help-27

[solemn atlas]

Ah...

Do we do vertex form?

[tame palm]

.... Yes.

(x - 190)^2 + 10000 - 190^2 = 0

The +190^2 gets absorbed into the completed square.

[solemn atlas]

Ah...

[solemn atlas]

So we dont subtract it from 10000?

[tame palm]

You will. I just left it as is to make the steps I'm using easier to see.

[solemn atlas]

Ah

[tame palm]

Too many textbooks will often do ten steps in one go and expect you to understand what just happened. I hated that. 😛

[solemn atlas]

Thats why its been frustrating

[tame palm]

From this point on, it's just algebra.

[solemn atlas]

I see

[crystal dawn]

dropping in to say, I agree so much

[solemn atlas]

-26100?...

[tame palm]

Yes, but once you move it to the right-hand side, it becomes positive.

[solemn atlas]

I have to figure this out

I see

[tame palm]

You have two values of x that will constitute part of the values of x that constrain the area to 20000 and 50000.

[solemn atlas]

Ohhh

[tame palm]

You need to do the same for A(x) = 50000 to the other two x values.

[solemn atlas]

Ohhhhhh

[tame palm]

If you plot the x-values, you will see they occur at the borders of the yellow area and the intersection of the parabola.

[solemn atlas]

I get it a bit more now

[tame palm]

So use the same steps for A(x)=50000 and see what you get.

[solemn atlas]

Ok

[tame palm]

You are solving for these values of x.

[solemn atlas]

I got (x-190)2=sqrroot 111000

[tame palm]

,calc 190 + sqrt(111000)

[woven radish]

Result:

523.16662497915

[solemn atlas]

Thats not it then...

[tame palm]

You mathed wrong somewhere. Can you show your work?

[solemn atlas]

Uhhhhh

[solemn atlas]

Ohhh I put in an extra zero some where

[tame palm]

111000

instead of 11100

[solemn atlas]

Yeah

[tame palm]

Now find the values of x and determine which values of x create an interval for the range given.

Because there are two intervals.

[solemn atlas]

Oops

Oh- the problem continues

[tame palm]

You will need to determine the domain of those two intervals.

[solemn atlas]

Uh...

[tame palm]

You have the values of x, you just need to determine which ones apply to which intervals.

[solemn atlas]

Um.

Do we need to try to solve?

[tame palm]

You should be able to reason it out without doing any calculations.

[solemn atlas]

I dont know dude I gotta do this test by 11:59 tonight and all day its like I forgot everything

[tame palm]

This is a test?

[solemn atlas]

No

Not yet

But I am seriously wondering if I will even do well

[tame palm]

This late in the day, probably not unfortunately.

[solemn atlas]

I cant even think straight

[tame palm]

If you get to that point, it's best to take a break, even for just a short while.

[solemn atlas]

Yeah thats true

I just pray theres not too many word promblems my dislexic tail wont even get close if there is

[tame palm]

You have dyslexia?

Probably not, I haven't seen any misspellings.

[solemn atlas]

Not diagnosed but conconsidering it taked a lot of focus to type (because i write) and phone correct helps- I struggled a lot as a kid when it came to reading and writing

[tame palm]

Mild dyslexia perhaps. Do you get accomodations in school?

[solemn atlas]

I am diagnosed with adhd so those two hsve a history in coexistence wouldnt be suprixed if i did

[solemn atlas]

I do have that- for my adhd.

Test anxiety is also a pain...

[tame palm]

Obviously you already know that stress can exacerbate ADHD symptoms. Work on relaxing first before continuing.

[solemn atlas]

I am trying to make sure all my study is in order so Im less likely to blank

Your right

Sorry about coming off inpatient earlier by the way

[tame palm]

A study suggestion. Find a large cardboard box and cut it out so that you can make a large wall to place in front of your study area. The lack of visual noise will help you focus.

[solemn atlas]

It would

I try to have calm music in my ears tk block out noise for now

[tame palm]

A clean desk also helps.

[solemn atlas]

I dont have much of a desk at the moment

But maybe I should also eat. I always forget to when Im too focused

[tame palm]

A dark room can help destress.

[solemn atlas]

Thanks I might do that for a few moments

That actually kinda helped

[proud sparrow]

but a cluttured desk is a sign of creativity

you lowk sound like my mom rn kookie

[tame palm]

But it doesn't help a person with ADHD.

[proud sparrow]

huh

like how..?

actually that makes sense ig

it would remove visual distractions hmm

lemme try it

[proud sparrow]

btw if you have no other doubts you can close the channel

[solemn atlas]

Well there are many but as time approaches I must take it.

Thank you for the tips @tame palm I will definitely use them some time

[devout snow]

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[devout snow]

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[mellow nova]

Heya, I’m trying to find the tangent points where a circle of a given radius would touch these two trapezoids with rounded corners. Is there a way to compute or approximate these points?

[supple knot]

#computing-software

[mellow nova]

so should I ask there? (and close this?)

[devout snow]

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[devout snow]

@mellow nova Has your question been resolved?

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[mellow nova]

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[solar goblet]

can (b) be shortened as $\forall T(x) (C(x) \land E(x))$?

[devout snow]

@solar goblet Has your question been resolved?

[devout snow]

@solar goblet Has your question been resolved?

[young spade]

To be honest, probably skip the (x) in the T

Tools are an element, no a property here

[solar goblet]

mmmm it sounds weird

[young spade]

mb, down its said to use T(x)

Then yeah

[solar goblet]

so this is acceptable?

[young spade]

Still, id say the $\to$ is still necessary here

[woven radish]

∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴

[young spade]

$\forall x T(x)$ implies that x is a tool.
From there, we conclude that all x which are tools, are in the correct place (C) and in Excellent condition (E)

[woven radish]

∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴

[young spade]

This leaves open the possibility that some "x", which arent tools, might not follow the same logic

[solar goblet]

i figure that if we do \forall T(x) instead of \forall x (T(x) -> ...) here, it's equivalent to describing the behaviors of x's that are tools, anything else are irrelevant and we don't give a shit about how they behave, since they still validate the proposition regardless

which is, basically the same to the latter

[young spade]

Not really

For a sense of why:

$\forall n \in \mathbb{Z}: n^2 \in \mathbb{Z}$

[woven radish]

∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴

[young spade]

Which means that all integers, when squared, give another integer

This is clearly not the same as writing

$\forall \mathbb{Z}: \mathbb{Z}^2 \in \mathbb{Z}$

[woven radish]

∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴

[young spade]

Which doesnt make much sense

[stone stump]

the thing after \forall has to be an element. not a statement

[solar goblet]

i see

[young spade]

The general idea, when you use any of the quantifiers, you are talking about some subset of elements from a "bigger" set.

[solar goblet]

then what about $\forall n \in \mathbb Z$? isn't $n \in \mathbb Z$ also a statement?

[young spade]

Here this is used as a condition

But yes, we could think about it as a statement

You could write it like:

$\forall n Z(n)$

[woven radish]

∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴

[young spade]

Supposing Z(n) is the condition such that n is an integer

But thats non-standard

[solar goblet]

can't the same be said to T(x) then? or does treating a statement after quantifier as a condition apply exclusively to an element \in set?

[young spade]

You were trying to do $\forall T(x)$

[woven radish]

∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴

[young spade]

which would read as

"For all statements"

Instead of "For all x that satisfy this statement"

[solar goblet]

mmm i see

[young spade]

Tbh, the way presented here isnt that standard to start with
But its just english -> logic, so it hasnt to be that serious.

[solar goblet]

why is it not standard? it's the way i am taught

[young spade]

Usually instead of a condition T(x) to indicate that x is a tool
You would define:

1. A set of all things X, with elements x
2. A subset of X, T, which is the set of all Tools
   And you would write it down like

$\forall x\in T: (C(x) \wedge E(x))$

[woven radish]

∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴

[young spade]

Mostly this is the "usual way", because most proofs of actual numbers are presented in this way

[solar goblet]

i don't see much difference here, just that the statement T(x) is now broken down into the set T. i assume that the universe of discourse here is defaulted to everything, and x is implicitly assumed to be in it

but either way, thanks for the clarifications

[young spade]

T(x) being a condition of the elements in X to be tools is logically speaking, the same as saying that T is a subset of X, which is all the tools.
But again, we usually go for the second, because that would be similar to saying

"The integer elements from the reals"

Just leads you to having to define more things

[solar goblet]

appreciate it

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[karmic lake]

hey im studying linear algebra, and I was wondering whats the difference (in usage) of column and row spaces? like I do know that you can take a span and turn it into a row space and then with elementary operations you can find out if they linearly independent but what are the other uses for those spaces

[young spade]

Ill suppose you have somewhat seen that linear independence is a big thing in algebra

[worthy raft]

There's a sense in which row vectors are linear functions taking column vectors to the field

[acoustic leaf]

• the column space is the range/image of the function T(x) = Ax
• the row space is the orthogonal compliment of the null space (don't worry if you don't know what that means yet)

also row operations can be thought of as operations that keep the row space the same

[karmic lake]

@acoustic leaf @worthy raft @young spade thanks!

[devout snow]

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[blazing bolt]

16th

[untold ravine]

,rccw

[untold ravine]

see the compound angle formula for tan((r+1)A - (r)A)

and try to figure out something

[blazing bolt]

👍

[blazing bolt]

I really can't

[untold ravine]

$\tan(A) = \tan((r+1)A - (r)A) = \frac{\tan((r+1)A) - \tan(rA)}{1+\tan(rA)\tan((r+1)A)}$

[woven radish]

CherryMan

[untold ravine]

so $\tan(rA)\tan((r+1)A) = \frac{1}{\tan A}(\tan((r+1)A) - \tan(rA)) -1$

[woven radish]

CherryMan

[untold ravine]

can we telescope the sum then?

[blazing bolt]

Yes 😭

[untold ravine]

right so what will it be

[blazing bolt]

Thanks

I got answer -10

[untold ravine]

wait how

oh nvm i got it

!done

[devout snow]

If you are done with this channel, please mark your problem as solved by typing .close

[blazing bolt]

Wait

@untold ravine
What's the mistake

[untold ravine]

the -8 should be outside the brackets

anlso tan 9A = -tan 36

[blazing bolt]

Oh

!done

[devout snow]

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[blazing bolt]

.close

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[devout snow]

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[worldly tapir]

Isnt the 2nd part of this piece function wrong and supposed to be x-1?

[harsh sierra]

I think you are right

[worldly tapir]

cause

isnt it y-int

right

[harsh sierra]

Yeah

[worldly tapir]

u think im correct or 😭

[harsh sierra]

Yeah you are right

All good

[worldly tapir]

👍

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[keen sundial]

Im just wondering if it to be multiplied by 2 from left to right

[keen sundial]

can another geometric series be divided by 2 from left to right

[versed juniper]

yes

[late scaffold]

what's your initial guess for the sequence in sigma notation?

[keen sundial]

I already watched it before you asked

well Its ok Ill find more

but I do have a question

[keen sundial]

does it always follow this rule?

[versed juniper]

yes

[keen sundial]

across series and sequences

[versed juniper]

only for geometric

[keen sundial]

I see

so I would need to memorise these formulas

[late scaffold]

what do you mean, memorize?

[crystal dawn]

it's fine

[pseudo basin]

if you think that you cannot internalize the formula for a geometric seq except by drilling, then yes

[keen sundial]

why did he make i=1

isnt it supposed to be 3

since it started at 3

[versed juniper]

it's the index not the term

the term is calculated from the index

[keen sundial]

whats an index

[versed juniper]

"counter"

[keen sundial]

1st term, second term, third term

etc

Is that what u mean

[late scaffold]

yes, that the idea of an index.

basically, an index is like a position tracker

[keen sundial]

got it

[devout snow]

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[restive river]

,rotate

[devout snow]

@rigid atlas Has your question been resolved?

[devout snow]

@rigid atlas Has your question been resolved?

[devout snow]

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[restive river]

Hii! I'm stuck on the last step here in this equation method problem, what should i do now? - 5 + 2x = 4x | -2x?

[pseudo basin]

yes subtract 2x

[restive river]

Okay thank you!

.close

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[restive river]

.reopen

[devout snow]

✅ Original question: #help-27 message

[restive river]

i need help again 🥲

one sec

I've put x = -2,5 in the x of the II equation, but i get 18, but the answers say i need to get (-2,5 | -30 )

which step did i do wrong 🥲

[wild grove]

4 * (-2.5) is -10

How did you get 6

[restive river]

Beacuse 4 - 10 is 6

[wild grove]

Not even close

[restive river]

i wrote after that: ⅓ y = 4 - 10

Oops

Wait lemme get my calculator

OHHH

-6

[wild grove]

Still wrong

[restive river]

huh

Wait

[wild grove]

You have 1/3 y = 4*x

So where did the minus come from

There is just multiplication

[restive river]

Beacuse i got -10..

Ohh

Wait

So it's 4 * 10 or 4 * (-10) now??

[wild grove]

nope

You found that x = -2.5

This is good

[restive river]

Ye

[wild grove]

Now instead of x, put -2.5 here

[restive river]

wait... is it ⅓ y = -10, i mean i used the 4 to calculate 4 * (-2,5)

[wild grove]

Yes

[restive river]

Ye that is 4 * (-2,5)

Okayyy i see nowww i kept using the 4

[wild grove]

Now find y

[restive river]

Alright

-10 ÷ ⅓ is -30

I got it: D

Tysmmm

[wild grove]

Awesome

Good job

[restive river]

Ty, well then ima close this now

[wild grove]

Bye

[restive river]

Byebyeee :D

.close

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[earnest rivet]

are there other ways of proving that there are no solutions, if this way works? thanks

[cerulean flicker]

lalalala

☠️

[earnest rivet]

what😭

[frosty portal]

You can use fermats las theorem

However that can be a bit overkill

[earnest rivet]

ok il have a look

[modern lance]

is x real? or positive real?

just real right?

[frosty portal]

check this graph out

[earnest rivet]

think so, but if x isn't real would there more solutions?

[earnest rivet]

yh i was trying to also consider a(x) = 5^x and b(x) = 3^x + 4^x, but i kinda had trouble proving that they wouldn't intersect after x = 2, and when x < 0

[frosty portal]

fermats last theorem says that their exist no solutions to the equation
a^n+b^n=c^n (where a,b,c are constants and x>2)

You hav alr found a case for n=2

[haughty hull]

Dividing both sides by 5^x gives u a constant function on the left side and the sum of 2 decreasing function which result to a decreasing on the right, that means there could be only one solution

[frosty portal]

its easy to show n=1,0 is not a solution

[earnest rivet]

sorry do u mean n>2?

[frosty portal]

yes

its like a 2 liner proof , but the theorem is like bringing a tank to a snowball fight

[earnest rivet]

ok ty

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[solar goblet]

not sure about (g)

[solar goblet]

$\exists x \exists y (x \neq y \land F(\text{Nancy}, x) \land F(\text{Nancy}, y))$

[solar goblet]

this is the way i do it, but i wonder if it really means nancy can fool exactly two people

[pseudo basin]

incomplete

[pseudo basin]

it doesn't

your stmt says there are at least two different ppl whom Nancy can fool

[solar goblet]

yeah thought so

what about

$\exists x \exists y \forall z(x \neq y \neq z \land F(\text{Nancy}, x) \land F(\text{Nancy}, y) \land \lnot F(\text{Nancy}, z))$

[solar goblet]

so nancy can fool precisely distinct x and y, but any z other than x and y, nancy can't fool

[drifting sierra]

Assuming you meant x ≠ y and x ≠ z and y ≠ z, that reads as "all people are different from person x and person y", which is not true

[solar goblet]

oh yeah

that's tricky

[drifting sierra]

You can use a quantifier inside the parentheses

[solar goblet]

$\exists x \exists y(x \neq y \land F(\text{Nancy}, x) \land F(\text{Nancy}, y) \land \forall z ((x \neq z \land y \neq z) \rightarrow \lnot F(\text{Nancy}, z)))$

how about this?

[drifting sierra]

That looks better, but x ≠ y ≠ z is kind of ambiguous

[solar goblet]

hm

[drifting sierra]

Yes

[solar goblet]

is it possible to clean this up?

[drifting sierra]

Clean up how?

I don't think you can make it shorter if that's your question

[solar goblet]

yeah that's what i meant

[drifting sierra]

Unless you do something like $\exists^2 x (F(\text{Nancy}, x))$ but that's not standard AFAIK (though you could define that new quantifier)

[woven radish]

Nel

[solar goblet]

mm i see

either way thanks for the help

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[spring oasis]

I need some help with this one

110x + 250y = 100
gcd(110,250) = gcd(110, 30) = gcd(20, 30) = gcd(20, 10) = gcd(0,10) = 10

11x + 25y = 10

gcd(11,25) = gcd(11,3) = gcd(2, 3) = gcd(2,1) = gcd(0,1) = 1

so by bezouts lemma we know 11x + 25y = gcd(11,25) exists and is solvable

so lets find a solution to 11x + 25y = 1

lets use extended euclidean algorithm

25 = 11(2) + 3
11 = 3(3) + 2
3 = 2(1) + 1

so 3 = 25 - 11(2)
and 2 = (11-3(3))
and 1 = 3 - 2(1)

so 1 = [25 - 11(2)] - [11-3(3)]
so 1 = 25 - 11(2) - 11 + 3(3)
so 1 = 25 - 11(2) - 11 + 25- 11(2)
so 1 = 25 - 11(2) - 11 + 25(3) + 11(-6)
so 1 = 25(1+3) + 11(-2-1-6)
so 1 = 25(4) + 11(-9)

11x + 25y = 1 so one solution is (x,y) = (-9,4)

now we multiply this solution by 10 so we get a solution to 11x + 25y = 10

11x + 25y = 10 has one solution (x,y) = (-90, 40)

and since 11(25) + 25(-11) = 0 all of the solutions to 11x + 25y = 10
are (x,y) = (-90 + 25k, 40 - 11k)

[gloomy aurora]

could you please translate? i didnt get it.

[spring oasis]

find all the solutions to _ that satisfy simultaneously _ _

so this is all of the solutions to 11x + 25y = 10
(x,y) = (-90 + 25k, 40 - 11k)

now we need to restrict our solutions such that

37^2 | (x-y)^(4321)

(x-y)^(4321) = 0 (mod 37^2)

this is when it gets nasty

🤔

[gloomy aurora]

so x= y mod 37^2 if im not wrong

[spring oasis]

how

[gloomy aurora]

it can be only

x = y mod 37^2

no

sorry

(x-y)^4321 = 0 mod 37^2

well by logic, for (x-y)^n to be 0 mod 37^2, (x-y)= 0 or 37 mod 37^2

so x = y mod 37^2

it cant be anything else.

[spring oasis]

how do u know dat

[gloomy aurora]

its odd.

the power is odd

[spring oasis]

what about it?

[gloomy aurora]

4321 is odd, so 37^4321 = 37^4320 into 37, = 37 mod 37^2

[spring oasis]

what?

[gloomy aurora]

uhh idk how to explain but 37^4321 leaves a remainder of 37 when divided by 37^2

cuz 37^4320 is divisible by 37^2

[pseudo basin]

does it tho

[gloomy aurora]

yes.

i think so

[pseudo basin]

37^4321 leaves a remainder of 0 when divided by 37^2, does it not.

not 37.

[gloomy aurora]

oh wait

my bad.

[pseudo basin]

like uhh $37^{4321} = 37^2 \cdot 37^{4319}$ and all that

[woven radish]

Ann

[gloomy aurora]

im really sorry. i got a little confused.

so its x=y mod 37^2

or x = y+37 mod 37^2

[spring oasis]

howdo u know

that x = y (mod 37^2)

[woven radish]

Annie Maqionde

[gloomy aurora]

$(x-y)^{4321} = 0 \mod {{37}^2}$

[woven radish]

Annie Maqionde

[gloomy aurora]

so if $(x-y) = A \mod {{37}^2}$

[woven radish]

Annie Maqionde

[gloomy aurora]

then $A^{4321} = {{37}^2}K$ for some natural K

[woven radish]

Annie Maqionde

[gloomy aurora]

so some power of A less than or equal to 4321 must be divisible by 37^2, i.e. by 37.

and if A is not divisible by 37, then no higher power of A can be divisible by 37 also, since 37 is prime

so $A = 0$ or $A = 37$

[woven radish]

Annie Maqionde

[gloomy aurora]

I'm really sorry if i confused you, i accidentally got confused a little bit.

[spring oasis]

the divisibility is transitive relation

37 | 37^2 and 37^2 | (x-y)^(4321)
so 37 | (x-y)^(4321)

[gloomy aurora]

yes.

[spring oasis]

the we can use euclids lemma

[gloomy aurora]

exactly.

[spring oasis]

so since we know 37 | (x-y)^(4321)

yeah so since we know 37 | (x-y)^(4321)
then either 37 | (x-y) or 37 | (x-y)^(4320)
and if 37 | (x-y)^(4320) then either 37 | (x-y) or 37 | (x-y)^(4319)

[gloomy aurora]

exactly.

so on so forth.

x = y mod 37 always.

[spring oasis]

yeah so coming back at this

(x,y) = (-90 + 25k, 40 - 11k)

-90 + 25k = [40 -11k] (mod 37)

-130 = -36k (mod 37)

[gloomy aurora]

i think you made a typo.

[spring oasis]

yes let me correct that

,calc -90 - 40

[woven radish]

Result:

-130

[spring oasis]

,calc -11-25

[woven radish]

Result:

-36

[spring oasis]

so we have

[gloomy aurora]

130 = 36k mod 37

[spring oasis]

-103 + 36k = 0 (mod 37)

[gloomy aurora]

now you can solve for k.

[spring oasis]

-130 = -36k (mod 37)
-130 = 37q - 36k
130 = -37q + 36k
130 = 37m + 36k
130 = 36k (mod 37)

gcd(37,36) = gcd(1,36) = gcd(1,0) = 1

[gloomy aurora]

since 36=37-1
and $36 = -1 \mod {37}$ you can find the inverse easily.

[woven radish]

Annie Maqionde

[spring oasis]

130 = 37m + 36k
using bezouts lemma
1 = 37m + 36k is solvable and it exist
that one solution to 1 = 37m + 36k is (m,n) = (1,-1)

[gloomy aurora]

just multiply the congruence by 36.

since ${{36}^2} = 1 \mod {37}$

[woven radish]

Annie Maqionde

[spring oasis]

130 = 37(130) + 36(-130)

,w 130 = 37(130) + 36(-130)

[woven radish]

Results provided by WolframAlpha

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

Requested by renatoxbz

[spring oasis]

130 = 36k (mod 37)
130 = 36(-130) + 37(130)
k = -130 (mod 37)

k = 18 (mod 37)

k = 37m + 18

(x,y) = (-90 + 25k, 40 - 11k)

(x,y) = (-90 + 25(37m+18), 40 - 11(37m + 18))

(x,y) = (-90 + 925m+450, 40 - 407m - 198)

(x,y) = (360 + 925m, - 407m - 158)

[spring oasis]

I appreciate the help

all this exercises are fascinating

.solved

[devout snow]

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[devout snow]

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[swift falcon]

im trying to solve 2c

[swift falcon]

this is a nightmare i hate integration

why does it have to be so difficult

we hav eto use substitution here

[dense jay]

indeed you do
Its easier if you rewrite it as 4sec^2(4+2x)

[swift falcon]

nah idk any of that secant stuff

i need to use substitution unfortuantely

[dense jay]

Its just a fairly recognisable derivative of a certain function

sec^2(x) I mean

you will have to do a sub regardless

[swift falcon]

yeah no srry i can't do sec yet

haven't learn that

we gotta work without sec

[cold haven]

sec(𝑥) = 1/cos(𝑥)

what AZ0 said, it’s probably better to work with it in this form.

[swift falcon]

yeah but i have never studied that stuff before

i hvae no idea what that is

[cold haven]

it’s just another trig function, like tangent, or cosine.

[hollow jolt]

Derivative of tanx is sec^2x

Just 1/cos^2x

[swift falcon]

.close

[devout snow]

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Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[fallen tartan]

Don’t abruptly lock

Over some hacker

[devout snow]

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[ionic heron]

hi

[versed juniper]

ask your question

[ionic heron]

I

[short hare]

it can be expressed as 20% of 50, hope this helps ❤️

is this a genuine question

سنه كام؟

do you actually need help with this? how old are you?

[ionic heron]

Yes im 13

[short hare]

ok thats fine then

[ionic heron]

why

[mystic scarab]

!xyproblem

[devout snow]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[ionic heron]

I said what is 50% OF 20

[short hare]

what is half of 20

[ionic heron]

5

[short hare]

crazy.

im out

[ionic heron]

?

[short hare]

or maybe you're genuinely trying to learn

omgim being gaslighted

[mystic scarab]

Half means divided by 2, you know?

[ionic heron]

oh its 10

[mystic scarab]

Yep

[short hare]

im so sorry 😭 i thought you were trolling

[ionic heron]

Il let it slide for now

[short hare]

so yeah! 50% of something is the same as "that something divided by 2"

[ionic heron]

can i also write it as uh wait

[short hare]

like if you have a piece of bread, and you cut it into two pieces, and you eat one, you ate 50% of your bread

[ionic heron]

0.5x20?

[short hare]

yes! very well

we can also express precentages as fractions

are you familiar with it

"fractions'

[ionic heron]

ye

[short hare]

wait no ignore that

ok lets redo the problem

50% of 20

that 50% can be expressed as a fraction

do yk how to?

turn the 50% into a fraction

[ionic heron]

uh i think 50 over 20 or 5 over 2

[short hare]

well no, i didnt mean that!

50% is the same as 1/2 is the same as 0.5
so...
50% of 20 is the same as 1/2 x 20 is the same as 0.5 x 20

which is 10!

[ionic heron]

what grade level is this

[short hare]

im assuming yours

do you have any more problems

[ionic heron]

im in 8th bru

[short hare]

that is 8th grade math! would you like me to create more problems for you

[ionic heron]

say wallah ur actually serious

[short hare]

boy it is 😭 wallahi

if it sounds hard just point what you dont understand

ill re-explain

[ionic heron]

they say its 6 grade

[short hare]

well perhaps my 8th grade is different but! ifyou needed to compute 50% of 20 then you probably need to know that type of information

again, would you like me to produce more exercises

[ionic heron]

yeah give me another problem

[short hare]

what is 70% of 100

[ionic heron]

0.7x100 so lets solve

uh

i think

[mystic scarab]

Awesome

That's correct 👍

[ionic heron]

i think its 70

[mystic scarab]

Yep perfect

[short hare]

yes

very well

good job

[ionic heron]

YEAHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

[short hare]

well- am i supposed to assume that you knowfractions? like 20% of 45 for example

that cant just be done with 0.2 x 45... atleast not with a calculato0r

[ionic heron]

i dont know fractions with this

[short hare]

oh fuck

[ionic heron]

bro

[mystic scarab]

What part of 100 is 20?

[short hare]

it can

[ionic heron]

4

[mystic scarab]

Mmhh

It's a fifth

Do you agree?

[ionic heron]

OH YEAH

5

[mystic scarab]

Because 20•5 = 100

[fierce viper]

@ionic heron it may help you think about the percentage sign % as basically dividing by 100

[mystic scarab]

So this means that 20% of 45 will be 45 divided by 5

[ionic heron]

ok

[fierce viper]

just to set the record straight:
$$1% = 1 \div 100 = \frac{1}{100} = 0.01$$

[ionic heron]

wait why is there two helpers

[short hare]

@ionic heron do you get this?

[ionic heron]

yeah

[short hare]

so... what is 20% of 45 is like saying 45/5

what is 45 divided by 5

[ionic heron]

wait

[short hare]

what is 20% of 20

go ahead

[ionic heron]

THE ANSWER IS 4

[short hare]

YEAAAAAAH

20% OF 20 IS 20/5

WHICH IS 4

[fierce viper]

What is 20% of 30% of 150?

[ionic heron]

yo get your ass out

[short hare]

?

[ionic heron]

is he the third teacher?

[short hare]

that's very rude

[short hare]

they are someone that did nothing for you to say "get your ass out"

they proposed a challenge which you can try

you could've just said "no, ty"

[ionic heron]

You influenced me to say bad things.

I think you see me as im at my grade level and i learn things fast

[short hare]

me?????

[short hare]

well the question that 'third teacher' proposed is not out of your reach, just needs a little bit of thinking

would you like to try

[ionic heron]

wait

[ionic heron]

ima solve urs

so how do i solve this?

is the answer 25?

[short hare]

so do yk that % is like multiplication... yk how 50% of something is 0.5 multiplied by that smth? do you know that multiplication is associative? a x b = b x a

3 x 2 = 2 x 3

5 x 6 = 6 x 5

[ionic heron]

im bouta name myself that

[short hare]

distrubutive property?

[ionic heron]

oh wait i do get what ur saying

[short hare]

so im just trying to get to the point of

30% of 20% of 150 is the same as 20% of 30% of 150

so we can split the problem to make it easier

so we said that 20% is like dividing by 5

so we can compute 20% of 150

what is 20% of 150

or in otherwords, 150/5

[ionic heron]

What does compute mean

[short hare]

ah just- you can ignore it

find 20% of 150

[ionic heron]

oh i get it

[short hare]

yeah!

[ionic heron]

what if i dont still get it

[short hare]

do you get that 20% of something is that something divided by 5

like 20% of 100 is 100/5 = 20

[ionic heron]

yes

[short hare]

ok! what is 20% of 150 or in other words 150/5

hint; think of "5 * what = 15"

[ionic heron]

30

[short hare]

yes i-

did you just change your name to car

okay

yes okay its 30

[ionic heron]

ur undergraduate

ya dood

[short hare]

so the question was 30% of 20% of 150
we turned it into 30% of 30

[short hare]

im actually in hs

[ionic heron]

grade?

[short hare]

senior

anyways

can you try to find
30% of 30

[short hare]

you can use a tip of that 'third teacher" you were very rude to earlier,

30% can be thought of as 30/100 or 3/10,

[ionic heron]

alr

[short hare]

ohwait... hmm

[ionic heron]

I GET IT no more

[short hare]

we can actually redo this to make this easier

30% of 20% of 150 was the main problem

instead of doing 20% of 150 first

lets turn it into
20% of 30% of 150

what is 30% of 150

[ionic heron]

is it like 3 or 10

[short hare]

no thats pretty far

[ionic heron]

45

[short hare]

there you goooo

now

[ionic heron]

Please stop yapping

[short hare]

20% of 45

[ionic heron]

ITS 9 OKAY

so what other subjects u like?

[short hare]

nah i stopped yapping lil bro

close the channel

.close

[ionic heron]

ok freshman

[devout snow]

@ionic heron Has your question been resolved?

[devout snow]

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[worldly tapir]

Whats the answer

to this

because im confused what the 2 is doing in g(2x)

[wicked turtle]

try plugging in a few values for x?

[worldly tapir]

im so confused since

isnt g(x) = y

and then what is g(2x)

[wicked turtle]

g(x) is the function plotted in the top graph

g(2x) is a different function obtained from g(x) by changing the "scale" of the x axis

plug in a few values for x and see what you get

for example, if x = 0, what is g(2x)?

[worldly tapir]

y = 0?

[wicked turtle]

ok

does that allow you to rule out any of the options?

[worldly tapir]

yea wait is it a)

cause

if u do it like how your saying

it should be a right

[wicked turtle]

it is a, can you say how you determined that?

[worldly tapir]

subbed in 1

and

y = 2

so yk

[wicked turtle]

wdym by y=2?

if you set x=1, then what is g(2x)?

it's not 2

[worldly tapir]

wait how

2 times 1 is 2

[wicked turtle]

sure

so g(2)

what is g(2)?

[worldly tapir]

thats where i got lost on

[wicked turtle]

look at the top graph

what is the y value when x=2?

[worldly tapir]

2

[wicked turtle]

no

[worldly tapir]

its 3

right

[wicked turtle]

i think it's meant to be 4, but it's hard to tell without putting it on graph paper

but anyway yea, somewhere around 3 or 4

[worldly tapir]

yea

[wicked turtle]

ok so when you set x=1, you got g(2x) = around 3 or 4

and you found that graph (a) has that property

[worldly tapir]

wait what

[wicked turtle]

you said your answer was (a)

how did you deduce that?

[worldly tapir]

yea because i subbed in x =2

[wicked turtle]

i'm concerned that your reasoning was erroneous

[worldly tapir]

and it got me 4

[wicked turtle]

subbed in x=2 into what

[worldly tapir]

g(4)

[wicked turtle]

and what got you 4?

[worldly tapir]

g(2x)

[wicked turtle]

ok and what is g(4)?

[worldly tapir]

when x = 4 OF THE ORIGINAL GRAPH?

[wicked turtle]

yes, the original graph is g(x) vs x

so in that graph, if you put x=4, the y value is g(4)

[worldly tapir]

I HAVE TO EAT RN BUT can i pign u later if i have issues with this

[worldly tapir]

Yeppp

[wicked turtle]

no i probably won't be around either, but you can just open a new channel and someone will help

[devout snow]

@worldly tapir Has your question been resolved?

[devout snow]

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[copper flax]

Integral of 1/(x^3-6x^2+11x-6)

[copper flax]

i watn here the day we did ints and im very

confused

wasnt

im lowkey failing rn

.close

[devout snow]

Channel closed

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[cold haven]

why’d you close?

[marble sage]

hey

.reopen

do u know how to solve this

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[soft umbra]

How do I convert this?

[soft umbra]

This is what the answer key says but apparently I'm missing some information

nvm, Ik what it's doing now

.close

[devout snow]

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[errant tapir]

I don’t know where to find more practice problems like these

[errant tapir]

These questions are from my geometry review from school

but I need more practice problems

please I don’t know where to find problems like these

[urban pivot]

check dms

[devout snow]

@errant tapir Has your question been resolved?

[errant tapir]

sry brother I think that resource u sent is a different topic

[urban pivot]

unfortunate, thats all i can come up with atm

[errant tapir]

all good

ty though

[devout snow]

@errant tapir Has your question been resolved?

[devout snow]

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[orchid umbra]

did i take the wrong approach or what

[orchid umbra]

smth is not right I think W my partial fraction

[wicked turtle]

right general approach but your A and B are wrong

[orchid umbra]

what did i do wrong

is it some arithmetic error

i just used heaviside's method

[wicked turtle]

you seem to have plugged in x = -2 instead of 2

[errant harbor]

Where did this -2 come from

There are more than 1 mistake

[orchid umbra]

because x cannot be -4 and 4

[errant harbor]

X cannot be -2 and 4

Not -4 and 4

[orchid umbra]

i meant to put -2

and i did plug in -2

[errant harbor]

But that's not possible, because x cannot be -2

[orchid umbra]

exactly

thats heaviside's method

?

[wicked turtle]

it's actually ok to plug in those values since the equation holds for all x besides -2 and 4 and both sides can be extended continuously to include those points in the domain

[orchid umbra]

riht

[wicked turtle]

so i think the unintentional inclusion of -2 in the term Matcha highlighted is the issue here

fix that and tell us what you get

[orchid umbra]

i dont get it

im just

[errant harbor]

Oh yep that's correct mb

[orchid umbra]

doing heavisides method thoooo

[orchid umbra]

Np

ok ya im so confused

idk why my a and b values are woing

wrong

[errant harbor]

The problem is the (-2) here

[orchid umbra]

OHHHHHHHHHHHHHH

sorryu

lmaooo

my badf

uhh

why is it still not right

tho

[wicked turtle]

you didn't change the coefficients?

-10/6 and 46/6 are wrong

[orchid umbra]

huh

ok im so confused

why did a 3 just spawn

and why did it become 6x+22

wtf

[errant harbor]

Polynomial long division

[orchid umbra]

😭

what

oh

ohhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

ok no wonder why my partial fraction inst workng

lol

ty

[devout snow]

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[glad sigil]

Hey, i would like a hint on this one

[glad sigil]

They ask me to solve it by induction and prove that its true for every n which is natural

[misty crest]

what’s the issue then?

have you made it to the induction step

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[blazing bolt]

26th

[blazing bolt]

,rccw

[devout snow]

@blazing bolt Has your question been resolved?

[pure stone]

hmm

[blazing bolt]

Sigma tanx
Is product tanx

[pure stone]

let (tan x)/2 = (tan y)/3 = (tan z)/5 = k

tan z is basically -tan(x+y)

[blazing bolt]

Yea

[pure stone]

replace tan x with 2k and tan y with 3k

what do you get

[blazing bolt]

Tanz= 5k/(6k^2 - 1)

[pure stone]

seems incorrect

alright you got it

now tan z/5 is just k so you can go solve for k

[blazing bolt]

k=1/√3

[pure stone]

,w k/(6k^2 - 1) = k

[woven radish]

Results provided by WolframAlpha

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Requested by dec2rbonized

[pure stone]

and there you have it, you can calculate what tan x, tan y and tan z equals to

[blazing bolt]

The very final Answer is 3

[blazing bolt]

Am I right

[pure stone]

yep correct answer

[blazing bolt]

Ty

.close

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[humble siren]

Prove that the expression equals 1/2 when n is odd

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[thorny lintel]

i need help with the 5 number summary & finding the range and IQR? my teacher hasn't explained how to work that out/hasn't talked about this before and i'm just really confused

[crystal dawn]

the five-number summary is basically the minimum, 1st/lower quartile, median, 3rd/upper quartile, and the maximum

the range is then max - min, and IQR is upper - lower quartile

have you heard of these terms?

[thorny lintel]

i havent heard of quartile but i have heard of median

[crystal dawn]

ok nice, we can develop the idea of a quartile from there

suppose you now have the median of the set of data

the data is thus partitioned into two subsets - one containing elements under the median, and one containing those over

the median of the first subset is the lower quartile, and the median of the second subset is the upper quartile

does this info help?

<@&268886789983436800>

oh oops

[thorny lintel]

yes thank you

[crystal dawn]

nps

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[verbal knot]

this doesnt seem right where did i go wrong

[tall linden]

12 * 7 = 74?

[verbal knot]

ah shit

[tall linden]

Also, you're actually using a generalized mathematical induction, not mathematical induction. So, your proof would still be incorrect.

[verbal knot]

whats a generalised mathematical induction

i thought there was only 1 mathematical induction 🥹

[thick ledge]

<@&268886789983436800>

[copper harbor]

@sullen sleet don't shit post in help channels

[upper schooner]

(also how did you get that 24^k as well(?) )

[devout snow]

@verbal knot Has your question been resolved?

[verbal knot]

ah shi \

iu give up

.close

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[real helm]

Chat why is 2^0=1
And 0!=1

[harsh sierra]

You could think about both of them as an empty product, which makes sense to be the multiplicitive identity (which is 1)

[real helm]

What do you mean by an empty product?

[fossil locust]

see if you can follow this argument:

4! = 4 * 3 * 2 * 1 = 4 * 3!
3! = 3 * 2 * 1 = 3 * 2!
2! = 2 * 1 = 2 * 1!
1! = ... = 1 * ?

[harsh sierra]

Product of 0 things

[real helm]

Shouldn't that be 0

[quaint fox]

Can any body help me?

[cold haven]

I like to think there’s a multiplication by 1 that you cannot see in exponents

||1 ×|| 2 × 2 = 2²
||1 ×|| 2 = 2¹
||1|| = 2⁰

Although that’s probably not valid.

[fossil locust]

!help

[devout snow]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[devout snow]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[harsh sierra]

Please delete this and claim your own channel

[real helm]

Uhh,1×1!,maybe?

[pale lily]

zero factorial is one because the argument for factorial is asking "how many ways can i aragne x amount of things?"

[fossil locust]

well, the pattern is 4 * 3!, 3 * 2!, 2 * 1!

[pale lily]

so 0! is one because there is only one way you can arange no things

[real helm]

Wait,so 1×0!?

[fossil locust]

yep!

1 = 1 * 0!

[pale lily]

yeah and thats the math logic behind

[real helm]

That brings us to my question

Why is 0! 1

[cold haven]

Axis answered it.

[pale lily]

and as for exponents the reason anything raised to the power of zero is one, is because it preserves (a^n)*(a^m) = a^(n+m)

[fossil locust]

the factorial is properly defined in terms of the Gamma function $(n! = \Gamma(n + 1))$

[woven radish]

south

[real helm]

Theoretically,that makes sense

[cold haven]

Factorials ask “how many aways can you arrange 𝑛 things?”

You can only arrange 0 things, 1 way, with nothing.

[fossil locust]

and also $\Gamma(n+1) = n \Gamma(n)$ by definition

[woven radish]

south

[fossil locust]

well if you are using the integral definition, it becomes an exercise to show that

[real helm]

My bad but I don't know about any of this

[fossil locust]

I think this is the easiest way to understand 0!

[cold haven]

there’s probably a better proof but that’s how I always understood it

[real helm]

What if we have only one exponential term?Not necessary we would always have two

[fossil locust]

it's not impossible to arrange 0 things

[real helm]

Why is it the assumption that nothing is also a way to arrange things?

[pale lily]

heres a little example of the exponent thing

[real helm]

Ohh

That make sense

[pale lily]

it preserves that property which is one of the most important of expnentials

[real helm]

I get it now

[pale lily]

its good to ask questions, ive asked ones like these plenty of times

it builds understanding

[real helm]

What about this?

[devout snow]

@real helm Has your question been resolved?

[real helm]

.close

[devout snow]

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[pulsar trellis]

Kinematic 2D Motion, confused with implementing the formulas

[proud sparrow]

could you give me an example in where you are confused

so many physics questions tday

[pulsar trellis]

This one is solved, but I cant seem to understand how to do the formulas

[viscid wagon]

you just plug in the values