help-33

[barren coyote]

am I correct?

and what about the second one?

is that false or not?

[stoic saddle]

#8 is false yes

[barren coyote]

am I correct in #7

[barren coyote]

because there must be 4 vector right?

[stoic saddle]

yes, but i prefer the simpler reason of 1 ∉ span {x-1, (x-1)^2, (x-1)^3}

[marsh citrus]

@barren coyote Has your question been resolved?

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[barren coyote]

Thanks a lot

[marsh citrus]

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[void sierra]

what do I use to solve this?

[whole hazel]

do you mean why is the answer C?

[void sierra]

yeah

pretty much

[tight furnace]

Squeeze theorem

[void sierra]

so I knnow 1-3(2)^2 is 11

[whole hazel]

squeeze theorem

yes

[void sierra]

ah

[whole hazel]

what monikanicity said

[void sierra]

let me look it up

ty

[tight furnace]

np

[still temple]

sammy theorem

[void sierra]

so lim x->2 of f(x) exists AND is = to 11?

[unreal oxide]

If g(x) <= f(x) <= h(x), and lim x->2 g(x) = lim x->2 h(x) = L, then lim x->2 f(x) = L as well

[tight furnace]

Well if it's equal to 11 then it exists

So yes

[marsh citrus]

@void sierra Has your question been resolved?

[marsh citrus]

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[shell igloo]

Good day everyone! I could really use some help with these geometry problems, I don't understand even how to start solving them... This is homework from 9th grade, so please don't use something like calculus😂
I guess it is supposed to be solved using this (and Tangent Properties):
The angle starting at the center of the circle is equal to the arc it cuts off, the angle starting at the circle is equal to half of the arc it cuts off etc (TW: Google translator) (there are more, I can write them all if needed)

[shell igloo]

<@&286206848099549185>

[marsh citrus]

@shell igloo Has your question been resolved?

[pine obsidian]

which one do u need help of in particular?

for 1.1 u have to find the angle in the origin by using angle at center twice angle at circumference

add the angle you find and ? u will get 64

sum of ext angles

[marsh citrus]

@shell igloo Has your question been resolved?

[marsh citrus]

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[sage heath]

is this troll?

<@&268886789983436800>

[marsh citrus]

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[still temple]

hi

[unreal oxide]

hi

[marsh citrus]

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[digital ivy]

Find the determinant of this matrix

[lilac bane]

Ok since this matrix is symmetrical

[distant peak]

$= a \begin{pmatrix} a & \cdots & \cdots & b & 0 \ \vdots & \ddots & \iddots & \vdots & \vdots \ \vdots & & \iddots & \vdots & \vdots \ b & \cdots & \cdots & a & 0 \ 0 & \cdots & \cdots & 0 & a \end{pmatrix}$

oops

how do you do those diagonals dots lol

[elfin berry]

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

[lilac bane]

Can we take this matrix as a sum of 2 matrices?

And find the determinant of each one?

Or is that not possible?

Because then the determinant of the first matrix will be just the product

[digital ivy]

I’ve been thinking for so long yet can’t think of a solution

[lilac bane]

If you're stuck, try a smaller set

Like square matrix 2x2 of
a b
b a

Then go for a 4x4
a 0 0 b
0 a b 0
0 b a 0
b 0 0 a

And notice any patterns

For example the 2x2 gives a determinant of a^2 - b^2

4x4 gives you a^4 - b^4

Here the pattern begins to take shape

Looks like the determinant of a 2nx2n matrix of that shape gives: a^{2n} - b^{2n}

[digital ivy]

I see..

Alright thanks

[lilac bane]

The matrix looked scary lol

But simplifying it by taking smaller sizes makes it easy

[digital ivy]

.close

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[cobalt zealot]

hello

[cobalt zealot]

so

in the brackets

the factor for the first one is -4

and the backers is x-2 and x+2

and the one below it

the factor is -1

and the brackets are 2x+1 and x-1

how do i know when to use negative or positive

oh yeah and the question is just

[nova totem]

The middle term usually can help you

[cobalt zealot]

whats this

[nova totem]

Factorization

But with drugs and more universal

[cobalt zealot]

ye im hella confused

[unreal oxide]

?

i dont understand what u r asking for

[cobalt zealot]

you see the brackets right

[cobalt zealot]

it can be something negative

or positive

but how am i suppose to know

[unreal oxide]

so maybe if u r given something like x^2 - x - 6, u r asking how to write this as a product of 2 brackets?

[cobalt zealot]

that'd be

(x^2+3)(x-2)

right?

wait no

[unreal oxide]

no

[cobalt zealot]

tf you mean no

so its

• then +

[unreal oxide]

its (x-3)(x+2)

[cobalt zealot]

and why isnt it

[unreal oxide]

so find two numbers that multiply to the last number in the expression

[cobalt zealot]

• then -?

[unreal oxide]

right?

[cobalt zealot]

ye

[unreal oxide]

so here find two numbers that multiply to -6

AND add up to -1

-1 being the coefficient of the term i nthe middle

[cobalt zealot]

-3times2

is -6

[unreal oxide]

yeh

[cobalt zealot]

oh

[unreal oxide]

so then

[cobalt zealot]

so

give me a sev

sec

[unreal oxide]

and this works coz -3 + 2 = -1 only

we also have -6 * 1 = -6, but u cant pick these two numbers coz -6 + 1 = -5, and not -1

[cobalt zealot]

this would be + -

because

wait

[unreal oxide]

wait

[cobalt zealot]

how does that make sense for that equation

k

[unreal oxide]

okay lets work with this

so u take the coefficient of x^2, and the constant term and multiply them together

here the coefficient of x^2 is 3, and the constant term is -2

is that okay?

multiply them together u get 3 * -2 = -6

find two numbers that multiply together to -6, and also add up to -5 (-5 being the coefficient of the x term in the middle)

can u do that

[cobalt zealot]

ye

[unreal oxide]

what two numbers can u pick

[cobalt zealot]

but our factor

is

-2

[unreal oxide]

what do u mean factor

dont worry about it yet, can u find two numebrs like i said

[cobalt zealot]

ok

thanks ig

.close

[marsh citrus]

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[unreal oxide]

r u sure

[marsh citrus]

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[native flint]

if i wanted to find the ceoefficeint of x^5 in (x+2)^8

[native flint]

would it be

70(x^5 * 2^3)

cause i got that

but it says that its wrong

[twin girder]

How did you get that?

(What is 8 choose 3)

[native flint]

in psacals triangle

the 8th row, and the 5th over

thus 70

[twin girder]

Its not 70

[twin girder]

.

[native flint]

if its x^5

is it not 8chooses 5

[twin girder]

It is 8 choose 5 (or equivalent 8 choose 3)

But that is not 70

[native flint]

it should be 56

but

like

how

if its to the power of 5

shouldnt it be 8 chooses 5

whihc is 5 to the right or left

on the 8th power

which is 70

@twin girder

sry for ping

[twin girder]

8 choose 5 is not equal to 70 like I have said a few times

,w 8 choose 5

[elfin berry]

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[twin girder]

See?

[native flint]

ye

[inland gull]

You can also use pascal's triangle of you want

8 choose 5 = the 8th number on the 5th row

[native flint]

u mean 8th row

cause theres no 56 on the 5th row

wait i got it

nvm

thanks

.close

[marsh citrus]

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[alpine pilot]

Does it matter if a slope is negative or positive when comparing it to another slope

[alpine pilot]

Like if a slope is 6, the other is -8, is 6 still the greater slope

[late hare]

this is very vague

[marsh peak]

Well 6 > -8, so yeah

[late hare]

it would be a matter of context

if we care about absolute values than 8 would be "greater"

[alpine pilot]

Well in my context

y = 13 + 6x; y = 16 - 8x

Which line has the greater slope?
Which line has the greater y intercept?

That's all I'm provided

I know that 16-8x has the greater y intercept, being 16

[marsh peak]

13 + 6x has greater slope than 16 - 8x

[alpine pilot]

But just to confirm, when comparing slopes do I use the absolute value-- ok ty

[late hare]

best way to confirm is asking teacher to be clear

usually they need to be seperated as steeper upward and downward

but technically speaking you should account for steep-ness only when talking "greater" and when it comes to high steep it is negative or positive direction wouldn't matter @alpine pilot

[alpine pilot]

Yep confirmed it with them it doesn't care about absolute steepness or anything

[late hare]

nice

if you are done just do .close

[alpine pilot]

I have another question

How would I figure out what makes it 0.7

Would I just do

0.7 = 3x+1/x+1

[ocean epoch]

yes

[alpine pilot]

.close

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[flat junco]

hello
guys, im trying to sovle this problem https://codeforces.com/contest/223/problem/B
Codeforces
Problem - B - Codeforces
Image
can someone tell me why me code is slow, even when i use memoization?

[main idol]

#old-network for cs server

[flat junco]

.close

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[eternal tundra]

hey

[eternal tundra]

i got some raelly confusing stuff

$a_n=n^5$

[elfin berry]

~Martin

[eternal tundra]

so we are looking at this series

obviously it diverges to infinity

but let's look at the quotient sequence

$QuO(n^5)(n)=\frac{(n+1)^5}{n^5}=1+\frac{5n^4+10n^3+10n^2+5n+1}{n^5}$

[elfin berry]

~Martin

[eternal tundra]

looking at points at large n, we notice that the fraction goes to 0

thus for large n, we get that two points next to each other are pretty equal

do i have a thought mistake somewhere?

because, looking at the slope of f(x)=x^5, the gradient increases

[crystal lintel]

the thought mistake might be just looking at large n and making a conclusion lol

[eternal tundra]

yeah that might be the case

[crystal lintel]

but yes the limit is 1

[eternal tundra]

i have to compare the growth of 5^n to various powers of n

which is why i took the quotient sequence

[crystal lintel]

you can find that the fraction goes to 0 by multiplying by (1/n^5)/(1/n^5)

[eternal tundra]

a^n has a growth of a, which i got from the quotient sequence

[crystal lintel]

5^n?

[eternal tundra]

yeah, for 5^n it is easy to see the growth

to translate:
compare the growth of 5^n with various powers of n. start by looking at examples for small n, then "point at" a proof by estimating the quotient of two following elements of the sequence to compare the growth.

i think with "point at" they mean i don't need a rigorous proof, but that is really strange, as that is usually required

[crystal lintel]

idt that’s what it was asking?

[eternal tundra]

yes i think so

i just got confused because that growth approaches 1

[crystal lintel]

why does that matter?

[eternal tundra]

the growth of 5^x is 5
assuming the growth of x^5 approaches 1, we could say that
for large n, 5^x grows faster than x^5

but that is wrong, isn't it?

[crystal lintel]

weirdly said

[eternal tundra]

ok, i just looked more closely at the graph, and it seems like for large n this is actually true

i just looked at small n, because the graph got so big lol

[crystal lintel]

are you sure it’s not asking you to look at 5^n/n^5 or something?

[eternal tundra]

why would i want that?

[crystal lintel]

it might not be, just checking

ok after reading it again what you were doing is probably what it was asking

[eternal tundra]

alright, thank you

.close

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[lucid grail]

this is regular right?

[lucid grail]

since it's over {0,1}* and doesn't accept w, it's empty set- so regular?

or is this M could accept the complement of w, so it'd accept epsilon^* - {0,1}*, which is undecideable?

[sly orchid]

mmm yes

[lucid grail]

to which of those

[marsh citrus]

@lucid grail Has your question been resolved?

[marsh citrus]

@lucid grail Has your question been resolved?

[marsh citrus]

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[still temple]

how do I find the hypotenuse of right angled triangle if I only know that medians of the base and attitude are √52 and √73?

[still temple]

.close

[marsh citrus]

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[rigid kelp]

this is just an example i can't think of the question that was on the test but how would you do this? 8-6x / x^2 - 36x + 2 ... is it quadratic equation?

[main idol]

is this your function?

$f(x) = \frac{8-6x}{x^2 - 36x+2}$

[elfin berry]

riemann

[main idol]

or is it something else

[rigid kelp]

yeah i think im honestly not sure what context it was in on the test... but the test is covering algebra and some pre-calc if that helps

pretty sure that's it though

[sour relic]

What do u have to do

[main idol]

what was the question

[rigid kelp]

i think it was to find x

or simplify

[main idol]

,calc (4/3)^2 - 36 * (4/3) + 2

[elfin berry]

Result:

-44.222222222222

[main idol]

,w roots x^2 - 36x + 2

[elfin berry]

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[main idol]

doesn't look like i can simplify

you probably remembered the numbers wrong?

[rigid kelp]

that wasnt the exact question but it was something similar

they prob had #'s that simplified

just dont know where to begin

is it a quadratic formula equation?

like what maths do i need to use to solve it

[main idol]

it's not equal to anything, so there's no "solving for x"

[rigid kelp]

well on the test they used nubers that simplify so if we have numbers that do simplify what's the process?

im not that great at math if you know what type of problem this is called ill google it to use better numbers

that simplify

[main idol]

something like rational functions
https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:reducing-rational-expressions-to-lowest-terms/a/reducing-rational-expressions-to-lowest-terms

[rigid kelp]

ahh ok that makes sense somewhat

so if you scroll down to the bottom of that what is the actual answer?

it has 3 answers?

[main idol]

which one?

[rigid kelp]

i just dont get the x doesnt equal part.. is that an acceptable answer?

[main idol]

the rational function is undefined when the denominator is 0

e.g. do a simpler problem

$g(x) = \frac{x-1}{x^2-1}$

[elfin berry]

riemann

[main idol]

here, x cannot be 1 or -1 because then you'd be dividing by 0

[rigid kelp]

ohhh

[main idol]

and you'd be dividing by 0 because (1)^2 - 1 = 0 and (-1)^2 - 1 = 0

so in order to simplify, you first have to explicitly state that $x \neq -1, 1$

[elfin berry]

riemann

[rigid kelp]

oh ok yah

[main idol]

and now you can factor and simplify

$g(x)= \frac{x-1}{(x-1)(x+1)} = \frac{1}{x+1}, x \neq -1, 1$

[elfin berry]

riemann

[rigid kelp]

i forgot everything in precalc but this is very helpful so thanks

if you dont mind one more question? suppose you have a Right triangle and you have the length of the base and the degrees of the 3 angles inside.. how would you find the other 2 sides of the triangle with that info

[cyan sierra]

That’s trigonometry… have you learnt that yet?

[rigid kelp]

yeah i forgot how to do it though

i havent been in hs for 15 years lol

[cyan sierra]

Simple substitute for sin cos tan, do you have a scientific calculator?

[rigid kelp]

there is one provided

on the test

would you mind sharing the answer

ahh i found a youtube video... thanks for telling me this was trig, completely forgot, have a great day

.close

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[long scaffold]

can someone tell me how we get whats after the line?

[long scaffold]

the (k^2 + k +2(k+1))/2

[marsh citrus]

@long scaffold Has your question been resolved?

[long scaffold]

.close

[marsh citrus]

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[wise fractal]

isnt the distance already given to us

[cyan sierra]

Is there a given diagrsam

[wise fractal]

no

[marsh citrus]

@wise fractal Has your question been resolved?

[wise fractal]

<@&286206848099549185>

[wise fractal]

.close

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[still temple]

I need help with this question im not sure how to approach it

[still temple]

I started off with just the outcomes for each die but how do i get the probability of it

do i figure out the combinations to get a number larger than 8

like by writing out each combo

[fathom vale]

what level of probability are you in

[still temple]

wdym

[fathom vale]

high school?

[still temple]

no im in uni

probability is a really small part of the course

[fathom vale]

P(X>8)=P(X=9,10,11,12) right?

[still temple]

yeah

i got that so far

[fathom vale]

i forgot how to set up the PMF dice, so i personally would just make a summation

[still temple]

so just figure out the # of combos to get larger than 8

[fathom vale]

4,5 5,4, 64, 46 65 56 66 63 36

[still temple]

and divide it by 36

[eternal epoch]

man jus write sample space and see

Favourable outcomes will be (3,6)(4,5)(4,6)(5,4)(5,5)(5,6)(6,4)(6,5)(6,6)

[still temple]

OK thanks i was doing that i just didnt know if there was a better way to do it

[fathom vale]

not really

[still temple]

kk tysm!

[still temple]

.close

[marsh citrus]

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[atomic flicker]

i dont get these questions

this is what i have so far

[trim quest]

what's the question

oh mb didn't see the first picture

So, your first line is right, but how did we get the second line?

[atomic flicker]

plug in one

[trim quest]

oh right duh

so in other words, the derivatives need to be equal at x=1, right?

[atomic flicker]

yeah

im trying to make it continuous

[trim quest]

what else needs to be true? in order for the function to be continuous

[atomic flicker]

wait

something like that

lim as x->b of f(b)=f(b)

that

[trim quest]

How can you guarantee that limit is even defined?

[atomic flicker]

wdym

[trim quest]

You need the two parts of the function to approach the same value at x=1

[atomic flicker]

you mean the right and the left?

[trim quest]

Yes

you equated the derivatives

[atomic flicker]

yeah right

[trim quest]

but you also need to equate the two original functions

[atomic flicker]

what would my next line of math be then

[trim quest]

Keep what you have so far, but also

1+3bx+2x^2 = mx+b

at x=1, this is

3b+3 = m+b

[atomic flicker]

oh oh oh

i see

then plug in what i found for m right

[trim quest]

Yes, now you have a system of equations

you can solve for m and b

[atomic flicker]

then its straigt foward from there

yes

ok thanks

[trim quest]

👍 np

[atomic flicker]

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[marsh citrus]

@still temple Has your question been resolved?

[still temple]

a) (1/5 1children x 4/8 2parents) + (3/5 x 2/8)
b) (1/5 x 4/8) + (3/5 x 2/8)

Is this right?

Nvm I think this should right

.close

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[cerulean orchid]

Is this saying does 7 divide by 42? That should be no because it becomes 1/6 right?

[worn nimbus]

42 is a multiple of 7

hence 7 divides 42

but

[viral lily]

a|b when there's a k such that a*k=b

[worn nimbus]

that

[cerulean orchid]

Oh, so it's asking if 7 goes into 42 and in this case, the answer would be yes because 42 = 7*6

[worn nimbus]

yes

[cerulean orchid]

Thanks

[marsh citrus]

@cerulean orchid Has your question been resolved?

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[still temple]

.close

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[stoic zodiac]

,rotate

[stoic zodiac]

Can someone explain me how to do this problem? I tried using mean value theorem

I got c) 6 but the answer key says d) 2

[main idol]

Show your work

[stoic zodiac]

Well my works was
[f(2) - f(0)] / 2-0

[steady eagle]

that gives you the average value of the derivative

hence you do the same thing with the integral to get the average value of the origina lfunction

[stoic zodiac]

Btw another question

To evaluate the integrals

You get the antiderivative out and then substract the upper bound minus the lower bound?

[steady eagle]

yeah, so an integral is basically saying "find the integral formula, plug in the upper bound and lower bound then subtract"

[stoic zodiac]

Thank you

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[cyan sierra]

Basic but forgot how to do quadratics

[steady eagle]

cross multiply to get them to have the same denominator, add the fractions then reduce for a first step

[marsh citrus]

@cyan sierra Has your question been resolved?

[marsh citrus]

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[tender minnow]

Why does this specific graph have an x infront of the equation, while others don’t?

Does it have to do with the fact that it crosses zero, but still had three real roots?

[eternal epoch]

it crosses origin

so

x=0 is a solution

thats why x is infront of eqn

[tender minnow]

Oh okay, thanks !!

[eternal epoch]

alr cool

[tender minnow]

Might come back later, but for now I’m gonna close this

.close

[marsh citrus]

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[wary talon]

need help finding area of shaded region

[wary talon]

I was first thinking of making two different integrals cuz the top function changes

[main idol]

yea that's a good idea

[wary talon]

ok so the first integral is from 0 to pi/6

[main idol]

,calc cos(pi/6) - sin(pi/6 * 2)

[elfin berry]

Result:

1.1102230246252e-16

[main idol]

sounds good

[wary talon]

so this is 1/4

like

after evaluating

[main idol]

,w int 0 to pi/6 of cos(x) - sin(2x) dx

[elfin berry]

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[wary talon]

my only problem is when I do the other integral im not getting the correct answer

[main idol]

write your other integral in this form

[wary talon]

yea

so this is what i was thinking was the second integral

[main idol]

and what answer did you get

[wary talon]

uh let me check real quic

oh

i think

i see

give me a min

even if I add both the results i dont get 1/2

[main idol]

,rotate

[main idol]

your area shouldn't be negative since it sits above the x-axis

try finding a sign error

[wary talon]

yea

ok

got it

this is another problem btw

so I know I need to do two integrals again

and

the y = |x-2| will be broken into two seperate eqautiosn

so the right part is y = x - 2

but im not sure what the equation of the left part is

@main idol

[main idol]

|x| = -x when x <= 0

[wary talon]

y = -x-2?

is that it?

yo

[wary talon]

in the graph x never goes lesser than 0

i have to find area from x = 1 to x = 4

[main idol]

nope

$-(x-2) \neq -x -2$

[elfin berry]

riemann

[wary talon]

i got the equation now

its y = -x+2

ill get back once I get an answer

thanks

ok so im doing same thing

two integrals

[marsh citrus]

@wary talon Has your question been resolved?

[wary talon]

i think thats correct

.close

[marsh citrus]

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[acoustic maple]

hello! i need help with this initial value problem! :)

[glass silo]

Any parts in particular?

[acoustic maple]

mostly the first one

[glass silo]

Ah, fair enough! What are your thoughts on it?

[acoustic maple]

not a clue how to do it

we’ve done one example of this kind of stuff

and i’m just prepping for my exam in like

30 mins

:’)

[glass silo]

Damn, ouch, best of luck for it!

[acoustic maple]

thank you!

[glass silo]

You know that velocity is the rate of change of your position right?

[acoustic maple]

maybe?

honestly i just want to be able how to understand to do it

physics hurts my brain

although this is for my calc class

[glass silo]

You have the velocity, and you want your position (displacement)

[acoustic maple]

the velocity is v(t) right?

[glass silo]

So you'd integrate your velocity function, not forgetting the constant

[glass silo]

yea

Then use what they said to find said constant

[acoustic maple]

that’s what i got

[glass silo]

Looking good there!

[acoustic maple]

is that all for the first part?

[glass silo]

No

Also best to not call your integrated function v(t), you used v for velocity

[acoustic maple]

oh she has us use like the capital letter of the thing to show it was the anti derivative

so v(t) vs V(t)

[glass silo]

Ah I get you now, ignore me then, I'm blind

[acoustic maple]

lmao you’re all good

it’s hard to see with Vs lmao

[glass silo]

Thought they were the same, sometimes it's hard to tell 😭

[acoustic maple]

haha it’s all good!

anyways

what now?

[glass silo]

Look what I replied to you with

[glass silo]

^

[acoustic maple]

ohhh

didn’t see that

mb

cos 0 is 1 right?

[glass silo]

,w cos(0)

[elfin berry]

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[glass silo]

[acoustic maple]

lmao thank you

[glass silo]

These days I don't even trust myself without a calculator

[acoustic maple]

do i set it equal to zero?

or 7

felt

[glass silo]

What you should get out of your V should have a 7 in it

Note the way I phrased that carefully

But you plug in t=0 to V

[acoustic maple]

squat now i’m confused

so it is equal to 7

like that?

[acoustic maple]

-7

[glass silo]

Yea I would go for that

[acoustic maple]

okay okay

C=1

[glass silo]

I'm taking your word for that!

or...

[glass silo]

,w y' = 2x - 5 + 8sin(x), y(0)=-7

[elfin berry]

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[glass silo]

Yep I agree

[acoustic maple]

yeah that’s what i got

lmao

so for part b i just plug pi/2 in for t?

[glass silo]

Nooooooo

[acoustic maple]

oh

i’m so confused

[acoustic maple]

so confused

[glass silo]

Try this

Spoiler: ||differentiate v(t)||

[acoustic maple]

wait what

take the derivative again?

…?

[glass silo]

Of your velocity

[acoustic maple]

double derivative

[glass silo]

No, just differentiate your velocity function - acceleration is your change in velocity

[acoustic maple]

i am so sorry

but i don’t understand anything with physics

is there anyway you can use words that don’t have like velocity or acceleration

my brain shuts off when i see those words

i take the derivative of v(t) not V(t)

[glass silo]

Yes, this

[acoustic maple]

if not then i don’t know what

[glass silo]

Not your V (capital), as that would be pointless

Differentiate little v

[acoustic maple]

then i plug in pi/2

[glass silo]

Yes

[acoustic maple]

10

[glass silo]

Hmmmm....

,w differentiate 2t - 5 + 8sin(t) dt, t=pi/2

[elfin berry]

Results provided by WolframAlpha

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[glass silo]

,w 8cos(pi/2) + 2

[elfin berry]

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Upgrade to WolframAlpha Pro!

Requested by chartbit#3847

[glass silo]

[acoustic maple]

i thought cos of pi/2 was 1

wait

it’s not

it’s 0

[glass silo]

Yee

[acoustic maple]

okay

i gotta go now

thank you sm!

have a good day :)

.close

[marsh citrus]

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[marsh citrus]

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[still temple]

same problem

[still temple]

stuck and dont know where to start

[north sparrow]

try putting the x value inside the function

[still temple]

Substitute

what do I do after putting -1 for the x's

[north sparrow]

whats the result?

[still temple]

a1+b-1+c

[fresh maple]

could i get help with my crushes homework

[north sparrow]

not here, get your own channel

[north sparrow]

are you sure chief?

[still temple]

not at all my brain is friend

fred*

fried*

jeez

[north sparrow]

where did the y go?

that ones critical here

[still temple]

where would I substitute the y into?

[north sparrow]

y=a-b+c

[north sparrow]

it always was there from the beginning

now, you know that y must by 1 for x=-1

so just put that 1 instead of y

[still temple]

1 = a1+b-1+c

dude i seem so dumb doing this i promise im not this dumb its just that i did so much finals today 💀

[north sparrow]

you kinda forget that its $b\times (-1)$

[elfin berry]

Jigglyproff

[still temple]

1 = a1+b*(-1)+c

oh so would it be this?

[north sparrow]

whats b*(-1)?

[still temple]

-b

lol ok

ohh so this

[hollow quest]

<@&268886789983436800>

[still temple]

right?

[north sparrow]

yes

[still temple]

thx

[knotty shard]

Fear not for he is dead

[hollow quest]

o7

[still temple]

real

why are u guys getting raided tho

[main idol]

ty dami

people raid us cuz they ain't us

[still temple]

real

.close

[marsh citrus]

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[sinful edge]

Can someone please show me how i figure out the bounds for non rectangular regions

[sinful edge]

ive always been getting this wrong

and idk what to do

ive watched so many youtube videos

and im still lost

[eternal tundra]

can you give an example?

[sinful edge]

sorry hold up

[marsh citrus]

@sinful edge Has your question been resolved?

[sinful edge]

<@&286206848099549185>

[proud ice]

You were saying you keep getting it wrong

What do you try?

[marsh citrus]

@sinful edge Has your question been resolved?

[marsh citrus]

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[steel folio]

hey,
if this graph represents f(x)

is f'(x) 0 at x = infinity?

[steel folio]

i know f'(x) = 0

@ x = -3, x = 4

but is it also at x = -infinity?

[marsh citrus]

@steel folio Has your question been resolved?

[marsh citrus]

@steel folio Has your question been resolved?

[unreal oxide]

so u cannot talk abt when x EQUALS infinity

u can only look at what happens when x APPROACHES infinity

u can check if the slope of the function looks like it is approaching 0 as x approaches infinty

also check what looks like is happening to the slope of the function as x approaches -infty

[marsh citrus]

@steel folio Has your question been resolved?

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[unreal oxide]

so write 0.0105 as a fraction

105 is multiple of 3

write it that way

actually

okay so

simplify 105/10000

before using the log thing

yeah

[marsh citrus]

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[trim pulsar]

for this limit, how could i solve it knowing that both functions diverge?

[trim pulsar]

is there a rule/theory that divergence/convergence cancels out?

[deft apex]

[trim pulsar]

cus csc 0 diverges

cot 0 also diverges

even the ratios

wait

[crystal lintel]

i suggest writing it in terms of sines and cosines

[trim pulsar]

OOP

[deft apex]

I think at x->0 your function is convergent

[trim pulsar]

wait

but 1/ sin and 1/ tan

the lim DNE then

but 1/0 - 1/0 is still 0?

[crystal lintel]

it does lol

[trim pulsar]

THATS ALLOWED?

[deft apex]

no it absolutely does exist

[deft apex]

not cus of this

[trim pulsar]

but why is it convergent though?

[crystal lintel]

try this 🙂

[trim pulsar]

knowing only the ratios

yeah

lim x-> 0

we got cscx - cotx

= lim x-> 0, 1/sinx - 1/tanx

sinx = 0, tanx = 0

but then the left and right side approach

for 0+ and 0-

they both approach 0

but the reciprocal they both diverge

[crystal lintel]

that's ok

[trim pulsar]

so then

that brings me back to the 1/0 - 1/0

= 0

im still bound to limit

in which i just multiply 0 both sides

thats cursed though

[crystal lintel]

saying that limit is 0 is not the same as saying 1/0 - 1/0 = 0

[trim pulsar]

1 - 1 = 0 then yeah that works

of course, the limit approach 0

unless i break upt he trig futher?

but its still 1 / sin x

• sinx/cos x

so its 1 - cos x / sin x

[crystal lintel]

cot is not sin/cos

[trim pulsar]

1 / tan

tan = sinx / cosx

wait lemme see if i can send a ss of what i have so far

[crystal lintel]

$\lim_{x\to 0}(\csc x-\cot x) = \lim_{x\to 0}\left(\frac{1}{\sin x} - \frac{\cos x}{\sin x}\right) = \lim_{x\to 0} \frac{1-\cos x}{\sin x}$

[trim pulsar]

yes thats what i got 👍

but then to solve that last part

[elfin berry]

💜𝓁𝒶𝓎𝓁𝒶💜

[trim pulsar]

without using lhopital's rule

wait

[crystal lintel]

any reason for no lhopital's rule? lol

[trim pulsar]

its just not allowed for my final xD

my prof was super strict about us not using it

[crystal lintel]

[trim pulsar]

actual cope

i konw

we even gotoa prove delta epsilon

and this one idek how to appraoch xD

maybe using infinitesimals?

ok im actuall lost 💀

@crystal lintel confirm me on it cus im going insane

but would cscx - cotx

multiply all that by sin x

work?

1/ sinx * sinx - cosx/sinx * sinx

= 1 - cos x

x approach 0

1- 1 = 0

lim = 0

[crystal lintel]

umm no?

[trim pulsar]

it doesnt work right?

what if x/x

multiply

so its x - xcosx / xsinx

im trying anything thats cursed

[crystal lintel]

no it sounds like total nonsense lol

let's compute $\lim_{x\to 0} 1$

[elfin berry]

💜𝓁𝒶𝓎𝓁𝒶💜

[crystal lintel]

multiply by sin

[crystal lintel]

$\lim_{x\to 0} \sin(x)$

equal to 0

[trim pulsar]

yeah

1 != 0

[elfin berry]

💜𝓁𝒶𝓎𝓁𝒶💜

[crystal lintel]

so this is 0

[trim pulsar]

yeah that wouldnt work

but then multiply by one

such that 1 = x/x?

[crystal lintel]

yes that sounds ok

[trim pulsar]

wow

...

thats really really dumb

$\frac{1x-xcosx}{xsinx}$

[elfin berry]

Hiphen

[trim pulsar]

so wait this works?

[crystal lintel]

sure

[trim pulsar]

that is so flawed but i guess it works 🤷

thanks homie

how do i close the chat?

[crystal lintel]

lol ok

.close

[marsh citrus]

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[empty socket]

given this aquavilance relation ~u
how do i show the aquavilence class of [g]~u , where g is in G (G is a group defined with * as its multiplication)
Image

[devout mauve]

show describe

hmm how to give a hint without dropping the keyword

[empty socket]

😄

[devout mauve]

can you give an "explicit" form of each element in [g] depending on g?

[empty socket]

hmm

so [g]~u = Ug , for every g in G
now if i i wanna prove this aquavilance i will need to proof bothsides

$h \subset [g]~u $

[devout mauve]

ah ok you know cosets already?

[empty socket]

you mean like set theory ?

[devout mauve]

the set Ug is called a (right) coset of U

[empty socket]

oh no i am using it without really understanding what it is

[devout mauve]

Ug = {u*g: u in U}

you take each element in U and multiply it by g (from the right)

[empty socket]

so when i say that [g]~u = Ug

i am saying that the aquavilance class is every element in U that is Aquavilant to g

[devout mauve]

no

you are saying that the sets are the same

h is in [g]_u iff it is in Ug

h is equivalent to g if and only if it is of the form u*g with some u in U

[devout mauve]

yes

[empty socket]

so here when i show this side
i am taking a h in the A.class
which means h~ug in G

[devout mauve]

and other direction is the same

[empty socket]

i am a bit confused tho here on what is u exacly

[devout mauve]

u is some element

you don't really know super much about it

except that it's equal to hg^(-1) and is in U

[empty socket]

and how is h then u*g ?

[devout mauve]

well u=hg^(-1)

multiply by g from the right

ug = h

[empty socket]

ohh

i feel so dumb some times

thanks 🙂

[devout mauve]

abstract algebra does that to you

wald vor lauter bäumen und so

[empty socket]

ah du sprichst deutsch ?

[devout mauve]

vielleicht

[empty socket]

haha

vielen dank 🙂

[devout mauve]

gern

[empty socket]

.close

[marsh citrus]

Channel closed

Closed by @empty socket

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[brave trellis]

x^+6x=0 i need help completing the sqaure

[nova totem]

To find the zeroes?

Seems like a waste of time imo

Just factor out x

[brave trellis]

i have to do it that way

:\

[proud ice]

Think you got some typos in your problem

[nova totem]

Crying

Well

[brave trellis]

mb

x^2+6x=0

[nova totem]

Add the square of half the coefficient of the x^1 term

To both sides

: D

[brave trellis]

3^2

[proud ice]

If you're completing the square, you want the left side to be something like (x+a)²

What does (x+a)² look like if you expand it?

[brave trellis]

(x+a) (x+a)

[proud ice]

I mean do the full multiplication

[brave trellis]

x^2 2ax a^2

[proud ice]

yeh

So you need 2a to equal 6

Because you have x²+6x

[brave trellis]

a would be 3

[proud ice]

mhm

So to complete the square, you need to add 3² to both sides

[brave trellis]

done

now what

@proud ice

[proud ice]

.

You found your a

[brave trellis]

how would i write that

idk what you mean

[proud ice]

Do you know what completing the square is?

[torpid cairn]

Whats going on

[brave trellis]

im not gonna lie

no lol

[proud ice]

sorry gtg

good luck

[torpid cairn]

What you tryna solve?

[brave trellis]

i need to solve this by completing the square

x^+6x=0

[torpid cairn]

You need to find ^?

[bright jay]

.

[brave trellis]

idk what that means

[bright jay]

You found your a, plug it in

[brave trellis]

ok well its (x+3^2) (x+3^2)

[bright jay]

No

Is a = 3^2?

[brave trellis]

thats what he said

[bright jay]

No they didn't

[bright jay]

.

[brave trellis]

but that area has to be a^2

right?

[bright jay]

Completing the square, allows you to put it in the form of $(x + a)^2$

[elfin berry]

dldh06

[bright jay]

You just said a = 3

Plug that into that form I just presented

[brave trellis]

(x+3) (x+3)

[bright jay]

Yes

[brave trellis]

so now what

@bright jay

.close

[marsh citrus]

Channel closed

Closed by @brave trellis

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[raven shuttle]

how do I do this? do I just evaluate the function from -3 to 2?

[quasi osprey]

Yes