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[wanton sail]

#help-15

[wanton sail]

.close

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[rare lance]

hi

[rare lance]

Quick question

is $C_U^A \cup A = A?$

[solid kiln]

everytimecrusader

[trail ingot]

what?

[rare lance]

Is the complement of a set A in relation to the universe union with A equals a itself?

[trail ingot]

no?

[rare lance]

How so

[trail ingot]

doesn't that equal U?

[rare lance]

Yeah, im just confused how did i miss in a problem, that's the only option wich will validade my equation

i'll send it here wait a sec

[trail ingot]

like why do you think that equals A

have you tried looking at an example?

[rare lance]

I don't think, is just that is the only option my equation would be true

I don't know what have a missed on this then

[trail ingot]

what's happening in that picture?

[rare lance]

I need to proof $A\Delta B = $(A-B)\cup(B-A)$

[solid kiln]

everytimecrusader
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[trail ingot]

well hmm that's the definition I know for symmetric difference

what's the definition you are using?

[rare lance]

Well i opened $A\Delta B \Rightarrow (A\cup B)-(A\cap B)$

[solid kiln]

everytimecrusader

[rare lance]

Wich is $(A\cup B)-(A\cap B) \Rightarrow (A\cup B)\cap(A\cap B)^c$

[solid kiln]

everytimecrusader

[rare lance]

With that i passed everything to the left side and make it to zero

[trail ingot]

the proof and those things don't make sense any sense to me

[rare lance]

wdym

[trail ingot]

isn't this basically what you are trying to prove?

[rare lance]

Yep

This need to be 0

[trail ingot]

what's "this"?

and if that's what you are trying to prove why are you starting with it

[rare lance]

You need to find a way to reduce this to 0

[trail ingot]

?

[rare lance]

.

You just wrote

[trail ingot]

what does "reduce this to 0" mean?

[rare lance]

To prove 5=5 you do 5-5=0 wich is true

Then you will get 0=0 Wich is a true statement

[trail ingot]

ok how about this

I'm going to prove -1 = 1

-1 = 1

square both sides

1 = 1

which is a true statement

[rare lance]

wait a sec, now im broke

No you just proved 1 = 1

The moment you squared the "-1"

And turned into 1

[trail ingot]

so is this just going to prove 0 = 0?

[rare lance]

if you reduce a thing to 0 means they are equal

[trail ingot]

ok I can also prove -2 = 100

multiply each side by 0

[rare lance]

You can manipulate the numbers the way you want, does not mean they will be the same you can square both sides, you will still mantain teh equality does not mean it will be by the same number

[trail ingot]

0 = 0

[rare lance]

Ok you proved 0 = 0 not that -2 = 100

-1 = 1 are not equal, if you want to make this a equality you gotta squared, then you will get 1 = 1 wich is true

<@&286206848099549185>

[rare lance]

I need help with that

[trail ingot]

if you are trying to prove this

and you start by assuming it's true

and end up at some true statement

[rare lance]

Yes

[trail ingot]

that doesn't show what you wanted to show

[rare lance]

Only if you don't modify the number

[trail ingot]

you're just making things up lol

[rare lance]

This is basic proof theory

reduction ad absurdium

[trail ingot]

it is not

[rare lance]

You dissert a expression until you get in to a contradiction

[trail ingot]

anyone else reading this and can back me up?

[rare lance]

Your wrong about that

Your sentence is true until is proven to be a falacy

[trail ingot]

you can't prove something is true by starting with it and deriving some true statement from it

[rare lance]

Like 2 = 5, if you reduce this to 3 = 0 you get in to contradiction, wich you reduced at maximum a preposition

[rare lance]

I guess you still in high school

You should look up at reduction ad absrudium

It helps a loot to prove

[trail ingot]

lol

[rare lance]

Let me send in english

wait a sec

https://en.wikipedia.org/wiki/Reductio_ad_absurdum

[trail ingot]

what you are doing is not reductio ad absurdum

[rare lance]

What do you think reduction ad adsurdum is. You firstly got a statement wich you claim to be true. Your stament is true until you get a contradiction

Like 5 = 3, if you want to proof this is true you dissert it, and get 2 = 0, Bullshit!, you just got in to a contradiction

[trail ingot]

you have some serious misunderstandings on what reductio ad absurdum is

[rare lance]

No i don't

Reduction ad absurdum comes from philosophy and that's what it means

[trail ingot]

yea

[trail ingot]

and that's not what this is

[rare lance]

That's just the beauty about it

A argument can destroy itself

by being contradicted

<@&286206848099549185>

[trail ingot]

and btw...

I'm doing a phd in pure math

like you really have it all wrong here

[halcyon cedar]

You didn't prove anything here lol

[trail ingot]

the way you are trying to prove what you were asked to prove is totally invalid

[rare lance]

I said that because they don't teach reduction to absurdity in high school, and it looks like you don't have a mastery on the subject

[rare lance]

0=0 it's a true statement

It cannot be reduced

[halcyon cedar]

You took two different assumptions and did true -> true which is true

[rare lance]

What?

0=0 is a preposition

It's a full declaratory sentence it reads "Read zero equals zero"

It has a predicate subject and can be classified as true or false, so it is a proposition

[halcyon cedar]

So 5=5 is not a proposition so you can magically modify it to whatever you want?

[rare lance]

LOL, how 5=5 is not a preposition

[trail ingot]

if you want complete the original problem you need to get over your blistering overconfidence in your understanding of what makes a proof valid

reductio ad absurdum says if a statement leads to a false statement, then the original is false
it does not say that if a statement leads to a true statement, then the original is true

those are not the same, and that's your whole misunderstanding

[rare lance]

That's just what i been saying all time...

There is towns of ways to represent a sentence

[trail ingot]

no, you have not been

[rare lance]

It's easy if you get a equivalent number that already have a valid proof

Like $(P \Rightarrow Q) \Leftrightarrow \neg P \lor Q$

[solid kiln]

everytimecrusader

[rare lance]

This prepositions are equivalents

they are the same

[trail ingot]

yea those are the same

so what?

[rare lance]

You just derivated they still mantain equivalence

[halcyon cedar]

You are literally saying 5=5 is true because 0=0

[rare lance]

If $5=5 \Rightarrow 0=0$

[solid kiln]

everytimecrusader

[rare lance]

This conditional is only false when we get a VF

in this case we got a VV

So it's a true statement

[halcyon cedar]

And when do we ever get that?

[rare lance]

Wait i think i got it how to proof im jut finishing here

[halcyon cedar]

I'm pretty new to logic so I'm interested in this also

From what I know you can only modify propositions with negation, conjunction, disjunction and implication

So since "5=5" is your proposition so you can't modify it by doing subtraction because then the proposition will be entirely different and nothing to do with the original statement, am I wrong?

[rare lance]

First of all define a preposition. "Needs to be a full sentence, declaratory and be able to be classified true or false", If you want to prove something are equal then your subtraction must be 0 right?

It's nothing like 0 = 5, that would be false. But if a = b then a - b MUST be equal 0

That's why we have implicance

Like, how do you know a number is rational?

You use condition to prove this number is rational

If a = b, then a-b= 0 if a-b is not zero then a is not equal to b

[trail ingot]

[rare lance]

When i started my studies of logic i liked to you phrases ill give you an example

P: Marco went to the cinema
Q: Marco called his friend
P➝Q: If Marco went to the cinema then Marco called his friend

How do you know P➝Q is false

[halcyon cedar]

I understand what a proposition is, "5=5" is a true statement, "0=0" is a true statement and if we label them as p or q to shorten them, I'm pretty sure you can't modify the propositions by doing subtraction

[rare lance]

P➝Q is false only when P is true and Q is false

[halcyon cedar]

I know this

[rare lance]

That's the same

P: a=b
q: a-b=0
p➝2: a=b ➝ a-b=0

If a=b and a-b is not zero then a is not equal to 0

That's a math axiom

You can use true axioms to prove a point

You are in no way modifying

Sometimes you can prove a preposition by another if one is related

5=5 is different then 0=0, but a number is only equal to another if your subtraction results 0

Then you have an implication

a➝q

[halcyon cedar]

But then Im saying 0=0 -> 0=0 no?

[rare lance]

That's also true

[halcyon cedar]

I know, so how does saying 0=0 -> 0=0 prove 5=5

[rare lance]

Ok, forget 5=5, think of a=b

If a=b, then a-b=0 right?

[halcyon cedar]

Depends on what a and b is

[rare lance]

How can you have a equalitie wich its subtraction is not 0?

$a=b \rightarrow a-b=b-b \rightarrow a-b=0$

[solid kiln]

everytimecrusader

[rare lance]

Then we conclude $a=b \leftrightarrow a-b=0$

[solid kiln]

everytimecrusader

[halcyon cedar]

Right

[rare lance]

Anyways, i figured out on how to prove this, but thx anyway

[halcyon cedar]

But I can't do this for logic because it doesn't support - + etc?

[rare lance]

You don't need to use -

You just proved a=b is equivalent to a-b

[halcyon cedar]

By doing -b

[rare lance]

p: a=b
q: a-b=0
p➝q: If a=b then a-b=0

I'll send you a very interest logic exercise

wait a sec

Try to make this

Right answer is D

It will open your mind for logic

.close

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[calm saffron]

idk what to do next

[calm saffron]

I raised everything to e and got to bottom part but idk what's next

[keen plover]

Try isolating the square root

Then squaring

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@calm saffron Has your question been resolved?

[calm saffron]

How do I do that @keen plover

[keen plover]

Start by isolating the square root

Get it by itself

[calm saffron]

is this looking good?

@keen plover

[keen plover]

Yes

You can expand (e^x - y)²

[calm saffron]

@keen plover am I good so far?

[keen plover]

Yep

[calm saffron]

what is the next step @keen plover

[keen plover]

Solve for y

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[solar heron]

are the set of positive integers a field?

[trail ingot]

"no" is probably a good answer

but the positive integers with what operations?

[solar heron]

which field axiom disproves this again?

[marble wharf]

no 0

no additive inverses

no multiplicative inverses

[solar heron]

wait

i thought there were?

can you provide an example

[marble wharf]

the additive inverse of 2 is -2

2 is in the set but -2 isn't

the multiplicative inverse of 2 is 1/2

[solar heron]

oh that's what you have to say?

[marble wharf]

2 is in the set but 1/2 isn't

[trail ingot]

plus you can't even talk about additive inverses when there is no additive identity...

[marble wharf]

lets assume that we are taking it as a subset of Q with the usual operations

and the question was instead "is the set a subfield of Q"

[solar heron]

.clsoe

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[wraith hinge]

.

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[wraith hinge]

.

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@wraith hinge Has your question been resolved?

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<@&286206848099549185>

[hallow spruce]

What's giving you issue?

[wraith hinge]

How do I set it up

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@wraith hinge Has your question been resolved?

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@wraith hinge Has your question been resolved?

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[hallow kayak]

.close

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[long basin]

Okay hopefully im not tripping my balls off because of a stupid debate I've gotten myself into. Can anyone confirm this statement is true because I swear to god it isn't I've made a fool of myself:

$$-\ln|\sec(x)| \equiv ln|\cos(x)|$$

[solid kiln]

Umbraleviathan

[long basin]

It's really dumb but like

I'm also on painkillers so like

Bdhdhfcuuvuiib

[wraith hinge]

u right

[trail ingot]

not true when cos(x) = 0

[dark quest]

$-\ln|\sec x| = (-1) \cdot \ln|\sec x| = \ln(|\sec x|^{-1})$

[solid kiln]

jimmy1234

[long basin]

I mean they're equivalent not necessarily equal so

That's why I put the funny 3 line in it but point is

[wraith hinge]

yeye

[long basin]

If I derive both I get the same shit

[wraith hinge]

correct

[long basin]

Which is where I'm actually going to smack the shit outta my friend

For making me panic a literal day before I have to turn something in

[dark quest]

And this should show the two evaluate to the same value whenever they are well defined 🙂

[long basin]

Ty lol

.close

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[olive vault]

is there a way to figure out these formulas or should i just memorize them?

[dark quest]

Well understanding them is good, but in exam you most probably want to memorise them…

I will say memorising the first two column is good enough, coz you then can derive the others easily.

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@olive vault Has your question been resolved?

[wraith hinge]

id do all of them takes not too long anyways

plus under exam pressure it can be easy to mix it up if your not sure!

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[earnest rivet]

talking about limits is sqrt((-inf)^2) even or odd?

[earnest rivet]

specifically in

[trim lichen]

$\sqrt{(-\infty)^2}$ is most charitably interpreted as $+\infty$, which is not an integer and hence the question of it being even or odd does not makke sense

[solid kiln]

Ann

[lament jewel]

being even or odd can mean an integer being even or odd or a function being even or odd but yea u kinda gave a value

not exactly a value idk

[trim lichen]

if you meant to ask whether a certain function is even or odd,
then ask about a function

not some infinite nonsense

[earnest rivet]

yes, however it's also equal to (-inf)^(2*1/2) which is (-inf)^1

[earnest rivet]

yeah fair, but I wasn't sure if that changes anything

[trim lichen]

...

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@earnest rivet Has your question been resolved?

[cyan zinc]

Ok lets look at this a bit more rigorously

We presumably want the limit:

$-\frac{3}{2} \lim_{x\to\infty} \sqrt{x^2}/x$

[solid kiln]

Mr. Gamer

[cyan zinc]

For x>0 we have that sqrt(x^2) = x

So the limit becomes -3/2

Does that clear things up

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[wraith hinge]

Help plz

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[wraith hinge]

<@&286206848099549185>

<@&286206848099549185>

[wraith hinge]

<@&286206848099549185>

<@&286206848099549185>

[wise sinew]

!15m

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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.

[wraith hinge]

Ik but I've been waiting for 40mins so allow it 😦

[trail lion]

it seems like there is something missing to ur question but idk im dumb so

[wise sinew]

You pinged 4 times, twice in ten seconds for the last two pings... There are people that wait hours sometimes. Respect the rules and be patient and people will help. We already get dozens of pings everyday from people who respect the rules, we don't really need more from people who can't wait a few minutes... There's not a lot of people ready to help you in every moment, we're just volunteers dedicating our time to that, so again, be patient and respect the rules, otherwise there's no point in having them

[wise sinew]

Do you know where the (potential) error comes from?

By that I mean what causes the measurement to be imprecise

[wraith hinge]

no

[wise sinew]

The clock you're measuring the time with is what causes the error, since it's approximating the time. It gives you 49.57s, but the actual time could be 49.572s or 49.5691s, for example

Both these times will give you 49.57s, after approximating them

Between which times the approximation will be 49.57s?

@wraith hinge

[wraith hinge]

um not sure

[wraith hinge]

I get what you said for this

But not sure what you mean with ur question

[wise sinew]

What's the smallest time that approximated to two decimal digits gives you 49.57s? What's the biggest?

For example approximate 49.5673s to two decimal digits. Do you get 49.57s?

[wraith hinge]

yes

[wise sinew]

What about 49.5652s?

[wraith hinge]

yes

[wise sinew]

What about 49.5649s instead?

[wraith hinge]

no

[wise sinew]

So what I'm asking is what's the smallest time that approximated still gives you 49.57s

[wraith hinge]

49.5651s smallest?

[wise sinew]

Are you sure you can't get a smaller number?

[wraith hinge]

49.5650s?

[wise sinew]

Yes, 49.565s seconds is the smallest

Now find the biggest one that still approximates to 49.57

[wraith hinge]

49.571s

[wise sinew]

Not really, you can go higher

[wraith hinge]

49.570s?

[wise sinew]

That's just 49.57

You can go higher than that

[wraith hinge]

49.5744s

[wise sinew]

How did you find that number?

49.5745 still approximates to 49.57, for example

To find the highest number, think about the smallest number

[wraith hinge]

49.5749s?

[wise sinew]

The difference between the time measured (49.57) and the smalles value (49.565) is 0.005. that's going to be the same as the difference between the highest time and the time measured

[wise sinew]

It would technically be anything smaller than 49.575, since 49.5749999999999 still approximates to 49.57

So we found the error: ±0.005s, which is the range in which the time still approximates to 49.57s

[solid kiln]

Andrea276

[wraith hinge]

right

so the answer is 0.0100

[wise sinew]

,w 0.005/49.57*100

[solid kiln]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Andrea276#3928

[wise sinew]

Yes, you want to approximate it to three significant figures though

So 0.0101%

[wraith hinge]

ahhhh right

[wise sinew]

No it actually asks for 3 decimal places, nevermind

Not 3 significant figures

[wise sinew]

So 0.010% is correct

[wraith hinge]

ok

T h x

.close

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[olive vault]

How can u tell when smth is a partial fraction problem? Can this be done with partial fraction decomposition or is there an easier method?

[dark quest]

Partial fraction method is needed, when you are dealing with “rational expression”, meaning both numerator and denominator is some high-order polynomial.

In your last step, numerators and denominators are not further “factoriable” in R, so what follows is no longer about partial fraction.

[olive vault]

so if numerator is a constant then i cnat use this method?

[dark quest]

Not necessarily, consider this example.

$\frac{7}{(x - 1)(x + 2)(x + 3)}$

[solid kiln]

jimmy1234

[dark quest]

Here denominator is formed by some linear factors, and you can still do partial fraction on it.

[olive vault]

ohhhh ok i got it

[olive vault]

thank you for finding the error i get it now

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[hazy light]

Shouldn't A ∩ B= A here?

(since A is a subset of B)

[wraith hinge]

no B is subset of A

[hazy light]

how?

[wraith hinge]

Event A is the machine works for more than 5 years which means 5.1 or 6 or 7 , 8, 10 and so on
But even B will include years greater than 8 only like 8.2 , 9, 10 and so on

So B is a subset of A

just think of A as a set which contains numbers greater than and B a set which contains numbers greater than 8

[hazy light]

Understood

Thank you

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[hot pebble]

hello, im trying to convert 6.2 picometers to meters. I searched 1m = 10^12pm but then 1 pm = 10^-12m so which one would I use

[burnt mulch]

They're the same thing, divide both sides of the first by 10^12 and you get the second

[hot pebble]

so it wouldnt matter which one I use

[stoic iron]

^^ the second form is the most useful to you

[hot pebble]

why is that

[stoic iron]

If 1pm=10^-12m then it's easier to see what 6.2pm=..

[hot pebble]

ok

ty

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[daring karma]

what does it mean if matrices are "of the same order?"

[daring karma]

okay thank you

[wraith hinge]

if they have the same number of rows and columns

[daring karma]

also what does the notation A[ i , j ] mean

[wraith hinge]

it just means the ith row and jth entry of an arbitrary matrix A

[marble wharf]

that's false btw

[daring karma]

oh so its like an x,y coordinate but for a matrix, right?

[wraith hinge]

correct

for x, y in Z+

[daring karma]

apparently its true, i think its false as well

[marble wharf]

should be (AB)^T=B^TA^T

[wraith hinge]

^

[marble wharf]

unless the ^T means something other than transposing

[daring karma]

oh wait no its false

i was looking at the wrong thing lol

[wraith hinge]

only true when A and B are diagonal matrices (i think?)

[marble wharf]

they would instead be called tensors. but they exist, yes

[wraith hinge]

i think its called tensor or something

[daring karma]

also how would i explain this that this is false? Could I say that simply transposing each of the factors will completely change the product?

cuz like, i cant really explain it with words without doing an actual example of the problem

[wraith hinge]

just do a simple counterexample, thats enough to disprove

[daring karma]

okay thank you

one last question, how is this false:

every matrix example that i do turns out prove this example correct

oh wait never mind

its true

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[kindred acorn]

How do I find the roots of f(x)=3÷2?

[dire kraken]

set f(x) to 0 and you’ll see the problem

[kindred acorn]

3÷2 = 0

Basically, 3÷2 = 0÷1

[valid moss]

3/2 is a constant function and therefore doesn't have a root

[kindred acorn]

Oh okay thanks

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[mellow nimbus]

Hi

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Please don't occupy multiple help channels.

[twin swan]

bye

[mellow nimbus]

Hi

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[loud venture]

help

[loud venture]

<@&286206848099549185>

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[fierce frigate]

need help

[fierce frigate]

Determine if the given is an expression or a sentence. Write E if the given is an
expression, otherwise write S. Then, translate the verbal expression/sentence to
algebraic expression/sentence. This section is 3 points each (1 for the
identification, 2 for translation).

1. Twenty-seven less than 11 times the number is one less than the number
   multiplied by three less than five times the number, and the entire result is
   divided by six less than the number.
   answer

(11x)-27x(5x-3)

(x-6)

2. The product of a number divided by six and another number multiply by
   negative five.
   answer
   x÷6x-5

3. The VAT from the first purchase of p pesos and second purchase of q pesos.
   answer E

4. Twenty-three is divided by two less than twice a quantity and the result is
   thirty-four.
   answer
   (23÷2)=34

5. An unknown quantity is decreased by eleven, then divided by fifteen and one is subtracted from this result hence five is obtained.
   answer
   (-11)
   ----- = 5
   15-1

6. The average of 3 distinct quantity.
   answer E

7. The product of 9 and the sum of a quantity and 2.
   answer
   (9+2)

8. Normal saline solution contains 0.9 percent sodium chloride (salt) and water.

9. Three inches converted to centimeters.

10. A combination of 30% flour, 57% sugar and 13% cocoa powder.

can you check if my answer right?

[dire kraken]

@fierce frigate is this a test ?

[fierce frigate]

just an assignment

is these correct?

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[median mica]

I dont seem to get anywhere with this problem, any intel on this will be helpful

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[stoic iron]

If I move something 12 units up and then move it 1 unit up how many units have I moved it up

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[median mica]

13?

wait so i just have to add the x and y coordinates?

doesnt it seem way to easy?

@stoic iron

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[queen linden]

Hello everyone I need help

[queen linden]

f (x) = 2 * sin 3x, f-1=?

I have no clue how to do this can anyone give me tips or anything? Thanks in advance

[dark quest]

Let $y = 2\sin 3x$, then express $x$ in terms of $y$.

[solid kiln]

jimmy1234

[valid moss]

$f-1$ or $f^{-1}(x)$

[amber python]

[solid kiln]

illuminator3

[amber python]

if the latter

do you have a domain restriction

[queen linden]

Ye I know its from x but idk how to replace it all

[amber python]

f isnt a surjection 🤔

[valid moss]

dear lord I always confuse them 😭

meant f isn't a bijection

[queen linden]

Its the 2nd one

[amber python]

the inverse depends on your domain

it might not even be well defined otherwise

[queen linden]

I wish I understand anything you say but I am kinda bad at english :'(

Let me translate to mine language

[queen linden]

The 2nd one

[valid moss]

yes

you can't find an inverse

[queen linden]

Really?

[valid moss]

without additional details

[queen linden]

Hmm

What kind of details?

[amber python]

the values of x that f is defined over

[queen linden]

Its not enough that I have f(x)?

[amber python]

it is not

because the inverse would otherwise by multivalued

[queen linden]

Thanks

Idk why teacher gave us this for homework :'(

[amber python]

well

if you assume for example that x is defined on [-pi/3, pi/3]

then you can take an inverse

using just arcsin

[queen linden]

I think that x€ {R}

[amber python]

hmm

then the inverse is not well defined

[queen linden]

Oh

We were actually using arcsin today on differenz examples so I think you may be right

[amber python]

hmm

then you should be able to give it a go

[queen linden]

She will check homework tommorow and she gives - if its not okay I hope I will do it fine 🥺

Thank you for help everyone

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[sinful scroll]

It’s wrong

And I’m confused

[night zodiac]

,rotate

[dark quest]

It does not have to be (A). A limit can occur graphically, if $f(x)$ at $x = a$ has a hole.

[sinful scroll]

Oh bruh I’m special

[solid kiln]

jimmy1234

[sinful scroll]

Could u explain C

Why it doesn’t work

[dark quest]

(C) also need not be true, by this same reasoning.

[sinful scroll]

How does f(a) ever equal L

[dark quest]

A limit is about the function behaviour in the neighborhood of a point. If no further info is given, a limit cannot tell us what happens exactly at that point.

[sinful scroll]

I see

I have another @dark quest

,rotate

[dark quest]

If you know what f(x) is, then what f(g(x) should be?

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[sinful scroll]

,rotate

[sinful scroll]

Do I use the function with x and a or h and a

<@&286206848099549185>

pls help

<@&286206848099549185> '

[verbal gulch]

wdym x and a or h and a

[sinful scroll]

these 2 formulas

[verbal gulch]

aren't these the same thing

[sinful scroll]

ok so i used the 2nd and i got $\frac{2a^2+7a-31}{a+1}$

[sinful scroll]

dont they give the same answer?

[verbal gulch]

no like they're the same formula

[sinful scroll]

at the end of the whole process

[solid kiln]

Bubbles

[sinful scroll]

i cant symplify this tho

like the a+1 doesnt cancel

so idk what to do

[verbal gulch]

if you replace h with a-x in the first equation, you get the second

yeah not exactly sure what you're doing here

[sinful scroll]

uh

how would u do it

[verbal gulch]

are you trying to find the derivative with the difference quotient?

[sinful scroll]

this is just what i learned in school 😭

[sinful scroll]

what does that mean sry

this is the only way i know how

[verbal gulch]

okay do you know what a derivative is?

[sinful scroll]

the slope at a point?

thats the tangent line

my teacher is so bad at teaching

[verbal gulch]

yeah that's basically it

and as for the two equations you've written

$f'(a) = \lim\limits_{h \rightarrow 0}\frac{f(a+h)-f(a)}{h} = \lim\limits_{x \rightarrow a} \frac{f(x) - f(a)}{x-a}$

[solid kiln]

Saccharine

[verbal gulch]

These are actually completely the same thing

[sinful scroll]

oh

wait yeah

[verbal gulch]

the first thing follows from the second by considering h = x-a

[sinful scroll]

make x=h+a

mhm

[verbal gulch]

but intuitively, the slope of a function at a given point is the derivative evaluated at that point

so the slope of f at x=a is given by f'(a)

agreed?

[sinful scroll]

yea

[verbal gulch]

so if you look at question 2a, you're asked to find the equation of the line tangent at that point, right?

and the point we're given is x = -1

[sinful scroll]

yep

[verbal gulch]

so we need two things for the equation of a line: the slope and a point on the line

[sinful scroll]

which is (-1,20)

[verbal gulch]

what's the slope of the tangent line of g at x = -1?

[sinful scroll]

thats what i cant find

[verbal gulch]

okay so we'll write that first as g'(-1), right?

[sinful scroll]

yep

[verbal gulch]

we should find g'(x) for arbitrary x, and then we can just substitute -1 in

or you could do it by taking limits

depends on really what your teacher will accept

g'(x) = 4x - 7 if you care

or you could write $g'(-1) = \lim\limits_{h \rightarrow 0} \frac{g(-1 + h) - g(-1)}{h}$

[solid kiln]

Saccharine

[verbal gulch]

and evaluate that limit

[sinful scroll]

uh for this we dont need to find the equation to find a slope of the tangent line just this specific point

thats what he said

[verbal gulch]

okay but all we need to find is g'(-1)

there are many ways of doing it

as long as you have a valid way of doing it, that's fine

that's basically the whole point of mathematics -- do something and make sure you justify it

Personally, I prefer not to write out the difference quotient, because it's rather gross

but if you want, we can do it that way

[sinful scroll]

ok

so

if i do it the way where u just find the slope of the tangent line at 1 point

can u walk me through that

[verbal gulch]

In any case, you can probably just take g'(x) = 4x-7 and therefore g'(-1) = -11

[sinful scroll]

because i did it and its not cacelling

[sinful scroll]

how did u do that

[verbal gulch]

okay so you want to write out the difference quotient

[sinful scroll]

oh power rule

[verbal gulch]

yeah

[sinful scroll]

we havent learned that yet

[verbal gulch]

okay

[sinful scroll]

i saw it on khan acadamy tho

i dont think he cares if i use it i hope

[verbal gulch]

I mean it's instructive to do it both ways

[sinful scroll]

ok thanks appreciate it better teacher than my teacher 😄

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[umbral whale]

can a 1 dimensional vector be negative, and why? what is the difference between a scalar and a 1d vector

[azure sonnet]

yes

because if you think of a 1 dimensional vecor

you have one axis

(the number line)

so [-4] is a vector that points to the number -4.

a scalar is something that doesnt exist on the number line, other than altering the effect of vectors

4 * [-4] = [-16]

you can only see the [-4] and [-16]

on the graph

but you dont see the scalar 4

because it scales by 4, but it is not [4]

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[azure sonnet]

@umbral whale

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[wraith hinge]

hi can you check one of my question but i did this with this method however there are some other methods too does this work everytime

[worn sun]

Your method is correct.

[wraith hinge]

and about if this works everytime, depends on what you mean but yes as long as you factor correctly and put the parenthesis around it, to then multiply both powers then sure

[wraith hinge]

actually there comes a question where you don’t have its cube root or neither a square root and that’s where you are unable to solve

like 126 ^ 2/3 like this one

so here some@other method has to be used

[wraith hinge]

can we see it?

i mean obviously it depends on the question, you can't always use the same method

there was a similar question

like this one

you can use that same method here @wraith hinge

what's 32 in powers of 2?

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[wraith hinge]

oh yes

thanks it’s 2^5

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[tepid rock]

That isn't what happens here

Have you tried anything?

Show your solution with appropriate reasoning.

Another way to look at the problem is, your factored form when expanded should give you the original expression.

So you can always check your answer's accountability.

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[split chasm]

<@&268886789983436800>

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[viral cliff]

Hi, if we need the open interval over which this graph is convex and concave, would that be (infinity, 0) for concave and (0, infinity) for convex?

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[viral cliff]

<@&286206848099549185>

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[marble wharf]

Yes

[amber python]

are we only looking for open intervals

0 can also be included

[viral cliff]

thanks guys

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[misty portal]

I am confused with negating logic, there are multiple answers online.

If I have the following statements:

p: The senator will attend the meeting
q: The senator will not vote for the motion.

Together, I get "The senator will attend the meeting and the senator will not vote for the motion".

The statement above, I am supposed to negate it.

[misty portal]

If I were to negate the two statements that are together, do I use "or" or "and"?

My initial answer was "The senator will not attend the meeting or the senator will vote for the motion"

[fathom folio]

What does de morgan say

I am assuming your 'together' = && = intersection

[fathom folio]

Despite me never remembering the actual law, it's nice to just refer to the law

[misty portal]

I have no clue on what the De Morgan's law is about

[fathom folio]

I think this is imprecise

[fathom folio]

If you want to negate the together statement you will be doing !(A && B)

And de morgan tells you how to do that on a per-statement basis, then set-operationed after

[misty portal]

I am looking up what De Morgan is, but I feel like this is irrelevant as I am dealing with truth tables?

As in converse, inverse, contrapositives and negation

I have clearly understood what the other three are, but I am at a loss with negation

"The senator will attend the meeting and the senator will not vote for the motion."

How do I negate this?

Is it "The senator will not attend the meeting and the senator will vote for the motion"

or

"The senator will not attend the meeting or the senator will vote for the motion"

Or is it something else different?

[trim jolt]

@misty portal Has your question been resolved?

[fathom folio]

De morgan tells you exactly which the negation is

[misty portal]

Correct me if I'm wrong, but that means the answer would be the latter?

Since "and" becomes "or" and vice versa

[verbal gulch]

indeed

these situations are exactly the opposite; exactly one of them must be true at all times

that's how you can check through your intuition whether a statement is negated I guess

[misty portal]

okay, thank you both

One more question, how is it different from the inverse?

[verbal gulch]

negation is of a proposition, something that is either true or false

inverse is of some conditional, like if you say "if p, then q," the inverse is "if not p, then not q"

the negation of "if p, then q" is "p and not q"

[misty portal]

I read that in the De Morgan law as well, I think I need to mull it over some more

But I think I already understand a good enough portion of it.

Thank you both! 💜

How do i close this uhh

.close

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[sharp portal]

is this wrong or not

[verbal gulch]

looks wrong to me

I get 56 minutes

[sharp portal]

how do you get it

[split chasm]

introduce variables for
time, number of people, number of problems, proportion factor
and set up an equation

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[wraith hinge]

3+9=9+6

[delicate jasper]

What?

[wraith hinge]

its a multi step equasion

[dire kraken]

missing a variable?

[tepid rock]

Trolling*

[wraith hinge]

the question is two shops rent pairs of skis for a rental fee plus a fee per hour. How many hours must a pair of skis be rented for a total cost to be the same
shop a shop b
rental fee=3$ rental fee=9$
hourly fee=9$ hourly fee=6$

and if you write it into a equasion its 3+9=9+6

[split chasm]

no

[wraith hinge]

im stuck on it

[split chasm]

3 + 9 is not equal to 9 + 6

12 is not equal to 15

note that 3 + 9 will not be the total cost for shop A,
that would only be the cost for a single hour,
same issue with shop B

start by introducing a variable (usually t for time) to represent what you want to find

[wraith hinge]

apperantly you have to solve for how many hours the cost the same

[split chasm]

how much would it cost to rent skis for t hours from shop A?

[wraith hinge]

ooooooh

i get it now

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[wraith hinge]

how is the probability for drawing a number strictly greater than k, (100 - k)%

from what I'm seeing the probability of the outcome is congruent to the cardinality of the set

but if you were to take k = 50, then you'd get a set from 51 to 100

100 - 50 = 50

but the cardinality of the set is 49 if im not mistaken

[sharp arrow]

Is it?

Try counting again

Lets take simple example k=90

So we have {91,92,93,94,95,96,97,98,99,100}

[wraith hinge]

Im mentally impaired

Thank you

sorry for that question.

[sharp arrow]

Np

[wraith hinge]

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[fleet pier]

what does the phrase 'reflection in a line' mean? i.e. '... is the result of reflections in any two lines...'

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[wraith hinge]

In exact differential equations after checking My and Nx.

[wraith hinge]

Why do we reverse this procedure? Taking the integration of Mx and Ny.

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[wraith hinge]

<@&286206848099549185>

[light crystal]

You're comparing the test which gives necessary and sufficient conditions for exactness and what exactness actually means.
If a differential equation M(x, y)dx + N(x, y)dy = 0 is exact then there exists a function f(x, y) such that it's differential is f_x dx + f_y dy = 0.
The test for such a function, f(x, y) existing is that it's second order mixed partial derivatives are equal, f_(xy) = f_(yx), this is why you test that M_y = M_x.
If you've confirmed it exists then you can integrate f_x = M(x, y) and f_y = N(x, y) to try and determine f(x, y).

[wraith hinge]

Thank you for this detailed explanation.

[light crystal]

If you find that f, is exact, you know M dx + N dy = df = 0.
Integrating df = 0 gives the implicit solution f(x, y) = c.

[wraith hinge]

One question. Why M dx + N dy would be equal to df?

[light crystal]

Read this again, please.

[wraith hinge]

Okay. Sorry, let me go through one more time.

[light crystal]

Specifically: "If a differential equation M(x, y)dx + N(x, y)dy = 0 is exact then there exists a function f(x, y) such that it's differential is f_x dx + fy dy = 0."

The differential of f(x, y) = df.

[wraith hinge]

I see.

Thank you 🙂

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[stark flint]

is this correct>

[wraith hinge]

Yes

((x + 2) (x - 6)) / (x - 6)

[stark flint]

yeah that was my working aswell

thank you

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[violet nest]

why is this wrong?

[violet nest]

when i plug in 3x i get 5-8(3x)^2

3x becomes 9x^2

[stoic iron]

you've typed x^3

[violet nest]

isnt (3x)^2

3x^3?

[stoic iron]

why do you think that

[violet nest]

with exponents dont we add?

[stoic iron]

what exponents are you adding?

[violet nest]

3x has an ^1

combine that with ^2

[stoic iron]

right but its $(3x)^1\cdot (3x)^1$

[solid kiln]

ΣAC

[stoic iron]

you're confusing $x^a\cdot x^b = x^{a+b}$ with $(x^a)^b = x^{ab}$

[solid kiln]

ΣAC

[violet nest]

oooooooo

[stoic iron]

its more simple here, $(3x)^2 = (3x)\cdot(3x)$

[solid kiln]

ΣAC

[stoic iron]

=$9x^2$

[solid kiln]

ΣAC

[violet nest]

that makes more sense

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[pastel mesa]

why is this equal to (16x^4 - y^4) (16x^4 + y^4)

[pastel mesa]

because 8 doesnt have a whole number square root

[dire kraken]

it doesn't need to, it just needs to be divisible by 2

[dire kraken]

because notice that when you FOIL this back up, the x^4 multiplies by x^4, and same with the y^4

and of course, x^4 * x^4 = x^8

[pastel mesa]

alright got it thanks @dire kraken

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[mystic grotto]

I can't read the whole q

[oblique sun]

oh

here

@stable bear

[stable bear]

Don’t ping individual helpers

!15m

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[stable bear]

^

[oblique sun]

bruh

@stable bear

its cherry sparkle

help

[trail ingot]

,rotate

[solid kiln]

Couldn't find an attached image in the last 10 messages.

Sep 11, 2022, 9:33 PM

[trail ingot]

,rotate

[oblique sun]

Oki

[trail ingot]

ok let's call the the number seats in section A as A, the number seats in section B as B, and the number seats in section C as C

then...

A + B + C = 49000 because there are 49000 total seats

25A + 20B + 15C = 1052000 because each seat from section makes $25 and so on, and the total is 1052000

and A = B + C because of the 2nd sentence

[oblique sun]

ohhhh okok thank yiou

and then ewould u isolate a variable?

[trail ingot]

sure you can do that

[oblique sun]

oki thanks

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[wraith hinge]

.help

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Commands:
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[wanton sail]

Could someone help me check this. I checked with a friend but we disagree on the last couple steps

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[wanton sail]

<@&286206848099549185>

[wanton sail]

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[wraith hinge]

can anyone help

[wraith hinge]

.close

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[lone mauve]

why am I only concerned with the denominator for this answer?

[loud kayak]

You don’t want the denominator to be 0

[night zodiac]

Because it's a rational function

[loud kayak]

If it is then it is undefined.

[night zodiac]

Aka

[lone mauve]

That’s literally the only reason?

[loud kayak]

Yes

[lone mauve]

Lol so simple

[loud kayak]

Any number divided by 0

Is technically infinite

That’s why when you plot 1/x

As you approach zero the graph shoots up

[lone mauve]

Not sure I follow

[lone mauve]

Because x can’t be 0?

[loud kayak]

If you take 1/0, 0 keeps going into 1 infinitely many times

Like 4/2

2 goes into 4 twice and you have reached 4 so you stop and conclude it’s 2

1/0 though?

0 keeps going into 1 infinitely many times

So when you look at my screenshot you can see as you look at x=0 the red line shoots to a positive infinity on the y-axis

[lone mauve]

I’m using Symbolab but something isn’t right

No lines added

[night zodiac]

Zoom out

Look at the scale

You are using a scale of 0.002

[lone mauve]

Oh

Thanks

This is a hyperbola

Conic section

1/x

[night zodiac]

No it's not

Hyperbolas are in the form of

Pretty sure 1/x is not that form

[lone mauve]

But it appears this way on the graph

[inland orbit]

1/x is a hyperbola

[inland orbit]

This is not the only form of a hyperbola

1/x is just rotated out of standard position but it's still a hyperbola

[night zodiac]

Typical hyperbolas I'm used to are like this so I'm not used to referring 1/x as a hyperbola

[inland orbit]

That form generally works but it only allows for hyperbolas that open toward the x or y axis

anyway, looking at @lone mauve's question, that doesn't really matter anyway lol

[lone mauve]

1/y gives the same result

[inland orbit]

well

y=1/x and x=1/y are equivalent

For example 2 = 1/0.5 and 0.5 = 1/2

[lone mauve]

Hmmm I’m trying to imagine how those would be written f(x)..

f(x) and f^-1(x)? Inverse function

[inland orbit]

Oh

sure

Yeah, a better way to phrase it would be that f(x) = 1/x is its own inverse

so f(x) = f^-1(x) in this case

This seems way off track from your original question lol. Sorry I kinda jumped in in the middle of it

[lone mauve]

inverse is just flipping numerator with denominator? That’s all it means?

[inland orbit]

no

[lone mauve]

It’s OK I’m enjoying this and learning

[inland orbit]

F and G are inverse functions if and only if F(G(x)) = x and G(F(x)) = x

So f(x) = x+2 and g(x) = x-2 are inverse

because f(g(x)) = x and g(f(x)) = x

for all x

[lone mauve]

Hmmm

I’m still learning F o G

It’s still very confusing to me

[inland orbit]

oh, same thing

[night zodiac]

Fyi, to find the inverse of a function, swap x and y, then set it equal to y again

[lone mauve]

Yeah

[inland orbit]

(F o G)(x) means the same as F(G(x))

[inland orbit]

also this

[night zodiac]

That's just notation for composite function. You plug in a function into a function

[lone mauve]

pretend f(x) is f(y) and solve for x instead of y

[lone mauve]

Fog is what I have in my brain when I read this

https://tenor.com/view/fog-mountains-trees-forest-cold-gif-5142601

[inland orbit]

Lol

If we say F(x) = x^2 and G(x) = x+1

Then would it make sense that F(G(x)) = F(x+1) = (x+1)^2 ?

[lone mauve]

Hmm let me think here.. does it matter both are simple linear functions or no difference at all when it comes to FoG?

[inland orbit]

Doesn't matter.

[lone mauve]

OK

[inland orbit]

And I actually just changed it so they're not both linear

[lone mauve]

Let’s see…