) being in B is pretty fast

wouldn't hurt to say 1-2 sentences more

[flat elbow]

something like, letting a subset X being all the elements of that form, then (1,1) is clearly in X and by transitivity (1,1) is also in B?

[crimson delta]

transitivity?

also just because b is in X and (1,1) is in X does not mean that (1,1) is in B

[flat elbow]

well if X is a subset of B then it would

[crimson delta]

well then you first have to show that X is a subset of B

[flat elbow]

yeah

which is the trouble now that I'm thinking about it

I think this is probably the wrong approach and there's a better way to show this

[crimson delta]

how do you show that 3Z is a maximal ideal in Z ?

[flat elbow]

I think, trying a similar approach, that if B is an ideal properly containing 3Z, then an element in B that is not in A must be congruent to 1 mod 3 or 2 mod 3, but since B contains 3Z, then all integers congruent to 0 mod 3 must be in B as well

which is all the integers

so B = Z

[crimson delta]

no

so far you only know that a single element congruent to 1 or 2 mod 3 is in B

not that all of them are

[flat elbow]

but one of the assumptions was that 3Z is a proper subset of B

[crimson delta]

so we know that B contains all integers that are 0 mod 3 and one integer that is either 1 or 2 mod 3

for example we could have $B=3\bZ\cup{4}$

[wraith dagger]

Denascite

[flat elbow]

alright I see now

[crimson delta]

what else do we know about B

[flat elbow]

that it's an ideal of Z

[crimson delta]

good. how can we use that

[flat elbow]

if r in Z then br must be in B, so B must have any multiple of b as well

so B is the union of principal ideals generated by 1 and 2

[crimson delta]

why 1 and 2

do you know bezouts lemma?

[flat elbow]

yeah

so, using the fact that B must have all multiples of 3 and at least one element congruent to 1 mod 3 or 2 mod 3

[crimson delta]

let k be that element congruent to 1 or 2 mod 3

what is gcd(k, 3)

what does bezout then tell us?

[flat elbow]

3 is prime and if 3 doesn't divide k then gcd(k,3) is 1

so some linear combination of elements of B must be equal to 1

which suggests that 1 is in B since addition in B is closed

so then the identity is in B and B=Z

[crimson delta]

good

now lets do the same thing but with the original question

essentially the second coordinate is just annoying, everything interesting happens in the first coordinate

[cedar kiln]

@flat elbow Has your question been resolved?

[flat elbow]

ok

feeling better about this now

[crimson delta]

yes

[flat elbow]

thanks for all your help @crimson delta

.close

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[dusty hazel]

yeah

As for d

You changed the sign before 2 in the end.

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[hallow elm]

can you show your work

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[cold briar]

wait what

[wraith dagger]

MarveI

[cold briar]

nvm

45*

[cold briar]

no

i messed up

the calculation

f

but the max height of the first segment is 45, if im not wrong

hmm

that's correct if im not wrong

it's 90 ig

[cedar kiln]

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[vagrant sage]

hello if i have cosxsinx = cosx
subtract from both sides do i get sinx = 0 or cosxsinx-cosx = 0 ?

[vagrant sage]

does subtracting cosx on the right cancel the left cosx?

[dusty hazel]

No subtracting gives you cosxsinx - cosx = 0

You'd get sinx = 0 if you divide by cosx.

[vagrant sage]

ooh!

[dusty hazel]

Yeah.

[vagrant sage]

ty! my original problem is this

[dusty hazel]

Then you definitely do not want to divide.

[vagrant sage]

simplified to cosx*sinx-cosx=0

[dusty hazel]

Yes.

[vagrant sage]

would i then factor it?

[dusty hazel]

Yes.

[vagrant sage]

so like cosx(1*sinx-1)=0 ?

[dusty hazel]

Yes.

[vagrant sage]

yay feels like im on the right track

should i keep channel open if i might have other questions later?

[dusty hazel]

You can open new channels I guess.

[vagrant sage]

okay ill close this for now ty!!

.close

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[proper plaza]

Guys why is he matching this with the number 3? What is going on here

[proper plaza]

What does the 3 refer to

[obsidian coral]

The y value

[proper plaza]

Ohhhh

My bad

Was a little misleading there as I was just learning limits

And I took a step back to piecewise functions

Thank you

.close

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[obsidian coral]

But weren't you don't periodic functions just a few hours ago?

[proper plaza]

Yes, I'm a little all over the place

I am trying to learn calculus

[obsidian coral]

You shouldn't rush the process

[proper plaza]

I definitely won't I just needed to understand what I'm looking at instead of it being a series of operations and logic done on a calculator

[cedar kiln]

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[oblique loom]

does anyone know a fast method to find this without drawing a factor tree

[oblique loom]

as in for the larger numbers

[tropic oxide]

break off factors of 2 one by one

then 3, then 5, then 7, etc.

@little pewter this channel is occupied. read #❓how-to-get-help. also if you just want two numbers divided then use a calculator.

@oblique loom heres what it might look like to do what i described:

9800 | 2
4900 | 2
2450 | 2
1225 | 5
 245 | 5
  49 | 7
   7 | 7
   1

exact formatting is unimportant but i hope my point gets across

[oblique loom]

im confused on how u got 1

[tropic oxide]

what do you mean

i broke off prime factors one at a time until there was nothing (i.e. 1) left

[oblique loom]

oh the formatting just conused me

[oblique loom]

but here its saying 245 = 49 x 7

[tropic oxide]

what's "it"

[oblique loom]

ur factor tree

[tropic oxide]

i am not saying 245 = 49 * 7.

here, let me make my work look like an actual factor tree

[oblique loom]

also do i have to divide the non prime factors by intervals of two because that takes a while especially for large nunmbers

oh i see

[oblique loom]

@tropic oxide

[tropic oxide]

idk what you mean by "intervals of two"

[oblique loom]

u see how u divided by intervals of two

to get to the prime factors

[tropic oxide]

i still do not know what you mean, sorry

[oblique loom]

u divided 9800 by 2 to get to 4900

[tropic oxide]

sure

i started with breaking off factors of 2 because 2 is the smallest prime

[oblique loom]

i see

but u can use other numbers right?

[tropic oxide]

if for whatever reason you notice factors other than 2 right away then by all means break them off first

i just personally like going in order so as to ensure nothing is missed and nothing is miscounted afterwards

[oblique loom]

thanks for the help ann you are always reliable

.close

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[tight cove]

Why is C not equivalent

[tropic oxide]

the constants work out to 625/2, not to 625

[tight cove]

Ok thanks

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[static hound]

I need some help with this question I'm unsure where I'm going wrong

[static hound]

I think I've done the first part of the question but it's the second part when I have to find the series expansion, my denominator doesn't factorise so I cannot use the method of partial fractions to get my series expansion

any help would be greatly appreciated

[sick orbit]

ok

@static hound

multiply 1+3x

with the expansion u found

which is right

the 1/2-x/2+x^2/8

i dont know why u divided it

[cedar kiln]

@static hound Has your question been resolved?

[static hound]

sorry I meant I divided it because it was a fraction / expression of (1+3x) ÷ (2+x) (the second part of the question)

[sick orbit]

i dont know what you mean

theres is no fraction

since the expansion you found is the expansion of (2+x)^-1

so theres no fraction at all

[static hound]

@sick orbit so I just multiply my answer and i get this:

[cedar kiln]

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[static hound]

.reopen

[cedar kiln]

✅

[sick orbit]

well i didnt multiply it like that

u have (1+3x)(1/2-x/4+x^2/8)

right

so just expand it normally

like multiplying each term

@static hound

[static hound]

Okay just expand normally, so the terms i get from expanding normally, these are the terms in the series, correct? Then I can find the range, right?

[sick orbit]

yes

nvm

[static hound]

Ok thank you

[sick orbit]

u do need it

i read the question wrong

u need the x^3 term

[static hound]

wait so what am i doing now? I'm confused.

[sick orbit]

just multiply it out

and work out the range

[static hound]

When I multiply it out like you suggested I got this

[sick orbit]

yh

that right

[static hound]

Cheers

[cedar kiln]

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[cedar kiln]

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[kind venture]

how can I solve this integeral a.) ?

[kind venture]

I know I need to use partial integration

what I did I just over complicated it smhw

[crimson sedge]

Set u = tan x

Just like the hint says

[kind venture]

nvm I think I kknow

[crimson sedge]

Draw a right triangle with an angle x

And then set the opposite to x u

And the adjacent to x 1

Solve for the hypotenuse then solve for the sin and cosine of x

Then find dx in terms of du when you make the substitution

[kind venture]

what I did is i subbed u = sin

[crimson sedge]

Why

[kind venture]

thought what would work out

i dont see how and where I could sub u = tan (x)

wow

this is a tricky one

....

damm

ok i got it

how would you guys solve it ? is there a different way ?

could use partial integration aswell ?

[proud barn]

idk if it works but you might be able to do something with a double angle formula

nvm actually

[cedar kiln]

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[fast aurora]

If I have a determinant of order three and I perform a transformation\
$R_1 \rightarrow R_1 + kR_2$\
Do we have any limitation to k?
Or $k \in \mathbb{C}$

[wraith dagger]

Darth Vader

[tropic oxide]

k can be anything

except that when it's 0 the transformation amounts to doing nothing

[fast aurora]

i see

thank you

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[crimson sedge]

It's 0.38 right?

[tropic oxide]

yes

[ocean badger]

Do you know if they are mutually exclusive?

[cedar kiln]

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[crimson sedge]

Thanks

[cedar kiln]

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[willow island]

isn't this step wrong

why do they say 2x^3

shouldn't it be 4x^3?

nvm I'm dumb

.close

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[vernal gorge]

I need to find everything from this graphic

[vernal gorge]

I have the Domain= R- (2)

x->2+ F(x)-infinite

x->2- F(x)+infinite

Vertical asymptote is x=2

Then I also have the zeros x=-3 x=0 x=3

Also the sign is

And I also have this

x-> +infinite F(x)0+

I don't know how to describe when

x->-infinite

and I think the vertical asymptote is y=0

I also don't know how to describe this part

[cedar kiln]

@vernal gorge Has your question been resolved?

[vernal gorge]

<@&286206848099549185>

[cedar kiln]

@vernal gorge Has your question been resolved?

[gaunt hamlet]

This channel is taken

[final wedge]

So where should i post?

[gaunt hamlet]

In the available channels section. It says that in #❓how-to-get-help

[final wedge]

Thnx

[cedar kiln]

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[lost chasm]

Why

[crimson delta]

compare the slopes of the red and blue triangle

[lost chasm]

Ok so?

[crimson delta]

what do you get?

[lost chasm]

The blue one is blue and the red one is red

[bold vine]

This guy's not trying - don't bother

[sage forge]

https://tenor.com/view/the-universe-tim-and-eric-mind-blown-mind-blown-meme-mind-explosion-mind-explosion-meme-gif-18002878

[lost chasm]

Ok i got it

Thx

.close

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[crimson sedge]

Np

[cedar kiln]

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[fresh ibex]

Is this the right graph produced from what has been asked in the question? Really need to get this 100% right so any communal marking would be really helpful.

[cedar kiln]

@fresh ibex Has your question been resolved?

[dire geode]

looks right

[fresh ibex]

cheers for feedback helps a lot

[toxic osprey]

is this channel available?

[dire geode]

stop spamming everywhere and read #❓how-to-get-help

[cedar kiln]

@fresh ibex Has your question been resolved?

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[young frigate]

Can someone help me with find a polynomial P(x) with real coefficients having a degree 4, leading coefficient 2, and zeros 2-i and 3i

[young frigate]

My camera is broken so I can’t show u my work sorry

[crimson sedge]

Look

If a polynomial has real coefficients

Then all the complex solutions come in conjugate pairs

[young frigate]

Ok

[crimson sedge]

So if we have zeros 2-i and 3i

Then we can find the conjugate of these zeros to find the other zeros

[young frigate]

Ok

[tribal sonnet]

2(x-(2-i))(x-3i)(x-(2+i))(x+3i)=0

[crimson sedge]

Bro

Let them work it out

Haha

[tribal sonnet]

sommry

[crimson sedge]

You can del it

[tribal sonnet]

it would hurt them 😦

[young frigate]

Ok I will do it now

Pogram I won’t look at it

.close

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[tribal sonnet]

(n-1)!

[tribal sonnet]

n(n-1)/2

whats the answer?

[brave widget]

it is unsolved

[brave widget]

how did you arrive at this

[tribal sonnet]

n^2 - (1+2+3.........................n)

[brave widget]

explain lol

[tribal sonnet]

first don makes n-1 calls

then n-2

then n-3

add all of them

to get total calls

[brave widget]

this

[brave widget]

and this are these the same?

[tribal sonnet]

yes if my calculation was correct

[pliant bear]

yuo don't need that many calls

[brave widget]

why

[pliant bear]

first step: don 1 calls don 2. don 3 calls don 4. don 5 calls don 6, etc. this is n/2 calls

[brave widget]

then

[pliant bear]

second step: don 1 calls don 3. don 2 calls don 4. don 5 calls don 6. don 7 calls don 8. n/2 more calls

third step: don 1 calls don 5. don 2 calls don 6, don 3 calls don 7, don 4 calls don 8. etc. n/2 more clals

fourth step: don 1 calls don 9. etc. n/2 more calls

at eac step k don 1 calls don 2^k+1, and so on

[brave widget]

each don calls 2 dons right?

[pliant bear]

if the number of dons is a power of 2, so n=2^k, then each don will make k calls, but since each call involves 2 dons, ther eare half as many calls as dons

so the total number of calls required is n*(log_2 n)/2

[brave widget]

log 2n?

[pliant bear]

if the number of dons is not a power of 2, you'll need somewhat fewer calls than this formula requires as some of the high numbered dons will not make calls in each round

log base 2 of n

[brave widget]

okay

[pliant bear]

it's a binary tree problem

if you look at the approach yoiu wer econsidering earlier, on each call at least one of the dons would be getting redundant information

in this approach , in each call both dons always get all new information

you can actually use binary notation to figure out who each don calls in each round

[brave widget]

oh

okay then

[pliant bear]

if you number the dons from 0, then write out the don's number in binary. for the nth round of calls, flip the nth bit of the binary representatition from 0 to 1 or 1 to 0; that number is who that don calls

[brave widget]

wait i didnt get you

[pliant bear]

so in the first round, don 5 will call don 4 because 5 is 0101 so you flip the low bit 1 to 0, getting 0100. in the second round don 5 calls don 7 (0110), in the third round don 5 calls (or is called by) don 1 (0001), and in the fourth round don 5 calls don 13 (1101)

and so on

i wish i had a tree generator, i'd show you how it works

[brave widget]

lol its pretty complex ill look it up

[pliant bear]

it's a really cleve problem forces you think about minimum knowledge exchange and how to organize it

[brave widget]

so whats the smallest number like a numeric value or expression

you wanna try another?

[cedar kiln]

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[midnight zealot]

The question is number 17

This is my answer

Is it correct?

Or is it y=x^3

[bold hinge]

how would you get x^3

[cedar kiln]

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[cedar kiln]

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[crimson sedge]

could someone explain to me the formula for compound interest

[crimson sedge]

i searched it up and still didnt understnad how it worked

[obsidian coral]

Videos exist too

https://www.youtube.com/watch?v=P182Abv3fOk&ab_channel=TheOrganicChemistryTutor

https://www.youtube.com/watch?v=U0Lwyh9ONMM&ab_channel=Mario'sMathTutoring

[crimson sedge]

i just watched one

still didnt understnad lol

[obsidian coral]

If one doesn't help, watch others

There are different ways it is explained

https://www.cuemath.com/commercial-math/compound-interest/

[crimson sedge]

wut

the heck

[obsidian coral]

A link as resource

[crimson sedge]

...

[obsidian coral]

https://byjus.com/maths/compound-interest/

[crimson sedge]

this is the question im supposed to do with compound interest

[obsidian coral]

That's the formula

[obsidian coral]

Plug in what you know

[crimson sedge]

the heck

k

so

100(1+.15/3)

i think thats it

but idk what the nt is

[obsidian coral]

Compound interest might not be the correct formula to use

[crimson sedge]

?

[obsidian coral]

You need to use the one you applied previously

[crimson sedge]

this?

it still has nt

which i dont understand

[obsidian coral]

You need to use the one you applied previously

The I = Prt

[crimson sedge]

ohhhhhhhhhhhhhhhh

1000 x 3 x .15

[obsidian coral]

For the actual compound interest formula to be applied, you need other details

[crimson sedge]

i got 450

so 1450

[crimson sedge]

i see

[obsidian coral]

This question applies the same logic as the last question you asked

[crimson sedge]

but how come the answer saids its not 1450

[obsidian coral]

What does it say?

[crimson sedge]

this is the answer

but that doesnt use the compound interest formula u gave me

nor does it use the prt

or is it just me that doesnt understand

[obsidian coral]

So it looks like what you do is apply the I = Prt formula, because it finds the interest after 1 year

[crimson sedge]

?

[obsidian coral]

You use the I = Prt

[crimson sedge]

thats what i did

i got 1450

[obsidian coral]

You find the interest amount after each year

So after 1 year, what's the interest amount?

Then what's the total amount after that one year

[crimson sedge]

1150

wait no 150 is the interest

amount

[obsidian coral]

Then the next year, using that new amount, find the interest amount

Then find the new amount

And so on

[crimson sedge]

the heck

what type of formula is this?

[obsidian coral]

It's just interest

Applied every year

[crimson sedge]

bryuh

so i use the total amount for the next year

then so on

[obsidian coral]

Yes

[crimson sedge]

thats so weird

but alr

so is there another formula for this type of question

like the one you gave me previously

or the only way was just as u said to just keep adding it up

[gray blade]

@crimson sedge The compound amount/interest formula: P(1 + r/n)^nt is also applicable here
P = 1000
r = 0.15
n = 1 (once per 3 years)
t = 3 years

therefore, 1000(1 + 0.15/1)^(1 * 3) also gives you the answer in one go

[gray blade]

but the method here also works, they just split up the 3 years into parts, using I = PRT and adding each part together

[crimson sedge]

ohhhhhhhhhhhhhhh

wait what

that gives me 3450 tho

[gray blade]

gives me 1520.875, check your math I guess

[crimson sedge]

brug

[gray blade]

make sure to use pemdas

[crimson sedge]

bruh

[crimson sedge]

pemdas????

[obsidian coral]

Probably didn't use parentheses for the exponent

[obsidian coral]

Order of operations

[crimson sedge]

oh

i got it

is there such thing

on a caculator

[obsidian coral]

As what?

[crimson sedge]

wdym by parentheses for the exponent

1000(1 + 0.15/1)^(1 * 3) would i able to type this on a caculator

[obsidian coral]

By order of operations, the calculator is doing $1000(1 + \frac{0.15}{1})^1 \cdot 3$

[wraith dagger]

dldh06

[obsidian coral]

Yes you can type this

[crimson sedge]

WTF

i have no clue what u just said

[gray blade]

@crimson sedge

[obsidian coral]

I literally told you what the calculator was doing

[crimson sedge]

this is the correct formula?

[obsidian coral]

Because the 3 wasn't in parentheses with the exponent, you got the wrong answer

[crimson sedge]

not formula like is that the correct way of caculating it

[obsidian coral]

No

[crimson sedge]

oh

what

[obsidian coral]

I'm telling you what the calculator was doing

[crimson sedge]

oh

[obsidian coral]

You need parentheses when you have multiple numbers getting multiplied in the exponent

[crimson sedge]

so how does that work

[gray blade]

essentially, make sure (1 * 3) is in the exponent

aka 3

[crimson sedge]

yea

so

1000(1 + 0.15/1)^(3)

shouldnt it be this

[gray blade]

yes

[crimson sedge]

then 1000(1.15)^(3)

[gray blade]

mhm

[crimson sedge]

1520875000

tf

[gray blade]

what are you entering...

in your calculator

[obsidian coral]

,w 1000(1.15)^3

[wraith dagger]

Results provided by WolframAlpha

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

Requested by dldh06#2659

[gray blade]

^

[crimson sedge]

bruh

[obsidian coral]

You should work on your calculator skills

[crimson sedge]

i did 1000x1.15

[obsidian coral]

No

[crimson sedge]

then i did the ^(3)

[obsidian coral]

Order of operations

PEMDAS

Or BEDMAS

[crimson sedge]

i did everything from left to right

oh

nvm

[gray blade]

that's not how order of operations work lol

https://youtu.be/OdFXImly2-I

see this video if you need it

[crimson sedge]

https://tenor.com/view/crying-meme-black-guy-cries-sad-man-thank-god-for-my-reefer-hood-news-gif-24902056

[gray blade]

it's a pretty important skill to have, just saying

[obsidian coral]

You said you were in grade 9, correct?

[crimson sedge]

correct

but i havent done math in like 3 months cause that was when the semester ended

[crimson sedge]

imma watch this later

[obsidian coral]

Yeah... There is no way you forgot order of operations

[crimson sedge]

yea i remember the basics

mutilplication and division comes first and stuff like that

[gray blade]

just remember this entire thing:
Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)

[crimson sedge]

but in gr 8 they never did these types of questions

[obsidian coral]

Wrong

[crimson sedge]

like they come before

addition and subtraction

[gray blade]

yes but parentheses and exponents matter too lol

[crimson sedge]

they didnt teach taht in gr 8 lol

[obsidian coral]

I doubt that

[crimson sedge]

no no im being serious

[gray blade]

right, they taught it in grade 5

okay perhaps they didn't for you

and that's okay

now you can learn it lol

[crimson sedge]

bruh

[obsidian coral]

There is no way teachers skip parentheses and exponents in a very important concept

[crimson sedge]

well they proballyh didnt teach it was because it wasnt used in gr 8

[gray blade]

they must've forgot, it's usually taught in elementary and often quite briefly

it's fine

[crimson sedge]

o

i see

[obsidian coral]

Doubt that too, once you learn order of operations, it gets used every where

[crimson sedge]

nah

not the exponents part

[gray blade]

so anyways, you understand how it's 1520.875?

[crimson sedge]

oh well thanks guys i get it now

[crimson sedge]

yea

[gray blade]

alright

np

[crimson sedge]

really appreciate it

imma close this now bye

.close

[cedar kiln]

Channel closed

Closed by @dense bramble

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[spring reef]

I'm not sure how to answer this problem

I get critical points for other functions, but for functions with trig I have no idea how to tell which is the absolute min and max

[compact junco]

well calculate the derivative between the critical points

this will show you whether its increasing and decreasing on that interval

that will help you determine whether its a minimum or maximum

[spring reef]

What do you mean by that? I took the derivative of the original function. I know for non-trig problems I plug back in whatever I find for x after setting the factors to 0.
Do you mean doing something like f(pi) = 4sin^2(pi)?

[compact junco]

wait what?

critical points are where the derivative is 0, correct?

@spring reef

so if we calculate the derivative in between critical points, we can find whether the function is increasing or decreasing on that interval

negative = decreasing

positive = increasing

[spring reef]

This is another problem I did

I plugged in the interval and the found points into the original function to find the abs min and max

[compact junco]

are you having trouble determining if its a maximum or minimum

[spring reef]

Specifically with trig functions, yes

[compact junco]

oh hold up im dumb

just evaluate the function at endpoints and critical points

and then compare

you do the same thing with trig functions

[spring reef]

right, so do I do something like f(pi) = 4sin^2(pi) and evaluate that?

[compact junco]

yes

what are the critical points and endpoints for this function?

[spring reef]

0 and 4?

well that was what I got for plugging in the interval points

yeah I got the question right, thanks

[compact junco]

alr yw

[spring reef]

.close

[cedar kiln]

Channel closed

Closed by @spring reef

Use .reopen if this was a mistake.

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Available help channel!

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[pale granite]

Did I get this right ??

[pale granite]

Or actually was I also supposed to involve the (X+4)?

For the 2nd question

[cedar kiln]

@pale granite Has your question been resolved?

[cedar kiln]

@pale granite Has your question been resolved?

[carmine bronze]

@pale granite You left out the 8y in #3 when determining the area.

$8y = (x+4)(x+5)$

[wraith dagger]

Kookiemon

[pale granite]

Thanks boss 🫡

.close

[cedar kiln]

Channel closed

Closed by @pale granite

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[upper basin]

I need help with 2-5

I have a google slide for it if someone tryna help

homework due in 30m

[obsidian coral]

None of us are here to do your work for you. We can assist you in teaching you what you need to know but 30 minutes isn't enough time for 4 questions, in my opinion

Like q5, teaching factoring, completing the square, and quadratic formula, would take more than 30 minutes already

[upper basin]

yall are L's

[obsidian coral]

Not really. That's mainly on you for leaving it last minute

[upper basin]

its not my fault tho

starting friday I was posed to do it from then to sunday

friday shabbat

saturday shabbat

sunday kinda my fault I had work

[obsidian coral]

Kinda is if you fail to time management

[upper basin]

but my teacher racist or smth not giving me extra time bc of friday and saturday

[obsidian coral]

When was that given?

[upper basin]

friday

after class ended