help-27

[rich summit]

by using log rules

[drowsy kite]

what log rules exactly?
I know that usable there are only log2(a^b)=blog2(a)
log2(a*b)=log2(a)+log2(b)
and log2 is strict increasing

[rich summit]

$$\log_{2}\left(n\right)+\frac{2}{n+1}=\log_{2}\left(n\cdot2^{\frac{2}{n+1}}\right)$$

[woven radish]

Jelle

[drowsy kite]

ok, i got this

[rich summit]

Not sure if this makes it easier

[drowsy kite]

i know that this derives from that

I think it's making it easier, but I need to get somehow to n+1, and i got there

i tried making that left member n+(sqrt2-1)n and prove that (sqrt(2)-1)n>1 but I think it uses another induction so its too exhaustive my thought

[rich summit]

Don't think the first inequality is true

[drowsy kite]

It is greater or equal, and n is natural, n>=1

Oh it is not

my bad

[rich summit]

Ooh, do you know the standard proof of showing that this series is divergent?

[drowsy kite]

idk what do you mean by standard
i know that
1+1/2+1/4+....=2

but I think that
sn=1+1/2+1/3+1/4+...+1/n>=1+1/2+1/4+1/4+1/8+1/8+1/8+1/8+.....=1+1/2+1/2+1/2+...=+inf =>> sn divergent

[rich summit]

yeah that's the one

so $$\sum_{k=1}^{2^{n}}\frac{1}{k}\ge1+\frac{n}{2}$$

[woven radish]

Jelle

[drowsy kite]

i proved that in previous task

same induction

[rich summit]

yeah, now substitute m = 2^n

and n = log_2(m)

[drowsy kite]

i know what you mean

and this inequality holds

but whats the use of this substitution?

[rich summit]

what do you get after subsituting?

[rich summit]

I meant this: $$\sum_{k=1}^{m}\frac{1}{k}\ge1+\frac{\log_{2}\left(m\right)}{2}$$

[woven radish]

Jelle

[rich summit]

from this

[drowsy kite]

ugh

didnt know where to sub

[drowsy kite]

so u mean for every m natural number this ineq holds

?

[rich summit]

yeah

[drowsy kite]

oh yeah

it gets me to the conclusion

qed

lol

[rich summit]

yeah

[drowsy kite]

thanks, I knew thats standard proof but I was too dumb to think for it

[rich summit]

I totally forgot about the 1/2 + 1/4 + 1/4 + 1/8 + .... stuff

[drowsy kite]

whats fun is that this proof used this relation that I have already proven in a previous task , by same manner

thx again

.close

[devout snow]

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[mortal crest]

I dont get this statement

[devout snow]

@mortal crest Has your question been resolved?

[sullen island]

two subsets of {0,1,2,3} are related if they have the same sum of elements

for example {1, 2} and {3} are related cause 1+2 = 3

{0, 1, 2} and {3} are related cause 0+1+2=3

[mortal crest]

Would this mean that R2 is reflexive, symmetric and transitive because "=" is reflexive, symmetric and transitive?

[sullen island]

pretty much, it's not hard to show that it's an equivalence relation

[mortal crest]

what about sigma?

[sullen island]

just work with it

that's why I said it's easy to see

I didn't say there's 0 work to do

[mortal crest]

i dont have to show it. I have to chose if it is

[sullen island]

"how did you choose ? randomly"

you have to show it in some way, even if it's just in your head

[mortal crest]

no like the question i have gives me options to choose from

[sullen island]

yeah well what's the options then

sounds good

sigma is not a relation so the other two options make no sense at all

[mortal crest]

ok

[sullen island]

that's true

[mortal crest]

the question is true or my statement is true?

[sullen island]

the question

[mortal crest]

hmm. ok

I have a couple more..

So the first is true because reflexive and irreflexive are two mutually exclusive properties of relations

The second statement is false

not sure about the third one

[sullen island]

3rd is false

{(1,2),(2,1),(1,3)}

it's not symmetric cause you have (1, 3) but not (3, 1)

and it's not anti-symmetric cause you have (1, 2) and (2, 1) but 1 != 2

4th is also false

it's possible to be symmetric and anti-symmetric at the same time

there's not a lot of choice for such a relation but it exists

and 5 and 6 are easily true

[mortal crest]

I was going to say (d) is true but what you said makes sense

this one

[sullen island]

you have a lot of questions lol

[mortal crest]

I do... 😅

First is true

second is false

third is true

fourth one idk maybe?

[sullen island]

yeah

symmetry is an implication pretty much

x R y -> y R x

you can prove an implication by contrapositive no problem with that

[mortal crest]

i see

so all of them are correct except b

[sullen island]

yea

alright

any ideas

[mortal crest]

I think this is true

[sullen island]

well it is yes

[mortal crest]

bcuz the pairs(a,a) are in both R2 and R4

[sullen island]

yup

[mortal crest]

only a couple more left i promise 😅

[sullen island]

that's the same q lol

[mortal crest]

nope

small modification

[sullen island]

ah nice

well what happens to the (a, a) here ?

[mortal crest]

even if R2 and R4 are individually irreflexive, their intersection may include pairs (a,a)

so its not guaranteed to be irreflexive

[sullen island]

you're really sure about that

[mortal crest]

i think?

[sullen island]

the intersection of R2 and R4 is smaller than R2 for example

if the (a,a) weren't in R2, they're not gonna magically appear in the intersection

[mortal crest]

hmm. i see

so true for this as well

[sullen island]

yea

[mortal crest]

true

[sullen island]

false here

it's not too hard to come up with a counter example

[mortal crest]

oh wait cuz that means there exist elements in the set for which the pair a,a might be present in both relations. So R2 and R4 might have those elements and might not

for this, first is correct i believe

[sullen island]

yeah, comes back to the "can a relation be symmetric and anti-symmetric"

[mortal crest]

second is also true

and the last 2 are false

[sullen island]

yup

do you really need help at this point lol

I'm just saying yes

[mortal crest]

for the last 2 i will

ok so from a-d "a" and "c" are right

[sullen island]

yea

[mortal crest]

is e false

[sullen island]

e just means not symmetric

[mortal crest]

oh ok

then f is true and idk about g

[sullen island]

gotta remember your total orders a little

g) means that forall x, y in your set, you have exactly one of x R y or y R x

how does that work out with an equivalence relation ?

[mortal crest]

ohh

thats true

[mortal crest]

for any two elements x and y in S, either x or y belong to the same equivalence class

wait so this means its false?

[sullen island]

it's false yeah

if you take x and y in the same equiv class, then you have both xRy and yRx

[mortal crest]

gotcha

last one

[sullen island]

ok

[mortal crest]

a is true

c and e are also true

wait

[sullen island]

sure about symmetric

the graph is directed

[mortal crest]

yea i was gonna say

a and e would be true

[sullen island]

and the rest is false yes

[mortal crest]

Great, thanks for the help!

.close

[devout snow]

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[devout snow]

@lime harbor Has your question been resolved?

[devout snow]

@lime harbor Has your question been resolved?

[brittle burrow]

because these two aren't the same, so you can't compare it to (tanx+1)/(tanx-1) where they are the same

in the steps of simplifying it into (tanx+1)/(tanx-1), you can see that the 1 changes, so they definitely aren't in the same form

[devout snow]

@lime harbor Has your question been resolved?

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[devout snow]

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[restive river]

can anyone help me out with this, ive tried to answer with multiple things but it resets the question every time im just confused how to do it

[restive river]

ping me if anyone is able to help me

[steady grove]

@restive river What up

<@&286206848099549185>

This person needs help

[smoky gyro]

That’s not how you use the helpers ping

You don’t ping helpers saying other people need help. The OP can do that themselves and you use it only if YOU require help

[near trout]

!15m

[devout snow]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[steady grove]

@restive river What do you need help with?

[restive river]

ive posted it above

[steady grove]

@restive river Can you measure the numbers?

[restive river]

measure them ?

what do you mean

ive got the regression equation

but im not sure what to do next

i just need help getting the final answer

<@&286206848099549185> well its been 15 minutes, sorry for the ping but is anyone able to assist me ?

i just need help getting the final answer

[steady grove]

@restive river Put number one Andrew answer

@restive river

[restive river]

huh

number one andrew answer?

[steady grove]

Yes

@restive river

[restive river]

what does that mean

[steady grove]

That is the numbers

@restive river

[restive river]

what does that mean

[steady grove]

Just put any number

@restive river

@devout snow .

[restive river]

???

i have to put a correct answer

whta

[steady grove]

@restive river Submit your answer

[restive river]

i have to put a final answer to submit it

[steady grove]

Put A3

[restive river]

dude what

[smoky nimbus]

If you cannot provide useful helpful, please do not provide wrong information

[restive river]

😭 😭

im so confused

[steady grove]

@smoky nimbus I’m just trying to help this person and told him to measure the numbers is there any other way Is there any other way to help him?

[smoky nimbus]

The final answer using the last sentence. It asks for you to find the projected number for 2008, and as it mentions, x is the number of years since 2000. So how many years is 2008 from 2000?

[smoky nimbus]

That is wrong help

You are not providing useful help

[restive river]

8? but that doesnt make sense

it hsould be in the thousands

like over a thousand

[steady grove]

What different suggestion should I give to him?

@smoky nimbus

[smoky nimbus]

So you know the x value, plug that into the equation that you got

[restive river]

oh

OH

bro god bless

real help ;sob

[steady grove]

@smoky nimbus

[smoky nimbus]

Please read #❓how-to-get-help

[steady grove]

@smoky nimbus I know how to get help

[smoky nimbus]

You don't need to ping me every time

[devout snow]

If you are done with this channel, please mark your problem as solved by typing .close

[smoky nimbus]

Just observe the server, and how people help.

[restive river]

.close

[devout snow]

Channel closed

Closed by @lapis dock

Use .reopen if this was a mistake.

[steady grove]

@restive river Anything else I can help you with

[devout snow]

Available help channel!

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[jagged lily]

How do I know I’m ready for calculus 1

[jagged lily]

(assuming I’m in high school)

[smoky nimbus]

Normally the pre reqs are what you need to prepare for calc 1

[jagged lily]

pre reqs?

What is a pre req

[smoky nimbus]

Prerequisite

[jagged lily]

What

What is a Prerprerequisite

[smoky nimbus]

Copy/paste/select all error my bad

[jagged lily]

Ok I think I know

So what is the

Pre requesisite

For calculus 1

Assuming I’m in HS

[smoky nimbus]

All the math courses that leads into calc 1

[jagged lily]

Like what subjects

[smoky nimbus]

It's whatever your math path is

[jagged lily]

Wdym

Ok say I take the normal path then

Assuming I’m a high school student taking the normal path

[smoky nimbus]

It's still whatever the path is that your school uses

[jagged lily]

Ok say it starts from algebra 1

Freshmen year algebra 1

so restating

Assuming I’m a high school student taking Algebra 1 in my Freshmen Year

[smoky nimbus]

Then you need algebra 1, whatever math from 10th grade, then 11th grade, then calc 1 in 12th

[jagged lily]

So what is that math

In 10th and 11th grade

[smoky nimbus]

Whatever math that your school uses

[jagged lily]

Ok algebra 2 and then algebra 3

[smoky nimbus]

I don't know the structure of your school

[jagged lily]

What is algebra 2 stuff

All about

And algebra 3 stuff

All about

[smoky nimbus]

Look it up

[jagged lily]

Bruh

[smoky nimbus]

Ask the teachers at your school

[jagged lily]

I can’t

[dense jay]

cant?

[jagged lily]

Yea

[smoky nimbus]

Get their syllabus, see what material is taught

[jagged lily]

Cuz it’s thanksgiving break

[jagged lily]

I don’t have their syllabus

[smoky nimbus]

That's why you ask

[jagged lily]

But I can’t

[dense jay]

dont you know anyones email

[smoky nimbus]

Then wait until after the holidays

[jagged lily]

Nope I don’t know any HS teachers school email

Maybe like one of them

[jagged lily]

Even then I can’t ask them

[smoky nimbus]

This is your school, and info you want. Ask the resources at your school, not us. We don't know how your school works

[jagged lily]

That’s why I said assume I’m a high school student

Cause im not in HS just really interested in math

Yes I am in MS

And yes I am above the age minimum

[smoky nimbus]

Then research, google what is normally taught in algebra 2. The structure for algebra 2 is very similar, in most schools

[jagged lily]

What is all this junk

[dense jay]

useful things

[jagged lily]

Well do you use it in calculus

[smoky nimbus]

More things for you to research

[jagged lily]

There is no way you use all this crap to take the derivative of something

[smoky nimbus]

You apply concepts of all that

[jagged lily]

am I gonna find the area of a series

Uh oh

Tis is a little hard

But I’ll be fineeee

This seems like EZ stuff

[smoky nimbus]

If it sounds hard, then that means you aren't ready for it yet

[jagged lily]

MS be the best time to learn calculus haha

Some of my friends can do some weird Gaussian Integral little thingy or whatever

[smoky nimbus]

If you don't have the pre reqs for calc, then it will be hard

[jagged lily]

Like some Gaussian

Or idk

And this

M?

[smoky nimbus]

Then ask your friends how they learned

[jagged lily]

Sideways but ye

[jagged lily]

I did they don’t reveal their secret

They’re in 6th

Probably had strict parents yonow

Idk calculus seems easy actually

Cuz if 6th grades can learn it

I can too

As an 8th grader ig

So what do you recommend

[smoky nimbus]

I told you want I recommanded already

Research what you need to do

[jagged lily]

But I already know

So

Where do I start

I already know all that now

So where do I start my calculus journey

[smoky nimbus]

Continue that math path that leads into calc 1, like I said

[jagged lily]

But. I already know it

[smoky nimbus]

Well good luck. I told you want you need to do, have fun learning

[jagged lily]

What?

Bruh I already know all that stuff

It’s ezpz

You can give me a quiz

Full marks

It’s just too easy bruh

Math ain’t hard

Bruh

Oh well I don’t need your help cuz I can get someone else help

.close

[devout snow]

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[strange arch]

another quick one: consider the simple sequence (inf., -inf., 0, 0, 0, 0, 0, 0, 0, 0, 0, ...)

[strange arch]

does the series as the partial sums of the above sequence converge (properly or improperly)?

ah solved it

.close

[devout snow]

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[elder quail]

can someone tell me what im doing wrong here? the answer is supposed to be square root of 3 but idk why i got a minus there

[rigid shadow]

you multiplied by $\frac{\sqrt{\frac{1}{x^2}})}{(\frac{1}{x})}$ instead of $\frac{\sqrt{\frac{1}{x^2}}}{(\frac{1}{\abs{x}})}$

[woven radish]

mud ツ

[rigid shadow]

remember that the absolute value of x is x when x is greater than or equal to zero, and negative x when x is less than zero?

[elder quail]

oh i see, and since x < 0 it would be -x, so is it just that every time i do these kind of problem, i have to put absolute value?

[rigid shadow]

yes

[elder quail]

ok got it, thanks for ur help

.close

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[mighty flume]

Quick question related to partial fractions

[mighty flume]

How do I equate the coefficients find C?

I know what to do

I just don’t know where to start

[wooden wraith]

,rotate

[crisp niche]

if you calcualted A and B correctly, then you can set any easy number into x, then you can easy find C

[mighty flume]

I was thinking of doing that

[crisp niche]

i often use 0 ro 1

[mighty flume]

my tutor reccommended I try equating the coefficients though

[crisp niche]

some easy nbumber

soemtiems i sue trick with compelx nmber i

[mighty flume]

I'll just use 1 for now

[crisp niche]

ok

[mighty flume]

thanks!

[crisp niche]

🙂

[mighty flume]

.close

[crisp niche]

yw

[devout snow]

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[glad ether]

Does the resulting power series look good?

[timber pebble]

,w Series[ x (1+9x^2)^(-2),{x,0,Infinity} ]

[woven radish]

Results provided by WolframAlpha

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

Requested by janniku

[timber pebble]

hmm

what a bizarre answer

[glad ether]

😭

[timber pebble]

i just didnt wanna do it by hand

1 sec

you should simplify your answer

I get $\sum _{k=0}^\infty (-1)^{k+1}9^{k-1}kx^{2k-1}$

[woven radish]

jan Niku

[glad ether]

Gotcha gotcha

I appreciate it ❤️

[timber pebble]

sure

[glad ether]

.close

[devout snow]

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[devout snow]

@modern frost Has your question been resolved?

[desert fulcrum]

can't be 105

should be 17c2

17c2 is 136

@modern frost are you sure its 105?

(n+r-1)C(r-1)

I think it still should be (15+3-1)C(3-1)

direct formula

[devout snow]

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[devout snow]

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[fervent sundial]

how would i do this

well i had

,, \frac{99 + ab}{99} = \frac nd

[woven radish]

kanna

[fervent sundial]

n+d = 198 + ab

now i need gcd(n+d,n) = 1 right

but all the options satisfy that

maybe except choice B

[jolly mountain]

the question asks about the maximum value of $n+d$, where now you know that $n=99$ and $d=99+10a+b$, with $a\ne b$ and $\gcd(n,d)=1$

[woven radish]

ミコ

[fervent sundial]

isn't it reversed

d = 99 and n = 99 + 10(a) + b

[jolly mountain]

so maybe you can try different possible values of $(a,b)$ and hope that $\gcd(n,d)=1$

[woven radish]

ミコ

[jolly mountain]

oh you are right

[fervent sundial]

that takes forever 😭 , right?

[jolly mountain]

no, $n=99+10a+b$ and it is obvious that how to assign $a$ and $b$

[woven radish]

ミコ

[jolly mountain]

and for gcd you only have to check if $n$ is divided by $3$ or $11$ since $99=3^2\times11$

[woven radish]

ミコ

[fervent sundial]

wait i forgot but where did you get 10a + b?

[jolly mountain]

I change the notation from $99+ab$ to $99+10a+b$ to avoid ambiguity

[woven radish]

ミコ

[jolly mountain]

since $a$ and $b$ are digits

[woven radish]

ミコ

[fervent sundial]

oh wait 😭 hahah i forgot my own notation

i was like how did you do that when ab is multiplication of two numbers

[jolly mountain]

lol

[fervent sundial]

okay maybe that's why i was stuck

let me recheck

[fervent sundial]

i'm not sure how to proceed

n + d = 99 + 10a + b + 99 = one of the answer choices

so 10a + b = 98 or 10a + b = 99 or 10a + b = 100 or 10a+b = 101 or 10a + b = 103

[jolly mountain]

yes

if we ignore the answers and I ask you how to maximum $10a+b$ where $a$ and $b$ are distinct 1-digit number, what would you try?

[woven radish]

ミコ

[fervent sundial]

a = 9 b = 8

[jolly mountain]

that's right

[jolly mountain]

and that's 98, which is the first option you got

and we now have to check if $\gcd(n,d)=1$

[woven radish]

ミコ

[jolly mountain]

which is $99$ and $197$

[woven radish]

ミコ

[fervent sundial]

I'm confused lol

n/d was (99 + 10a + b)/99

n+d = 99 + 99 + 10a + b

to maximize this where a and b are one digit numbers and distinct a = 9 and b = 8

[woven radish]

Result:

296

[fervent sundial]

oh which is choice A

[jolly mountain]

yes

[fervent sundial]

i'll take a break and think about it again lol

thanks

[jolly mountain]

you're welcome

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[steel pelican]

.close

[steel pelican]

The questions are on swedish
a) enter the valurnorna set of the function
b) solve the equation 2•f(x+2)=6 with help from the graphene

[mild sail]

what is valurnorna set

[steel pelican]

amount of value

maybe

i dont know what is is in english

[mild sail]

oh swedish word eh wait lemme translate

[steel pelican]

like the Y level

[mild sail]

it says the ballot of boxes

[steel pelican]

?

[mild sail]

idk

[steel pelican]

Decimal pair for specifying a quantity range with a unit of measure.

[mild sail]

i think it's trying to say the domain set of the function

[steel pelican]

maybe

[mild sail]

so then considering it is asking domain of the given function in which it is defined then .. it is [-2,∞)

[steel pelican]

for y

[mild sail]

we can deduce this from the given graph that it starts from -2 where it gives 0 and till x =∞

[mild sail]

that is called range and it is [0.∞) again from the graph it starts taking value of y from x=-2 which gives y=0 and proceed to y =∞ when x=∞

[steel pelican]

so its not y> sqaure root of 2

?

[mild sail]

no

[steel pelican]

ok

[mild sail]

it's y>0

[steel pelican]

alr

[mild sail]

as the graph give all positive values of y

[steel pelican]

i see

how do i do b)

[mild sail]

just shift the given graph of function by 2 units in the left direction..

[steel pelican]

i dont get it

[mild sail]

or just replace x with x+2 so the function will become f(x+2)=sqrt((x+2)+2)

then simply solve the equation

[steel pelican]

i think i understand now

[mild sail]

yes oky

[steel pelican]

but how do i solve that equation?

[mild sail]

2.sqrt(x+4)=6 (just open the parentheses)
=>sqrt(x+4)=3 (divide 2 on both the sides)
=>x+4=9 (square both the sides)
=>x=5 (subtract 4 on both side)

as f(x+2) is now sqrt((x+2)+2)

[steel pelican]

ahh

ok

thanks

[mild sail]

it's oky

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[rigid wolf]

aa + bb = cdc

• • / / -
    ee + cc = aa
    = = = = =
    cc × b = bb

[devout snow]

Please don't occupy multiple help channels.

[rigid wolf]

its an calcrostic puzzle

i dont really understand what they really are

[stone stump]

how about a picture

[rigid wolf]

alright

here (:

idrk if the colours mean something

[stone stump]

do you have a problem statement that came along with this?

[rigid wolf]

nope

just solve it

said my teacher

nothing else really

[stone stump]

well you can start with the last line

that gives you c

[rigid wolf]

c is 11

thats pretty simple

but e is probably the hardest

since theres nothing else that uses e

so if we find a we can also find e

[stone stump]

well you can figure out d from that

cdc is divisible by 11

and then you can just go through the options for a

[rigid wolf]

damn

it makes sense now

[devout snow]

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[restive river]

I'm having difficulty in trying to find a way to approach solving this recursive function. I thought of approaching it as a difference equation, but the form does not really fit. or does it? I don't really know.

[devout snow]

@restive river Has your question been resolved?

[restive river]

by the way, the values for time and Pgas are controlled by a data set I've made.

<@&286206848099549185>

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@restive river Has your question been resolved?

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@restive river Has your question been resolved?

[devout snow]

@restive river Has your question been resolved?

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@restive river Has your question been resolved?

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[devout snow]

@torpid ocean Has your question been resolved?

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[nova bramble]

Hello I have an exam coming up today and I'm still stuck with this exercise. can someone walk me through it. explain it like i play fortnite pls

[devout snow]

@nova bramble Has your question been resolved?

[earnest kite]

write it as a matrix system

@nova bramble

find eigenvalues

then eigenvectors

write homogeneous solution

then find particular solution

solve particular solution

then write general solution

then solve using initial conditions

[devout snow]

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[lime stream]

i used multisets once in a paper. we just wrote them with normal set notation like {4,4,4} or something.

formally, you have an underlying set A, and then a function m : A --> Z^+ that gives the multiplicity of each element in A

so the "formal" construction in ZFC would be a set like {1} and the function m : {1} -> Z^+ defined by m(1) = 5. this would be the multiset {{1,1,1,1,1}} (writing a multiset as {{ }})

hmm that's bad notation. maybe [1,1,1,1,1] is better

what is your problem?

logic puzzle

lol

you can write it as like {n \in \N | <n satisfies some thing>} or just "let A be a multiset of..."

then people will know its a set with possible duplicates in it

[devout snow]

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[earnest sphinx]

<@&286206848099549185>

[winter torrent]

"expand the brackets" = FOIL

[earnest sphinx]

Huh😭😭

[devout snow]

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[river gorge]

F - First terms in each bracket
O - Outer terms in each bracket
I - Inner terms in each bracket
L - Last terms in each bracket

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[vivid topaz]

hello

[vivid topaz]

i have a question

for the function Arccos(sinx)

why the domain is R but the range is [0:pi] ?

the domain depend of the () and the range depend of arccos ?

[frozen aurora]

what's the range of arccos?

[vivid topaz]

[0;pi]

the domain is R because x can be everything ?

[frozen aurora]

yes

[vivid topaz]

and the range is [0:pi] because it's Arccos

but i have another question

if it was sin(arccosx)

the domain would be [-1:1]

and range R ?

[frozen aurora]

what's the range of sin?

[vivid topaz]

[-1;1]

oh yeah

[frozen aurora]

exactly, so the range can't be R

beware, it's not [-1;1] either tho

a bit less than that

[vivid topaz]

its an arccos

its only from 0 to 1 for X

sin can only have the value from 0 to pi/2

?

@frozen aurora hey sorry to ping are u still here

[prisma snow]

@vivid topaz we know sin(x) is defined for all real numbers, and the output of sin(x) is a number between [-1,1]
arccos(sin(x)), the arccos() function used the range of sin(x) which is a number between [-1,1]
if you feed arccos() a number between [-1,1], you get the range of [0, pi]

[vivid topaz]

the output of sinx is between [0:1] because of the arccos ?

[prisma snow]

no no no

think of arccos being dependent on the output of sinx

we give sinx any real number ‘x’

[vivid topaz]

output mean range or domain

[prisma snow]

output = range

[vivid topaz]

ok

sinx is [-1;1] --> R

[prisma snow]

and then sinx gives us an output (range) between [-1,1]

[prisma snow]

other way around

[vivid topaz]

yeah

other way

but why you wrote [0;1]

[prisma snow]

accident sorry

[vivid topaz]

ok nppp

[prisma snow]

we know that by default arccos is defined between [-1,1] right

[vivid topaz]

yeah

[prisma snow]

so then the output of sinx must be within these boundaries

which it indeed is

so when arccos takes an input of a values between [-1,1]

its range must be between [0, pi]

[vivid topaz]

yeah

[prisma snow]

also by default this is the range of arccos

does this answer your question

[vivid topaz]

but i was talking about sin(arccosx)

not arccos(sinx)

[prisma snow]

?

[vivid topaz]

no here

[prisma snow]

oh sorry

[vivid topaz]

np

[prisma snow]

ok let’s do the same process

we know that arccos(x) has a domain for a number between [-1,1]

[vivid topaz]

and range [0;pi[

]

[prisma snow]

and this will produce an output (range) between [0,pi]

yes

[vivid topaz]

sinx is R --> [-1;1]

[prisma snow]

if we feed sin the range of [0, pi]

[vivid topaz]

what feed mean

[prisma snow]

like input

[vivid topaz]

ok

[prisma snow]

we get an output (range) of [0,1]
because sin(0) = 0
because sin(pi) = 1

[vivid topaz]

but how we find the domain

the domain is about the arccos ?

[prisma snow]

domain is [-1,1] because this is the maximal domain of arccosx

and the output of this satisfies sin

[vivid topaz]

why we dont take the domain of sin

i dont understand this

[prisma snow]

it’s a composite function

we work from the inner function to the outer function

we know sin(x) has a domain for all real numbers

but in this case it’s sin(arccos(x))

we need to satisfy where arccos(x) is defined for values of x

[vivid topaz]

oh ok

[prisma snow]

and then check whether what arccos(x) outputs, is an ok input for sin

[vivid topaz]

ok thanks

[prisma snow]

does it make sense

[vivid topaz]

yes

[prisma snow]

okay cool any other questions?

[vivid topaz]

maybe 1 hour later i will get other questions

[prisma snow]

okay good luck!

[vivid topaz]

thanks

.close

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[marble quail]

$5x^{7x}$

[woven radish]

Merineth

[marble quail]

If i have a function like this

and i'm supposed to find the derivate

Is there any advice on where to start?

[prisma snow]

apply chain rule

[marble quail]

i tried that but i got stuck

for example

7x falls down infront of 5x

7x decreases by 1

[hybrid snow]

Rewrite $x^{7x}$as $e^{7x\ln(x)}$

[woven radish]

Umbraleviathan

[marble quail]

Yes i was thinking that at first

[hybrid snow]

Should be easier to do chain rule

You'll just have to deal with product rule

[marble quail]

but

that should be

e^7x(ln5x), no?

[hybrid snow]

The 5 is a coefficient of x^(7x)

It's not (5x)^(7x)

[marble quail]

https://gyazo.com/f5f78ef5f3409980a4ea2d1d1f33bec0

our a is 5x

[hybrid snow]

Nope

[marble quail]

and our x is 7x

no?

[hybrid snow]

You have it in a form of ab^x

a = 5

b = x

x -> 7x

(5x)^(7x) ≠ 5x^(7x)

[marble quail]

https://gyazo.com/682a2a9933d422ce0b9864365519ddb1

sorry

my initial post was wrong

it's parantheses there

[hybrid snow]

Then why didn't you place the parentheses around 5x lmao

Okay so

$e^{7x\ln(5x)$

[woven radish]

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

[marble quail]

Yes! Sorry

And now i can do chain rule on that?

[hybrid snow]

Yeah

[marble quail]

e^x is e^x

and then product rule on 7x*ln(5x) ?

[hybrid snow]

Yeah

It's not too bad tbh

[marble quail]

For me it is ;-;

Still calculating ,one moment Q.Q

[hybrid snow]

The derivative of ln(ax) is still 1/x

So the 5 in the 5x shouldn't be too much of a hassle

[marble quail]

dont i just disregard the 5x inside the ln for now

and do *5 after product rule

or rather 5x = x

[hybrid snow]

I mean, you could, but then you'd just do being 1/(5x) * 5 somewhere in there

Which simplifies down to 1/x

[hybrid snow]

Hence this

If you want, you can also rewrite ln(5x) as ln(x) + ln(5)

And you get 7xln(x) + 7ln(5)x

[marble quail]

$e^{7xln(5x)} * 7x * \frac{1}{5x} + 7 * ln(5x) * 5$

[woven radish]

Merineth

[marble quail]

Am i thinking correct so far?

Chain rule makes e^x stay the same

multiplied with the product rule of 7x * ln(5x)

• 5 at the end for the final (5x) chain rule

[hybrid snow]

Should be 7x • 1/(5x) • 5

Then just + 7 • ln(5)

[marble quail]

I'm not sure i follow

I'm using the f(x) * g'(x) + f'(x) * g(x)
Where:

f(x) = 7x
g(x) ln(5x)

f(x) * g'(x) + f'(x) * g(x)
7x * 1/5x + 7 * ln(5x)

[devout snow]

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[marble quail]

.close

[devout snow]

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[crude temple]

@dry robin I kinda need help in a geometry problem but is in my language,not in English so...

[red heath]

send it

[crude temple]

6

Oh,I got it, sorry

[devout snow]

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[devout snow]

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[remote ember]

Can someone please explain how I can factorise a cubic?

Question 14

[valid iron]

its asking for you to compare

so look at rhs , and see what one factor it has done for you

[remote ember]

I meant 14b

[valid iron]

trial and error, check for multiple values of x for which y gives 0

i.e factor

and notice how the cubic is same so...

[remote ember]

Oh okay, but is there no one method to factorise them?

[radiant dune]

They've given you a root, x=3 divide the cubic with (x-3) to get a qudratic quotient

That quadratic quotient is easily factorisable

[remote ember]

Oh okay thanks

Why is it (x-3) instead of (X+3) tho?

[radiant dune]

Mb, x+3 it is

[remote ember]

Oh okay

I tried that but I keep getting a remainder and idk what to do with it

[radiant dune]

You should not

Get a remainder

[remote ember]

Can you show me where I've gone wrong?

[jade oak]

U do not have to divide you already found the result in part a

[remote ember]

I've not done part a yet, idk how to do it

[jade oak]

Expand and compare

[remote ember]

Oh okay thank you

[remote ember]

But can you still show me where I've gone wrong in here?

[jade oak]

Howd you get -15x

[remote ember]

I brought it down from that top line

Oh wait, you're talking about something else

[jade oak]

Yeah

Should have got -5x

[remote ember]

Oh yeah true

Thank you

[devout snow]

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[restive river]

Hi yuh, wondering if someone can explain how to do this, thax

[dry oxide]

conservation of momentum i believe🙃

[restive river]

but how

u1m1 - u2m2

but that equals 0

[quaint citrus]

Tell us more about the collision

Show the whole prompt

@restive river

[restive river]

thats it

nothing else

[quaint citrus]

It just says Part A

There’s no text above it?

[restive river]

shows you the valuse for the questions

they change for every question

[quaint citrus]

So do Alfie and Beth stick together after the collision?

[restive river]

yeah

mb

[quaint citrus]

Lol

Ok so our formula is

m1v1 + m2v2 = v_f (m1 + m2)

[restive river]

v_f ?

[quaint citrus]

Final velocity

[restive river]

oh

we use

[quaint citrus]

Velocity after they get stuck

[restive river]

u for initial

and v for final

[quaint citrus]

Ah ok

Yea suvat ig

[restive river]

uh huh

[quaint citrus]

Anyways

[restive river]

so lemme try

120 = v(70)

120/70 = v

oh shoot

thanks so much

it worked

[quaint citrus]

Np homez

[restive river]

🥲🥲

[quaint citrus]

Show work

[restive river]

-84 -84 = v(90)

-168 = 90v

168/90 = v

[quaint citrus]

How’d u get -84-84?

[restive river]

(I've tried doing negative)

[restive river]

(60)(-1.4)

-(30)(2.8)

= -84 - 84

[quaint citrus]

Where’d u get this minus sign from

[restive river]

oh uhh

i mixed it up with a different equation

m1u1-m2u2 = momentum before

i think

[restive river]

okay so: -84 + 84 = 70v?

[quaint citrus]

90v but yes

[restive river]

but then isnt the answer 0

[quaint citrus]

Think about the problem logically

One ball is moving rightwards with a momentum of 84 kg * m/s

The other ball is moving leftwards with a momentum of 84 kg * m/s

What’s gonna happen when they collide and stick?

[restive river]

it will be very loud i can imagine

[quaint citrus]

What if they’re tennis balls lol

But what will happen to their motion

If u collide them like that and they have tape so they stick together

What’s gonna happen

[restive river]

v = 0 in a 1d world

[quaint citrus]

What’s gonna happen?

Tell me in words

[restive river]

stationary?

[quaint citrus]

So ur saying upon the collision, both balls stick and don’t move?

[restive river]

thats what the answer says

[quaint citrus]

Yep

[restive river]

;c

Stephen

[quaint citrus]

Try doing some physics experiments irl

[quaint citrus]

Yo

[restive river]

I done it again

[quaint citrus]

Bruh just apply the same formula

[restive river]

180 + 80x = 0*200

i did

idk why im acting stupid today

80x = -180

x = -2.25

[quaint citrus]

Hmm

That seems right

[restive river]

oh

it wants it to 2sf

thats why

[quaint citrus]

Lol

[restive river]

bare in mind it says that no where

anyway tysm

[quaint citrus]

Stupid

Np

[restive river]

shu

[quaint citrus]

?

[quaint citrus]

I was referring to this lol

[restive river]

Stephennnnnn

360 - 31d = 240d

she is really light

or i done somethign wrong

either way round

oh wait

i got it

she is 3.6 kg

[devout snow]

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[full flare]

Am i not supposed to be getting the same answer with both of these methods, or am i imputting it wrong?

[upper schooner]

,calc 1.357/50

[woven radish]

Result:

0.02714

[full flare]

its right with the parentheses, i dont understand why though 😨 teacher im following doesnt do it

[upper schooner]

Order of operations - in writing it's clearer to show what you intend to mean, it's easy to e.g. see what you mean by $1.357^{\frac1{50}}$

[woven radish]

@upper schooner

[upper schooner]

You can see that's supposed to mean that the 1/50 is the whole exponent, but for the calculator it isn't when you input it like that

[full flare]

ahhh i see, calculator dumb and needs more precise stuff

[upper schooner]

As powers take precedence it's interpreting the original as doing 1.357^1 first then dividing that by 50, hence this

[upper schooner]

Wellll I'd more put it that it can't read your mind

[full flare]

thank you v much for the help, been sittin with this for 2h 💀

.close

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[supple knot]

"continuous" doesn't refer to the graph, it refers to the function

The function f(x) is continuous"

why can’t I just say a function is continuous excluding points x y and z
you can say whatever you want, but your intuition disagrees with textbooks, so you're just gonna confuse yourself

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[final sable]

Hi this is an algebra question

[final sable]

these are the axioms i am using

all i'd like to know is how to start a question like this? i'm referring to (b)

so you're only allowed to assume the axioms and the fact that x and y not equal to 0, but i'm unsure what to do now

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.close

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[lunar rampart]

The angle between the lines x=1, y=2 and y=-1, z=0 is

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[orchid sierra]

@lunar rampart

[languid ore]

!xy

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[honest thorn]

An elephant and a lion are currently $1$ mile apart. The elephant runs directly away from the lion at $19$ miles per hour, while the lion runs directly towards the elephant at $24$ miles per hour. How many minutes will it take for the lion to catch the elephant?
Your Answer: 7.2
Solution:
Every hour, the lion runs 24 miles while the elephant runs 19. Thus, the distance between the two animals closes at a rate of 5 miles every hour. The lion catches the elephant after this distance has closed 1 mile, which takes $\frac{1}{5}$ hours to do, or $\frac{1}{5}\cdot 60 = \boxed{12}$ minutes.

[woven radish]

龖

[honest thorn]

why cant u just find the LCM

then divide by 60 for minutes

i got 7.2

why doesnt it work

[desert fulcrum]

19x + 1 = 24x

[grim goblet]

you can do that. why not?
but that'll be true if they're approaching each other

[honest thorn]

ohh

thanks guys

.cloes

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[hybrid snow]

Hm

Jjst find when f'(x) = tan(21.8°)

But

You'd also have to understand that typically means 21.8° from the horizontal

Since f(x) is a parabola, it should only@be one point

[neon folio]

so the angle on the right is 21

and on the left is -21

?

but technically the left one is also 21

.close

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[honest thorn]

Trey receives a $5%$ commission on every sale he makes. On the sale of a $$60$ coat (before any discounts), how many more cents will he receive if his commission is based on the original price of the coat rather than the price of the coat after a $20%$ discount?
Your First Answer: 3
Your Second Answer: 12.6
Solution:
A $60 coat with a 20$%$ discount costs $60(0.8) = 48$ dollars. The difference in commission is $0.05(60 - 48) = 0.05(12) = 0.6$ dollars, or $\boxed{60}$ cents.