help-13

[jaunty shoal]

i need help with this one

@grand forge

[grand forge]

first rectange is the one at the top or bottom?

[jaunty shoal]

top

4 x 4

[grand forge]

nope

4 x 4 is working out the square

ur trying to work out the rectangle

[jaunty shoal]

40

[grand forge]

nope

[jaunty shoal]

24

[grand forge]

Nope

this help?

[jaunty shoal]

36

[grand forge]

Yep

2nd one?

[jaunty shoal]

30

[grand forge]

Yep

and the third one

[jaunty shoal]

24

[grand forge]

Yep

now add em all up

[jaunty shoal]

60 + 36 + 30 + 24

150

is that correct?

yup

[grand forge]

:O

congrats

[cedar kiln]

@jaunty shoal Has your question been resolved?

Channel closed

Closed by @jaunty shoal

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[steady wing]

how can i quickly tell the sequence from such a recursive relation

[steady wing]

i have to figure out the lots of seqs from such recurrence relations and i always mess up

[red pumice]

calculate a couple of terms

then try spot the pattern

[marsh vapor]

thank you heavy from tf2

[crimson delta]

there isn't always an easy way to find a closed formula

[steady wing]

okay

thank you

.close

[cedar kiln]

Channel closed

Closed by @steady wing

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[plucky notch]

I have a Patterning and Algebra math test at February 2th and I'm looking for anyone that can help me improve, I also need to learn order of operations since I messed up on an assessment because I ordered them wrong

[short blade]

we can really only help if you have specific problems, do you have any specific questions you need help with?

[plucky notch]

do you have any recourses to help me improve orders of operation

?

[frosty thicket]

the youtube

[lethal jackal]

order of operations is just something you memorize

[dull oxide]

Practice problems

No amount of watching someone else do it will make you better

You need to work on it yourself

[lethal jackal]

also I would be confused as to why that wouldn't be something you learn in like 5 minutes unless you have other gaps in your understanding

[dull oxide]

Share some problems you struggled with

[plucky notch]

the only way I can explain is by just saying

I am dumb

[dull oxide]

You are inexperienced

[lethal jackal]

what I'm saying is that you probably are missing more than just order of operations

and you should review other things first

[dull oxide]

Dumb people don't try

[plucky notch]

I was doing it in school but I forgot to

[toxic edge]

dawg

[dull oxide]

Looks like an algebra problem

Like it want to solve for b

[plucky notch]

yeah I know

[dull oxide]

Are these the type of problems you need help with?

[plucky notch]

I mean I could solve it

but

I need to do it in the teachers way

[dull oxide]

What do you mean

How does your teacher do it?

How do you do it?

[plucky notch]

I'm basically trying to say

that

I can't explain

I'm an ELL

[dull oxide]

ELL?

[plucky notch]

I'm not good at english

English Language Learner

[dull oxide]

What is your primary language

[plucky notch]

hebrew

[dull oxide]

Ah

[frosty thicket]

hmm

do you, guess it? divide by 5 first? distribute first?

[dull oxide]

If you learn another language, then you are not dumb

[plucky notch]

I a lot of hebrew words

I forgot*

[dull oxide]

I don't know any

Maybe shalom?

[plucky notch]

now I only know the words I would learn in grade one

[plucky notch]

that means hello

[dull oxide]

Shalom!

[plucky notch]

shalom

[dull oxide]

If you want to learn, then you need to practice

You need to try. You might fail. You are going to make a lot of mistakes.

But you must always try

[plucky notch]

okay

Ill go watch khan academy

[cosmic steppe]

The biggest failure is the one who doesn't try

[dull oxide]

Show me. How would you solve this?

[cosmic steppe]

That applies to me because I'm too chickeny to try ask anyone out

[plucky notch]

so

I remove the 6

I think

for that I will

do

(b - 6 + 6)

and then add 6 to 30

so then it would be

5b - 30

then

[dull oxide]

Close

You understand the ideas.

But you need help with the order. Just like you said earlier

[plucky notch]

Do you know where I can look to learn that?

[dull oxide]

Instead of adding 6 to both sides, you must add 5*6 to both sides. (Or you divide both sides by 5 first, then add 6 to both sides)

Khan academy seems to be what everyone recommends

I learn through books, but everyone else seems to prefer YouTube

[plucky notch]

oh okay

[plucky notch]

but why would I add five

?

[dull oxide]

Add 5*6

[plucky notch]

5 x 6

to both sides?

[dull oxide]

Because the left side is 5(b-6)

Do you know how to distribute multiplication?

[plucky notch]

the disruptive property?

[dull oxide]

Subtracting b and 6, then multiplying that by 5, is the same as multiplying b by 5 and then 6 by 5, then subtracting both of those

That is 5(b-6)=(5b)-(5*6)

So you're equation is really 5b-30=30

So you wanted to add 30 to both sides, not 6

[plucky notch]

what?

you're saying

that

5(b-6)

is the same as if I would multiply five by six?

[short blade]

SWR is saying you should distribute the 5 before you add or subtract anything

do you know how to distribute the 5 in 5(b-6)

[plucky notch]

b - 30?

[short blade]

why did you say 1b?

[plucky notch]

mb

my bad

[short blade]

you're good, im just wondering why you said 1b

the -30 is correct

[plucky notch]

1b = b

right?

[short blade]

yes

but we want to distribute the 5 to the b and the 6

[plucky notch]

yeah I don't know why I did that either

[short blade]

so then 5(b-6) = ?

[plucky notch]

30

?

[short blade]

5b - 30

[plucky notch]

oh

[short blade]

we multiply the 5 into the b and the 6

[plucky notch]

OH WAIt

MY BAD

omg I thought five was 1 when I was doing B for some reason

[short blade]

np

so our original equation was 5(b-6) = 30

after we distribute, what does the equation look like?

[plucky notch]

5b - 30 = 30?

[short blade]

yes

how would you solve for b from here?

[plucky notch]

remove 30?

[short blade]

let's call it "add 30 to both sides"

[plucky notch]

yeah

okay

so then

5b = 60?

[short blade]

yes

and what now?

[plucky notch]

we

would

divide

by 5?

[short blade]

yes

[plucky notch]

okay

so

5b = 30

60*

would be

b = 6

[short blade]

b = 60/5

[dull oxide]

Try again

[short blade]

what is 60/5

[plucky notch]

oh wai

ti

I thought it was 30

12

21

12

12

I'm lagging

b would equal 12

[short blade]

yes

[plucky notch]

I meant b

not 1

could anyone help me with orders of operaiton

because I'm having trouble with that

[dull oxide]

@plucky notch if you want practice

Then consider this a gift

[plucky notch]

okay thanks

[plucky notch]

I'm going to write the answers here if you don't mind

[dull oxide]

I'm busy so I'll reply slowly, but anyone should be able to help

[plucky notch]

okay

thank you

10x = 120 / 10

x = 12

I'm not sure if this would be the correct way of doing it but for 2. I would do 25 - 13 = n

[dull oxide]

Here. I numbered them:

[plucky notch]

okay thank you

[dull oxide]

👍

[plucky notch]

5a + 11 - 11 = 21 - 11

5a = 10

5a = 10 / 5

a = 2

[latent bloom]

Yep

[plucky notch]

okay

[latent bloom]

I suggest here that you write "5a/5" to indicate that you're also dividing the left side

[plucky notch]

would I do

5a/5 = 10/5

[latent bloom]

Yep

That's better

[plucky notch]

alright thank you

4. 2k - 6 = 30

2k - 6 + 6 = 30 + 6

2k = 36

2k/2 = 36/2

1 = 16

[latent bloom]

Hmm

[plucky notch]

18

mb

my bad

1 = 18

[latent bloom]

k = 18

[plucky notch]

k

yeah

oops

k = 18

5. 2(c + 1) = 14

2c + 2 = 14

2c + 2 - 2 = 14 - 2

2c = 12

2c/2 = 12/2

=

c = 6

[dull oxide]

fun fact on this problem

you can also divide both sides by 2 first

[plucky notch]

you can>

?

[latent bloom]

Yep

Try it

[dull oxide]

2(c+1)/2=14/2
c+1=7
c=6

[dull oxide]

oops. spoiler alert >>

[plucky notch]

2(c + 1)/2 = 14/2

[dull oxide]

you can try it on the next problem also. Just an alternative to consider. Either way works.

[plucky notch]

1C + 1 = 7

1C + 1 - 1 = 7 -1

=

C = 6

[latent bloom]

Yep yep

[plucky notch]

oh

it does work

[plucky notch]

It's fine I didn't look at it

[dull oxide]

https://tenor.com/view/muppet-student-math-shock-gif-21366236

[plucky notch]

so would it work with anything?

[plucky notch]

yeah

[dull oxide]

Hard to say yes to "anything"

[plucky notch]

well

I meant

[dull oxide]

But for this setup, yes

[plucky notch]

yeah ojay

okay

[dull oxide]

Like, it'll work on the next problem

[plucky notch]

6. 4(7 - 2) = 32

Ill try it here

4(y-2)/4 = 32/4

y = 8

wait

I don't think I did it right

[latent bloom]

That's true

After you divided by 4 on both sides

What were you left with?

[plucky notch]

1Y - 2 = 8?

[latent bloom]

Yep

[plucky notch]

oh

so then

1Y - 2 + 2 = 8 + 2

y = 10

[latent bloom]

Yep yep

[plucky notch]

ohhh

I get it

[plucky notch]

let me try this one know

would this be

like this

2( x + 3 ) = 7 ( x - 4)

[latent bloom]

Nope

[plucky notch]

2( 3 + x ) = 7( 4 - x)

[latent bloom]

Cross multiply

Yep

[plucky notch]

oh okay

I don't know why I did that

I guess it felt normal when x was near the number

[dull oxide]

I love hearing that

[plucky notch]

thank you

:).

[dull oxide]

uhhh. reread it

[plucky notch]

2( 3 + x ) = 7( 4 - x)

so I would do

[dull oxide]

this is incorrect

[plucky notch]

oh?

[latent bloom]

Oops

[dull oxide]

Do you know how to cross multiply?

[plucky notch]

ohh

I guess I don't

so

2 (4 - x) = 7( 3 + x)

yay

okay

8 - 2x = 21 + 7x

hmm

eight

wait

okay

so

8 + 8 - 2x = 21 + 8 + 7x

2x = 29 + 7x

umm

[latent bloom]

Psst

[plucky notch]

yeah? 👂

[latent bloom]

You can add 2x to both sides

[plucky notch]

8 - 2x = 21 + 7x

wdym

could you demonstrate?

[latent bloom]

8 -2x +2x = 21 + 7x + 2x

[plucky notch]

oh

because we only need x on one side?

[latent bloom]

Yep

[plucky notch]

okay

8 -2x +2x = 21 + 7x + 2x

8 = 21 + 9x

would I remove 28?

[latent bloom]

Why specifically 28?

[plucky notch]

9x + 21 = 8 also can I flip it?

[latent bloom]

Yep

[plucky notch]

I meant 21

[latent bloom]

Oh yeah you can remove 21 from the x's side

[plucky notch]

okay

9x + 21 = 8

9x + 21 - 21 = 8 - 21

9x = -13

9x/9 = -13/9

I'm going to need a calculator for this one sec

x = 1.4-

[latent bloom]

You can keep it as a fraction

[plucky notch]

wdym?

[latent bloom]

x = -13/9

[plucky notch]

oh I can?

[latent bloom]

Yeah

[plucky notch]

if we cant use calculators then that would be very useful

[latent bloom]

Yep

More experience with fractions will make you spot the decimal form of numbers just by looking at them

[plucky notch]

it will?

I don't think that will happen to me anytime soon

maybe during the summer

I could practice a lot of math

because I don't have enough time in the day for all my homework

anways

7. -4z = -8

so

-4z/4 = -8/4

z = -2

no

something is wrong

if its negative then

-4 x -2 = +8

I'm not sure what I'm doing wrong here

[latent bloom]

Your step here was correct

[latent bloom]

But this is wrong

[plucky notch]

oh wait

negative / positive = negative?

right?

[latent bloom]

In addition, it's not always the case

But in multiplication, it is a property

negative * positive = negative

[plucky notch]

I meant division

[latent bloom]

And negative/positive = negative too

[plucky notch]

division and multiplication would be the same right?

[latent bloom]

Wdym same?

[plucky notch]

like if

• x + = -

• / + = -

[latent bloom]

Yep

What if it was ( - x - )?

[plucky notch]

positive

[latent bloom]

Yep

Same case for division

[plucky notch]

yeah

-4z/4 = -8/4

so this would be

z = -2?

or

positive

[latent bloom]

If you divided by 4 only, then you will get -z = -2

[plucky notch]

so what was I doing wrong

is it the -z?

[latent bloom]

Yep

[plucky notch]

and if it was normal z

it would be

z = 2

[latent bloom]

Yep

[plucky notch]

oh I see

[latent bloom]

Here's a quicker way to clear out -4z = -8

[dull oxide]

I'm glad I put that problem in hehe

[latent bloom]

-4z/(-4) = -8/(-4)

[plucky notch]

yeah thanks

[latent bloom]

z = 2

[plucky notch]

oh

that is faster

thanks :).

[latent bloom]

[plucky notch]

if I get that on my tests then you guys saved me from losing marks 🙂

8. 2h = h + 7

2h - h = h - h + 7

1h = 7?

[latent bloom]

Yep

[plucky notch]

okay!

9. 3( 2 + g) = 4g - 9

so

would it be

6 + g =

or

6g

=

6G = 4g - 9

[latent bloom]

Nope

[plucky notch]

6 + g = 4g - 9?

[latent bloom]

Something is missing here

[plucky notch]

hmm

oh

found it

6 + 3g = 4g - 9

hopefully I don't make mistakes like this on my test

[latent bloom]

It takes practice

[plucky notch]

6 + 3g - 3g = 4g - 3g - 9

[plucky notch]

yeah

[latent bloom]

And patience 🙂

[plucky notch]

6 = 1g - 9

[plucky notch]

every time I have a test I stress a lot

and make silly mistakes

on time I forgot to answer a question in a test

because I didn't see it

6 = 1g - 9

6 + 9 = 1g - 9 + 9

15 = 1g

1g = 15

10. 6(2 - m) = -3(4m - 9)

6(4m - 9) =-3(2 - m)

[latent bloom]

Hmm

Why did you switch them?

[plucky notch]

?

I thought I needed to do this for some reason

my bad

is it only for fractions?

[latent bloom]

Yep

Both sides are fractions

[plucky notch]

6(2 - m) = -3(4m - 9)

[latent bloom]

You'll see in the next problem that cross multiplication won't work

[plucky notch]

12 - 6m = -12m - 27

[plucky notch]

okay

-3(4m - 9) for this

is

-3(4m - 9)

would it be -9?

[latent bloom]

Yep

[plucky notch]

okay

12 - 6m = -12m - 27

12 - 6m + 6m = -12m + 6m - 27

[latent bloom]

Multiplication here is incorrect

[latent bloom]

Wait

[plucky notch]

what?

[latent bloom]

This is incorrect

Or rather something is wrong in it

[plucky notch]

wait

[latent bloom]

You pointed out that -9

Which was good

And it is being multiplied by -3

[plucky notch]

yeah?

do I remove the minus?

into plus?

[latent bloom]

Yep

-3*-9 = +27

[plucky notch]

12 - 6m = -12m + 27

so like this>?

[latent bloom]

Yep

[plucky notch]

oaky

okay

12 - 6m + 6m = -12m + 6m + 27

[latent bloom]

Mhm

[plucky notch]

12 = -6m + 27

12 - 27 = -6m + 27 - 27

-15 = -6m

Ill flip it

because I like the M on the other side

-6m = -15

-6m/6 =15/6

[latent bloom]

Wait

[plucky notch]

wiat

you showed me

something earlier

that I can do

I think

[latent bloom]

Yep

[plucky notch]

let me check

I can't find it

could you remind me what you showed me earlier??

[latent bloom]

.

[plucky notch]

okay thanks

-6m/-6 = -15/-6

m = 2.5

[latent bloom]

Yep

[plucky notch]

okay

Ill repost the question

oh

11. 2/3x + 4/5 = 1/2

this is difficult

[latent bloom]

Hmm

Why is it?

[plucky notch]

I don't know how to start

[latent bloom]

[plucky notch]

wait

remove 4/5?

[latent bloom]

Yep

[plucky notch]

2/3x + 4/5 - 4/5 = 1/2 - 4/5

2/3x = -3/5

[latent bloom]

Hmm

Nope

[plucky notch]

I kind of forgot how to subtract fractions

[latent bloom]

Hint: common denominator

[plucky notch]

oh wait

1/2 x 4 = 4/8 - 4/5?

[latent bloom]

You made them have a common numerator

[plucky notch]

oh

yeah

but I don't know

how to make the denominator

because 5 is odd

and 2 is even

[latent bloom]

Well

Multiply 1/2 by 5/5

What do you get?

[plucky notch]

5/10

?

[latent bloom]

Okay

Now multiply-4/5 by 2/2

[plucky notch]

uhm

-8/10?

[latent bloom]

Yep

[plucky notch]

oh

so

-8/10 - 5/10?

[latent bloom]

5/10 -8/10

[plucky notch]

oh

okay

uhm one second

2/3x + 4/5 - 4/5 = 5/10 -8/10

2/3x = -3/10?

[latent bloom]

Yep

[plucky notch]

then I do

2/3x % 2/3 -3/10 % 2/3

?

[latent bloom]

This is a bit confusing

It's better to do this

[plucky notch]

here

[latent bloom]

$\frac{2}{3} x \times \frac{3}{2} = \frac{-3}{10} \times \frac{3}{2}$

[wraith dagger]

VulcanOne

[plucky notch]

oh wow

that's useful

wait

is it times

because it fractions

are like

division?

[latent bloom]

Wdym?

[plucky notch]

like

isn't it supposed to be 2/3 divided by 2/3

[latent bloom]

Yep

But this is confusing

However

It is equal to multiplying by the reciprocal

[plucky notch]

wdym

?

[latent bloom]

Reciprocal of 2/3 is 3/2

[plucky notch]

you swapped 2/3 to 3/2

[plucky notch]

okay

oh

so that would turn division into multiplication

??

[latent bloom]

If you divide a fraction by another fraction, then the fraction on the denominator can be reciprocated and multiplied to the fraction on top instead

Like so

$\frac{\frac{2}{3}}{\frac{2}{3}} = \frac{2}{3} \times \frac{3}{2}$

[wraith dagger]

VulcanOne

[plucky notch]

hm

so if it was

oh wiat

so we just changed the denominator and the nominator

and replaced the division

with multiplication?

oh I see

[latent bloom]

The numerator stays the same but we just reciprocated the denominator and made division into multiplication yes

[plucky notch]

oh okay

2/3x = -3/10

would be

2/3 x 3/2

we need to find greatest common multiple?

[latent bloom]

Nope

[plucky notch]

ooPS

IM EANT

we need to find

change

their denominators to be the smae

same

[latent bloom]

That's only when you add fractions

[plucky notch]

what would I do if it is multiplication?

just

[latent bloom]

Multiply numerator by numerator and multiply denominator by denominator

[plucky notch]

wdym

like cross

[latent bloom]

Nope

[plucky notch]

oh

wAIT

I red it wrong

I thought you said

numerator by denominator

2/3x = -3/10

2/3x times 3/2 = 6.6

6/6

[latent bloom]

Yep

[plucky notch]

-3/10 x 3/2

9/20?

[latent bloom]

-9/20 yep

[plucky notch]

6/6 = -9/20

x

x = -9/20

yeah you were right

this one was complicated

last question!
!

[latent bloom]

[plucky notch]

2/3+x = 7/4-x

I think its that

[latent bloom]

You did this before

[plucky notch]

12. 2/3+x = 7/4-x

[latent bloom]

Btw

[plucky notch]

wdym

[latent bloom]

Please write parentheses when you have fractions that have complex numerators and denominators

Like

2/(3+x) = 7/(4-x)

[plucky notch]

oh okay

I don't think my test is going to have anything as complicated as the last two questions

but it's still good to go over them

[plucky notch]

we need one x

so I would remove

[latent bloom]

Remember cross multiplication

[plucky notch]

oh

2/(4-x) = 7/(3+x)

2/(4-x + x) = 7/(3+x + x)

[latent bloom]

Nope

[plucky notch]

okay

2/(4-x) = 7/(3+x)

I would remove three first?

[latent bloom]

Nope

https://cdn.discordapp.com/attachments/903430334681608232/1069049097090240522/v4-460px-Cross-Multiply-Step-3-Version-3.png

[plucky notch]

but didn't we change the order?

2/(4-x) = 7/(3+x)

[latent bloom]

Still applies

When both sides are fractions

[plucky notch]

wdym

2/(3+x) = 7/(4-x)

it was like this

before we changed

[lethal jackal]

honestly I kinda hate how it's taught as "cross-multiply" instead of "multiply both sides by 13x"

like why do they have to teach it that way

it's not immediately obvious why cross-multiplication works

and then people try to cross-multiply a/b + c/d

[latent bloom]

It's taught as cross multiplication because it looks like a cross

So it's easier to remember

[plucky notch]

I'm confused

[latent bloom]

I suggest that you take a small 5 minutes break

Then return to the problem

[plucky notch]

okay

Ill brb

I'm back

2/(3+x) = 7/(4-x)

so because of cross multiplication we change it to 2/(4-x) = 7/(3+x)

or do we do something else?

hello?

hello?

<@&286206848099549185>

what?

[lethal jackal]

try multiplying both sides by (3+x), what do you get?

[plucky notch]

so do I do

2/(3+x) x 3+x

and the same to the other side?

hello?

@latent bloom I'm sorry for pinging but are you still online?

okay I guess Ill answer the last one tomorrow

[latent bloom]

<@&268886789983436800> spammer

[latent bloom]

I'm here now sorry

[calm sierra]

ty

[cedar kiln]

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[wheat quarry]

I'm stuck with this question and have no idea how to approach it

[fair geyser]

Solve is one thing, that's (x!)y + x - 1

But I've no idea how to describe it or what's the application

oh maybe they mean describe all recursive relations that makes more sense

[wheat quarry]

Its a recursive function that returns y when x = 1 otherwise returns f(x-1, x+y) +1

We have to derive a general formula for it I suppose

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[marble hedge]

Can someone help me here? Pretty sure AL=CP (what Jan has here) isn't equal

And Nancy is wrong here bc to prove something false, you gotta show at least one counter example, so her argument is valid.

[cedar kiln]

@marble hedge Has your question been resolved?

[marble hedge]

?

[livid hound]

if your concern was with AL and CP not being equal,
the above diagram / considering stuff like perp bisection theorem addresses why its possible

i'll add in more labels to make explanation easier if needed

[marble hedge]

Can you explain how AL and CP are equal? Shouldn't AL and CP would look equal if this were the case

[livid hound]

in this diagram do you have any issue with AL = CM?

[marble hedge]

Yes

I mean

No

I thought u asked if I agreed* whoops

[livid hound]

now focussing on triangle PCM

there is a point P where CP = CM

[marble hedge]

Yep

[livid hound]

so overall its possible to have a P as drawn in the diagram such that
AL = CM = CP
AL = CP

[marble hedge]

CP = CM

Ok I have an issue with this.. How can CP=CM... After you touch M, you go up to touch P... Both of which are in two different places

[livid hound]

now focussing on triangle PCM
there is a point P where CP = CM
you responded with yep

implying you had no issue with that

[marble hedge]

I said yep bc I was letting you continue (I wanted to see with what you were gonna conclude with)

[livid hound]

then you should say so immediately to avoid confusion,
saying yes implies you accept / have no issue with what I'm saying

After you touch M, you go up to touch P... Both of which are in two different places
the two lines have the same length

consider a basic isosceles triangle

JK has a certain length,
and if you move further down the line to point L,
JL has that exact same length

[marble hedge]

Aight I think I get what you're saying

.close

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[crimson sedge]

Are we still using this??

SOS

It doesn't seem like the formula is used

Ik how both works but why suddenly different

[cosmic steppe]

No

It's just PDF, splitting the fraction, and then using u-sub whenever appropriate

[crimson sedge]

Wdum

Whats PDF

And u-sub

[cosmic steppe]

Practical fraction decomposition

I meant PFD

Autocorrect changed it

[crimson sedge]

Oh yea yea I know why we do that

But why is

[cosmic steppe]

You haven't done u-subs?

Could you solve this:

$$\int 3x^2e^{x^3}dx$$

[wraith dagger]

Umbraleviathan

[cosmic steppe]

That's from a u-sub

[crimson sedge]

Not

[cosmic steppe]

If you let u = 3x^2

[crimson sedge]

U sub?

[cosmic steppe]

_ _

[crimson sedge]

Yea ik that

[cosmic steppe]

Like what's your process for solving that

It's essentially the same

If we isolate that term

[crimson sedge]

This

[cosmic steppe]

Well yeah that's basically a u-sub but for some reason you've been taught it a really notation-heavy way

$$\int \frac{6x}{1 + 3x^2}dx$$

Let $u = 3x^2$. Then $du = 6x dx$. From direct substitution:

$$\int \frac{6x}{1+3x^2}dx = \int\frac 1{1+u} du$$

Using our knowledge of common integrands:

$$\ln|1+u|$$

Plug back in $u = 3x^2$:

$$\ln|1+3x^2|$$

[wraith dagger]

Umbraleviathan

[cosmic steppe]

https://en.m.wikipedia.org/wiki/Integration_by_substitution

[crimson sedge]

Okok thanks

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[tropic stone]

Recently got into quadratic equations and Vieta's formulas ( hope that's what they are called ) and want to see if I'm doing everything correctly. Here I need to find m and solve the equation and I'm given one of the roots

[cedar kiln]

@tropic stone Has your question been resolved?

[tropic stone]

<@&286206848099549185>

[crimson sedge]

It is correct

[tropic stone]

Okay

.close

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[trim crescent]

Hello, could someone try and help me understand this concept ?

[trim crescent]

I’m not too sure i understand fully what a set is, does anyone have an example ?

[earnest socket]

the intersection of the family of sets is the set of elements that belong to all of the sets in the family

[trim crescent]

My man ❤️

[earnest socket]

similarly, the union of the family of sets is the set of elements that belong to some (at least one) of the sets in the family

[trim crescent]

I see

[trim crescent]

Wait the union isn’t the "sum" of the interval of each set ?

[earnest socket]

what do you mean "the interval of each set"?

[trim crescent]

A1, A2 etc

[earnest socket]

the index set I?

I is just a subset of the natural numbers

[trim crescent]

I’m not too sure what that is

So I is just N ?

[earnest socket]

actually no it defines it as the integers

if you see above

[trim crescent]

Defines what as the integers ?

I ok

Well this is just an example so lets consider the general form

Lets consider A1, it could for example be {1,2,3,4}, correct ?

And A2 could be {1,2}

[earnest socket]

sure

the sets could be anything

the index set is what controls the indices/labels/names of the set

[trim crescent]

Ok and is it {} or [] ?

[earnest socket]

curly braces

{}

[trim crescent]

Okokok

The index is I right ?

[earnest socket]

I is the set of all possible indices for said family of sets

so if you have an infinite collection of sets {A1, A2, A3, ...}, I would be {1, 2, 3, ...}

[trim crescent]

So I can’t be R for example ? Because we’d have an infinit number of indexes

[earnest socket]

you are allowed to have an infinite number of indices

[trim crescent]

Ok i see

[earnest socket]

as above

called an infinite intersection/infinite union

[trim crescent]

But we’d have an infinite amount between 1 and 2

Or 0.1 and 0.2

Etc

[earnest socket]

typically indices are integers

[trim crescent]

So we couln’t event define I_o to I_1

[earnest socket]

because there's a difference between a countable union and an uncountable union

[trim crescent]

?

[earnest socket]

although you might not be familiar with this fact

[trim crescent]

Nope not yet haha

[earnest socket]

too advanced for now

you can ignore

[trim crescent]

Ok i think the index and set concept is understood now

[earnest socket]

if you had a finite collection of sets {A1, A2, A3}, then I would be {1, 2, 3}

[trim crescent]

I see

But how is the union a part of the set ? ( might not be the best formulation )

Lets say A1 = {1,2}, A2 = {2,3} and A3 = {4,5} the union for I = {1,2,3} would be {1,2,3,4,5} surely ?

[earnest socket]

yes

[trim crescent]

And the intersection is the null space ?

[wraith dagger]

tushar

[earnest socket]

yes

[trim crescent]

Ok great

[earnest socket]

because there are no elements x such that x is in A_i for all i in I

that is what the image you posted tells you

[trim crescent]

Does this concept extend to vectors for example ?

[earnest socket]

sure

sets are probably the most general things you can talk about in math

[trim crescent]

Yeah ofc makes sense

[earnest socket]

this applies to sets of vectors for that reason

[trim crescent]

This was just a recap in our probability class

[earnest socket]

the image you posted simply extends the definition of union and intersection between two sets to many sets

[trim crescent]

So i expect we’ll only be using integrals ?

[trim crescent]

I see i see

Actually pretty simple

The Ai notation was messing with me though

[earnest socket]

union is the elements in either of the sets, intersection is the elements in both

that screenshot replaces either -> some and both -> all

existential and universal, respectively

[trim crescent]

I see

[earnest socket]

that's the key takeaway

[trim crescent]

Thx man everything seems to be crystal clear now

Take care brother you’re the man

❤️❤️

[earnest socket]

you too

[trim crescent]

.close

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[south cobalt]

i keep messing up here-

[south cobalt]

im gonna use the washroom ill be back in 3 minutes :)

[copper crest]

Show work

[upper garnet]

!status

[cedar kiln]

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

[south cobalt]

i did it

but i think im wrong

so deleted the answer

can you help?

.close

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[warm cypress]

Help!!!

[cedar kiln]

@warm cypress Has your question been resolved?

[crimson delta]

partial fractions

[warm cypress]

How

[crimson delta]

maybe do it by hand for m=3 or m=4 and then you see how the general case goes

do the cover up method, dont multiply everything out

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[digital shell]

hello, how can I solve this?

[lusty grotto]

if g is a horizontally scaled version of f, and the scaling factor was some number k, what would the equation of g be?

in terms of k

[digital shell]

4x

4 times larger

[lusty grotto]

what?

[digital shell]

so the same equation but 4x

since it's scaled by a factor of 4

[lusty grotto]

okay so thats ur answer

[digital shell]

but it tells me it's wrong

[lusty grotto]

g is what u get when u put 4x into f, isntead of just x

[lusty grotto]

how did u enter ur answer?

actually wait

no

[digital shell]

well there's some options i'll send a ss

[lusty grotto]

g is not this

yeah

[digital shell]

I thought it was top one

[lusty grotto]

okay so u want g to prduce the same output as f does at x=1, but at x=4

[digital shell]

then g needs to be 1/4th of f

[lusty grotto]

yeah

[digital shell]

okay so that was correct, but I keep confusing these things

[digital shell]

how can I know this solely from looking at my question

[lusty grotto]

clearly u can see from the pic that g is equal to 2 at x=4, but f is equal to 2 at x=1

to get the same output from g, u want a bigger input

[digital shell]

but g is scaled horizontally by a factor of 4 by looking at the graph. Then it doesn't make sense to me

[lusty grotto]

its when u divide the input to a function by some number that the function gets stretched horizontally by that factor

if u multiply the input to a function by a number the function gets compressed horizontally by that factor

basically, if a graph looks stretched out horizontally, the input needs to be divided by that factor, if it looks compressed, the input needs to be multipled

[digital shell]

I'm not following, how could I solve this problem if you didn't tell me

[lusty grotto]

lol idk whats going on in ur mind

[lusty grotto]

what exactly are u not follwing

[digital shell]

well you told me how I could solve this. But what should my approach be to similar problems

I wouldn't be able to solve this unless you told me how to

so I want to be able to solve these kind of problems myself

[lusty grotto]

oh

[digital shell]

but I don't know what method I can use

[lusty grotto]

well can u by looking at a picture decide whether a graph looks stretched out or compressed

[digital shell]

I believe so

[lusty grotto]

okay u see then that the dotted graph here looks like a stretched out version of f

?

[digital shell]

yes

[lusty grotto]

and u see that its stretched out by a factor of 4?

[digital shell]

yeah

[lusty grotto]

then its equation must be f(x/4)

if it was stretched out by some other factor k

then its equation wud be f(x/k)

[digital shell]

how can it? f should be 1/4 of g and g should be 4x f

[lusty grotto]

no we are talking abt horizontal scaling not vertical scaling

[digital shell]

horizontally speaking f is 1/4th of g

so then the equation for g should be 4 times

[lusty grotto]

f is a compressed version of g yes

[digital shell]

yeah f is compressed

[lusty grotto]

so f gets the inputs that g gets, before g gets them

if f is compressed

yeah?

[digital shell]

what do you mean by that? could you give example

[lusty grotto]

g gets the input to produce the output 2 at x = 4, but f gets the input to produce the output 2 before x = 4, i.e., when x is a number smaller than 4

[digital shell]

yeah

[lusty grotto]

what must u do to a number smaller than 4, so that when u input that number to f, the number equal to 4

[digital shell]

you mean the range of the function?

[lusty grotto]

no

okay so

g is stretched out version of f, meaning g gets the input to produce the output 2, AFTER f gets the input to produce the output 2

[digital shell]

yes

[lusty grotto]

f gets the input to produce the output 2, at x = 1 right

g gets the input to produce the output 2, at x = 4

[digital shell]

yeah

[lusty grotto]

g produces the output that f produces at x = 1, but at x = 4
what can u do to the number 4, so that u can get the same output by inputting it into f