help-0

[alpine nacelle]

once the 2b etc are correct, you should get -3 at x = -3 and -21 at x = 3

[lilac jolt]

hmmmm

how do i do item 12?

[alpine nacelle]

you need to know polynomial reminder theorem, and understand accurately what is the problem at x = -2

try to calculate the limit at x = -2 and see the problem, then what you have to do will seem clearer

[lilac jolt]

division by zero?

[alpine nacelle]

yup, that's the problem

-2 is a root of x²+x-2

what is the little detail about the numerator that could make this problem disappear ?

factor x²+x-2, and try to imagine what you would like to see as a factor in the numerator

[lilac jolt]

i have (x - 1)(x+2) on the denominator

i cant seem to see an x + 2 on the numerator

[alpine nacelle]

well, that's because it depends on b, that's the whole point! you accurately pinpointed the problem

you would like to choose b such that you can factor a x+2 on the numerator

the question is, how to find this b

[lilac jolt]

yes, idk how

[alpine nacelle]

you want to factor numerator by x+2, ie you want x+2 to divide the numerator

do you know polynomial remainder theorem ?

[lilac jolt]

no

[alpine nacelle]

if you have a polynomial P(x) that you divide by (x+2), you get P(x) = (x+2)Q(x) + r, where Q(x) is some polynomial we don't care about right now, and r is the remainder

so when you look at x = -2, you get P(-2) = r

https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-div/x2ec2f6f830c9fb89:remainder-theorem/v/polynomial-remainder-theorem

this video may help you understand the theorem better

[lilac jolt]

erm

[alpine nacelle]

you want x+2 to divide bx²+15x+b+15
said differently, you want the reminder of bx²+15x+b+15 in the division by x+2 to be 0, right ?
so you know your problem has 2 steps: calculating the remainder, and solving remainder = 0

this polynomial remainder theorem solves the first step

[lilac jolt]

what if i just sub -2 on the numerator

and then i got 5b - 15

and solved for b

[alpine nacelle]

you find the remainder!

: )

b(-2)²+15(-2)+b+15 = 5b-15

and the remainder has to be 0 for x+2 to divide, that's what dividing means

so what is b ?

[lilac jolt]

3

[alpine nacelle]

yup

[lilac jolt]

do i subbb?

[alpine nacelle]

now you know that b = 3 is the value that make it so you can factor both numerator and denominator by x+2

which will allow you to calculate the limit after simplification

[lilac jolt]

i got -1 after evaluating

[alpine nacelle]

num = 3x²+15x+18 = 3(x²+5x+6) = 3(x+2)(x+3)
denom = (x+2)(x-1)
so the quotient is 3(x+3)/(x-1), at x = -2 you get -(-2+3) = -1

that's correct

[lilac jolt]

thank you!!

is the answer for the bonus item, no?

[alpine nacelle]

the answer is no, you can have a limit at a point without being defined at this point

one well known example of this is sin(x)/x which has a limit of 1 at x = 0, despite not being defined at x = 0

[lilac jolt]

thank youu

[lone heart]

@lilac jolt Has your question been resolved?

[lone heart]

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[waxen turtle]

Idk how to do 27

[marsh hamlet]

Sketch it!

What is the graph of sqrt(4-x^2)

[waxen turtle]

Idk wat it looks liek

ohh

like

2-x

isk

idk

wait that's not how that works

IDK

[marsh hamlet]

Semicircle

,w plot sqrt(4-x^2)

[ocean seal]

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Requested by mathisfun111

[waxen turtle]

So cool

does the +3 raise it up

[marsh hamlet]

Yep

[waxen turtle]

How do I find it's area

It's liek all stretched

[marsh hamlet]

(Semicircle)

[waxen turtle]

Umm that is not a circle that is a whole oval

[marsh hamlet]

It looks wonky lol

Trust me, it's a semicircle

Let me draw something out on desmos

[waxen turtle]

Oh wait

I can split it up

Fr

where should I split it

at 2

[marsh hamlet]

Green area + red area

[waxen turtle]

at 3

[marsh hamlet]

(Semicircle of radius 2 + square of side length 3)

[waxen turtle]

So cool

TY

.close

[lone heart]

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[tight mauve]

Hi, just had a quick question. Is (x-1) not written as (x-1)^2 because it's taken as common factor, just wanted to double check my thinking. Thank you

[marsh hamlet]

Yes

[tight mauve]

Thank you!

.solved

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[obsidian mango]

Could someone please explain why the sign changed on the left-hand side? And in which cases should I change the sign like this

[lone heart]

@obsidian mango Has your question been resolved?

[cosmic mortar]

guys what is the formula to find the volume of a square pyramid using delta

?

[gray isle]

which part are you referring to exaclty?

[obsidian mango]

The highlighted part

[gray isle]

they factored out -1 from the numerator in the fraction after it

here its so they can get the result of their goal

(also looks more aesthetically pleasing without excessive - signs)

[obsidian mango]

I don't get it

[gray isle]

look at the induction hypoteheses

[obsidian mango]

Yes

[gray isle]

that's why they factored out the -

so they could get that

$2 + \frac{(-k-3)}{2^{k+1}} = 2 - \frac{k+3}{2^{k+1}}$

[ocean seal]

ℝαμOmeganato5

[obsidian mango]

Oh I got you
Thank you very much

But is there another way to solve it without factoring out the -

[gray isle]

not really no

[obsidian mango]

Okay, thanks,
Have a great day 🫡

[lone heart]

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[scarlet heart]

can someone show me how to do this? Idk where I went wrong

[vale wigeon]

@scarlet heart show what you did and then we can tell you where you messed up

[scarlet heart]

im on my laptop, idk how to send the picture

but essentially I use the sin(a-b) formula
compared coefficients
solved for r using sqrt(4^2+3^2)

still my answer is wrong my teaccher didn't even show where

[vale wigeon]

what did you get for R

[scarlet heart]

5

brb btw

[vale wigeon]

that's correct

show how you got alpha and its value then

[scarlet heart]

kk maybe theangle, can you pls show me?

[scarlet heart]

I compared coefficients

can u js tell me the right answer

[vale wigeon]

no

!noans

[lone heart]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[scarlet heart]

okay

[vale wigeon]

if you want your answer validated or checked, you have to post your answer

[scarlet heart]

uh ok ill type it ig

i use this

wait a sec

@vale wigeon if u think Im cheating check my msg history lol this is my assignment finished

[vale wigeon]

im adhering to the rules of this server.

show your work still.

[lone heart]

@scarlet heart Has your question been resolved?

[lone heart]

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[scarlet heart]

no

@vale wigeon

i got -36.9

[vale wigeon]

.reopen

[scarlet heart]

degree

[lone heart]

✅

[vale wigeon]

minus 36.9?

how did that happen

[scarlet heart]

tanx = -3/4

[vale wigeon]

also you do see that your problem said to round the angle to 2 decimal places, yes?

[vale wigeon]

how did the minus sign make its way in there?

[scarlet heart]

so 3/4thts

ok

[vale wigeon]

you have not shown your work nor answered my question.

[scarlet heart]

rsinx/rcosx = -3/4

4sinx - 3cosx so -3

??

[vale wigeon]

can you show what your expansion for $R \sin(\theta - \alpha)$ is?

[ocean seal]

Ann

[scarlet heart]

rsinthetacosalpha - rcosthetasinalpha

[vale wigeon]

ok could be done way better with some brackets

[scarlet heart]

this is ez

[vale wigeon]

but you see that R cos(alpha) should be 4 and R sin(alpha) should be 3, not -3 yes?

[scarlet heart]

need help part 2

this is problem

[vale wigeon]

that is part 3

do you need help with this or with the real part 2?

[scarlet heart]

yeah plz

i skip

2theta to theta

[vale wigeon]

you are becoming harder to understand

but ok

you have found, correctly, that 4 sin(θ) - 3 cos(θ) = 5 sin(θ - something).

[scarlet heart]

i think i can do

let me confirm my answer

don ttell me

60.5 and 193.3 @vale wigeon

[vale wigeon]

very far off. how did you get these?

[scarlet heart]

ouch

@vale wigeon idk what wrong

[scarlet heart]

liar itr right

[vale wigeon]

well, if you want to consider me a liar, then i guess i'll just go away.

[scarlet heart]

pls do

ok i got everything right nice

.close

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[static wagon]

with 4(a), why do we multiply the combinations and not add them to get our final result?

[static wagon]

like 12C5 x 8C3 and not 12C5 + 8C3

[vale wigeon]

bc you pick 5 men and 3 women

it's the same reason why a two-digit combination lock has 100 and not 20 combinations

[static wagon]

but doesn’t ‘and’ imply like P(A) + P(B) or is that not related here

[vale wigeon]

no i think you misunderstand

think of it this way

there are 12C5 ways to pick which of the men go

[static wagon]

yes

[vale wigeon]

but for each of those selections you have to make a selection of which of the women go

in one of 8C3 ways

you can think of it with like a tree diagram or something

or like a combination lock again

[static wagon]

oh because it’s a multi-stage event right?

[vale wigeon]

like if you have a 4 digit PIN lock you understand why there are not 40 combinations, yes?

[static wagon]

yes

[vale wigeon]

yeah same idea

call it multi stage or whatever else you want

[static wagon]

okay

then when do we add combinations?

i think that’s where i struggle

[vale wigeon]

if there are m ways to do A and there are n ways to do B and these don't overlap and you have to count the ways to do A or B

[static wagon]

is this considered an independent event?

cus i thought u multiply independent events

oh hold on

i sort of get it now

could you provide like an example for what you said?

[vale wigeon]

no. if you want to speak of events at all the word is mutually exclusive

[static wagon]

P(A) + P(B) - P(A intersection B)?

[vale wigeon]

overthinking.

[static wagon]

oops that’s not mutually exclusive

[vale wigeon]

you need to choose either a cake or a pie to buy. you have to buy exactly one thing. there are 13 different cakes and 8 different pies at the bakery. how many choices do you have in all?

[static wagon]

oooo 21 ways

that makes more sense now

then how would the question be rephrased if you have to multiply the combinations?

[vale wigeon]

you need to buy 1 cake and 1 pie

[static wagon]

so it’s 13 x 8

.close

[lone heart]

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[static wagon]

with 5e, why isn’t it 70-1 = 69?

[alpine sable]

hi

MY CHANNEL

go away beluga

anyway

[static wagon]

bc the amount of combinations of all even is 1 so 70 -1

mate

the channel has my username

[alpine sable]

oops

[lone heart]

@static wagon Has your question been resolved?

[serene scarab]

Yeah looks correct

I don’t understand how they have taken it to be 4

[static wagon]

yea i thought that too

i think they just got confused or wtvr

but thanks

.close

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[copper siren]

help me here

[small lance]

what are you looking for? Looks like you have selected the answer

[copper siren]

no that was the solution actually

[wintry wadi]

have you gotten the equation for that line?

[wintry wadi]

then can you solve y and z in terms of x?
because then, we can just plug those into the plane equation and solve it

[copper siren]

thank u very much

.close

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[alpine sable]

Is this a One Sample Test of Hypothesis?

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

<@&286206848099549185>

[alpine sable]

<@&286206848099549185>

[wide harness]

!status

[lone heart]

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

[wide harness]

Also there are 6 questions, which one is it?

[alpine sable]

I would like to ask If this a One Sample Test of Hypothesis.

[alpine sable]

I guess 1?

[wide harness]

It looks like two populations and not one.

[alpine sable]

Like this?

[wide harness]

One Sample t-Test doesn't exactly apply to two populations?

[alpine sable]

Hm

[wide harness]

This example is one population.

[alpine sable]

Like this?

[wide harness]

Possibly!

[alpine sable]

Okay!

Thank you!

[wide harness]

Also you should look for one more thing.

[alpine sable]

Which is?

[wide harness]

It's called Paired t-Test too, if there's something in common between the population.

With all that said, good luck.

[alpine sable]

Like this?

[wide harness]

Hmm not sure. Doesn't look like it mentions Paired t-Test?

Yes, it does measure on differences so it is possibly that.

Take my answers with a grain of salt though.

[alpine sable]

How about this?

[alpine sable]

It is fine. I will take it one by one for any incorrect usage :)

[wide harness]

The best idea you should try is to try the formulas to see if they fit with the variables.

[alpine sable]

Okay Thank you!

!status

[lone heart]

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

[alpine sable]

1

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

!status

[lone heart]

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

[alpine sable]

4

[alpine sable]

<@&286206848099549185>

[fading trench]

paired t-test is only applicable when you can make 1:1 pairs between two groups, e.g. when the two groups are the same people but at different points of time
just for clarification

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[zinc willow]

Could anyone tell where did I do my mistake as the answer is π/9,5π/9 and 7π/9

<@&286206848099549185>

why + and -

[forest marsh]

Why did you write 5pi/3 ?

Oh isee

Ok

Nvm

[zinc willow]

2pie - theta

[forest marsh]

Well you forgot the mod 2pi

And when you divide by 3

Became mod 2pi/3

So pi/9 + 2pi/3

Became 7pi/9

[zinc willow]

sry what does mod mean

[forest marsh]

Modular

[zinc willow]

ooh

[forest marsh]

This kind

[zinc willow]

is this like a rule for this specific math

[forest marsh]

Cos(x) = cos(a)
=> x = +-a mod 2pi

[zinc willow]

as i just stared trig

[forest marsh]

A must know with trig

Your circle is 2pi periodic

[zinc willow]

ohh

[forest marsh]

13pi/2 describe the same point than pi/2

For example

Also

When you multiple or divide

It affect the mod

3x = 3 [9]
x = 1[3]

[zinc willow]

i really dont gett u as i just started like basic pure math trig

could u use simpler terms 🤡

[forest marsh]

Ok

What didn't you get ?

The mod thing ?

[zinc willow]

yes

[forest marsh]

Ok you see the unit circle ?

If you do a whole turn on it

Starting from one point

You will end up at the same point

Right?

[zinc willow]

what is a unit circle

[forest marsh]

The circle you use to know the values of cos and sin

[zinc willow]

like the CAST chart

?

[forest marsh]

Idk what this is

,w graph x² + y² = 1

[ocean seal]

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[forest marsh]

Already seen it before ?

[zinc willow]

i was talking about this

[forest marsh]

Well as long you see it as circle its good

So

You start from one point and you do a whole turn on the circle you will end up at the same point right ?

[zinc willow]

yes

[forest marsh]

And what is a full turn in terms of rad angle

[zinc willow]

umm idk

[forest marsh]

What do you do if you turn on yourself to trickshot someone in a videogame ?

What is it call

[zinc willow]

😿 dont know

dont play that much game

[forest marsh]

Ok

[nimble orchid]

hello

[forest marsh]

Its called a 360

[zinc willow]

ohh

[forest marsh]

But its in °

[zinc willow]

2pie

[forest marsh]

Yessir

So a full turn in trig speaking is 2pi

So

Now we know this imma introduce you to modular

[zinc willow]

okey

[forest marsh]

This is JUST a notation to type +2kpi with k integers

But we lazy

So we use mod

So

[zinc willow]

ohh

[forest marsh]

If you have lets say 5pi/2 = ... mod 2pi it is ?

[zinc willow]

5/4

-5/4

?

[forest marsh]

When you have something like this

You want to know how much there is 2pi in 5pi/2

So here

5pi/2 = 4pi/2 + pi/2 = 2pi + pi/2

[zinc willow]

umm i dont get u like what are u supposed to when u inverse cosine something in radian

[forest marsh]

Wdym ?

[zinc willow]

in my math i did in the pic

[forest marsh]

When you want to get the cos or sin out what you did is correct except that you forgot to put mod 2pi

This mod 2pi is important cuz as we seen earlier it makes you have all the possible solutions

So you have something like 3x = +-pi/3 mod 2pi

Which is litterally

3x = +-pi/3 + 2kpi

And so

If you divide by 3

You have x = +-pi/3 + 2kpi/3

And now you need to get all the values that are in [0,pi[ by changing values of k

[zinc willow]

so we use this mod2pie to get all the possible values of cosin

[forest marsh]

All possible angles yeah

[zinc willow]

what are the constant supposed to be

[forest marsh]

The amount of whole turn you do

[zinc willow]

and how do i know that amount

w8 is it 3 times

because 3 theta

[forest marsh]

You don't need to know the amount, you replace k by integers value and if the result is in 0 pi you add it to solution set

[forest marsh]

No

[zinc willow]

u mean 1/3

[forest marsh]

?

What 1/3

[zinc willow]

the integer value

[forest marsh]

1/3 isn't an integer

[zinc willow]

w8 sry

[zinc willow]

yeah i forgot

like this ?

[forest marsh]

And when you divide by 3 to get theta alone

[zinc willow]

yes

[forest marsh]

You also divide the thing in the mod

So it will be mod 2pi/3

I don't like the use of arccos here tbh

It make you forget one solution !

[zinc willow]

why dont i have do it to find basic acute angle

[forest marsh]

Cua you can't have the 5pi/9 else

[zinc willow]

did u just multiply 2pie with the mod

[forest marsh]

No 2pi is the mod

[] is notation

Mod 2pi <=> [2pi]

[zinc willow]

could u again tell me how to get the other solution

[forest marsh]

Ok

You have 3theta = +- pi/3 [2pi] right ?

[zinc willow]

like do i multiply the first solution with mod

[zinc willow]

yes

[forest marsh]

You divide by 3

[zinc willow]

yes

[forest marsh]

Giving you theta = +- pi/9 [2pi/3]

Lets do the positive case first

So we have that for k = 0

Pi/9 is in 0,pi so its a sol

For k = 1

We have pi/9 + 2pi/3 = pi/9 + 6pi/9 = 7pi/9

Which is also in 0,pi

So its a sol

For k = 2 it won't be the case

So we stop here for the positive case

Lets do the negative

Theta = -pi/9 + 2kpi/3

k = 1 makes you have -pi/9 + 2pi/3 = -pi/9 + 6pi/9 = 5pi/9

Which is in 0,pi

So its a sol

For k = 2 it won't be the case

So we stop here

And we have all our three solutions

[zinc willow]

what u mean by 0 , pi

[forest marsh]

The values that theta can have

0 <= theta < pi

[zinc willow]

so it can be 1,2and 3

?

[forest marsh]

Theta is a real number

Not an integer

k is an integer

[zinc willow]

umm not getting it

[forest marsh]

How

[zinc willow]

is k 1,2and 3

[forest marsh]

k is an arbitrary integer value

That you choose in order to make theta in the set of values that theta can have

[zinc willow]

?

[forest marsh]

Yeah you can replace k by 2 and see that it will be greater than pi

And so its useless to continue further

Theta will always be taller than pi for k >= 2

[zinc willow]

yes got it

so we try until we reach the limit

[forest marsh]

Yeah

[zinc willow]

why did u give +and-

is it like a rule

[forest marsh]

You can also write 5pi/3 as you did

<@&268886789983436800>

[forest marsh]

And do the same work with it

Its just that for explain

Its better to have +- so that i can make things clearer between which case i do

Positive vs negative

[forest marsh]

The [2pi] are missing for the two first line else thats good

[zinc willow]

like this

[forest marsh]

Without k

Its either

[zinc willow]

why

[forest marsh]

[2pi] or + 2kpi, with k in Z

[forest marsh]

Just writing convention

[zinc willow]

ohh

[forest marsh]

Choose the one that you rather do

They both the same

[forest marsh]

No +

Sry i miss it at the first time

[zinc willow]

ooh

[forest marsh]

Yep

Sure

[zinc willow]

i think i get it know

thx for explaining it my friend

[forest marsh]

You're welcome

[zinc willow]

. close

[forest marsh]

.close

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[waxen turtle]

Idk how to do it at all

[high rapids]

What do you know about probability?

[waxen turtle]

Umm I can do like those marble problems

anddd

mean median and mode

and like quartiles

And number summaries

[high rapids]

Heard of conditional probability?

Maybe were used in those marble problems

[dusty fox]

lets hope this person heard of binomial distributions otherwise this will be a long one

[honest nacelle]

the probability of k successes in n trials is given by (n choose k) * p^k * (1-p)^(n-k), where p is the probability of success
think of being a homeowner as a success and the number selected as the number of trials

[lone heart]

@waxen turtle Has your question been resolved?

[waxen turtle]

That's the name of the assignment but idrk anything Abt it

[dusty fox]

and you didnt have this in class?

[gilded ore]

Is this a basic statistics course?

[lone heart]

@waxen turtle Has your question been resolved?

[waxen turtle]

idk i didn't pay attention

[waxen turtle]

Fr

[gilded ore]

No I mean like dont they have a formula sheet?

[lone heart]

@waxen turtle Has your question been resolved?

[waxen turtle]

Idk

[gilded ore]

Uhh

Then idk what to tell you

But yea use binomial

[modest fox]

Is anybody free to help?

I need to know

If my constraint of 2x(5) + 2y(5) = 700 makes sense

10x + 10y = 700

y = 70 - x

A = xy

A = x(70 - x)

A = 70x - x^2

A'(x) = 70 - 2x

70 - 2x = 0

x = 35

[modest fox]

But when I plug 35 back into this

I get 1225

Which it says is wrong

<@&286206848099549185>

[dusty fox]

this aint yo fucking channel

get your own

[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).

[alpine sable]

I don't know who's channel this is but yes. Please get your own channel.

[modest fox]

Sorry

[modest fox]

You can use better words

[alpine sable]

On behalf of them, My apologies. I hope you have a wonderful learning. :)

[modest fox]

Thank you! Could you help me on another channel?

I'll switch to #help-5

[lone heart]

@waxen turtle Has your question been resolved?

[waxen turtle]

Idk how

[primal ore]

what is a partial derivitive?

[crude parrot]

!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).

[lavish cave]

that's not correct

how did you get that?

you should be using the numbers 2, 1, 5 before you simplify

[pseudo ice]

(that isn't OP )

[wheat isle]

CATTBITTTTT

[lone heart]

@waxen turtle Has your question been resolved?

[lavish cave]

dam.

[modest fox]

To answer your question, I was not using the formula correctly

I was taking the 2x + 2y equation, and simply multiplying this by the cost of the respective sides

It should've acc just been (5x + 4y + y = 700) which equals (5x + 5y = 700)

I believe my answer was x = 70

And I forgot what y was

[lavish cave]

yep that's correct now

y is the height and x is the length of the field

[modest fox]

Yes

[gilded ore]

He explained it above

So you have a set amount of trials which is 35 your probability of success (i,e home owners is .60) and your failure is 1-.60

[waxen turtle]

Do I like plug stuff in

[gilded ore]

Yea

Basically

N is 35 and K successes is 20 or whatever is defined by the problem

[waxen turtle]

im in bed but I'll try it in a bit Fr

[north rover]

3 hours?!

[waxen turtle]

im still in bed

[clever folio]

@alpine sable please don't delete mod pings

Please try to keep things mature here.

[waxen turtle]

wat is n choose k

[honest nacelle]

in this case it's the number of ways to arrange k successes in n trials

like if you have 3 trials and one success you don't care whether your order of events is SFF, FSF, or FFS, so you multiply the probability by (3 choose 1)=3

the formula to compute (n choose k) is n!/(k!(n-k)!)

[hazy echo]

Can someone can help me with math hw quiz

[sly bluff]

Maybe. I a wee bit special.

[hazy echo]

If you can help me

[sly bluff]

What grade are you?

[hazy echo]

College

[sly bluff]

I would suggest chatgpt

I barely started highschool 💀

[modest robin]

!nogpt

[lone heart]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[modest robin]

!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).

[hazy echo]

can someone can help me with the math hw quiz

[teal orbit]

!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).

[lone heart]

@waxen turtle Has your question been resolved?

[modest robin]

the answers to your question are parts of this sum as other helper have noted but for that to make sense you need to learn basic probability theory and from what I’m reading what is n choose k (the binomial coefficients).

$\sum_{k=0}^n \binom {n}{k} p^k(1-p)^{n-k}$

[ocean seal]

pola_touche

[modest robin]

https://www.khanacademy.org/math/statistics-probability/counting-permutations-and-combinations

what you need imo in what I sent is part of unit 7 unit 8 and 9

[gilded ore]

Honestly its literally just plug and chug

The formula explains itself

n trials, k successes and the probability of success p

They defined in the problem that p = 0.6

n = 35

k is either 22 or the other numbers

You need to find

[gilded ore]

<@&268886789983436800> can somebody close this channel its been open for really long

[tardy stag]

it's not hurting anybody

[gilded ore]

Its hurting me the dude has been in bed for 24 hours

And hadn’t attempted his problem or let us know of any progress

[crude parrot]

just don't open this channel then. if the person hasn't attempted it then that's on that person for not learning it. only hurts him

[lone heart]

@waxen turtle Has your question been resolved?

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[idle kettle]

solved math ama

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[static wagon]

can someone tell me why for question 1, the answer is -2sqrt3/3 < x < 2sqrt3/3?

[static wagon]

i know it’s rationalised but why is x in between those two values

[tropic plaza]

Actually u made a slight mistake while putting f'(x) = 0

what u did-
3x²-4=0
x²= 4/3
x=2/√3

Actual solution-
3x²-4=0
x²= 4/3
x=±2/√3

Reason-
For eg. x²=4
We have two solutions x=2 and x=-2. U forgot to consider the negative solution

[static wagon]

ohhhh

[tropic plaza]

@static wagon ur pfp is haunting me

[static wagon]

LOL

[tropic plaza]

😭 👍 bye

[static wagon]

so am i meant to do two brackets?

one with the positive solution

[tropic plaza]

yes

[static wagon]

and one with the negative?

alr

[tropic plaza]

:)

3x²-4<0
x²<4/3
|x|<2/√3
So
-2/√3<x<2/√3

[static wagon]

yes got that

.close

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[primal dagger]

to solve the problem using method of undetermined coefficients i get that u have to like guess what the form on the left would be like (At+B) but how do you know like what ur guessing is correct ?

[vale wigeon]

you work out the roots of the characteristic equation as well as what characteristic values each term on the RHS would correspond to

[primal dagger]

the roots for this would be just 3,-1

and then i wrote it in the homogeneous solution

using the roots

and then i didnt know what to do with the right side for this like how to form a guess for the particular solution

[sharp citrus]

u can use variation of parameters method

[vale wigeon]

right so the RHS corersponds to -1

so there is resonance

so you will need $(At^2 + Bt)e^{-t}$

[ocean seal]

Ann

[primal dagger]

yeah im just confused on how to work out this step logically

like everything else i understand but that

how did u know that it would be that that i need if my question makes sense

[primal dagger]

specific problem asks for method of undetermined coefficients

[vale wigeon]

ok right basically

terms of the form $P_k(t) e^{at} \cos(bt)$ or $P_k(t) e^{at} \sin(bt)$ correspond to the characteristic value $\lambda = a+bi$

[ocean seal]

Ann

[vale wigeon]

where P_k is an arbitrary polynomial of degree k

the key is the multiplicity of λ as a root of the char eq

if λ is a root of multiplicity s, then your guess needs to be of the same form but contain a polynomial of degree k+s

(and both a sine and cosine term if b ≠ 0)

[primal dagger]

hm okok

[mystic rivet]

what is (a+b)whole cube

[primal dagger]

.close

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[dusk brook]

Hi everyone!

I'm preparing for the entrance exam at the University of Bucharest, Faculty of Mathematics and Computer Science (Unibuc FMI). This is a problem from the 2023 admission exam, and I'm stuck on part (d).

Here’s the problem statement in English:

University of Bucharest
Faculty of Mathematics and Computer Science

Entrance Exam – July 2023

I. Algebra
Let the matrix
A = ( 4 2
-3 -1 )
be in M₂(R), and define the set
T = { xI₂ + yA | x, y ∈ Z },
where I₂ is the 2×2 identity matrix.

(a)
Prove the equality:
A² = 3A - 2I₂.
Determine the real number α such that:
(I₂ - A)² = α (I₂ - A).

(b)
Prove that the matrix
( 2 2
-3 -3 )
belongs to T, then check whether
( 4 4
-6 -3 )
is in T.

(c)
Show that for any natural number n ≥ 1, there exists a natural number xₙ such that:
Aⁿ = xₙ A + (1 - xₙ)I₂.

(d)
Verify whether the set { I₂ - A, -I₂ + A } forms a group under matrix multiplication.
Then, determine all two-element subsets of T that form groups under matrix multiplication.

[vale wigeon]

christ almighty! that text paste!

ok

so you want to check whether or not {I - A, I + A} forms a group under matrix multiplication

yes? is that what you're looking for?

[dusk brook]

Yes

[vale wigeon]

ok do you know what a group is

[dusk brook]

yes

[vale wigeon]

ok can you tell me what properties a group must satisfy

[dusk brook]

a moment

To be associative, to have a neutral element, and to have an invertible element.

[vale wigeon]

ok

when the operation is matrix multiplication, what should the neutral element be?

[dusk brook]

I

identity matrix

right?

I have (more or less) proven that it is a group, but I have a problem with the next part:
Then, determine all two-element subsets of T that form groups under matrix multiplication.

[vale wigeon]

I have (more or less) proven that it is a group,
you have?

how can you have proven that {I-A, I+A} is a group when the identity matrix I doesn't belong to this set???

[dusk brook]

Whait, I worked on this problem some time ago.

[vale wigeon]

aaaaaaa

[dusk brook]

English is not my first language; I use a translator.

[vale wigeon]

whatever translation software you're using, it completely destroys all the math notation you feed into it

making it absolutely unreadable

[dusk brook]

I defined
x= I2 − A
and
y = −I2 + A
then I computed
x⋅x, y⋅y, x⋅y, y⋅x, and
From this, I found that the neutral element is
𝑦.

[dusk brook]

Ik

[vale wigeon]

so you found that y^2 = y and xy = yx = x...?

[dusk brook]

yes

[vale wigeon]

hm

ok, looks like it is a group, despite neither matrix being the identity...

wait, what did you get for x^2?

[dusk brook]

I have proven that it is a closed set under multiplication, that it is associative, and that it has a neutral element, but proving the existence of an invertible element... that's where I'm stuck.

[vale wigeon]

i don't see your calculation for x*x

[dusk brook]

yea...

[vale wigeon]

so you got xx = y

[dusk brook]

yea

[vale wigeon]

and y is the neutral

[dusk brook]

yes

[vale wigeon]

therefore, within this group, x is its own inverse

[dusk brook]

ooooo

I see

Now, I have a problem with the next part:
Then, determine all two-element subsets of T that form groups under matrix multiplication.

[vale wigeon]

ok that one looks quite difficult without some brute force sorry

[dusk brook]

I think we need to use this from the previous subpoint
A^n = x_n * A + (1 - x_n) * I_2

or

where α = -1

[lone heart]

@dusk brook Has your question been resolved?

[dusk brook]

<@&286206848099549185>

University of Bucharest
Faculty of Mathematics and Computer Science
Admission Exam – July 2023

I. Algebra.
Let the matrix
( 4 2 )
A = ( -3 -1 ) ∈ M_2(R)
and the set
T = { x · I_2 + y · A | x, y ∈ Z },
where I_2 is the identity matrix of order 2.

(a) Prove the equality:
A^2 = 3 · A - 2 · I_2.
Find the real number alpha ∈ R such that
(I_2 - A)^2 = alpha · (I_2 - A).

(b) Prove that
( 2 2 )
( -3 -3 )
belongs to T, then verify whether
( 4 4 )
( -6 -3 )
belongs to T.

(c) Show that for any natural number n, n ≥ 1, there exists a natural number x_n such that
A^n = x_n · A + (1 - x_n) · I_2.

(d) Verify that the set { I_2 - A, -I_2 + A } forms a group under matrix multiplication. Then, determine all subsets of T with two elements that are groups under matrix multiplication.

I need help with d)

[lone heart]

@dusk brook Has your question been resolved?

[kindred anchor]

<@&268886789983436800>

[vale wigeon]

<@&268886789983436800> advertising

[lone heart]

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[quasi oak]

is this correct?

[vale wigeon]

seems so

[quasi oak]

thanks

[lone heart]

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[lilac stag]

how do i tell based of this data

how many people watched a serie in the past month for

less than 2 times

2-10 times

and more than 10 times

I dont understand at all

[twin nimbus]

So the box and whisker plot will tell you the quartiles

[lilac stag]

Yes

[twin nimbus]

So 25% watch less than 2 times

[lilac stag]

how do you know that

[twin nimbus]

Because the whisker extends from 0 to 2

and the whisker represents 25% of the population

[lilac stag]

Hmm

Wait

This

Part, is it that part your talking about

[twin nimbus]

yes

[lilac stag]

How does it show 25

procent

[twin nimbus]

that's just what the whisker represents

---|     |     |-----
25%   25%  25%    25%

[lilac stag]

hmmm

Wait

Let me draw

[twin nimbus]

bbiab

[lilac stag]

This is how I have understood it

Less than 2 times then we are talking about 0-2 right? but theres nothing there not a box nothing. Thats where my brain goes blank @twin nimbus

[odd lion]

Isn't the green box represents how many peoples actually watched the film between 2 to 10 times which is 40% total!!

[lilac stag]

With ur method I can see that you split it up too 4 parts where all is 25% even though they arent as big as each other

[lilac stag]

No shes correct its 50%, 25%, 25%

Thats what it says on the answer sheet

But I dont know how to interpret it,

Cause the parts are not as big as each other

[odd lion]

@lilac stag oh I see my bad

[lilac stag]

All good

[twin nimbus]

hi I'm back

so the green box is a total of 50% of people

you have the 25th to 75th percentile in the box

0 to 25 in the whisker under the box

75 to 100 in the whisker above it

@lilac stag

[lilac stag]

wait

i think i get

it

[twin nimbus]

nice!

[lilac stag]

yes

since it goes from 25% to 75%

it must be 50%

[twin nimbus]

yup

[lilac stag]

thats the part I get now

And the one from 0-2 that looks obv like 25%

the only thing left is more than 10 and that looks so weird but the only reasoning we have there is

100-75=25?

[twin nimbus]

so what might be throwing you off

is that it's not balanced.

[lilac stag]

yes

[twin nimbus]

But the data isn't balanced, instead think about it this way. Let's say we have 100 people

let's say 15 people watched 0 movies, and 10 watched 1 movie.

13 watched 2 movies, 12 watched 3 movies,

[lilac stag]

mhm

but im just scared, now that i learned this that an even more unbalanced box or whatever its called pops up

[twin nimbus]

10 watched 4 movies, 4 watched 5, 5 watched 6, 2 watched 7, 2 watched 8, and 2 watched 9

when the box is large, that means the values are less clustered.

the same amount of people are stretched thinner.

[lilac stag]

ok ty

[vale crag]

<@&268886789983436800> huge spam

[lone heart]

@lilac stag Has your question been resolved?

[lone heart]

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[limber willow]

Hi

[limber willow]

could someone explain to me how the y-intercept was calculated? this is a graph representing f(x) = 3x-5/x-5. in part c, i had to show that f(x) is an inverse function. however, in this task, i had to graph this function and draw all asymptotes/intercepts.

from my calculations, the y-intercept is (0,1) but it's (0,5/3)

[tacit arch]

$f(x) = \frac{3x-5}{x-5}$

is that your function

[ocean seal]

riemann

[limber willow]

yes!

[tacit arch]

,w plot (3x - 5)/(x-5)

did you get the function wrong?

[limber willow]

i mean my x-intercept is (5/3,0) and my y-intercept is (0,1) but the markscheme says that the y-intercept is supposed to be (0,5/3)

[tacit arch]

can't tell unless you show the function

[limber willow]

point d, so i calculated that it is an inverse function. i set y to 0 to calculate the x-intercept, which is (5/3, 0) and it's correct. after that, i set x to 0 to calculate the y-intercept, which gave me (0,1), which is wrong

[lone heart]

@limber willow Has your question been resolved?

[limber willow]

<@&286206848099549185>

okay i got it now i wrote the number down 😭 thank you

.close

[lone heart]

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[winter umbra]

Whats 0!

[crude parrot]

1

[twin nimbus]

1

[winter umbra]

Would it not be 0 becae 0×0 is 0

[crude parrot]

definition of factorial

how many ways can you arrange x objects

[twin nimbus]

Instead, think of it as the number of ways you can reorder 0 objects

[crude parrot]

you can only arrange 0 objects in one way

[vale wigeon]

the definition of factorial is tricky to apply to zero objects

i like to think of it as "the product of nothing is 1"

just as the sum of nothing is 0

[twin nimbus]

Oooh, that's good

[winter umbra]

👍

[worthy void]

hallo

[lone heart]

@winter umbra Has your question been resolved?

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• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[blazing widget]

thx

not sure how to solve this

Modeling with linear equations and inequalities

[lone heart]

@blazing widget Has your question been resolved?

[alpine sable]

I can help

149-95t
170-110t

2 expressions

We can then plug in

Values

For example 1, chimiake is faster, 2 chimiake is faster

[tacit arch]

<@&268886789983436800>

[alpine sable]

What is this

What was that

Was that a phiser

Or smth

I took a photo

[sly mantle]

they ded

[alpine sable]

Ok

Yo

Is the work above correct

Nvm

Oh I did it wrong

149-95t 170-110t

We can say

That oringinal Ly

149-95t is greater than 170-110t

[blazing widget]

this is the answer I got

[alpine sable]

Uh

Yes

After we can simplify

1.4=t

[blazing widget]

how did you simplify it

[alpine sable]

Divide 21 by 15

[blazing widget]

yes

[alpine sable]

It’s a fraction

[blazing widget]

is that all the steps

[alpine sable]

We can divide

Yes

U want me to explain it

To u

[blazing widget]

1.4 hours

[alpine sable]

How I got 1.4

Uh yea

[blazing widget]

t<1.4?

or greater then

[blazing widget]

this would be fantastic

[alpine sable]

Uh

The whole problem

?

T is not equal

To 1.4

[blazing widget]

yes

[alpine sable]

Ok

So first

We can get the expressions

Post this here rq

[alpine sable]

Ok

We get the expression 170-110t is less than 149-95t

So we can fight at what value can t be less than

170-110t can eventually be greater

But we need to find out what t can the greatest of t can be

My grammar

[blazing widget]

how

[alpine sable]

So after doing that

[blazing widget]

how can t eventually be greater

[alpine sable]

Oh so after 1.4

Like 1.5

Plug it in

170-110(1.5’

149-95(1.5’

As u can see

[blazing widget]

nah I might need to skip this lesson

this is mad confusing

[alpine sable]

Wait lemme write it out

It easier

[alpine sable]

Don’t

Later u will need to do complex distance

[blazing widget]

ill be paitient

[alpine sable]

Alr

Finished

Tell me if u got questions

@blazing widget we good?

[blazing widget]

thank you

what in the beginning equation gave you greater than sign

like what word

or phrasing

@alpine sable

[alpine sable]

?

Oh

Hmmm

Well

It’s to tell us like

What the greatest value of t would be if chimiake was closer than valente

Then after

Yea

[blazing widget]

what do you mean

im saying like what word here tells you this is an inequality

[alpine sable]

Oh

It’s because

We wanna find

When

When valente is closer than chimiake to the university

And then we can say

When valente is closer it means the distance is less

And chimiake is tester

Greater

So we say

I’m getting confused now lol

[blazing widget]

Bro

[alpine sable]

Bro

Ah hell nah

U can get banned for that

It’s very hard to explain to a 5th grader

😭

Where u even find this

[blazing widget]

Im trolling

[blazing widget]

Fr though explain it

You don’t truly know math until you can explain it to a 5th grader

[alpine sable]

What grade are u even in

?

[blazing widget]

11