help-23

[weary osprey]

Since it’s a degree of 3, it must have 3 roots, so if you make a graph crosses the x-axis then you have a real solution

The rest two will be imaginary

[merry vessel]

oh that makes sense

thx

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[wraith spruce]

Hi, can anyone help me with this question:

The 50th term of a sequence is 102 with a difference of 2. Find the first term.

[neat kiln]

Can you identify the type of sequence? Arithmetic or geometric?

[safe radish]

@wraith spruce Has your question been resolved?

[wraith spruce]

Arithmetic

[proper crypt]

Okay, do you know the formula for a general term in an arithmetic sequence?

[wraith spruce]

tn= a + (n - 1) x d

[proper crypt]

a is the first term in the sequence, and d is the difference.

[wraith spruce]

Yes

[proper crypt]

You know that t_50 = 102, and d = 2. Try to use those to construct an equation and solve for a

[wraith spruce]

Ok thanks ☺️

[safe radish]

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[carmine saffron]

Hi, I'm reviewing for a test and need some help understanding on some problem example.

First one is

[carmine saffron]

I did -15n^21 but it was wrong

I also did -15^3 n^21

[thin bridge]

do you have access to a list of exponent laws?

[carmine saffron]

I know you have to multiply

[thin bridge]

too vague

[carmine saffron]

but maybe the negative sign changes things

[thin bridge]

and doesnt answer my question

[carmine saffron]

I can google it

[foggy salmon]

LOL

yes u can

[thin bridge]

that would be a good idea, you should probably already have one in your notes

[carmine saffron]

the rules are vague to begin with anyway lol

[thin bridge]

not really

[foggy salmon]

WHAT LOL

[thin bridge]

what rules are you looking at

[carmine saffron]

most look like this

[thin bridge]

what do you think is vague about them

[carmine saffron]

when they stack rules

[thin bridge]

wdym

[carmine saffron]

anyway

[foggy salmon]

yes

[thin bridge]

anyway, which rule listed do you think would be most applicable to your question

[dusk vapor]

i thnk the last one

[carmine saffron]

I know this is the power of product rule..

[dusk vapor]

🐓

[thin bridge]

power of product yes

[carmine saffron]

if you read after my question

I posted my thoughts

oh wait

[neat kiln]

You did 5*3 instead of 5^3

[thin bridge]

it did not look like you were applying the law properly and/or doing something else

and in your second attempt you did (5*3)^3

[carmine saffron]

yeah looks like I'm not suppose to multiply the base

let me cube that

thanks for pointing that out

I'm still rusty

.close

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[lean otter]

i used an graphing calc and got these points

[lean otter]

i checked for the local min and max

[safe radish]

@lean otter Has your question been resolved?

[thin bridge]

they want 3dp, you only gave 2

[lean otter]

oh i see

my calculator only goes up to 2

ok desmos got me,ty!

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[slow raptor]

could sm1 help me

i dont know how to take the dervative of this function

using limit definition

[compact ferry]

$\sqrt{x} = x^{\frac{1}{2}}$

[flat frigate]

Gijs

[compact ferry]

$\frac{1}{\sqrt{x}} = \frac{1}{x^{\frac{1}{2}}}$

[flat frigate]

Gijs

[slow raptor]

or

we can do

x^-1/2

[compact ferry]

$\frac{1}{\sqrt{x}} = \frac{1}{x^{\frac{1}{2}}} = x^\frac{-1}{2}$

[flat frigate]

Gijs

[slow raptor]

yea

now we plug that

into f(x+h)-f(x)/h

right

[compact ferry]

arent you allowed to just not do that

like sure you can do it with the definition

[slow raptor]

we can use the dervative definition but

i wnat to get more used to the limit definition

[green lichen]

but why

[green lichen]

oh

[compact ferry]

yeah sure go for it

[slow raptor]

I just want to see how to do it both ways

[green lichen]

okay

[slow raptor]

yeah we are allowed to use any way except if the question asks only using limit way

so thats why

[slow raptor]

so

would the equation be

this

[compact ferry]

yes with the limit of h going to 0

[slow raptor]

yea im just showing my work

i got stuck here

[compact ferry]

you can simplify

[slow raptor]

i assume we have to multiply each side by 1?

to simply further

[slow raptor]

how so

[compact ferry]

just try stuff youll get there

[slow raptor]

i did 😭

ive been stuck on this question since yesterday

[compact ferry]

oh

[slow raptor]

do we factor

the root x?

[compact ferry]

factor?

[slow raptor]

nvm

i multiplied each side

[compact ferry]

also

$\frac{\frac{a}{b}}{c} = \frac{a}{bc}$

[flat frigate]

Gijs

[compact ferry]

might be helpul

[slow raptor]

is this correct?

[compact ferry]

yeah its correct

idk where to go from here though

but i have to go

[slow raptor]

conjucate ?

[slow raptor]

are u able to help?

[queen parcel]

That is very difficult to see

[slow raptor]

i can rewrite it

[queen parcel]

Yes, do that, and lmk what you're trying to do with it

[queen parcel]

Find f'(x) using the limit definition?

[slow raptor]

this is the original function and we are trying to get the dervative

using limit

yes

[queen parcel]

I see

[slow raptor]

i got to this part and idk what to do

[queen parcel]

Okay, so have you found f(x + h), f(x), and subtract one from the other?

[slow raptor]

yes

[slow raptor]

.

[queen parcel]

Here you'd rationalize the numerator by multiply by the conjugate

Ideally show all of your steps in one photo on a piece of paper - easier to keep track that way

[queen parcel]

Looks good so far, I think the (x + h) in the denominator should be under a √

[slow raptor]

oh yea it shoukd

i forgot to add it

[slow raptor]

what do from here

multiply it out?

[queen parcel]

Now you can let h go to 0, because you now have no 0 in the denominator

[queen parcel]

You can check your derivative by using derivative calculator (it'll be the first result that pops up when you google it)

[queen parcel]

Close, you have √x √x • (√x + √x) in the denominator

[slow raptor]

oh

so this

wait no

[slow raptor]

this is correct?

[queen parcel]

Try dealing with what's in the parentheses first

√x • √x • (√x + √x)

[slow raptor]

ok so 2rootx

[queen parcel]

Correct 🙂

√x • √x • 2√x

[slow raptor]

x*2rootx

[slow raptor]

?

[queen parcel]

yup

Now you just have to write the steps together

[slow raptor]

then 2xrootx

[queen parcel]

I think you missed a negative sign somewhere in there

The derivative of 1/sqrt(x) = ( -1 )/ (2 x^(3/2))

[slow raptor]

so

like this

[slow raptor]

?

[queen parcel]

Well, you missed a - sign, probably before what you have

Start by writing down the initial problem and showing your work every step of the way

[safe radish]

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[safe radish]

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[wide wolf]

I did not understand how to solve these quastions

[foggy salmon]

which first

[wide wolf]

Especially these cube problems, the part that I do not understand that which length I give d and which part of the cube I express

Maybe my problem is not math but english😄

[wide wolf]

start with 10

[foggy salmon]

try drawing a diagram

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[safe radish]

@wide wolf Has your question been resolved?

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[safe radish]

@lean otter Has your question been resolved?

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[plucky moon]

A function f follows the dependence 3⋅y+5⋅x , and the results obtained are x=7±1, y=9±1. Calculate the error estimate Δf for f using the total differential or, if possible, the relative error. Round your answer to the nearest integer.

How would I go about solving this?
I tried to look up examples on the internet but didnt find much about estimating the error

[plucky moon]

Δx=Δy=1 right?

and we got the function 3 * y+5 * x

But what is the actual formula for estimating the error

This is for my lab prep practise

But we havent went over how to calculate the error (Im taking a thermodynamics course)

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[halcyon carbon]

I’m struggling to understand why line 5 implies p divides 3 and line 7 implies q divides 2.

[halcyon carbon]

Original question

[thick sparrow]

Line 5 is easy. Take modulo 3 on the equation, and you will get $$2p^3 = 0 \mod 3$$

In this case, consider three cases
(1) p = 3k + 0
(2) p = 3k + 1
(3) p = 3k + 2

You will find only (1) can satisfy our derived equation for p.

[halcyon carbon]

You mean modulo 2 or 3?

[flat frigate]

jimmy1234

[thick sparrow]

Ohh should be mod 3.

[halcyon carbon]

Oh

Doesn’t that mean p is a multiple of 3?

Because if p is 1 then that doesn’t work

So p doesn’t divide 3 but rather a multiple of 3

Is this logic wrong?

[thick sparrow]

Guess so(?) You can try put back $p = \pm 1$ into the equation, I guess it won’t work.

[flat frigate]

jimmy1234

[halcyon carbon]

Yeah but then the statement p|3 is wrong meaning p can be any multiple of 3 (but not multiple of 6)

When I tried plugging in p=6n+3 and q=6n+_2 into the equation, I got that it’s congruent to 0 mod 6

But this means

Idk

I meant to say plugging in p = 3 mod 6 and q=+-2 mod 6 into the thing

[thick sparrow]

Ohh ok. From line 5, you can move terms around and single out 3. $$3 = \dfrac{-(p)(\cdots)}{q^3}$$

[flat frigate]

jimmy1234

[halcyon carbon]

Right

[thick sparrow]

Since gcd of p and q is 1, we should have $p$ and $\dfrac{(\cdots)}{q}$ as two separate integers.

[flat frigate]

jimmy1234

[thick sparrow]

And since $p$ clearly is a factor of 3, we can say $p$ divides 3.

[flat frigate]

jimmy1234

[halcyon carbon]

Sorry I’m not following from here

[thick sparrow]

You see from this expression, $p$ and $q^3$ cannot have common factor. It just means $p$ alone forms a factor of 3.

[flat frigate]

jimmy1234

[halcyon carbon]

Why can’t $\frac{(…)}{p^3}$ form a factor of 3?

[flat frigate]

Pure

[thick sparrow]

I should say, from $$3 = \dfrac{-(p)(\cdots)}{q^3}$$, by gcd-1 condition, $p$ and $\dfrac{(\cdots)}{q^3}$ both form an integer factor of 3.

[flat frigate]

jimmy1234

[halcyon carbon]

Yes

[thick sparrow]

But in line 5, we only concern $p$, so we only make statement about $p$ there.

[flat frigate]

jimmy1234

[halcyon carbon]

Ah so p is either $\pm 1, or \pm 3$

[flat frigate]

Pure

[halcyon carbon]

Got it

And I assume we can make the same argument for line 7?

[thick sparrow]

Yes

[halcyon carbon]

Ah wait how would we know that $\frac{(…)}{q^3}$ is an integer?

[flat frigate]

Pure

[thick sparrow]

Omg… Forget what i say…

Turns out I was over-complicating things. Just take modulo p on equation in line 5.

$$3q^3 = 0 \mod p$$

[flat frigate]

jimmy1234

[thick sparrow]

Since we have gcd btw p and q = 1, we must have $$3 = 0 \mod p$$.

[flat frigate]

jimmy1234

[thick sparrow]

That shd be way simpler that what i just try to deduce…..

[halcyon carbon]

Ahhhhh

That makes so much sense

Thanks @thick sparrow

Appreciate it.

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[safe radish]

@azure dome Has your question been resolved?

[pulsar pelican]

Well there is a 6/7 chance that the Bloon she picked didn't have the prize then she has a 1/6 chance assuming there is a prize that she picked it so you multiply both and you get with the chance

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[humble shore]

how could i express that x is defined in every number that is bigger than 2 and smaller or equel 4?
using ℝ symbol instead of Dom

[slate hedge]

so it's between 2 and 4 ?

[humble shore]

yes

[dense lynx]

With parantheses or what?

[slate hedge]

]2;4] ?

[humble shore]

and the 4 isincluded

[humble shore]

i mean like

one second

[dense lynx]

Or just use the >< thing

[humble shore]

i am going to try to explain myself

[slate hedge]

ℝ ∈ ]2:4]

idk

could work

[slate hedge]

please give more details about the function

[dense lynx]

2<x=<4, x in Real

[humble shore]

ok one second i am going to show you

this is the function and i want to say that the first piece is defined everywhere as long as its bigger than 0

[chrome flame]

Poopy

[humble shore]

using R symbole

[humble shore]

sorry?

[chrome flame]

What you wanna do

Is z

X5

/

Diameter

Square root 2/2

[humble shore]

what?

[chrome flame]

1

[dense lynx]

Yo, dont disturb other

[lean otter]

kek

[humble shore]

so

um

what's happening

well anyways

as i was saying

[lean otter]

where's the problem ?

[lean otter]

less than 0

[humble shore]

i whant to know how can i express that in the first piece of the function x is defined in every number as long as it's less than 0, yes sorry for that, using R symboel

NOT including 0

[lean otter]

x^2 +2 will always give a real value for real value of x less than or equal to 0

[humble shore]

yes, but is there a way to say it in a non textual way?

[lean otter]

since on squaring a real number

[humble shore]

like without words

[lean otter]

you will get a real number

and adding an integer to it

will give another real number

[lean otter]

well i don't know if there is

[humble shore]

oh

[dense lynx]

You dont have to always use symbol in math

Communication is key, as long as its understandable

[humble shore]

i hope my teacher thinks the same

thanks anyway

[lean otter]

ask your teacher

[humble shore]

i can't

[lean otter]

your teacher must have a done a similar problem in class too right

[humble shore]

yeah

oh now that I remember

yes you are right

thanks

[lean otter]

np

[humble shore]

.close

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[velvet cobalt]

Operations on functions

[velvet cobalt]

I just wanted to know if i did it correctly

f(x)= x/2x+1 g(x)=2x+1

[wind stream]

is the black dot supposed to denote multiplication?

[velvet cobalt]

Yes

[wind stream]

then you did everything correctly, just dont forget to include that x can not be equal to -1/2

also terrible notation for product of functions imo

[velvet cobalt]

Ohh alright

[pure glacier]

true that looks like composition

[velvet cobalt]

Isnt composition open?

Multiplication is closed

[wind stream]

it doesnt matter because people are going to mix them up, we are humans after all, so handwritings are not consistent

to deal with this, products are just denotes as (fg)(x)

[velvet cobalt]

Oh

[wind stream]

also the exact reason why fg is never referred to as compositions

[velvet cobalt]

Composition: f(x)= √4x+9 g(x)=x^2-3x

Also on this one should i square root them?

[wind stream]

everything looks correct

[velvet cobalt]

Oh alright

So thats my final answer?

[pure glacier]

thats (2x - 3)^2

so the sqr and sqrt cancel

[velvet cobalt]

Oh

Do i need to change the last part?

[pure glacier]

no

[cedar rover]

sqrt(x²) is |x|, so it's |2x - 3|, they don't cancel

[pure glacier]

its not necessary to take the absolute value in every context

[velvet cobalt]

I turned (x^2-3x) into (x-3x)^2

[wind stream]

it is

especially in the context where the argument is not strictly positive

[velvet cobalt]

This is correct right?

[wind stream]

like i said, yes

but if you want to further simplify, you can do it

[velvet cobalt]

Alrightt thanksss

Oh i can still simplify it?

.close

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[full lotus]

shouldnt this be (-1)^3+3 ?

[safe radish]

Please don't occupy multiple help channels.

@full lotus Has your question been resolved?

[safe radish]

@full lotus Has your question been resolved?

[safe radish]

@full lotus Has your question been resolved?

[peak estuary]

yes

not that it makes a difference

[safe radish]

@full lotus Has your question been resolved?

[safe radish]

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[lean otter]

Why is the answer 5 instead of 7

He said largest number

It should be 7

(I hate epsilon and delta)

[weak dirge]

the wording is confusing

$\delta = 7$ gives $x \in (6,20)$, and $\delta = 5$ gives $x\in (8,18)$ While $x<20$ is a valid solution, any $x<8$ is not

[flat frigate]

KurtDee

[lean otter]

What?

Where did u get (6,20)

And (8,18)

On what basis did u say that x<8

Is not a valid solution

[weak dirge]

$0<|x-13|< 7 \implies x \in (6,20)$

[flat frigate]

KurtDee

[weak dirge]

$8<x<20$ by your work

[flat frigate]

KurtDee

[safe radish]

@lean otter Has your question been resolved?

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[sweet kite]

Write the domain and range of the following relation: R = {(-3, 5), (-2, 5), (-1, 5), (0, 5), (1, 5), (2, 5)}
Draw the arrow diagrams to represent the relation: R = {(4, 10), (4, 13), (4, 16), (5, 13), (6, 16)}

[sweet kite]

.close

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[vocal gazelle]

Hello this is a combination question. I am very lost on how I would solve this question. If anybody could help, thank you!

[merry sleet]

lets call E the set of students that can play an instrument

and E(instruments) the set of students that can play the given instruments

for example E({clarinet,guitar})

has 4 elements

[vocal gazelle]

yep

[merry sleet]

so now express E = E(guitar) U E(clarinet) U E(trombone) U E(saxaphone)

right?

[vocal gazelle]

yeah

[merry sleet]

so do you know the formula for the cardinality of a union of sets?

[vocal gazelle]

yeah

n(A u B ) = a (A) + n(B) - n(A n B)

[merry sleet]

yeah and if you have more than 2 sets?

[vocal gazelle]

the n(A u B u C) formula ?

[merry sleet]

well in that case its

AuBuCuD

we have 4 sets

[vocal gazelle]

hmm

What would the formula look like

I found this on the internet:

P (A U B U C U D) = P(A) + P(B) + P(C) +P(D) - P(A ∩ B) - P(A ∩ C) - P(A ∩ D)- P(B ∩ C) - P(B ∩ D) - P(C ∩ D) + P(A ∩ B ∩ C) + P(A ∩ B ∩ D) + P(A ∩ C ∩ D) + P(B ∩ C ∩ D) - P(A ∩ B ∩ C ∩ D)

[safe radish]

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[vocal gazelle]

.close

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[burnt bloom]

Sub in

[limber cloak]

Hello

3(2)/6 +3

[merry sleet]

dont forget

the +a

[limber cloak]

ok

3 + 2 / 6 + 3?

[crisp nacelle]

no, he meant ((3+2)/(6+3))+2

As you can see, a is being added to the fraction

[limber cloak]

Oo

[crisp nacelle]

Now simplify the numerator and the denominator by doing the operations

[limber cloak]

Ok

Is the answer c?

[limber cloak]

.​

Wait

[crisp nacelle]

No

[limber cloak]

Wait im wrong

[crisp nacelle]

Yeah, it's not C.

3(2) = 6, that is the numerator

6+3 = 9, that is the denominator

[limber cloak]

Yes

[crisp nacelle]

now you want to add a to it

a = a/1

[limber cloak]

2/1

[crisp nacelle]

yeah, since any number that's divided by 1 is equal to the number that's being divided, it's just the same

now you can add it as a fraction

[limber cloak]

Ok

6/9 + 2/1

[crisp nacelle]

you need to use this method

which works with unlike denominators, in case the denominator was the same, you could just sum the numerator and be done with it

I'll call the first fraction as A and the second fraction as B

you multiply the numerator of A with the denominator of B

then the numerator of B with the denominator of A

[limber cloak]

Then multiply the denominator of A with the numerator of B

Yes

[crisp nacelle]

after doing those multiplications, you write them down, as x+y

then you add the line which means fraction, and multiply the denominator of A with the denominator B and that's the denominator of your addition of fractions

[limber cloak]

okay

So

The final answer is A

[crisp nacelle]

no

[limber cloak]

...

[crisp nacelle]

(6/9) + 2/1

6*1 = 6

9*2 = 18

9*1 = 9

(6+18)/9

24/9

now you simplify it

[limber cloak]

8/3

[crisp nacelle]

Yeah

I'm curious how you get A

[limber cloak]

I can't understand much about math in english

It my second language

[crisp nacelle]

Mine too, my first one is spanish

I could have explain it better tbh

I tend to over explain and in the end I make it more difficult to understand, my apologies.

[limber cloak]

But thank u very much for ur help, appreciate it!

[crisp nacelle]

no problem

[safe radish]

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[vague atlas]

hey can anyone help me solve this prombelem.

[safe radish]

@vague atlas Has your question been resolved?

[merry sleet]

<@&268886789983436800>

[vague atlas]

@elder stirrup stop spamming

[wild cape]

ty

[merry sleet]

[vague atlas]

can anyone solve this question:-

[merry sleet]

this is not a png how infuriating

[vague atlas]

find if (x-2) is a factor of x^2+3x-2

[still charm]

Product sum method

Factors of -2 that add to equal 3

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[silent axle]

How do I prove (3x+2)(3y+2) equals (3z+1) where x,y,and z are all integers

[robust stream]

did you expand

[silent axle]

I proved a similar problem cuz it was way easier

show (3x+1)(3y+2) = (3z+2)

expand and get 9xy + 6x + 3y +2 . factor 3 and get 3(3xy + 2x + y) + 2. which is in the form 3z+2, as 3xy + 2x + y is an integer. z = 3xy + 2x + y. Not completely sure if this is correct but I could at least attempt it unlike the first one

[robust stream]

+2 is wrong

3y also wrong though irrelevant

oh wait

mb

uhh

[lean otter]

expand the first product, and try to rewrite it as 3 * something + 1

[robust stream]

oh

there are 2 qns

[silent axle]

yea

The second one i think i solved

The first one i couldnt solve

[robust stream]

expand this

its like the same question man

[silent axle]

really?

How do I get 1

[robust stream]

expand 3x+2 times 3y+2

like you did with the other one

[silent axle]

the second problem i already have 2 but the first problem i have 4

[robust stream]

issue is

you aren't considering 4 is 3+1

just be a bit more flexible and ur good

[lean otter]

$(3x + 2)(3y + 2) = 9xy + 6x +6y + 4 = 3(3xy + 2x + 2y + 1) + 1$

[flat frigate]

trololol !

[silent axle]

Thanks

I shouldve seen it

.close

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[cloud ermine]

is this correct
vertex: (-4,2)
focus: (-4,-4)
directrix: 4
axis: 4
latus rectum: ??

[safe radish]

@cloud ermine Has your question been resolved?

[vague atlas]

l

[safe radish]

@cloud ermine Has your question been resolved?

[safe radish]

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[jolly epoch]

I could figure out the formula of blue

But not the white

[lean otter]

n^2-number of blues

[jolly epoch]

How?

[lean otter]

There are n squared total number of tiles

[jolly epoch]

I could also figure out the total

[lean otter]

Then you have the answer

Just subtract

[jolly epoch]

With the blue?

Is there is any other way to get white

[lean otter]

Yeah but it's more laborious

[jolly epoch]

Aha, wait I think I'm not right with the total,

[lean otter]

It would be something like
$$4\times\left(\sum_{k=0}^{s-2}2k+1\right)$$
Where $s$ is the step number

[flat frigate]

Brudimann

[jolly epoch]

Oh that is really complicated

[lean otter]

Yep

So just subtract the number of whites from the total

[jolly epoch]

.

[lean otter]

The total number of squares for figure number s is
(s+(s-1))^2 = (2s-1)^2

[safe radish]

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[jolly epoch]

I know what u did but can I have a explation for why ^2 or how I supposed to think?

[lean otter]

You know how x^2 is called x squared

[jolly epoch]

@lean otter why did the room closed 😂

[jolly epoch]

Yh

[lean otter]

It's because it's the number of tiles in a square of side length x

And the side length of figure number s is
s+(s-1)
Whih you get by observing the pattern

[jolly epoch]

Aha

I think I got the point

[lean otter]

Good

[jolly epoch]

@lean otter thanks a lot, I was struggling with that question from yesterday and didn't get answer that make sense

[lean otter]

Var så god

[jolly epoch]

Oh u speak Swedish?

[lean otter]

Jag förstår svenska

[jolly epoch]

Ohh hur?

[lean otter]

Men kan inte prata bra

[jolly epoch]

Aha, bor du Sverige?

[lean otter]

Nej, jag kommer från Finland

[jolly epoch]

i*

[jolly epoch]

Ahaaa Finland, jag tror de lär sig Svenska I skolor

[lean otter]

Ja, jusst så

[jolly epoch]

Coolt

[lean otter]

[jolly epoch]

@lean otter one question, did u understood the question in Sweden?

[lean otter]

Yep

Idk what skapa means but everything else

[jolly epoch]

That's pretty good, Sweden is not my native language too, but I live there

[jolly epoch]

Skapa means create

.close

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[grave jolt]

Which websites do you all recommend for maths exercises for Calc A and functions and their inverse?

Considering, that I'm searching for websites that provide wide-ranging exercises with different ideas tho

[halcyon carbon]

Madasmaths is a good one

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[sleek path]

if its x(2x^2 + 7x - 15)=0 you can just like cancel x right because the eqution is equal to 0??? i think? so it will be a quadratic equation

[viral knoll]

yes, you can cancel the x that's outside the brackets

[sleek path]

oh ok thanks im just confirming tahny ou

[green lichen]

don’t cancel

[sleek path]

.close

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[sleek path]

.repon

.reopen

ok what

[safe radish]

✅

[green lichen]

x=0 is one solution

[sleek path]

hmm no im not finding x tho

[green lichen]

ohh what’s the question?

simplify?

[sleek path]

finding the discriminant

[green lichen]

uhh

[green lichen]

of a cubic?

[sleek path]

quadratic equation

discriminant is the uh b^2 - 4ac

[sleek path]

but tthis is ok right?

[green lichen]

what’s the given equation

[unique bison]

This is kinda dumb... you can just get the roots easily because it's already factored

[green lichen]

how do you find the discriminant of a cubic?

[unique bison]

But ig they want you to find the discriminant of the quadratic that you get when you divide the equation by x

[sleek path]

uh what im confused

[green lichen]

question seems weird to me

but yea I think they want discriminant of the quadratic

[sleek path]

alr alr thank you

[green lichen]

but don’t cancel ya

no prob!

[sleek path]

wait why wont i cancel tho

how will i get quadratic equation ax^2 + bx + c if when i dont cancel x it will be uh yeah

[unique bison]

Wait there's a thing called discriminant of a cubic

[green lichen]

you get x= 0 and 2x^2+7x-15=0

don’t cancel

you’ll lose one solution

and you need to check the nature of it

[sleek path]

ok ok

wait isnt like i dont need to find x because the question is just discriminant b^2 - 4ac ??

[green lichen]

yea discriminant is for the quadratic

but x=0 is still there

[sleek path]

alr alr

ahhh

yeah mb

thanks

[green lichen]

[sleek path]

.close

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[rancid basin]

how to create get help

[rancid basin]

somebody help me how to convert mac addresses

[worthy hemlock]

Do you know how to convert numbers in general?

[rancid basin]

yes like hexadecimal to binary and all others. the mac address is what i am confused about to convert

[worthy hemlock]

Here's a hint, Mac addresses are in hexadecimal

If you know how to convert from hexadecimal to other bases, you should be good

[rancid basin]

thanks man, i thought it was a different conversion/formula for mac addresses

im fucking dumb

[worthy hemlock]

The reason why this didn't work is probably the spaces in between. The question put spaces, for readability

[worthy hemlock]

Nope Mac addresses are in hexadecimal

@rancid basin If you are done with the channel, please close it using .close

[rancid basin]

thanks man i appreciate it

.close

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[vivid current]

how does one solve this simultaneous equation?

[fresh igloo]

put x = y + 5 in equation 2 and substitute in all the value of x in equation 1

[vivid current]

ah

[fresh igloo]

you must get the value of y here and then you can find the value of x

[vivid current]

like this?

[fresh igloo]

that is also one of the options

the one I provided you should be easier

[vivid current]

which value do i use though?

ah

i thought that was what you meant

how do i know which one of -2 or -3 is correct?

[fresh igloo]

no sorry that was exactly what I meant

[fresh igloo]

both of them are correct, put both the values simultaneously

in the equation

you will get two values for x too

Note - an equation can have more than two roots (solutions)

[vivid current]

ah okay

[fresh igloo]

ye

[fresh igloo]

if your issue is resolved you can close the issue by using the .close command

[vivid current]

thanks

.close

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[misty notch]

this one is hard to explain in text

can u vc?

[wraith nymph]

Ok.

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[visual dust]

any tips on how to show part b?

[visual dust]

I'm guessing I have to show that this is cauchy since I have no numbers to work with

But I'm not sure how to start showing that this is cauchy

I guess it's like each iteration bisects the interval, so it would be like max distance from $a_n$ to $a$(the limit) would be like $\frac{1}{2^n}(a_2-a_1)$

[flat frigate]

Mirinim

[visual dust]

or something like that but i'm not sure if that is the correct direction to go

[safe radish]

@visual dust Has your question been resolved?

[proper crypt]

Show that's it's bounded I think

If a sequence is monotonic and bounded it is convergent. Do this for a_(2k) and a_(2k+1).

When a sequence is increasing and bounded it will converge to the supremum of it's elements.
When a sequence is decreasing and bounded it will converge to the infimum of it's elements.

If you show that both the sub-sequences converge to the same number, then a_n will also converge to that number.

@visual dust

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[lean otter]

I calculated the intersect point

but for x it's some weird value

does anyone know what it means?

[maiden jetty]

$-1.54E-14$ means $-1.54 \times 10^{-14}$

[flat frigate]

秋水

[maiden jetty]

I think it's 0, but because of the accuracy of the calculator's numerical algorithm, the display looks like this

[lean otter]

yeah I calculated it by hand and got 0

[lean otter]

sorry could you explain why the calc outputs this?

instead of 0

[maiden jetty]

emm, I don't know, I think it relates to the algorithm used in the calculator

[lean otter]

hmm ok

ty

.close

c.lose

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[visual dust]

thank you, just saw this

[proper crypt]

No problem!

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[deft folio]

How do I work this out?

[safe radish]

@deft folio Has your question been resolved?

[thin bridge]

have you solved linear equations before?

[deft folio]

Yes

I believe it is 6b4a - 12b = c

I don't know where to go from there

[thin bridge]

e.g. if I gave you something like,
solve (3x+5)/2 = 7 (for x)
would you be able to solve it?

[deft folio]

uhm

x = 0.83?

[thin bridge]

can you give the exact value?

no decimal approximation

also it's wrong

[mint jewel]

is this correct?

[thin bridge]

yes

similar approach could be applied to your question,
note that although distributing would be legal,
it's more efficient to divide both sides by 6b

[mint jewel]

i feel like i am wrong

[deft folio]

okay thanks

[deft folio]

I will check it

no wrong

answer is c+12b/24b

[mint jewel]

can you explain how?

[deft folio]

sure hold on

[mint jewel]

ok got it thanks

[deft folio]

No worries

I got another one

nvm I worked it out.

Okay I got another one

How do I work that out?

[mortal sandal]

get both terms with a on the same side

and everything else on the other side

[deft folio]

so -5ac(a+4b) = 3d?

[mortal sandal]

what operation did you do to get that?

looks like you did very different things to the left and right sides

[deft folio]

-5ac from both sides

[mortal sandal]

looks like you multiplied the left side by -5ac

you didn't subtract 5ac from it

[deft folio]

oh

idk then

[mortal sandal]

well just subtract 5ac from both sides instead

@deft folio pinging since i've been gone for 23 minutes lol

[deft folio]

okay

so (a+4b)-5ac= 3d

[mortal sandal]

yeah

and then we need to get the thing without a on it to the right side

[deft folio]

idk how to do that

[mortal sandal]

you have a+4b-5ac = 3d

[mortal sandal]

you want to move the +4b over

[deft folio]

a-5ac = 3d - 4b

[mortal sandal]

yeah good

now you factor out an a from the left

[safe radish]

@deft folio Has your question been resolved?

[safe radish]

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[swift wharf]

why is the example using the data of freshman?

and how do u figure that P(m I S) uses that specific formula?

[jaunty owl]

the formula for P(A|B) is P(A n B)/P(B)

ingeneral

[swift wharf]

oh ok

but why is it using data of freshman?

isnt it asking for that of seniors

[jaunty owl]

im not sure of the notation

but it has S with the overline

so perhaps it means not senior?

[swift wharf]

ohhh i see

that makes sense now

thankss

[jaunty owl]

ah yes

it means everything but

S

i looked it up

[swift wharf]

got it

tysm

[jaunty owl]

npp

[swift wharf]

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[hearty wagon]

how are the two parts equal? in other words.. in which sequence is the matrix multiplied?

[hearty wagon]

multiplying the 0 (third element in the array) with any elements of the rotation matrix should not give me something like -(R2 + R1 * cos angle) * sin angle.... how did we get there x.x

article: https://www.a1k0n.net/2011/07/20/donut-math.html

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[dark tapir]

.open

.help

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Commands:
clopen: .close, .reopen, .solved, .unsolved
consensus: .poll
factoids: .tag
help: .help

Type .help <command name> for more info on a command.

[dark tapir]

.help

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Commands:
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consensus: .poll
factoids: .tag
help: .help

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[dark tapir]

how do i open this

[dark tapir]

plz

help

can someone explain to me

why is (2x^3-x)/x^5 even and not odd

[zinc sorrel]

It’s not?

[dark tapir]

its even lolz

[zinc sorrel]

x=1

[dark tapir]

think its cuz u facotr out -1 cuz of the denominator?

nah i got this on my calc test

lmfaoo

[zinc sorrel]

What?

[dark tapir]

<@&286206848099549185>

[trim swan]

It is an even function

Divide the numerator by the denominator

@dark tapir

Do you know what an even or odd function is? Or how to identify them in general

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[dark tapir]

@trim swan yees

its only dis one

bassically if u plug in

its the opposite

but for this function

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[dark tapir]

why is (2x^3-x)/x^5 even and not odd

<@&286206848099549185>

can i get help

been an hour

[trim swan]

What about it implies that it's odd?

[dark tapir]

f(x) = f(-x)

-f(x)

u plug in -1

u get -2x + x / -x

which is opposite

but u can factor out -1

so its even

but why do u factor out -1

[trim swan]

Even means this, right?

It means, f(-1) = f(1), for example

Not f(-1) = 1

[dark tapir]

yes

[trim swan]

Plug in 1 and -1, and you'll get the same thing, because it's even.

[dark tapir]

oooh ic

[trim swan]

Idk exactly what the problem stated, but that's not really enough to prove that it's even, because that has to work for every number on the domain

in order for it to be an even function

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[exotic jackal]

How does 1 / sqrt(2) = sqrt(2) / 2?

[stray socket]

Multiply by sqrt(2)/sqrt(2)

[exotic jackal]

Ahhhh ok that makes sense

Thanks

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[sturdy spindle]

Quick question I had trouble googling: Is [1, 0, 0] a 3x1 matrix or a 1x3 matrix?

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@sturdy spindle Has your question been resolved?

[sturdy spindle]

<@&286206848099549185>

If the format varies from textbook to textbook then I'd also like to know if that's the case

[cosmic grove]

it is a 1x3 matrix

one line
3 columns

[sturdy spindle]

so the transpose of it will be 3x1 yes?

[cosmic grove]

yea

[sturdy spindle]

with 3 different x vals

ok thank you

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[silent roost]

I know this isnt a great place for this but I need a lot of help with a bunch of random chem questions on reactions

[silent roost]

I can't find a good place to ask people this and math servers are filled with a lot more ppl that could help me so I want to try to ask here

What's are some examples of weak electrolytes and strong electrolytes and what's the difference

what differs the structure of ionic and covalent bonds

[cosmic grove]

ionic bonds evolve electrostatic attraction between the electron, covalent bonds do not

[silent roost]

that helps

ionic bonds are stronger right

[cosmic grove]

I dont know, im not a chemistry enjoyer

[silent roost]

xD

im not either but its a necessity

[cosmic grove]

I need it for engineering, thats it

but i hate it with passion

[silent roost]

yep

[nova creek]

I doubt ionic bonds are stronger than covalent bonds

Because in covalent bonds the atoms are physically sharing the electrons

[worthy hemlock]

Actually, from google

Ionic bond is much stronger than covalent bond because it involves complete transfer of electrons because of which there is formation of cation and anion and there exist huge electrostatic forces of attraction.

[nova creek]

Shit

[worthy hemlock]

Oh god, google is giving me mixed info

[silent roost]

waat

[worthy hemlock]

Ionic bonds are usually stronger than covalent bonds. A defining characteristic of ionic bonds is that an electron from one atom is "taken" by another atom, whereas in covalent bonds, the electron is shared between the two atoms.

[silent roost]

i mean id love to show my chemistry teacher a bunch of physics and mixed research on bonds and make his head spin as much as mine XD

[cosmic grove]

quantum mechanics

[silent roost]

how do u do that quote thing

[silent roost]

o cool

like that

i see

ok ok i c

[idle parrot]

did you get answer?

[silent roost]

i dunno honestly

[idle parrot]

hmm

[silent roost]

videos are somewhat long and show me covalent metallic and ionic

and molecular solids

[idle parrot]

well in strong electrolytes the solvent is more ionic in nature

[silent roost]

yeah i did those ya

[idle parrot]

while in weak it has more covalent character

[silent roost]

-understanding strong/weak/non electrolytes
Strong electrolytes:

Strong electrolyte conducts electricity well.

• Ionize completely
  strong acids include strong acids, strong bases, and ionic compounds that are soluble.

Weak electrolytes:
Weak electrolytes conducts electricity slightly but to a small extent.

• Don’t ionize entirely. Only slightly
  insoluble compounds, insoluble ionic compound, weak acid, weak base.

[idle parrot]

it isn’t black and white thing

like if you study more, you’ll see covalent character is dependent on %s character of a molecule in a hybrid orbital

and more the ionic more it is stable

it all revolves around thermodynamics

uhh do you get what i said?

[silent roost]

ya

we havent gone over thermo yet tho

[idle parrot]

well you don’t need to know it yet, uhh idk how to put it but remember thermodynamics answers many factors chemistry

[silent roost]

are acids like aqueious

or can they be solid or and stuff im kinda confused on like

explaining how they break apart for net ionic equations

[idle parrot]

when we say acid, we generally consider them as a solution

same with base

because in solids they don’t react, as you mentioned

also it should be a solution, and not liquid state

[silent roost]

ok ima just copy and paste this cuz this is my notes im working on

o its too long .-.

-understanding ionic solids vs covalent solids (structure)

ionic bonds evolve electrostatic attraction between the electron, covalent bonds do not

-solubility of an ionic solid ionizing and breaking apart vs covalent solid

-Reaction Types, predicting the products of: SR, DR, Synthesis, Decomp, Acid Base (strong acids only)

-Writing Net Ionic reactions (aq) for double rep. rxns

-like dissolves like and Polar vs. Nonpolar ie: why water won’t dissolve oil etc.
Aqueous

-understanding when DR reactions form a precipitate (solid) ppt.

-hydration and the arrangement of water and cations and anions

CONCENTRATION (AKA) MOLARITY
-given grams and liters, find the molarity (concentration)
Apply formula:

-given a stock solution find the molarity of a diluted solution

Molarity (Stock) times Volume(stock) = Molarity (Diluted) times Volume (Diluted)

Molarity (Stock) times Volume(stock) divided by Volume (Diluted) = Molarity (Diluted)

-given a balanced reaction, use molarity and volume to find the moles, then use the mole ratio and stoich to solve for how much product was produced (we will review this before your test)
Molarity times volume of solute = moles.

-strong acids and bases
Strong acids:
HCl, HBr, HI-, HNO3, HCl4, H2SO4

Strong Bases: (hydroxides)
NaOH, KOH, MG(OH)2, Ca(OH)2

-oxidation states/charges given a reaction indicate the charge of each element in the reaction

[cosmic grove]

i thought it was about ionic and covalent bonds tho, why there is mineral chemistry here

[silent roost]

mineral chem??

im so confused