help-33

[amber ruin]

ur teacher's high

unless its actually 3-1*(8-2*3) in which case its correct and it's probably what they meant. their writing is terrible tho

is this extended euclidean algorithm

[round magnet]

yeah I think it's a 1

[round magnet]

all I know is that it is some sort of euclidean algorithm

We are learning it very superficially

[amber ruin]

https://youtu.be/6KmhCKxFWOs
if you want to understand extended euclidean algorithm better you can watch this video, this guy seems to cover it well

[round magnet]

alr Ill give it a try, thanks

[amber ruin]

np

[marsh citrus]

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[untold wyvern]

I was doing this problem and for the case where a=0, i got x2(t)=t as a solution but the question says it has no solution, could anyone help verify? And also, the solution says assume a>=0, i did the same but im not sure where this assumption comes from

[main idol]

a^2 >= 0

So without loss of generality you can take a>=0

[untold wyvern]

how do we know that a^2>=0

[main idol]

Your solution doesn't satisfy the original DE it equals -a^2 = 0 which is degenerate

,w plot x^2

[elfin berry]

Results provided by WolframAlpha

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Requested by riemann#2529

[main idol]

Any real number squared is nonnegative

[untold wyvern]

but we don't yet know that a is real

[untold wyvern]

if we are considering the case a=0, so this reduces to 0=0 right?

[untold wyvern]

but even aside from whether a>=0 positive, my bigger question would still be whether this is wrong or not. Since the solution manual says that x2 dne if a=0

<@&286206848099549185>

[marsh citrus]

@untold wyvern Has your question been resolved?

[marsh citrus]

@untold wyvern Has your question been resolved?

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[marsh citrus]

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[marsh citrus]

Please don't occupy multiple help channels.

[river summit]

Would question 1 be 7

Just making sure

[rugged cobalt]

not only 7

[bright jay]

You already have #help-19, don't open multiple channels

[river summit]

How do i close it

[bright jay]

.close

[river summit]

y=7?

I mean x

[rugged cobalt]

7 works

but 2 * 8 = 16 works aswell right

16 is also bigger than 14

[river summit]

No but the sign is equals right?

This thing means equals

[rugged cobalt]

$\geq$ this?

[river summit]

What

[elfin berry]

Køter

[river summit]

Yes

Thatt means equals

Doesnt it

[rugged cobalt]

it means equal OR greater than

[river summit]

Oh

Im just gonna put 7

[rugged cobalt]

what

you have to put all x

that works

[river summit]

I thought 7 was right?

[rugged cobalt]

7 is just one x that works

[river summit]

Wdym

[rugged cobalt]

8 works aswell i just told you

[river summit]

K

[rugged cobalt]

what else works?

[river summit]

Anything greater than 7?

[rugged cobalt]

yes

how do you type that

[river summit]

Wdym

[rugged cobalt]

as an inequality

[river summit]

7 < x?

[rugged cobalt]

yes but 7=x works aswell

so not just greater than

but greater than OR equal

$x \geq 7$

[elfin berry]

Køter

[marsh citrus]

@river summit Has your question been resolved?

[marsh citrus]

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[still temple]

How do I move it

How did u get -3x

This what I did

[quasi minnow]

-3k*

f(-3+)=f(-3-)

[still temple]

Where u get 6k

[quasi minnow]

Factorize

[still temple]

3(k^2+k-18)?

Where the 6k

@quasi minnow

[quasi minnow]

3k=6k-3k

Or simply use quadratic formula

[still temple]

I did my factoring wrong

So if it’s continuous both the x should be the same?

[quasi minnow]

Yes

[still temple]

Bruh what

I got 6 and -9

@quasi minnow

[quasi minnow]

This is correct

I seem to have made some mistake

[still temple]

@quasi minnow how I find derivative of -x/y

[quasi minnow]

Write the full function

[still temple]

?

That’s first

Now I have to find second

[quasi minnow]

d2y /dx2 = - [ y-xy']

[still temple]

?

[quasi minnow]

-[y- x dy/dx]/ y^2

[still temple]

I need@to show the steps

Do I use quotient rule

.close

[marsh citrus]

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[rich sluice]

I'm trying to proof a theorem with coq, and I exhausted google and DallE to the maximum it can't help me further on the coq side.. so I'm guessing my problem lies in the idea of the proof itself?

The Theorem:

Theorem split_after_combine_iff : 
    forall (X Y:Type) (l1 : list X) (l2 : list Y),
    split (combine l1 l2) = (l1, l2) -> (| l1 |) = (| l2 |).

Definitions of combine and split:

fix combine (l : list A) (l' : list B) {struct l} : list (A * B) :=
  match l with
  | [] => []
  | x :: tl =>
      match l' with
      | [] => []
      | y :: tl' => (x, y) :: combine tl tl'
      end
  end

fix split (l : list (A * B)) : list A * list B :=
  match l with
  | [] => ([], [])
  | p :: tl =>
      let (x, y) := p in
      let (left, right) := split tl in (x :: left, y :: right)
  end

The core point why the lengths has to be the same, is that if they're not combine will drop elements. so I thought this should just sort itself out in induction over l1 and l2. and the cases for either l1 or l2 being an empty list are trivial. The last case where however where l1 and l2 are not empty seems to be hard. It feels like I'm ending up where I started PLUS that the usual replacing part in basic induction proofs doesn't work cause goal and hypothesis are flipped?

[marsh citrus]

@rich sluice Has your question been resolved?

[rich sluice]

<@&286206848099549185> coq expertise or basic induction knowledge required 🤪

[marsh citrus]

@rich sluice Has your question been resolved?

[marsh citrus]

@rich sluice Has your question been resolved?

[marsh citrus]

@rich sluice Has your question been resolved?

[marsh citrus]

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[marsh citrus]

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[void patio]

can someone explain to me the transformation they did with sin(alpha-pi/2)/cos(alpha-pi/2)?

[lusty ermine]

tan(x)=sin(x)/cos(x) right?

this is true for any input other that x

so also for a-pi/2

and

then they use opposite angles, and complementary angles.

[main idol]

how'd you get this?

for this fraction

also i don't follow where this came from

[void patio]

this is the given solution

so I am also trying to understand it

i have no clue

[main idol]

is this not the only thing that's given?

[void patio]

yes

that's the whole question

[main idol]

the solution says "Your score is 0 points" what does that mean?

[void patio]

that my answer is wrong haha

i just put a random number to see the solution

[main idol]

but you're saying it's the given solution

can you separate what's given and what's your work

[void patio]

all of it is what's given

just when i type my answer and if it's wrong, i get the correct solution and score 0 points for my wrong answer

first pic is the question, second pic is solution

nothing is my work

[void patio]

doesn't sin (a-pi/2) equal cos not cos (a-pi/2)?

and same for cos(a-pi/2)

[main idol]

yes

[void patio]

so how did the get cos(a-pi/2) / -sin(a-pi/2)

[main idol]

no idea. probably a typo in solution

[void patio]

i don't think it is tho

because the other question that are the same but with different values for tan (a) have the same type of solution

questions*

[main idol]

it is a typo

[main idol]

you pointed it out yourself here

[void patio]

okay then ignore the solution

do you have an idea how to solve the question

[main idol]

fix this with what you pointed out

using the correct cofunction identities

then use tan(a) = 2

[void patio]

so i have tan (a-pi/2) = cos(a)/sin (a), and i also have that sin (a)/cos(a) =2

what can i do with that

[main idol]

.

you have a missing minus sign somewhere i can't find

[void patio]

right cause the formula is pi/2 - a

i'll try to find i t

[main idol]

oh this should be -cos(a)

[void patio]

yes

so tan (a-pi/2) = - cos(a)/sin (a)

and sin (a) / cos (a) = 2

can this be solved any further?

[main idol]

yes

compare the two previous equations

do you know $\frac{1}{\frac{a}{b}} = ?$

[elfin berry]

riemann

[void patio]

b/a

[main idol]

good good

[void patio]

yeah, i got -1/2

thanks

a lot

.close

[marsh citrus]

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[frosty knot]

is ΣUn divergent or a convergent series

i tried Cauchy, d'Alembert, absolute convergence..

[tacit fjord]

it seems to me you want to compare it to (-1)^n (n^-.5) in some way

[marsh citrus]

@frosty knot Has your question been resolved?

[main idol]

did you use @tacit fjord 's hint yet

compare => comparison test

[marsh citrus]

@frosty knot Has your question been resolved?

[marsh citrus]

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[still pumice]

A square ABCD (0, 0) (1, 0) (1, 1) (0, 1) rolls counterclockwise along a right-angled wall corner. What is the trajectory equation of point B?

[marsh citrus]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[still pumice]

<@&286206848099549185>

[leaden monolith]

!15m

[marsh citrus]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[odd turret]

what step are you on

[leaden monolith]

Does it mean there’s a wall at x=0

[still pumice]

yep

[leaden monolith]

And the square is rotating upwards?

[still pumice]

yes

[still vortex]

can you describle what you mean by rolling along a right-angled wall?

[leaden monolith]

Think about what constraints you have on this movement

[odd turret]

||could you draw it||

[leaden monolith]

You know the wall is solid

The square is solid

So the distances between things on the square is always the same

Where is the square going to pivot off?

I assume the square doesn’t slide

Otherwise it’ll be too hard for me to do

[gusty oasis]

I know it personally - jk

[still pumice]

like that

[still vortex]

oh ok

[gusty oasis]

nice visualization

[odd turret]

thanks maybe

[leaden monolith]

Oh dear

[gusty oasis]

question doesn't seem easy

[leaden monolith]

That’s got some wack constraints I would have to think about

[gusty oasis]

as you have to account for the square being pushed away by the wall

[leaden monolith]

It’s a related rates problem I think

[gusty oasis]

it's probably the best to presume an angle on the wall theta

[leaden monolith]

You just have to consider how the points D and A move

[gusty oasis]

and then calculate B's coordinates accordingly

[leaden monolith]

When you know that you can find out B

I would say make a parametric equation for the points but I’m not too familiar with this type of question

[still pumice]

AD is basically moving on the axis

[leaden monolith]

I know but the rate at which A moves depends on D

[leaden monolith]

And depends on the angle

So you can parametrise the points to the angle

Or do it all on 0, 1 interval for some t

[leaden monolith]

That’s a pretty cool problem I’ll attempt by myself when I got some time

[still vortex]

$B$ should equal to $(\cos\theta+\sin\theta,\cos\theta)$ where $\theta=DAO$ and $O$ is the origin

[elfin berry]

Math Is Fun

[gusty oasis]

and then you'd need to do likewise for the rest of the points

[gusty oasis]

I think height is sin(theta)

if you chose the same angle as me

[still vortex]

I used ∠DAO for the angle

[gusty oasis]

ah good

that would only parameterize the first 90 degrees spin

for the rest you do likewise

(you can parameterize A,C,D on this same diagram btw and it would apply to B due to symtery)

also if you knew how fast the spinning goes, you could replace theta with a time parameter

[marsh citrus]

@still pumice Has your question been resolved?

[still temple]

You know... Something fun about this is that we can go from (sin(t)+cos(t),sin(t)) to x^2-1=sin(2t), y=sin(t)

[still vortex]

what is $s$?

[elfin berry]

Math Is Fun

[still vortex]

oh wait I misread it

[still temple]

How the frick

Oh same

[still pumice]

yeah its the same

[still temple]

That's not what I meant but sure

[still pumice]

uh what could I do next…

[still temple]

Where is that 1-s coming from?

[still pumice]

The side length of this square is 1

[still temple]

Yes, then what?

[still pumice]

so…distance from D to 0,0?

[still temple]

That's what I thought you were thinking

But it's incorrect

Yes, the sidelength is 1, but what you're thinking about is not the sidelength

[still vortex]

is the question you posted the original question?

[still pumice]

yes

[still vortex]

ok

[still temple]

if you look here, the bottom red part is actually longer than the square's sidelength

Still no

The problem is that 1

What you're picturing is not in fact the square's sidelength

What you're picturing is the bottom red part in the image

1-s is not the distance from the origin to D

[still pumice]

oh i got it

sqrt 1-t^2

[still temple]

By the way, MIF basically just gave out the answer

[still temple]

s^2*
Other than that, you got the idea

[still vortex]

I think he's looking for the answer with s as the parameter

instead of theta

[still temple]

Assuming pronouns?? no way ❌ that's like wtf

[still vortex]

what

[still temple]

he

[still vortex]

oh

[still temple]

EXPOSED

Alright sorry

[still vortex]

ok I'll call QAQ next time

for $B$ in terms of $s$ is $(s+\sqrt{1-s^2},s)$

[elfin berry]

Math Is Fun

[still temple]

@still pumice Can you send your current solution?

Alright gotta go, good luck to MIF to explain why trigonometry is unnecessary here

[still pumice]

thank you all//

.close

[marsh citrus]

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[marsh citrus]

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[night shale]

Please help!

[night shale]

Im am fully stuck please help someone fast

@marsh citrus can you help

[proper zodiac]

#help-12

.close

[marsh citrus]

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[night shale]

.close

[hazy lion]

parenthesis error

youre calculating $\frac{50.3}{4}\pi$

[elfin berry]

jan Niku

[marsh citrus]

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[cold sequoia]

Ur girl back on her can't do calculus arc. Partial integration with this funky problem

This is how he wanted us to start it in class but like thats a lot of terms and less to work with

[whole sleet]

That's messy for sure. I don't think the "plug in a value for x" method works very well here

[cold sequoia]

Real

[cinder dune]

Try long division on (x^3 + x^2 + 1) / (x^2 + 1) maybe.

,w Long division (x^3 + x^2 + 1) / (x^2 + 1)

[elfin berry]

Results provided by WolframAlpha

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Requested by jimmy1234#2729

[cinder dune]

And you can get lower degree of rational function integration to work with 🙂

[cold sequoia]

Yeah but like the whole point of the activity is partial fractions

[cinder dune]

If the point is to solve for the integral instead, I don’t think blindly applying partial decomposition into a giant monster is the smartest way in doing so 🙂

[cold sequoia]

Real

It's not the smartest but alas, all well

Ohh but I see what u mean with the long division part

I am forcing it to work with this but HEY there's technically fractions in there

Ty

.close

[marsh citrus]

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[safe briar]

Hey guys, thanks for your help with the question I asked before this one. I'm now trying to compute the probability that I will roll 4 dice such that the numbers 1,2,3 and 4 show up in the outcome. I think the answer is
$$4!\cdot \left(\frac{1}{6}\right)^4 = \frac{1}{54}$$
but I'm not entirely sure if it's correct because the order doesn't matter

[elfin berry]

_Kookie

[still temple]

I remember explaining this before... It's a bit counterintuitive but you have to consider order because it doesn't matter

There's a difference between "1,2,3,4 and 4,3,2,1 are counted as the same" and "1,2,3,4 and 4,3,2,1 are both valid outcomes"

If it was the former then it would just be (1/6)^4

But because it's the latter you need to count them separately

Think of it this way: The order doesn't matter for determining whether an outcome is valid or not, but it does matter for counting them up

So, in short, you have the right answer

[safe briar]

I see

thanks

.close

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[wanton quartz]

Please help me to solve the skill competency, the number 1 and explain it to me how to solve it and how it works thank you

[wanton quartz]

[proper zodiac]

Looks like a misprint, there are supposed to be two equations

You can just about see the top of the second equation hidden behind the 2nd question

[wanton quartz]

Oh?

My teacher just gave me that should I tell her there's something wrong with it?

How should I tell it lol

[proper zodiac]

Tell her there is a printing error on the first question

[wanton quartz]

Thank you but is the 2nd question? Is there also a mistake

Or I'm I able to solve it?

.close

[marsh citrus]

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[gaunt yarrow]

hello, I have a probability problem I am trying to solve (it is for a hobby, I am not studying probability)

the problem is basically, I am calculating for the probability of a certain status effect happening when I shoot an enemy with a gun for a game I play.
the gun shoots 3 projectiles with a 30% chance to shoot a fourth per shot, and each projectile has 3 independent chances to proc the status effect.

the 3 independent odds of procing status are 30%, 12.727272...%, and 6.363636...% (per projectile)

If i wanted to set up a xy graph to show the total odds (chance, y axis) against the total # of status effect (times it happens per shot, x axis), how could i set up an equation for this? (im using google sheets to set up equations)

what if i wanted to graph it on a xyz plane where z is also # projectiles?

[gaunt yarrow]

also, how sould i calculate the average amount of status procced per shot

if the events are independent, do i just add them together take that % of 3.3 (avg projectiles per shot) to find average status per shot or some other way

[hazy lion]

youre saying the fourth shot doesnt have a chance, right

[whole sleet]

The fourth shot has a 30%, a 12.7%, and a 6.36%

[gaunt yarrow]

each shot shoots 3 projectiles but theres a 30% chance of the gun firing another projectile in the same shot

each projectile has a 30%, 12.727272...%, and 6.363636...% chance to proc a status effect

[hazy lion]

ah

[gaunt yarrow]

hypothetically one projecile could proc it 3 times

[whole sleet]

Does proccing multiple times matter?

[gaunt yarrow]

wdym

[whole sleet]

Ah it does

[gaunt yarrow]

everything is independant from one anohter i think

[whole sleet]

So for example, the probability that you get two procs:

• Find any way two procs can happen
• Multiply the success of those two procs, and multiply the failure of every other proc to get the probability two procs can happen that way.
• Sum all probabilities where two procs can happen

[gaunt yarrow]

why multiply

wouldnt it be add them all and div by adding all other options

o

wiat

so the problem is i need to make a automated way to do this in sheets

is there a mathematical way to express all the ways 2 proc can happen

and use that in another equation to solve for probability

[whole sleet]

A tree diagram is a helpful way to think about it

[gaunt yarrow]

ye

[whole sleet]

Just, your tree diagram is going to be massive and messy.

[gaunt yarrow]

no way i ahve to do that manually right

[whole sleet]

You can get exact answers with a program, I wouldn't try it by hand, haha

[gaunt yarrow]

:c

hmm

i think

idc about the individual possible combinations

i can solve for the negative result

the odds of them not happening

but

since they are independant

am i supposed to add ot multiply their probability

when its like not really and or or

[whole sleet]

An easier way to think about it:
Imagine it shoots 9 or 12 bullets, each has a single chance of proccing

That should be essentially the same, no?

[gaunt yarrow]

if its a tree diagram

and each branch was a diff color based on how much or how little status proced

would there be a easier way to count up the number of branches in each color

bc then u can just divide by the total number of branches for probability

or wait

if thats the case then they are additive

since each main branch has the same proportion of colors

wait

ok brb

[marsh citrus]

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[marsh citrus]

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.reopen

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✅

[gaunt yarrow]

how do you find the odds that exactly 1 event of 3 independent events happens, when they have different probabilities

if i open three boxes, a b and c, and a has a 30% chance to contain a item, b has a 12.72% chance, and c has a 6.36% chance, what is the likelyhood i will only have 1 item after opening all 3

what about 0, 2, or 3 items? how do i solve for this

[marsh citrus]

@gaunt yarrow Has your question been resolved?

[marsh citrus]

@gaunt yarrow Has your question been resolved?

[whole sleet]

@gaunt yarrow
Probability the item is only in the first box:
(0.30)(1 - 0.1272)(1 -0.0636)

Do the similar thing to find the probability the item is only in the second box

And again to find the probability the item is only in the third box

Then sum all three cases.

That's the probability you get exactly one item upon opening all three boxes

Your gun question earlier is the same, except there's 12 checks, not 3 checks.

[gaunt yarrow]

if i did this two times in a row

would the odds i still only have one item be the odds i had previously squared

because

https://i.imgur.com/hruR4WF.png

leftmost column = items aquired

top row = times attempted

same probabilities I solved the first column manually but am unsure how to proceed

to me it makes sense that for example to get the odds of 2 items after 2 attempts = odds of getting 1 item * odds of getting 1 item + odds of getting 0 item * odds of getting 2

but this method doesnt add up to 100% when you fill the whole column

[whole sleet]

If we're repeating it, we can use the binomial distribution.

[marsh citrus]

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[marsh citrus]

Please don't occupy multiple help channels.

[little mortar]

I'm trying to understand z-tables but like even in this example. 1.96 isn't anywhere on the p value table so I don't understand how it can be the critical value

[main idol]

i'll close your other channel

[little mortar]

Nah id rather close this one

@main idol

[main idol]

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[viscid knot]

How to solve cos 5pi/8

[whole sleet]

Do you have any more specific instructions?

That's not a special angle so that causes some problems

[tight furnace]

Could be done using half-angle identities

[marsh citrus]

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[viscid knot]

How

[marsh citrus]

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[calm jungle]

m = tan(theta)
if i am tryna find the angle of two lines, ill sub in the gradient and get theta. my question is do i subtract 180 - theta?

[main idol]

Depends

What angle do you have exactly

And what angle are you looking for

[main idol]

Yea so the angle at BC is less than 180

[calm jungle]

oh yea, so then you subtract 180, right?

and if b is the red line, you wouldnt need to subtract 180?

@main idol

[marsh citrus]

@calm jungle Has your question been resolved?

[main idol]

Depends

[main idol]

What is m here

And what is the theta in the picture

[marsh citrus]

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[scenic depot]

Let f(n) denote number of elements a in group Z^*_n, such that a^{-1} = a

[scenic depot]

Now which of the following statements is real:
a. there exists n > 3 such that f(n) is an odd number
b. f(n) = 2 for n > 3
c. f is unbounded

I struggle to comprehend what n in f(n) even stands for, what's the input to the function, a group an element or what?

[cinder dune]

$Z^*_n$ denotes the set of elements that have multiplicative inverse in $Z_n$. For each natural number n, we can map n to the number of elements s.t. $a^{-1} = a$, and the question just name such mapping as $f(n)$.

[elfin berry]

jimmy1234

[scenic depot]

Okay, but how is $n$ related to the number of elements $a$?

[elfin berry]

szahu420

[scenic depot]

Sorry, today was the first lecture about group theory and I don't really get anything yet

Also that does the notation mean, is Z like a reserved name or is is just some name, I assume the start denotes the group operation but what is n, is it the same n as in f(n)?

[scenic depot]

Could you maybe elaborate or show an example please?

<@&286206848099549185>

[marsh citrus]

@scenic depot Has your question been resolved?

[scenic depot]

<@&286206848099549185>

[scenic depot]

<@&286206848099549185> s

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[near tapir]

is it possible to integrate n!

[devout mauve]

you can extend the factorial to the gamma function

which "connects" the points of the factorial function in a certain nice way

and then you can integrate that

[still temple]

Double integral

[devout mauve]

well at least you can integrate it numerically

[near tapir]

I'm sorry, whats gamma function

[still temple]

POV: Random mathematician deciding it'll be z-1 instead of just z because to anger random math enthusiasts for millenias to come

[near tapir]

ok I give up xD i was expecting something more basic for my brain

.close

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[empty nova]

Help please

[unreal oyster]

Nonlinear of course!

Polynomials of degree 1 are linear functions

[marsh citrus]

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[empty nova]

Thanks

[marsh citrus]

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[forest stump]

stuff like this i can slice up really fast

but what to do in this case

i tried both gauß and sarrus here

need to show for what t these 3 Vektors are linearly independent

[twilit grove]

did you learn Laplace expansion?

[forest stump]

yeah

[twilit grove]

actually nevermind that won't be used here

[forest stump]

yeah Laplace usually gets used at big matrices with many 0's

[twilit grove]

well you want the the diagonal elements to equal 1

it'd be easier if you got rid of the "t" in row 2, column 3

[forest stump]

i mean are there any other methods?

or does this have to be a solution with ^2

[twilit grove]

it's possible, yea

[marsh citrus]

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[eternal shadow]

hi

[cobalt sentinel]

<@&268886789983436800> this guy is a weirdo!!!!

[viscid dirge]

.close

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[proud sky]

What is skewed data and outliers?

[marsh citrus]

Please don't occupy multiple help channels.

[proud sky]

<@&286206848099549185>

[marsh citrus]

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[desert prairie]

For question 28 is what I did mathematically correct

[desert prairie]

Mainly between line 5-6

Ok

So I’m basically trying to prove that n=k+1 is true

[elfin berry]

marc

[desert prairie]

But on lines 4

I could divide it all by 9 since 3(6k)

So I decided to turn the 6k

Into 3x3k

Then timed the 3 by -3

Do u understand the part I explained ?

[midnight relic]

For as core pure to get any marks on this type of question you need heading for each part for working

[desert prairie]

Yea I forgot about that

I’m basically doing what the induction part

I’m doing is proof by induction btw

[midnight relic]

For me the heading help alot as i go along it reminds me where i am

So prove n=1 is true

And so on

[marsh citrus]

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[elfin berry]

marc

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[gray shale]

An idea to calculate this determinant?

[gray shale]

A[i,j] = a_i - b_i

[marsh citrus]

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[frosty thicket]

My answer is

$-6x³sinx+18x²cosx-4xcosx-4sinx-5cscxcotx$

[elfin berry]

Sterling

[frosty thicket]

Is this correct?

If that's correct, is there anyway to simplify it or is that the final answer

[silk haven]

um whats the question

[frosty thicket]

derivative of trigo functions

[frosty thicket]

Here's the question

[silk haven]

so what's the question?

that's just a function

[frosty thicket]

I mean this is the question

[odd turret]

could just plug it into a calcuator

[frosty thicket]

no

[silk haven]

desmos

[frosty thicket]

like I mean lowest terms

[odd turret]

y

[silk haven]

jk i havent learned any calc yet, sorry

[odd turret]

could you show your work

:/

[frosty thicket]

ok wait

[stark trail]

no you are forgetting to apply the product rule

[frosty thicket]

I did apply the product rule

[stark trail]

oh ya

[odd turret]

just wait for the work

[stark trail]

didn't really look

[frosty thicket]

@odd turret hi

[marsh citrus]

@frosty thicket Has your question been resolved?

[frosty thicket]

<@&286206848099549185>

[lavish kestrel]

yeah your answer seems to be right

looks good

I mean there is simple simplifying by just combining like terms with respect to sinx and cosx

other than that no I think that's about as simplified as it would be

[marsh citrus]

@frosty thicket Has your question been resolved?

[frosty thicket]

No lowest terms?

[marsh citrus]

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[celest plinth]

1420ft
2
(
1ft
0.3048m
​
)
2
=132m
2

[celest plinth]

1420ft^2 x (.3048m/1ft)^2 = 132m^2

how is that possible when i get 432.8160

[deft apex]

,calc 1420 * (0.3048)^2

[elfin berry]

Result:

131.9223168

[celest plinth]

but if ft is squared doesnt that cancel out?

[deft apex]

,calc 1420 * (0.3048)

[elfin berry]

Result:

432.816

[deft apex]

Youre forgetting to square

[deft apex]

No

[celest plinth]

oh

may i ask why

[deft apex]

?

Right now the dimensions are

[ft^2] * ([m]/[ft])^2

[celest plinth]

oh my god

[deft apex]

Which is the same as [ft^2] * [m^2]/[ft^2]

Thats where youre left with youre [m^2]

[celest plinth]

the ft^2 is referring to the dimensions while the other is for multiplying

[deft apex]

ft^2 sure, but even if you had some number squared, it would really ‘cancel’ just because youre multiplying it with another thing that is also being squared

[celest plinth]

okay i see now

thanks so much

✅

[marsh citrus]

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[chrome mango]

can someone help me with this?

[marsh citrus]

Please don't occupy multiple help channels.

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[late geode]

practice

get comfortable with doing it on paper first

before attempting to do it in your head

refer to what i typed above

comes with practice

doing enough addition/multiplication you'll have a decent idea of the approximate size of your values

what table

oh,

doesn't really matter

[marsh citrus]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[humble nebula]

you can try practicing lots of questions and seeing what you get wrong

deliberately

[marsh citrus]

@still temple Has your question been resolved?

[twilit grove]

prove what?

and what is your first step?

I mean what did you do for the first step

separated them into 2 fractions?

also, don't use "x" for multiplication. it is confusing since there is the variable "x"

that's unfortunate

anyway, you don't need to write it as a multiplication like that, unless it helps you

use the definition of cosecant

get a common denominator first, then add the 2 terms together

then you'll have the numerator divided by a fraction

yes, so working with the denominator, make that into a single fraction

you have $1 + \frac{1}{\sin{x}}$ in the denominator. how would you simplify it?

[elfin berry]

cwatson

[twilit grove]

yes. now you have $\frac{1 + \sin{x}}{\frac{\sin{x} + 1}{\sin{x}}}$

[elfin berry]

cwatson

[twilit grove]

exactly

[marsh citrus]

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[restive blaze]

i have this formula and want to make the pattern repeat x amount of times e.g. if x was 3 tye formula would be the image i sent

[proper zodiac]

,rccw

[proper zodiac]

summation notation is your friend

[restive blaze]

how would i use it in this context

[proper zodiac]

$\sum_{n = 0}^{m} \frac16 \left(\frac56\right)^n$

[elfin berry]

ΣAC

[proper zodiac]

m is the number of terms you want

[restive blaze]

right

so if i were to square the answer would the brackets to do so go around the symbol thing or not

[proper zodiac]

you wanna square this?

[restive blaze]

yeah

[proper zodiac]

yeah the brackets would go around the entirety of this

[restive blaze]

thanks

[marsh citrus]

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[silk haven]

A fair 6-sided die is repeatedly rolled until an odd number appears. What is the probability that every even number appears at least once before the first occurrence of an odd number?

A: 1/120 B: 1/32 C:1/20 D:3/20 E:1/6

source: 2021 AMC 10B, problem 18

[silk haven]

can someone help me understand the solution?

[elfin berry]

starlight

[silk haven]

why can we ignore every single other case, where something like 4 appears twice, and go straight here?

P.S. please no precalc level/calculus explanations

ping me if you have a response

nevermind i get it now

!close

.close

[marsh citrus]

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[humble crest]

Can someone help me with this. I seem to be getting the wrong answers

[humble crest]

so I need theta by itself so i multiplied each side by sin-1

then I get theta=sin-1(-0.5592)

or is that wrong

[lucid zenith]

you dont "multiply" both sides by sin^-1

you take the inverse sin on both sides

but you are right

[humble crest]

oh okay, wrong terms but right idea?

I put in -34 but I got it wrong

[lucid zenith]

you wrote the correct expression

[lucid zenith]

well

you need the angle to be in the 4th quadrant

[humble crest]

isn't Q4 of sin negative?

[lucid zenith]

technically you are right

try adding 360

maybe it wants a positive angle

[humble crest]

oh well I can't anymore 💀 that was my last attempt but I'll try again when I redo this study guide

thank you

.close

[marsh citrus]

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[lucid zenith]

you should also try giving more than 0 decimal places in your answer

unless it tells u to round to a particular no of decimal places

[humble crest]

neareast tenth but like the last 2 decimal places are 0's

so yeah

[marsh citrus]

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[knotty trellis]

If S is a set of all numbers in form of an % b for constant a and b and some integer n, and T is set of all numbers in form of m*gcd(a,b) % b (m is an integer), prove that for any integers a and b, T=S.

I suppose I will have to prove that every element in T is also in S, and every element in S is also in T. But im not sure how to do that

[knotty trellis]

btw is that question worded correctly?

[devout mauve]

did you ask that question in a different form a few days ago or was that someone else?

that if you go through the multiples of a mod b you get all the multiples of the gcd

[knotty trellis]

Oh yeah, it was me. Sorry, I completely forgot bout that and I still have this question unanswered in my notes for some reason. I will check your previous answer, tysm

.close

[marsh citrus]

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[knotty trellis]

Oh yeah, ic now. I will write it down imidiately so I dont forget it

[devout mauve]

np easy to forget stuff like this

[marsh citrus]

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[gray shale]

how can i prove that the series $\sum cos(n)$ diverge

[elfin berry]

Max.cc

[stoic saddle]

what convergence tests do you know of for series

whats the simplest one and the first one you learn

[gray shale]

hum with an equivalent?

[stoic saddle]

no even simpler

what can tell you definitively that a series diverges

[gray shale]

trying to minor it with a diverging series

[stoic saddle]

no, even simpler

for $\sum u_n$ to converge, a necessary condition is that $\lim u_n = 0$.

consequently, if $\lim u_n \neq 0$ (whether because it equals something else or fails to exist), then $\sum u_n$ diverges.

[elfin berry]

Ann (glomed)

[gray shale]

ok i remember that there's a sens where it is wrong

[stoic saddle]

??

you have a counterexample to this?

[gray shale]

well the series 1/n tend to 0 but it's divergence

[stoic saddle]

do you claim that this contradicts my point?

because it doesn't...

i said u_n -> 0 was a NECESSARY condition for convergence! i didn't say it was SUFFICIENT (and in fact it isn't sufficient)!

[gray shale]

ah ok it got it

and it's exactly the same with sum of sin(n), right?

[main idol]

No

[gray shale]

it's not converging to 0 too

[stoic saddle]

yes, sin(n) does not approach 0

[devout mauve]

is there any easy way to see that? which doesnt involve handwaving?

[main idol]

Not trivial, but you can find a contradiction to the Pythagorean theorem

[marsh citrus]

@gray shale Has your question been resolved?

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[summer karma]

if i have a function

[summer karma]

f(x,y)

with (x,y) = (3,9) then f(x,y) = 90

[silk haven]

wdym

[summer karma]

(x,y) = (4,2) then f(x,y) = 20

[silk haven]

f(3,9) = 90?

[summer karma]

could i figure out a function f(x,y) using elementary operators

[silk haven]

ok nvm i havent learned this math yet

sorry

[fathom ridge]

I mean sure

ax + by = 90
ax + by = 20

Plug in x, y and solve

[summer karma]

i forgor

mb

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[gray shale]

there's something that i don't get
i'm using the alambert criteria on the series sum of 1/n!

so u(n+1)/u(n) = n+1 wich is >1 so 1/n! diverge but it's not the case

[stoic saddle]

can you state the d'alembert criterion in full?

[gray shale]

lim u(n+1)/u(n) = L
if L > 1 then it diverges

[stoic saddle]

also is u(n+1)/u(n) really n+1?

[gray shale]

ye it's maybe because it can't say it's L

wait no

[stoic saddle]

because i think it is 1/(n+1) and you messed up.

[gray shale]

ah ye

thx

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[marsh citrus]

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[still temple]

can someone explain how 2+2 is 4?

and not 3?

[viscid dirge]

dont troll.

[marsh citrus]

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[digital raven]

How would you go about this>

[digital raven]

I made two equations (NOT related to each other)

5w + 3v = w + v + 50
13v - 20w -30 = w + 4v

so equation 1 is 4w + 2v = 50
equation 2 is 9v - 21w = 30

what do i do from here?

[quaint raft]

ah, you can either use the substitution method or elimination method. Are you familiar with those?

[digital raven]

yes

but how will you substitute?

theyre not related to each other...

ohhh wait nvm i got it

[quaint raft]

ah, good

[digital raven]

since the values of w and v are same in both equations, we can use both equations to find their values

right?

[quaint raft]

yup

[digital raven]

thanks!

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[rose heart]

hi

[rose heart]

im doing boolean algebra

I had to simplify this question

`(A ^ B) ^ (`A V B) ^ (`B V B)

which I changed to

!(A * B) * (!A + B) * (!B + B)

!(A * B) * (!A + B) * 1

I used demorgans law on !(A * B)

to get

(A + B) * (!A + B)

B * (A + !A)

B *(1)

then B

is this correct?

[chilly coral]

Not sure why you switched notations but oh well

!(A * B) = (!A + !B) 😳

[rose heart]

It makes more sense to me

[rose heart]

so demorgans law just changes things around. It doesnt literally negate the not 🤔

the video im watching makes it seem like it can remove the nots but adding more nots

[chilly coral]

Yes you can think of it as expanding the bracket and putting the nots inside

but you must remember to switch "and" and "or"

[chilly coral]

it does help simplify though

[rose heart]

I see 🤔

[rose heart]

thank you c:

[chilly coral]

yw :)

[rose heart]

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[marsh citrus]

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[gilded turtle]

why is this reasoning wrong?

[gilded turtle]

.cloose

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[marsh citrus]

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[gilded turtle]

i had an epiphany nvm

yea lmao

ty

the way you solve it is this btw: complete the square

(3cos2x - 2)^2 + 3

no thats trivial

lol

anyways we must minimize mod 3cos2x - 2

as 0 <= cos2x < = 1
0 <= 3cos2x <= 3
-2 <= 3cos2x - 2<= 1

clearly, least value of mod(3cos2x-2) = 0
so least value of f(x) = 3

[marsh citrus]

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[oblique coral]

How do I find bc using trigonometry like double angle identities if possible

[desert socket]

write two equations for BC

then use

[oblique coral]

Lemme try

Is the question possible to do no calc?

Got it thank you-

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[raw grove]

I hate how dead slow I am with mental arithmetic - anyone have advice on how I can improve? I thought about just inventing excercises, but my issue lies more with transforming expressions, such as simplifying radicals and fractions.

[still temple]

I just find the outer most operation, do the inverse, then simplify the same values. or sth similar

[fervent cairn]

for me it all comes down to practice.

[green scaffold]

I personally discovered that mental exercise as well as a sorted mind is very helpfull

[humble mortar]

With addition try to round stuff to the nearest ten and account for the changes you made

Thats what I do

Just manipulate the numbers and split them up as much as you can to make the problem easier

[raw grove]

What about practicing something like factorization?

[humble mortar]

Really just repetition

[raw grove]

you just write down a complex expression and then try to factor it?

[humble mortar]

Well like 66 + 83

Same as 60 + 80 + 9

Which is 149

[humble mortar]

And yea

Or just look for practice sheets online

[raw grove]

I'm talking about things like partial root extraction 😄

[marsh citrus]

@raw grove Has your question been resolved?

[marsh citrus]

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[marsh citrus]

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[vagrant dagger]

I would just like to know if someone could translate this score to act score

So I think this classifies as “math help” because I need help understanding my accuplacer score on math

[main idol]

It really isn't a math question. Google the test name and convert ACT in the query

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[still temple]

can any1 explain the assumptions and stuff

i think i heard somewhere that a has to be 1 or something

[devout mauve]

for some reason they factored a out of the expression? not sure why. not the standard way to write it

now this isnt valid anymore for a=0 (not that a=0 is a difficult case)

[still temple]

ofc

[still temple]

whats the standard way

[devout mauve]

oh wait I didnt see n in Q. then I suppose it makes sense

cause for that most of the time you write (1+x)^n

and then (a+b)^n = a^n (1+b/a)^n reduces to that

you need |b/a| < 1 for this to converge

[still temple]

ok

yeah

[still temple]

typically i do that

i dont want to deal with the a^n

i made this equation into y^2+4y-3=0

where y = 2^x

where did i go wrong

then i solved for y and then solved for x

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[harsh dune]

I need help

If this seems to be write

As well as this problem

[marsh citrus]

@harsh dune Has your question been resolved?

[chilly mango]

Simplify it.

[marsh citrus]

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[nimble mason]

Q10: This model is formed of a pyramid on top of a prism, and its total height is 22 inches. Which has a
greater surface area, the prism or the pyramid?

[marsh citrus]

Please don't occupy multiple help channels.

[nimble mason]

Q2: If a part of a cube, whose edge length is 7 cm, is cut to form a cuboid with side lengths of 3 cm, 4 cm,
and 4 cm, find the surface area of the remaining part of the cube.

YO PLS

anyone help me

[proud ice]

Stay in original channel please. Do not open multiples

[nimble mason]

my Bad

can u help tho

[proud ice]

one sec

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[nimble mason]

.close

[marsh citrus]

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[unique mural]

How to solve cosx=-cos2x

[rough coral]

Put them on one side and use a trig identity

I think 2cos(A)cos(B)=cos(A-B)+cos(A+B) is a fine one to use here

[unique mural]

I don't know how this helps

[rough coral]

Because you can just find the interval where cos(A) = 0 and the interval where cos(B) = 0

and that's your solutions for x

[unique mural]

Doesn't the above identity give cos2x = 1-2cos^2(x)

I did A = B =X

[rough coral]

There are lots of identities

The one I gave is nice because it combines both terms and lets you just make any term 0

To use the one I gave you

You must find some A and B such that A-B = x and A + B = 2x

$A = \frac{3x}{2}, B = \frac{x}{2}$

[elfin berry]

Cosack

[rough coral]

So $cos(x)=-cos(2x) \rightarrow 2cos(\frac{3x}{2})cos(\frac{x}{2})=0$ works fine

[shadow ibex]

You do want that double angle identity here.

[elfin berry]

Cosack

[shadow ibex]

Turn this into a quadratic

[unique mural]

Uh move everything to one side of the equation?

[unique mural]

This seems to work, thanks

I am interested in disorganized's solution though

[shadow ibex]

Ok, well

cos(x) + cos(2x) = 0

cos(x) + 2cos^2(x) - 1 = 0

2cos^2(x) + cos(x) - 1 = 0

2w^2 + w - 1 = 0

w = (-1+-sqrt5)/4

[unique mural]

Damn

[shadow ibex]

cos(x) = (-1 - sqrt5)/4
-->
x = 144 deg or 216 deg

cos(x) = (-1+sqrt5)/4
-->
x = 72 deg or 288 deg