help-28

[cursive condor]

Good.

[gentle sequoia]

Yay thanks!! Is that all the question asks? Like I just identify them and stuff like idk

Yay!

I feel like I’m missing sum

Haha love the car replies

Alr thanks so much guys

[devout valley]

(At best, write out F(x) with what C is explicitly)

[gentle sequoia]

Anyone tryna check da rest of the quiz ❤️‍🔥❤️‍🔥❤️‍🔥

[gentle sequoia]

Smart

Thank you

[cursive condor]

Yep

All good

[gentle sequoia]

Yayyy thanks sm!! Ur fast wow

That took me forever to do

U guys are actually amazing thanks sm have an amazing day all

Thank you!!!

.close

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[raven mauve]

can i please get help guys, i honestly don’t know where to start

i know the tp for one graph is (2,1)

[lime ether]

if (x - k) is a factor of a polynomial then k is a root

[raven mauve]

do i just sub in one of the x intercepts

so either 0 or 4??

[lime ether]

start with the third one

[raven mauve]

hm

[lime ether]

what are the roots of the third parabola

[raven mauve]

how do you i know which graph is which??

[lime ether]

^

[lime ether]

^

[raven mauve]

3

and b

[lime ether]

nope

if you let x = 3 you get (3 + b)(3 + 3)

which is zero if b = -3

so no

try again

[raven mauve]

hmmm

im not to sure

oh its 1

[lime ether]

what

oh you mean b

[raven mauve]

is it not 1??

[lime ether]

b does equal 1

[raven mauve]

i just thought since the other x intercept = 1

[lime ether]

and you were correct to think that

oh wait it’s + b i’m bugging lmao

b is not 1

(x + b) = (x - (-b))

the root is 1 so -b = 1

[raven mauve]

uhhhhh

wait

im confuse

d

[lime ether]

if b was 1 then the factor would be (x + 1)

[raven mauve]

shouldn’t it be (x+1)(x+3)

[lime ether]

x = 1 is not a root

if x = 1 then youd get (1 + 1)(1 + 3)

that is not zero

b = -1

x + b = x - 1

now x = 1 is a root

[raven mauve]

oh i see

ok

what do we do next’

[lime ether]

now do the second one

what is the vertex of the second one

you said it already

(2, 1)

now to find a judt plug in any point on the graph

like (0,0)

0 = a(0-2)^2 + 1

solve for a

then do the same thing for the first one to find c

make sense?

[raven mauve]

so a =-4

c = -1

cause there’s where the y intercept is

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[lunar grove]

Can someone help me

[lunar grove]

.

With queation 7

Thars the solution but i dont understand why tjey can choose any value for x

[rugged cypress]

Hello am I right to think that a possion distribution essentially plots the same probabilities as a binomial would , for example a binomial case is just the proabilities of X number of success occuring over n intervals lets 60 seconds,

and the possion basicallly sees it as the same thing aka the probabilities of X number of success occuring in a minute but you dont need to know abt the number of intervals or p etc you just need to know the average

[lunar grove]

And then solve for y and z

[rugged cypress]

ah edexcel

[lunar grove]

Bros waffling

[rugged cypress]

just say you lack the intellect to decipher such a unique composition of words

[lunar grove]

U know the answer to my q?

[rugged cypress]

nah bro im asking a question myself

[lunar grove]

Is it alevel or harder

[rugged cypress]

its alevel fm stats

[lunar grove]

Oh wait sorry i didnf read it

I thought uwas tryna answer my q w a poisson distribution

[rugged cypress]

nah 😂

[lunar grove]

Nah i dont thonk its right

Poisson approximation only works when p is small and n is large

[rugged cypress]

yeah but all possions are the limiting approx of a binomial

[lunar grove]

They are derived from each other but poisson is the infinity version of binomial

[rugged cypress]

yeah

[lunar grove]

But it is a approximation whvih is only valid when p is small n is large

[rugged cypress]

but that would mean they should essentially plot the same probabilities for X then

for when n is large

and p is small

[lunar grove]

Well yeah

[rugged cypress]

ok boss thank you

I always need validation

[lunar grove]

Take back what u saod about my intellect

Fs1 light work

[rugged cypress]

icl im getting by

[lunar grove]

Bro idk why u even need to question it

Like that

[rugged cypress]

retracted

[lunar grove]

It was simple bro

[rugged cypress]

I dont trust my intuition

[lunar grove]

Poisson is a approximation

The question you asked is not relevant to anu exam question

[rugged cypress]

yeah I know but thats not the point of learning

[lunar grove]

Btw u can approximate

Fair enough i understand what you mean but it was a weird q

[rugged cypress]

did we not establish this already?

[rugged cypress]

weird as in obvious?

[lunar grove]

Yes and no

It isnt obvious if you haven't seen the proof and just know whar a poisson distribution is

But it is at the same time if you know it

[full forum]

@lunar grove Has your question been resolved?

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[faint iron]

Why is the answer D? where does the implication symbol go to?

[faint iron]

like i get ~(q^r) is q and ~r but where does the => go

[sudden cargo]

What is the negation of an if-then statement?

if p then q

[faint iron]

if p then not q?

[trim leaf]

when is p then q false

[subtle hatch]

Do u know the negation of p implies q and de morgans theorem?

[faint iron]

its false when p but not q?

[trim leaf]

p and not q

[faint iron]

yeah

[trim leaf]

so that would be the negation

~(p then q) = p and not q

using that, what is ~(p then (q and r))

[whole lily]

billy boy

[trim leaf]

the real roy 🤯

[faint iron]

p and not (q and r)

?

Wait is not (p and q) become (not p or not q)?

[whole lily]

Yea de morgan's laws

[trim leaf]

yeah

[faint iron]

Oh

Where can I find demorgans law

[whole lily]

not (A or B) = (not A) and (not B)
not (A and B) = (not A) or (not B)

[faint iron]

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[modern sigil]

me again but I promise this is the last one

[modern sigil]

I have 0 idea how to prove that AB and AE are equal

none whatsoever

[lunar veldt]

Maybe by Chasles relation ?

[modern sigil]

all I know is that the answer should be able to be solved using this summary

[modern sigil]

no idea what that is

[lunar veldt]

$AC=AB+BC$

[glossy valve]

tm

[modern sigil]

don't think that's it

[twilit leaf]

funny thing is this isnt true

[lunar veldt]

i don’t think it would work mb

[twilit leaf]

there are situations in which two possible lengths of AB are possible

[sacred sparrow]

I mean we can't prove something false

[modern sigil]

do you think I will get away with it if I say "cannot be proven" or something like that?

[modern sigil]

yep idk what this is

[sacred sparrow]

suppose the point B were given

then there are two possible points E in the illustration

therefore AB = AE isn't strictly true

[modern sigil]

welp

[lunar veldt]

i think that’s why chasles doesn’t work lol

[modern sigil]

then I'll choose something else

[modern sigil]

yeah could be

what about this?

[twilit leaf]

HL

oh nvm

use sas

[modern sigil]

I am too tierd to make a "sass" joke

ok I will try ty

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[fierce roost]

can someone explaun how/why this is wrong?

[analog wraith]

did you solve it

[fierce roost]

yes

oh thats probably not what i was supposed to do huh

[craggy tapir]

,w 3cos(pi/15)*3sqrt(3)cos(14pi/15) - 3sin(pi/15)*3sqrt(3)sin(14pi/15)

[fierce roost]

huh...

you forgot the i

[analog wraith]

it's -9√3

[craggy tapir]

i know, i took a guess that you forgot the i

[fierce roost]

wait did i forget the i

no it cancels out

[glossy valve]

Results provided by WolframAlpha

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Requested by fungusdesu

[simple ridge]

it is better to show your work so that someone points out what you did wrong

[craggy tapir]

yeah, do show your work

[fierce roost]

yes sorry

[craggy tapir]

[simple ridge]

well you didnt do anything wrong to say sorry

[fierce roost]

yo!!

[analog wraith]

that's it?

[simple ridge]

so 9sqrt(3)(cos(π)+isin(π))?

[fierce roost]

yes

[analog wraith]

yes

[fierce roost]

yes

[simple ridge]

well then what is the value of cos(π) and sin(π)

[analog wraith]

[fierce roost]

it was cos(0pi) and sin(0pi) sorry

[analog wraith]

how did you get 0π ?

[simple ridge]

i see

[simple ridge]

[analog wraith]

cause I think
π/15 + 14π/15 = π

[fierce roost]

oh i now realize what i did wrong

i have no idea how that happened i had a brain fart sorry

[analog wraith]

don't apologise, it's ok

[craggy tapir]

canonically accurate an

[fierce roost]

fr 😭

okay i can do it from here sorry it was just a silly mistake

thank you so much!!!

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[high sable]

Just learnt sandwich theorem

Was wondering if I first need to manipulate it with algebra then get the inequalities

[umbral dome]

for most of these you just need the basic property of sin and cos

[high sable]

For cos its a constant oscillation between -1 and 1

When x = 0, cos is 1

And x^2 when you sub in it becomes 0

So I got 0 =< lim =< 1

But thats not right

[umbral dome]

don't think about substituting anything in

all you need to know is that -1 <= cos(anything) <= 1

[modern sigil]

could i get some help after this person?

[high sable]

How would I get the range

[high sable]

https://discord.com/channels/268882317391429632/488120190538743810

[modern sigil]

i tried man

[umbral dome]

please be patient and don't intrude on other's channels

so if you have a limit in the form
f(x) * cos(g(x))
then you already have
-f(x) <= f(x) * cos(g(x)) <= f(x)
which should be enough for you to do the squeeze theorem

[high sable]

Hmm

Can you actually do that

[umbral dome]

wdym?

[high sable]

Is that like a rule

[umbral dome]

it is just using the inequality
-1 <= cos(x) <= 1
and multiplying each side by whatever other function

[high sable]

OH

OHHHH

Srry this is my first question doing sandwiche thereom

Im a bit slow

Got 0

How would this work for b)

Since sinx has no limit when it approaches infinity

[umbral dome]

the same thing applies to sin(x) because it's also bounded between -1 and 1

[high sable]

Oh wait

Oh that makes sense

For d)

Do we take it as first 0 =< e^x^2 =< 0

[umbral dome]

that's not true

[high sable]

I remember in a lecture my uni said they dont say its infinity

[full forum]

@high sable Has your question been resolved?

[umbral dome]

you might think about how you could bound e^(-x^2)

[high sable]

It doesnt exist right

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[umbral dome]

wdym by that?

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[stuck elk]

whats the sandwhich theroem

[stuck elk]

/close

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[vivid berry]

for the dom of inverse of g I got all real numbers

[vivid berry]

ohh but it can’t equal 3

how do I write a domain that says it can equal anything but 3

[slender onyx]

u can just say x in R and x != 3

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[tall ibex]

how to apply wavy curve method properly here?

[tall ibex]

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[distant hull]

Guys can someone explain this to me? I know the question is simple i was going through my old notebooks and theres this question that i kept getting wrong the answer key was always different to my answer I must’ve tried like 5 times and each time i get the same answer i feel so dumb that i cant answer a grade 9 question

The answer key says its 1 2/3

I keep getting 1/30

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[distant hull]

<@&286206848099549185>

[distant hull]

Oh it hasnt been 15 mins sry

[graceful horizon]

wutchu want 😡

[distant hull]

that

[graceful horizon]

how old are you

/jk

[graceful horizon]

i assume you know what pemdas is right

[distant hull]

obviously

[distant hull]

17

can u just explain it yes im struggling with ts

[graceful horizon]

lol

make them all "improper"

[distant hull]

i did

[graceful horizon]

ok

[distant hull]

7/2 - 4/3 x 13/5

[graceful horizon]

now make them decimals 🤯

[distant hull]

why decimals if we can just solve them while theyre fractions

Wait

[graceful horizon]

because decimals are easy in a calculator

[distant hull]

I forgot to

Flip the divison

[graceful horizon]

ok

regular

[distant hull]

The recipricil

[graceful horizon]

Kfc

erm

kcf

keep

change

flip

[distant hull]

keep

change

flip

[graceful horizon]

✅

[distant hull]

i forgot to make it a reciprocal fuck im stupid

[undone vector]

How did u get this

[distant hull]

im stupid

can u close this channel so no one else sees this😔

[graceful horizon]

.close

😦

[undone vector]

If you truly desire you can type .close but it is ok to make mistakes. Even the best mathematicians screw up arithmetic all the time

[distant hull]

.close

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[distant hull]

I wjas LOOKING AT THE WRONG ANSWER KEY I DONT THINK IM STUPID ANYMORE

[graceful horizon]

🤓

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[graceful horizon]

🤨

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[distant hull]

🙂‍↔️

[graceful horizon]

+🧏🏻‍♂️

😦

[gritty flax]

<@&268886789983436800>

[distant hull]

hi

<@&268886789983436800>

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[torn jolt]

.close

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[torn jolt]

.reopen

[full forum]

✅

[torn jolt]

part two coming

[torn jolt]

ignore that floating 2

heeelp

[austere cove]

!original I cannot be entirely certain about what is written there? Can you show the original question?

[torn jolt]

??

[full forum]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[torn jolt]

look at the top

[torn jolt]

wear glasses

[torn jolt]

in the first pic

top line (:

[austere cove]

Same deal

[torn jolt]

k

[austere cove]

Your handwriting is somewhat difficult to read

[torn jolt]

wait

[austere cove]

Is it:

[
\frac{5x+1}{4} - \frac{2x - 1}{2} = x^2
]

[glossy valve]

OmnipotentEntity

[austere cove]

?

[torn jolt]

yep

see wasnt that bad

xd

[austere cove]

My dude, everyone is here helping solely because they enjoy it. It would behoove you to make it as painless as possible to help you.

Having to decipher your chicken scratch, and telling us to "get glasses" when we ask you to clarify isn't making anyone want to help you more.

Just... something to keep in mind

!show

[full forum]

Show your work, and if possible, explain where you are stuck.

[torn jolt]

ok

[austere cove]

And please rewrite it.

[torn jolt]

ok

[torn jolt]

look

[austere cove]

Thank you

[torn jolt]

yep

[austere cove]

Should be +4 there

[torn jolt]

okie

[austere cove]

Also minor notational gripe here, you are not multiplying by 2 and 4 but 2/2 and 4/4. You perform the calculations correctly, of course.

[torn jolt]

ok

ill do it again

[torn jolt]

anything else?

vory noice red

[austere cove]

There are other errors, yes, but they occur after your initial error, so they are not relevant

@torn jolt

If you correct the initial error, everything after changes.

[austere cove]

But it's here, if you are curious

[torn jolt]

sorry, dcord is muted

im lowkey so cnofused

@austere cove mommy

[torn jolt]

about the -( thnig

.close

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[torn jolt]

.reopen

[full forum]

✅

[torn jolt]

how much angles are in a dodecagon

like if u add them all up

ask ur mom

[austere cove]

!occupied @torn jolt

[full forum]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[austere cove]

Be polite please.

[torn jolt]

it is okay she is is not here gith now so i cannaot thank you for trying

its an ai

[austere cove]

@torn jolt pic ^ you forgot to multiply top and bottom by 8, only did the bottom.

[torn jolt]

what is ai?

im polite

[torn jolt]

ure right

that obesity is

.close

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[silent yacht]

i dont understand when and when not i am supposed to add 180 degrees to the angle someone help. like for part i for example, i got theta = -30, but then in the answers they added 180 degrees to it why?

[silent yacht]

smn help me bru pls

hello?

[void nova]

Draw the number in the Argand complex plane

And remember that the range of the function tan^-1 is (-π/2, π/2)

[violet haven]

so you need to add 180 whenever the number is in quadrant II or III

[silent yacht]

so then why when figuring out theta for this

which is tan inverse of (sqrt3 / 1)

which equals to 60

[silent yacht]

the answers have subtracted 180 from it to make it -120

[violet haven]

well they dint need to do that if u took 240 also it will be the same

you get one soln as 2^(1/3)cis(80) if u took 240

u can write the 2 others using that

cis(240) = cis(-180) = cis(-480)

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[snow mural]

Please help

[snow mural]

How do I do last question

I forgot

[void nova]

What's the task?

[snow mural]

Find a formula of each sequence

[void nova]

I would see it in this way:
3 = 1³ + 2
12 = 2³ + 4
35 = 3³ + 8
80 = 4³ + 16
...

Therefore the next would be 5³ + 32, which is 157

And I'll let you find the general formula

[snow mural]

Thanks

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@snow mural Has your question been resolved?

[snow mural]

This one question 2

I mean 12

Idk if I should do lcm or hcf

Nvm I got the answer

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[full forum]

@crisp turtle Has your question been resolved?

[crisp turtle]

<@&286206848099549185>

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[rigid glen]

Currently on systems, I just solved this system and went on Photomath to check my answers it found x=8 y=2
I found that y=-1.2
x=6.4
And I can't seem to find my mistake can anyone help?

[onyx glen]

,rccw

[rigid glen]

so?

is there any mistake, if so where?

[brazen stirrup]

@rigid glen Hello! I can take a look

[rigid glen]

thanks!

[brazen stirrup]

@rigid glen Mistake spotted!

Oops

[rigid glen]

oh right

[rigid glen]

would have never noticed

[brazen stirrup]

Happens to everyone 😅

[rigid glen]

thank you, appreaciate it!

[brazen stirrup]

Yw

[rigid glen]

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[woven tusk]

how do i differentiate $4*2^t +3$

[glossy valve]

taf ☆

[alpine flower]

$\frac{d}{dx} a^t = a^t \cdot ln(a)$

[glossy valve]

clair //

[onyx glen]

\ln

[woven tusk]

oh i hate that 😭

thank you :]

.cose

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.reopen

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✅

[woven tusk]

how do i differentiate x

thats all i need

[onyx glen]

use this + the chain rule

[woven tusk]

i dont really get uhhh

differentiating 2^-t

wouldnt it be

uhh

(2^-t)(ln(2))

[onyx glen]

that times -1

[woven tusk]

OH WHY?

caps

[hot herald]

chain rule, * derivative of -t

[woven tusk]

.CLOSE

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[torn jolt]

Anyone is able to know where is the mistake? I am stucked since 5 hours on here

[flint hull]

advise going on the comp sci or some science discord for this, unless someone here knows it

[torn jolt]

what is comp sci?

[flint hull]

computer science

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[normal spoke]

y' = xy^3-xy

[lime ether]

what’s the problem

[normal spoke]

i got to integral(1/(y^3-y)) = 1/2x^2+c

[lime ether]

this is separable sir

[normal spoke]

but I don't know how to get the integral(1/(y^3-y))

[leaden ermine]

partial frac dec

[normal spoke]

aha

thank you

[lime ether]

y(y-1)(y+1)

[normal spoke]

thank you guys

completely escaped my mind

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[forest snow]

help

[void nova]

!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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[forest snow]

2

[void nova]

Then send what you've done so far

[forest snow]

I've been solving with the help of a I've been solving with the help of an app Since in videos there was not what I needed

[onyx glen]

immediate major screwup over here

the 3/5 x became just 3/5

oh nevermind it is just a typo and you recovered from it

[forest snow]

I have a whole questionnaire to solve and I really don't understand at all I have a whole questionnaire to solve and I really don't understand at all, YouTube videos don't have what I need haha.

[onyx glen]

how come part of your message keeps getting duplicated

[forest snow]

I was using an app to try to solve I was using an app to try to solve it by guiding myself

[forest snow]

I've guided myself so I don't know if I did anything wrong

[dark flume]

what is the goal when we have a problem like this?

[onyx glen]

well in your blind copying from the app you missed the x

which is kind of worrying that you've done that a second time in this solution alone

[forest snow]

Can you help me solve it from the beginning?

[onyx glen]

ok but let me feel around for some of your existing knowledge first

so that we can take this one step at a time without being overwhelmed

[dark flume]

yea

[lunar grove]

You collate all x terms and constants on each side

[onyx glen]

@dark flume i think it's better if only one of us does the talking here

[lunar grove]

Solve for x

And voila

[onyx glen]

@lunar grove same applies to you

[dark flume]

yea thats alright 🫡

[onyx glen]

@forest snow can you send the entire questionnaire? i want to see if there's any problems in there of the type that i'm looking for

(and if not, i'll just make up some new ones)

[forest snow]

I have a questionnaire with 46 different exercises to solve haha

[onyx glen]

yeah i want to see that

just the exercises

so we can look at some of them in more detail if they have what i'm looking for

[onyx glen]

right ok unfortunately it doesnt

that's ok, i'll just make up some new ones

wanna strip away the layers of complexity one by one until we have a solid ground to work on

so let's look at the following equation:

5x - 18 = 3x + 2

do you think you can solve this by yourself?

[forest snow]

honestly no.

[onyx glen]

that's alright.

[forest snow]

I never understand math and it is usually difficult for me to learn it.

[onyx glen]

well thats what im here for innit

let's go back one more level of complexity

[forest snow]

wait

I think I understand something

[onyx glen]

i'd like you not to use photomath for any of these btw

put the app down cause we're trying to stretch your mathematical muscles.

[forest snow]

I won't do it

[onyx glen]

ok

[onyx glen]

you want to try your hand at 5x-18 = 3x+2?

[forest snow]

If I'm not mistaken, I should change the location of the x's and the numbers that don't have one, right?

[onyx glen]

mmm

i don't like phrasing it this way at all.

but if you think you can do it, write out the solution and show it to me.

[forest snow]

I'll try

I want to believe that I did well.

[onyx glen]

,rccw

[onyx glen]

ok right

yeah that's good

just to spell something out for what you did:

in step 1 you subtracted 3x and added 18 to both sides

the purpose of doing that was to get all of the x terms on one side and all of the non-x terms on the other, and to then clean up in each

alright, wonderful.

[forest snow]

This is how they taught me and how I remember it haha

[onyx glen]

the process is OK for simple stuff like this

but if you try to speak about "moving" stuff around for more complicated equations

it opens up many ways to mess up

which is why i think it's not good

but anyway.

so going back to the equation in 1a):
$$\frac{3}{2}x + 8 = \frac{3}{5}x - 1$$ structurally, this equation is pretty damn similar to the one i had you do just now. the difference is that some of the numbers are now fractions, yeah?

[glossy valve]

Ann

[onyx glen]

(don't do anything with it yet!)

(just want you to acknowledge this structural similarity)

[forest snow]

understand

[onyx glen]

ok right

so one thing i like to do

is to do a little thing at the beginning to make all the numbers into not fractions

simply bc fractions are harder to deal with than whole numbers

so it's just a matter of making your life easier

the way to do this is to multiply both sides by something that'll cancel out all denominators that are present.

in this case, the denominators (bottom numbers in the fractions) are 2 and 5, so the simplest choice for what to multiply by is their product, 10. which gives us: $$10 \paren{\frac{3}{2}x + 8} = 10\paren{\frac{3}{5}x - 1}$$ (we'll simplify/clean up stuff in the next step)

[glossy valve]

Ann

[onyx glen]

does this make sense to you thus far?

[forest snow]

yes, something like that

[onyx glen]

right

so the way this simplifies is that we expand the brackets (carefully, and don't forget to multiply the tens by every term in there)

which gives us:

15x + 80 = 6x - 10

does that make sense?

[forest snow]

2 and 5 don't count anymore?

[onyx glen]

wdym "don't count"?

$10 \cdot \frac{3}{2}$ simplifies down into $15$, and $10 \cdot \frac{3}{5}$ simplifies down to $6$.

[glossy valve]

Ann

[onyx glen]

this was our (well, my) idea all along

[forest snow]

I understand the previous one more than the one you just showed me

[onyx glen]

ok let me try writing it out in more detail

[forest snow]

I mean that since they are what you multiply to get the "10" they are no longer there.

[onyx glen]

$10 \paren{\frac{3}{2}x + 8} = 10\paren{\frac{3}{5}x - 1} \ \ 10 \cdot \frac32 x + 10 \cdot 8 = 10 \cdot \frac35x - 10 \cdot 1 \ \ 15x + 80 = 6x - 10$

[glossy valve]

Ann

[onyx glen]

that make sense?

like you understand 10*3/2 = 15 right?

[forest snow]

I already understood hahaha

[onyx glen]

yeah ok

so from here on out, it should be familiar territory for you

do you want to continue this one to completion or can we move on to 1b)?

oh this was 1b lol. i guess 1c is next

[forest snow]

until the end

[onyx glen]

ok sure

go ahead and solve 15x+80 = 6x-10 now

[forest snow]

There are actually 4, but I have omitted one because I have been able to solve it.

[forest snow]

I want to believe I did it right

[onyx glen]

-10 - 80 = -90 not +90

[forest snow]

I understand that numbers with equal signs are added together.

[onyx glen]

if you owe 10 euro to one person and 80 euro to another that doesn't somehow become a profit of 90 euro, it means you are 90 euro in debt :PPP

i am saying that you forgot the minus sign

[forest snow]

AAAAAAAAAAAAAAAAAAAA

[void nova]

And you have to keep the same sign

[forest snow]

Sorry, I tend to forget the signs haha

[void nova]

Try not to 😬

[onyx glen]

this was the only thing you did wrong tho

shall we move on to this one then?

[forest snow]

yeah

[onyx glen]

ok

don't do any algebra to it yet

and tell me only this:

what denominators do you see?

[forest snow]

3

only 1

[onyx glen]

indeed

so by what should we multiply both sides to clear this 3 denominator?

[forest snow]

uhhm.. to have only integers?

[onyx glen]

that's our goal, yes

but im asking you for how to do it

in the same way that i showed you for 1b)

in that one i multiplied both sides by 10

in this one, we multiply both sides by...?

[forest snow]

3

[onyx glen]

right

do it

and then either stop there, or if you feel like you can continue, then continue and show me your completed work

[forest snow]

I will do as much as I understand

[onyx glen]

ok

well, show me how far you get.

i'll be there to catch you if you fall

[forest snow]

Ok.

I've finished it

I've finished it, I think it's fine.

[onyx glen]

uh oh

[forest snow]

and..?

[onyx glen]

ok so here on the right everything's fine

but on the left you messed up

pretty severely at that

the correct simplification in this case is actually just 4(x+1)

you've got 3 * 4/3 * (x+1) and the 3 * 4/3 combine into 4, that's it.

there was no need (and in fact it would be wrong) to multiply the 4/3 by 3 and the (x+1) by another 3

(not to mention that 3*4/3 is 4, not 3)

do you understand?

[forest snow]

In fact I realized that I could have simply eliminated the 2 "3" that were there.

[onyx glen]

yes

my point exactly

so your third line will need to read:

4(x+1) = 6x - 3

erase everything at and after that line and redo it

[forest snow]

I'll correct it now

Now it's okay, right?

[onyx glen]

4x - 6x = -2x

not 2x as you wrote

another sign error

aside from this, yes it's ok

[forest snow]

I forget the signs 😞

[onyx glen]

yeah you gotta work on that

you'll get -2x = -7 and from there x = +7/2

[forest snow]

+7?

[onyx glen]

i am saying +7/2 just to emphasize that it's positive

as opposed to the -7/2 which you got

[forest snow]

okok

[onyx glen]

so, on to this one?

[forest snow]

yea

[onyx glen]

maybe you already see what to do -- but if you don't, that's ok.

[forest snow]

uhh..

do you have to multiply by 2x?

[onyx glen]

why 2x?

[forest snow]

nononono

[onyx glen]

x itself will do just fine, won't it?

[forest snow]

wait

uhh..

I'm already confused

[onyx glen]

you had the right idea still

we're gonna need to clear the denominators again

the only one we've got is x (it appears twice, but that doesn't really change things)

so for our first step we just multiply by x like before

[forest snow]

This time I need you to explain everything to me haha

[onyx glen]

well

ok let's just do it the same as before and then i'll tell you about the extra stuff that will happen

so our equation is $\frac{1}{x} + 1 = \frac{3}{x} - 3$

[glossy valve]

Ann

[forest snow]

understand

[onyx glen]

we multiply both sides by $x$ (not caring that it's a letter and not just a number anymore, really!) and get: $$x \paren{\frac{1}{x} + 1} = x\paren{\frac{3}{x} - 3}$$

[glossy valve]

Ann

[onyx glen]

and then we simplify, as before, and get:

$x \cdot \frac{1}{x} + x \cdot 1 = x \cdot \frac{3}{x} - x \cdot 3 \ \ 1 + x = 3 - 3x$

[glossy valve]

Ann

[forest snow]

Ok, I understand.

I will try to solve it

[onyx glen]

uh oh sign bullshit again

fourth line should be x + 3x = 3 - 1

[forest snow]

and..?

[void nova]

Simplify the fraction 2/4

[forest snow]

I imagine that this is already fine.

[void nova]

You simplified correctly, so why did you write 2 instead of 1/2 ??

You should pay WAY MORE attention to the numeric calculation (see the signs thing and here the fractions)

[forest snow]

the one is understood, so we normally don't put it.

[void nova]

Therefore $$\frac{1}{5} = 5\ ??$

[glossy valve]

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

[forest snow]

uhm.. my teacher teaches it like this, in the result whenever it is simplified and there is a "1" that is not written.

[void nova]

Are you sure about this?

Revise your notes, I would say 🤔

[forest snow]

yep

Anyway, I will continue studying, I will come back if I don't manage to understand.

@onyx glen thanks for the help.

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[onyx glen]

np

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[serene hazel]

what have you tried?

[forest snow]

nothing

I have tried looking for tutorials but I have not found anything similar.

[serene hazel]

have you tried anything like this before

this is just algebraic equation

[forest snow]

I don't understand how to solve it

[serene hazel]

start multiplying them by 3

for both sides, what do you get?

[forest snow]

I don't understand.

You mean multiplying 3 with everything, right?

[serene hazel]

yes but just keep 2x+1 as it is

just make it as x(2x+1)

just making sure cause my vision is so bad, is this 1 or 4?

[forest snow]

4

[serene hazel]

ok then replace the one as 4

x(2x+4)

what happens if you multiple 6 by 3 and 8 by 3? we are trying to get rid of 3 in the denominator

[forest snow]

Like this?

[serene hazel]

not quite

ill make it for you gimme a sec

[serene hazel]

does this makes sense?

@forest snow

once you do this, your step is expand and then you'll get a quadratic equation

also dont forget make everything in one side and equal to 0 so then you can use quadratic formula if its not factorable

,tex .quadratic formula

[glossy valve]

KωΚιχ

[serene hazel]

btw this is quadratic formula if you never seen it before

hope this helps i gtg for iftar

[full forum]

@forest snow Has your question been resolved?

[abstract zodiac]

@forest snow I can help

[cold agate]

can u just make it one equation

like get it in the form ax^2 + bx + c = 0

[cold agate]

what would've been faster is to subtract six both sides first

[serene hazel]

true but you could do this when expanding

just get rid of fraction

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[median drum]

Hi I got these right but I don’t understand why 2 is correct and 6 is incorrect

[graceful horizon]

i dont either

[median drum]

:(( can anyone else help?

[abstract zodiac]

Not me

[fervent owl]

if you can't help, can you at least not spam useless text?

i've checked your recent message history and you seem to have a habit of doing that, please don't troll here

[fervent owl]

whilst it is true that sum 1/nln(n) diverges, their reasoning is not correct

effectively, you can think of it as "clearly either sum 1/nln(n) converges or is infinity"

now 1/nln(n) < 2/n

and summing over 2/n = infinity

therefore summing over 1/nln(n) < infinity

which doesn't tell you that it's also infinite

[hidden harbor]

that 2/n diverges doesnt tell you anything when comparing it to a series that is smaller than it

[median drum]

I’m confused about when I can use the comparison test then

[hidden harbor]

for example, 1/n^3 (example 2) is lower than 2/n for all n>1; 2/n diverges. But that does not give you information on 1/n^3

because it basically only tells you "it's smaller than this particular order of infinity"

[fervent owl]

i mean if you stop thinking about them as weird infinite sums and think about them as normal numbers

i tell you i have some number n

if i wanna show you that it's bigger than 5 say

i need to show n > 5

if i tell you "well n < 10" that doesn't tell you anything in terms of its size compared with 5

now it's something similarish here

we want to know if the last sum (1/nlogn) is infinite or finite

but if i tell you that it's "less than infinity" then that doesn't tell you that 1/nlogn is also "infinity"

(this isn't rigorous but this should be ur intuition for how bounds work)

[median drum]

Ohhh okay I understand now thank you

I really appreciate it😊 both of you!!

[fervent owl]

nw!

[median drum]

sorry one more thing, can someone explain number 2 to me?

because I don’t understand why arctan(n)/n^3 is < pi/2n^3 for all n>1

[hidden harbor]

okay, ignore the /n^3 for now

arctan(x) moves between -pi/2 and pi/2

so arctan(x) < pi/2, no matter what x is

which means that if you divide both sides by n^3 (positive) you get what you have

[median drum]

Ohhhh I had my calculator in degree mode while looking at n large for both and that’s why I was getting off numbers!! whoops rookie mistake thank you for explaining

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[midnight lotus]

am i able to get quick chem 12 help

[midnight lotus]

is a balanced reaction the same as a balanced equilibrium reaction?

[sweet sky]

depends on the reaction

some proceed to completion, others proceed to an equilibrium

so you only write the double arrow if the reaction doesnt basically proceed to completion, and that indicates a balanced equilibrium reaction

[midnight lotus]

how to write balanced reaction of salt dissolving in water with no excess solid

it would be just solid salt and then forward arrow then both ions right?

[sweet sky]

depends how soluble the salt is

typically that reaction proceeds to equilibrium defined by the salt's Ksp so you would use the double arrow

instead of the forward arrow

ex: Ca(OH)2 (s) <-> Ca2+ (aq) + 2 OH- (aq)

[midnight lotus]

but it is not at equilibrium

[sweet sky]

it is

as long as you dissolve enough solid the solution will become saturated

and the concentrations of the ions at equilibrium will be defined by the Ksp

you can just show the problem if ur still confused

[midnight lotus]

but for it to be at equilibrium i thought there has to be solid present

[sweet sky]

solid is forming at the same rate the ions are when the reaction is at equilibrium

so there is no net formation of solid or ions at equilibrium

but both are being formed

[midnight lotus]

yes so not at equilibrium if there is no solid (if the solution is saturated) is that right?

[sweet sky]

a saturated solution is at equilibrium

[midnight lotus]

ya but if it is not saturated

then only one arrow right

forward arrow?

[sweet sky]

not quite

even if the solution is not saturated, the reaction proceeds in both directions

but the rate of the forward reaction (ion formation) will be greater than the rate of the reverse reaction

what's special about a saturated solution is that the ion concentrations stay constant

whereas in an unsaturated solution, the ion concentrations are changing due to unequal reaction rates

[midnight lotus]

so if my teacher said to add salt but not make it saturated so there is no solid undissolved, i would include both arrows?

[sweet sky]

yes, both reactions are happening

the forward reaction is just happening faster

[midnight lotus]

but no solid is being formed

doesnt the reaction go to completion

also another question: my lab says to look for ksp value in data booklet for NaCl and compare to the value i calculte and I cant find it. do you know why?

[sweet sky]

again, solid is being formed. it's just that the rate at which solid is being formed is lower than the rate at which it is being consumed

NaCl is very soluble in water, so sometimes they dont list the Ksp for those

[midnight lotus]

oh

because my lab wants me to compare to the ksp value in the data booklet and its nowhere to be found in the data bookle

booklet

[sweet sky]

Ksp usually isn't useful for a salt that is as soluble as NaCl is in water

you just assume it's all ions in solution

[midnight lotus]

thas not true tho like according to the lab activuty

if u press add salt there is a point reached quite quickly where there is excess

i calculated ksp to be

idk if that is true and dont know what to do for the part that wants me to compare the value of this to the data bookle

[sweet sky]

i mean if it asks you to compare to the value listed in the data booklet and there isnt one, idk what you can do

but like i said, highly soluble salts dont typically have a Ksp listed

may i ask how you calculated the Ksp of NaCl?

[midnight lotus]

wait it is possible to get a value?

in my actvity the max ions that dissolved were 180 of na and 180 of cl

in a small amount of water

[sweet sky]

how do you know how many ions dissolved

[midnight lotus]

cause it has a counter

of dissolved

[sweet sky]

dont think im understanding what you did here

if you put some NaCl in some water

how are you "counting" how much dissolved

[midnight lotus]

can i just do 1/6.022x10^23 and this times 181/5.0x10^-23

[sweet sky]

oh it's a simulation smh

[midnight lotus]

but im not sure how exactly the 1/6.022x1023 is valid here

doesnt that mean 1 mol of water can dissolve that many ions?

of Na

[sweet sky]

182 ion Na+ (mol Na+/(6.022 * 10^23 Na+ ion)(1/(5.00 * 10^-23 L)) will give you equilibrium concentration of Na+ in M

just add a lot of salt and see what the max values you can get for dissolved ion counts are

[midnight lotus]

yes but what does that 1/6.022x1023 mean

i get like 36 for ksp btw

[sweet sky]

number of Na+ ions in one mole of Na+

[midnight lotus]

number of Na ions in one mole of Na?

wdym

[sweet sky]

6.022*10^23 is the number of Na+ ions in one mole of Na+

one mole is 6.022*10^23 things

[midnight lotus]

o so if it was 2na then it would double?

i think i get it

[sweet sky]

i dont know what this means

2 Na+ ions is 2/(6.022 * 10^23) mol Na+
1 Na+ ion is 1/(6.022 * 10^23) mol Na+

[midnight lotus]

do you tutor chemistry by chance?

is this the right ksp for this. this is my data booklet but i think googles value is accurate

[sweet sky]

id just do what it says in your book

i dont know the ksp value for that particular salt

[sweet sky]

no, but ive taken a few chemistry classes

[full forum]

@midnight lotus Has your question been resolved?

[midnight lotus]

the thing is i calculated it to be the value that google says

[full forum]

@midnight lotus Has your question been resolved?

[full forum]

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[cold island]

calculating the pearson correlation coefficient of the following data

[balmy karma]

thats what desmos is for

[cold island]

?

you are meant to do it on paper step by step

[balmy karma]

oh

[cold island]

ya bro

[balmy karma]

the average of x is 3.5, y is 4.833333 or 29/6.

i think your formula is confusing in the numerator, so ill use the more accepted definition

[cold island]

no its one answer, this is for stats if you dont get it its ok cuz ur confusing me further, thanks

[balmy karma]

hol on im doing math'

the numerator is -20.5

[cold island]

did you square x and y scores

[balmy karma]

you dont square the numerator

[cold island]

the x and y scores provided above

[balmy karma]

yeah no you still dont

[cold island]

you are supposed to take each x score and y score and square them

[balmy karma]

you dont square anything I dont think

except for the bottom

[cold island]

you do for this problem you are solving it wrong

[balmy karma]

we meet need helpers

cause I dont think u square

or I could grab someone

[cold island]

look

[balmy karma]

yeah but you dont need to plug that in at all.

[cold island]

to the formula yes you do

this is pearson correlation

:(

[balmy karma]

i am using this formula, am I using the right one? cause thats what I see

[cold island]

no what the heck is that, im using the one that is provided

[balmy karma]

yeah but this one is easier for me

im gonna go grab someone

[cold island]

ok thank you