help-28

[timid heart]

you made a calculation error going from this line to the next

[fast marlin]

oh i see

[bright flame]

o

im briandead tysm 😭

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[shell glen]

Here is the question---

Two hunters A and B set out to hunt ducks. Each of them hits as often as he misses when shooting ducks. Hunter A shoots at 50 ducks and hunter B shoots at 51 ducks. Find the probability that B bags more ducks than A.

How should I proceed with this one.

[undone vector]

The chance each hunter hits n ducks is binomial

There are many ways to approach it once you get that

[shell glen]

I know that. So I can get expression for both hunters to hit n ducks. Then what?

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@shell glen Has your question been resolved?

[shell glen]

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[flat rose]

can i get help with these questions

[flat rose]

i was away during the lesson plan of this worksheet

[full forum]

@flat rose Has your question been resolved?

[flat rose]

<@&286206848099549185>

[errant kraken]

hey

[flat rose]

hi

[errant kraken]

have you been taught quadartic formula yet?

[flat rose]

not yet

it’s just factoring

[errant kraken]

cross method?

[flat rose]

think so

[errant kraken]

alr

[flat rose]

i think my teacher might’ve called it something else

[errant kraken]

do you want me to explain how it works?

[flat rose]

but i think it’s the same thing

sure

[errant kraken]

usually its visualissed

ok

usually you would visualise it with a cross

but

i cant exactly do that

cuz i suck at drawing digitally

[flat rose]

which question is that

[errant kraken]

its explaining the cross method

uh

u could just like

google it ig

and then

thatll help

i rlly suck at explaining sry

[flat rose]

okay no problem

can you help me walk through questio number 5?

[errant kraken]

no problem!
$x^2+7xy+6y^2$

[glossy valve]

i like cheese

[errant kraken]

this?

[flat rose]

yes

[errant kraken]

alr so

assume y = 1

[flat rose]

okay

[errant kraken]

so

$x^2 + 7x + 6$

[glossy valve]

i like cheese

[errant kraken]

do you know how to factorise this?

[flat rose]

x (x +7x + 6)?

[errant kraken]

no

you can't take a factor of x from 6

alr so

we take it as genearl form ok?

$ax^2+bx+c$

[flat rose]

okay

[glossy valve]

i like cheese

[errant kraken]

whats a, whats b, whats c?

[flat rose]

a would be 1?

[errant kraken]

yes

$a=1$, $b=7$, $c=6$ correct?

[glossy valve]

i like cheese

[flat rose]

yes

[errant kraken]

ok so

what are 1's factors?

just 1 and 1 correct?

[flat rose]

yes

[errant kraken]

(_ + _)(_ + _)

so we have 1 and 1

[flat rose]

right

[errant kraken]

(x + _)(x + _)
yes?

[flat rose]

correct

[errant kraken]

now, what are the factors of c?

[flat rose]

3 and 2

6 and 1

[errant kraken]

ok so

[flat rose]

oh wait

6 and 1

is the right answer

[errant kraken]

mhm

do yk y?

[flat rose]

y=1?

[errant kraken]

why it is the right answer?

[flat rose]

1 sec

my teacher showed me a way to make sure it’s right

[errant kraken]

kk

[flat rose]

wouldn’t 6 and 1 have a y variable?

[errant kraken]

1 sec

yes

since we substited y = 1

so now we put y back in

so $(x+1)(x+6) = (x+y)(x+6y)$

[glossy valve]

i like cheese

[errant kraken]

and if you expand the brakets, you can see it is correct

[flat rose]

yeah that’s the way my teacher showed on how to correct it

[errant kraken]

also, 1 and 6 is correct, becuase
$11+16 = 7 = b$

...

[glossy valve]

i like cheese

[errant kraken]

there

ok

so

the first 1's is the coefficient of the x

the 1 and the 6 is the coefficient of y

[flat rose]

okay thank you

[errant kraken]

no problem!

have a good day

[flat rose]

so the final answer would be (x+6y) (x+1y?

[errant kraken]

yes

but you can remove the 1 from the y

because 1y = y

[flat rose]

okay thank you

[errant kraken]

np

[flat rose]

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[safe forge]

Can someone tell me if I’m right, how do I verify my answer by using opposite cos I keep getting it wrong in verify

[split swift]

cos(135) should give you -0.7134 back

but you've rounded that angle quite a lot

and also you're working in degrees, but your calculator appears to be in radians

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[hollow summit]

Can someone tell me where is my mistake

[formal scarab]

can you explain this

also 2sinx+cosx isn't sin2x

[hollow summit]

Isn’t is the double angle identity?

[formal scarab]

2sinxcosx, the product

not +

[hollow summit]

Ohhh m’y bad

[hollow summit]

And this

Wait top or bottom

Wait bottom does it equal to cos/cos?

Like this

[plain fox]

(cos+1)/cos

[hollow summit]

Ahhh my bad

Tired asf

What should I do after this

[plain fox]

sincos + sin is not equal to 2sin cos

its equal to sincos + sin

[hollow summit]

so the result is sincos+sin/cos+1

=sin

what can i do next 😅

[plain fox]

whats the question?

prove that its equal to sin

[hollow summit]

i have to prove that all that = sin

yes

[plain fox]

or find theta?

[hollow summit]

ill try to expand the 1 in cos+1

[plain fox]

multiply and divide by 1-cos

u cant expand cos+1

[hollow summit]

yeah i tried to turn 1 into sin/sin

doenst work

[hollow summit]

ill try this

[plain fox]

yeah

@hollow summit wait wait

[hollow summit]

.yes

[plain fox]

dont multiply and divide

u are left with
sincos + sin / 1+cos , right?

u can factor out sin from numerator
sin(cos+1)/(cos+1)

which is equal to sin

[hollow summit]

omg

okay tysm i totally overlooked that

!

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[rotund pulsar]

am i tripping or is the red option (the answer in the textbook) wrong?

like if you do matrix multiplication with the rows * columns, shouldn't it be A?

[jade quarry]

i do agree that it's the first choice

[rotund pulsar]

ok i think the book is just off thanks

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[rotund pulsar]

this is another question from same book

[jade quarry]

i think you should reopen it

[rotund pulsar]

.reopen

[full forum]

✅

[rotund pulsar]

i'm also just confused on the wording of this

i know it's not C cuz 1 + 1 isn't contained in the subspace

but like if they're all the same vector, then again, vector addition isn't contained right?

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[rustic goblet]

@unborn oasis

That's maopiggys question, I just posted it for him

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[bright jewel]

how do I solve this

[real monolith]

have you learnt the formula for Binomial distribution?

[bright jewel]

I think so

[real monolith]

so just use it, should be just substituting the values

[bright jewel]

b(x; n, P) = nCx * Px * (1 – P)n – x

right?

[real monolith]

$b(x; n, P) = C^n_x \cdot P^x \cdot (1 – P)^{n – x}$

[glossy valve]

Dee3Cay

[real monolith]

ok so now you just put the values in

what's $n, P$ in this question?

[glossy valve]

Dee3Cay

[bright jewel]

0 is n and P is 0.695 right?

or do we not put 0 in there yet

my fault n is 8 right?

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[bright jewel]

.reopen

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✅

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@bright jewel Has your question been resolved?

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@bright jewel Has your question been resolved?

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[zealous vale]

Could somebody help me understand the difference between adjoining to gain a ring vs adjoining to gain a field

[zealous vale]

Example: 

Z(i) and Z[i]

I get confused due to the notation of the polynomring Z[T]. 
So Z[i] is the normal ringadjoining.
And Z(i) would be fieldadjoining right?

And Z[i] would be all integers and all integers * i 
While Z(i) would be C right?

And another similiar question:

if f,g,h,... are polynoms of K[T1,...,Tn] and none of them are associated and all of them are prime then
K[T1,...,Tn]/ <f,g,h...> does not have any nilpotent elements

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[zealous vale]

<@&286206848099549185>

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[torn jolt]

helppp

[torn jolt]

can someone factorize 4x^3-6x^2y+9xy^2

[onyx glen]

!status

[full forum]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[torn jolt]

2

so far i have only taken x common is there anyother steps i could do or is that the final answer?

[thorn matrix]

so you have x(4x^2-6xy+9y^2)?

[torn jolt]

yes

[thorn matrix]

is there anything you notice about the rest

[torn jolt]

uhhh not really

could take 2x common from 4x^2-6xy

[worthy sundial]

think about the (a - b)^2 form

[torn jolt]

that wont work

cuz like 2x2x3=12 not 6

[worthy sundial]

oh sorry i saw it wrong

[torn jolt]

its fine

[worthy sundial]

you could still complete the square ig

[thorn matrix]

yeah there is a trick you could use, but it doesnt make it any prettier

[torn jolt]

how

[thorn matrix]

well the (a - b)^2 is very close to what you want

[worthy sundial]

have you learnt completing the square?

[torn jolt]

i never pay attention in class lol

[worthy sundial]

if not i think this the final solution they are looking for

[torn jolt]

its like 3 marks question the process cant be that short

[thorn matrix]

well if you copied it correctly

[torn jolt]

i have copied it correctly

[thorn matrix]

also the trick is if you write out (2x - 3y)^2

which is 4x^2 - 12xy + 9y^2

[worthy sundial]

well thats another way to do it

[thorn matrix]

you could somehow transform that into what you want and leave it outside

[torn jolt]

uhhhhh

[worthy sundial]

i think completing the sqaure is what they are looking for ngl

[thorn matrix]

possibly

[torn jolt]

how do i do that

[thorn matrix]

how would you get from (4x^2 -6xy + 9y^2) to (4x^2 - 12xy + 9y^2)

[torn jolt]

by adding -6xy

[thorn matrix]

yes but since this isnt an equation you cant just add

you have to keep it the same

[torn jolt]

i guess i add 6xy as well then

[thorn matrix]

so you add and do another step

yes

[torn jolt]

oo cool

[thorn matrix]

you see the square now?

[torn jolt]

yes

let me see how that turns out

well now i get

x[(2x-3y)^2+6xy]

[thorn matrix]

yep seems good to me

[torn jolt]

alright ig

thanks for everything

[thorn matrix]

np 🙂

[torn jolt]

👍

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[royal belfry]

Please help me understand what the fuck this means

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@royal belfry Has your question been resolved?

[royal belfry]

<@&286206848099549185>

[torn jolt]

hi

[solemn coral]

ratio

do you know how ratios work

[torn jolt]

it's indices, ain't it?

[solemn coral]

4:8
= 1:4 or 1/4 but yh

[royal belfry]

L+Ratio?

[solemn coral]

both

[royal belfry]

Im kidding im kidding

Yeah

[torn jolt]

yeah

[solemn coral]

do you know how indices work

haha 😐

[royal belfry]

Not really i dont think

Dude im in 9th grade i aint smart

[torn jolt]

fuck this shit is hard

[solemn coral]

do you know what 2^3 is

[royal belfry]

Yes

[solemn coral]

what is it

[royal belfry]

8

[solemn coral]

yup

2 multiplied 3 times

[royal belfry]

Idk what its called in english

[solemn coral]

thats indices

👍

[royal belfry]

ooooh

We call them powers or something

[solemn coral]

if its negativ power, its the reciprocal of the positive indices

yeah

[royal belfry]

So 2^-1 is 1/2 yea that i know

[solemn coral]

2^-3 = 1/(2^3) = 1/8

yeah

what about

[royal belfry]

But its a friction

Fraction

Threeway

[torn jolt]

what's your nationality?

[royal belfry]

Italian

[torn jolt]

ooo

ic

[solemn coral]

evaluate each part of the fraction

[torn jolt]

aren't indians basically called the gods of math?

[royal belfry]

INDIANS

I MAKE PIZZA

DUDE

[torn jolt]

bro

it was random

ik you're italian

chill

they are gods of math too

[royal belfry]

Isnt that a stereotype of chinese people

[torn jolt]

india's math is the most superior when compared to the world

[torn jolt]

no

[solemn coral]

1+2^-1 is 3/2
1/3/2 = 2/3
2-2/3 = 4/3
1/2 divided by 4/3 = 3/8
this might be wrong but u get the point

[solemn coral]

not really- or do you mean the curriculums in school or mathematicians in general

cuz in general you cant attribute a race being superior in math

[gritty rose]

can you stop interrupting in help channels

[torn jolt]

um, sorry

[solemn coral]

theres pizza in india?

[torn jolt]

i'll say both

[solemn coral]

thats wild

[royal belfry]

Bruh again

I T A L Y

[torn jolt]

obvi

[royal belfry]

alr we fuckin around lemme close the channel

[gritty rose]

alright @royal belfry your channel got invaded. i suggest closing and opening a new one and don't engage with people who aren't helping you

[royal belfry]

.close

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[solemn coral]

neither- non of the top 10 smartest mathematicians are indian. there are extremely smart indian mathematicians tho

[torn jolt]

wait

adi

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[torn jolt]

have you heard of shakuntala devi?

[gritty rose]

holy shit

#chill or #discussion ffs

[royal belfry]

Omfg dude

[gritty rose]

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[nocturne ledge]

Hello I just wan to be sure if i did this correctly

[honest osprey]

youre good

[nocturne ledge]

oh okok

[glossy valve]

Girl

[honest osprey]

whoops yeah

there we go

[nocturne ledge]

an I have no clue on how to start b

can you give a hand?

[limpid knoll]

Common denominator

Try putting the right side on a common denominator

[nocturne ledge]

ok

[honest osprey]

as for b, try to find out how you can factorise v² - 9v + 18

youll see the common denominator

[nocturne ledge]

v

I am doing it at the same time sorry

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[nocturne eagle]

I tried solving in quadratic equations way but it gave me only one value

[narrow ermine]

That's normal.

If the discriminant is 0, then you will only get one solution with multiplicity 2.

You also have a hidden solution from when you divided everything by 0 at the beginning. Doing this assumes that p is not zero, and zero is clearly a solution of your original problem.

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[nocturne eagle]

I wonder if I made some mistake

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[jade bough]

how to compare 2^845 and 5^362

[rough tundra]

prime factorization?

[jade bough]

💀

it's already prime factorized

wait

[jade bough]

are you talking about the exponent?

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[jade bough]

<@&286206848099549185>

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@jade bough Has your question been resolved?

[jade bough]

<@&286206848099549185>

[hasty wing]

Try dividing one number by the other

[jade bough]

ok

[jade bough]

uhhh

(2^362 * 2^483)/5^362

[hasty wing]

keep going

[jade bough]

what can i do now though

[hasty wing]

You have 2 and 5 to the same power

[jade bough]

2^483 * (2/5)^362

[hasty wing]

yeah, now I think the easiest thing to do is set up an inequality

[jade bough]

what would it be

*the inequality

[hasty wing]

I don't want to give too much away, but I think it's obvious that we want an inequality involving 2/5 and a power of 2

[jade bough]

like

comparing (2/5)^362 to 2^483?

[hasty wing]

Start simpler

is 2/5 bigger or smaller than 1/2

[jade bough]

smaller

[hasty wing]

There's your inequality imo

2/5 < 1/2

[jade bough]

what?

how can i use that

[hasty wing]

Now wrestle the lhs to resemble 2^483 * (2/5)^362

You can raise both sides of an inequality to a power, multiple by a positive number without flipping it

etc

Another one you can use: 1/4 < 2/5

But start with the first

[jade bough]

oh i think i got it

wait let me confirm

wait

i got

(2 x 2/5)^362 x 2^121 < (1/2 x 2)^362 * 2^121

[jade bough]

^

[hasty wing]

Sorry, I have to go, but I don't think my method puts a tight enough bound

You may have to use their difference

[jade bough]

ok

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[torpid epoch]

Need help with (c)

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[torpid epoch]

<@&286206848099549185>

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<@&286206848099549185>

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[unborn quarry]

Hello 👋🏽 . What have you tried? 🤔

Wait I was going to say you know that length, but that's now true

Mmm

The height could be anything I think

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[torn jolt]

Why do they state the fact I circled in red?

[proper hawk]

To prove t>0

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@torn jolt Has your question been resolved?

[torn jolt]

how does that prove t>0

and how do you know to do that?

[proper hawk]

From the equality we have $\sqrt{9\sin^2{\theta}-8}<3\sin{\theta}$ so $3\sin{\theta}-\sqrt{9\sin^2{\theta}-8}>0

[glossy valve]

WhereWolf(ping if needed)
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

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@torn jolt Has your question been resolved?

[torn jolt]

Yeah but WHERE did the 3sintheta come into the inequality?

Why’d they just think to do that?

And how did they do it?

@proper hawk

<@&286206848099549185>

[proper hawk]

since $9\sin^2{\theta}-8<(3\sin{\theta})^2$ we get this

oops I forgot the square lemme fix it

[glossy valve]

WhereWolf(ping if needed)

[proper hawk]

$\sqrt{9\sin^2{\theta}-8}<3\sin{\theta}$ so $3\sin{\theta}-\sqrt{9\sin^2{\theta}-8}>0$

[glossy valve]

WhereWolf(ping if needed)

[proper hawk]

and it's pretty obvious if you notice that without the $-8$, $\sqrt{9\sin^2{\theta}-8}$ can be simplified to $3\sin{\theta}}$

@torn jolt

[glossy valve]

WhereWolf(ping if needed)
Compile Error! Click the reaction for more information.
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[upper stirrup]

No idea how to do this

[magic rover]

Connect points B and D

Then use the properties of cyclic quads.

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@upper stirrup Has your question been resolved?

[upper stirrup]

mhmm

[upper stirrup]

lemme try

@magic rover it still doesnt work

<@&286206848099549185>

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[upper stirrup]

<@&286206848099549185>

[torn jolt]

i solved it i just don't know how to explain it. wanna massage me on my dm?

[upper stirrup]

Sure

[upper stirrup]

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[midnight elm]

yo, my math midterm is tmrw lol, im fairly confident but i need to be exposed to harder questions, since they barely provide any 7-8 questions (problems in familair and unfamliar situations) and these i always get wrong in the exam, can any1 help me practice more? Maybe u got questions similar to what i took, and your exposed to more problems?

till now i took, factorization (sum and product) (AC method) (diff of 2 squares) (grouping)
expanding and simplifying simple stuff
indices, and exponential equations
arithmetic and geometric sequences not series but sequences

any1 got hard q's for those kinda topics?? Tried to look online, couldnt find much tbh
Thanks

[midnight elm]

that's an example of what a 7-8 could be like

[robust slate]

Hint: Express all the terms in terms of the first term and common ratio

This is a fairly common technique for geometric series questions

Similarly, for arithmetic sequence questions, it's common to express all the terms in terms of the first term and common difference

[short crest]

I think that was just an example, he's just asking for similar questions to test his knowledge.

[midnight elm]

no i dont mean i want thea nswer of it

[midnight elm]

yeah

[robust slate]

Oh mb

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@midnight elm Has your question been resolved?

[robust slate]

1. For each positive integer $k,$ let $S_k$ denote the increasing arithmetic sequence of integers whose first term is 1 and whose common difference is $k.$ For example, $S_3$ is the sequence $1,4,7,10,\ldots.$ For how many values of $k$ does $S_k$ contain the term 2005? \ \ 2. The terms of an arithmetic sequence add to $715$. The first term of the sequence is increased by $1$, the second term is increased by $3$, the third term is increased by $5$, and in general, the $k$th term is increased by the $k$th odd positive integer. The terms of the new sequence add to $836$. Find the sum of the first, last, and middle term of the original sequence. \ \ 3. Find the smallest prime that is the fifth term of an increasing arithmetic sequence, all four preceding terms also being prime. \ \ 4. A four-term sequence is formed by adding each term of a four-term arithmetic sequence of positive integers to the corresponding term of a four-term geometric sequence of positive integers. The first three terms of the resulting four-term sequence are $57$, $60$, and $91$. What is the fourth term of this sequence? \ \ 5. Five numbers are in arithmetic progression. The sum of these five numbers is $25$ and the product of the five numbers is $2520$. If one of these five numbers is $-1/2$, then what is the greatest number amongst them?

[glossy valve]

Civil Service Pigeon

[midnight elm]

yoooo

thank you so so so much

didnt even expect 5 questions

holy

[robust slate]

👍

When I get home I can dig up some questions from my old exams if you want

[midnight elm]

oh you got old exams?

yeah that would be perfect

when do you get home?

[robust slate]

Well you might have slim pickings because the stuff you have is the fundamental stuff so chances are the questions with this material will be mixed with something else

I'll see if I can modify them tho

[midnight elm]

no thats fine

alright sure

[robust slate]

~ 30 min?

[midnight elm]

should i keep this channel open then?

[midnight elm]

yeah thats good its still 5:40pm for me, so i got time

[robust slate]

Yeah cause otherwise I'll probably forget lol

[midnight elm]

alright, thanks :)

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[robust slate]

.reopen

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✅

[robust slate]

@midnight elm keep an eye on this ig lol

I forgot how often it asks

[midnight elm]

yeah dw

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@midnight elm Has your question been resolved?

[robust slate]

@midnight elm 👋

alright time to flood you with questions lol

[midnight elm]

hello

alright sure lmao

[robust slate]

till now i took, factorization (sum and product) (AC method) (diff of 2 squares) (grouping)
expanding and simplifying simple stuff
indices, and exponential equations
arithmetic and geometric sequences not series but sequences

this might be a stretch but here you go

[midnight elm]

yeah lmao, but it seems doubale ill see

[robust slate]

oh this one I can modify

[midnight elm]

mhm

sure

[robust slate]

Find a formula for the product $$\left(1+\frac{1}{2^{2^0}} \right) \left(1+\frac{1}{2^{2^1}} \right) \left(1+\frac{1}{2^{2^2}} \right) \cdots \left(1+\frac{1}{2^{2^n}} \right)$$ in terms of $n$. You may leave your answer in exponential form.

[lament badge]

Is the answer to this 2/31

[glossy valve]

Civil Service Pigeon

[midnight elm]

does this have to do with series?

[robust slate]

no

[midnight elm]

seems similair to an investigation exam i had 3 days ago

oh well

thanks tho

[lament badge]

What grade u in my brotha

[midnight elm]

10

[robust slate]

<@&268886789983436800> #help-28 message

[midnight elm]

💀

[lament badge]

Not here budy

[lament badge]

I have a dead man waiting for u

[calm nacelle]

Yeah, banned. Thanks.

[robust slate]

@midnight elm how much coordinate geometry do yk

[midnight elm]

no need

but if u have to know

a little lol

we took 1 unit for it so yea

[robust slate]

I'll skip that one then

[midnight elm]

hey @robust slate what grade are these q's for lol?

[robust slate]

eh it's the easier stuff so ig grade 10?

[midnight elm]

these r indeed helpful for harder q's

but most of my exam is gonna be like this

[robust slate]

oh yeah I don't have that 😭

[midnight elm]

way simpler stuff xd

[robust slate]

oh I was under the impression you wanted the 'harder' stuff 💀

[midnight elm]

but what ur giving me is still insnaley useful

since i always get the hardder ones wrong

[midnight elm]

yaya

but i think u gave out enough xD

if it

covers

all possible

[robust slate]

yeah I gotta dip 👋

[midnight elm]

ideas

[robust slate]

gl on your exam

[midnight elm]

then im good

thank u so much

:)

[robust slate]

👍

[midnight elm]

.close

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[rugged lagoon]

hi i have a small stupid problem with maths, how would be
35 * (sqrt3/2)?
i mean like without making it into one number like 38.9711....

[rugged lagoon]

im studying triangles thing and its just made me stop on assigment for a while

[spiral vigil]

do you mean like $35\cdot\f{\sqrt3}2$ or do you mean $35\cdot\sqrt{\f32}$?

[glossy valve]

hayleyGhost

[spiral vigil]

either way you can't really do much with it

[rugged lagoon]

the first one

so i just leave it like that?

[spiral vigil]

I'd probably write it as $\f{35}2\sqrt3$ but yeah you can't really do anything to make it "better"

[glossy valve]

hayleyGhost

[rugged lagoon]

mhm alr thanks

[cloud shore]

congrats on being a moderator

[spiral vigil]

ty

[serene hazel]

what's the comment when someone deletes the message in help channel

do you know

[spiral vigil]

i don't know the exact words... it's something like channel closed because the original message was deleted

[serene hazel]

!mgdelete or smth

[spiral vigil]

anyway stop talking about me in Olivia's channel

[serene hazel]

okay

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[proven dove]

Im not sure how i should start/solve question 4, could anyone help?

[proven dove]

oh and the answer is : " 11.6 years after 1990 , so halfway through 2001"

[cyan walrus]

how did you get that ans?

[proven dove]

its given

[cyan walrus]

weird

[proven dove]

solution sheet, but they dont show the way to solve it, im as lost as you are if not more so

[cyan walrus]

no I mean

the answer is literally wrong?

after 11.6 years, the population becomes 3.43 times not 4 times

Suppose,
number of Europeans = x, number of chinese = 3x

let, after t years, number of chinese becomes 4 times number of Europeans

(3x + 0.02xt) = 4(x - 0.005xt)
or, 3x + 0.02xt = 4x - 0.02xt
or, (0.02 +0.02)xt = 4x - 3x
or, 0.04xt = x
or, 0.04t = 1
therefore, t = 25

so, after 25 years.

here's the actual solution

unless Im missing something, 25 years should be the answer

[proven dove]

ill write this down for now, and try to figure out if its wrong, thank you!

.close

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[silk rock]

I have to prove this

[silk rock]

First of all I have to prove that 1 is an upper bound right

Supossing n is even, then:
0 ≤ 1/n
1 - 1 ≤ 1/n
(-1)^n - 1 ≤ 1/n
n[(-1)^n - 1] ≤ 1
n(-1)^n - n ≤ 1
n(-1)^n ≤ n + 1
(-1)^n ≤ 1 + 1/n
(-1)^n - 1/n ≤ 1

for n odd the proof is similar

how do I prove that
(-1)^n - 1/n ≥ 1 - e? e > 0

[naive hatch]

if n is even, the two sides of the inequality look very similar

[silk rock]

yup, but that would only prove that 1 is an upper bound of this set

we want to prove 1 is the supremum

[naive hatch]

for all e, can you always find an N such that 1/n < e for all n>N?

once you can, follow through with the epsilon N proof

[silk rock]

Archimedean property?

[naive hatch]

it's even simpler than that

set N = ceil(1/e)

[silk rock]

Oh I see, I'm not into real analysis yet so I'm not sure what the epsilon N proof is

Is there any definition about that?

[full forum]

@silk rock Has your question been resolved?

[full forum]

@silk rock Has your question been resolved?

[silk rock]

Heyo @naive hatch are you still around?

[full forum]

@silk rock Has your question been resolved?

[silk rock]

it easy follows if we assume n is even

1/n < e
1/n - 1 < e -1
1 - 1/n > 1 - e
(-1)^n - 1/n > 1 - e

[naive hatch]

that's sufficient here

[silk rock]

wait really

how about the case when n is odd? since (-1)^n = -1

oh wait I'm stupid

we are looking for just one element in the set such that:

1- e < (-1)^n - 1/n < 1

lets gooooo

[silk rock]

thanks @naive hatch

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[gritty mesa]

how do I take the derivative of

[gritty mesa]

using chain rule?

[stuck dove]

Hello I have a question about finding the equation for tangent planes:

I attatched the image of the question above.

I used the equation of a tangent plane to solve this question and got:

6x + 3y - 11.

However, the tangent plane equation only took the partial derivative of x, and the partial derivative of y, so I did not use the z parameter in (3,1,0).

I was wondering, do I just ignore the 0 in (3,1,0) because this is a function of f(x,y) not f(x,y,z)?

Thank you

oops

[gritty mesa]

lol

[stuck dove]

mbmb

[gritty mesa]

all good

I think I inturrupted you while u typed lmao

[stuck dove]

xdd npnp

and btw, you can use the chain rule for that im pretty sure

((y-1)^4)(y^2 + 2y)^(-5)

let u = (y - 1)^4 and v = (y^2 + 2y)^(-5)

and then take u'v + v'u

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[plucky pewter]

hey guys, i have no idea what this question wants me to do

[plucky pewter]

like the first few just give me an equation and stuff and idek what to do w it

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[proven vigil]

what did i do wrong?

[proven vigil]

the answer is supposed to be (1/4)( x^3 -2)^4 +c

[empty sapphire]

Whenever you set u = x^3 - 2 and got du = 3x^2 dx, you can directly subtitute that in

You should get

$\int u^3 du$

[glossy valve]

MellowDramaLlama

[proven vigil]

so on the second line it would be (substituted integral) (u^3 du)?

like this?

[empty sapphire]

not quite

[proven vigil]

wait i subsituted that wrong

[empty sapphire]

try rearranging it like this

$\int 3x^2(x^3 - 2)dx = \int (x^3 - 2)^3 3x^2 dx$

[glossy valve]

MellowDramaLlama

[empty sapphire]

you should see the direct substitution there

[proven vigil]

OOOH

ok

that makes sence

[empty sapphire]

Sometimes you'll have to try what you tried in your attempt

[proven vigil]

thanks

[empty sapphire]

but it's more uncommon

of course!

[proven vigil]

.sloved

whats the command?

.close

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[stuck island]

How do u do the problem with the chart

[wide scaffold]

Do you know the formula for average rate of change?

Also if it’s your work then your answer is right

[empty sapphire]

,rccw

[stuck island]

hello any1?

[empty sapphire]

So the average rate of change is $\frac{y_2 - y_1}{x_2 - x_1}$. You are given as $[-1, 3]$. So we need to look at the y values for $x = -1$ and $x = 3$

[glossy valve]

MellowDramaLlama

[stuck island]

ye

[empty sapphire]

so in the chart below, what is the y value for x = -1? what about x = 3

?

[stuck island]

8

[empty sapphire]

bingo

[stuck island]

lol

[empty sapphire]

so $y_2 = y_1 = 8$. And $x_2 = 3$ and $x_1 = -1$. Just use the formula above and you'll get the average rate of change

[glossy valve]

MellowDramaLlama

[stuck island]

2?

[empty sapphire]

no ignore your teachers note

what is $y_2 - y_1$?

[stuck island]

mhm

[glossy valve]

MellowDramaLlama

[stuck island]

oh 0

[empty sapphire]

bingo

and 0 over anything is 0

so the average rate of change is 0

[stuck island]

mhm

oh

[empty sapphire]

which should make sense, right?

because the y values don't change

here let me see if i can see if I can find an example real quick

give me a moment

[stuck island]

thx

that would be awesome

[empty sapphire]

so this is our initial example

y = x^2

so we can keep it simple

[stuck island]

mhm

[empty sapphire]

let's look at what the average rate of change for some sample points

let's say from [-2, 1]

[stuck island]

mhm

[empty sapphire]

ok

sorry it takes a second lol

so for the average rate of change from (x_1, y_1) and (x_2, y_2) is -1

and as we can see the average rate of change represents the slope between those points

Now let's do it between [-2, 0]

and as we can see, the average rate of change is -2

so the average rate of change represents the slope between two ponits

Now for your problem

let's say if we pick two points that are equal, aka the line between them has a slope of 0 aka the average rate of change of 0

Let me know if that doesn't make sense

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@stuck island Has your question been resolved?

[stuck island]

oh okkk

i see

thx

.close

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[unborn moth]

When do prodigies learn calculus

[unborn moth]

*start learning calculus

[undone vector]

If you aint learnin calculus at 3 you arent worthy of the title

[torn kite]

Excuse @unborn moth how do i get my own help?

[unborn moth]

Another help channel

[undone vector]

Type in one of the available help channels

[torn kite]

alr thx

i gtg

[unborn moth]

Wait fr

[undone vector]

No

[unborn moth]

Or just playing

What

[white smelt]

prodigies dont learn calculus, they invent their own version of it unknowingly

[undone vector]

Your question has no definite answer

It depends on how rigorous the calculus they learn is for example

[torn kite]

so any help that is inactive?

[undone vector]

Yeah under ✅ Math Help (Available)

[placid oar]

check this channel out https://discordapp.com/channels/268882317391429632/488120190538743810

[torn kite]

thanks

[torn kite]

i cant understand im just new here

[placid oar]

yeah just click this link. It will bring you to the "How to get help" channel and it explains it there :)

[torn kite]

alr thanks

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[lapis flower]

Is the area

1.5

Someone plz check

[glossy valve]

The following error occured while calculating:
Error: Parenthesis ) expected (char 35)

[empty sapphire]

,calc (1/2)(1.5)(sqrt((2.5)^2 - (1.5)^2))

[glossy valve]

Result:

1.5

[empty sapphire]

yep!

[lapis flower]

Does that mean tes

YAY

Ty

[empty sapphire]

nice work

no problem!

[lapis flower]

.close

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[unborn moth]

Hi

[unborn moth]

What is the average grade for learning calculus and linear algebra in the us

Calculus 1

Hi

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[forest widget]

the only entity capable of answering that question is the us dept of education and i suspect they won’t have an answer for you

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[modest wraith]

how do add scientific notation together

for example 1.2x10^5+1.6x10^3

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Please don't occupy multiple help channels.

[wild sleet]

it's just 1.2x10^5 again?

@modest wraithi didn't like confirm it but you should get 1.2x10^5

because it's assumed to be approximate

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[modest wraith]

help me with these pls

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[modest wraith]

.close

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[modest wraith]

.close

[bronze snow]

do u need help ;-;

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[timid pine]

Hello, I need help with understanding when events are independent in propability and how can I calculate it?

[timid pine]

I can't quite understand how can I know based one P(A) and P(A|B) that they are either dependent or independent

Does it mean that if P(A) != P(A|B) they are dependent?

[wild sleet]

yes

that is the entire distinction

[timid pine]

Oh so I was overthinking I assume 😅

[wild sleet]

it's surprising yeah

[timid pine]

I think that answers my question then, thank you for help!

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[fast peak]

would you be able to do it if the sets were A={a1,a2} and B={b1,b2}

[minor crater]

why not?

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[turbid bluff]

i have no idea where to start

[proper hawk]

find the perpendicular vector that goes from the point to the line

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[turbid bluff]

hmmm

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[median anvil]

anyone knows how to find the equation for the g-force in this scenario? basically im finding an expression for g-force in terms of s (the distance travelled along the loop), but i can't find it for the clothoid shape

[median anvil]

this is a graph i found online which gives the plot i need but there's no equation nor explanations given

so i have no idea how they got it

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[median anvil]

<@&286206848099549185>

[north charm]

uh

what?

is the question

hm nvm

sorry

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[neat laurel]

this is complicated ;-;

[median anvil]

yehh :((

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[smoky locust]

y varies directly with z and the square of x, find x when y=2 and z=4 if x=3, y=9, and z=1/18

[smoky locust]

this is what i have so far:

1. use the equation y = kxz.
2. substitute: 9 = k(3^2)(1/18).
3. simplify 3^2: 9 = k(9)(1/18).
4. multiply on the right side: 9 = k(0.5).
5. divide both sides by 0.5 to find k: 18 = k.

then i made the next equation 2 = (18)(x)(4) but got a random fraction as the answer
the answer choices are 6 and 18, not sure what to do

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[smoky locust]

<@&286206848099549185>

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[smoky locust]

.close

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[scenic otter]

At noon, person A is 2 miles east of person B. Person A is walking east at 4 miles per hour and person B is walking north at 6 miles per hour. How fast is the distance between the people changing at 3
PM?

[scenic otter]

Can someone solve this please i beg

ive tried 10 times now

At noon, person A is 2 miles east of person B. Person A is walking east at 4 miles per hour and person B is walking north at 6 miles per hour. How fast is the distance between the people changing at 3 PM.

[smoky locust]

the direction in which both of them are walking form the base and height of a triangle, and every mile the length of each will change. for the answer, you need to use the hypotenuse of said triangle since it will form a straight line, connecting both people.

(rounding to the nearest hundredth for each)
at 1 pm the legth of the hypotenuse will be 8.49 miles, 2 pm will be 15.62 miles, and 3 pm will be 22.8 miles.

to find the hypotenuse you use the pythagorean theorem, a^2 + b^2 = c^2

does that answer your question?

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[scenic otter]

ive tried this problem 11 times now and got one attempt left so i pray this right

[smoky locust]

does it say to round to a specific amount?

[scenic otter]

nah answer should be a fraction

[smoky locust]

hmm

[scenic otter]

this is a similar problem worked out

same wording different numbers

[smoky locust]

i myself haven't covered this topic as much as others so i'm not sure how much i can help, your process looks good for the other one though

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[meager dew]

first thing you can do is combine like terms

[torn jolt]

6tu 6t 4 u

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[worn matrix]

@torn jolt

!status

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What step are you on?
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3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

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[outer mantle]

hi

[outer mantle]

this

[worn matrix]

this what?

[outer mantle]

lol

how would you simplify that

[dusty sphinx]

you can take out e^x from the numerator

[outer mantle]

if someone answers, ping me

right

[dusty sphinx]

and e^2x = e^x * e^x

[outer mantle]

but

like

both e^x

would this be okay?

[dusty sphinx]

no. e^2x != e^2x * e^2x

[outer mantle]

but where did the e^2x come from?

[dusty sphinx]

in this one you added in an extra e^2x

should be (5x^4 - x^5) / 2e^x

[outer mantle]

but then how did we eliminate both e^x from the numerator

[dusty sphinx]

like this

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