help-0

[lethal belfry]

Use this form of the line:- $\frac{x}{a}+\frac{y}{b}=1$

[ocean seal]

physicsrocks

[vale wigeon]

now incorporate the fact that the line goes thru (4,0)

[alpine sable]

how

[vale wigeon]

do you know what it means for a line to go through the point (4, 0)?

[alpine sable]

no

@vale wigeon

[vale wigeon]

it means that if you put x=4 and y=0 into the line's equation, it remains true.

you should maybe review the whole topic of equations of straight lines after this

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

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[lone heart]

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[warped topaz]

https://i.imgur.com/tWhqcXD.png

[rustic notch]

Oh shoot mb

[warped topaz]

Npnp

Part d, I thought it was going to be an easy question but I couldnt figure it out

I got the derivative of (x^2 + x + 1)/(x + 1) = 0
First using long division to get x + 1/(x + 1) = 0
Then using quotient rule to get 1 + 1/(x + 1) = 0
x + 1 = -1
x = 0
Did I do something wrong?

[hushed locust]

how did you get that derivative

[warped topaz]

Using quotient rule

Oh wait I see my mistake

Its supposed to be 1 - 1/(x + 1)^2 = 0

[tacit arch]

f(x) doesn't have a maximum

[hushed locust]

i assume they mean a local maximum

[tacit arch]

oh

[warped topaz]

So x = 2, sub that in to f(x) and I have the coordinates? Thats the answer?

Wait no 1 min

[hushed locust]

still need to revisit that derivarive

[tacit arch]

i recommend simplifying the function first

[warped topaz]

x = 0 and x = -2
I assume this is my max and min

[warped topaz]

What do I still need to do with the derivative sry?

Nvm I think I got the answer

Thank you!

❤️

.close

[lone heart]

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[rustic notch]

\

[rustic notch]

Yo Im back

Where this base bro

"

<@&286206848099549185>

[lone heart]

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.

[rustic notch]

Oh ight

[wary stream]

What's the full question?

[rustic notch]

How do i get the area of this

[upper whale]

You need to use a different formula, Area = pq/2 where p and q are the two diagonals of the rhombus

[rustic notch]

Ohh

So i find the distance between the diagonsl

then divide by 2

[upper whale]

Each diagonal is the distance from one to the opposite point so for this example

p = Distance from F to H
q = Distance from I to G

[rustic notch]

Alright

[upper whale]

and then multiply them and divide them by two

[rustic notch]

Oh so i get both of the diagonsl

then mulitpy them

then divided by 2

[upper whale]

Yea

[rustic notch]

Ight

Thank u again br

[upper whale]

Np

[wary stream]

Btw I suggest you look up things you don't know, ie area of rhombus, you can look up the formula and try it yourself

[rustic notch]

Yea it worked

[rustic notch]

Oh mb

[lone heart]

@rustic notch Has your question been resolved?

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[rustic notch]

@upper whale yo sorry to disturb but I need your help

[lone heart]

Please don't occupy multiple help channels.

[rustic notch]

Wym

[wary stream]

Don't ping specific people and don't open multiple channels

[rustic notch]

Ye I accidentally opened another one

Mb bro

[upper whale]

What's up?

[wary stream]

Repost your question

[rustic notch]

Here you go guys

[upper whale]

The opposite angles of a parellogram are equal

[wary stream]

Hint, opposite angles are equal

Adjacent angles add to 180

[rustic notch]

Hm

So y is 85

x is 95

z is 95

[upper whale]

No, -4y + 5 = 85

So you have to solve for y

[rustic notch]

OHH

Alr ik what to do now

Thank u

[upper whale]

Yup

[rustic notch]

I got a negative number

-209

-20

[wary stream]

Yeah that's fine

[upper whale]

That's fine

[rustic notch]

Ohh

Alr

[upper whale]

The angle can't be negative, but when you plug it back in you get a positive angle

[rustic notch]

ye i got 85 now

[wary stream]

That website checks your answer so you can submit it to see if you got the values correct

[upper whale]

Teachers can set it to only 1 try

[rustic notch]

Yea they did

I get pentalty if i get it wrong

[wary stream]

And a penalty is fine, it just shows what you need to review

[rustic notch]

Oh i got it wrong

8x+7=71?

[wary stream]

If you only submitted just the answer to y, that's the reason. I'm pretty sure you have to submit all of the parts at the same time

[wary stream]

Yes

[rustic notch]

o

Ight

Okay i got 8

Do i put 8 inside 8x+7 to get the angle?

8(8)+7

[wary stream]

Why are you looking for angles?

[rustic notch]

Oh yeah

Im dumb

I mean X

[wary stream]

This question has nothing to do with angles

[rustic notch]

Yea i mean x

Do i put it in to find x

[wary stream]

No

[rustic notch]

So 8 is X?

[wary stream]

You already found it

[rustic notch]

Igh

[wary stream]

Yes

Now do the same for y

[rustic notch]

I got -168

-167

-y+3=170

[wary stream]

That's it

[rustic notch]

Alr How do i do this one

[wary stream]

Literally what was stated before

opposite angles are equal
Adjacent angles add to 180

[rustic notch]

ight i got 58 for y

how do i get the others one now

[wary stream]

Did you not read what I said?

[rustic notch]

Yea i did

So do i do 180-58 to find z

[wary stream]

Not exactly

The sum of adjacent angles equal to 180, how can you form the equation based on that

[rustic notch]

-3z-8=180

[wary stream]

Not quite

Sum of adjacent angles

What angle is adjacent to -3z - 8?

[rustic notch]

65

[wary stream]

And the sum of adjacent angles, how would you write that?

[rustic notch]

-3z-8=65

[wary stream]

That is not a sum

[rustic notch]

Huh

[wary stream]

Do you know what sum means?

It means to add

So the sum of adjacent angles means, one angle plus the adjacent one

[rustic notch]

65+58

[wary stream]

Where did 58 come from

[rustic notch]

58 is y

[wary stream]

You have -3z - 8 and as you stated the angle adjacent is 65, what is the sum?

[rustic notch]

Yea

Bro

Im confused

[wary stream]

Add them

That's what a sum means, to add

[rustic notch]

-3z-8+65

[wary stream]

Yes

And the sum equals 180

How do you include that?

[rustic notch]

-3z+73=180

[wary stream]

Good

Solve for z

Then apply the same process with x

You have -x + 1 and the angle adjacent is 65

And the sum of adjacent angles is equal to 180

[rustic notch]

i got

-35.6

[wary stream]

Also this was wrong

-3z-8+65 = 180

-8 + 65 is not 73

[rustic notch]

Ye

ah

whjat

oh ye

i foprgot ot add negative

57

Honestly ima just give up

i got a 96

.close

[lone heart]

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[silk crown]

Anybody know how to prove \bigcap {U_i:i = 1,2,…,n} = \bigcup {X-U_i:i = 1,2,…,n} ?

Given that \tau = {U \subset X:U = \emptyset or X-U is a finite set}

[silk crown]

I’m having a bit of trouble visualizing this

[real gazelle]

Are you studying the cofinite topology 👀

[real gazelle]

[\bigcap {U_i\mid i=1,2,\dots,n} = \bigcup {X-U_i\mid i=1,2,\dots,n}]

[ocean seal]

eulerEMILYteristic

[real gazelle]

I don't think this is true?

Like it's not true for the case where n=1

I think you might've typoed

[silk crown]

Lemee just send the proof and where I’m getting lost

[real gazelle]

sounds good!

oh yeah you're the category theory high schooler

[silk crown]

2.2.8

[real gazelle]

Hope you're enjoying topology

[silk crown]

It’s beating my ass.

[real gazelle]

Ah you missed the X -

[silk crown]

Oop my bad

[real gazelle]

[X\setminus\bigcap {U_i\mid i=1,2,\dots,n} = \bigcup {X\setminus U_i\mid i=1,2,\dots,n}]

[ocean seal]

eulerEMILYteristic

[silk crown]

Sorry I typed that on a phone 💀

[real gazelle]

hahaha you're good

so what's the usual technique for proving equality of two sets?

[silk crown]

Showing that they’re subsets of each other?

[real gazelle]

yup!

which direction do you wanna start with

[silk crown]

Wdym

Oh

Uhh left?

[real gazelle]

okay so suppose
[x \in \bigcup {X\setminus U_i\mid i=1,2,\dots,n}]
we want to show that
[x \in X\setminus\bigcap {U_i\mid i=1,2,\dots,n}]

[ocean seal]

eulerEMILYteristic

[real gazelle]

where should we start?

[silk crown]

Proving that x is also an element in the second one

Or am I missing something

[real gazelle]

right

but how do we start doing that

[silk crown]

Okay good

[real gazelle]

Btw this is just an example of ||demorgan's laws||

[silk crown]

I was thinking that 😭

[silk crown]

Assuming that x is an element of the second one and therefore x is an element of each X\U_i

Oh and then that x isn’t an element of U_i

[real gazelle]

I'm not sure what you mean here

We're assuming the first line and trying to get to the second line right?

So if
[x \in \bigcup {X\setminus U_i\mid i=1,2,\dots,n}]

[ocean seal]

eulerEMILYteristic

[real gazelle]

What must be true about x?

By definition of union

[silk crown]

x must be an element of at least one X-U_i

[real gazelle]

yup perfect

So what does that imply

[silk crown]

It implies that it’s also an element of the union?

[real gazelle]

Well we just did it's an element of the union => it's an element of at least one X - U_i

So we don't wanna just go backwards

Can you see anything that would help us progress towards the thing we want to prove?

[silk crown]

That if x is an element of the intersection it isn’t an element of X\(intersection stuff)?

[real gazelle]

If x is an element of X - U_j for some 1 ≤ j ≤ n then can it be an element of \bigcap {U_i}?

[silk crown]

No

At least that’s what I’m trying to say lol

[real gazelle]

And if x is in X - U_j, is it in X?

ah lol

[silk crown]

Sorry I’m typing all this out on a phone so it’s kinda hard to do LaTex

[real gazelle]

So yeah do you see why x being in the first one implies that it's in the second one?

Oops wrong message

[real gazelle]

^

[silk crown]

Yes

[real gazelle]

Yup

So x being in the union implies that x is in X minus the intersection

[silk crown]

Yep okay that makes sense

[real gazelle]

Okay awesome

[silk crown]

Is that it?

[real gazelle]

Yup it should be pretty clear how to go the other way too

But make sure you see how to do the other direction too

Also for future topology questions, #point-set-topology is a good channel to ask questions :)

[silk crown]

Thank you!!!

[silk crown]

I just got told to ask here 💀

[real gazelle]

oh LOL

Yeah this is also fine

[silk crown]

Thank you for helping a high schooler with topology 🙏

[real gazelle]

Probably TTerra didn't think your question was that advanced so they directed you here lol

But I think you should be fine to post in #point-set-topology since it's from a topology book

[silk crown]

.close

[lone heart]

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[barren scroll]

Can someone please explain how to solve this

[barren scroll]

I tried using quadratic method to just insane numbers

[proven leaf]

can you show the whole question? :)

[barren scroll]

Yes

[proven leaf]

ah! this is classic example of the SAT trying to trick you into doing more work, the product of the roots of a quadratic is c/a :)

where c is the last coefficent, and a is the first coefficent

[barren scroll]

Oh

[grave quartz]

Vieta formulas*

[barren scroll]

Where are these things taught

My school just taught me how to do the quadratic formula

Is there any resource for this

[proven leaf]

https://en.wikipedia.org/wiki/Vieta's_formulas

[grave quartz]

Given a quadratic $$ax^2+bx+c=0$$ with roots $X_1,X_2$ we can say $X_1+X_2=-\frac{b}{a}$ and also that $X_1X_2=\frac{c}{a}$

[proven leaf]

the logic: $(x-a)(x-b)=x^2-(a+b)x+ab$ :)

[ocean seal]

MrFancy

SWF ;)

[barren scroll]

Ohhh

This is my first time studying for the sat

[proven leaf]

no need for the messy expanding of radicals

[barren scroll]

Yeah that’s what they r making me do

And it didn’t make any sense

[proven leaf]

the SAT really likes to give of the illusion that questions are harder then they are, usually there's always a simple way, usually

[grave quartz]

There is more formulas of the same for cubics and quartics although idk if u need them I didn't do SAT

[proven leaf]

I remember a few of those curveball questions the first time I took it

[barren scroll]

How did you study for the math section

[proven leaf]

train for the tricks they may throw at you, manage time well, and get good at algebra, those are the methods I've learned :)

they also love to have tricks with systems of equations

[barren scroll]

R there any books

Teaching this content

[proven leaf]

I just looked online for some worked examples and applied those in some practice tests which you can find online https://satsuite.collegeboard.org/sat/practice-preparation/practice-tests/paper

oh wait sorry nvm just dumbed

yes there are plently of books

sorry awful tired today

I have a nice 2021 edition

https://www.amazon.com/SAT-Prep-Plus-2021-Strategies/dp/1506262678

this one helped me with my reading a TON

[lone heart]

@barren scroll Has your question been resolved?

[barren scroll]

@proven leaf thx so much

[proven leaf]

yw

[lone heart]

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[terse atlas]

oh wait

$$\lim \sqrt{n^2 +1} -n$$

wonderful

[lone heart]

Channel closed

Closed due to the original message being deleted

[terse atlas]

just trying to figure out how these channels work #sowwy 🥲

[young finch]

$\lim_{n\to\infty}\sqrt{n^2+1}-n$

hm whats the arrow

[terse atlas]

i use /to sometimes

\to

[ocean seal]

Arctic

[young finch]

yeah

you need help with this problem?

[terse atlas]

not quite yet i havent taken a crack at it

[young finch]

ah

[terse atlas]

i just wanted to try out the latex and claim a channel

[young finch]

#latex-testing

next time go here

and get a channel afterwards if you cannot figure out your problem

[terse atlas]

ahh got u! im sorry about that

[young finch]

its alright

[terse atlas]

the other thing; the channels always retain history?

[young finch]

this channel will close soon since you deleted og message

[terse atlas]

got u

ok nice! i will begin on these and probably be back soon

thanks!

oh actually just one more thing if its ok to ask u: is the forum appropriate for advanced mathematics

like analysis questions n such

i dont see a tag for those subjects in there

[young finch]

you mean #get-advanced-access stuff?

[terse atlas]

no like in the help-forum channel

[young finch]

the threads?

i never look at those lol

i bet you could ask advanced level questions there

[terse atlas]

yeah the threads

i think discord calls them posts but that

i see you can tag them by subject but i dont see any tags for advanced topics

[young finch]

i dont even know when they became a thing

[lone heart]

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[terse atlas]

thank u!

if it ever gets that far ill just throw em in there

[lone heart]

Channel closed

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[young finch]

you can also do .close to close

[terse atlas]

oh lit ty!

[lone heart]

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[fossil mulch]

Is it possible to solve this question with this formula y=a(b)^x for this question

[upbeat gorge]

Yeah, what’s your working equation

[fossil mulch]

y=55000 a=3700 b=1.07

55000=3700(1.07)

[upbeat gorge]

Read the problem

[fossil mulch]

55000(1-7%)=37000

[strange meadow]

93% of 55000 is not 37000

[fossil mulch]

How do you get the 93% of 55000

By dividing the 7% to 55000?

[lone heart]

@fossil mulch Has your question been resolved?

[fossil mulch]

What was the point of 55000(1-7%) if we know we going to get 0.93

[lone heart]

@fossil mulch Has your question been resolved?

[fossil mulch]

Anyone help

<@&286206848099549185>

its been an hour

[fossil mulch]

.close

[lone heart]

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[lone heart]

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[rich basin]

So what I did was f' +2g=0

g' -21f + 13g = 0

But stuck on what to do next?

Right now I'm thinking of this objectively

[real gazelle]

for this you can note that g = -1/2 f'

and then plug it into the second equation

and then you have a single ODE just in terms of f that you can solve

[rich basin]

So what I did then was f'' = -2g'

and then plugged it into the second equation.

[real gazelle]

Can you show me what you got?

[rich basin]

This was what I got after solving the ODE

So what i did was g = -1/2f'

and then differentiate both sides again and got g' = -1/2f''

and then substitued into equation 1

-1/2f'' -21f + 13f'/2 = 0

f'' + 42f -13f' = 0.

@real gazelle Was my wokring out right?

[real gazelle]

yup that looks correct for f

and then did you figure out what g should be?

[rich basin]

shouldn't g be the differentiation of- exp(-7*x)/2?

[real gazelle]

Well we konw that f is C1 e^-6x + C2 e^-7x

So it should be the derivative of that, times -1/2

[rich basin]

Actually it is positive -6x

because -13*diff(f(x),x)

[real gazelle]

oh huh, I think it should be +13?

[real gazelle]

this part should be - 13f' / 2 I believe

[rich basin]

Ahh, yes

[real gazelle]

Yeah so -6x and -7x

@rich basin do you need any more help from there

I have to go now, but hopefully someone else can help you figure out the rest if so

[rich basin]

I got it thanks

.close

[lone heart]

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[lone heart]

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[limpid stone]

whats the difference between the two

[limpid stone]

is X1 + X2 not equal to 2X

[tardy stag]

no, imagine rolling two dice

X1 + X2 would be the distribution that is the sum of the two dice

2X would be if you took the first die and multiplied it by 2

[limpid stone]

so

thats why 2X has a higher variance

cause its like ur basing the value from 1 roll and multiplying it

[tardy stag]

yeah exactly

[limpid stone]

ok

[tardy stag]

while if you did 2 rolls you're more likely to be in the middle

[limpid stone]

ok thakns

.close

[lone heart]

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[restive sigil]

hello

[restive sigil]

https://sites.math.washington.edu/~burke/crs/408/fin-proj/mark1.pdf

I don't understand this part of how they went from

this to this

what happend to the xoi?

[rigid smelt]

What xoi? You also shouldn't cropped it out like that, can create confusion when you just look at your screenshot.
What happened is x_o is a common factor of every terms in the sum, so they factored it out of the sum

[restive sigil]

xoi

X0i

[rigid smelt]

Yes, and what's wrong with it?

The sunf of investments are the sum of each terms x0i for i=1 up to n

Since each invesment are computed omega_i * x_0. They just replaced x_{0i} with it

Eesh

[real gazelle]

(I think it's a w for "weight", not an omega)

[rigid smelt]

Is it? Haven't seen this font before

[restive sigil]

yes

[restive sigil]

wait how can they interchange it like that?

[rigid smelt]

They didn't interchange anything, it's just substituting one for another.

I guess you could call that an interchange

[restive sigil]

ok can you show me some examples of where you do that? I don't know much about summation.

[rigid smelt]

Well if it's confusing you why, what you are doing is essentially replace every x_{0i} term with its corresponding w_i*x_0
I.e, we are having (im replacing x_{0i} with x_i for easier typing)
x_1 + x_2 + ... x_n=w_1 * x_0 + w_2 *x_0 + ... + w_n * x _0

As you can see, both sums are equivalent to each other

[restive sigil]

@broken needle

[restive sigil]

thanks

[rigid smelt]

If you have no further questions then .close to close the channel.

[restive sigil]

thanks

.close

[lone heart]

Channel closed

Closed by @restive sigil

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.

[median pelican]

A logics question: If a predicate P(x) is negated, and the predicate contains logical connectives such as a disjunction or conjunction, would the connectives remain or switch as well? (Sorry if this is a beginner question)

[real gazelle]

they would switch (de morgan's law)

[median pelican]

Alright thanks!

[real gazelle]

so if P is A OR B then NOT P would be NOT (A OR B) which is equivalent to (NOT A) AND (NOT B)

[median pelican]

I see

alright yeo it's de morgans laws

I didn't knew it apply to that as well

Thanks!

[maiden glen]

you can't just negate every connective in a proposition directly though to negate it

you have to use de morgan's laws in layers, if it has nested connectives

[median pelican]

i don't quite understand??

I understand that it only needs two statements and a connective

[maiden glen]

i you have a bunch of connectives like, A and B and C or D and (not B or A), etc

(for example)

you can't just negate every and into an or

and every or into an and

[median pelican]

what would be the action then?

[maiden glen]

you'd have to bracket everything out and use de morgan's laws on each part

[median pelican]

ah

alright thanksss!!!

.close

[lone heart]

Channel closed

Closed by @median pelican

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.

[ebon torrent]

I have basic question

[ebon torrent]

Square root 27 is equal to 3 square root 3

[upbeat hornet]

Yes

[ebon torrent]

but my question is why is it actually +-3 square root 3

[fallen verge]

show the original question

[ebon torrent]

I know that the square root cannot be a negative number

one minut then

the question is numbered 19. and the rest below the answer I marked inside a rectangle is unrelated

[agile grove]

Write so we have to state our restrictions first.

[ebon torrent]

I don't understand what you are saying

[agile grove]

Sometimes when we solve radicals they can be arranged such that we get an extraneous solution, which means we solved the problem correctly however the answer we found does not hold true for all of the radicals in a certain question, thus its extraneous.

Our restrictions are what x cannot be. But here we observe that sicne there is an x^2, x can be any real number and the solution will be true.

Where is the +-3. Why do you have just 3?

[ebon torrent]

its +-3 square root 3 that is the answer

I just want to understand the +- sign here

[agile grove]

I'll explain it you in a second give me a second to verify the algebra

[ebon torrent]

thanks

[agile grove]

Alright the algebra looks fine to me. Now lets tackle your question, so your wondering why is x + and - in this instance as you say a square root cannot be negative right?

[ebon torrent]

yes

and its not 3-+ square root 3 because than its not multiplying right

I understand that to get 9 you can do 3^2 or -3^2

[pale kestrel]

The working in here is wrong.

[agile grove]

Uhhhhhh no Dudev thats wrong.

[pale kestrel]

This is definitely wrong, I haven't checked the rest.

[agile grove]

Because if we integrate +-3sqrt3 we see that its true

[pale kestrel]

@ebon torrent Let me point out a simpler example

[ebon torrent]

how is it wrong?

[pale kestrel]

,,x^2 = 1

[pale kestrel]

What are all solutions to this.

[ebon torrent]

-1 , 1

[pale kestrel]

yes

$$x^2 = 1$$
$$x = \pm\sqrt1$$

[pale kestrel]

= +-1

[pale kestrel]

That's what you shouldve done here

[pale kestrel]

The other thing I should point out however

Is when you are solving equations

you need to check the answers you get by plugging it back in to the original

Certain steps can yield extra solutions which were not part of the original like squaring both sides.

[ebon torrent]

thats what im suppose to write?

[pale kestrel]

no

its x = +-sqrt27

[pale kestrel]

theres a missing +-in each of the boxed steps

sqrt27 itself is positive as you identified earlier

sqrt(anything) is always not negative

[pale kestrel]

yes

[agile grove]

Yeah and if you plug it in to the solution dudev we can verify that its true because it will be 0 for either positive or negative

[ebon torrent]

can I ask another question ?

I got a solution for question 20.

but it says that the solution is that there is no solution

[ebon torrent]

what I did was wrong? or is it that I just didn't do this part ^ checking if its correct by plugging the nunber for x

[agile grove]

This ties back to what I said about extraneous solutions

A good way to avoid your confusion dudev is to always plug your answer back into the original question and see if its equal on both sides. If it is then is true, if not then its not true.

[ebon torrent]

so I put 39/36 for x

[agile grove]

Wait let me look at question 20

gimme a second

here ima solve it and show u

[ebon torrent]

I already messed up actually I noticed

should have been -6 on the third line

actually it doesnt matter here

[agile grove]

gimme a second

[ebon torrent]

its alright im solving the next question for now

question 21.

[agile grove]

solved it.

[ebon torrent]

I don't know how but I'm constantly fucking up on every question here

[agile grove]

Its alright take a deep breath. We have all been there. You just don't know the process, and that is why you are constantly messing up.

Before we even proceed on any other question. Stop what you are doing. This right here will change all of the problems you are facing. Trust me.

[ebon torrent]

thanks, but if I look at your sheet of paper I don't process every thing I see the way you do

[agile grove]

A few minutes and you will not mess up on other questions, because you will know the way.

I don't expect you to, not that I thought any less.

That is why I am going to explain it to you.

[ebon torrent]

thanks

[agile grove]

Alright. So first order of business we know no matter what that a square root can never be negative correct?

[ebon torrent]

yes

[agile grove]

With this said, with any radical equation the first thing we always do is state what x cannot be. It is quite simply x can be anything as long as ensure its not negative, and we have to consider all numbers, so we use an inequality. In simple words, we use things called restrictions that says what values x can be and can't be.

[ebon torrent]

I know that usually x cannot equal to 0 in my questions so far

[agile grove]

The reason this is SOOO IMPORTANT. Is because in nature when we solve radical problems for x, we sometimes get "extraneous" solutions (A solution that does not exist). What it means is that we have solved for it correctly, but when we plug in the value that we found into the original equation both sides of the equal sign are not equal to one another which means it does not work.

[ebon torrent]

did I solve it correctly then?

[ebon torrent]

here

[agile grove]

The way you verify if you solved it correctly is if both sides are equal for the x value that you solved and plugged in,.

You ALWAYS do this.

ALWAYS.

[ebon torrent]

plugging 39/36 is a bit of headache

[pale kestrel]

I have an interesting problem for you

[pale kestrel]

what's wrong with the proof

It highlights the above point.

[agile grove]

Don't overthink this duvdev just simply think why is this wrong. There is no secret trick or anything. Just look in front of you.

[ebon torrent]

I dont understand this part

[pale kestrel]

I multiplied it out

x(x^2 + x + 1) - (x^2 + x + 1)

[agile grove]

mhmmmmmmm.

[pale kestrel]

you can trust the algebra, but check if you like

[ebon torrent]

I dont understand it

[pale kestrel]

see this

[agile grove]

Okay I will hint you. Just what we were discussing above. What should you do for any solution you find?

[pale kestrel]

But which part exactly doesnt make sense

[ebon torrent]

check if its true

[agile grove]

RIGHT

THAT IS IMPORTANT

VERIFYING.

[ebon torrent]

if x is 1 then the solution would be 3

[agile grove]

Does 3 = 0?

[pale kestrel]

if x = 1, then we need 3 = 0

[ebon torrent]

no the solution is wrong

[agile grove]

Exactly

[pale kestrel]

The mathematical explanation for this is how we define the word 'solution'

[agile grove]

if it was 0 = 0 then we know its right because that is true

[pale kestrel]

the solutions to an equation in x are all possible x values that solve the equation

[agile grove]

Right.

That is why we always have to verify, because otherwise we are gambling essentially.

[ebon torrent]

so can I ask again did I do it correctly here ?

[pale kestrel]

Let's label the set of solutions $A$.

Then we want
$$x\in A \iff \text{$x$ is a solution to your equation}$$

[agile grove]

We are not going to tell you. What do your logic tell you according to what we have just said.

[ebon torrent]

if I put 39/36 for x

[agile grove]

We will help but you have to show your train of thought even if its wrong atleast you are thinking

Right so stick that in

[pale kestrel]

The implies arrows not only have to go forwards in a proof. But backwards. To show x=1 is a solution.

plugging x=1 back in is the backwards

[agile grove]

and tell me what you get.

[pale kestrel]

Squaring both sides is one of the steps that cannot be reversed with a backwards implication.
It can introduce new solutions.

[ebon torrent]

I get square root ( 39/36 - 3 ) - 3 = square root (39/36)

[pale kestrel]

(that was your line 2)

[agile grove]

mk, so is that right or wrong?

[ebon torrent]

so it can't be correct because on the left I have the same number - 3

[agile grove]

Exactly

So lets analyze what went wrong

drop your image down here once again, and instead of just solving it again.

Look at process as to how you got 39/36 think about the algebra and just analyze it.

See if there was an error made

[ebon torrent]

couldn't I spot that this is a trick question right from the beginning and instead of solving it just outright say that the solution = is there is no solution?

[agile grove]

And how would you exactly do that?

[ebon torrent]

this?

[agile grove]

Yes this is the image, now observe your algebra and tell me your thought.

Observe how you got to 39/36

and then I'll give you my two cents on it.

[ebon torrent]

I forgot to multiply -6 by -3

wait actually its 36 times -3

[agile grove]

so we have x = 4

Now how do we know thats true though?

Because we solved for it, but do keep in mind in nature when we solve for an x value we have to stick it back in to verify.

[ebon torrent]

-2 does not equal + 2

[agile grove]

Right, so then what does that tell us for this question?

[ebon torrent]

that there is simply no real solution for this problem

[agile grove]

Because we algebraically solved it and got only x = 4 that fact will never change

[agile grove]

Exactly there is no solution for this problem.

Lets do another problem to ensure you have the steps together

[ebon torrent]

may I ?

[agile grove]

But dudev although you algebraically solved this problem just fine. There was an easier way you could have solved it in less time.

[ebon torrent]

this is my last question for this subject before I move on to the next one and I got it wrong too

[ebon torrent]

if I just put any value I wanted for x that is?

[agile grove]

Before we move on to the question, just on minute.

Observe my image do you see how I brought the 3 over to the other side and then solved for it?

[ebon torrent]

what I can see I will say it in steps

[agile grove]

What was my first order of business?

[ebon torrent]

you made it clear that x must equal more than 0

there is this sign >

[agile grove]

correct. And why is this important?

[ebon torrent]

because the number cannot be negative inside a square root

[agile grove]

Exactly, but also because when we solve for a solution

[ebon torrent]

otherwise it wont be a real number is what I understand

[agile grove]

Lets say we had an insanely large radical

[ebon torrent]

I dont know what a radical is stil

I see that you moved the -3 to the other side of equation making it a +3

so it already wouldn't make sense in mind that this equation has a real answer

[agile grove]

No no.

I simply just algebraically reduced the amount of work it took for me to get to x = 4

[ebon torrent]

because you have the same number one is subtracted by 3 and that some how equals to the same number added by 3

[agile grove]

what you did is correct and perfectly fine, but what I am saying is that there is an efficient way of solving these problems vs an inefficient way where you will get the right answer, but efficiency is the goal.

[agile grove]

No you are overthinking it.

We are just speaking in terms of algebraic manipulation.

[ebon torrent]

but actually the left side the -3 is inside a root

[agile grove]

We don't care about that -3

we care about that -3 that was outside the root

[ebon torrent]

so what am I looking for just the process?

[agile grove]

I brought that over the other side

and then just algebraically solved it for x = 4, just like you except it took me less work.

The point is being efficient what you did is perfectly fine, but when you algebraically manipulate something there is an easy way and a hard way of doing it. By knowing a few tricks like this it will save you time.

[ebon torrent]

is there a meaning behind the 3 dots where you wrote no solution?

[agile grove]

The 3 dots means therefore.

thats all

[ebon torrent]

is it a math sign?

[agile grove]

Its a shorthand for therefore mathematicians and many people use it

yep

its a math sign

alright forget about algebraically manipulating it just know what I did was an efficient way of solving it which saved time. What you did is perfectly fine my friend my point was there is an easy way and a hard way of solving it.

[ebon torrent]

I understand it up to here

[agile grove]

Okay what confuses you next?

the -12 =6 sqrt x right?

[ebon torrent]

wait im calculating

now I understand this part as well

yes I understand it all

[agile grove]

Good its simply just a property in algebra. Duvdev you are smart, and you don't know it. Think about the process and don't panick. Take your time to think.

[ebon torrent]

not the right side as much

[agile grove]

Okay don't worry.

So what we are doing is we are simply plugging x = 4 back in to the original question to see if both sides will be equal, and IF both sides are equal then we know the solution we found is true.

But if not then its not true.

[ebon torrent]

actually

this

[agile grove]

What I did was I plugged it back in and I determined its not true. Remember for any x we find we always want to verify.

[ebon torrent]

I only learned a^2 + 2ab + b^2

but you have a 3 there

[agile grove]

3sqrtx + 3sqrtx

[ebon torrent]

yes

[agile grove]

Well let me ask you where does x^2 + 2ab + b^2 come from?

[ebon torrent]

is it different? the x^2

I know its (a+b)^2

[agile grove]

are you confused on sqrt x multiplied by sqrt x ?

[ebon torrent]

first im confused with x^2 + 2ab I learned its a^2 + 2ab

[agile grove]

We are stating the same think, but the thing is we have different coefficients

a and b are not unique values they are just random variables we chose to display a^2 + 2ab

[ebon torrent]

I dont understand this

its a 3 and not a 2

[agile grove]

mk so 3 multiplied by sqrt x = 3sqrtx

[agile grove]

What do you not understand?

[ebon torrent]

I was taught that ( sqrt x + 3 )^2 = (sqrt x)^2 + 2 * sqrt x * 3 + 3^2

[agile grove]

Alright I see let me show you something cool then okay?

[ebon torrent]

ye

it might be just how im suppose to solve these equations now , and that I will learn other more efficient ways later

I have just one final question here which I got wrong as well a few minutes ago

[agile grove]

No offence, but you have a horrible math teacher.

,rotate

[ebon torrent]

my math teacher is an online preparation course for now

[agile grove]

So what I did on the right side

was I factored 3sqrtx

[ebon torrent]

what is ( | + | ) ?

are these 1's?

[agile grove]

( ) is the parentheses. and the stuff inside is 1 + 1

exactly

[ebon torrent]

I think I understand it but not this

because you get the same number twice essentailly in the parantheses and you add them together

but shouldn't the 2 * effect the square root x as well?

[agile grove]

nope it doesn't.

[ebon torrent]

I actually don't know what 2 * square root x is

I guess its just 2 square root x

[agile grove]

let me think of an example

[ebon torrent]

then it just effects the 3

[agile grove]

one second

3 x 3sqrt9

[ebon torrent]

yea you just take 3 square roots of some thing and you multiply it by 2

I understand it now

that is 9 square root 9

[agile grove]

right.

[ebon torrent]

which is equal to 27

[agile grove]

and we also know if we say

9sqrt9

what does that equal?

[ebon torrent]

9 * 3

[agile grove]

which is?

[ebon torrent]

27

[agile grove]

right so what I just showed was an example of why it works.

Solve it the way you know how to solve it. There is no point in spending a few hours teaching a lesson I just thought it would be nice to show you for your own understanding.

Lets tackle question 21.

[ebon torrent]

thanks a lot

[agile grove]

yes.

My goal is for you to understand my friend and to ace that test of yours.

[ebon torrent]

this is the question

[agile grove]

Ahhhh! A big question. How exciting.

[ebon torrent]

the test will be in 5 months from now roughly and I will need to learn far more complex things than this

[agile grove]

where do you live?

[ebon torrent]

Israel

[agile grove]

Mk, how old are you?

[ebon torrent]

26

[agile grove]

Are you lying to me?

26 years old?

[ebon torrent]

no, I will be 27 by the time I do that test

[agile grove]

No worries. Everyone has their own path to achieving success.

[ebon torrent]

I'll have 2 more tests to do along side it in 2 other subjects unrelated to math

[agile grove]

Anyways.

[ebon torrent]

so far you explaining it better than a 16 year old that helped me yesterday , but he was very helpful too

he just took longer

[agile grove]

My goal is for you to understand and although I am taking a lot out of my day to help you. I love helping others.

[ebon torrent]

I appreciate it , it will probably make you better in math yourself

[agile grove]

Thats why I do it.

Alright so it seems you have found a solution

Now what is the first thing you do when you find a solution?

[ebon torrent]

I check it , but I did cheat and looked for the actual solution and saw that both of these are wrong

[agile grove]

Mk, so look over your algebra and tell me what you think is wrong.

Think about it.

Just analyze.

Im gonna solve for it really quickly so give me a second in the meantime analyze

[ebon torrent]

I did it all over again and found the same 2 solutions

with no errors

[agile grove]

alright give me a second

[ebon torrent]

this is the formula I used

[agile grove]

Alright.

So is the answer just -3. Pretty sure I just want to make sure there are no problems with your textbook.

[ebon torrent]

the answer is +3

[agile grove]

double check.

[agile grove]

mk one second.

your instructor is really getting on my nerves

That is incorrect

[ebon torrent]

where did I go wrong ?

[agile grove]

No wonder you find it difficult. The course is poorly structured.

Poor you.

[ebon torrent]

this looks right to me I glanced over it multiple times

[agile grove]

Anyways where did you go wrong let me see.

right so that is the quadratic formula

[pale kestrel]

Honestly, I find making people solve equations with idiotic numbers to be bad teaching most of the time

[agile grove]

so where you went wrong

is (-22 +- sqrt16) / 6

you forget to take the square root of 16

your algebra was fine.

[ebon torrent]

so far every piece of this course has 50% trick questions and im suppose to get it after only solving 10 equations and then move on to the next subject

[agile grove]

Stupid teacher. Honestly.

[ebon torrent]

oh man... I keep doing that

[agile grove]

its okay, just be careful!

[ebon torrent]

I saw that it was equal to 16 and how convenient of a number it was and kept it

how could I look for it so many times and not see that

[agile grove]

No worries

its alright, just look and think. Don't just look.

so we have x1,2 = (-22 +- 4 )/6

now write out the two possible solutions

[ebon torrent]

so I get x1 = -3 , x2 = -4 1/3

I will check now

[agile grove]

alright.

[pale kestrel]

@ebon torrent what you could do is improve the way you lay out your solutions

it helped me in hs with these issues ur having rn

[pale kestrel]

So

[agile grove]

Good advice.

[ebon torrent]

-3 means its 0 = 0

[pale kestrel]

See how I used the => sign on each line to say there is an implication

[agile grove]

Right so what does that tell us?

[pale kestrel]

(lmk when ur done)

[ebon torrent]

well then -3 is correct

[agile grove]

Right!

[ebon torrent]

but it says its 3

[agile grove]

The solution is wrong

100% wrong 3 is not correct.

Again the instructors of your course baffle me.

and we know that 3 is wrong how?

[agile grove]

lets try integrating 3 into the original equation and see what integrating just 3 tells us.

[ebon torrent]

I'll do it right now

[agile grove]

kk.

[ebon torrent]

it means square root 12 = 12

can't be right

[agile grove]

exactly

[ebon torrent]

I mean I'm not trolling

[agile grove]

now lets try plugging in the second possible solutoon we found 4 (1/3)

[agile grove]

Of course, it happens. There are wrong answers in answer key sometimes.

alright plug in 13/3

[ebon torrent]

I'll use a calculator

[agile grove]

We see that its not true, therefore x = -3 is our only solution.

[ebon torrent]

yes

they messed up on that one

from like question 10 to 21 I couldn't solve a single problem on my own

I will take all I learned today with me

thanks a lot to you

[ebon torrent]

coming back to math at 26 when I have a full time job and so many other things is not ideal, but many people do it so will I

[pale kestrel]

lmk if ur interested - you can ping me another time/day if you want

[agile grove]

Save this screenshot for future reference write this down on your notes.

[agile grove]

Its alright we all start somewhere.

Atleast your are starting which is good.

[ebon torrent]

yes I would love to

[pale kestrel]

now?

[agile grove]

Feel free to ping me as well dudev but save the screenshot I just sent you and apply it whenever using a problem and eventually you will be able to recall all those steps on your own.

Shuri. Duvdev he is determined and a hard worker, but learns in a certain way. The manner his instructors teach the material is taught to him is appalling. He learns in a special manner according to the content he is taught. So I had to find ways to work around and help him understand.

[ebon torrent]

can we do it later today?

[agile grove]

If you want Duvdev ping me later today as well.

I will try to help, but I think I did help a fair bit.

Now save that screenshot I sent you, and take care. Take a break and come back to this later. You deserve it.

[ebon torrent]

thanks I did save it , I dont know why its explained like this. It's kinda what you get as an external student

[agile grove]

The content you are taught or what I wrote in the screenshot?

[ebon torrent]

how I'm taught

[agile grove]

Don't blame yourself. But make sure you watch all the videos and material and think about each and every step. But lastly, learn the process. Don't do problems without learning the process of solving a problem and then jumping to another.

use the image I sent you when solving these problems and eventually the steps will be able to recall without referring to the image.

[ebon torrent]

I would believe you are 14 just by your math skills , but the way you conduct yourself is impressive

I was told at my workplace that I wont be able to learn math again at my age 26, but I want to prove em wrong

[agile grove]

Wonderful.

Keep going at it.

I know you got this.

[ebon torrent]

thanks a lot

.close

[lone heart]

Channel closed

Closed by @ebon torrent

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
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[white crater]

sry this seems dumb but u cant take the inverse cosine of a negative number right?

[agile grove]

Don't worry its okay.

[pale kestrel]

Its all down to how you define the inverse function

[agile grove]

You can [-1,1]

[pale kestrel]

The choice of domain

And the usual choice does not include negative numbers.

[agile grove]

Do you know the unit circle?

[agile grove]

Ahhh we are seeing if the function is invertible

[white crater]

ye ive seen it

[pale kestrel]

The issue is, that blue line is not a function.

[agile grove]

I think we restrict the domain

from [-pi/2, pi/2]

[pale kestrel]

Oh I'm high, this is completely wrong

[agile grove]

that way it passes horizontal line test and we know we can find the inverse of a function therefore its invertible.

[pale kestrel]

Yeah you can definitely take the inverse cos of anything between -1 and 1

[agile grove]

yeah.

[white crater]

so if i were to say

arccos of -3/2

i camt do that

[agile grove]

nope

[pale kestrel]

thats undefined yes

(unless you use the extended definition of cos as a complex function)

[agile grove]

cus cos must be -1 <= x <= 1

[agile grove]

do you know the unit circle?

[white crater]

sorta i tocuhed on it

[agile grove]

Mk.

well for sin and cosine

[pale kestrel]

So in order to make arccos a function, this is the usual thing we do

We only let it output angles between 0 and pi radians (which is 0 and 180 degrees)

[agile grove]

Im gonna let Shuri do the rest. Gl taro. Ping me later if need be.

[white crater]

okok

[white crater]

mhm im following

[pale kestrel]

So the arccos function is a function which has domain

the closed interval [-1, 1]

and range

[white crater]

-1, 1

right

[pale kestrel]

the closed interval [0, pi]

[white crater]

0, pi

ahhh okay that makes sense

[pale kestrel]

We could choose other ranges

but the default is [0, pi]

Like for example, the range being [2pi, 3pi] 'works' as a function

but yeah - its sensible to have a default, and thats what your calculator does too.

[white crater]

ahh okok

tyty

.close

[lone heart]

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[pale kestrel]

(and same story for arcsin and arctan)

[lone heart]

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[neat void]

Draw a near-linear space with three points.

[vale wigeon]

what is a "near-linear space"?

[neat void]

Definealinearspacetobeanear–linearspacein whichanytwopointsareonaline. A linearspace isanincidencestructure I=(P,L)suchthat AxiomLS1:anylineisincidentwithatleasttwo points,and AxiomLS2:anytwopointsareonpreciselyone line.

[vale wigeon]

whyareallthespacesgone?whatwentwrongwiththecopypaste?

there are not actually that many options for which subsets of your 3 point space you get to designate as lines

[pale kestrel]

what have you tried

if you draw 3 points and try to satisfy the axioms, you should be able to get an example...

[lone heart]

@neat void Has your question been resolved?

[lone heart]

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[drifting seal]

REPORT

[subtle birch]

<@&268886789983436800> (spamming in multiple channels)

[pale kestrel]

.close

[lone heart]

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[lone heart]

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[alpine sable]

I'm trying to graph [
\map g t = (t-1)\map{u_1}t -2(t-2)\map {u_2} t + (t-3)\map {u_3}t ]
For which I get [
\map g t =\begin{dcases*} 0, &if $0 \le t < 1$ \ t-1, &if $1\le t < 2$ \ (t-1)+(-2(t-2)), &if $2 \le t < 3$ \ (t-1)+(-2(t-2))+ (t-3), &if $t \ge 3$\end{dcases*}]
As a piecewise representation of $\map g t$. Would that be correct?

[vale wigeon]

what are these u_k(t)

[alpine sable]

Unit step functions defined as [
\map{u_c}t = \begin{dcases*} 0, &if $t < c$ \ 1, &if $t \ge c$ \end{dcases*}]

[vale wigeon]

right

in that case yeah

[alpine sable]

Alrighty ty

. close

.close

[lone heart]

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[normal walrus]

if d(2)/dx = 5 and y = x^2 + Kx + 5 , get the value of K

is this question even right?

[lone heart]

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.

[gray isle]

is that supposed to be
$$\dv[2]{y}{x}=5$$

[ocean seal]

ℝam()n()v

[tardy tapir]

its dy/dx at x=2

no

[white marsh]

ok

i see

[gray isle]

$\dv{y}{x} \bigg|_{x=2} = 5$

[ocean seal]

ℝam()n()v

[gray isle]

that?

[tardy tapir]

yes

[white marsh]

so K=1 ?

[tardy tapir]

the question is correct

[lone heart]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[normal walrus]

well how is the value of K = 1

[normal walrus]

yes

[gray isle]

did you find dy/dx

[white marsh]

since dy/dx = 2x +k

put x=2

4+k=5