help-0

[lost belfry]

did you mean this to be 1?

[patent vale]

yes

[lost belfry]

this drawing is making little sense

what are the numbers supposed to indicate?

[patent vale]

negative just means going down

or backwards

all red lines are vertical or horizontal

[lost belfry]

can you write your problem in terms of a proper question?

[patent vale]

i dont know how to write this up but ill try

[lost belfry]

its presumably just asking to find a slope, so it cant be that hard

if you can explain your diagram properly also it would be great

[patent vale]

i dont know if reflection is the proper way to describe this

[lost belfry]

okay, so the negative numbers in the original make no sense

[patent vale]

yeah that was just brainblast

[tranquil lagoon]

This problem will be left as an exercise to the reader

[patent vale]

[fluid compass]

I like how you made the angles to hide that it's 45 degrees

[patent vale]

lmao bro knows my game

i know the answer and im not looking for why its the answer im looking for how

[fluid compass]

best method would be to 'complete the rectangle'

and join the 2 points

[patent vale]

yeah but how do you knowwwwwwwwwwwww its a rectangle

[lost belfry]

here is a more bashy solution:
suppose the angle made by the line with $AB$ is $t$.\
then $BG = \tan(t)$. So $GC = 3 - BG = 3- tan(t)$. \
then note that angle $FGC$ is also equal to $t$. \
$So FC = tan(t)(3-tan(t))$\
So $DF = 3 - FC = tan^2(t) - 3tan(t) + 3$\
finally we know angle $EFD$ is also $t$\
So $tan(t) = \frac{1}{tan^2(t) - 3tan(t) + 3}$. Solve this cubic in tan(t) to get the slope of the line

[patent vale]

,w tan(t) = 1/tan^2(t) - 3tan(t) + 3 solve ts

[ocean seal]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by steelballbell

[patent vale]

,w tan(t) = 1/tan^2(t) - 3tan(t) + 3

[ocean seal]

Results provided by WolframAlpha

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

Requested by steelballbell

fastrack_and_backtrack

[patent vale]

,w tan(t) = 1/(tan^2(t) - 3tan(t) + 3)

[ocean seal]

Results provided by WolframAlpha

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

Requested by steelballbell

[patent vale]

pi/4

okay

[lost belfry]

as you can see, we indeed get pi/4 to be the principal colution

that is 45 degrees

[patent vale]

isnt it negative though

oh wait

[lost belfry]

you can read my solution, where t is the angle made by the line and AB

it should not be negative just be looking at it

[patent vale]

yeah i just noticed okay this problem makes sense now

[lost belfry]

this is t, in my solution

its just chasing angles and lengths till you reach full circle

to get an equation

[patent vale]

ok thanks i gurt it

.close

[lone heart]

Channel closed

Closed by @patent vale

Use .reopen if this was a mistake.

[lone heart]

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.

[crude cloud]

How to find externally

[rustic coral]

Do yk what the diagram would look like for external division

[crude cloud]

No

But pq should be 3?

[rustic coral]

I’m using 2 and 1 to represent the ratio

Not the actual lengths

Call them 2k and k if it makes you happy

Wait the length of PQ isn’t even 3

What

Where is 3 coming from

[crude cloud]

2+1

[rustic coral]

???

You’re not dividing it internally, but externally

[crude cloud]

Pr-2 rq -1

[rustic coral]

By definition, external division means that you extend the line segment to a point beyond the line segment

So if we divide externally in the ratio 2:1, then you’re extending to the segment to a point such that the “new” part is half the length of the overall new segment

[crude cloud]

Ok

[rustic coral]

Granted the question is a little ambiguous cause it never says whether you extend beyond P or beyond Q

So there’s that

[crude cloud]

The question says r divides pq

R divides pq ?

@rustic coral

[rustic coral]

“divides the line joining”

So R is on the line, not necessarily the segment

And like I said earlier, for external division, it won’t be on the segment

In general, if R divides PQ in the ratio m:n, then PR:RQ=m:n

(Assuming that you extend beyond Q and not P)

Note that this is the same ratio as internal division, it’s just that the location of R differs (on vs off the segment PQ)

[crude cloud]

Ok

I got it now

[lone heart]

@crude cloud Has your question been resolved?

Channel closed

Closed by @crude cloud

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.

[alpine sable]

In the modulus inequalities , i do realize how it makes sense to include '+' and '-' for individual modulus in wavy curve method in a single equation but dont know how it does in the multiple modulus equation.

[buoyant saddle]

wavy curvy

🤔

[alpine sable]

yes its the wavy curve method

[buoyant saddle]

i don’t know what that is but it’s best to just use the definition of absolute value for each

then break it up into intervals based on that

[tacit arch]

,tex .abs def

[ocean seal]

riemann

[alpine sable]

how would you do it your way for multiple modulus inequalitites

[buoyant saddle]

^

[alpine sable]

sorry but its the way i was taught , not well versed about the other method . Whats it called ? ill look up for it

[alpine sable]

umm so wut i am understanding is

[buoyant saddle]

it doesnt have a name as far as i’m aware

it’s just using definitions

,av vivseul05

[ocean seal]

vivseul05's Avatar

Click here to view the image.

[alpine sable]

hmm didnt get it , i know ill have to make cases for each and every modulus then , but dont know how to integrate together

[buoyant saddle]

i’ll do a simpler example only involving two ||

|x - 1| + |x| < 2

so we know that for x >= 0, |x| = x and for x < 0, |x| = -x. likewise we know that for x >= 1, |x - 1| = x - 1 and for x < 1, |x - 1| = -x + 1

then if x >= 1 we have |x - 1| + |x| = x - 1 + x (note that since x >= 1 we also have that x >= 0)

then for x < 0 we have |x - 1| + |x| = -x + 1 - x

and for 0 <= x < 1 we have |x - 1| + |x| = -x + 1 + x

this exhausts all the intervals now

just analyze each interval separately

x >= 1 : x - 1 + x = 2x - 1 > 2 —> x > 3/2

[alpine sable]

i really appreciate your effort , but itll take some time to really feel it

[tacit arch]

Should draw one of your patented screenshot hand drawn graphs again

[buoyant saddle]

need the keyboard in it too

[alpine sable]

😂

[alpine sable]

but really i'd be really grateful to have someone to answer this query

[buoyant saddle]

lmao

[tacit arch]

It'll help to do the simpler one knief gave you first

[buoyant saddle]

doesn’t have the attention span for it i guess

[alpine sable]

hmm i know desmos just dont know how to use it for the complex ones

[tacit arch]

abs(x) also works

[alpine sable]

how do you do that for this?

[buoyant saddle]

it’s positive after the zero point for each of them and negative before it

if you read my written out example it would make sense

[alpine sable]

oh there are no sol for it

.close

[lone heart]

Channel closed

Closed by @lyric scaffold

Use .reopen if this was a mistake.

[lone heart]

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.

[hot vale]

How do I do this

[hot vale]

Do I need to use multinomial expansion theorem

[jolly notch]

not necessarily, you can treat this as a binomial system as well

[hot vale]

how

[jolly notch]

[(1+x)+(x^2)]^5

two terms

[hot vale]

oh ok

ima try that then

Would this be the best way to do the expansion

.close

[lone heart]

Channel closed

Closed by @hot vale

Use .reopen if this was a mistake.

[lone heart]

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.

[carmine topaz]

why does the series have to be >5 ? does the integral guarantee anything about the series value ?

[lethal belfry]

you mean why does the sum of the series have to be more than 5?

[carmine topaz]

ummm the answer is D and it says the series > 5

so...

yea

[woeful zenith]

Because integrals are a continuous area and sums are a sum of rectangles

Like this

[keen idol]

there is another relevant hypothesis here: decreasing function

[mossy reef]

It can be helpful to visualize an Upper Riemann Sum of a positive, continuous, and decreasing function.

[sour mica]

Its the upper riemann sum coz f is decreasing

[woeful zenith]

Might help to clarify that these have width 1

[carmine topaz]

wait why does the sum has to be like that

[woeful zenith]

F is decreasing

and the sum and integral start at the same point

[carmine topaz]

i mean yea but is that what series are?

[woeful zenith]

Sum of rectangles?

Yeah

[carmine topaz]

that sum is js bunch of rectangles?

[sour mica]

the series just sums f(1) + f(2) + ..., which is simply f(1) * 1 + f(2) * 1 + ... which you can claim represents the area of rectangles

[carmine topaz]

i thought its some continuous numer typa thing

[woeful zenith]

Basically you're taking the value of the function at those discrete points, which can be visualised as a rectangle with height y and width 1

[carmine topaz]

wait this doesnt make sense why is a series like that

am i tripping 😭

[woeful zenith]

If that makes sense

[woeful zenith]

Nah my explanation is kinda shit

[keen idol]

what is the area of a rectangle?

in general

like the formula

[carmine topaz]

height * width

[keen idol]

great now look at this

f(1)*1 can be seen as width 1 and height f(1)

f(2)*1 can again be seen as width 1 and height f(2)

[woeful zenith]

wait are my msgs sending

Okay now they are

[carmine topaz]

wait so series are js bunch of rectangles and i wasnt told this thing this whole time?

[woeful zenith]

Thése rectangles have width 1 btw

[woeful zenith]

It's just another way of looking at it

[woeful zenith]

And the left end of the first one is at the start of the sum, x=1

[keen idol]

just for better visualization

[carmine topaz]

hmmm ok but why should it be greater then the integral? nowwhere did it said to use certain type of sum so it kinda depends? no?

[woeful zenith]

The sum starts at x=1 and so does the integral

[carmine topaz]

ohhh i get it

its js lowkey weird thing of series as a sum

wait no the series here is sum right

[woeful zenith]

So the sequence decreases only when you get to x=2, which is the next term, but the function f(x) is decreasing the whole way

[carmine topaz]

yea but like expressing series using bunch of rectangular feels wacky 😭

[woeful zenith]

technically an integral is the same idea

But instead of rectangles of width 1 you use vanishingly/infinitesimally thin rectangles

[carmine topaz]

but why is the series like that? shouldnt it be some smooth number?

[lone heart]

@carmine topaz Has your question been resolved?

[winter light]

What do you mean by smooth number?

[carmine topaz]

like isnt that what series are ? cuz some rectangles doesnt feel right ? no ?

[buoyant saddle]

well it’s just that you can interpret it as that

taking the width of each rectangle to be 1

and the height of the nth rectangle to be the nth term in the sum

[buoyant saddle]

but what is a smooth number

[carmine topaz]

bunch of overestimate rectangle aint smooth idk how to explain but

[buoyant saddle]

smooth has a precise mathematical definition that isn’t relevant here

[carmine topaz]

ok

[buoyant saddle]

you didn’t understand the pictures they sent?

[buoyant saddle]

here

[carmine topaz]

i understood but i dont like thinking series in that way like it aint smooth 😭

[buoyant saddle]

an integral is a series

just with decreasing width of rectangles

[carmine topaz]

so its like the integral expression is the exact one and the series are goofy verison of that ?

[buoyant saddle]

again, series can be interpreted as the sum of areas of rectangles with width 1

[carmine topaz]

imma js accept this 😭

[buoyant saddle]

i mean do you disagree that it gives that area?

[carmine topaz]

no but my brain cant be convinced to think of series as some wacky rectangle 😭

in my head series = smooth number

[buoyant saddle]

$\sum_{n = 1}^{\infty} \frac{1}{n^2} = (1)(1) + (1)\left(\frac{1}{4}\right) + (1)\left(\frac{1}{9}\right) + \dots$

[buoyant saddle]

don’t do this

[carmine topaz]

so it js same width with changing height ?

[buoyant saddle]

yes

let me make it on desmos

hold on

[carmine topaz]

the overestimate rectangle diagram js aint it 😭

[buoyant saddle]

https://www.desmos.com/calculator/m1eatavnrr

[ocean seal]

knief

[buoyant saddle]

the area of those rectangles is precisely this sum

but since 1/n^2 is decreasing, the series is larger than the integral

like a left riemann sum

[carmine topaz]

so its like series could be anything like a sum it doesnt really have to be smooth ?

[buoyant saddle]

wdym by smooth though

i mean you’re ok with left/right riemann sums right

[carmine topaz]

yea

[buoyant saddle]

this is just taking the width of each subinterval/rectangle to be 1

and it’s a left endpoint sum

[carmine topaz]

so its js sum

series shouldn't be sum 😭

[buoyant saddle]

a series is a sum

doesn’t have to be interpreted as a riemann sum

but i mean by definition it’s an infinite sum

[carmine topaz]

ok

i get it

its js my brain doesnt like it

thanks for explaining 😀

.close

[lone heart]

Channel closed

Closed by @carmine topaz

Use .reopen if this was a mistake.

[buoyant saddle]

you’re welcome

[lone heart]

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.

[frail walrus]

why does delta t go on the bottom when simplifying

dividing something is the same thing as multiplying by the reciprocal?

so why isnt it at the top

[north rover]

Change in time, no?

[frail walrus]

yes delta t

[hushed locust]

,, \frac{\Delta s/r}{\Delta t} = \frac{\Delta s}{r} \cdot \frac{1}{\Delta t}

[north rover]

The reciprocal of $\Delta t$ is $\frac1{\Delta t}$ lmao

[ocean seal]

cloud

;(

[frail walrus]

yes but its already 1/delta t

right?

[proven leaf]

(\frac{\frac{\Delta s}{r}}{\Delta t}=\frac{\Delta s}{r}\div\frac{\Delta t}{1}=\frac{\Delta s}{r}\cdot\frac{1}{\Delta t}=\frac{\Delta s}{r\Delta t})

[ocean seal]

PajamaMamaLlama

[frail walrus]

dude typing texit so fast wtf

[north rover]

"dividing by something" which you're dividing by $\Delta t$ here

[modern sedge]

dividing by sth is the same thing as multiplying by the reciprocal of sth

[ocean seal]

;(

[frail dagger]

LaTeX gods.

[frail walrus]

bro im being overstimulated

[north rover]

Does this make sense

[frail walrus]

this helped

[frail walrus]

yeah this makes sense now

ok thanks guys

latex gods

.close

[lone heart]

Channel closed

Closed by @frail walrus

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.

[weak latch]

Help me solve for x.

[weak latch]

Also dont help too much, id prefer to do most of the thinking

[potent mirage]

open all the brackets

[weak latch]

Ok

[potent mirage]

also do u just have to get x in terms of a?

[weak latch]

in terms of everything else

[potent mirage]

ohk continue

[weak latch]

How did i get x=x+2

💔

[potent mirage]

show ur work pls

[modern sedge]

im getting the same thing

[hasty hill]

Equation is wrong..check how you got this..maybe try posting the original question

[potent mirage]

ok that just means that no value of x satisfies the equation

[weak latch]

Ohh

The question does have a marking

Hint

[potent mirage]

what is it

[weak latch]

It just said the answer

No value satisfy

[potent mirage]

yeah thats it

[weak latch]

How do i close

[potent mirage]

.close

[weak latch]

.close

[potent mirage]

type this

[lone heart]

Channel closed

Closed by @weak latch

Use .reopen if this was a mistake.

[lone heart]

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.

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.

[north rover]

skel

[meager kindle]

I don't get the b)

[meager kindle]

I need it to translate from german bc i have no clue how the english terms are

[tacit arch]

!msgdel

[lone heart]

The original post of this help channel has been deleted, and it will abruptly close and possibly lock. (This is irreversible.) Please claim a new channel, and don't delete the first message of any future channel you claim.

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.

[slow plume]

help

[cobalt oriole]

oh

[slow plume]

sorry 😭

[cobalt oriole]

:D

[slow plume]

anyway i dont undertsand jack also why did they use +6 as the asymptote instead of 4? erm yeah

[kind trellis]

what part don't u understand

[slow plume]

well basically the equations

so 2 and 3

[kind trellis]

a * b^x + q and a/x + 6?

[slow plume]

yes

[kind trellis]

im GUESSING they want you to solve for a b and q

[slow plume]

yes they do sorry for not mentioning

[kind trellis]

so we know f goes through the points (0,4) and (-2,-12) right

[slow plume]

yes

[kind trellis]

from the graph

so what happens if you put x = 0 and f(x) = 4 in the equation?

[slow plume]

well see i need to solve a and b

q is fine as it would be +4, and we'd substitute 4 into f(x) the +4 becomes -4 cancelling it out and making a =0

that frmo what i've tried

and that can't be true as if it was it would make b^x = 0 and the answer as q

[kind trellis]

if x = 0 and f(x) = 4, then we get a * b^0 + q = 4

which is a + q = 4

[slow plume]

yes...

[kind trellis]

so a = 4 - q

[slow plume]

yeahhh im stumped

lmao forget it im clocking in early

.close

[lone heart]

Channel closed

Closed by @slow plume

Use .reopen if this was a mistake.

[lone heart]

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.

[feral drum]

What's wrong

[kind trellis]

pressed the wrong - sign?

[hushed locust]

yeah make sure to use the (-) button

[feral drum]

I hate calculators

[kind trellis]

I have exactly the same one

you can check all ur answers on tests

it's so good

[onyx swallow]

crazy that they can't code that in so that both - are the same

[feral drum]

EXACTLY

[kind trellis]

why it makes perfect sense

[feral drum]

I've only ever used desmos in a math class

[undone ledge]

yikes

[kind trellis]

(-) means Times -1

and - means subtracting

[undone ledge]

oh they are atleast different buttons for them?

[hushed locust]

they do actually mean different things, but it's certainly possible to get a (not 100% reliable!) program which distinguishes them based on context (plenty of other calculator brands do), so it was a conscious choice on the TI programmer's part

[onyx swallow]

this is correct, but - can be viewed simply as a shorthand for adding the multiplicative inverse.

additive inverse

typo

[kind trellis]

Yes

[onyx swallow]

and in all the cases the context is very clear so this shorthand could be justified and not be confused with the inverse operator

[feral drum]

Why doesn't sin^-1(-0.2) give me the right answer

Like why do I have to add pi

[onyx swallow]

need context

[north rover]

!xy

[lone heart]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[feral drum]

Not the -0.7cos

[hushed locust]

can you show a picture of the entire question?

[hushed locust]

so then sin^(-1) would give you this solution over here

[north rover]

Because of the interval of (0, 2pi), arcsin(-x) is not positive for x>0

[onyx swallow]

think of $sin^{-1}$ as the inverse of this small piece of the sin function

[ocean seal]

qwertytrewq

[onyx swallow]

because sin is periodic and behaves nicely, this small piece of sin gives us all the information about sin. But when you want a solution on a given interval, taking inverse is not enough. You would need to use this inverse, and the properties of sin function to actually translate the solution to the given interval (in this case [0,2pi]

[lone heart]

@feral drum Has your question been resolved?

[feral drum]

Oh

[lone heart]

Channel closed

Closed by @feral drum

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.

[meager kindle]

How do I get Omega(w)?

[meager kindle]

,rotate

[static saffron]

you know about trig pythagoras?

[meager kindle]

Yes

[meager kindle]

R u german?

[static saffron]

yes

[meager kindle]

Können wir dann Deutsch reden oder ist das am Server nicht erlaubt

[static saffron]

Technically allowed, i suppose.
Lets do it in german then

Du musst die ebene dir erstmal überlegen in dem der Winkel ist

[undone ledge]

you can no issues

[static saffron]

darauf basierend musst du mit den gegebenen seiten die winkel und die seiten drumherumg ausrechnen

[meager kindle]

Ja aber in meiner Vorstellung wären das 90°

[static saffron]

Vorstellung ist kein Beweis^^

Daher, wenn du es voll mathematisch ausrechnen willst brauchst du die ebene in dem der Winkel existiert.

Weißt du wie die Strecken lauten in dem der Winkel steht?

Du hast sie ja da auch gezeichnet in farbe

[meager kindle]

BG und BE

[static saffron]

Richtig, diese strecken musst du ausrechnen

[meager kindle]

Oder meinst du die Länge der Strecken

Ohhhhh

[static saffron]

Die längen kannste dann ja mittels pythagoras

[meager kindle]

Jaja

Und dann einfach Cosinussatz

[static saffron]

das würde gehen ja

Kannst dir auch nen rechtwinkliges dreieck definieren was den winkel oder einen teil des winkels beinhaltet

Aber ja cosinussatz ist vlt am schnellsten

[grave matrix]

(Ist doch erlaubt; Englisch zu sprechen wird nur empfohlen, denn die Wahrscheinlichkeit eine Sprache reden zu können ist im Allgemein am höchstens wenn jene Sprache Englisch ist :D)
-# (It is allowed; speaking English is just recommended, because the likelihood to be able to speak a language is generally highest when that language is English :D)

(wohl oder übel lol)
-# (for better or worse lol)

(hab keine Ahnung worum das Problem hier geht, hab einfach nur Deutsch gefunden 🤣)
-# (I've no clue what this problem's about, just found German 🤣)

[static saffron]

Geht einfach nur um einen Winkel der nicht in die typischen Kardinalen Richtungen geht

Ist technisch etwas anspruchsvoller aber ja, Lafez hat effektiv die Lösungsstrategie, muss man nur einmal durchrechnen

[grave matrix]

Ah cool

[grave matrix]

einverstanden

[meager kindle]

Irgendwo habe ich mich sicher verrechnet

[grave matrix]

,rotate

[meager kindle]

Ist Omega=87,2°?

[grave matrix]

2 . 8,1 . 10,8 sei gleich was?

[meager kindle]

174,96

Oder meinst du wieso es dort drinnen steht

[grave matrix]

Warum hast du also 7,29 cosw geschrieben

[meager kindle]

Ohhhhh

Ich habe zuerst die Subtraktion gemacht und das cos ausgelassen

Thx

[grave matrix]

oh lol

Ja, die Multiplikation zuerst

dh du hättest [etwas] minus [etwas mal cosw] oder so was

[static saffron]

es ist in diesem problem auch sehr hilfreich einfach die wurzeln stehen zu lassen. Kommazahlen geben immer etwas fehler. Ganz am ende kannste die einsetzen

[grave matrix]

Hängt davon ab, dass du gut mit dem(? grammatik) Algebra arbeiten kannst

[static saffron]

e = sqrt(65)
d = sqrt(116)
z = sqrt(149)

[grave matrix]

oh ja das auch

Wurzeln stehen zu lassen geht besser

[static saffron]

Jup, nimmt dir auch keiner Übel

[grave matrix]

ach, "die Algebra" (im Nom.)?

[static saffron]

Jup

[meager kindle]

So

w=79°

[grave matrix]

Klingt korrect

[meager kindle]

Ich mache es nachher dann nochmal mit den Wurzeln
Danke für eure Hilfe❤️

[grave matrix]

(hab ne andere Ahnung - die Linien als Vectors zu nehmen, zwei Vectors konstruieren und dann ein Cross-Produkt rechnen)

(unnötig aber vielleicht interessant zu versuchen)

[grave matrix]

aber keine Sorge 🫡

[meager kindle]

.close

[lone heart]

Channel closed

Closed by @meager kindle

Use .reopen if this was a mistake.

[tawdry matrix]

yo guys pppllllllssssssss dm me help me to understand powers must talk frensh but its ok if its english

[lone heart]

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.

[robust nebula]

For part d of question 9

[robust nebula]

This is what i have been doing but the answers apparently 20

Dont kind the area at the top that was a previous try

C is O btw mb

[woven hedge]

i think you didn't use the appopriate formula for this case

the formula you have used only works if and only if:

• those two segments are perpendicular
• both are bases and heights of the triangle
  which is not the case

[robust nebula]

But since its an isosceles cant i split it in half and work that way?

[woven hedge]

actually yes

but either way 4*sqrt(2) is wrong for the length of AB

it should be 8*sqrt(2)

[robust nebula]

Yes

I split it in hlf

[woven hedge]

either way, when you have the coordinates of the triangle, save yourself from all this work

[robust nebula]

Thats why i took 4 swuarw root 2

[woven hedge]

and use the coordinate formula

[robust nebula]

Whats that

[woven hedge]

for any triangle with coordinates known (x_1, y_2) (x_2,y_2) (x_3,y_3)

A = 1/2 | x_1 (y_2 - y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2) |

just plug the 3 vertices in this formula

saves a lot of headache

[woven hedge]

yea, but for the whole triangle, you need to multiply it by 2 again

right know you are calculating just half of the triangle

[robust nebula]

No cause i didnt put in the half no?

Like half of the triangle would be 1/2 x bm x o m

Ffs autocorrect

O M

But i just removed th e half from the start

[woven hedge]

oh true

[robust nebula]

Let me try with the formula

[woven hedge]

it'll give 24

i though you've included the half

my bad

[robust nebula]

It also gives me 14

24

[woven hedge]

for the coordinate formula, i've calculated rn and it gave A = 1/2 | 32 - 5 + 21 |

[robust nebula]

Is the book wrong

[woven hedge]

= 24

[robust nebula]

Ye ty

[woven hedge]

i can calculate in the computer

since the book gave the formula

one sec

[robust nebula]

Okok ty

[woven hedge]

i'm 99% sure it is 24

i plugged almost everything in an algorithm and it gave 24.001

[robust nebula]

Okay yeah maybe the books weing

[robust nebula]

Ill ask my teacher tomorrow ty

[woven hedge]

no problem!

[robust nebula]

@woven hedge my bad

O isnt the center

[woven hedge]

no problem! glad you found out

[robust nebula]

Ty very much

.close

[lone heart]

Channel closed

Closed by @robust nebula

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.

[leaden niche]

I need help drawing this out and the resultant of it

I will let you know if I need help solving if it dosent work out but so far its just hard to visualize

[leaden niche]

anbody know how to draw this out?

would be much appreciated

is it any of these options?

[queen mirage]

Lable N S E W

[leaden niche]

since its from north east the line at the bottom is what im using

unless its supposed to end when it hits origin

im not sure

[meager kindle]

Wait

Im trying to sketch it too

[leaden niche]

Ok thanks

[queen mirage]

Is R the resultant vector?

[leaden niche]

yes

[queen mirage]

The diagram is correct

[leaden niche]

im not sure if i drew it properly tho

ok thanks but do i use the one on the right or left

or does it not matter

[queen mirage]

If you're asking the right or left diagram, it doesn't matter both are same

[leaden niche]

ok thanks

i had one more small question

would the angle be 135?

since 180 - 45

[queen mirage]

Of the resultant vector with east ?

Which angle are you talking about

[leaden niche]

this one

the feta

[queen mirage]

90+45

135

Yes

[leaden niche]

ok thanks

.close

[lone heart]

Channel closed

Closed by @leaden niche

Use .reopen if this was a mistake.

[lone heart]

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.

[mellow crane]

Ok so for question 1 i like combined all the resistances and got 18.4 ohms, idk if that's correct but like from there idk where to go like i have the total voltage and so i calculated total current but then what

for question 3 i just have no idea like i'm assuming i have to somehow like work backwards but i don't understand how to make sure like one of the resistors has 0.55A. like i think if one resistor must have a voltage drop of 26.0v across it then it just has to be in series with the source and the resistance total i think would be 26/1.09 which is 23.9? but then past that i'm just kinda lost

[lone heart]

@mellow crane Has your question been resolved?

[lone heart]

@mellow crane Has your question been resolved?

[shell agate]

Have you asked this in the physics server?

[shell agate]

for question 1 what else do you need to find

[mellow crane]

wait what i didn't know there was a physics server

um question 1 wants me to solve the circuit so i have to find all of the unknowns

like all the currents, voltages and resistances

[shell agate]

Yea there are servers for every subject

Yea

Only current is unknown?

[shell agate]

#old-network

[mellow crane]

? they gave me voltage total and all the resistances

[shell agate]

yes

[mellow crane]

but like i have to find the voltage and current going thru each resistor

[shell agate]

Oh so current and voltage through each

so V1=IR1

[mellow crane]

yea

[shell agate]

So you get voltage through first resistor

[mellow crane]

i thought that voltage was split in a series circuit so like isn't the voltage thru r1 something smaller than 45.0

but idk what it is

[shell agate]

thats why I wrote V1

[mellow crane]

ohh ok

[shell agate]

Just use that

I think you can find everything

In series current is same

In parallel voltage is

[mellow crane]

so like cuz the totsl current is around 2.45A so it's that thru r1 too? and then i have resistance so i can calculate voltage right?

and also r4 and r5 are in series right? my friend said they were parallel so i wasn't sure

[shell agate]

total current is total voltage/ total resistance

yes r4 r5 series

[mellow crane]

okk, yeah so like 45.0/18.4

[shell agate]

yes

[mellow crane]

ok so if i don't use the rounded number i get 2.44539... so it's about 2.45

[shell agate]

ok

it's not exactly 18.4 also

[mellow crane]

yeahhh, it's like 18.40196077...

[shell agate]

yes

[mellow crane]

okkk, and then V1=ItR1 so i do v1= 2.44539...*10.0

[shell agate]

yea ig u can do 2.45

[mellow crane]

ohhh, ic, ok i understand now

[shell agate]

So you can solve ?

Ok try

[mellow crane]

v123=ItR123

[shell agate]

what 123

[mellow crane]

like from when i combined the resistances to find the equivalent one

cuz now i have to work backwards right

[shell agate]

You have to find separate

For each

The part where I am not sure is

Voltage for r2 and r3

[mellow crane]

yeah but once i have that then i can separate them right?

[shell agate]

yes

voltage for r2= voltage for r3

[mellow crane]

right okk

so like for them combined i got 34.810868...volts

and then i can find for v23

and then get v 2 and v 3 separately

[shell agate]

Ah I seem to have made a mistake

[mellow crane]

?

[shell agate]

If you had the answer key it would be easier to figure it out

I think you should ask this in the physics server

[mellow crane]

okk i'll try

do u know how to do q3 by any chance

[shell agate]

draw 4 resistors, draw voltage 26v , current is 1.09 so 26=1.09 * R

idk about the rest

[mellow crane]

okk tysm, i'll ask in the physics server

.close

[lone heart]

Channel closed

Closed by @mellow crane

Use .reopen if this was a mistake.

[slate wind]

@swanqueen doublt

[shell agate]

?

[lone heart]

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.

[thin atlas]

what to do 😭😭😭😭😭

[vale wigeon]

derivative of 1 is 0 not 1

[thin atlas]

ok yea I'm still not getting

oh

ngm

got it

.close

[lone heart]

Channel closed

Closed by @thin atlas

Use .reopen if this was a mistake.

[hollow crypt]

Sup

How did they arrive at the second step?

[vale wigeon]

!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).

[vale wigeon]

(this channel still has somebody else's name on it. get your own)

[lone heart]

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.

[cerulean garnet]

how did they get that final result of 145.5mA

im trying to find right hand triangles to use trigonometry but idk i cant find it

are they doing the difference of hypotenuse between l2 and l1

wait lemme try that

nvm not sure

[lone heart]

@cerulean garnet Has your question been resolved?

Channel closed

Closed by @cerulean garnet

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.

[hardy terrace]

"Find the number of ways in which r letters can be posted in n letter boxes in a town"
how would i approach this question?

[vale wigeon]

wrong discord?

[vale wigeon]

imagine you are the postman and you decide for each letter individually which of the n boxes it goes into

[nimble sleet]

<@&268886789983436800>

[lethal belfry]

<@&268886789983436800>

[vale wigeon]

you will do anything? then stop spamming

[lethal belfry]

that was disturbing

[vale wigeon]

good riddance

[hardy terrace]

so for every postbox i pick one letter and im left with (r-1) letters?

[nimble sleet]

But also, are the letters distinct or identical?

I believe the answer changes depending on which it is

[hardy terrace]

theyre distinct if im correct

but that is all that is mentioned

[nimble sleet]

Each letter independently has n choices in that case - any of the letter boxes would work

[coral veldt]

hi

[hardy terrace]

i see thank you

[lone heart]

@hardy terrace Has your question been resolved?

Channel closed

Closed by @hardy terrace

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.

[thin atlas]

what next...

[lone heart]

@thin atlas Has your question been resolved?

[thin atlas]

[lone heart]

@thin atlas Has your question been resolved?

[thin atlas]

https://tenor.com/view/pigeon-pigeon-falling-falling-jump-fall-gif-23036577

[lone heart]

@thin atlas Has your question been resolved?

[thin atlas]

.close

[lone heart]

Channel closed

Closed by @thin atlas

Use .reopen if this was a mistake.

[thin atlas]

.reopen

[lone heart]

✅

[thin atlas]

.

[ivory igloo]

i think you will get it simplified with some awful trig substitutions

maybe you can isolate all the terms with a y in the beginning and then differentiate both sides

with respect to either x (d/dx) or y (d/dy)

which simplifies it very nicely

[lone heart]

@thin atlas Has your question been resolved?

Channel closed

Closed by @thin atlas

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.

[short vapor]

Point P is any point on the plane of a rectangle ABCD. Prove that
PA^2 + PC^2 = PB^2 + PD^2
Using vector methods

I am not entirely sure how to approach this problem. I have tried equating some sides so far, but that has not seemed to work

BP - AP = CP - DP
BP + DP = AP + CP
??

[short vapor]

I have tried equating some sides so far, but that has not seemed to work

[crude cloud]

Show work

[short vapor]

it's a lot of incoherent rambling uhhh

along with the above

one can equate the side lengths of the diagonals

(BP + DP)^2 = (AP + CP)^2

similar reasoning for sides AD and BC instead of AB and DC, although with similar results

[tiny fable]

a potentially useful hint: any time you see the magnitude of a vector squared, you can think of it another way using a certain vector operation

[short vapor]

the vector dot itself?

im just not sure how to get to PA^2 + PC^2 = PB^2 + PD^2

like PABCD are vectors

hm

i use ^2 as shorthand to mean dot itself most of the time

with vector PX = x
(b + d)^2 = (c + a)^2
b^2 + 2bd + d^2 = c^2 + 2ca + a^2
which is rly close to what is need but has those pesky 2bd, and 2ca terms.
probrably need to stop thinking of it in algebra terms

[tiny fable]

I would agree with your last statement lol

[short vapor]

lol

[tiny fable]

I'd try writing your vectors out explicitly, like PA = (a1, a2), etc

[short vapor]

like components?

[tiny fable]

yep, it does say to solve it using vectors

[short vapor]

im not given basis vectors tho

and my math teacher does not like it when i redefine my basis vectors to make problems easier...

but i'll give it a shot

oh no

got it

how to close

.close

[lone heart]

Channel closed

Closed by @short vapor

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.

[soft pecan]

can someone help me with this probability exercise

[soft pecan]

so I think for a is just 35 for the expected total time and 245 for it's variance

and for the second one am I supposed to use gamma distribution?

[lone heart]

@soft pecan Has your question been resolved?

[soft pecan]

.close

[lone heart]

Channel closed

Closed by @soft pecan

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.

[vale wigeon]

what's troubling you

[ornate bronze]

the 6.04*10^5

[vale wigeon]

ok so do you know in general

how to convert numbers from standard form into ordinary

[ornate bronze]

yes

[vale wigeon]

ok how do you do it

describe to me in words how you understand it

[crude cloud]

Just solve it simply

[ornate bronze]

so like u put it into calculator and u get the ans

[vale wigeon]

no

this does not need a calculator

[ornate bronze]

but i wanna learn without calc

[crude cloud]

No

[vale wigeon]

ok first off

do you know what 10^5 means

[ornate bronze]

yes

[vale wigeon]

what does it mean

[ornate bronze]

1000000

[vale wigeon]

no

[crude cloud]

6.04 = 604/100

[vale wigeon]

that's a million

[ornate bronze]

yes

[vale wigeon]

a million is 10^6

what is 10^5

[pliant sphinx]

In a teach store , there are 9 different gadgets and 8 available display racks. how manu distinct ways can the gadgets be arranged on the racks, ensuring that each rack hold at least one gadget and all 9 gadgets are used.

[vale wigeon]

!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).

[ornate bronze]

100k

[vale wigeon]

ok

so what's 6.04 * 100,000

[crude cloud]

@vale wigeon I think he's trolling

[vale wigeon]

@crude cloud benefit of the doubt.

[ornate bronze]

according to my calculator 604000

[vale wigeon]

you should be able to do this WITHOUT a calculator.

do you know how to multiply a number by ten?

[ornate bronze]

yes

u add a 0

[vale wigeon]

you slide the decimal point 1 slot to the right

[ornate bronze]

yes

u add a 0

[vale wigeon]

which, if the number is whole, looks like appending a zero

you should be saying "append" and not "add"

bc "add a 0" sounds like +0

which is not right

ok

[ornate bronze]

englissh my second language

[vale wigeon]

what's your first language

[ornate bronze]

Russian

[pliant sphinx]

Chatgpt give me another answer and gemini give me another answer can you explain me how you do it please

[vale wigeon]

нули не прибавляются, а дописываются

[vale wigeon]

!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).

[ornate bronze]

о, ты русская?

[vale wigeon]

да

[ornate bronze]

прикольно

[pliant sphinx]

Please english

[ornate bronze]

щ

no

[vale wigeon]

@pliant sphinx you are not the one getting help

helping someone in a language that they speak is 100% kosher

@ornate bronze так вот, умножение числа на 10^n -- то же самое, что сдвиг десятичной точки (или запятой) на n позиций вправо

[heavy prairie]

Ann you are very impressive sorry for interrupting I just wanted to say you are very impressive to me!

[vale wigeon]

это можно и нежно делать безо всяких калькуляторов

[vale wigeon]

thank you

[ornate bronze]

получается к примеру 6.4*10=64?

[vale wigeon]

да

[ornate bronze]

получается 605000

ой

604000

[vale wigeon]

да

[ornate bronze]

спасибо за помощь 🙂

[vale wigeon]

пожалуйста

[ornate bronze]

а как насчет

_4

-4

[vale wigeon]

при умножении на отрицательную степень десятки точка движется влево

[ornate bronze]

тоже самое но влево, получается 0.0005012

[vale wigeon]

именно так

[ornate bronze]

спасибо:)

.close

[lone heart]

Channel closed

Closed by @ornate bronze

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.

[mossy reef]

Squaring both sides does not work like that.

Notice how, if you plug your x values into the left side, it evaluates to -1.

$$\sqrt{13 - x^2} = 1$$
$$13 - x^2 = 1$$
$$\sqrt 1 =-1$$

[ocean seal]

@mossy reef

[mossy reef]

Give me a few minutes to take a closer look at your work.

[empty mason]

Yeah that’s pretty much it, there is a range restriction with the square root function. However when you square the equation you actually consider extra solutions than if there existed ones originally, and since you found that there weren’t any complex solutions at the end then there wouldn’t exist complex solutions for that equation

[mossy reef]

This top right expression is equal to 1. Can you multiply both sides by sqrt(13 - x^2)?

[empty mason]

Uh, it’s actually equal to 0 because she moved the 1 to the LHS

Yes

[lone heart]

Channel closed

Closed by @fallow quest

Use .reopen if this was a mistake.

[mossy reef]

There is a real solution though. Try multiplying both sides by u here.

[lone heart]

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.

[carmine topaz]

why is this A not B I lowkey figured it out and then forgot

[summer dirge]

because if it were B, f' would be positive at 1 and 3, and therefore f would be increasing at 1 and 3

[buoyant saddle]

because it’s only increasing in [1, 3] which means f’(x) < 0 for x not in [1, 3] but in B between 0 and 1 it’s not

[summer dirge]

but we know that f is not increasing there

[buoyant saddle]

by intermediate value theorem

[carmine topaz]

isnt both only increasing at 1,3 cuz f' > 0 only in that part ?

[buoyant saddle]

since at x = 0 it’s -1 and at x = 1 it’s 1 means that f’ is positive for some x in between 0 and 1

[cold cargo]

You have to think about what happens just to the left of 1 and just to the right of 3 in B

[carmine topaz]

does that matter ? cuz there might be a larger jump or...

[buoyant saddle]

no it’s continuous

so it can’t have a jump by intermediate value theorem for example there exists x in (0, 1) such that f’(x) = 0.5

which means it’s increasing there

[carmine topaz]

continuous doenst mean it cant move 2 at once?

[buoyant saddle]

contradicting the assumption that f’ is only increasing in [1, 3]

[buoyant saddle]

yes..

intermediate value theorem

no jumps

a jump is a discontinuity

[carmine topaz]

but then why does f' between 1 and 3 in option A move 2

[buoyant saddle]

because they only gave you information on integer inputs

it doesn’t mean f’ is only defined at integer inputs

they just listed value of f’ at integers

and didn’t give you information about for example f’(sqrt(2))

this should be familiar by now no?

this is a very common type of question

[carmine topaz]

is B wrong cuz its increasing on other parts too or cuz its discontinuous

[buoyant saddle]

if i made a table of for example y = x^2 and listed the values of x and y where x is say -1, 0, 1, 2, 3 does that mean x^2 is discontinuous just because i decided to make a table of the integer values?

[carmine topaz]

not really

[buoyant saddle]

you didn’t read what i said

[carmine topaz]

but like wdym IVT why does it appear here

[buoyant saddle]

they state that f is only increasing in [1, 3]

so if we can demonstrate that there exists some point where f’ > 0 outside of this interval then we’ve contradicted this assumption

now

[carmine topaz]

ohhhh i get it

[buoyant saddle]

since f’(0) = -1 and f’(1) = 1 and f’ is continuous this means that f’ has to pass through all values between -1 and 1 through the interval [0, 1]

[carmine topaz]

f' > 0 only between 1 and 3 so B have violated that cuz it hit positive before 1

[buoyant saddle]

for example it must go through y = 1/2 between 0 and 1 now since this is outside the interval [1, 3] this means we have arrived at a contradiction

[buoyant saddle]

yes

and this is valid by intermediate value theorem

since f’ is continuous

[carmine topaz]

solving ts when i have apush in 3hr 💔

thanks for helping!

.close

[lone heart]

Channel closed

Closed by @carmine topaz

Use .reopen if this was a mistake.

[buoyant saddle]

lol good luck

[oblique egret]

Hola

[buoyant saddle]

louisiana purchase

[carmine topaz]

about to bomb the leq 😭

[lone heart]

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.

[strange beacon]

how can it appears to ln C suddenly instead of just +C

[kind trellis]

C is a arbitrary constant

[undone ledge]

c is an arbitary constant, we just expressed it as ln c for convinience

[zinc bolt]

c is just a constant so ln|c| is also one and vice versa.

[strange beacon]

so i can just express C as what it is i want it to be as long as itt helps me solve the problem?

[kind trellis]

C could be C + 23902309 or ln|C + 239239| or e^C^2^2^2

as long as C is a real number

[zinc bolt]

There are some restrictions, and it doesn't always work, especially in cases like higher order differentials but yes for most general bijective functions you can prolly do that no issue

[strange beacon]

but there time like when changes happen to C, i need declare it as another variable, for example if C is multiplied by 2, i need to say A, A=2C, or is this not revelant rn

[undone ledge]

thats just for reference dw

thats if you define c first tho , here it directly wrote ln|c|

so thats a constant too and there were no change

hence no decleration , you could write it with your method but just a extra step( check with your grading teacher tbh)

[strange beacon]

alright thank you

[lone heart]

@strange beacon Has your question been resolved?

Channel closed

Closed by @strange beacon

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.

[cloud palm]

Hello guys, i'm struggling with Matrix. I made this matrix - Determinant. I decided to made my row elimination i/o column. I have different determinant, wolfram has different on chat gpt i feel lost... where i made mistake ?

[twin nimbus]

So I have the correct value for this determinant

!nogpt also

[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).

[twin nimbus]

if you can provide me with a value that you think is correct, I can let you know if it's correct.

other than that, you can try to use row reduction to find the determinant, it's probably faster than finding 4 determinants of 3x3 matrices.

[fading trench]

you forgot minus in front of 4
third row second column

[cloud palm]

as u can see above i made row reduction of 4th column. Correct answer is 211, but i don't know where i made mistake

[cloud palm]

right, i will try this

[cloud palm]

thx m8, that was the problem

.close

[lone heart]

Channel closed

Closed by @cloud palm

Use .reopen if this was a mistake.

[fading trench]

nmzc byq

[cloud palm]

Jeden minus a tyle problemu

[lone heart]

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.

[warm quarry]

$a_0 = 1 - 1 = 0 $, that is correct. $a_1 = 6 + 1 = 7$ which is also correct.
Induction hypothesis, Let k element of N and k greater / equal 1.
$a_k = 6^k - (-1)^k ?$

[jaunty olive]

Yikes

[ocean seal]

Brett

[jaunty olive]

Yeah now put this is in the equation

[warm quarry]

in a n+2?

but I must do it for k+1 right?

$a_{k+1} = 6^{k+1} - (-1)^{k+1}$ but normally u just split it and stuff and it will be fine or is it strong induction?

[ocean seal]

Brett

[warm quarry]

aah i might have figured it out

got it :)

.close

[lone heart]

Channel closed

Closed by @warm quarry

Use .reopen if this was a mistake.

[lone heart]

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.

[grizzled ermine]

did i multiply the fractions correctly here? something tells me FOIL is making no sense

[vale wigeon]

your $\cos^4(x)$ comes dangerously close to looking like $\cos(4x)$

[ocean seal]

Ann

[grizzled ermine]

yea i suck at writing

[vale wigeon]

also the last 3 lines look weird

[grizzled ermine]

how so?

[tranquil tartan]

What even do they mean

[grizzled ermine]

…as in the last 3 lines?

[tranquil tartan]

Yes

[grizzled ermine]

there

[tranquil tartan]

Oh my

Thats not

How you cancel out fractions

[grizzled ermine]

did i screw up the terms again

god i suck at that lmao

[tranquil tartan]

(4+4)/2=4+2?

[grizzled ermine]

yeah no lol

ok wait let me redo it then in that case

i need something to remind me when not to cancel out

[tranquil tartan]

Besides your whole fraction is kinda pointless

As it has denominater cos^2 x

Just like rhs

So you could just multiply both sides by cos ^2 x

[grizzled ermine]

what do you mean multiply both sides

as in both the LS and RS?

[tranquil tartan]

Yes

Thats kinda what u usually do to equations

[north rover]

Uh, I think the first thing you should do is note that $\sin^2(x)+\cos^2(x)=1$.

[ocean seal]

;(

[north rover]

Makes life hella easier

[tranquil tartan]

Yes

Definitely

[grizzled ermine]

oh i’m so dumb

how did i miss that lol

i knew that smh

ok thanks give me a sec folks

[north rover]

You get it with practice

[grizzled ermine]

i’ve been practicing like crazy for the past 2 days

and i’m still missing it 😭

[north rover]

Bruh

Well, don't worry

After that it should reduce to a simpler equation

[north rover]

And then you can apply this again

[proven leaf]

comes quicker for some, took me ages to master trig identities if this random stranger's anecdote is any consolation

[grizzled ermine]

theeeere we go

that was a doozy

alright so i went way too far in the wrong direction

thanks yall

.close

[lone heart]

Channel closed

Closed by @grizzled ermine

Use .reopen if this was a mistake.

[north rover]

Well

Not necessarily

[grizzled ermine]

i’d rather not waste time like that honestly

[north rover]

Yeah

You did take the harder route

[grizzled ermine]

especially if it comes to the point where i’m doing that on a test 😭

[lone heart]

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.

[vale wigeon]

can you highlight the earliest line which makes no sense to you

(also i will say the limits in terms of h should all really have $h \to 0^+$ not merely $h \to 0$)

[ocean seal]

Ann

[vale wigeon]

get what exactly

[forest marsh]

They take off the parentheses and simplify the 5 together

(5-h)-5 = 5-h-5 = -h

What is f(x) ?

[vale wigeon]

thats where

they plugged that shit into the formula for f(x)

[winged pawn]

thats erm the input for the function? its |x-5|

x = 5 - h and 5 + h

erm wha

erm the first 5 is the input, i say again

you have x = 5 - h

the second 5 is just part of the function

|x-5|

[lone heart]

Channel closed

Closed by @wicked gazelle

Use .reopen if this was a mistake.

[lone heart]

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.

[harsh lantern]

Can someone explain Q2 wouldn't the Y= 3 and x=-5 ?