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[low drift]

bottom of circle doesnt exist

thank you

[livid sage]

🎉

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[lucid kindle]

How do I get a compound exponent expression like a^n + b^n to a^(n+1) + b^(n+1) algebraically?
The specific problem I'm working on and the work I've done so far is in the below picture.
I'm wondering if I'm in a dead end and I need to try a new method outright? Any guidance would be appreciated.

[lament forge]

this would be way easier with modular arithmetic

if we are doing it with this inductive argument, then uh, hm

$6 \cdot 7^{n+1} - 2 \cdot 3^{n+1} = 6 \cdot (4+3) \cdot 7^n - 2 \cdot 3 \cdot 3^n = 4 \cdot (6 \cdot 7^n) + 3 \cdot (6 \cdot 7^n - 2 \cdot 3^n)$

[ocean seal]

bee [it/its]

[lament forge]

(argument with modular arithmetic: it's equal mod $4$ to $2 \cdot 3^n - 2 \cdot 3^n$ which is obviously $0$)

[ocean seal]

bee [it/its]

[lament forge]

the basic idea: if it's convenient we can take out terms that are multiples of 4

as long as each term in the final sum has some factor that's divisible by 4, whether that's the number 4 or the expression in the inductive hypothesis

[lucid kindle]

that makes more sense, so i dont necessarily have to treat the expression with n as my starting point and the one with n+1 as my endpoint

[lament forge]

yeah normally what i'd do is start from the n+1 and just do stuff to it until it's a multiple of 4

[lucid kindle]

right, thank you! :)

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[hushed locust]

r = 7 is a circle of radius 7. so if you were to plot (r,θ) and have that include the entire circle you'd need to plot all angles from 0 to 2π (as with any "normal" circle)

yes

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[eager kraken]

@hushed locust how to solve this ?

[frail grove]

$\lim_{x\to 0} \frac{\sin \left(ax\right)}{x} = a$

[ocean seal]

Adam Chebil

[placid zinc]

Which Roblox game is throwing limits at you, lol

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[foggy knot]

does anyone know how the sum of the forces was taken here

mechanics of deformable bodies

or solids ig

I think u can just figure this out with statics I just dont see it tho

this class fucking sucks lol

dynamics is like 10000 times better

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@foggy knot Has your question been resolved?

[foggy knot]

no

cuz no one wants to help with this stupid fucking class understandably

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[vagrant lark]

whats the right answer lmaop

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[thick lynx]

How'd we do this?

dim U <= 3

Actually < 3 because the tuple is l.d.

Either 1 or 2

[echo socket]

Since they are linearly independent, you can express one of the vectors as a linear combination of others, remove that vector from {u1, u2, u3} and see if the remaining set is also linearly dependent/independent

[thick lynx]

Can we say because no two pairs are just scalar multiples of each other it can't be 1

Thus it has to be 2?

[echo socket]

Sure

[thick lynx]

Yeah, that's all we need

It just asks for the dim

Thank you

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[west lance]

how do i show D is true

[west lance]

like how do you get there

i looked at the answers and its true

but idk how

[open perch]

💀 that looks terrifying

i aint there yet but sh man

[west lance]

i got this sequence formula when i integrated it by parts but idk what to do next

[charred flint]

that's good just try to change it into In/In+1

[west lance]

i divided by I(n+1) and got here now what

[charred flint]

that's good, so hopefully the left side is 1, and you get to use c) that nI+n goes to 0

like 1/(n+1) goes to 0 and e*(n+1)*I_n+1 goes to 0 because of c)

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[native wharf]

hi

[native wharf]

how would we factor -22d^2 + 29d - 9

i’m kinda confused ngl

[stuck meadow]

what math are you taking

cause it kinda depends on the level

[native wharf]

algebra 1

in 9th grade

[stuck meadow]

are you trying to find what d is equal to or what it only factors to

[native wharf]

factors

just factoring the equation

not like finding the value of d

[stuck meadow]

(-11x+9)(2x-1)

use mathpapa.com if you want the steps

[native wharf]

wait what can you explain

how you got that

[stuck meadow]

do you know what busting the bee is?

[native wharf]

no

[stuck meadow]

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-intro/v/factoring-quadratic-expressions

khan academy does a good job explaining

[native wharf]

yea but can you just explain it cuz i prefer like having someone talk me through it rather than watching a vid

<@&286206848099549185>

how would we factor -22d^2 + 29d - 9

that’s the question

i just pasted it again

so u don’t gotta scroll up

[buoyant saddle]

two numbers that multiply to (22)(9) but add to 29

[native wharf]

yea

[buoyant saddle]

22*9=198

[native wharf]

and that’s where i struggled

yea so it’s 198

[buoyant saddle]

11*18=198

[native wharf]

but no factor of them add up to 29

oh

oh wait

how did i miss that

[buoyant saddle]

🤷🏼‍♂️

[native wharf]

dang

oh ok

[buoyant saddle]

a trick is

[native wharf]

gimme a sec so i can solve it now

?

[buoyant saddle]

to break up what you had

notice

22*9

= 2 * 11 * 9

=18 * 11

always try to rearrange the order

[native wharf]

ohh

[buoyant saddle]

of multiplication

to see how they add together

[native wharf]

yea

so basically after we get those factors

it would be 22d + 11 + 18 + 9

[buoyant saddle]

no

-22d^2+11d+18d-9

then factor

[native wharf]

oh yea

[buoyant saddle]

by grouping

[native wharf]

so it’s gonna be (-11d+9)(2d-1)

[stuck meadow]

yea

[native wharf]

aight

and also for solving 14b^2 - 2 = -3b

we should rearrange it to 14b^2 - 2 - 3b right

or no

it would be +

wait

it should be 14b^2 + 3b - 2

alr ima need some of my work to be checked

now

for 4 i got 8(v+3)(v-2), for 8 i got 9(r-5)(r+1), for 12 i got (2w-5)(5w-3), and for 16 i got (9v+6)(2v-3)

for 20 i got -(8h-3)(h+2), for 22 i got (-11d+9)(2d-1), and for 28 i got b=2/7 or b=-1/2

and then for 32 i got -1/3 and 5

lmk if these are all right

<@&286206848099549185>

@helper

<@&286206848099549185>

[alpine sable]

Looks correct at first glance

[native wharf]

u started from here right

[native wharf]

^

[alpine sable]

yes

[native wharf]

aight

thanks

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[vocal pivot]

Hi i need some excel help. My min slope is bigger than the slope of my trendline and idk what to do

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[uneven fiber]

Should a graph of a log amplifier be linear or exponential

[uneven fiber]

these are the values i got

and graph that was generated looks like this

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[rough flax]

can someone help me with this linear algebra problem? I've never seen one like this

[rare gale]

!status

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What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[charred flint]

polynomials can be seen as vectors too but there's nothing special about them because there's nothing you can do to turn t into t^2, so it's just asking you for (-2,1,1,1) in terms of (1,-1,0,0), (1,0,1,0), and (1,1,0,-1)

[rough flax]

so just look at the coefficients basically?

[charred flint]

yea

[rare gale]

yeah, expressing that polynomial as a LC of the others is just writing:
-2+t+t^2+t^3 = a(1-t) + b(1+t^2) + c(1+t-t^3) and then look at coefficients

[rough flax]

ah okay, thank you

wait could someone explain a bit more how a matrix would be set up using the above info?

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[unborn burrow]

For simpsons rule how does the number of intervals increase effect the error

[unborn burrow]

I read it simpsons rule is ex^4

So if we increaase the interbals by 5 times

is that original error times 5^4

[charred flint]

yes, that's how the upper bound on the error would change

original error divided by 5^4 since it's error ~ 1/n^4

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[mystic swallow]

!status

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What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[rare carbon]

i belive that tan(theta) = sqrt(2)/4

@mystic swallow please help

3. I got an answer but I was told that it's wrong.

[gray isle]

you would be correct, the value they have there is wrong

[rare carbon]

okay thx

my teacher said that the answer key wouldn't 100% correct

so I just wanted to check

.close

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[mystic swallow]

please don't ping me

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[winter chasm]

.

Cont @charred flint

[winter chasm]

I know the period is the order of 10 mod p

But i still don’t know what to do

[charred flint]

uhh the equation is like 10^n-1=0 mod p

anyways with a prime like 10001 you know it's not a divisor of 9,99,999, or 9999 right?

so period at least 5

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[mossy knoll]

anyone good enough to help me with this question

[mossy knoll]

completely flopped it

i have everything else solved but this is the full image if needed

just 44b stumped me

[tawny crown]

That's 17y I believe, not 7y

[mossy knoll]

oh poop im dumb

other than that how would i get past that step when i have the 2 eqqquations sitting there

[tawny crown]

Wdym, you have to solve this system of equations

[mossy knoll]

after tthat step i mean

lemme fix it up rq

[tawny crown]

You solve them either by elimination or substitution as you did

[mossy knoll]

okok thank you

ill check back if i have any issues

i think i did it right

i think i cooked

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[woven hearth]

solve in Z the following system

[winter chasm]

U mean =1?

[small fog]

Context?

[woven hearth]

the lesson is aritmetics in Z and there isn't any prior context besides another system

the other one only has 2 lines

now that am looking at it i think the first system may help solve the 2nd

[tribal haven]

for low mod you can brute force this extremely fast

but my guess is you should google chinese remainder theorem

[woven hearth]

i heard a classmate talk about this theorem i'll google it

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[misty nebula]

can i use here the thing which says lim x->0 sinx/x = 1 ?

cuz pi/2 = 0 when its inside the sin

[tardy tapir]

pi/2 is not zero, it's a constant

also, sin(pi/2) is 1 not 0

[misty nebula]

oh

ok ty

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[small fog]

,rotate

[small fog]

so we want to have some expression a/b where b is 0 at 2/3

and we wanna add 1 to this so that there is a horizontal asymptote at 1

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[raw bolt]

do you remember the side relation for cosine?

[lament wraith]

root 3/2

[raw bolt]

thats for a specific value

what side over what side for cosine?

[lament wraith]

adjacent leg over hypotenuse

[raw bolt]

yes

which is the adjacent side in this triangle?

[lament wraith]

6 root 2

[raw bolt]

no

[lament wraith]

6

[raw bolt]

yes

6sqrt(2) would be the opposite side

and the hypotenuse is 6sqrt(3)

[lament wraith]

yeah

[raw bolt]

now that you know the values you can plug them into the cosine relation

[lament wraith]

its wrong

it says

[raw bolt]

we just agreed that 6sqrt(2) was the opposite side

[lament wraith]

yes

OHH

[raw bolt]

which is NOT used for cosine

[lament wraith]

its 6/6 root 3

?

wait no

[raw bolt]

yes

[lament wraith]

oh

its still

wrong

😭

what

[raw bolt]

try simplifying it

[lament wraith]

ok

thanks

its root 3 over 3

[raw bolt]

yes

[lament wraith]

.close

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[indigo herald]

can someone please help me with my MATH IA

[alpine sable]

ye

[indigo herald]

I am using the Gale-Shapley Algorithm- the Stable Marriage problem to connect it with matches in a show

but my teacher said the math isn't complex enough

since the algorithm really is just matrices

he said I should explore abstract algebra related to the problem and I have no idea how it works

<@&286206848099549185>

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[indigo herald]

<@&286206848099549185>

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[austere plinth]

hello everyone

can someone help me with it?

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@indigo herald Has your question been resolved?

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@indigo herald Has your question been resolved?

[green shoal]

Brody this is a help channel

[indigo herald]

.close

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[mellow iris]

how many way to get 5 cards with following constraints

told order doesnt matter

[steel olive]

do you know the principle of inclusion and exclusion

[mellow iris]

yes

but idk how to use it in problems like this

[mellow iris]

bc there is like possibility of no 8, no face, or, 1 face

to account fo

r

[mellow iris]

so how would I implement this?

is the answer 4* 12C2 * 49C2

[steel olive]

wait my bad it will be tough to apply this here

i think we will have to do this by casework

[mellow iris]

the logic is 4 ways of an 8, 12 face cards choose 2 then we get 12C2, then last cards can be any of the remaining

is that right?

[steel olive]

that will lead to repetitions

because imagine that when choosing any one 8 card, you choose 8 of diamonds and in 49c2, you choose 8 of hearts

now

when choosing any one 8 card, you choose 8 of hearts and in 49c2,you choose 8 of diamonds

[mellow iris]

so the last part is 46c2?

[steel olive]

no

wait

also the question says atleast 2 face card

not exactly 2

[mellow iris]

ya but wont it be coutned in the remaining cards part

[prime badge]

don't use pie, add 6 cases

[mellow iris]

which cases

[steel olive]

these will be the 3 cases

[prime badge]

yeah, so 2 more when there's two eights

and 1 one more when there's 3 eights

[steel olive]

the question says just 1 eight

im guessing if we were allowed to pick more eights,it would have said atleast 1 eight

[prime badge]

maybe

[mellow iris]

oh so then add these

[steel olive]

yea

[mellow iris]

makes sense now thx

[lone heart]

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[last aurora]

Hallo

[last aurora]

if vector r= <x,y,z>

is dr = <dx,dy,dz>??

[golden grail]

in cartesian coordinates, yup

[last aurora]

Thank you c:

[lone heart]

@last aurora Has your question been resolved?

[alpine sable]

hi i have a question

[golden grail]

yep ?

[lone heart]

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[alpine sable]

um

it went to another log

help 4

can you check there please

[lone heart]

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[stiff cape]

could someone explain this answer from my textbook, I get the basics of determinants but for some reason I am so confused when it comes to that of unknown values within it

[sharp gate]

It should be the same as with numbers

[stiff cape]

wdym?

[lament forge]

yeah a and x are just numbers

[sharp gate]

Just pretend the unknowns are numbers

Then it’s just a matter of algebra

[stiff cape]

ok cool thank you

also could I ask an additional question or do I have to start a new one

yeah I going to ask it 😭

Could someone assist with these question?

[lone heart]

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[mortal root]

Hello, I was wondering how to rigorously argue part (b). I think it is a quite intuitive result but I don't know how I can use mathematical language to justify the proof. Would someone like to drop some hints?

[proud pine]

Looks a lot like PIE to me

(principle of inclusion-exclusion)

[mortal root]

Yes, but how to argue in the integral context?

[proud pine]

I'd use a linearity argument

And the fact that integrals are separable

the integral from a to c of f(x) is equal to the integral from a to b of f(x) plus the integral from b to c of f(x) for some b in the interval (a,c)

[mortal root]

Yes of course.

But this is the multivariable case.

[proud pine]

An interesting conundrum

I'm sorry, I don't have any more insight than that

[rose sigil]

https://proofwiki.org/wiki/Additive_Function_is_Strongly_Additive reading this will help me thinks

[lone heart]

@mortal root Has your question been resolved?

[mortal root]

<@&286206848099549185>

[lone heart]

@mortal root Has your question been resolved?

[tacit edge]

you could fiddle about with indicator functions perhaps?

eg, I_{S_1 u S_2} = I_{S_1} + I_{S_2} - I_{S_1 n S_2}

then you could start with the integral on the left

$\int_{S_1 \cup S_2} f = \int_{S_1 \cup S_2} f * 1_{{S_1 \cup S_2}$

[tacit edge]

then substitute this, apply linearity, and then pull the indicator function into the integration bounds

[ocean seal]

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

[tacit edge]

then the result follows

this suffices as a proof as long as you already have linearity of the integral pretty much

as you can prove eg that $\int_{S_1 \cup S_2} f1_{S_1} = \int_{S_1} f$ by linearity too I think

[ocean seal]

Waffloid

[tacit edge]

(if you really wanted to)

[mortal root]

Let me try, thanks!

[lone heart]

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[rain axle]

Hey! I have an RPG bot that rolls fate dices and I run some iterations to see if it is accurate. I would like to know if my approach is already good enough, would work accurate when scaled down or should I use fixed chance random.

The test results and how a fate dice works:

[rain axle]

First of all, a fate dice works like this:

• It is a dice with 6 sides,
• 2 of the sides are -1,
• 2 of the sides are 0
• And the last 2 sides are 1

You roll this dice 4 times and add the results. For example, 1, 1, 0, 1 would be a fate dice that rolled 3.

In the test I have done, the one with 100 million iterations returned this:
(The numbers are just: how many times a dice was rolled / total rolled dices or iterations)

• -4 dice -> 0.012239 (%1.22)

• -3 dice -> 0.049862 (%4.986)

• -2 dice -> 0.123553 (%12.35)

• -1 dice -> 0.196806 (%19.68)

• 0 dice -> 0.235358 (%23.53)

• 1 dice -> 0.196912 (%19.69)

• 2 dice -> 0.123535 (%12.35)

• 3 dice -> 0.049218 (%4.92)

• 4 dice -> 0.012517 (%1.25)

These results seems pretty similar to someone's test I have found:

But I wonder since in my version, there are little differences such as -3 is %4.98 while 3 is %4.92. I know this is a really small difference, probably at a lot higher iterations this should vanish but I'm not sure if it is problematic or not. Is 100 million iterations enough to understand?

And if there is a tiny inaccuracy, would this amount of difference cause problems when the number of iteration is a lot lower? Or is this unnoticeable?

If this is significant, I will use fixed chances but more importantly I would like to understand the logic and probability behind, would love to learn the "why".

[stark scroll]

the probabilities seem correct to me

[stark scroll]

of course, if the iteration is a lot lower you are going to have a lot more variability

but since your code works, each roll should have a fixed probability

[placid zinc]

Hopefully it's clear that this is symmetric. Probability of getting a -4 is the same as getting a 4

,calc (1/3)^4

[ocean seal]

Result:

0.012345679012346

[rain axle]

So to my understanding, opposite numbers should have the same odd of rolling. Like 3 should be same with -3. But I have opposite variability even at 100 million iterations.

Would using fixed chances fix this opposite variability?

[placid zinc]

And that's the exact probability you roll a 4 or -4

[stark scroll]

Your code should have fixed probabilities already

Even if you set the chances manually, you'll still see variation if you iterate 100 million times

[rain axle]

hmmm, it makes sense I guess

[placid zinc]

,calc 4(1/3)^4

[ocean seal]

Result:

0.049382716049383

[placid zinc]

That's the 3 or -3

[rain axle]

My implementation was trying to be authentic, like I have defined a dice [1, 1, 0, 0, -1, -1], before each roll I shuffle this list and then roll this dice 4 times :D

But I guess just using fixed probability is wiser

[placid zinc]

But the rest are going to be pretty complicated haha

[rain axle]

and more accurate?

[stark scroll]

In theory they should both have the same accuracy

[rain axle]

Hmmm

[placid zinc]

Do whichever is faster, so you can do more of them imo

[rain axle]

Yeah that is a true aspect :D

[stark scroll]

yeah

[rain axle]

Okay then! Thank you sm for the help. If both has the same accuracy, I'll just use the faster one

[stark scroll]

you can calculate the exact probabilities as kaynex did here

[rain axle]

how does that work tho

[stark scroll]

To roll a 4, you have to roll 1 each time

since there is a 1/3 chance to roll 1, the probability to roll a 4 is (1/3)^4

[stark scroll]

^ and keep this in mind

To roll a 3, you have to roll a 1 thrice and a 0 once

The possibilities for the rolls are 1110, 1101, 1011, 0111, each with (1/3)^4 probability

so the probability of rolling 3 is 4(1/3)^4

you can keep doing this

[rain axle]

oh

that makes sense

[rain axle]

how though? Is this something I need to keep in mind? Wouldn't just having all the numbers from -4 to 4 and randomly choosing them with a fixed odd should work?

[stark scroll]

I meant that the probability of 4 is the same as probability of -4 so you only have to calculate one of them

[rain axle]

ohh okay :D I thought you meant it for something else

[stark scroll]

Anyway the probabilities should be:
4: 1/81
3: 4/81
2: 10/81
1: 16/81
0: 19/81

[rain axle]

I need to learn fundamental probability calculation

[stark scroll]

Or something like that

[rain axle]

Do you know any resources for this?

[stark scroll]

I'm not so sure, sorry

I learned from doing contest math

[rain axle]

okay, thank you anyways for the help!

how do I mark this as solved

[stark scroll]

it should be .close

[rain axle]

.close

[lone heart]

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[upbeat eagle]

Hello

[alpine sable]

?

[upbeat eagle]

This is probably a silly question,
but does anyone know where I could find useful resources, which practice rearanging simple equations/ into certain forms.

Eg,
I had a question of

dx 1 / (X-X^2)

and ur supposed to do

1/ X(1-X) = 1/X + 1/(1-X) dx

to make it easier

But i cant spot that stuff

So im trying to find stuff which helps me able to spot this kinda stuff

thank you

Like ik, a lot of them alrdy but i feel like there is so much more I can know/ (perhaps even forgotten)

or maybe ill just go through the basics again

.close

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[raven crag]

@Equity Fostering algebraic thinking a guide for teachers, grades -- Driscoll, Mark J -- 1999 --

[rustic matrix]

How can i solve AH² = HB × HC ?

[lavish cave]

Similar triangles

[upbeat eagle]

ty ill have a look!

[lavish cave]

Please don't ping helpers that early

Wait until 15 minutes have passed to ping helpers

Besides I'm already helping you

[rustic matrix]

I didnt understand anything from similar triangles

[upbeat eagle]

its two right angles triangles

[lavish cave]

But you know what similar triangles are right

[rustic matrix]

No

[lavish cave]

triangles semblables

[rustic matrix]

Yes

[lavish cave]

Try redrawing the two smaller triangles, ABH and ACH

So that they look like this

You'll have to rotate the triangles

[rustic matrix]

Then?

????

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[rustic matrix]

Bro can u actually like make things clear ?

[alpine sable]

how can i help you

[rustic matrix]

I need to solve AH² = HB × HC

[alpine sable]

hmmm

[crimson field]

So passive aggressive

[alpine sable]

have you tried?

or do you not know how to start?

[rustic matrix]

Exactly

[alpine sable]

ok ig you are familiar with the pythagoras thorem

[rustic matrix]

Yes

[alpine sable]

now using that can you give all the possible triplets?

like uk

CH² +AH² = AC² (this is an example)

[rustic matrix]

Ab² = ha² + hb ²
Ac² = ah² + ch²

Bc ² = ac² + ab²

[alpine sable]

alright

[alpine sable]

can we say that BC² - AC² = AB²?

[rustic matrix]

Yes

[alpine sable]

so.... BC² - AC² = AH² + HB ² ?

[rustic matrix]

Right

[alpine sable]

wait wait wait......

i am really sorry

[rustic matrix]

This is correct

[alpine sable]

did you want to prove AH² = HB × HC?

[rustic matrix]

Yes

[alpine sable]

oh ok my bad just a sec

i didnt see the values

yeah alright

so now take triangle ABC

its right angled right (it has 90 degrees)?

[rustic matrix]

Yes

In A

[alpine sable]

so what is the pythagoras theorem you got for that?

[rustic matrix]

Bc ² = ab ² + ac²

[alpine sable]

now put the values for AB and AC respectively

[rustic matrix]

We already have the values

Bc = 5 . Ac = 4 . Ab = 3

[alpine sable]

oh...

my mistake i will try solving it

uk i got confused cos i was scrolling up and down

[rustic matrix]

Ur good

My teacher said something about airs

Do we need to like calculate airs of the triangles?

Also the guy before u stated that theyre similar triangles

[alpine sable]

i hope you do know abt similarities

[rustic matrix]

No

No clue

[alpine sable]

oh ok

uk cos similarity is another concept

by which we can solve this

ik how to solve that because its easy

i am trying to solve it by pythagorean theorem

its why its taking time

[lavish cave]

Yep by similarity you just get AH/HC = HB/AH

[unkempt rivet]

you cant??

[alpine sable]

we can it just the matter of which is easy and which is not

[unkempt rivet]

just use the proportion

[rustic matrix]

Cos Abc = cos AbH

[lavish cave]

AH is the shorter side of AHC and BH is the shorter side of ABH

[lavish cave]

No need trig here lol

[rustic matrix]

Isnt it Ah / hb = hc / bc?

[alpine sable]

💀 bro which do you want:

• similarity way
• pythagorean way
• trigno way

[lavish cave]

HC and AH are both the longer sides (not the hypotenuse) of their respective triangles

AH/HB = HC/AH also, yes that works

[lavish cave]

Nope, BC is a hypotenuse

None of the other sides are hypotenuses

[rustic matrix]

Couldnt figure it out

My teacher said something about finding the airs of the triangles . Will that help?

[alpine sable]

area of triangles?

[rustic matrix]

I found it out i think

[alpine sable]

cos there is no concept called "airs of triangles"

[rustic matrix]

Wait so if
Surface Ahb = AH² / 2 or AH × HB / 2.
Surface ACH = AH × CH / 2 or AH² / 2.

I see that AH ² = AH × CH
AH ² = AH × BH
SO AH² = HB × CH

[alpine sable]

:/ pythagoras

[rustic matrix]

Is this right tho?

[alpine sable]

totally

[rustic matrix]

Im goated fr

[alpine sable]

lol

[rustic matrix]

EASY 2 BONUS POINTS IN THE EXAM

[alpine sable]

preparing for examination huh?

[rustic matrix]

No

He said that if we get this correct hed give us 2 bonus points

Since we havent studied this yet

[lavish cave]

Ahhh nice

[alpine sable]

oh

$$ CH^2+AH^2=AC^2 //HB^2+AH^2=AB^2 \mbox{then} //CH^2+HB^2+2AH^2=CB^2 \mbox{or} // CH^2+HB^2+2AH^2=(CH+BH)^2 //CH^2+HB^2+2AH^2=CH^2+BH^2-2CHHB //2AH^2=-2BHHC //AH^2=-BHHC$$

[ocean seal]

Tuf Dawg

[alpine sable]

this si not working!!!!!!!!!1

[rustic matrix]

.close

[lone heart]

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[uneven osprey]

rlly need help with thus

[uneven osprey]

the line with “integrate both sides” why does it turn into logs?

more like HOW

and wheres the vx0 coming from

[charred flint]

they do 2 steps there at the same time. when you integrate dvx/vx (looks like 1/x) you get ln(vx) evaluated between where vx starts (vx0) and an arbitrary vx, giving ln(vx)-ln(vx0)
and then they add ln(vx0) over

for the integral on the other side of 1.2dt it's from t=0 to t

in general for physics problems the start of an integral of anything besides time is just the initial value like vx0

[uneven osprey]

ah i get the first part, just not rlly that vx0 bit

just unsure where its actually coming from

can u explain it a little more if thats okay? @charred flint

[charred flint]

it's like you're integrating from the initial state to the final state of the physical system

[uneven osprey]

oh i understand its the initial velocity but why is that dragged in mid calculation

[charred flint]

it's the only lower bound for the integral that you have to work with I guess

[uneven osprey]

oohhhh

thank u v much

i see now

[lone heart]

@uneven osprey Has your question been resolved?

[uneven osprey]

the green writing ^^

idk if this is a mistake but this is confusing me

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[uneven osprey]

.reopen

[lone heart]

✅

[uneven osprey]

<@&286206848099549185>

please anyone? 🥲

how?

and even if, it doesn’t show before the log?

i get it now

alright

lol mb

i was literally about to question this hahaha

yep

i agree with this

and yeah the notes show a lack of working which makes it harder to follow lol

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[pure ginkgo]

I am trying to solve this problem. I can easily figure out the volume part but I need help with actually figuring out the radius of the sphere.

[limpid turret]

you have to remove the linear terms (6x, 12y, 16z) by completing the square for each component, and turning the sphere equation into the form (x-h)²+(y-k)²+(z-m)²=r²

[pure ginkgo]

i need help with that

[limpid turret]

what exactly is confusing you?

[pure ginkgo]

I know that I need to move one of the variables to its own side and do that for x, y, and z but don't know where to go next

i also dont really understand how to use completing the square to assist me

[lone heart]

@pure ginkgo Has your question been resolved?

[lone heart]

@pure ginkgo Has your question been resolved?

[pure ginkgo]

i was able to figure out the answer to the question

.close

[lone heart]

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[white dock]

someone pls help me3

[pure ginkgo]

This channel has not been officially closed

Please use one of the open ones in the Math Help (Available) channel group

but i can help you

what are you trying to find

.reopen

[lone heart]

✅

[rugged plover]

u make it a traingle

[pure ginkgo]

if you are trying to find the unknown length

you can use Pythagorean theorem

Please use one of the open help channels in the Math Help (Available) channel group

.close

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[serene trout]

So question 15

this is abt the power series and I did solved it out

which is r=1 and center is x=3

but when my teach check the end pts which is 2 and 4

I am confused abt how she did it?

someone pls explain

like how did she get1/2n+1

[white dock]

anyone pls

i have gotten 7/21 wrong

[acoustic sand]

Do you know the formula?

[acoustic sand]

Do you need help?

[twin nimbus]

!occupied

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[twin nimbus]

@acoustic sand @white dock ^

[acoustic sand]

yes?

[twin nimbus]

It's not Astro BugZ's channel

[acoustic sand]

Oh

Im not worried anymore anyhow im trying too do my own work

[twin nimbus]

@serene trout so you got the right answer with r = 1 and center = 3, which gives (2, 4) at least. Your teacher just also checked the endpoints to see if the series converges to the function.

She got 1/(2n+1) from (-1)^2n/(2n+1) which is just a result of (-1)^2 = 1 so this is 1^n

[serene trout]

ya I just realized I plug 2 to n instead of x

ty

.close

[twin nimbus]

Yw

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[shadow pilot]

Need help

[shadow pilot]

Ignore the work on the bottom

I split the triangle in half but how do I find the value on the line I used to split it

[stark scroll]

Do you know the sine law?

[shadow pilot]

No I haven’t learned that

[stark scroll]

Or law of sines?

[shadow pilot]

But which angle am I suppose to use first

[stark scroll]

Use the triangle with the side length you know

[stark scroll]

Wait is that angle supposed to be 101 degrees or a right angle?

[shadow pilot]

I think right angle but aren’t right angles 90 degrees

Okay

So the 101 doesn’t matter?

[stark scroll]

Wait but I don’t think you can use tan(50)=23/x

It isn’t a right angle

[shadow pilot]

I’m confused

[shadow pilot]

So what do I do?

[stark scroll]

If you don’t know the law of sines yet

[shadow pilot]

Shall I split the triangle ?

[stark scroll]

You can split the triangle

Then, you can solve for the altitude and then for x

[shadow pilot]

How to solve for the altitude

[stark scroll]

When you split the triangle, can you find the angles that form?

[shadow pilot]

Yea I think

[stark scroll]

Try it

[shadow pilot]

Sorry wrong one

Nvm

[stark scroll]

When you draw the altitude

You should note that you can’t just split the 101 degree angle in half

Instead use the fact the the sum of the interior angles of a triangle is 180 degrees

[stark scroll]

Looks good to me

[stark scroll]

Looks good to me!

[shadow pilot]

Thank you for the help! Also any tips on understanding trig word problems? I have a math test tomorrow

[white dock]

no thank you i got it

[shadow pilot]

@stark scroll

[stark scroll]

Tbh I don’t have many tips but always draw a diagram

[shadow pilot]

Thanks

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[rose sun]

I've been asked whether the maximum distance between an arbitrary point $A$ inside of an $n$ sided irregular polygon will always be the distance of $A$ and one of the polygon's vertices. Where do I start?

[ocean seal]

Väinämöinen

[rose sun]

I haven't been able to think of a single case in which that is false, but I still have no proof.

[median oar]

This sounds like you’d want to go proof by contradiction

Or contrapositive

[rose sun]

Thank you! I'll try it.

So, I thought of something;

Let $P_1, P_2, \cdots, P_n$ be the vertices of the polygon which I'll call $P$.

Let $B$ be a point on any side. $B$ is not a vertex.

Let $C$ be the closest vertex to $B$ which is farther from $A$ on that particular side. In case $B$ lies exactly halfway that side, and the distance between the two vertices of that side and $A$ are the same, let $B$ be any of the two.

Then, $d(A,C)>d(A,B)$.

Did I miss anything? I'm so new to proofwriting.

[ocean seal]

Väinämöinen

[lone heart]

@rose sun Has your question been resolved?

[rose sun]

Bro, get another channel.

[lone heart]

@rose sun Has your question been resolved?

[trail jewel]

go get another help channel bro

this is specifically in the MATH HELP (OCCUPIED) category

go to the MATH HELP (AVAILABLE) category and get a channel there or go into the #1021175428326633542

ok im not 100% sure if i explain this well or how ur going to phrase it, but think of it like if you choose a point on an edge (not vertex) then if you go towards one vertex on that edge it will get closer to point A while the other one will go further away from point A compared to the point on the edge

[rose sun]

Unless the distance between both vertices and $A$ are the same.

[ocean seal]

Väinämöinen

[trail jewel]

that can't be possible

unless it's a circle

which is not cuz there's a vertex

[rose sun]

Better yet,

[trail jewel]

well the point on the edge is not in the circle is it?

oh right u didnt talk about the edge

yea then it is still a vertex that is furthest away

[rose sun]

What about the proof though?

Does it look alright?

[trail jewel]

it works but not very understandable without the base question i think

im not sure, im bad at english

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[rose sun]

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[alpine sable]

.close

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[austere moss]

hello, can anyone help my with this question. I got an answer but I am not sure if its right please help me I gotta show this to my teacher tomorrow.
btw the angle is 35 degrees its not translating.

[long axle]

do we know if thats a right triangle?

@austere moss

[austere moss]

it is

[long axle]

ok

what have you tried?

[austere moss]

wait let my fix the picture rq

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@austere moss Has your question been resolved?

[austere moss]

first i got (sc) by doing : 25tan(35) = 17.5

then i got (ds) witch would be 25(squared) + 17.5(squared) = the root of 931.25 witch is 30.5

now i know that the angle (c) would be 90 on both sides and then i get the triangle's (s) angle wich would be 180 - (90+35) = 55

and the green (s)'s angle would be 125

now i went to the Green quadrilateral and cut it into 2 triangles By setting the diameter from s to b
and this is the part that i am not sure of witch is if i did that would the angle lets say (s) witch is 125 degrees would it be cutten into half ?

I assumed that it would so no i have the quadrilateral witch is now two triangles and the one down is right triangles ( i will send a picture of what i did)

@long axle

i still didnt finish sorry if you didn't understand idk how to translate math lol

[long axle]

i dont think u need to do all that

just find the length of ab using the angle 35 and the hypotenuse (trig)

hold on, lemme try it rq and lyk

ok u still here @austere moss ?

[austere moss]

yes

[long axle]

ok cool

so i did this just using trig and similar triangles

i didnt break it up into any more shapes

start by calculating the length of ab

[austere moss]

how did u do it

[long axle]

lmk when u get ab

[austere moss]

i already got it and i have an answer but i think its wrong

[long axle]

just tell me

[austere moss]

i got 17.5 ik its wrong

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[long axle]

for the length of AB?

.reopen

[lone heart]

✅

[long axle]

how did u get that @austere moss

[austere moss]

17.5tan(45) witch was the angle of b after i put the tri

[long axle]

dont use this anymore

just ignore that

[austere moss]

what should i use

[long axle]

we will calculate what you will use

ok

look at the big triangle

[austere moss]

ok

[long axle]

we have the angle of 35, and the hypotenuse of 70m, how do you find the length of ab

[austere moss]

i am not sure but is it 70cos(35)

sorry i suck at math but i still like it

[long axle]

no

[long axle]

no need to be sorry

before we continue with this, i recommend you watch a refresher video on sin, cos, and tan ratios so that we can get through this problem faster

https://youtu.be/O74LFU4VmlE?si=-A_0sZkCt1gFRdJb

maybe this will help

[austere moss]

i think I'll continue it tomorrow its 2 am on my time thanks for your time @long axle i will try to solve it and I'll send u my answer

[long axle]

ok

no problem

have a good one

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[fiery iris]

solve inequality
ax+1>x
where a is a parameter

[fiery iris]

this is the solution:
xe(-inf, 1/(1-a)), a<1
xe(-inf,+inf), a=1
xe(-1/(a-1),+inf), a>1

<@&286206848099549185>

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@fiery iris Has your question been resolved?

[fiery iris]

no

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[icy zodiac]

Now I'm confused on what to do after this

or if what I'm doing is even right

.close

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[dawn herald]

In these cases where the integrals cannot be solved, what should I do?

[lone heart]

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.

[dawn herald]

They are differential equation problems.

[fallen verge]

what are you told to do

send the instructions

[dawn herald]

I have to determine an explicit solution

[fallen verge]

send the instructions

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@dawn herald Has your question been resolved?

[buoyant thunder]

Use simultaneous equations boi

[dawn herald]

how 🥀

[buoyant thunder]

It’s the sussy baka shi mannn

Basically

It is the infinity

X y

It’s infinite

X is - infinite ♾️ y is positive infinite ♾️

@dawn herald do you understand

[dawn herald]

no 🥀

[buoyant thunder]

Same

Idk what tf I just said boi

[dawn herald]

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[dawn herald]

.close

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[scenic bolt]

@alpine sable Hi

[atomic herald]

help..

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[little swan]

A bag contains exactly 50 coins. The coins are either worth 10 cents, 20 cents or 50 cents, and there is at least one of each. The total value of the coins is $10. How many different ways can this occur?
A-2 B-4 C-8 D-12 E-16

[lone heart]

Please don't occupy multiple help channels.

[little swan]

ok

A bag contains exactly 50 coins. The coins are either worth 10 cents, 20 cents or 50 cents, and there is at least one of each. The total value of the coins is $10. How many different ways can this occur?
A-2 B-4 C-8 D-12 E-16

which option is correct?

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[little swan]

my question is in the process of being solved by another person

[little swan]

it has been resolved

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[smoky island]

doin some practice questions Have to find oblique asymptote of this not to sure, can someone help

[mossy laurel]

For the vertical can you solve the equation denominator = 0

[smoky island]

Yea i know how to get the vertical asympotote i just dont know how to find oblique

[winter bone]

Hi can I ask you guys a math question??

[wanton granite]

!occupied

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[smoky island]

Bro this is claimed

Get another pannel

[wanton granite]

You acquainted with polynomial division?

[smoky island]

Sorry u talking to me or this person

[wanton granite]

You

[winter bone]

How do I ask people for help on math what channel do I use I'm sorry

[wanton granite]

#help-24 is free

Any of these

[smoky island]

by polynomial division u mean long division?

im not too sure how to use that strat

[wanton granite]

Yeah long division

[winter bone]

Ok thanks

[wanton granite]

If you can do long division then basically just do it and you'll get the eqn of the asymptote lol

[smoky island]

lemme try rq

Would it be something like the whole numerator divided by (x+4) @wanton granite

[wanton granite]

There might be a faster way that I'm missing (this stuff went into matlab as soon as I got past the pure maths part of my degree)

But tbh

I'd just expand both top and bottom

Then long divide as you would any other fraction

[smoky island]

got the answer, thanks

.close

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[gray isle]

your interval includes 1/3 where the fraction would be undefined

[torpid roost]

how do i get the right answer?

[gleaming ridge]

by excluding the value of x which is causing the fraction to be undefined (1/3) 😛

[torpid roost]

so would it by (1/3,6]?

since its greater than 1/3?

not equal to or greater?

[gleaming ridge]

exactlyyy

[void swift]

when you solved the inequality by (presumably) multiplying both sides by 3x-1 you made the assumption that 3x-1 is positive

thus 3x-1 > 0 => x > 1/3

[torpid roost]

what does that mean?

[void swift]

what does what mean

[torpid roost]

what did i do wrong?

[void swift]

i didn't say you did something wrong?

i was explaining why its x > 1/3 not x >= 1/3

in addition to x being undefined at x=1/3

[torpid roost]

would this be right or do i need to do more?

[void swift]

its correct

[torpid roost]

yay

i just get confused easily thats all i think

thank you

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[strong shard]

would the answer be real because the coeffients can be any real number

[placid zinc]

I'm guessing that's supposed to be the answer, yes

Scalars don't need to be real numbers though. But your class probably treats them that way

[strong shard]

hmm Okay thank you!

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[chrome tapir]

how do you do this

[naive valley]

try computing f'(x) from the given formula

[bright hedge]

^

Then plug in those points and you get 2 variables in 2 equations

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@chrome tapir Has your question been resolved?

[chrome tapir]

@naive valley @bright hedge like this?

[naive valley]

except f'(2) is given as 5, not 6

so the third line is wrong

[chrome tapir]

sad

i missread

[naive valley]

yea i do that all the time haha

[chrome tapir]

now how do i do this

this seems a lot harder