help-27

[crisp cliff]

How am I meant to answer this question?

[wooden wraith]

Partial fraction decomposition

You can find specific values for a and b

[crisp cliff]

I don't see how

I've been doing this specific problem for like an hour or longer.

maybe 2 hours now

[wooden wraith]

Do you know what I mean by this?

[crisp cliff]

Not really

[wooden wraith]

Notice that the denominator on the right, x^2-1 is factorable

specifically its factors are x+1 and x-1, which are the denominators on the left

[crisp cliff]

Yea I see that

[wooden wraith]

So, what we can do is make a common denominator on the left

[crisp cliff]

I basically did that with the left side

[wooden wraith]

oh

Can I see your work?

[crisp cliff]

It's all over the place and messy bc I was struggling lol

that wouldn't be easy to show lol

I'll try to rewrite it

[wooden wraith]

I'm just curious what you mean by this

You made a common denominator on the left side?

[crisp cliff]

@wooden wraith Solved for a and b from there.

After that, I ignored the denominator and set the numerater equal to 1

[devout snow]

@crisp cliff Has your question been resolved?

[crisp cliff]

rip

[devout snow]

@crisp cliff Has your question been resolved?

[wooden wraith]

Sorry, I had to do something for work.

You still here @crisp cliff ?

[wooden wraith]

What you've got here is good, this is exactly what you want to do

a(x-1) + b(x+1) = 1

[devout snow]

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[hallow sail]

does anyone know why i got this wrong

[regal torrent]

-11 and 3
Not
-3 and 11

You put the x values for wavy curve

[hallow sail]

sorry>

i dont understanf

<@&286206848099549185>

[jolly mango]

@hallow sailbasically

for lets say (x+11) = 0

then x would = -11

so instead of using 11 for your sign chart

you use -11

[hallow sail]

@jolly mango thank you !!!

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[honest meadow]

i believe i got this right

but i want to double check

is the answer simply just pi^2?

after integrating it i got

$\frac{x^2}{2}-cosx$

[woven radish]

Scarecrow

[honest meadow]

and then pi/2 and 3pi/2 are 0 for the cosx

so it's 9pi^2/8-pi^2/8

which simplifies to pi^2

at least that's my thinking

[violet wind]

seems right

,w integral from pi/2 to 3pi/2 of x+sin(x)

[woven radish]

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[violet wind]

yeah

[honest meadow]

ty

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[violet wind]

np

[devout snow]

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[mental sigil]

Hi, so I'm struggling with the following trig problem:

• There are two right triangles that share a side (h)
• When the lengths of the non-shared sides of the triangles are added, the sum is 140 units
• One triangle has an angle of depression of 41 degrees, while the other has an angle of depression of 48 degrees
• Find h
  The problem is represented by the attached image. I believe that I'm supposed to represent the adjacent sides as 140 and 140 - x. However, I am not sure as to how I would go about isolating x

[mental sigil]

If anyone needs to know, I found this question in my math textbook while studying for a final (it was not assigned as work)

[wooden wraith]

When you about "the non-shared sides"

Do you mean a+b+c+d = 140?

[stark anvil]

I think he means the sum of just c and d

[mental sigil]

the sum of c and d

[vale estuary]

c+d=140

[mental sigil]

sorry, my explanation of the problem wasn't super clear

[stark anvil]

Tan(41°) = h/(140 - x)

Tan(48°) = h/x

[mental sigil]

that's the point that i was able to get to before asking the question, but i'm not sure how to isolate x

[stark anvil]

You have two equations now

[mental sigil]

would i just express h in terms of x and substitute it into the other equation?

[vale estuary]

xTan(48°)=h?

[stark anvil]

Yes

First you have to substitute the value of tan

In the equations

,w tan(41°)

[woven radish]

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[stark anvil]

0.8

,w tan(48°)

[woven radish]

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[stark anvil]

1.1

Now you can solve for h

[mental sigil]

alright, thanks for your help everyone! i was able to solve the problem :)

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[tiny rain]

hi can someoe help me with this?

[hybrid snow]

Have you tried LHopital?

[tiny rain]

yes

[hazy quail]

multiply by the conjugate of the numerator on both sides

maybe

[hybrid snow]

Oh no no you got confused

[tiny rain]

hmm okay

[hybrid snow]

You took the whole derivative of the whole fraction

You just take the derivative of the numerator and denominator seperstely

[tiny rain]

oh wait

OHHHH

OOPS

[hazy quail]

oh yeah you did that

f

[tiny rain]

lemme try again

[hybrid snow]

Skull emoji . Png

[tiny rain]

liek tis?

[hybrid snow]

Ye

[tiny rain]

thank u 3000

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[dense crow]

I tried using the distance over speed and time formula

And I did 36*30 giving me 1080

Ik I did something wrong

Idk what I did wrong tho

[quaint citrus]

36 km traveled = 1 hr. x km traveled = 0.5 hr

see if u can work out that proportion

[dense crow]

Wouldn't that just be 18?

[quaint citrus]

ye

[dense crow]

oh. idk what just happened

is that the answer?

[quaint citrus]

seems like it

what does the answer key say

[dense crow]

Yup its 18

[dense crow]

Can u explain this part, I didnt really understand

[quaint citrus]

sure

lemme give an example first

[dense crow]

okay

[quaint citrus]

lets say im going at 10 miles/hr and my workplace is 10 miles away. assuming no interruptions, how long will it take me to get there?

[dense crow]

In 1 hour

[quaint citrus]

correct

we can verify that by using the distance/velocity = time formula. d = 10, t= ?, and v =10 mph. 10/10 = t, t =1 hr

now looking at a problem similar to ours

if im going at 20 miles an hour, and I travel for 1 hour, how far will i have traveled by the time 1 hour has elapsed?

[dense crow]

20miles

[quaint citrus]

how about if i travel for 2 hours

[dense crow]

40 miles

[quaint citrus]

how about if i travel for a half hour

[dense crow]

10 miles

[quaint citrus]

good!

[dense crow]

OH

[quaint citrus]

this is just like our problem (half hour = 30 mins)

[dense crow]

OHH

I get it noww

[quaint citrus]

cool

[dense crow]

Thanks!

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[tacit shard]

i wanna know if my process was good

[tacit shard]

I used chat gpt after to confirm my answer but it gave me something else, but i don't know if its just being dumb since it has given me wrong answers before

[turbid shuttle]

do not use chatgpt to confirm math stuff

it doesn't work like that

[tacit shard]

so my approach wasn't correct??

[turbid shuttle]

i have no idea

i'm just saying chatgpt doesn't know math

[turbid shuttle]

no you're right

i'm just saying, checking via chatgpt is useless, because most of the time chatgpt isn't right

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[restive river]

Trying to find the characteristic polynomial of
[
\begin{bmatrix}
1& 0& -1 \
2& 3& -1 \
0& 6& 0 \
\end{bmatrix}
]
What I did was:
[
\text{det}(A-\lambda I) = \text{det}\begin{bmatrix}
1-\lambda & 0& -1 \
2& 3- \lambda& -1 \
0& 6& 0 -\lambda \
\end{bmatrix}
]
[ \to \text{det}(A-\lambda I) = (\lambda^2 -4\lambda +3)(\lambda) -12 + 6-6\lambda
]
[
\to \text{det}(A-\lambda I) = \lambda^3 -4\lambda^2 -3\lambda -6
]

[woven radish]

♡A(lex)♡

[restive river]

Which is wrong, but I can't see where

It's probably some calculation mistake

[jovial mauve]

,w det{{1-k,0,-1},{2,3-k,-1},{0,6,-k}}

[woven radish]

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[jovial mauve]

[restive river]

Oh okay ty

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[unkempt crescent]

Hello, who Can help me for that's exercice: (please french if no i will translate)

[unkempt crescent]

If nobody*

[pseudo basin]

d'où vient le u_n dans le 1er problème ?

[unkempt crescent]

Mhm, déjà faudrait pas enft vérifier pour le 1. Qu'elle est arithmétique?

En faisant Un+1-Un

Mais sans Un on peut pas c'est vrai

[pseudo basin]

quoi ??

personne ne dit que (u_n) est une suite arithmétique non ??

[zenith jacinth]

je crois pas que (p_n) ressemble à une suite arithmétique

[unkempt crescent]

J'ai pas lu le bon exo 🥲 désolé 🤣

En effet elle est plutôt géométrique xD

Mais faut p_n pour trouver pn+1?

[zenith jacinth]

euh, t'es sur ?

Là on n'en sait rien

[unkempt crescent]

Ben faut le démontrer ?

Mais sa servira pas dcp

Parce que c'est pas la question je mettais trompé d'exercice ')

[zenith jacinth]

tu essaies de faire quel exercice là ?

ou quel question ?

[unkempt crescent]

Celui là x)

[zenith jacinth]

quel question ?
le 1) ?

[unkempt crescent]

Je suis perturbé il y a des probabilités et des suites

[unkempt crescent]

Oui

Le reste je serai le faire normalement

[zenith jacinth]

Mais c'est quoi u_n en fait ? Ils n'ont pas défini ce que ca représente

[unkempt crescent]

Justement enfaite

Faut le trouver dans l'énoncé

D'après mon prof

[zenith jacinth]

ah ok

bah on va essayer d'aller doucement alors

le premier term

p_1 = 1

p_n représente la probabilité de gagner la n-ième partie

[unkempt crescent]

Yes

[zenith jacinth]

sachant qu'il gagne la première partie, la probabilité qu'il gagne la suivante est 2/5

Le contraire pour ça donne : 1-2/5 = 3/5

cest a dire la probabilité de perdre la partie suivante

je suppose

🤔

[unkempt crescent]

Yes

Mais en relisant

[zenith jacinth]

c'est mieux de faire un arbre de choix pour bien représenter

[unkempt crescent]

On a p_n = P(G_n)

[zenith jacinth]

Bah oui, c'est la probabilité que l'évenement G_n se realise

et j'ai deja dit ce que cest

[zenith jacinth]

.

[unkempt crescent]

Okk

Donc faut déterminer la probabilité de Gn?

[zenith jacinth]

c'est ce qu'on est entrain de faire

mais le mieux serait de raisonner avec un arbre de choix

[unkempt crescent]

Ok, je vois.

[zenith jacinth]

pour ne pas se perdre quoi

donc essaie de dessiner un arbre

[unkempt crescent]

Bien, je vais tenter de faire l'arbre de probabilité.

[zenith jacinth]

tu as déjà tous les evenement possible

[radiant drift]

Je aime @pseudo basin

[pseudo basin]

it's j'aime.

[radiant drift]

Mb

[unkempt crescent]

Haha va boire du thé

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[mossy saffron]

can someone explain the second and third lines?

[stark anvil]

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

[woven radish]

ColdTee

[mossy saffron]

can you explain the second line a bit further

[stark anvil]

What part did you not understand?

[mossy saffron]

how did x^-1 become -1(x^-2)

$x^{-1} \stackrel{?}{=} \frac{1}{x^2}$

[woven radish]

PranshuTG

[stark anvil]

$\frac{d}{dx}x^n = nx^{n-1}$

[woven radish]

ColdTee

[stark anvil]

Differentiating f(x) and using this

[mossy saffron]

how would you explain it if i was 12

[stark anvil]

x^12?

Im sorry can you explain a bit

What you are asking

[mossy saffron]

if I was 12

if myself was 12 years old

[stark anvil]

Do you understand what differentiation means?

[mossy saffron]

no

[stark anvil]

Well do you know what a function is?

[mossy saffron]

yes

kinda

i understand the function of a function

[stark anvil]

You mean composite functions

[mossy saffron]

no, the use of a function

thats what i mean

[stark anvil]

Well the derivative of a function basically tells us the slope of the function at a particular point, the instantaneous rate of change at a point.

https://www.khanacademy.org/math/precalculus

You can visit this site to learn more before starting calculus, if you are really 12 then you have a long way to go before calculus but if you really wanna then i recommend this site.

[mossy saffron]

im 16

¯_(ツ)_/¯

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[restive river]

What have you tried yet?

[green kelp]

Just multiply both equations

[restive river]

ok i

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[low granite]

stuck on iii)

so

n has to be greater than 7 as your taking away 2m so must atleast be 8^2 =64

i think it cant be odd square numbers greater than 7 because that would lead to an odd number and therefore cant substract even number to get even

so the domain would be something like {(2k)^2 | k > 4}

for some natural number k

idk about the image

(8,7), (10,25),(12,47) (14,73)

m seems to be odd

<@&286206848099549185>

[devout snow]

@low granite Has your question been resolved?

[woven radish]

Welf

[fiery pivot]

Um, I don't think I'm in the same page here ._.

<@&286206848099549185>

[devout snow]

@low granite Has your question been resolved?

[low granite]

huh

[low granite]

is this the answer to my question?

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[vagrant saffron]

log x^(3/5)=2

[vagrant saffron]

I know the answer but i dont know how to get there

[spiral violet]

$$\log\left(x^{\frac{3}{5}}\right)=\frac{3}{5}\log x=2\Rightarrow\log x=\frac{10}{3}\Rightarrow x=10^{\frac{10}{3}}$$

[woven radish]

Михаил Колесников

[devout snow]

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[restive river]

by first rounding each number to 1 significant figure estimate the answer to 6.3 x 4

[restive river]

can i get the answer please 💀

[pseudo basin]

we don't give answers here.

[fresh horizon]

seems a little ambigious

[pseudo basin]

it is unambiguous

but we aren't a "do your homework for you" server anyway

[bitter kraken]

calculate $63\times 4$

[woven radish]

demiryolu mühendisi

[bitter kraken]

then you put the ,

somewhere

[pseudo basin]

no, that's not what was asked for.

[restive river]

huh

[bitter kraken]

?

[restive river]

so 252 is the answer?

[bitter kraken]

you should put the , somewhere

its beter when done by hand

[restive river]

2,52

[bitter kraken]

no

[restive river]

25,2

[bitter kraken]

logically, $6 \times 4 >2,52$

[restive river]

?

[woven radish]

demiryolu mühendisi

[bitter kraken]

this is the answer

[restive river]

u sure

[bitter kraken]

but you should give it more time next time

[restive river]

oh

[bitter kraken]

not quite

[restive river]

im confused

[bitter kraken]

you need to round it now

[restive river]

lmao the emoji reactions

[bitter kraken]

im confusd too lol

[restive river]

hmmmmmmm

[pseudo basin]

...

yeah no wonder @bitter kraken youve said something thats got nothing to do with the problem

[restive river]

help

[bitter kraken]

thanks

[restive river]

plz

[pseudo basin]

you were supposed to round 6.3 and 4 each to one significant figure, then multiply.

do you know how rounding works in general?

[bitter kraken]

i dont

[restive river]

um yes

so 6.3 would be 6?

[pseudo basin]

yes, 6.3 rounds to 6

[restive river]

and then 4 stays the same

[pseudo basin]

yes, 4 is already given with only one significant figure.

[restive river]

so its 24?

[pseudo basin]

yes

[restive river]

ok thanks

[devout snow]

@restive river Has your question been resolved?

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[umbral roost]

Can someone explain to we how the green circled part makes sense? I have the formula and I need to write it in logarithmic form. But I don’t understand the answer

[main python]

,rotate

[main python]

$\log \dfrac{a}{b} = \log a - \log b$

[woven radish]

sopinha

[umbral roost]

And multiplication is addition?

[main python]

yes

[umbral roost]

Ah oke thanks

But what about a formula? Say we have E=mc^2. Is that log(E)=log(m)+log(c)^2?

@main python

[main python]

No

$\log(c^2) = \log(c\cdot c)$

[woven radish]

sopinha

[umbral roost]

Log(E)=log(m)*log(c^2)?

[main python]

dude

[umbral roost]

Whatup

[main python]

$E = mc^2\implies \log(E) = \log(mc^2) = \log(m\cdot c^2)$

complete

[woven radish]

sopinha

[umbral roost]

Oh I mean log(E)=log(m)+log(c^2)

Is that right?

[main python]

yes

procede

[umbral roost]

Ok good

And @main python do you also know how do determine the slope of the function I gave you on the whiteboard? Only if it’s +1 or -1

[main python]

what function

[umbral roost]

The blue letters

[main python]

I have no idea what this means

[umbral roost]

Ignore the green letters….. I’m only talking about the log function. At the top

[main python]

I mean, usually when whe talk about slopes, we are talking about lines

that is not a line

[umbral roost]

They say the slope is +1.. why’s that

Okay anyways I’ll ask tomorrow

Thank you

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[devout snow]

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[undone stream]

anyone good with R? is making plots with R a valid math question to get help with? or should i seek help elsewhere?

[supple knot]

https://discord.com/invite/wmkCdwK

[undone stream]

thanks

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[sage kernel]

Is (x^-1 + x^-2)^-2 equivalent to x^2 + x^4?

[scarlet peak]

No

[topaz axle]

not at all

[scarlet peak]

Is (x+y)^2 = x^2 + y^2?

[devout snow]

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[placid fjord]

Could someone help me understand this?

[placid fjord]

How would I go about solving this?

[devout snow]

@placid fjord Has your question been resolved?

[devout snow]

@placid fjord Has your question been resolved?

[fiery pivot]

Try to split it into 2 statement and use the definition of absolute value

Example:
"p < |x| ≤ q" is the same as "p<|x| and |x|≤q"

Then use definition of absolute value

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[gusty silo]

Can non-helpers help in these channels too?

[sick fulcrum]

yes

ofc

[gusty silo]

Ty

[sick fulcrum]

bruh this is a khanacademy question

[lusty sapphire]

By all means, contribute if you can

@gusty silo but do not give solutions

[gusty silo]

Uh, sorry

[lusty sapphire]

We offer help, not full solutions

[gusty silo]

Should I delete it?

Ok

[lusty sapphire]

Our goal is to guide the students to their own solution

[gusty silo]

@azure orchid try to use dimensional analysis

You have to do a subtraction between equal unities, then you have to find the product of unities that will give the desired one

[azure orchid]

idk how to apply it here

wait nvm I think I got it, thanks :)

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[bold chasm]

Can anyone help me with a simple but i can't understand it :/

QUESTION
What is X if X2 is 30
Please write it in order ima be back in abt 5 minutes, thanks in advance.

[midnight dirge]

well

X2 seems to be completely independent of X

unless its 2 * X in which case

X is 15

[pseudo basin]

@bold chasm what is meant by "X2"?

[cloud remnant]

if you mean $x^2$ then its $\sqrt{30}$

[woven radish]

Shockshwat

[bold chasm]

X ²

[cloud remnant]

If you mean 2x then its 15

[low holly]

or -sqrt(30)

[cloud remnant]

[bold chasm]

what is X if X² is 30

I just knew how to write the small ²

so is it clear now?

[pseudo basin]

you could have written X^2

anyway, do you know what a square root is

[low holly]

if x^2 is 30, then x is a number whose square is 30

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[heavy terrace]

quick question regarding absolute values

[heavy terrace]

|a|=-a if a<0

but isn't it absolute value?

shouldn't it equal positive a

sorry my brain is burned out

[jovial mauve]

Take for example, a=(-3) which is less than zero

|a|=-a for a<0 makes it -(-3) which is +3.

[heavy terrace]

ohhhhhhhhh

yeah makes sense

[jovial mauve]

That's how the function is defined

[heavy terrace]

thank you @jovial mauve

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[winter patrol]

don't assume
-some variable
is negative just because there's a - sign present

[jovial mauve]

[devout snow]

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[sick marsh]

Bit confused on what exactly a pivot point is. Could someone help me out with pointing them out in this matrix?

[sick marsh]

Surely all the diagonal 1s are a pivot point in the Left side

So is the middle 1

And the first column on the right

But is the 5 in the second column on the right also a pivot point?

[radiant drift]

@arctic field

[devout snow]

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[devout snow]

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[robust socket]

Hey

[robust socket]

-1/x^2

I want to solve for zerois

and im confused a bit

[midnight dirge]

there are no zeroes

[robust socket]

You sure??

[radiant drift]

rectangle is certain in her decision

[devout snow]

@robust socket Has your question been resolved?

[restive river]

There are 0 solutions for this question

U can check graphically and u will see that the parabola won't touch x axis

[devout snow]

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[devout snow]

Channel closed

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[boreal leaf]

.close

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[ebon oasis]

is this [-5,infinity) or [-5,infinity]

[winter patrol]

infinity is not a number,
always open

[devout snow]

@ebon oasis Has your question been resolved?

[ebon oasis]

so )?

[winter patrol]

yes

[ebon oasis]

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[halcyon mango]

Is this answer correct? Is this the correct steps to take?

[restive river]

you did not multiply the 3/r term by t

[winter patrol]

step 1 is wrong already

[halcyon mango]

Yeah it seemed wrong

.close

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[halcyon mango]

.reopen

[devout snow]

✅

[halcyon mango]

So when multiplying you have to multiply all terms, not just sides?

[restive river]

not sure what differentiates "all terms" and "just sides" for you, but yes

[halcyon mango]

Is it different for division? I understand that if I have 3x + 15 = 90 I don’t have to divide the 15 to get rid of the 3

[halcyon mango]

A side being like just dividing the 3 from the x like in the example above

So then the next step would be” x + 15 = 30” rather than “x + 5 = 30”

[winter patrol]

apply the operator and simplify based on standard algebraic rules

starting with $3x +15=90$, the act of dividing both sides by 3 gives
$$\frac{3x+15}{3} = \frac{90}{3}$$
before simplifying

[woven radish]

ℝamonov

[winter patrol]

from fraction and division rules, the left side would simplify to
x + 5

[halcyon mango]

Oh wow so the correct answer to 3x + 15 = 90 would be x = 25?

[winter patrol]

yes

[halcyon mango]

Wow

Crazy I’ve been passing this entire time without knowing that maybe I’ve been unintentionally doing it

Thank you so much 🫡

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[winter patrol]

always remember operation to the whole side
write the intermediate step if you aren't confident
preemptively put parentheses around each side to be extra safe

[devout snow]

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[boreal leaf]

need someone to confirm

6 i. x=1/2, -3

ii. (-inf,-3)U(1/2,inf)

iii. -3 is a point of local max

7. 6e^2x+15sin(3x-1)+8^x in8

[fresh horizon]

ln8

but yes, correct

[boreal leaf]

for all?

[fresh horizon]

yep

[boreal leaf]

thanks

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[fleet gorge]

Show that An=2n/2n+1 sequence is rising sequence

[topaz beacon]

2n=2n+1-1

[fleet gorge]

I don't understand

I mean it is not rising

[torn vessel]

rewrite the numerator of your fraction as 2n+1 - 1 and split it

[fleet gorge]

I still don't get it so nvm ty

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[restive river]

i just need help to show me the method

[torn vessel]

complex roots come in pairs

if a-bi is a root, then so is a+bi

[restive river]

i have the solve, but i did not get how the result was found

let me send ss

[torn vessel]

ah, smart

[restive river]

i did not get how 9/2 was found

[torn vessel]

if you have a cubic polynomial you can factor it as a(x-h)(x-j)(x-k), which you'd then distribute and get something like $ax^3-a(h+j+k)x^2+a(hj+jk+hk)x-hjk$
something like Varik's formula i think?

[woven radish]

Zybikron

[torn vessel]

basically, if you have 3 roots, their product is the last term (after dividing by the leading coefficient)

and their sum is the coefficient on the second term (after dividing by the leading coefficient)

so the 9/2 comes from the coefficient on x^2 being -9, and the leading coefficient being -2
so the sum of the roots is 9/2

[restive river]

i am sorry i am very dumb, i still did not get it

ooohhh, now i got it

ok, now i got how to solve, thanks

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[open pendant]

in a question

[open pendant]

(5x + 7y + 8 ) x 5

is that 5 multiplied to all 3 separately

or just the 8

ive yet o see multiplication AFTER parenthesis

[restive river]

Hello

So, it will be multiplied to all three terms

[open pendant]

ok thats what i thought

all 3 in steps or at the same time

like it wouldnt be

5 x 8

and then 8 x the rest

[devout snow]

@open pendant Has your question been resolved?

[stone stump]

$(5x+7y+8)\cdot 5 = 5x\cdot 5 + 7y\cdot 5 + 8\cdot 5$

[woven radish]

Denascite

[stone stump]

it's the same as if the 5 was before the parenthesis

remember that a*b=b*a

so (5x+7y+8)*5 = 5*(5x+7y+8) if that helps

@open pendant

[open pendant]

thats all i needed to know thanks @stone stump

@chrome agate wrong channel bruh

@stone stump But what if its
(5y + 7x +5) x5 (6y +8x +3)

which bracket does it apply to

or both

[stone stump]

it's a multiplication of three things

you can pick the order in which you want to multiply them

so you can do first bracket times 5, get some result and then that times the second bracket

or second bracket times 5, get some result and that then times the first bracket

more explicitly, $(5x+7y+8)\cdot 5\cdot (6y+8x+3) = (25x+35y+40)\cdot (6y+8x+3)$ or $(5x+7y+8)\cdot 5\cdot (6y+8x+3) = (5x+7y+8)\cdot (30y+40x+14)$

[woven radish]

Denascite

[stone stump]

if you multiply either of those out you will see that you get the same

[lusty sapphire]

This is an application of two laws of algebra

[woven radish]

SWR

[open pendant]

hmmm

[lusty sapphire]

I know you already had that question answered, but it'll lead to answering your next question

Your original expression was $(5x+7y+8)\times 5$

[woven radish]

SWR

[lusty sapphire]

You can use commutative law to switch the order of multiplying $(5x+7y+8)$ and $5$.

[woven radish]

SWR

[lusty sapphire]

Commutative law says that if you switch them, it'll be the same thing

And then you can use distributive law for $5 \times (5x+7y+8)$

[woven radish]

SWR

[open pendant]

so the middle 5 only applies to one set of brackets

but the result from that multiplies into the next bracket

ok i think i get it

[lusty sapphire]

cool

[open pendant]

thank youuuu

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[lusty sapphire]

.reopen

[devout snow]

✅

[open pendant]

oh?

[lusty sapphire]

Did you still need help with your other question too?

[open pendant]

which was that

i bought a new calculator that works better if thats what youre refferring to

[lusty sapphire]

this question

Did you need help with that still?

Or do you get how to do it?

[open pendant]

i think i understand that

[lusty sapphire]

okay cool

[open pendant]

5 can go into either parenthesis

but the result of that

[lusty sapphire]

yes

[open pendant]

goes into the leftover parenthesis

but 5 isnt divided between the two

its one than another

thank u

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[spark cove]

if a sequence goes to inf is considered divergent right?

[spark cove]

i'm talking about this

'

i'm confused

[torn vessel]

it doesn't have negative values

[spark cove]

it does

why not

n=-100

an is -99

[hollow pollen]

n is an element on N

so positive integers

[spark cove]

omg

bro this exercises should specify that

so n is always element in N?

[fresh horizon]

I mean in sequences that is almost always an "assumption" that is taken to be

[spark cove]

from now on i'll keep that in mind

[fresh horizon]

if not what would the term $a_{-73}$ be

[spark cove]

thanks

[woven radish]

biggboy

[spark cove]

sth negative

[devout snow]

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[twilit maple]

I forgot how to add/ subtract radicals lol

[twilit maple]

I need to find the domain of this, is it ideal to first combine the radicals, since they both share the same base?

[wooden veldt]

there is nothing you can do here, you can only "combine" them when its a product

[dark dawn]

dont even worry about combining them

just solve each for when they are real

[twilit maple]

Okay bet

[dark dawn]

if t>3 ?

if t < -2 ?

shit hits the fan

[twilit maple]

So like this?

[dark dawn]

no the inside

the purpose is to solve for when its < 0 and hence imaginary and not real

[twilit maple]

hmm so how would i find the domain of this

[dark dawn]

when is 3-x < 0 ?

and exclude that from your domain

[twilit maple]

Because isn’t the whole point to find the number because the limit of a radical function has to be greater than 0

[dark dawn]

then do the same process for when 2+t < 0

[twilit maple]

o

So i just ignore the radical signs?

for now^^

[dark dawn]

well, you ignore them to solve but consider them to get the answer

the reason this works is because the radical is there

but the method to solve it doesnt directly involve them

do you understand what the logic is?

if you have a negative in the sqrt

[twilit maple]

Yea ofc

[dark dawn]

the output is no longer real

[twilit maple]

But the one part thats throwing mw off

Is that - infront of 2

[dark dawn]

so solving 3-x > 0 , and 2+x > 0 gives you your domain

[twilit maple]

Wouldn’t that carry into the inside?

[dark dawn]

or 3-x < 0 and 2+x < 0 then exluding

no

we dont care about it

if it was + it would change the shape of the graph

but the domain stays the same

[twilit maple]

O

Its a reflection

[dark dawn]

both of these work out to be arbitrary values a,b

it just changes the combination of a and b

[twilit maple]

Okok

So this, right?

[dark dawn]

correct

[twilit maple]

thank you!

[dark dawn]

and as for the graph

,w plot (3-x)^(1/2) - (2+x)^(1/2)

[woven radish]

Results provided by WolframAlpha

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[dark dawn]

,w plot (3-x)^(1/2) + (2+x)^(1/2)

[woven radish]

Results provided by WolframAlpha

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[twilit maple]

perfect

[dark dawn]

just different combinations of constants

[twilit maple]

So lets say just for reference

It was like this

[dark dawn]

stays the same

2 is just manipulating the constant output by the radical

,w plot 2(3-x)^(1/2) - (2+x)^(1/2)

[woven radish]

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Requested by Clarkie#5208

[dark dawn]

best thing for domains is just looking for when your values are real and where the singularities are

[twilit maple]

i see, so always just look inside the radical

Sorry for late response wifi dipped lol

thank you that clears it up a lot

[dark dawn]

if a radical is present its certainly something to consider

[devout snow]

@twilit maple Has your question been resolved?

[devout snow]

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[lunar garnet]

Hey guys I'm unsure if a sort of video game related question would be welcome here but if not I will delete it. There are 18 skills in this game (skyrim) and the mastery of each skill is a skill level of 100. I would like to get this done by level 80, so I think I need to increase the skill levelling rate. In order to do this the number 1800/80 would give me the correct number to increase the skill rate right? I am using a mod to be able to change this. I just want to double check my math here.

[supple knot]

are you asking what's 1800/80 ?

[lunar garnet]

I'm asking if the answer would be what my needs are

[wintry coral]

hey even if your math is right you start each skill at lvl15 no ?

lol

[supple knot]

what math are you unsure about

18 * 100 ?

[lunar garnet]

Just how to get the skill rate, if my problem is correct

[supple knot]

what's the formula for skill rate

[wintry coral]

skills/level

yes, it's 1800/80.

[supple knot]

,calc 1800/80

[woven radish]

Result:

22.5

[supple knot]

round up to 23 and you're done

[lunar garnet]

Cool thanks sorry I think I'm over thinking stuff

Thought it would be harder for some reason

.close

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[lunar garnet]

Forgot about this and also some start at 20/25 to but I know the basic formula so I should be good

[devout snow]

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[hollow inlet]

Anyone have any idea to approach 5 and 6?

[wintry coral]

choose one point directly to the right at the same y value

and another directly up with the same x value

for 5

for 6, just try make an equilateral since they're always acute

[hollow inlet]

Ok

And then after do I use length formula

To find sides

[wintry coral]

yes

[hollow inlet]

And use soh cah Toa to find angles?

[supple knot]

Don't be afraid to try

[hollow inlet]

I just don’t know if it’s right or not

[supple knot]

You can still try calculating

Be not afraid

[hollow inlet]

Ok

[devout snow]

@hollow inlet Has your question been resolved?

[devout snow]

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[devout snow]

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[tender knoll]

Can someone help, I am in polynomials and I don't understand with problem: (-5x^2-8x+2)+(3xy^2-x^2y+z)

[tender knoll]

<@&286206848099549185>

[devout snow]

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[tender knoll]

.close

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[tender knoll]

d

Why is the graphs like that, time is suppost to be on the bottom?

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[spiral pollen]

Hey, I have a question about limits.
If direct substitution works on a limit, how is it a limit?
It's just a random point on any arbitrary curve.

[spiral pollen]

.close

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[spiral pollen]

.reopen

[devout snow]

✅

[spiral pollen]

See?

[restive river]

yes

what do you have doubt in

[spiral pollen]

If the limit exists at that point then... what's the point of it being a limit?

It's just a normal function.

[restive river]

i think it is trying to see how close this graph is getting to the x -asis

axis

[spiral pollen]

Hmm...

[restive river]

i mean i dont think this problem would have been possible is the limit was x is to -2 as for that, you would have needed to be able to factor the numerator in such as way that the x + 2 would cancel out and that is not possible with this numerator

[spiral pollen]

The graph looks like this.

[restive river]

yes

[spiral pollen]

It never reaches negative 2.

[restive river]

yeah, i said if the limit was stated to -2

[spiral pollen]

But then there is no limit at 2. The limit is at negative 2.

[restive river]

yeah

[spiral pollen]

Why bring up positive 2 at all? The function is smooth and defined there. There's no limit there.

You could replace 2 with infinitely many other numbers (3,4,5,100, ten billion). The only limit is when x = -2.

What's the point?

There's nothing there.

[restive river]

well, i think it is just to get the fundamental theory and understandment of introduction of calculus

to be honest, idk why there would be a limit at 2 for that question that this is what i think

[spiral pollen]

It's from TOCT: https://www.youtube.com/watch?v=9brk313DjV8

It's just a point.

Thanks for talking to me, I guess this was just an example problem.

.close

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[open pendant]

how come when u remove a variable with a number from one side, its add/subtract

but when u separate the integers from the variable

its division

[unkempt quiver]

Because we're trying to isolate the variable

So in order to do that

We need to make everything else equal 0 on the side of x

So for example

[open pendant]

so when removing integars from variables

its division

[unkempt quiver]

x + 5 = 0

We need to get rid of the 5

To ISOLATE x, right?

So 5 plus -5 = 0

So we subtract 5

[open pendant]

yes

but if it was

[unkempt quiver]

But now what if we had 3x = 6

[open pendant]

5x=0

we divide

[unkempt quiver]

Ok let me finish

I'm getting there

[open pendant]

ok

[unkempt quiver]

So

3x = 6

Or 5x = 0

We need to isolate x

So get rid of the 5 right?

So 5 times 1/5 = 1

And 1 times x = x

So if we multiply both sides by 1/5

That will get rid of the 5 on the x side

[open pendant]

wait what

[unkempt quiver]

And multiplying by 1/5 is the same as dividing by 5

[open pendant]

is multiplying by 1/5 the same as dividing by 5

ah

[unkempt quiver]

Like 10 * 1/5 = 2

10 ÷ 5 = 2

[open pendant]

why would u multiply rather than divide

[unkempt quiver]

Same thing

Just makes me sense to me!

[open pendant]

ok

[unkempt quiver]

But

[open pendant]

thank u very much for your time

[unkempt quiver]

5 ÷ 5 = 1

Same thing

[open pendant]

multiplication right

[unkempt quiver]

Sry if I confused you with the multiply thing

Yeah

[open pendant]

ok i think i get it

[unkempt quiver]

Multiplication is really just division but the reciprocal

[open pendant]

so hey one sec

[unkempt quiver]

Yeah?

[open pendant]

5 /5 = 1

which 5 do i divide

and the leftover 5 is not longer division right

[unkempt quiver]

You divide by 5 on both sides

[open pendant]

like the last 5 would be subtraction

[unkempt quiver]

Let's go back to the 3x = 6 exam

Or how about

3x - 1 = 5

[open pendant]

like say its
5 /6 x 6 = 2

[unkempt quiver]

You divide whatever is on the x side

Which would be the left

[open pendant]

both the 5 and 6

or just one

[unkempt quiver]

But you have to do the same on the other side

[unkempt quiver]

Idk what you mean exactly

[open pendant]

5 divided by 6 x 6 = 2

i multiply 5 on both sides

so not i have

[unkempt quiver]

Uh what question are you going by

[open pendant]

6 x 6 = 10

right?

[unkempt quiver]

It's hard for me to follow

[open pendant]

ok lets clean up

one sec

..

.

.

[unkempt quiver]

Kk

[open pendant]

5÷5 - 6x = 7

multiply 5

5-6x = 35?

[unkempt quiver]

Ok this is your equation you have to solve for

[open pendant]

its just an example im curious about

[unkempt quiver]

No

You have to multiply 5 by everything

[open pendant]

i do not multiply a divison 5?

[unkempt quiver]

Honestly it's easier to just

Ok ok

[open pendant]

hmmm

[unkempt quiver]

Before u multiple anything

5÷ 5 is what?

[open pendant]

1

[unkempt quiver]

It's 1 yeah

[unkempt quiver]

Just simplify that first

[open pendant]

ok

[unkempt quiver]

1 - 6x = 7

[open pendant]

that makes sense i suppose

[unkempt quiver]

A lot easier right lol

[open pendant]

ye

still im curious but its ok

[unkempt quiver]

Ok let's say we did do that

5 ÷ 5 - 6x = 7

In math

We never use ÷ sign beyond 8th grade

[open pendant]

does the remaining 5 keep the division symbol, or does it just become basically positive 5

[unkempt quiver]

So let's rewrite it

[open pendant]

i know that

[unkempt quiver]

5/5 - 6x = 7

Multiply everything by 5 right?

So 25/5 - 30x = 35

Then simplying

[open pendant]

if were isolating x?

why would we multiply everything

[unkempt quiver]

5 - 30x = 35

[unkempt quiver]

Oh I'm just showing up

Wait sorry

Bad example

How about

x/5 = 3

Multiply 5 on both sides

x = 15

[open pendant]

bruh what lol

[unkempt quiver]

Because that's how equations work

[open pendant]

nah i dont believe u

[unkempt quiver]

You have to multiply every term