help-0

[thick lynx]

Find the angle TXA/alpha

Now in the solution, they say "Let TA be x, then TXA = 360° - x"

But I don't understand how they can subtract a length from an angle

[alpine sable]

I think they mean the measure of major arc TA

[thick lynx]

But after that they say "TXA = 360° - x"

So if x is the major arc, how can they subtract it from 360 degrees?

[vale wigeon]

that is a strangely worded solution for sure

[gray isle]

can you show exactly what they said

preferably in image

[thick lynx]

one sec

[gray isle]

the arc above those letters indicates "arc measure"

[thick lynx]

Subtracting an arc measure (that is let's say in cm) from an angle

[gray isle]

arc(TA) refers to the measure of the red arc

[thick lynx]

yes

[gray isle]

arc(TXA) refers to the measure of the measure of the blue arc

[thick lynx]

now x is the red

[gray isle]

both arcs form the full circle

and the measures will sum to 360°

[thick lynx]

but let's say red is 5cm, blue is 4cm, how do they sum up to 360°?

[gray isle]

arc measure,

not arc length

[thick lynx]

oh

[alpine sable]

They subtract it from the total measure of the circle

[gray isle]

arc measure
equivalent to the central angle the arc subtends

[thick lynx]

Denotes arc measure

what denotes arc length?

[alpine sable]

sometimes I see it as m(TA) with the curve on TA to denote arc measure

[thick lynx]

arc(TA) refers to $\alpha$, right?

[ocean seal]

Kepe

[gray isle]

no

[thick lynx]

but

that's a sector

[gray isle]

arc measure
equivalent to the central angle the arc subtends

alpha isn't a central angle

[thick lynx]

oh

so this

[gray isle]

yeh

i think that notation technically refers to the arc itself (neither measure nor length) but measure was implied based on what they were doing

[thick lynx]

alr, thank you

[gray isle]

usually an m would be included

[thick lynx]

.close

[lone heart]

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[glacial spear]

Hello I am practicing project Euler i am stuck with a problem

[karmic rapids]

don't ask to ask

[glacial spear]

def toreverse(n):
rev = 0
while n > 0:
rev = 10 * rev + n % 10
n = n//10
return rev

lep = []
for i in range(100,999):
for j in range(100,999):
if toreverse(ij) == ij:
lep.append(i*j)
print(lep[-3])

Over above are the question and solution(atleast a try)

I output of the answer suppose to be last item if the array

But it chooses -3 place of array

Can anyone help

[alpine sable]

print(lep[-1])

?

[glacial spear]

This code is a solution

The correct is held up in -3

I found out when I listed the all the elements

[alpine sable]

I see

[glacial spear]

Of the array

[alpine sable]

one sec

fix your code

so I can read it better

do ```

followed by the word python

then another ```

under the code

@glacial spear

[glacial spear]

Give me a min

[hushed mica]

def toreverse(n):
    rev = 0
    while n > 0:
        rev = 10 * rev + n % 10 
        n = n//10
    return rev

lep = []
for i in range(100,999):
    for j in range(100,999):
        if toreverse(ij) == ij:
            lep.append(i*j)
print(lep[-3])

[alpine sable]

3rd line from the end

is wrong

what does to reverse even do

oh

such a convoluted solution

just make a function that check if it's a palindrome

and starts going down

can you elaborate on your solution

and you don't need nested for loops

@glacial spear

you do but not like what you wrote

[alpine sable]

oh

you have redundant data

try this

for k in range(999,100):
    for j in range (k,999):
        if(toreverse(i*j) =(i*j):
            print(i*j)
            break

this is way easier

[glacial spear]

I will try

.close

[lone heart]

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[native nebula]

Help

[native nebula]

I am not able to prove the anticipated

But the one i have done is correct or not?

[tall hearth]

it is

but as you can see, its hard to proceed

the easiest way here is to simplify RHS

tan(65) = tan(20 + 45)

expand it and express in terms of sin and cos and you'll get LHS

[tall hearth]

40 = 30 + 10
you can get trig ratios for 10 with some sub-multiple angle formula but it'll be way too tedious

[native nebula]

What will I be doing with the 20°s?

[tall hearth]

.

[native nebula]

Will they get cancelled away?

[tall hearth]

idk what you mean

yeah there will be some cancelling out I suppose

[native nebula]

Hey if i do componendo and dividendo?

[tall hearth]

how exactly?

[native nebula]

Showing

[tall hearth]

I have no idea what you've done

but it's dead wrong

[native nebula]

How bruv?

[tall hearth]

you explain what you did?

how did you apply componendo-dividendo?

[native nebula]

Ohh yeah

Man i have done wrong

I am doing the one you told

But i have a question

[tall hearth]

yeah?

[native nebula]

I should use the LHS to prove the RHS, it's okay if i do otherwise, but is that a good practice?

[tall hearth]

yeah it's ok

[native nebula]

Ah cool

Thanx

.close

[lone heart]

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[gaunt peak]

Difference between countable and finite?

[noble sinew]

A countable set is either a finite set or countably infinite set

[lone heart]

@gaunt peak Has your question been resolved?

[gaunt peak]

Yea thats what I found online, but what does that mean

I get countable infinities, with huberts infintite hotel or whatever the name was

But still kind of counfueses me

Does uncountable then mean, that there is no relation that could relate a countable set into the uncountable?

[true pulsar]

Yeah they're not equivalent, like the set of all reals is uncountable
https://en.wikipedia.org/wiki/Cantor's_theorem

[gaunt peak]

Right, and whole numbers are countable, because of the diagonal proof (idk what the name was, where you take a real number between 0 and 1 and fit each of those in between?

[gaunt peak]

Ill give this a read

Thanks

[noble sinew]

A set A is uncountable if no injective function from A to N

[gaunt peak]

so every finite set is countable

[true pulsar]

https://en.wikipedia.org/wiki/Cantor's_diagonal_argument the diagonalization argument shows that the reals are uncountable

[gaunt peak]

Right, we would use a function, because relations could relate multiple originals to however many images

[true pulsar]

Yes

[gaunt peak]

So to conclude, countability is just a properity of a set, infinite or finite.

[true pulsar]

Yeah basically

[gaunt peak]

A question on a test was : "There is number of algorithms: countable, uncountable, continuous, finite"

Thats what sparked my interest in the difference

And Im guessing its related to the halting problem, which I am not familiar enough with to know whether its a countable or finite set

[true pulsar]

Same

[lone heart]

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[gaunt peak]

Thank you for the help everyone

.close

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[keen python]

any ideas

[keen python]

what I did wrong here

[worn fox]

What's the original function?

Second line of f'''(x), you have e^x*e^x

And you pull out an e^x

What's missing

[keen python]

first and 2nd deritive are correct

[worn fox]

It's what I said then

You pulled out an e^x in the third line but there should be one left over in the second term

[keen python]

agggh god

i thought

e^x * e^x = 2*e^x LOL

so stupid

na

still not correct

i think i didnt deriviate correctly

[worn fox]

What did you now arrive at?

[keen python]

this line is already wrong

[worn fox]

Why do you think its wrong

[lone heart]

@keen python Has your question been resolved?

[lone heart]

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[alpine sable]

All I know if I square both sides to get 4R=2k^5

[languid bolt]

what?

[vale wigeon]

no, that's not what you get when you square both sides

as i said last time

[alpine sable]

What the

the last helped

helper

said thats what u get

and then he just dipped

[vale wigeon]

do you have screenshots

[alpine sable]

no

[vale wigeon]

$(4\sqrt{2R})^2 = 4^2 \cdot (\sqrt{2R})^2 = 16 \cdot 2R = 32R$

[ocean seal]

Ann

[alpine sable]

okay so 32r

equals

[native cloud]

32R = (2K)^(5)

[alpine sable]

4k^5?

[vale wigeon]

you are both wrong

the right-hand side is (2K)^5

or 32K^5

[native cloud]

Sorry for the misleading notation

[alpine sable]

so 32r

equals

4k^5?

[native cloud]

Where did that come from

[native cloud]

Read

[alpine sable]

(2k)^5/2 squared is 4k^5

wait nvm

[native cloud]

How

[alpine sable]

nvm

i understand now

what do i do after?

[native cloud]

?

You're telling me you can't compute (32R = (2K)^(5))?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[dawn quail]

If c is a zero of f, then c is a/an ___________________ of the graph of f.

[dawn quail]

Would you answer this "root" or "intercept"?

Or would both be acceptable answers?

[languid bolt]

should be intercept

[nocturne dove]

root

[dawn quail]

lol

[languid bolt]

doesnt say whether c is x or y

[nocturne dove]

If f(c) =0

[dawn quail]

right

[languid bolt]

root is for x intercept no?

[nocturne dove]

Is it a function of x or y?

Depends. Yea

[dawn quail]

it doesnt say

[languid bolt]

exactly

[tender dew]

both are correct

[dawn quail]

hmmm

If c is a zero of f, then (x - c) is a factor of ___________________?

[tender dew]

f

[dawn quail]

these feel like trick questions

[gray isle]

no they're not trick questions, they're just definitions/theorems

[tender dew]

for previous should be intercept

[dawn quail]

you would answer this one "f"?

[tender dew]

since root is.not part of a GRAPH

yeah

[languid bolt]

what do you mean

not part of a graph?

[dawn quail]

this is the correct answer

[tender dew]

intercept is graphical term

[languid bolt]

root is also a graphical term tho

isnt it?

[tender dew]

root is algebraic

[nocturne dove]

Correct.

[tender dew]

I'd say

[dawn quail]

we dont know if f is x or y

[nocturne dove]

I think it should say zero not root.

[dawn quail]

lol

[nocturne dove]

But who knows

[tender dew]

f is y

[languid bolt]

?

[dawn quail]

If c is a zero of f, then c is a "zero" of the graph of f.

that just repeats the question

[tender dew]

independant variable

if you prefer

[languid bolt]

btw why is root not a graphical term?

it's literally a point on a graph

[tender dew]

if f(c) = 0 then f(x)mod(x-c) = 0

[dawn quail]

this is why I feel they are trick questions, for how they can be interpreted

see discussion above

[languid bolt]

there is no discussion, the answer is intercept, everyone is agreeing on it

[dawn quail]

what about this one?
" If c is a zero of f, then (x - c) is a factor of ___________________?"

[tender dew]

f(x)

[dawn quail]

wrong. "the original polynomial" is the correct answer

i'm worried i would get these wrong for how I word them

[tender dew]

it's the same

just more... cancerous

[dawn quail]

but it's not described with the same wording

it's like saying root or zero both are the same but different ways of wording

i hope teacher will be forgiving

[tender dew]

if not, demand your score to be fixed

[dawn quail]

yeah

i will need to be diligent with this, interpretations can be different but if they lead to the same answer it should be considered correct

.close

[lone heart]

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[uneven pond]

Could i receive help for a topic involving Discrete Mathematics called "Predicate Logic", i understand the basics of the topic but I find myself getting stuck on some questions, need help for some things to be clarified and getting rid of confusion.

[pliant sun]

yep, ask away

[uneven pond]

elements of the following sets:```

{ y - x | x ∈ P ∧ y ∈ Q ∧ (x < 3 ⇒ y < 3) }

i understand that x is going to contain all the elements of set P and y is going to contain all of elements from set Q

[pliant sun]

right yep

[uneven pond]

but the constraint doesnt make sense to me

[pliant sun]

so in this case, the set is asking for all possible values of y - x where $x\in{P} and y\in{Q}$

[uneven pond]

x < 3 implies that y < 3, this part confused me a lot

[ocean seal]

ethan

[pliant sun]

oh wait

I didn't see the implication symbol hold on

[pliant sun]

so this means that if the chosen value of x is less than 3, then the corresponding y value must also be less than 3

[uneven pond]

so is it going to correspond to a boolean output?

or is it a constraint

[pliant sun]

it's a constraint

the set is all numbers "y - x"

[uneven pond]

how would this entire calculation work step-by-step?

cause thinking in steps helps me understand

[pliant sun]

hmm what I'd do is start with x values

if x=1, then the possible values of y are 1 and 2

then repeat with x=2,3,4

and perform the calculation y - x for each pair of values

so what you can do is write every possible pair from P and Q

and then perform the calculation

[uneven pond]

the thing im still confused on is i dont understand how u know what elements to remove from the set with "if x<3 then y < 3"

would it not be x = {1,2} y = { ∅ }

as these elements less than 3

[lone heart]

@uneven pond Has your question been resolved?

[unreal crow]

Sorry I didn't mean to ignore you. I thought I had already given all the information needed for the problem.

Sorry I forgot to mention that it was the first two terms of the taylor series of the sine function, sorry about that.

[uneven pond]

.close

[lone heart]

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[lone heart]

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[nocturne wolf]

I need help expanding an equation

[nocturne wolf]

(2y-3x)^4

i tried step by step to expand it and ended up with a wild amount of different answers none of which were right, kind of hard to explain.

Anyways, I thought i would rewrite the equation as (2y-3x)(2y-3x)(2y-3x)(2y-3x)

[vernal thunder]

That’s how you should write it

[nocturne wolf]

then i began foiling each bracket

[wary stream]

Binominal expansion, if you know that

Pascal's triangle

[nocturne wolf]

so

for the question im answering, it says to use pascals triangle

but i am trying to do it without that

[wary stream]

I don't suggest that

[nocturne wolf]

so I can understand how pascal's triangle helps

[wary stream]

If it suggests Pascal's triangle, use it because it's a shortcut

[nocturne wolf]

no i get that

[wary stream]

Instead of doing this (2y-3x)(2y-3x)(2y-3x)(2y-3x)

[nocturne wolf]

but im trying to understand how to do it without pascal's triangle so that I can develop that skill just because

[wary stream]

Because if you did that by hand, you'll maybe make lots of mistakes

[nocturne wolf]

well im trying to make sure i don't make mistakes, and I don't know where I keep going wrong

[wary stream]

What if you have (2y-3x)^10? Would you do that by hand too?

[nocturne wolf]

well it is possible to do it

and I'd like to learn how to properly do it

[wary stream]

It's possible but you would spend too much time doing it

[nocturne wolf]

i understand that

but I am willing to try it anywyas, because one of my classmates did

and I am trying to follow along but they are smart and skipped a lot of steps

and I am trying to figure it out on my own and I am not succeeding

[wary stream]

Maybe because they used Pascal's triangle?

[nocturne wolf]

they didn't

at first anyways

look I am just trying to find help/knowledge on how to properly expand things by hand without making mistakes

so if you could help/point me in the right direction aside from pascal's triangle I'd appreciate it, since avoiding it is the purpose of this challenge

[wary stream]

Anything higher than power 4, is tedious to do by hand, and if you are in a test, you would spend probably half the time expanding it

My suggestion, is no, don't do it by hand. But if you are, it's distribution

[nocturne wolf]

why is distribution not working then

like

[wary stream]

Because you're messing up math

[nocturne wolf]

ill do 2y-3x(2y-3x) for the first set of brackets

then i take the result from that and continue on forward

because i multiply in the order it comes

[wary stream]

If you are do it by hand, you are going to make more mistakes than using the shortcut

[nocturne wolf]

how do i know when it's a mistake if it is normally the right thing to do

maybe ill write down a couple steps

[wary stream]

The reason why the problem says to use Pascal's triangle, is to minimize the mistakes you make and not waste your time

[nocturne wolf]

i know

[wary stream]

Algebra

Like failing to multiply properly

[nocturne wolf]

but im trying to understand how to do it without pascal's triangle anyways

[wary stream]

You can understand it with smaller powers

[nocturne wolf]

let me write out a step

[wary stream]

As mentioned, bigger powers = more mistakes = more time wasted

[wary stream]

So you are going to spend, maybe 10 - 15 minutes expanding. If you make a mistake, then add on another 10 - 15 because you're going to relook at everything to see where went wrong. But using Pascal's triangle, if you did it properly, 5 minutes max

[nocturne wolf]

does that first step make sense

[wary stream]

That's how distribution works

[nocturne wolf]

ok, so am i good to do the second step now?

[wary stream]

Sure

[nocturne wolf]

ok

[wary stream]

Just don't make any mistakes

[nocturne wolf]

ill try not to

[wary stream]

And then if you do, you'll see that doing this by hand is pointless

And Pascal's triangle is better

[nocturne wolf]

nvm scribbled, i ran out of space

does that make sense?

[wary stream]

Oh that too, you'll run out of space if you do it by hand

[nocturne wolf]

but did i do that right

[wary stream]

You can simplify, I believe

[nocturne wolf]

so i have -12y^2x -24y^2x

does that become -36y^4x^1

or do i not add the exponents

multiply exponents

[wary stream]

No

[nocturne wolf]

i don't?

[wary stream]

You don't

Exponents stay the same

[nocturne wolf]

aren't you supposed to multiply exponents when adding/subtraction bases?

[wary stream]

Nope

[nocturne wolf]

why is that

[wary stream]

Because you're think of multiplying two values

That's when you add/subtract exponents

Like 2x + 3x, is that 5x or 5x^2?

[nocturne wolf]

i

idfk

5x

but like

if it was 2x^3 + 3x^3

what would it be then

5x^3?

[wary stream]

Yes

[nocturne wolf]

what if is a^2 x a^4

is it a^6?

[wary stream]

Because adding/subtracting values with the same base, the base stays the same

[wary stream]

Yes

[wary stream]

Because that's multiplying

[wary stream]

#❓how-to-get-help

[nocturne wolf]

what if it was a^3 + a^2

[wary stream]

Bases aren't the same

So no

[nocturne wolf]

what

[regal moat]

Can someone plz help me on this problem the 2nd problem

[nocturne wolf]

how are they not the same

pari stop hogging my channel

[wary stream]

a^3 and a^2

Different powers

[nocturne wolf]

the exponents are differet

but

the base is 1a no?

[wary stream]

No

The base is normally the variable and power

[nocturne wolf]

how is it the variable and the power

[wary stream]

So because you have different powers, the base is different

[nocturne wolf]

how is it not just the variable

[wary stream]

Because it's like adding cats and dogs, the exponents are different hence different values

[nocturne wolf]

i dont understand that analogy

because i see it like adding cats and cats, except a different number of cats

[wary stream]

If you see it like that, then it's two different types of cats

Not different numbers

[nocturne wolf]

how is it diffirent types of cats

like if i have only tabby cats

[wary stream]

a^2 is one type, a^3 is a different type

[nocturne wolf]

and i have two groups of tabby cats

im not following

[wary stream]

For you to add like terms, the base needs to be the same. For a base to be the same, you must have the same variable and the same exponent

[nocturne wolf]

what is a base then

i thought a base was just the variable and its coefficient

not also the exponent

[wary stream]

So a^2 and a^3 so have the same variable but not the same power so you can not add them

[nocturne wolf]

but if they had the same power i could?

[wary stream]

Yes

So if it was a^2 + a^2, you can do that

But a^2 + a^3, you can not

[nocturne wolf]

so does that become a^4?

[wary stream]

No

[nocturne wolf]

2a^2?

[wary stream]

You don't add the exponents

[wary stream]

Yes

[nocturne wolf]

i was multiplying them

why don't you multiply the exponents when adding bases

[wary stream]

Because that's not how it works

You don't multiply the exponents when you add/subtract

[nocturne wolf]

then why is my educational institution gas lighting me

ive learned all throughout my years of math that's what you do

[wary stream]

I'm suggesting that you should look back into exponents and adding like terms

[nocturne wolf]

but what you're saying appears to be right

[wary stream]

You probably misunderstood the concept

[nocturne wolf]

i swear that's what they said

[wary stream]

No

[nocturne wolf]

and if that's not what they meant, then they said it improperly

[wary stream]

No way a teacher said that

[nocturne wolf]

because that's what I heard and that's what I wrote down

i swear

[wary stream]

Then that's on you because you mostly misunderstood it

[nocturne wolf]

mmmm no

they should have explained it better

that's exactly what they said, i just wrote down what they sai

[wary stream]

A teacher is teacher for a reason. Sure, some are garbage at teaching but there is no way they would present something incorrect

[nocturne wolf]

sometimes they do

often times they make mistakes and we have to correct them

assuming they're infallible wouldn't be fair

[wary stream]

They make mistakes because they're rushing examples. Concepts, most likely not

So as I stated, it's probably you, that misunderstood

[nocturne wolf]

well idk what to say. that's what I remember being taught

and clearly it was wrong

[wary stream]

Then you recall the wrong info

Still on you

[nocturne wolf]

you can't say that for certain

I can't say that for certain

it happened years ago, and the evidence is merely on memory at this point

[wary stream]

And I can say for certain, that it's on you for not verifying that logic and see if that made sense at the time

[nocturne wolf]

ok that's fair, but simultaneoulsly, i didn't have a lot of time to verify every little thing

and I did assume what they were saying is 100% correct all the time because back then i blindly followed authroity

anyways Im getting side tracked. let me take this into account and simply

so, to be clear, i do not add/multiply/change the exponents in any way when adding bases

im merely just combining the coefficients?

[wary stream]

Yes

[nocturne wolf]

ok

aight

i got the right answer thanks

the only reason i needed to do this practice for myself was because im not confident with expanding, factoring, and other stuff like that and so it was going to help me in understand why pascal's triangle is useful. now ill go do the question

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[edgy flare]

Complex Variables: not sure how to interpret this one.

[real gazelle]

what are you having trouble with

[edgy flare]

What does it mean taking in the positive orientation and all z “not on the curve”

[lone heart]

@edgy flare Has your question been resolved?

[real gazelle]

positive orientation is counterclockwise

z not on the curve means all z not on C (consider why we can't have g(z) for some z on C)

[edgy flare]

Sorry I was busy.

Okay.

[real gazelle]

I was too lol so I wasn't checking anyways

[tacit arch]

It's just two cases

z inside C and z outside

The outside one is trivial

[edgy flare]

I’m confused. It says “g(z) for all z not on the curve C as follows:”

So g only describes z not on the contour?

I’m also confused by the zeta symbols

I don’t know what those mean.

Maybe I need to try this one later and move on to the next one.

[mortal trellis]

it's just an integration variable

replace it by x or u if you want

but zeta is pretty standard for complex integrals

[edgy flare]

So if that, then Z=zeta is a pole, why am I worried about zeta not being in the contour?

[mortal trellis]

well if z was on the curve C then you would have a problem

but z isn't

z is fixed, zeta runs along the curve C

[edgy flare]

I’m gonna try later

Thanks though.

.close

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[terse oak]

h(t) = this integral

[terse oak]

h(0) = ?

is there an easy way to find this without calculationg the integral

[alpine sable]

cos is even, sin and 1/w are odd

[terse oak]

yes

overall its even

[alpine sable]

yup

[terse oak]

so?

limit 0 to inf

2 times

what?

zzero?

no way

[alpine sable]

not zero

[marsh rapids]

He messed up even and odd don't worry

[alpine sable]

^

[marsh rapids]

The integral converges but I don't know where

[terse oak]

😮

[marsh rapids]

Intuitively I don't see this thing diverging anytime

[terse oak]

it doesnt

[marsh rapids]

That's why I wasn't saying anything. It's that I don't have anything useful to say

[terse oak]

lol

[alpine sable]

,w int \frac{2\cos\left(x\right)\sin\left(2x\right)}{x} dx

[marsh rapids]

I think bots are broken rn, go use the website if you really want to

[alpine sable]

ah

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[lone heart]

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[vast bobcat]

the max points achieved in a tournament is 30 points for 5 teams right?

with 10 games won

and then 45 for 6 teams right

[heady pollen]

i dont think you can win 10 games

since each team plays against every other team once

so each team plays only 4 rounds

such a matrix might be helpfull

this would be a possible outcome

the 3,0 means 3 points for team 1 and 0 points for team 2

team 1: 12 points
team 2: 9 points
team 3: 6 points
team 4: 3 points
team 5: 0 points

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[hollow lark]

How 2

[hollow lark]

Do part b

Onward

im clueless

[waxen flame]

What is the formula for the distance between two points?

[hollow lark]

d=sqrt((x1-x2)^2+(y1-y2)^2)

[waxen flame]

You are given the values for the two points, P and S. Substitute those values into the distance formula.

Through algebraic manipulation, you can simplify the equation.

\begin{align*}
\text{Distance} &= \sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}} \
&= \sqrt{(a \cdot \cos{t} - ae)^{2} + (b \cdot \sin{t} - 0)^{2}}
\end{align*}

[ocean seal]

Kookiemon

[hollow lark]

mhmm

[waxen flame]

My one tip is to utilize the part of the question where it says b^2 = ...

[hollow lark]

oooooooooooo

ill see what i can do

it worked

thank you! @waxen flame

[waxen flame]

🙂

[hollow lark]

.close

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[azure trout]

This question is worded so strange... can somebody help?

[last ether]

Well I guess by "arm" they mean like a segment

Basically restrict the parabola so that y-values don't repeat

[azure trout]

How?

[last ether]

Just cut the domain

What is h(x)

Like the actual function

[azure trout]

I have no idea 😭 he didnt teach us LOL

[last ether]

Well lemme rephrase, I don't need to know what it is

Well did your teacher not define h(x)

Like what it is equal to?

It's just straight out h(x)?

[azure trout]

no it equals

f(x)

[last ether]

What is f(x) defined as

[azure trout]

the value

of the function

?

[last ether]

Like what is it equal to

[vocal quiver]

just paste the whole question lol

[last ether]

I mean like this is just to help you visualize what is going on

[azure trout]

that is the whole question lol

[vocal quiver]

d.

[last ether]

Well forget what h(x) is

[azure trout]

a b c are diff questions

[last ether]

You have two options

[vocal quiver]

this is the first place it mentions h(x)?

[azure trout]

no, i know what h(x) is

its like the function of x

idk how to explain it

[last ether]

Let $(a, b)$ be the coordinate point of the vertex of parabola $h(x)$. In order to domain-restrict it so that its inverse exists, we have to restrict it so no y-value repeats. You have two options:

$$x \leq a$$
$$x \geq a$$

[ocean seal]

Umbraleviathan

[azure trout]

so we just choose values?

[last ether]

I mean what's the vertex of h(x)

[azure trout]

a,b

[last ether]

No like the actual value of its vertex

[azure trout]

the question didnt give any values 😭

[last ether]

You have the equation right?

[azure trout]

no?

this is the entire question

[last ether]

Show me the entire problem

Like

A b c d

[azure trout]

i already did a b c

[last ether]

Bruh so you were given h(x$

[azure trout]

oh so we're supposed to use

[last ether]

Yes

[azure trout]

the h x given in the other questions?

LOL i was so confused omg

[last ether]

Yes because it's a part-by-part question

[azure trout]

so still... how would I do this?

[last ether]

Find h(x)'s vertex

[azure trout]

-5,-9

[last ether]

Yeah so

[last ether]

Apply this

[azure trout]

I don’t get it 😭

How would I apply that?

[last ether]

You have the vertex

[azure trout]

x >_ -5?

[last ether]

That could work

Yeah if you use the second option

Although now that I realize it

It's really dependent on your inverse

What did you get for (c)

[azure trout]

I have the inverse

[last ether]

Inverses cannot be $\pm$, then it wouldn't be a function

[ocean seal]

Umbraleviathan

[last ether]

Just choose positive or minus

[azure trout]

I can do either?

[last ether]

Any

Your answe for (d) is dependent on (c)

[azure trout]

Okay i choose positive

[last ether]

If you choose positive, then restrict h(x) as ${x | x\geq -5}$

If you choose negative, restrict h(x) as ${x | x\leq -5}$

[azure trout]

Wait what 😭

[ocean seal]

Umbraleviathan

[last ether]

Hold on lemme check

Yeah that's right

[azure trout]

How did you do that tho

[last ether]

I can visualize it in my head

But if I were you, graph it

[azure trout]

Graph what?

[last ether]

Graph h(x) and reflect it across y=x

[azure trout]

It doesnt

work

[last ether]

It is

Ready for a magic trick

Also graph the negative inverse

[azure trout]

OH

Now what?

[azure trout]

??

[last ether]

Well now reflect h(x) over y = x

So like

Graph y = x

And note how the part where x > -5 will map onto the positive inverse

[azure trout]

how?

[last ether]

Wdym how to graph y = x

Just literally type "x"

[azure trout]

OH

lol

[last ether]

Yeah so note how some parts of the parabola are equidistant to y = x from their inverse

So this is more of a mental math thing

It's gonna be hard to explain if you cannot picture it in your head

If you don't wanna visualize, just take this phenomenon that happens:

Right side of parabola maps to positive inverse, left to negative

It just does

Uh I can't really explain it other than to look and cry and shit pant

[azure trout]

LOL

so

how would i complete d?

[lone heart]

@azure trout Has your question been resolved?

[azure trout]

??

[lone heart]

@azure trout Has your question been resolved?

[azure trout]

<@&286206848099549185>

Can somebody help me with d?

[lone heart]

@azure trout Has your question been resolved?

[lone heart]

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[sharp moth]

What is the purpose of what is circled in red in my calculator?

[sharp moth]

Is it a different way to express the answer?

Like 5pi/2 is equal to 2pi pi/2?

Or does that mean something else

[tacit arch]

This is just a calculator question

Read the manual in your calculator

[sharp moth]

It’s a plug-in for nspire in French

translating the forums page

Calculation application extending the capabilities of the TI-Nspire CAS and non-CAS calculation engines.
Lua interface, OS 3.2 or higher required

On TI-Nspire CAS:

• specifies if the limits are reached higher or lower values
• specifies the main measure of the results in radians
• specifies the algebraic and exponential forms of complex numbers

On non-CAS TI-Nspire:

• exact results thanks to an exact calculation engine managing many forms (fractions, radicals, radians and trigonometry, exponentials, logarithms...)
• solving equations with one or more numerical solutions
• calculation of limits
• specifies if the limits are reached higher or lower values
• specifies the main measure of the results in radians
• specifies the algebraic and exponential forms of complex numbers

Customizable interface:

I think it's results in radians

Let me know what you think because it's not exactly in the manual

It may be in this forums post but I don't really know if that means something else

[tacit arch]

No idea. Don't know that calculator

[sharp moth]

Okay it's probably not important anyway

.close

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[pure bolt]

idk how to do this question

its a multivar calc question

i got x_i=1/lambda*p_i

don't know where to go from there

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@pure bolt Has your question been resolved?

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@pure bolt Has your question been resolved?

[pure bolt]

.close

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[azure trout]

So confused

[fossil gate]

Draw a right angle triangle

And label the possible length values in which one variable is larger than the other

(Hypotenuse is always the longest)

So this cannot be cosine, since cosine is a / h

And just eliminate

From then on

[azure trout]

so it cant be sec either then?

theres 4 answers

[fossil gate]

It can be sec

Because sec is h / a

[azure trout]

oh yea

[fossil gate]

And as long as h>a then this works

[azure trout]

omg

wait i get it now

my teacher explained it so weirdly

he put a 1 on all the numerators

[fossil gate]

R u in class rn?

[azure trout]

no

[fossil gate]

oh lol

[fossil gate]

Wai

[azure trout]

oops

[fossil gate]

is it wrong 😭 shit

what does 1.33 /4 mean

[azure trout]

i have no mf clue

cuz

how many

OH

was there only 3 answers or somethign

[fossil gate]

no there are 4 points right

Ohhh

thats prolly it

let me rethink this

my bad

[azure trout]

no no its ok

[fossil gate]

It cannot be sin my bad

i am so silly

[azure trout]

i got cot wrong too

cuz cot is a/o

[fossil gate]

Its csc, sec, cot and tan. I am confident tan is correct

[azure trout]

wait no

[fossil gate]

a/o can still be 7/5

[azure trout]

4 answers?

[fossil gate]

its just any equation where h is either non existent, or at the front

since 7 > 5

numerator is larger i mean'

[slender gull]

Neither sine nor cosine can be 7/5

For a real angle.

[alpine sable]

But the rest work

[languid bolt]

yes

[fossil gate]

Yeh there are 4 answers

cot and tan work

[azure trout]

okay lemme put it in

[alpine sable]

Csc and sec work

[azure trout]

WOOOO

it worked!

thank you guys!!

[fossil gate]

why was it 1.33 /4 before? you only got 1 wrong

[azure trout]

i know so weird

[fossil gate]

ohj well

[azure trout]

canadian online school sucks balls fr

[gray isle]

there were two wrong

selecting sin
and not selecting csc

[fossil gate]

yeah true 1 wrong answer and clicked a wrong one. but 2.66 lost is werid imo idk

[azure trout]

yeah - the original wouldve gotten me a 77% instead of 100% just for clicking the wrong one

so stupid

thanks again ❤️

.close

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[fossil gate]

alg

[lone heart]

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[tender dagger]

pls help

[lone heart]

@tender dagger Has your question been resolved?

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@tender dagger Has your question been resolved?

[tender dagger]

<@&286206848099549185> question d) pelase

[ocean seal]

Laplace's 👹

[tender dagger]

$\frac{s(t)}{76} = 0.004 \ S(t)=0.304 \ \frac{91.2}{7} - \frac{91.2}{7}*e^{\frac{-7t}{4560}}=0.304 \ \frac{-7t}{4560}=-0.02361 \ t = 15.38014104$

[ocean seal]

Laplace's 👹

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[strange fractal]

help pls!

[strange fractal]

how do i find which one is not similar?

[slender gull]

Similar triangles have same angles and corresponding sides' ratio.

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[alpine sable]

Hi, is the cross product defined for complex vectors? (By complex vectors, I mean vectors whose elements are complex numbers). If yes, is it still defined only for 3D complex vectors?
I can't find any readable resource on this and I'm not a math genius, so if anyone can send me a link or explain it that'd be great 🙂

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

I have read that.

But as I said, I didn’t understand what I found.

I don’t understand the rationales. From my understanding that link seems to approach the fact that the cross product for complex vectors is only defined for 2D

Unless I have misread the article, of course

As for the stackoverflow post I also did find that and read it already. But I am still a bit confused: is the first comment basically saying that the normal cross product defined in R3 applies for complex vectors in 3D, but what differs is that instead we take the complex conjugate of the usual results?

(Also, by the way, I think I was pretty clear that I did my research, but whatever I found wasn’t as easy for me to understand 🙂 )

[alpine sable]

.close

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[raven oriole]

Is this correct?

[lone heart]

@raven oriole Has your question been resolved?

[raven oriole]

<@&286206848099549185>

[lone heart]

@raven oriole Has your question been resolved?

[languid bolt]

maybe ask in another channel

this one is occupied

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@raven oriole Has your question been resolved?

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@raven oriole Has your question been resolved?

[raven oriole]

All the angles in a triangle add up to 180º

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[abstract fractal]

Can you post the full question

[normal ingot]

AFAIK ur correct

The question is probably incorrect

Yes

What do you get if you write it out

[normal ingot]

Yes

Ofc u could write sqrt(2)/2 as 1/sqrt(2)

And do the same for cos

Yea

Yes because we want to show all three expressions are equal

[normal ingot]

That should be sufficient

Doesnt hurt to write qed lol

U could if u wanted to

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[vital robin]

Hello, I have a question about this problem

[vital robin]

So the top row is how a teacher did it, the second row is how I did it, is my answer wrong?

Or are they both correct?

[marsh rapids]

You got every power inverted at the 2nd equal. It should be 1/(what you wrote)

[vital robin]

So 1/7z^7y^4

[marsh rapids]

No. It should be what the teacher wrote.

[vital robin]

Hmm ok

[marsh rapids]

1/x^k = x^(-k), you did that the other way round

If you look just at the z, you said (with z^5) that x^k = x^-k and (with 1/z^(-2)) that 1/x^k = x^k
These equalities only hold if |x| = 1 or k =0

[vital robin]

Hmm ok, I see how I'm wrong

.close

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[swift mesa]

Can the hyperbolic plane be represented in full as a subset of any finite dimensional euclidian space? If so, what is the minimum dimensionality needed? I know it can't be done in 3 dimensional euclidian space.

[mortal trellis]

https://en.wikipedia.org/wiki/Hyperbolic_space#Euclidean_embeddings

according to this 4

[swift mesa]

Thanks

Is it possible to have an elliptic plane (infinite) with constant positive curvature at every point?

A sphere has constant positive curvature at every point but it closes back on itself and is finite

[mortal trellis]

https://math.stackexchange.com/questions/1714179/can-elliptic-space-be-infinite

google found this post

[swift mesa]

I saw that and I didn't see an answer there

[mortal trellis]

I would probably try it in #diff-geo-diff-top

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[kindred tiger]

Need help with geometry 😁 please help

[alpine sable]

What do you need help in?

[kindred tiger]

I don’t get how to do proofs 😥

[heady pollen]

a more visible screenshot might help

[merry depot]

Two column proofs usually start with the givens

Your statement is correct, and will be part of the proof, but you should start with the given congruences first.

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[lucid skiff]

how do i turn this into an exponential equation?

[edgy flare]

Use the points to plug into the equation and get a system of equations to solve for the a b and c

[lucid skiff]

i dont understand the second part of what you said

[edgy flare]

Plug in both of those points and you should get two equations of just a, b, and c.

For instance:

At (0,-7)

Your equation become -7 = (a * b^0) + c

Which becomes: -7 = a + c

Do the same for the second point and get another equation

[lucid skiff]

oh

thank you

.close

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[rotund grove]

can someone explain to me how to do this number

[swift shore]

Do you know what continuous means

[rotund grove]

yes i do

[vernal thunder]

Do you know where they intersect

Both functions

[rotund grove]

i donttt

[vernal thunder]

Where they intersect is where x equals k

[vernal thunder]

Put both equations equal to each other and solve for x, that x value should theoretically equal k

[rotund grove]

ohh okk i see thxx

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@rotund grove Has your question been resolved?

[vernal thunder]

#❓how-to-get-help

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[neat anvil]

isosceles trapazoid ABCS, having a height equal to 2 cm and 4 cm, respectivily

[vernal thunder]

Draw it out please

[neat anvil]

that the thing idk how to do that

[vernal thunder]

Plus what do you need to solve

[neat anvil]

idk how to

[vernal thunder]

What concept of a trapezoid

[neat anvil]

idk

[vernal thunder]

Area? Perimeter?

[neat anvil]

idk

[vernal thunder]

Post the full question

[neat anvil]

the question is contrusct a quadrilateral having the following propreties

[vernal thunder]

Oh no

[neat anvil]

are u able to help me?

[vernal thunder]

I can’t

Sorry

[neat anvil]

its okay

so do i wait here

for someone else to come?

<@&286206848099549185>

<@&286206848099549185>

.close

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[foggy shale]

Hi can someone help me with this problem 😅

[chrome plank]

What have you tried

[foggy shale]

Idk how to wven start it