help-13

[vast coral]

The question needed me to find the radius basically

Thanks a lot

!close

[shut reef]

smh

.

[vast coral]

Srry

.close

[cedar kiln]

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[azure tartan]

A rectangle has an area of 6x^2 - 7x+ 2cm^ 2. Determine the expressions that could represent the length and width of the rectangle

[azure tartan]

<@&286206848099549185>

.

@gaunt hamlet this one has my name

[gaunt hamlet]

Then construct a system of equations

x + y = 12 and xy = 12

[azure tartan]

I tried I didn't get an answer

[gaunt hamlet]

Show work

[gaunt hamlet]

The answer isn't gonna be an integer

That's why you gotta construct the system of equations

[azure tartan]

Is it going to be negative

[gaunt hamlet]

No. Both numbers will be positive

[azure tartan]

So it's a decimal number

[gaunt hamlet]

Yes

[azure tartan]

I was trying to do this question but I need a whole number for it

[gaunt hamlet]

What have you tried in regards to that problem?

[azure tartan]

I did a= 6 b= 7 c= 2 and ac= 12

[gaunt hamlet]

Are you trying to factor the polynomial?

[azure tartan]

Yeah

[gaunt hamlet]

How do you plan on doing that?

[cedar kiln]

@azure tartan Has your question been resolved?

[cedar kiln]

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[cedar kiln]

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[quasi compass]

<@&286206848099549185>

[crimson oyster]

okay first off

.15

It hasn’t been 15 at all

Second, post your question first man

[pseudo skiff]

What the fuck bruh

[crimson oyster]

Read the instructions

[pseudo skiff]

!15min

[cedar kiln]

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

[crimson oyster]

.close

[cedar kiln]

Channel closed

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[crimson oyster]

fuck you dude :/

[quasi compass]

How do u solve this? Ive not tried anything yet to figure this out can someone give a hint

[upper abyss]

Uh okay

[quasi compass]

Sorry dude u gotta be...

[pseudo skiff]

You need to read the rules

[quasi compass]

Sorry

I didnt see him

[upper abyss]

Still a strange response

[pseudo skiff]

.open

.reopen

[cedar kiln]

✅

[pseudo skiff]

I’m not helping with this tho so gl and don’t unnecessarily ping again 👍🏻

[upper abyss]

I don't see a u-sub. Luckily ln falls nicely to ibp

[quasi compass]

Ibp?

[upper abyss]

Integration by parts?

Not there yet?

So you specifically want a u-sub solution?

[quasi compass]

Wait
...

[quasi compass]

Is that possible?

[rugged palm]

What's the numerator I can't read it

?

[upper abyss]

I think the question is
∫ ln(x² + a) / (x² + a) dx

[upper abyss]

Not necessarily, haha. I'm asking if your teachers would expect a u-sub solution

Because if they expect it, then it should be possible?

[rugged palm]

f I read (1-(x²+4))/(x² + 4) and thought it wasn't that bad

[upper abyss]

f

[cedar kiln]

@quasi compass Has your question been resolved?

[cedar kiln]

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[gaunt trench]

i have no clue what the question is asking...

[west dome]

does the psuedocode currently do what the question asks

[flint plinth]

can you see why the current pseudocode is wrong?

[west dome]

they want you to fix it

[gaunt trench]

uhh

[west dome]

(by changing only one word or symbol, for grading purposes presumably)

[gaunt trench]

shoulde it be not (A and B) or C

[gaunt trench]

its a paper copy xd

[west dome]

what happens if A is True, B is true, and C is true here?

[gaunt trench]

T

[west dome]

so which statement gets executed

[gaunt trench]

statement 1

hmm

[west dome]

and we wanted statement 2, right?

[gaunt trench]

yes

[west dome]

you can write a truth table if need be

if that would help

[gaunt trench]

trurth table for this will be very long lol

[west dome]

theres only 3 inputs

which test case does the psuedocode currently fail

try from that angle

[gaunt trench]

well if A is true and B is true and C is true

then it executes statement 2

[west dome]

i mean the psuedo-code in the question

(theirs is closer to correct)

[quasi compass]

Use quick table

[gaunt trench]

hmm

[gaunt trench]

whats that?

[gaunt trench]

im sorry i dont know lol

[west dome]

so you think it passes all of them?

youve checked them all?

[gaunt trench]

okay so i made this

[west dome]

ok, do all of these have the desired result?

[gaunt trench]

only 3 of them do

[west dome]

The only one which should be true is F F T

"execute statement 1 when A is F, B is F, and C is T, statement 2 otherwise"

[gaunt trench]

oh

umm

[west dome]

so which ones are wrong here

[gaunt trench]

the first and second true statement

[west dome]

right

now think about why they did not give the desired result

[gaunt trench]

uhhh

the desired result is F right toexecute stament 2?

[west dome]

yes

[gaunt trench]

thats because C was alos true

we need to make C false

would it be (A and B) not C

[west dome]

that is not the reason

just look at not(A and B)

we want this to be true only whenever A and B are both false

this is currently not the case

fix that

[quasi compass]

When you deal with long statements use indirect table to calculate things easily

[cedar kiln]

@gaunt trench Has your question been resolved?

[cedar kiln]

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[sharp helm]

im reviewing u substitution and have a simple error im making somewhere

[sharp helm]

its just integral of cos^2(2x)

after i rewrite as integral .5(1+cos(2x))

I understand I can separate and rewrite as two integrals and then solve the one with cos(2x) using u sub

but if I keep them together: u=2x -> du = 2dx -> dx = du/2 -> .5 * integral (1+cos(u)) du/2

[torpid fulcrum]

it should be cos^2(2x)=.5(1+cos(4x))

[sharp helm]

pause where

oh wait what

oh my bad

nvm nvm ty

.close

[cedar kiln]

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[sharp helm]

ah reopen reopen

i wrote it wrong

cos^2(x)...

my point was that .5 integral (1+cos(u)) du/2

am i treating the du/2 wrong when i write it as .25 integral (1+cos(u)) du

[cedar kiln]

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[torn atlas]

i do not get this. if someone can provide keywords for youtube video which can explain this concept, that would help

[torn atlas]

i don't know why there are two x's, and i don't see how this is an equation since it isn't equal to anything

[dire geode]

What the heck is y=?

i?

[torn atlas]

i am doing example 3

[dire geode]

Yea

What's it say under the figure

[dire geode]

What letter is that

Or symbol

[torn atlas]

lambda

λ

[dire geode]

So what's lambda equal to

[torn atlas]

usually stands for a constant

[dire geode]

That plane in the figure does not look like y= constant

[tropic oxide]

that does not look like lambda to me

that looks to me like x with its top cut off by bad typesetting/printing/photocopying/whatever

[dire geode]

Ooooo

[torn atlas]

why are there so many normal looking x's there then

[dire geode]

Yes makes much more sense now

Also it matches the graph

[torn atlas]

ughhh

i love it when textbooks needlessly make things more confusing

is there any where else i can learn these concepts? i learn so much faster if it is just youtube or something

even paul's math notes

[dire geode]

The book's not at fault. The printer is

[torn atlas]

its not pritned

printed

its an ebook

[dire geode]

Scanner's fault

[torn atlas]

do you guys know of anywhere else that covers these topics?

i guess that makes sense tho

thanks.

.close

[cedar kiln]

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[opal sierra]

https://youtu.be/sdYdnpYn-1o In this video at 1:40-2:17 can you explain exactly what he did?

[opal sierra]

I might be offline soon so feel free to direct message me if you feel like it.

[rugged palm]

He just simplified and then used

$\int k f(x) dx = k \int f(x) dx$

[wraith dagger]

Nonna

[rugged palm]

k is a constant

[opal sierra]

Can u explain what he simplified, why and how?

[rugged palm]

du/2x with 4x

x cancels out

you are left with 2

[opal sierra]

Is this an integral rule

And 2x was equal to 4x?

[opal sierra]

And can you please answer this

[rugged palm]

$\int4\cancel{x}[u]^3 \frac {du}{2\cancel{x}}\
\int2[u]^3 \frac {du}{\cancel 2}$

[opal sierra]

Yup what next?

[wraith dagger]

Nonna

[rugged palm]

I simplified the 4

[opal sierra]

How did u simplify it?

[rugged palm]

Uhm

[dusty hazel]

4/2

= ??

[opal sierra]

2

[dusty hazel]

So yeah that's what they did.

[rugged palm]

$4 \cdot \frac {something} 2$

[wraith dagger]

Nonna

[opal sierra]

Ok

[opal sierra]

How could they do that?

[dusty hazel]

This has a four in the numerator. A 2 in the denominator, you tell me why would you not do that?

If I give you 4x/2 wouldn't you just say it's 2x?

[opal sierra]

Du is in the numerator

[dusty hazel]

yeah

We aren't cancelling du

[dusty hazel]

Here you have x in the numberator also.

Does that stop you from doing 4/2?

It doesn't.

[opal sierra]

Ok

And finally what’s with the 2 in front of the integral sign?

[rugged palm]

Its because of this rule

[opal sierra]

Ohhhhh

Ok

[opal sierra]

It doesn’t make it possible though

[dusty hazel]

?

[opal sierra]

The x doesn’t tell you u can do 4/2

[dusty hazel]

Neither does du

[opal sierra]

So why can u

[dusty hazel]

4/2 is independent of the two.

[opal sierra]

Wdym?

[dusty hazel]

It's probably basic algebra stuff, check it out.

ab/c = a/c * b or a * b/c

Put a = 4, b = x, c = 2

4x/2 = 4/2 * x

That's why

It's allowed.

[opal sierra]

Ohhhh that’s ittt

Thanks both of you guys

Probably one of the best explanations I’ve ever seen

Thanks and .Close

[rugged palm]

Btw this works with derivatives too, it's just that with derivatives it's natural to just do it

Thanks

[opal sierra]

.close

[rugged palm]

@opal sierra you have to write .close only

[cedar kiln]

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[rugged palm]

ok nice

[opal sierra]

Ohh

Thx

[cedar kiln]

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[errant hazel]

I need help creating an equation

or would this be correct

[cedar kiln]

@errant hazel Has your question been resolved?

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[fierce stag]

weird language mean equal

[cedar kiln]

@fierce stag Has your question been resolved?

[fierce stag]

<@&286206848099549185>

[warm slate]

I'm taking a look now. This question looks tricky!

[fierce stag]

thank you

take your time

[sacred stone]

$$1+n^2+n^4 = (1 - n + n^2) (1 + n + n^2)$$

[wraith dagger]

秋水

[sacred stone]

then you can do partial fraction decomposition
$$\frac{1}{1+n^2+n^4}=\frac{1}{2 \left(n^2-n+1\right)}-\frac{1}{2 \left(n^2+n+1\right)}$$

[wraith dagger]

秋水

[lofty portal]

I'm currently here, still working on it

but I think this is a telescopic series

[warm slate]

Yeah indeed this is telescopic

[fierce stag]

should i do it manually?

[warm slate]

This would do it, right?

Because $(n+1)^2 - (n+1) + 1 = n^2 + n + 1$

[wraith dagger]

Boytjie

[sacred stone]

yes