help-27

[rough copper]

this representation is important because it states exactly which values y can take

so for this diagram right

you have a function which can be represented on this graph

where if you plug a value of x into it you get a value for y

you can plot this point and for every point for the function and you get this graph

because this function is restricted

as in its not true for all values of x and y

you have to use inequalities to represent the values which are true

which part do you think is confusing?

or is it all a bit confusing

[sour shard]

Dude honestly I’m a HUGE air head, it’s like I can hear what you’re saying, but I can’t understand most of what you’re saying because I can’t visualize it, and when I do understand it, it still feels like there is something I don’t understand.

[rough copper]

thats honestly how i feel when i study at my level too

but thats the learning process

eventually with practice all of this stuff will seem a lot more intuitive

okay lets start from the beginning if you'll let me

[sour shard]

Yes sir

[rough copper]

okay so i think its important for me to understand where you are so i can explain this in a way that will be more intuitive to you

do you know what a function is?

[sour shard]

Yes an equation that has in input and output

[rough copper]

okay perfect

so in maths we like to have sets of things

basically

for every function

they will all have a set of inputs

and a set of outputs

for y = x +2

if your set of inputs is {1,2,3}

your set of outputs will be {3,4,5}

because the function tells you to take this set of inputs add 2 to them

and produce a set of outputs

am i making sense so far?

[sour shard]

Yes

It’s like putting puzzle pieces together

[exotic kernel]

Can i help

[rough copper]

up to caleb i guess

[sour shard]

Let Hapus finish up and then you can share your knowledge

[exotic kernel]

Ok

[sour shard]

If you have anything to say about what Hapus says like a correction that would be helpful to both of us though

[rough copper]

right so your domain is basically your set of inputs

and your range is your set of outputs

thats really all it is

[sour shard]

Ok so that had a nice click to it

[rough copper]

so lets clear up the bit about inequalities

lets say -5≤y≤5

all this tells the reader is the values that y can take

because they are ≤ and not <

you can include the numbers on either side

because y can also be equal to -5 and 5

so if i was going to only pick integers on -5≤y≤5

my set of numbers would be {-5,-4,-3,-2,-1,0,1,2,3,4,5}

if it was -5<y<5

{-4,-3,-2,-1,0,1,2,3,4}

because of the notation we are using

so i mentioned that this function represented by this graph was restricted

how so? well you see each end of this curve is cut off

so if i tried to plug in x = -6 into this function it wouldnt be defined

there would be no answer

because the function is restricted to values in an inequality

rather than being able to use all the numbers

this is what you're being asked to find in the question

for the first question at least

the values in which the outputs can take

something crucial to understand about functions when theyre graphs, is you still treat them like functions with inputs and outputs

except your inputs are the x values

and the outputs are the y values

if i plug in x = 0, what do you think the y value would be?

for the first one

its also fine to not be sure but try and guess anyway if thats the case

[sour shard]

0

[rough copper]

okay so unfortunately thats not correct but nice try

so this graph tells you what the function does

which is why graphs are so useful

if you look at the center of the graph

this is where x=0 and y = 0

so the y line is the one pointing upward and down

and the x line is the one pointing left and right

the numbers on this line are the values of x and y

at that particular point

so if i chose x= 0

lets call the function f

so f(0) = 2

this notation just means f(input) = output

or f(domain) = range

do you see the two in the middle of the curve

this is the point im refering to

[sour shard]

I see C and B

You’re talking about question 1 right?

[rough copper]

yes only 1 for now

[sour shard]

Yes in the middle is C and sorta of B

[rough copper]

so this cross right

almost looks like crosshairs

the horizontal line is your values of x

and the verticle line is your values of y right

have you done coordinates?

like could you point to (1,1)

[sour shard]

Yes

[rough copper]

cool

so the values where x = 0

i.e (0,0) or (0,1) or (0,-1)

this all forms a line right

a verticle line

its actually the same as the verticle line i pointed out earlier

every point on that verticle line is where x = 0

similarly every point on the horizontal line is y = 0

you can check this using coordinates

so if i wanted to find (0,-6) on this diagram

it sits on this line

same for (0,6)

in fact as long as the left number in the coordinate is 0 or x = 0, this will always be the case

let me know where you're stuck if you are stuck

if you ask me a question about anything ive said so far ill try my best to explain

its just slightly difficult to do this without drawing my own diagram

still there mate?

[sour shard]

Yes

[rough copper]

im going to try and draw my own diagram and ill send it to the chat when its done

[sour shard]

Ok

[rough copper]

sorry the internet didnt work on my phone had to use data lol

does this help?

its fine if it doesnt yet. i can explain why i drew it this way

its also slightly incorrect but its correct in the ways that matter for this question

its a lot wider than its supposed to be lol

[sour shard]

No it helps

But why does the x axis have all points on it make it to where y = 0

[rough copper]

because the value of y for every point on the x axis is 0

the x axis you could say is the line where y = 0

vice versa for the y axis ( line where x = 0)

so what inequalitys tell you is the nature of this restriction

(how is it actually restricted, which points is it restricted between)

[sour shard]

Ohh ok

The reason both of them have all points be 0 for the other is because there are restrictions

[rough copper]

the axis?

its the function which is restricted

okay lets take another example

for this example y = x+2

if i restrict y

-1≤y≤1

lets say

this means the y on the left can only range between the values -1 and 1

this will inherantly limit which values of x can make this condition true

so for y = -1 x must be -3

and y = 1 , x must be -1

so the range would be -1≤y≤1

the domain would be -3≤x≤-1

its easier to see it the other way around

so y = x -1

if we say

our domain is 1≤x≤7

this is the same as {1,2,3,4,5,6,7}

as we said earlier

this is all the possible values x can take

if we take the end points and put them through our function we can find the range of values for y

can you find the range of this function given this restricted domain?

either an inequality in terms of y or a set of numbers will do fine

let me just clarify the question

our set of inputs is {1,2,3,4,5,6,7} = x

our function is y = x -1

whats our set of outputs

do you want me to explain?

[sour shard]

Yes please

[rough copper]

ill explain why this is useful to our example in a second

so our function is y = x -1

this tells us that the output is the input -1

so if we give our function a set of inputs to work through

all we do is subtract 1 from each of the inputs

to get our range

so our inputs are x = {1,2,3,4,5,6,7}

our function transforms those numbers

using y = x -1

to y = {0,1,2,3,4,5,6}

we subtract 1 from each of these numbers in the input set

if we did this for one point

lets say x = {1}

y = 1 -1

so y = 0

the same thing is happening with the inequalities

so x = {1,2,3,4,5,6,7} is the same as 1≤x≤7 (inputs or domain)

and y = {0,1,2,3,4,5,6} is the same as 0≤y≤6 (outputs or range)

so lets put this a different way perhaps it might help

im going to ask you some questions about this curve in 1

[sour shard]

Okay

[rough copper]

what is the largest value of y this curve can take

so look at the y axis

maybe draw a line from the y axis to the highest point of the curve

[sour shard]

8

[rough copper]

very close

so you see the y axis right

[sour shard]

Yes

[rough copper]

the y axis tells us how high or low we are

x axis tells us how far left or right we are

im sure u know that

just being sure

so if you draw a line from the very top of the curve

horizontally to the y axis

what number would it say at the y axis

[sour shard]

At this top of the curve?

Where d is?

[rough copper]

where A is

the largest value of y the function can take

[sour shard]

7

[rough copper]

perfect

similarly

whats the lowest

[sour shard]

-7

[rough copper]

nice

so that will be the range of values your function can give

or just the range

everything between those points

[sour shard]

So the answer is A

[rough copper]

the function exists

everywhere outside of those points it doesnt

yes

[sour shard]

The domain is 7

The range is -7

[rough copper]

we are only talking about y here

y is our outputs remember

and outputs are the range

so -7≤y≤7

is our range

because our function cannot go outside this inequality

[sour shard]

Ohh I see what I did wrong

[rough copper]

okay what would be the domain of this function

[sour shard]

7

[rough copper]

itll be the same thing you did for the y values

but the x

cause now we focus on the inputs

x is always inputs

y is always outputs

[sour shard]

Oh ok let me figure it out

It’s gotta be -7

[rough copper]

whys that?

[sour shard]

To find the domain do I go to the lowest point for the x axis?

[rough copper]

lowest and highest

you want to find its minimum and maximum in terms of x

[sour shard]

Ohh wait I did it wrong

It’s 6

I measured the x against the y axis

[rough copper]

thats the maximum whats the minimum

we need both to establish the full picture

[sour shard]

Yea I’m lost

[rough copper]

thats okay

let me do a simpler curve

and explain where the domain and range come from

then we can come back to this curve and do the same

[sour shard]

Ok

[rough copper]

again the graph is dodgey but it represents the idea that we need

but yeah, key points are. domain is a fancy word for set of inputs, and range is a fancy word for set of outputs

so the two coordinates in the bottom left and bottom right

are our maximum and minimum points of this curve

its a line but im going to call it a curve

so our minimum is (-6,-7)

so minimum of x is -6 and minimum of y is -7

similiarly our maximum is (8,7)

so our maximum for x is 8, and maximum of y is 7

so to find our domain for this

we take max and min of x

which is -6 and 8

and our max and min for y

which is -7 and 7

so we can write and inequality for each

which tells us

i can pick any value between -6 and 8 for x (or more formally -6 ≤ x ≤ 8) for the domain

i can also pick any value between -7 and 7 for y (or more formally -7 ≤ y ≤ 7) for the range

this tells us the values that the function is defined for

which is useful

because if someone tried to plug y = 8 into our function we wouldnt have a definition at that point for the curve

so we gotta tell them, just use these values (-7 ≤ y ≤ 7)

does this make sense?

[sour shard]

Yes it does

[rough copper]

nice!

[sour shard]

Though it’s hard to pick up on every single detail I got the jest of what you’re saying

[rough copper]

i can try keep it brief from here on then

you can look back on my drawings or messages to help

can you explain briefly why A is the correct answer here?

[sour shard]

Ok

On the highest point for A the range for that is 7 because A is at the point of 7

The - 7 is at the point of E where that is the lowest point of the curve

You said this sign with the < like at the bottom means it’s either equal or less than

-7 is less than 7 while the 7 is greater which explains why there are two of the same signs and the y is the output

[rough copper]

its a good answer actually

but

we can simplify it

shall i tell you how id justify A Being correct

[sour shard]

Yes sir

[rough copper]

the highest point the function can take is at A, and the lowest point is at E.
the y coordinate at A is 7 and the y coordinate at E is -7, the function only covers values between these two extreme points. so the range of the function must be -7 ≤ y ≤ 7

id say this answers the question well because in mathematics we like to keep to definitions

[sour shard]

Yes that was way better

[rough copper]

we could define a range to be all the points which the function can output

and the domain to be all the points we can input into the function to get an output

there is no number i can input into the function to get a bigger output than 7

its the same for -7

okay could you tell me what the domain is?

≤

here is the symbol if you want to copy it

(remember its the same as how we find the range but for x values(input values).)

i can give u a hint if you get stuck

[sour shard]

Wait I’m confused

[rough copper]

okay so

the domain will look like this a≤x≤b, where a is the minimum x value and b is the maximum

so your minimum x value will still be at A

instead of looking up and down

we are now looking left and right

where left is minimum and right is maximum

also side note lol

question 2 on ur paper is wrong

if you wanna get really mathematical about it, its not rigorous enough at all

still there dude?

[sour shard]

Hey sorry for the inactivity dude

I’ll be back

[rough copper]

dw mate i got nothing better to do rn

[devout snow]

@sour shard Has your question been resolved?

[sour shard]

Sorry I’m back

I did a group pizza project with my aunt and little bro

[rough copper]

hi

[sour shard]

Hello

[rough copper]

sorry dude i gotta go unfortunately

gotta cook dinner and wind down

im sure if u ping the helpers someone will come and help you out

sorry dude

[sour shard]

No worries man thank you so much for your time and effort in helping

I’m really thankful you helped

[rough copper]

ur welcom bro

[devout snow]

@sour shard Has your question been resolved?

Channel closed

Closed by @sour shard

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

Please don't occupy multiple help channels.

[warm breach]

<@&268886789983436800>

[devout snow]

Channel closed

Closed by @slender mirage

Use .reopen if this was a mistake.

[warm breach]

such hacked accs are everywhere

ong

[devout snow]

Available help channel!

Send your question here to claim the channel.

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

[hoary loom]

hello can someone help ?

[winter patrol]

what have your tried?

[hoary loom]

wait ill take a pic

i actually tried this and it didnt work

it was like a loop i keep doing the same shit idk whats wrong

[shell scarab]

what course are you in?

[hoary loom]

mechanical eng

[shell scarab]

no like what class

[hoary loom]

its called Hidva idk if u call it the same

its all about limits

and lopital

and integrals

[shell scarab]

Have you tried substitution? I think that might work

[winter patrol]

consider stuff like liate,
where you usually want to differentiate the power component
and also take note of what e^x^2 differentiated to

and choose a more appropriate v' and u

hint: ||x^3 = x^2 * x||

[hoary loom]

uff

[sturdy mango]

di method useful here

since this is gonna be long

oh wait

[hoary loom]

that shit is impressive

[sturdy mango]

u sub should work better

[winter patrol]

not really

[shell scarab]

Looks shorter to me if you do u-sub then partial integration

[sturdy mango]

i mean no harm trying

[winter patrol]

you'd end up having to do ibp anyway

[hoary loom]

do u think this would work ?

[sturdy mango]

but

reduces work

if u do it later

as less ibp possible

[winter patrol]

yeh, that should work

[hoary loom]

ok thank u so much guys for help

.close

[devout snow]

Channel closed

Closed by @hoary loom

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

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

[woven radish]

938c2cc0dcc05f2b68c4287040cfcf71

[rose rock]

What have you tried so far?

[spring oasis]

I was looking for help on how to start

[rose rock]

Oh okay

Getting the matrix representation of f would be a good start

Then if you recall
det(A - L I) = 0 when L is an eigenvalue of A (I is the identity matrix)

[spring oasis]

,, M_{BB} = \begin{pmatrix} 2 & 1 & 1 \ 0 & 2 & 1 \ k & 0 & -5 \end{pmatrix}

,w transpose {{2,0,k},{1,2,0},{1,1,-5}}

[woven radish]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by 938c2cc0dcc05f2b68c4287040cfcf71

[rose rock]

Yeah haha

[woven radish]

938c2cc0dcc05f2b68c4287040cfcf71

[spring oasis]

so?

[rose rock]

^

[spring oasis]

ok

[rose rock]

You can sub L = 3 before taking the determinant as well

[spring oasis]

,w det {{2-L,1,1},{0,2-L,1},{k,0,-5-L}} = 0 where L = 3

[wicked turtle]

gnarly

could just do row reduction and find what value(s) of k give you a nontrivial solution

[woven radish]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by ansh_3502

[rose rock]

Yeah

[spring oasis]

I appreciate all the help

.solved

[devout snow]

Channel closed

Closed by @spring oasis

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

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

[south plume]

So, basically my teacher has given the theorem lim x->p f(x) = lim x->p g(x), however, he doesn't explained how I was supposed to find g(x), if anyone could help I would be grateful. (I tried L'Hopital btw, still didn't work.)

[runic prawn]

what happens if plug in x=-2 in the top and bottom

[south plume]

0/0

[runic prawn]

l'hopital should work

[south plume]

It still gives 0/0 tho

[runic prawn]

g(x) could be anything, depends on the theorem

[slender mirage]

Then use L'Hopital again

Repeat till it no longer gives 0/0

[south plume]

I can? (I just started calculus I, so I have no idea.)

[runic prawn]

yes why not

it's just another limit

[south plume]

Alr then

Imma do it, hold on

[slender mirage]

Yes, as long as you verify your steps with us

So, it's just (-2x - 1)/(x - 2)

Did you get answer?

[south plume]

L'Hopital gives me -24/-16 (If I didn't miss), and the correct answer is -3/4

[slender mirage]

You probably did a mistake

[south plume]

Lemme redo, holdon

[slender mirage]

Also, answer is -3/4

[south plume]

Ah, yeah, misstyped

Mb

[south plume]

Yeah, I just did the math with 2 instead of -2 🤡 , it worked tho

Ty guys for the help

.close

[devout snow]

Channel closed

Closed by @south plume

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

[late cedar]

I'm confused as to what this is asking me to do. I have been able to fill in the first few cells involving P(X=x | p=0.05/0.1/0.2) but without the actual value for P(p=0.05/0.1/0.2) how am I supposed to be able to fill in the rest?

[late cedar]

I found the P(X=x | p=0.05/0.1/0.2) values with the geometric distribution formula p*(1-p)^(x-1)

[gusty nexus]

<@&268886789983436800>

[devout snow]

@late cedar Has your question been resolved?

[devout snow]

@late cedar Has your question been resolved?

[devout snow]

@late cedar Has your question been resolved?

Channel closed

Closed by @late cedar

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

[flint spade]

I think most of its right and would like someone to confirm

[flint spade]

(sorry for the handwriting)

[tropic skiff]

It doesnt seem like you fully simplified #1

[flint spade]

Thanks

[wind mason]

is that $8+(2x+1)7$?

[woven radish]

;(

[flint spade]

Which problem

[wind mason]

For #1.

[flint spade]

Yea

[devout snow]

@flint spade Has your question been resolved?

Channel closed

Closed by @flint spade

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

[last tartan]

should i prove this using induction? ive found that theres a cyclic result in the remainders of 3,9,1

[wind mason]

What exactly is the cyclic result?

And if there is one, induction is probably the way, though you could use casework here.

[last tartan]

just from doing the first few

$3^1 \equiv 3 \mod 13

    3^2 \equiv 9 \mod 13 

    3^3 \equiv 1 \mod 13$

and it repeats the 3,9,1 as u increase the exponent

oh me when backslashes on discord

[woven radish]

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

[wind mason]

Yeah.

Casework goes well here.

[last tartan]

so what exactly would my 3 cases be? i had $3^n \equiv 3 \mod 13$ if $n \equiv1\mod 3$ for the first case

[woven radish]

jess

[wind mason]

$n=3k+1$, $n=3k+2$, $n=3k+3$.

[woven radish]

;(

[wind mason]

Since you said it yourself, it repeats.

[devout snow]

@last tartan Has your question been resolved?

[last tartan]

why +1,2,3 instead of 0,1,2?

[faint gorge]

this looks like it starts with k = 0

and then you always add 3

[last tartan]

could you elaborate?

i have
$3^k\equiv 1 (mod 13) \text{ when } k\equiv0 (mod 3)

3^k\equiv 3 (mod 13) \text{ when } k\equiv1 (mod 3)

3^k\equiv 9 (mod 13)\text{ when } k\equiv 2 (mod 3)$

i don't fully understand how to prove this for all n+1

[woven radish]

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

[faint gorge]

You got 3 cases for $n \in \mbb{N}.\$
Suppose $k \in \mbb{N}_0.\$
The first case is $n = 3k+1$ which means $3^{3k+1} \equiv 3 \pmod {13}.\$
Then the second case is $n = 3k+2$ which means $3^{3k+2} \equiv 9 \pmod {13}.\$
Then the third case is $n = 3k+3$ which means $3^{3k+3} \equiv 1 \pmod {13}.\$
All three cases cover each eventuality of $n$ so you would be done.

[sturdy mango]

3k 3k+1 3k+2

these are possibilities

or that too yeah

[faint gorge]

Notice 3^(3k+3) = 3^(3k)

As said, I think the reason he chose 3k+3 is because k starts with 0, so wih 3^(3k) you would have first 3^0 but n starts with 1

but that's a technicality

You can write your answer as a piece wise function

[last tartan]

3^(3k+3) = 3^(3k) mod 13 right

[faint gorge]

yes

3^(3k+3) = 3^3k * 3^3 = 3^3k * 1 mod 13

[last tartan]

• 1 mod 13? not congruent?

[faint gorge]

use \ to remove the dot

[last tartan]

so for the first case

$3^{3k+1} \equiv 3 \pmod{13}$

i can simplify that to

$3^{3k} * 3^{1} \equiv 3\pmod{13}$

so then how can i use the previous facts we established?

[faint gorge]

I would just leave it as it is

[woven radish]

jess

[last tartan]

so for case 2 i can do the same
$ 3^{3k+2} \equiv 9 \pmod {13}$
rewrite as
$3^{3k} \cdot 3^{2} \equiv 9 \pmod {13}$

and same for 3

[faint gorge]

no

not +

\cdot

[last tartan]

oops

typo yes

[woven radish]

jess

[faint gorge]

yes

if that's better for you

[last tartan]

ok thank you for the help!

.close

[devout snow]

Channel closed

Closed by @last tartan

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

[last tartan]

im back

[misty crest]

they’re squares

find out what squares can be mod 5

[faint prawn]

t⁴ = 1 or 0 mod 5

[last tartan]

how did you come to that conclusion>

[faint prawn]

see numbers from 1 through 9

[distant helm]

just try t=0, t=1, t=2 and so on and see the loop

[faint prawn]

Yeah exactly

[last tartan]

so you're saying to compute
$0 \equiv 0 \pmod{5}$

[woven radish]

jess

[misty crest]

what

[last tartan]

im lawst

[misty crest]

it’s easier to work with squares first

1^2 = 1 mod 5
2^2 = 4 mod 5
3^2 = 4 mod 5
4^2 = 1 mod 5
5^2 = 0 mod 5
6^2 = 1 mod 5
7^2 = 4 mod 5
8^2 = 4 mod 5
9^2 = 1 mod 5

[last tartan]

how do we relate that to ^4?

[distant helm]

square both sides

[last tartan]

so its just all either 1 or 0 after squaring both sides

[misty crest]

yep because the 4 mod 5 ones become 1 and the 1s and 0s stay the same

[last tartan]

so that means a^4 , b^4, c^4 their sums are either 0,1,2,3 mod 5

therefore never congruent 4 mod 5

hot thank u

.close

[devout snow]

Channel closed

Closed by @last tartan

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

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

[tropic skiff]

,rotate

[chrome vault]

can someone help me figure out this question? i dont understand the way its worded

plus im not the best at this kinda math

[tropic skiff]

Dyk where the third quadrant is?

[chrome vault]

yeah

[tropic skiff]

In the third quadrant:
x is pos/neg?
y is pos/neg?

[chrome vault]

x is neg, y is neg

[tropic skiff]

,tex $+$

[woven radish]

King Leo

[tropic skiff]

Do you understand this?

[chrome vault]

yeah…? like do i understand the line is in the third quadrant?

[tropic skiff]

Ok

Can you draw a right triangle that includes

• the hypotenuse as the green line

and which horizontal leg stemming from the origin touches this triangle

I gtg

[tropic skiff]

,rotate

[restive river]

were you given a formula sheet?

[chrome vault]

i wont have one for the test, but i can give you all the ones they taught us

[restive river]

do you know double angle identities

[chrome vault]

i dont know the names, but if you write one out, i could give you the other two probably

[restive river]

one sec

[chrome vault]

like if you give cos, i could give you sin and tan

[restive river]

,rotate

[restive river]

do you know these

[chrome vault]

sin, yeah

cos, still getting the memorizing part down, but i got a general idea

tan, hell nah

its really just these identities that are the hardest ones that i dont know yet tho

[restive river]

now that is the basic bit

you can now pick like the sin one plug everything in then do that with one of the cos ones then the tan one

do you get it?

[restive river]

if you want I can solve a part for you as an example

[devout snow]

@chrome vault Has your question been resolved?

[chrome vault]

oop sorry didnt see ur msg

oooooh shit i get it now

i didnt even think to use those identities for triangle problems

tysm 🙏🙏🙏

[restive river]

np

[devout snow]

Channel closed

Closed by @chrome vault

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

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

[clear geode]

hello :)

[clear geode]

i'm trying to solve and equation

i need the intersection of a line

and a torus

defined by the red equation

before i try to solve it

i would like to know if it's a solvable equation

i know it's a quartic

[regal moat]

In case u dont have desmos and dont want to waste ur time?

[clear geode]

what

wdym

[regal moat]

Like with desmos, u only need to see if the line cross the torus

[clear geode]

no i need to find an equation

[regal moat]

If it does cross, the its a solvable equation

[clear geode]

i need to be able to find the solution analytically

it's for my code

i'm making a torus planet and i need the entry and exit points

to make the atmosphere

so i get an arbitrary vector and origin

for each pixel

and then

[regal moat]

Then trying to solve it, if there's no possible output, then its unsolvable

[clear geode]

i have a, b, and c as the radii of the torus

[regal moat]

Oh

[clear geode]

i know solving it will take a very longt time

so im wondering if it's solvable analytically

[regal moat]

The easiest way I could think of is

compute the shortest distance d from the line to the torus center C

If d > R +r, the line cannot intersect the torus, and you can skip the expensive check

U can imagine the R + r is just the radius for a sphere that would enclose ur torus

[clear geode]

no i want to know if the equation is solvable

like

[regal moat]

Bruh

[clear geode]

if it's possible to get the whole equation

[regal moat]

If the shortest distance from the line > than the R + r; then its not solvable

[clear geode]

i'm not asking if there's a real solution

i'm asking if the equation is able to be solved in terms of t

[regal moat]

idk then, pretty sure the only way to know its solvable or not is just to solve it ig

[clear geode]

like the constant t

ok

thank u

[devout snow]

@clear geode Has your question been resolved?

[clear geode]

ok so

i tried to solve the equation

and i'm left with this

do i have to

substitute the x, y, and z values into the function?

that will make a lot of terms

[clear geode]

that's 53 terms

:(

[devout snow]

@clear geode Has your question been resolved?

[spare crypt]

if the line stays at the origin it becomes a 2d problem that should be fine, otherwise I assume it's really ugly. there's a formula in section 2 here https://arxiv.org/pdf/2301.03191, or you can use something like z3 in python I think?

[clear geode]

ok but

the line being at the origin doesnt allow for ray tracing

wait a sec

[spare crypt]

yea anything off-origin is basically working with ellipses which always suck

[clear geode]

i just had an idea

what if

i get the equation for a ring

and then

seth the equation to be

(ring equation) = (thickness of torus)

and then solve

[clear geode]

@spare crypt i tried to do that

and i ended up

with the exact same equation :(

[devout snow]

@clear geode Has your question been resolved?

Channel closed

Closed by @clear geode

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

[celest sable]

Is this considered a "clear" proof or would it benefit more with steps shown?

[celest sable]

Let $\phi(\cdot)$ be the p.d.f of $\mathcal{N}(0,1),$ i.e. $\phi(t) = \frac{1}{\sqrt{2\pi}} e^{-\frac{t^2}{2}}$. For any $u \geq 0$, let $\Phi(u) := \int_{t \geq u} \phi (t) dt$ be the c.d.f
\ \
Prove the following bounds for all $u \geq 0$
[
\bigg (\frac{1}{u} - \frac{1}{u^3} \bigg) \phi(u) \leq \Phi(u) \leq \frac{1}{u}\phi(u)
]

\begin{proof} To obtain the upper bound, integration by parts is necessary.
[
\Phi(u) = \int_u^\infty \phi (t) dt = \int_u^\infty \frac{1}{t}(t\phi (t)) dt \hspace{2em}
\begin{tabular}{c|c}
\textbf{D} & \textbf{I} \ \hline
$1/t$ & $t\phi(t)$ \
$-1/t^2$ & $-\phi(t)$ \
\end{tabular}
]
[
\implies -\frac{1}{t}\phi(t)\bigg]u^\infty - \underbrace{\int_u^\infty \frac{1}{t^2}\phi(t) dt}{\geq \ 0, \ \forall \ u\geq 0} \leq \underbrace{\lim_{t\rightarrow\infty}\bigg(-\frac{1}{t}\phi(t)\bigg)}_{= \ 0} - \bigg(-\frac{1}{u}\phi(u)\bigg) = \frac{1}{u}\phi(u)
]
[
\implies \ \Phi(u) \leq \frac{1}{u}\phi(u)
]
To obtain the lower bound, another iteration of integration by parts on the remaining integral is necessary.

[
\int_u^\infty -\frac{1}{t^2}\phi(t)dt = \int_u^\infty -\frac{1}{t^3}(t\phi(t))dt \hspace{2em}
\begin{tabular}{c|c}
\textbf{D} & \textbf{I} \ \hline
$-1/t^3$ & $t\phi(t)$ \
$1/t^4$ & $-\phi(t)$ \
\end{tabular}
]
[
\implies \frac{1}{t^3}\phi(t) \bigg]u^\infty + \underbrace{\int_u^\infty \frac{1}{t^4}\phi(t)dt}{\geq \ 0, \ \forall \ u\geq 0} \geq \underbrace{\lim_{t\rightarrow\infty}\bigg(\frac{1}{t^3}\phi(t)\bigg)}_{= \ 0} - \bigg(\frac{1}{u^3}\phi(u)\bigg) = -\frac{1}{u^3}\phi(u)
]
[
\implies \ \Phi(u) \geq \bigg(\frac{1}{u} - \frac{1}{u^3}\bigg)\phi(u)
]
Combining the upper and lower bound gives the final bound as follows
[
\bigg (\frac{1}{u} - \frac{1}{u^3} \bigg) \phi(u) \leq \Phi(u) \leq \frac{1}{u}\phi(u)
]
\end{proof}

[woven radish]

cameron

[celest sable]

I ask if this is clear because I have been getting mixed answers from different people and I want to know if anyone else had their own thoughts

[devout snow]

@celest sable Has your question been resolved?

[devout snow]

@celest sable Has your question been resolved?

[devout snow]

@celest sable Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

[granite arch]

How do you diagonalize a matrix?

[granite arch]

I know that i have to find the eigenvalues

Then do Ax = λx

So (A-λ)x = 0

This is the part i have a problem with

[granite arch]

Its kind of tedious to do this line

My calculator simply tells me infinite solutions, how do i find a set of (x,y,z) that satisfies (A-λ)x = 0 quickly

[strange arch]

Yes, you need the characteristic polynomial

find its roots to get the eigenvalues

for each eigenvalue solve (A-lambda)x = 0 to get the eigenvectors (or eigenspaces)

[granite arch]

yes

how do i solve it?

is there a fast way

[strange arch]

hm at this point you can probably only use regular quick methods like Gauss

assuming you try to calculate it by hand

[granite arch]

yes i have to sadly

[finite helm]

you don't need eigenvalues to diagonalize

[granite arch]

do i have to make one row (0, 0, 0)

[granite arch]

What really

[strange arch]

wdym

for Gauss you solve for the staircase form

which is pretty quick

[finite helm]

^^

[granite arch]

gaussian elimination?

[strange arch]

yes

[granite arch]

do you mind giving an example of what i should make it look like please?

thank you

[finite helm]

Look at the first column of the matrix, find the least common multiple of those numbers, multiply all the rows so that the first entry is the LCM, subtract first row from all other rows, rinse and repeat for the submatrix

[strange arch]

probably faster to watch the process online :D

but if you've seen the process before

then you can take this as reminder

getting all 0's below the diagonal column-wise, and then 0's above the diagonal row-wise

[granite arch]

damn that's quite some work lol

[strange arch]

sure

after doing gauss a few times, it probably only takes about a minute though

[granite arch]

i see, thank you

@strange arch this can be done WITHOUT gauss?

the marking scheme's method uses 3x3 determinant

[devout snow]

@granite arch Has your question been resolved?

[devout snow]

@granite arch Has your question been resolved?

[topaz crag]

Did you do the first question ?

[devout snow]

@granite arch Has your question been resolved?

[granite arch]

yes

[topaz crag]

I don’t really understand your question. This looks solved without gauss

[granite arch]

But i don't get the steps

I want an explanation for it

[devout snow]

@granite arch Has your question been resolved?

[topaz crag]

Ok let's take this step by step

How do you do this ?

[devout snow]

@granite arch Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

[brave spear]

hi! could someone please explain how to do this, im so confuzzled. thank youuu

[lusty sapphire]

try writing sec and csc in terms of cos and sin

[brave spear]

isnt sec = 1/cos ??

and then csc = 1/sin ??

[runic prawn]

yes

[brave spear]

so sec (theta) = 5 , which means it would equal cos (theta) = 1/5 ??

[runic prawn]

yes

btw is that madison beer in your pfp

[brave spear]

i got cos, csc is the one im struggling with

[runic prawn]

find sin

[brave spear]

yes lol, ppl said i looked like her in that pic

so i just kept it

its been there even since i got discord

lmao

youre the first person that actually asked me

[runic prawn]

damn

[brave spear]

no like in a good way

would i do cos^2theta + sin^2theta = 1 to find sin?

[runic prawn]

i also meant damn in a good way

[lusty sapphire]

yes, and then you'll need to use the knowledge of your quadrant to determine the sign of sin

that pfp looks like an old friend of mine from my cell bio class, but that was a million years ago

[misty crest]

damn bro you were in there with a madison beer lookalike?

🤝🏻

[lusty sapphire]

madison beer?

[misty crest]

yea she’s famous, it’s the girl in her pfp

[brave spear]

alright i got it correct! thanks for the help.

.close

[devout snow]

Channel closed

Closed by @brave spear

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

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

[stray orbit]

Can someone check these

[tropic skiff]

,w 4((-(xxxx + 2xx + 3)^(-2))/2) = integral of ((xxx + x)/(xxxx + 2xx + 3))

[woven radish]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by .king.leo.

[stray orbit]

Is it right?

.close

[devout snow]

Channel closed

Closed by @stray orbit

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

[spice wing]

How would i solve this im confused

[spice wing]

i need some explanation

[latent quarry]

Uhh

Wait

Let me prove that

Nah it's wrong

[forest yarrow]

What type of geometry is this bro

[latent quarry]

It's not congruent

[forest yarrow]

What is it asking for

[spice wing]

its asking for x

[crisp tapir]

x is not a point

[spice wing]

its intersection of ca and eb

[latent quarry]

Asking for coordinate or

What

[crisp tapir]

bro what how will you solve for a point

[spice wing]

the angle

[latent quarry]

Oh

That is easier

CBX = 30

XCB = 45

Use this

[spice wing]

ohhhh

ok that makes life easier

thank you

[latent quarry]

[spice wing]

.close

[devout snow]

Channel closed

Closed by @spice wing

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

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

Is the math and sig figs correct on this

[sturdy mango]

yea

u pick the least

sig figures

as u lose precision upto it when multiplying

[blazing juniper]

So for this one

How much sigs would I use

[devout snow]

@blazing juniper Has your question been resolved?

[blazing juniper]

<@&286206848099549185>

[devout snow]

@blazing juniper Has your question been resolved?

[lethal pollen]

Depends on what your teacher wants

In my syallbus final answer is given to 3s.f with 5s.f for intermediate steps

But this differs for country to country

In this case you get exact values though so maybe you don't need to round using sig fig

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

[restive tree]

.reopen

[devout snow]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[rugged sparrow]

wut

[restive tree]

/reopen

[rugged sparrow]

open a new channel

[restive tree]

oh mah bad bro

[rugged sparrow]

this wont reopen

[restive tree]

/close

go to 31

whoops

[devout snow]

Available help channel!

Send your question here to claim the channel.

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

[bold saffron]

I don't understand smth max area yea we differentiate it to get max area
But why can't use take max amplitude of sin and cos =1 and solve for a
Yea as sin 2(t) and sin (t) they are not in phase but I changed it to sin (t)(x+ycos(t)=a

Can't I take max amp =1 for sin t and cos t and find a? What's wrong with that method I don't fully understand

[devout snow]

@bold saffron Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[bold saffron]

.reopen

[devout snow]

✅

@bold saffron Has your question been resolved?

[devout snow]

@bold saffron Has your question been resolved?

[devout snow]

@bold saffron Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

[devout snow]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

Available help channel!

Send your question here to claim the channel.

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

[sand quarry]

Let $G$ be a finitely generated group, and let ${N_i}{i\in\N}$ be a descending chain of normal subgroups: [
G = N_0\supseteq N_1\supseteq N_2 \cdots
]
such that each quotient $\5{N_i}{N{i+1}}$ is finite.

\bigskip
How do I prove that if $G$ is residually finite, then $\bigcap_{i=0}^\infty N_i$ is trivial?

[woven radish]

Aero

[devout snow]

@sand quarry Has your question been resolved?

[last sequoia]

no one will answer you

go on an alt account, post a chatgpt response

then someone will mad and correct it for u

[wind mason]

Maybe post in https://discord.com/channels/268882317391429632/496784958430380033 . They might be more helpful. As for now, just wait until the next bot cycle comes. If nobody has answered by then, just close the post here and post in the channel provided.

[sand quarry]

sounds good

[devout snow]

@sand quarry Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

[serene horizon]

hello, help me please

[serene horizon]

.close

[devout snow]

Channel closed

Closed by @serene horizon

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

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

[oblique mulch]

why do they take tan(22/3) instead of tan(22/-3)? since the 3 is in the second quarant. im getting confused on like how i need to adjust these angles all the time. do i need to like add 180 or something after taking tan(22/-3)?

[oblique mulch]

also why did they do tan(3/22) isnt it oppsoite over adjacen

[winter patrol]

did you draw a pic for this problem?

[frosty mantle]

<@&268886789983436800>

[oblique mulch]

I put 22 at the head of -3

[frosty mantle]

try drawing just the triangle without the graph part

and write the side lengths

[oblique mulch]

Idk what you mean

[winter patrol]

your arctan(22/-3) gives the red

[oblique mulch]

that’s very confusing, how do I memorize like all the adjustments I need to do to get the right answer?

[winter patrol]

consider which angle you want in your diagram

ultimately you want to measure the deviation from North, in this case the green angle

and the simplest way to do that would be to consider

[oblique mulch]

You do the red angle - 180

[winter patrol]

consider that triangle

which gives you the angle you want directly

ignore the negative sign in the -3 when calculating that

[oblique mulch]

how did you know to flip the triangle how would I know to do that

[winter patrol]

by having a clear idea of which angle you want in your end goal

and marking that in your diagram

[oblique mulch]

My plan was the get the angle and then like subtract 90 or whatever to get this angle

[winter patrol]

you can do that

if you want to first get this angle

[oblique mulch]

yeah but why is that arctan 22/-3 gives the angle in quadrant 4? I wouldn’t know that and it would make me get the problem wrong

[winter patrol]

you can take the arctan of (22/3),
ignore the sign of -3 for your reference triangle

the range of arctan is (-90°, 90°)
info about quadrant is lost when putting values into the arctan function
you'd either get something in Q1 or Q4 or 0

arctan(22/-3) would give you the red,
adding 180° would get you the blue
and subtracting 90° from that would give you the green angle

[oblique mulch]

But 1.7 radians is 97 degrees

arctan(22.3) give 1.7

[winter patrol]

where's 22.3 coming from

[oblique mulch]

22/3

Typo

[winter patrol]

doing arctan(22/3) gives you the size of the green angle

,w arctan(22/3) in degrees

[oblique mulch]

Oh yeah I was looking at tan my bad

[woven radish]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by ramonov

[winter patrol]

and subtracting that from 90° gives you what you want

,calc 90 - 82.23

[woven radish]

Result:

7.77

[oblique mulch]

So you’re saying whenever you need to do arctan….just make the input positive and then manipulate it to get to the actual quadrant you need it

bc if you make it positive then you know it will always be in quadrant 1

[winter patrol]

that's the way i'd recommend doing it

[oblique mulch]

Thanks for your advice

[devout snow]

@oblique mulch Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

[quartz scroll]

is this formulation of Thales' theorem correct? "If a straight line is drawn in a triangle parallel to one of its sides, then this straight line divides the other two sides into proportional segments."?

[rotund umbra]

I think soo

There apears to be two "thale's theorem"s

https://en.wikipedia.org/wiki/Thales's_theorem
https://en.wikipedia.org/wiki/Intercept_theorem

[devout snow]

@quartz scroll Has your question been resolved?

[rotund umbra]

Ah.

• "Thales' Theorem": "If a triangle is inscribed in a circle with one side equal to the diameter, then this opposite angle is 90 degrees"
• "Thale's Intercept Theorem": "IF two parallel lines cut two rays, then they divide them into equal ratios".

So yes, you have the right wording, but for Thale's Intercept Theorem.

(also known as the Basic Proportionality Theorem)

[devout snow]

Channel closed

Closed by @quartz scroll

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

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

[vernal cave]

Part A should be (0.35 * 0.01) + (0.65 * 0.03) according to the Law of Total Probability

Part B can be expressed as P(A | D) but I don't know what method to apply here to solve the conditional probability

[near trout]

bayes rule

[vernal cave]

Nobody expects the bayes theorem

Let me try it rq

[vernal cave]

I know Bayes is often expressed as

$P(A|B) = \frac{P(B|A)P(A)}{P(B)}$

I think

I'd have to double check that one

The conditional probability formula is

$P(A|B) = \frac{P(A \land B)}{P(B)}$

[woven radish]

Eyesonjune

[vernal cave]

What is it about this that makes it use Bayes and not conditional probability

[woven radish]

Eyesonjune

[vernal cave]

Fixed Bayes theorem

<@&286206848099549185>

[warm grotto]

What do you mean by conditional probability?

[vernal cave]

This

.close

[devout snow]

Channel closed

Closed by @vernal cave

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

[crimson vale]

Hello

[crimson vale]

Soo I have a problem in surface area and vol. Chapter

It's question no. 48

Anybody know how to get the height??

[warm grotto]

Height?

[crimson vale]

Ye i guess how to do this

Tell from beninging

The formula for hollow cylinder is π(R²-r²) h

Soo I guessed we need to find height...

[warm grotto]

If I'm reading the problem correctly, you aren't dealing with a cylinder.

[crimson vale]

Bro a tube is a cylinder right?

Soo how to do?

[warm grotto]

@slender mirage ||Am I being dumb? With the measurements given I'm assuming the pipe makes a torus, no?||

[crimson vale]

Nah bro it isn't a torus

[warm grotto]

Then you, indeed, don't have the length of the pipe.

[crimson vale]

Bruh

[warm grotto]

And we're, at this point, imagining a tube which is 35cm thick

Not the tube itself, the material

[crimson vale]

Yeah okay

[warm grotto]

Seems silly, but if we concede that, it might just be asking for area per unit of length

[crimson vale]

Bro i don't think so

[warm grotto]

The idea of a truck having a pipe in the shape of a torus being similarly ridiculous, so it's not like I can put my interpretation on a high ground

[crimson vale]

Bro let me send u a diagram of the fig

It's a rough diagram don't gudge

Bruh leave it I'll come back to it later

Thanks for spending your time on my dumbass @warm grotto

.close

[devout snow]

Channel closed

Closed by @crimson vale

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

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

[slender mirage]

.@crimson vale Yes it is a Torus. With radius of cross-section given as 28cm. My response was to "a tube is a cylinder"

[crimson vale]

Oo shit, thanks dude

[crimson vale]

I found the ans either eay

Way*

Thanks again 🙂

[slender mirage]

^^ no

Worries

[crimson vale]

I guess close the chat

.close

[devout snow]

Channel closed

Closed by @crimson vale

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

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

[gray galleon]

what is the method to derive the right from the left

[junior flax]

Personally, I’d cross multiply the right of the equation. If you aren’t given the right hand side, or have to manipulate the left hand side, I’d do long division

[gray galleon]

this is what I get with long division, what am i doing wrong

[junior flax]

Somethings definitely wrong with your long division. I don’t know synthetic division, so I’m not sure where you went wrong, but you shouldn’t have an x greater than the first power.

[gray galleon]

can you show me what you know, the method you use for division?

[junior flax]

Hold up for a second, I need to grab some pen and paper

[gray galleon]

okk thank you!!

[junior flax]

Sorry if it’s a bit messy, I always skipped my handwriting class

Essentially, through long division. You can confirm that (x-2)(x^3+2x^2+x)+(3x^2+2x+1) = (x^4+1)

[gray galleon]

I gOt iT

thank you so much

[devout snow]

@gray galleon Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

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

[elder pelican]

Hi! So I need help in understanding using the quotient rule when it comes to negative exponents. There would be times I’d understand it and times when I don’t. For example (6x^3)^3/x^15.
I’m not sure how to solve it.

[elder pelican]

This is a positive exponent but how would I proceed if they were negative?

[vital sedge]

you're asking what if it was (6x^-3)^3?

[elder pelican]

Yes