help-13

[formal river]

Right?

[crimson sedge]

could you wait for somoene else to respond

busy rn

[formal river]

K

[cedar kiln]

@formal river Has your question been resolved?

[crimson sedge]

no one responded ?💀

yes but what we need to find is the maximum rate

not the maximum P

@formal river

wakeeeee uppp

[cedar kiln]

@formal river Has your question been resolved?

[formal river]

Hi

I think the answer is 99

90

Right

D^2p/dt^2

Set equal to 0

Found critical point at 90

Then I did second d/dx test or third d/dx test in this case

Then 90 was negative

Nvm I checked with number line

Found that it was concave down so it’s a rel max right

[crimson sedge]

Yes the maximum would be when P=9p

90

But what they asked for is dp/dt not P

@formal river

[formal river]

Yeah

So if it was P I would’ve done dp/dt= 0

But if it was o’

P’

I would’ve done p’’=0

I see

But p’’’ would be a constant right

Actually can’t u just do number line on p’’

To determine if it’s a rel max

Or abs max

[crimson sedge]

E

I didn't get you

[crimson sedge]

You should probably react to this bte

Btw

[cedar kiln]

@formal river Has your question been resolved?

[cedar kiln]

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[gray moon]

how would i go about solving this?

[gray moon]

ive just subbed in letters as coefficients but its kind of disgusting rn

[cedar kiln]

@gray moon Has your question been resolved?

[dire geode]

Did you learn matrices are invertible if and only if their determinant is nonzero

[cedar kiln]

@gray moon Has your question been resolved?

[gray moon]

yes

[dire geode]

Yea just use det(AB) = det(A) det(B) then

[cedar kiln]

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[languid bison]

What do you want to ask about it

[slim plume]

g double prime

idk how to do it

[quaint berry]

Slope at 3

[eternal gale]

Yea

Find the average slope from 2 to4

[slim plume]

idk why im blanking on how to do this

[eternal gale]

This is how

[dusk goblet]

average slope

[eternal gale]

Yea?

Huh

[dusk goblet]

lol

[eternal gale]

What

[dusk goblet]

g’’ = f’

[eternal gale]

Mhm

[dusk goblet]

g’’(3) = f’(3) = slope at x = 3

[eternal gale]

Yea

[quaint berry]

You take the th change in y coordinates from 2 to 4 and divide them by change in x Co ordinates from 2 to 4

[dusk goblet]

which is the slope of that line segment

[eternal gale]

What is the problem

[dusk goblet]

why say average

it’s constant

[eternal gale]

$\frac{f(4)-f(2)}{4-2}$

I dont know that’s what my mind went to

[dusk goblet]

i mean sure that’s one way you’d find it

it’s not wrong

maybe i’m just being pedantic

[eternal gale]

Bruh

[dusk goblet]

\

\frac{a}{b}

bruh

[eternal gale]

I over thought it 😭

[dusk goblet]

https://www.overleaf.com/learn/latex/Learn_LaTeX_in_30_minutes

help yourself

[wraith dagger]

ℰ𝓁𝓁𝒶

[dusk goblet]

(

[eternal gale]

Im on my phone xhill

This shit hard

[dusk goblet]

so am i

[eternal gale]

No you’re not 😭 I can tell my the uncapitalized s

[dusk goblet]

no i just don’t use caps

[eternal gale]

I don’t either it’s auto tf

[dire geode]

"Autocorrect is for noobs" --knief

[dusk goblet]

a girl called me weird for using caps in 8th grade

never used it again

[eternal gale]

Lmao

Now that is weird

And no way yall expect me to learn that stupid language imma never use that shit in my life

[dusk goblet]

use it for homework

your teachers will thank you

and it just looks way nicer

instead of writing it by hand

[cedar kiln]

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[trim wagon]

what is this

[trim wagon]

id guess c but idk

wait nvm not c

b

i think b

[blazing zephyr]

easiest way is to just put random numbers on a,b,c

like a,b,c=2,1,-1 and youll see the answer p quickly

[trim wagon]

ok ill try that next time

.close

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[civic coral]

Is it correct

[twilit bison]

the first line -

each of the two statements is false? or the conjunction of the statements is false?

do you understand "conjunction"?

[stone prairie]

Handwriting on its peak

[civic coral]

shouldn't it be "at" its peak

[civic coral]

The conjunction from English, yes.

[twilit bison]

https://zh.wikipedia.org/wiki/逻辑与

is that the right language?

here's the english

https://en.wikipedia.org/wiki/Logical_conjunction

another way to ask -
"x+7 =/= 7 and x-y =/= 8" is false?
or
"x+7 =/= 7" is false and "x-y =/= 8" is false?

[stone prairie]

Fr it should be "at" sometimes idk what i was typing xD

My grammer is dead tbh

@civic coral you gotta correct it

[civic coral]

It is

[civic coral]

I wish to solve the question by true table

[twilit bison]

i think it will be hard to express it as a truth table if you can't answer my question

you've used the plural "are", which implies each statement is false independently

but i wanted to confirm

[civic coral]

Both statements are false

[twilit bison]

all right

then what you've written is correct

do you still wish to make a truth table?

[cedar kiln]

@civic coral Has your question been resolved?

[civic coral]

Sure.

[twilit bison]

okay maybe you can let p be the first statement, and q the second

then the first two columns in the table can be p and q

and you can have 4 rows

p. q

T. T
T. F
F. T
F. F

[twilit bison]

sorry i have to go to bed

[cedar kiln]

@civic coral Has your question been resolved?

[cedar kiln]

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[lethal jungle]

can someone help with my probability question i'm really confused on how you do this question

[lethal jungle]

number 26

[steel heart]

The question is a little bit ambiguous, the question asks the probability of passing, does that mean answering all questions correctly, or some number of questions correctly?

[calm idol]

where are yous tuc

stuck*

[lethal jungle]

some number of questions correctly

[lethal jungle]

i'm stuck with how to visualise this and solve it

[calm idol]

read the question again

and then tell me exactly where you stuck

i could solve it for you but thats not gonna help you

i dont buy that i cant visualize everything

[lethal jungle]

so i'm confused because she's got a quiz with four multiple choice questions so would i have to draw four seperate branches

and she has four different options

[calm idol]

Does that help

[lethal jungle]

why would we only draw two branches

[calm idol]

The 2 diagram shows the probability for guessing one question

[lethal jungle]

that's what i'm confused about

[calm idol]

Come on think about it

You got this

[lethal jungle]

assuming she does all the questions

[calm idol]

I didn't draw the 4 question because

Shit would get messy

[lethal jungle]

this is such a long question

omds

i get it nvm

.close

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[calm idol]

Don't run from math john

🤣

[steel heart]

wbt binomial probability formula?

[calm idol]

yes but he said hes confused on how to draw the tree

so i tired showing that

in the next step i would tell him isnt it easier to

calculate the probability of failing instead

but he run away

[calm idol]

That's how I would do it and would've tried to explain

[cedar kiln]

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[dusky forge]

Help

[dusky forge]

i need help why break the shape into a parallelogram and a triangle(double integration)

The answer i got is different to the 1 in the memo why🤥

<@&286206848099549185>

[pastel vault]

you calculated the area of this region

[calm idol]

Yep you use different bounds that explains why you got other results

[pastel vault]

here is their solution, annotated

you can clearly see the setup of the two different integrals

top 1 and bottom 1
top 2 and bottom 2

wait should be y = 0.6 to 0.8, sorry, for the 2nd integral

[dusky forge]

Can someone explain this again like which one is top and bottom... I do not understand

<@&286206848099549185>

[pastel vault]

which part don't you understand

[dusky forge]

How to setup the integrals

[pastel vault]

I literally just told you

[dusky forge]

Never mind

.close

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[calm idol]

Teaching is difficult

[pastel vault]

it's really not

a lot of problems come from when the person isn't at the right skill level to do the problem

[calm idol]

To find a connection to the student and yes that too

[pastel vault]

I mean this isn't teaching

[calm idol]

They don't wanna put in the work to understand

[pastel vault]

if you were a teacher you'd be dealing with 20 students in a classroom

it's not really tutoring either

it's just helping

[calm idol]

True lol we are just helping but I wanna do a better job in that little helping

Than most of my incompetent teachers

Or professors who rush every topic

[cedar kiln]

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[remote swallow]

Why do you need continuity in order to guarantee that a function reaches a max and a min in a compact set?

[remote swallow]

Just looking for a counterexample, I cannot think of any

[humble karma]

You don’t need continuity.

Continuity guarantees it

[remote swallow]

True, lemme word it better

[gritty viper]

consider f(x)=1/x on [0,1] where f(0)=0

[remote swallow]

Yes

Yeah lemme word my question better

Why isn't it
Compact -> exists a max and a min

Like, why do we need continuity to guarantee to have the ->

[lyric narwhal]

Consider f(x)=1/x on [0,1] where f(0)=1

[south tundra]

Dreyuk just provided a counterexample to compact -> max and min exist

[remote swallow]

Oh lmfao

I guess asking both the domain and the image to be compact would work

Or at least a bounded image

[south tundra]

The image being compact already tells you max and min exist

[remote swallow]

True

[south tundra]

Bounded image doesn't imply max and min to exist btw

[remote swallow]

Ye

But compact domain and bounded image should?

[south tundra]

Yeah

[remote swallow]

Yeah but checking for continuity will be easier most of the times anyway

Okay, thank you all so much!!!

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[outer canopy]

A Major League baseball diamond has four bases forming a square whose sides measure 90
feet each. The pitcher’s mound is 60.5 feet from home plate on a line joining home plate and second base. Find the distance from the pitcher’s mound to first base.

[outer canopy]

what i did was assume the pitcher's mound was in the middle (which i think is wrong) and then formed a right triangle with angles 90, 45, 45 and solved for the distance using law of cosines

i then got 63.72ft

I am 99% sure this is wrong so I need help

[cedar kiln]

@outer canopy Has your question been resolved?

[cedar kiln]

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[keen burrow]

Solve for x

[keen burrow]

Explain the process also plz

[crimson sedge]

id start by squaring both sides of the equation

to get rid of the square root at the bottom

[trail tulip]

yep, or you can multiply both sides by "sqrt(x+1)", whichever one you find easier

[cedar kiln]

@keen burrow Has your question been resolved?

[keen burrow]

That affects the top part of the equation too right? Could you show me what that would look like

[crimson sedge]

yes

(2x + 1)² / (x + 4)

[keen burrow]

ok

[crimson sedge]

and continue from here

[keen burrow]

what would be the next step

[crimson sedge]

well, squaring the numerator

[keen burrow]

numerator is the upper part right

[crimson sedge]

yeah

[keen burrow]

This basically

[crimson sedge]

yeah but i didnt distribute it

i left that for you to do

then after you're done cross multiply and its easy from there

[keen burrow]

k

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[grim lantern]

Am i correct in saying that Eulerian Path is where exactly 2 vertices have odd edges and a Eulerian circuit is where all vertices have even edges.

So
G1 is neither
G2 is neither
G3 is Eulerian Circuit

[fair geyser]

that's exactly right, i haven't checked the examples

G1 has a path

[grim lantern]

oh yea your right i miss counted its edges

thanks

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[copper meteor]

хи

[cedar kiln]

Please don't occupy multiple help channels.

[copper meteor]

i want help

[copper meteor]

can u help me>]

[cedar kiln]

@copper meteor Has your question been resolved?

[copper meteor]

<@&286206848099549185>

[cedar kiln]

@copper meteor Has your question been resolved?

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[vagrant wave]

Calculate the lengths of the diagonals of the side faces and the length of the space diagonals of a cuboid with

a = 3cm
b = 4cm
c = 5cm

[vagrant wave]

this is what i got

but im confused because my teacher got something else

[ornate rune]

how did you get good writing

[vagrant wave]

ermmm

i dont know

[ornate rune]

did you draw that too lol

[vagrant wave]

yes

[ornate rune]

w

[vagrant wave]

thank u!!

[coral jewel]

you forgot to calculate another faces' diagonals

[vagrant wave]

huh

where

[vagrant wave]

ou

but my teacher said that we only need to calculate the diagonal of one face

[coral jewel]

then that's great, your question mentioned multiple diagonals so i thought you would need to calculate all of them

other than that, your solution is correct

[vagrant wave]

i ahve another question

this was my teachers solution

(d and e are switched)

she labeled the cuboid differently and got another answer for d (e in my case) and that confuses me

[cedar kiln]

@vagrant wave Has your question been resolved?

[vagrant wave]

<@&286206848099549185> help pls

[glossy shard]

You and your teacher are calculating the lengths of different diagonals. Your 'e' is the length of the diagonal of the 3-4 face. While your teacher's 'd' is the length of the diagonal of the 3-5 face.

[cedar kiln]

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[cedar kiln]

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[quiet shadow]

Why does this modular exponentiation algorithm work?

int result = 1;
  for (int i = 0; i < exponent; i++) {
    result = (result * base) % modulus;
  }

I understand it has something to do with the property of the modulus where you can separate (a * b) mod n into** [(a mod n) * (b mod n)] mod n**, but I don't understand why doing what the code does works

[quiet shadow]

Or if anyone has any idea what doing this is called (if it has a name) I would also appreciate it a lot

[dire geode]

wut

don't ask people to read chatgpt's garbage

!nogpt

[cedar kiln]

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).

[dire geode]

exists for a reason

[dire geode]

#old-network for CS server for CS questions

[quiet shadow]

I mean it's still math, I just showed it as code.

And sorry about the chatGPT then, just showed it as context because I can't find a reference anywhere as to what I'm trying to say

Which is why I'm here

[dire geode]

write your question in math then

"how does this code work" is more appropriate for CS server

#old-network message

[quiet shadow]

The answer is still going to be mathematical, but sure I'll give it a shot.

I don't believe the logic behind it is hard to understand

[chrome quail]

honestly i dont see the harm in posting math-adjacent questions in the server.

if someone can help you, they will. way easier to find someone who can help when the server is 20x as large as the cs one

[prisma laurel]

the question does seem to be about the underlying math so I think this is fair

[cedar kiln]

@quiet shadow Has your question been resolved?

[cedar kiln]

@quiet shadow Has your question been resolved?

[cedar kiln]

@quiet shadow Has your question been resolved?

[quiet shadow]

.close

[cedar kiln]

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[crimson sedge]

I have a few questions that are rather similar to this and I'm struggling to figure out what to do.
I understand plugging in things and have all the equations necessary, but I'm having a hard time figuring out what needs to be done in order to use the equations properly.

Finding vertices and the foci of an ellipse don't make any sense at all.

[crimson sedge]

A method I was also taught was to set up:
H = ?, K = ?, A = ?, B = ?, C =?
I have all their values as followed: H = -4, K = 6, A = 6/5, B = 1, C = Radical 6 / 25
Finding them was a little slow, but now I don't know what to do with them.

[last plaza]

did they teach you that vertices of standard ellipse are (+-a, 0)?

here a is 6/5

[crimson sedge]

I can't recall tbh 😭
Would that make the ellipses (-6/5, 0) and (6/5, 0)?

[last plaza]

yep that is the vertex

[crimson sedge]

Ohh, ok ok

[last plaza]

wait

sorry

[crimson sedge]

oh

[last plaza]

that is a shifted ellipse

[crimson sedge]

Because the center isn't at (0, 0), right?

[last plaza]

exactly

[crimson sedge]

Ohh ok

But if the center were at that, then I would've been right?

[last plaza]

you'll now have to adjust according to the centre

yes

[crimson sedge]

Ohhh

[last plaza]

do you know how to do that

[crimson sedge]

Ehhh, I don't exactly remember, I'm a little slow 😭

I WOULD count but the fact that a point is at 6/5 is a little annoying to me

[last plaza]

lets take an example

lets say you have y = x^2

now if you replace x with x-2, you get y = (x-2)^2. this curve will shift 2 unit towards positive x axis

can you tell me if we replace y with y-6 in a curve, where will it shift towards to?

[crimson sedge]

6 units toward the right

[last plaza]

no that is with the x

[crimson sedge]

OH y

I wasnt looking

[last plaza]

lol its okay

[crimson sedge]

y would be negative, so wouldn't that move down 6 units

[last plaza]

okay so now tell me for x+4?

[last plaza]

no

[crimson sedge]

4 units to the left?

[last plaza]

correct

[crimson sedge]

I'm switching things up 😭😭

it's whatever makes it 0, right?

that's my thought process

[last plaza]

yeah, for x+4 -4 makes it 0 so it will shift towards negative side

you can remember it like that

[crimson sedge]

Ok ok

[last plaza]

for y-6 it would be 6, so towards positive y

[crimson sedge]

I see

[last plaza]

okay so now we've learnt that, in a standard ellipse our vertices would be (6/5,0)

but since its a shifted one, we will subract 4 and add 6 in x and y respectively

you understand why?

[crimson sedge]

Not really 😭, feeling it has to do with the center being at (-4, 6)

[last plaza]

yes that is why

[crimson sedge]

Ohh

[last plaza]

basically, in a normal ellipse centre is at 0,0

we shifted the ellipse 4 units negative x and 6 units positive y

so everything related to it, foci and vertices will also shift accordingly

[crimson sedge]

so subtract 4 to (-6/5, y) and (6/5, y) and then add 6 to (x, 0) ?

maybe idk

[last plaza]

subract 4 from the x coordinate

and add 6 in the y coordinate

[crimson sedge]

so...
center: (-4, 6)
vertices: (-6/5, 0) & (6/5, 0)
final pts: (-14/5, 6) or (-2.8, 6) & (-26/5) or (-5.2, 6)

[last plaza]

correct!!

[crimson sedge]

so would my final pts be my foci?

[last plaza]

no those are your vertices

[crimson sedge]

ohh

I really hate this chapter, my teacher is cramming this in before finals week 😭

[cedar kiln]

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[stone stream]

Does anyone know how I can solve this? I'm trying to study for my test, but I can't find the answer or figure out how to do it.

[rugged tundra]

I'm assuming the function is a parabola, i.e. has something like x^2 appearing?

[stone stream]

Yess I'm just really bad at doing these equations

Its a parabola

[rugged tundra]

Okay, do you know how different transformations of y=x^2 work, like what does y = 2x^2 look like, what does y = x^2 + 5 look like, what does y=(x-1)^2 look like, etc.?

[stone stream]

Yes, I understand the basics of transformations, but I'm a bit confused about applying them in detail n stuff

like for example ik that y=x^2 makes the graph narrower

y=x^2+5 shifts it up by 5 units, but i just dont know how to create the equuation

im better at just reading it and graphing itt

[rugged tundra]

Okay, the first thing we should try and do is translation, vertically and horizontally. The original turning point of y=x^2 is at (0,0), so we need to translate this to the new point it is at now

What point are we aiming for?

[stone stream]

The vertex ?

Would it be (1,3) in this situation

[rugged tundra]

Yeah exactly, so we need to "translate" the original turning point (0,0) to (1,3)

[stone stream]

so to translate the vertex it'd be y=(x-1)^2+3?

[rugged tundra]

Yeah exactly, that's step one

[stone stream]

okok what do we do for the next step?

[rugged tundra]

Another point of interest is the y-intercept

It looks like here the graph cuts the y-axis at 3.2?

[stone stream]

yes

[rugged tundra]

So what is this saying?

[stone stream]

should i subsitute x=0 into the equation y=(x-1)^2+3?

[twilit bison]

It's one unit to the left of the vertex

By default it rises one unit when it goes one to the left

But here it rises only 0.2

This is one line of thought. There might be other approaches

[stone stream]

Does that mean the equation is affected by a vertical stretch or compression?

[twilit bison]

Yes

[stone stream]

so should I update the equation to y=0.2(x-1)^2+3?

[twilit bison]

At least, that reasoning works for parabolas

[twilit bison]

That seems right

Or

Yes I think that's right

[stone stream]

omg thank you guys both !!

i finally get it nowwww

[twilit bison]

You're welcome

[cedar kiln]

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[crude veldt]

What is an inverse function? How do they work

[twilit escarp]

An inverse function, when it exist, is the unique function written f^-1 satisfying f(f^-1(x)) = x = f^-1(f(x))

Also those channels are really efficient for specific questions like on an exercice, when its for concept we advise to watch a video and possibly after ask questions about some exemples shown in the videos

[crude veldt]

10-4

.close

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[twilit escarp]

@dusk goblet its affirmative code in police langage according to google

[dusk goblet]

oh lol yes that makes more sense

[twilit escarp]

Bro roger me xd

[dusk goblet]

yea i’ve heard 10-4 before

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[unborn mauve]

hello! I’m having trouble understand how to do this problem for my test tomorrow, pls help

[golden raven]

so what are alpha and beta in this case?

[unborn mauve]

pi/3 is alpha and pi/4 is beta

[golden raven]

close

if we plugged in pi/3 and pi/4 for alpha and beta

this would give us a calculation for sin(pi/3+pi/4)

we want pi/3-pi/4 instead

so we plug in negative pi/4 for beta instead

does that make sense?

[unborn mauve]

ya

[golden raven]

ok

so now can you plug in pi/3 and -pi/4

[unborn mauve]

would you turn it into the coord like sin(pi/3) is squareroot 3/2?

[golden raven]

yes, that is what the problem intended for you to do

[unborn mauve]

Oka

I got (squareroot 3/2)*(-squareroot 2/2)+(squareroot 2/2)(1/2)

is that what I’m supposed to do 😭

[golden raven]

yes this is! can you now simplify that expression?

[unborn mauve]

how would I simplify the square roots? for squarerot 3 and squareroot 2

[golden raven]

oh um

[unborn mauve]

Would it be squareroot 6?

[golden raven]

when you multiply them together it is square root of 6 yes

[unborn mauve]

I got -squareroot 6/4 + square root2/2

would I have to simplify more by doubling squareroot 2/2 and adding them together or is this fine?

[golden raven]

wait a minute, your answer should actually be the negative of that

you had the -squareroot(2)/2 and squareroot(2)/2 switched around?

[unborn mauve]

sorry I’m not rlly following

[golden raven]

you calculated sin(-pi/4) and cos(-pi/4) wrong. you switched them around

[golden raven]

the squareroot(2)/2 and negative squareroot(2)/2 should be switched around

[unborn mauve]

Ohhh I see

squareroot 6/4 - square root2/2?

[golden raven]

correct

[unborn mauve]

would I need to simplify more or is that ok?

[golden raven]

that should be good enough. some people would write it as (sqrt(6)-2sqrt(2))/4, but thats just a matter of personal opinion and both are acceptable

[unborn mauve]

ok thank you!

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[crimson sedge]

HAI

i need help

[dusk goblet]

with

[crimson sedge]

this

[dusk goblet]

all of them?

[crimson sedge]

yeah i dont know how to start

[dusk goblet]

consider drawing a triangle that satisfies sin(theta) = 4/7

then use your knowledge of the unit circle to determine the sign of each

[crimson sedge]

ohhh

thank you

[dusk goblet]

or if you’d like you can start with a unit circle and draw triangle in Q3 that satisfies that

[crimson sedge]

that should be enough

i just felt a bit lost

ill come back later with some questions

okay so it would be
(a) cos(θ) = (-√33)/ 7
(b) tan(θ) = (4√33)/ 33
(c) sec(θ) = (-7√33)/ 33
(d) csc(θ) = -7/4
(e) cot(θ) = √33/4

right?

[dusk goblet]

yep

[crimson sedge]

tyy

[dusk goblet]

you’re welcome

[crimson sedge]

how do i start this one?

never mind i did it but

im not sure if im right

sin(θ) = -5 / √34
cos(θ) = -3 / √34
tan(θ) = 5/3
cot(θ) = 3/5
sec(θ) = -√34 / 3
csc(θ) = -√34 / 5

@dusk goblet

[cedar kiln]

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@crimson sedge Has your question been resolved?

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[vapid grotto]

Is the one with the star correct

[cedar kiln]

Please don't occupy multiple help channels.

[clear umbra]

is that supposed to be a 13

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[vapid grotto]

I’m not sure

[wraith nacelle]

I think it's a 3, if it is then correct

[cedar kiln]

@vapid grotto Has your question been resolved?

[vapid grotto]

I don’t understand why these are wrong ( seperate problems )

Again I don’t know what I’m doing wrong

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[magic ore]

the derivative of this. I'm stuck at f'(x) = (8x^2-20)-(4x^2+4x)/4x^2-20x^2+25

[vague sparrow]

how do you know you're stuck

I will say the second term in the numerator is wrong but that's where I stopped checking, should be (16x^2+4x) I believe

[magic ore]

idk how to distribute the negative

[vague sparrow]

are you expected to expand it all out? I know when I took calculus 1 the teacher didn't want us to expand it at all, so you might not have to

that being said, knowing how to distribute the negative is important so I'll help with that too

you can rewrite -(a+b) as (-1)*(a+b)

and distribute it that way as (-1)a+(-1)b and rewrite that as -a-b if you like

that make sense or kinda confusing still?

I hate to inform you that that's the denominator 😬

[magic ore]

brainfart...

[vague sparrow]

all good!

[magic ore]

how did you get 16x^2 for the numerator

[vague sparrow]

so just that second term in the numerator: (4x+1)*(2x^2-5)'

that becomes (4x+1)*(4x)

we on the same page so far?

cool, ok so now when you distribute the 4x term you get 4x*4x+4x

that's where the 16x^2+4x comes from

another way to write that term is (4x)^2 + 4x if that helps, kind of looks like yours

but we have to be careful that we have both 4 and x squared there

which is why that became 16x^2, since the ^2 is only on the x now

[magic ore]

how this is what the worked example gives ???

[vague sparrow]

they skip some steps, we're sorta halfway between those two steps

having that second term correct, now we can subtract it from the first term:

(8x^2-20) - (16x^2+4x)

that'll turn into -8x^2-4x-20

that make sense where all the pieces are coming from?

[magic ore]

i understand it now

[vague sparrow]

cool

[magic ore]

thanks

[vague sparrow]

yeah you're welcome, any time feel free to ping me

[magic ore]

ok

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[dusk goblet]

b

[cedar kiln]

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[indigo valve]

I calculated z1 to be equal to cos(2pi/3)+isin(2pi/3), how would I shade an argand diagram in a region R defined by |z-z1|<=1 and 0 <= arg(z-z1)<=3pi/4?

[cedar kiln]

@indigo valve Has your question been resolved?

[rugged tundra]

Firstly, what does |z - z_1| <= 1 correspond to?

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[pure lark]

am i supposed to look for angle BHD or…? bc the answer says 55.9 :/

[cedar kiln]

@pure lark Has your question been resolved?

[cedar kiln]

@pure lark Has your question been resolved?

[indigo valve]

yes

the angle that bh makes with adhe is bhd

[pure lark]

ahh ok

am i doing something wrong then? i got 59.73 rather than 55.9

[indigo valve]

oh im sorry im wrong

i havent done this in such a long time

the triangle in question is BHA

you have to do pythagoras of 9. 2 and 4.5

then use your original method

you cant do it with bhd because they are in a different plane

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[half quarry]

Pls explain 6 cause T-43 mins until exam

[desert nova]

hii what specific part do you need an explanation with?

[half quarry]

Just wondering how the algebra works out

[desert nova]

ooh okay

[desert nova]

for the second line, they didn't show it but it looks like they multiplied the entire fraction with sqrt(x-1)/sqrt(x-1)

to get (1 - sqrt(x-1))/((sqrt(x-1)*(x-2))

which cancels out the fraction in the numerator to get a cleaner fraction

and then to get rid of the square root, they multiplied the numerator's conjugate over itself which is (1 + sqrt(x-1)) / (1 + sqrt(x-1))

so you're left with the difference of squares in the numerator, which is 1^2 - (sqrt(x-1))^2 or simply 1 - (x - 1) for the numerator

since that simplifies to -(x-2) in the numerator, you can see that there is actually an (x-2) in the denominator which we can cancel out

so you are left with -1 / [sqrt(x-1) * (1 + sqrt(x-1))]

then yes just substitute the 2 and it's done :DD

[half quarry]

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[storm zenith]

Can anyone help me with the 12th one

[storm zenith]

<@&286206848099549185>

Can anyone help me with the 12th one

[steel heart]

!show

[cedar kiln]

Show your work, and if possible, explain where you are stuck.

[storm zenith]

I can’t get anything of this

I just did this

[steel heart]

If any list is AP, then it should have a common difference between its terms

[storm zenith]

I’m clueless

Yes

How do I show that

[stark crypt]

if an = a + 4n
an+1 = a + 4(n+1)
and the diff is 4

[storm zenith]

How’s it 4(n+1)

Wouldnt it be just 4n+1

[stark crypt]

Replace n by n+1

Nope

[storm zenith]

Oh k

Then

[stark crypt]

It’ll be in brackets

[steel heart]

or, $a_n =\frac{a_{n+1} + a_{n-1}}{2} \implies$list formed by $a_n$ is an A.P.

[wraith dagger]

Pro_Hecker

[stark crypt]

The diff will be 4, cus a will get cancelled 4(n+1-n) = 4

[storm zenith]

Oh k thank u for help

Ty

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[glacial tendon]

hello

[glacial tendon]

please help

[steel heart]

which question?

[glacial tendon]

2

[glacial tendon]

2

[steel heart]

The image is bit unclear

but anyways what do you understand by congruence?

[glacial tendon]

i understand the meaning i just dont understand how to solve for x and y

[steel heart]

okay ABC and EDF are congruent right?

so, what can you say about their angles?

[glacial tendon]

ty

i got it

[cedar kiln]

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[sinful zephyr]

3y - 4 = 56

3x - 10 = 50

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[cinder jay]

for

[cinder jay]

I dont really know how to use the derivate definition method

[earnest socket]

what is the value of a such that f'(a) = the limit you posted

[cinder jay]

I think its 4 because of the first one is used for the 2nd function

there is no additional information. it says determine (first image) for the function (second image) and explain what you have determined

[earnest socket]

well the last image you posted shows that the task of finding lim h to 0 of (f(4+h) - f(4)) / h is equivalent to the task of finding f'(4)

[cinder jay]

anyhow I dont know how to utilize it. the answer is supposed to become 4+e^12 and it says the first image gives f'(4) in the answer sheet

[earnest socket]

yes so you just need to find the derivative of f and substitute 4

[cinder jay]

?

[earnest socket]

you want to find lim h to 0 of (f(4+h) - f(4)) / h

but you know f'(4) = lim h to 0 of (f(4+h) - f(4)) / h from the last screenshot you posted

hence it suffices to find f'(4)

[cinder jay]

= f'(4)

is what i dont understand

how do you break it out

[earnest socket]

just replace a with 4 in this

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[frigid breach]

Hey, I got a question, why is it that Rad12 equals 2(Rad3)

[crimson sedge]

$$\sqrt{12} = \sqrt{2^{2}\text{×}3}$$

so the 2 goes outside

[frigid breach]

Thank you so much

[wraith dagger]

CUPS

[crimson sedge]

the bot is fucking up

there

[earnest socket]

you probably want \times instead

[crimson sedge]

my bad

[frigid breach]

Thank you again

[crimson sedge]

np

[frigid breach]

.close

[cedar kiln]

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[cedar kiln]

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[zinc crypt]

im confused on the squared box part in red

since it's undefined do I just don't worry about it I assume

[quaint berry]

It's 0 cause the denominator increase faster than the numerator

@zinc crypt

[zinc crypt]

ok ln (b)/ infinity is 0 then because

your dividing by infinity is what you saying

[quaint berry]

Ln increase slower than b^b

[twilit bison]

you can use l'hopital for that limit

ln(b)/(6b^6) is of type infinity / infinity

[zinc crypt]

oh ok that makes sense then

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[cedar kiln]

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[crimson sedge]

hi

[half quarry]

Hi

[crimson sedge]

i think when you realize that sqrt(x⁴) = x² the integral becomes pretty easy

[half quarry]

Ermm, pls explain

[copper cove]

except that is false

[crimson sedge]

well damn

[half quarry]

Oof

[crimson sedge]

OH

[nova snow]

https://tenor.com/view/pineapple-express-pineapple-express-gif-7402252

[crimson sedge]

i misread the integral

my bad

[half quarry]

Sooo how would u integrate it

[nova snow]

oh its actually pretty easy

let u = x^4 + 2 and see what you can do from there

[half quarry]

I got this far

But idk how to do u sub

[nova snow]

have u learnt u sub?

[nova snow]

thats correct just take the 1/4 out now

[half quarry]

I did but it make no sense

Ok..

[nova snow]

$\frac{1}{4}\int_{ }^{ }\left(u-2\right)\sqrt{u}du$

[wraith dagger]

water beam

[nova snow]

ok perhaps the letter "u" is confusing you

imagine this was x

could you integrate that

[half quarry]

No...

The multiplication messes me up

[nova snow]

do you know how to expand?

[half quarry]

Ermmm

No...

[nova snow]

a(b-c)

can you simplify that

[half quarry]

Ab -ac

[nova snow]

right

so can you do that here

what will you get?

[half quarry]

Sqrt(u)udu-2sqrt(u)du

[nova snow]

yes

well

dont forget avbout the 1/4

$\frac{1}{4}\int_{ }^{ }\left(u\sqrt{u}-2\sqrt{u}\right)du$

[wraith dagger]

water beam

[half quarry]

Okok

[nova snow]

can you simplify $u^{1}\cdot u^{\frac{1}{2}}$

[wraith dagger]

water beam

[nova snow]

thats u*sqrt(u)

[half quarry]

Then what abt the du?

[nova snow]

dont worry about du

worry about the algebra

[nova snow]

do you know how to simplify this?

using law of exponents

[nova snow]

yes but its better to keep the 1.5 as 3/2

[half quarry]

Okok

[nova snow]

$\frac{1}{4}\int_{ }^{ }\left(u^{\frac{3}{2}}-2u^{\frac{1}{2}}\right)du$

[wraith dagger]

water beam

[nova snow]

now you have this

you can easily integrate this using the reverse power rule

can you do that?

[half quarry]

So du doesn't matter in the end?

[nova snow]

what do you mean?

du is just part of the notation, it tells us what variable we are integrating with respect to

[nova snow]

yes

$\frac{1}{4}\left(\frac{2}{5}u^{\frac{5}{2}}-\frac{4}{3}u^{\frac{3}{2}}\right)+C$

[wraith dagger]

water beam

[nova snow]

now lets just multiply the 1/4

$\frac{2}{20}u^{\frac{5}{2}}-\frac{4}{12}u^{\frac{3}{2}}+C=\frac{u^{\frac{5}{2}}}{10}-\frac{u^{\frac{3}{2}}}{3}+C$

[wraith dagger]

water beam

[nova snow]

yes

nice

now we are pretty much done, all thats left is to substitute in back our "u"

we said u = x^4 + 2

[half quarry]

Yuh

[nova snow]

so replace u with that

$\frac{\left(x^{4}+2\right)^{\frac{5}{2}}}{10}-\frac{\left(x^{4}+2\right)^{\frac{3}{2}}}{3}+C$

[wraith dagger]

water beam

[nova snow]

nice

2/20 u can just make that 1/10 btw

[half quarry]

Okok

[nova snow]

but yeah ur correct

thats it

[half quarry]

Yayy

This was on my exam and I had no idea how to do it so I just yapped 😔 hoping for a 90 on it, it was the same with related rates, couldn't add right

Anyways thank you

[nova snow]

[half quarry]

☺️☺️

[nova snow]

no worries hope you understood

[half quarry]

It made more sense, I was studying washer ans disk method all day yesterday, should've focused on integration instead

[nova snow]

ah solids of revolution ya i remember doing that annoying stuff

[half quarry]

Should I drop out, pursing a math minor ain't it

[nova snow]

depends what u wanna do in the future but i suggest talking to a teacher or something about it before doing anything like that

[half quarry]

😔

[nova snow]

but its not so bad when you keep practicing

[half quarry]

I have one more exam to go today and I don't speak the language 😔

Anyways thank you

Good luck with life 👍

[nova snow]

no worries, GL!

[half quarry]

.close

[cedar kiln]

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[cedar kiln]

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[half lintel]

Consider the equation $x^{y}-y^{x}=17$, why does the graph below show points that does not even a solution such as (6, 6)?

[wraith dagger]

xCirno

[lyric narwhal]

it's probably not exactly (6, 6)

zoom in on it

but yeah it makes sense that the larger solutions are very close to the line y=x

it's not (6, 6)

[half lintel]

oh

on desmos, how to find an intersection between two functions

like this doesnt show the intersection point

[lyric narwhal]

it should

hmm you're right, it doesn't show it for some reason

[half lintel]

yeah

I also used geogebra and I used the intersection tool

but it said "?"

[lyric narwhal]

lol

you could use wolframalpha I guess

,w x^y-y^x=17, x=5

[wraith dagger]

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

Requested by kheer257

[lyric narwhal]

oh no

[versed jasper]

trolled

[lyric narwhal]

we're doomed

,w 5^y - y^5 = 17

[wraith dagger]

Results provided by WolframAlpha

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

Requested by kheer257

[versed jasper]

crazy

[half lintel]

why is there a negative value there

[lyric narwhal]

because wolfram is weird

[half lintel]

where in the graph there is none

oh

[lyric narwhal]

actually it's more like your graph is incomplete/only considering positive bases for the exponent

because technically integer powers CAN be defined for negative numbers but they won't show up on your graph since they would be isolated points

[half lintel]

hmm

so from now on I cant rely on graphs...

[lyric narwhal]

no, the graph is fine

exponents are weird for negative values

and we usually don't care about them anyway

I was just telling you why wolfram gave us a negative value as well

[half lintel]

oh okay

thanks

!close

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[misty frost]

Hi i have this problem:
Solve this functional equation $f:\mathbb{N}^* \to \mathbb{N}^*, \frac{xf(x)+3x^2y}{f(x)+y^2+2xy}+\frac{y^3+3xf(y)}{f(y)+x^2+2xy}=\frac{(x+y)^3}{f(x+y)}$, until now I have found the solution by trial and error $f(x)=x^2$, how can I prove this and are there any other?

[wraith dagger]

Popescu V2

[lyric narwhal]

what happens if you set x=y

the general way of solving functional equations like this are to try different values of x and y and get enough relations in f so that you can conclude what f can be

basically getting more and more properties that f must satisfy

[misty frost]

i get $\frac{f(x)+x^2}{f(x)+3x^2}=\frac{2x^2}{f(2x)}$

[wraith dagger]

Popescu V2

[misty frost]

Now what?

<@&286206848099549185>

How can I prove it is the only solution?

<@&286206848099549185>

[cedar kiln]

@misty frost Has your question been resolved?

[misty frost]

<@&286206848099549185>

[misty frost]

<@&286206848099549185>

[uneven kiln]

romanian?

@misty frost

[misty frost]

yes

[uneven kiln]

asa bun

imi poti da enuntul original?

[misty frost]

Determinati functiile $f:\mathbb{N}^* \to \mathbb{N}^*$, care verifică egalitatea $\frac{xf(x)+3x^2y}{f(x)+y^2+2xy}+\frac{y^3+3xf(y)}{f(y)+x^2+2xy}=\frac{(x+y)^3}{f(x+y)}$

[wraith dagger]

Popescu V2

[uneven kiln]

ce ai incercat pana acuma?

si asta e problema de liceu?

[misty frost]

Am bagat f(x)=x^2

Da

[uneven kiln]

ce clasa?

[misty frost]

10

[uneven kiln]

bun

[misty frost]

Acum cum zic ca nu mai sunt si altele?

[uneven kiln]

well, eu unu as incerca sa dau valori mici sa vad daca e liniara sau nu.

te pregatesti pt cv olimpiada nu?

[misty frost]

da

am gasit un subiect si problema asta e naspa

[uneven kiln]

bun stii ce e functie liniara?

nu?

[misty frost]

da

f(x)=ax+b

zici ca ar putea merge si ea?

[uneven kiln]

eu la asta ma gandesc

sa aratam ca e functie liniara

[misty frost]

Mai am asta: $\frac{f(x)+x^2}{f(x)+3x^2}=\frac{2x^2}{f(2x)}$

[wraith dagger]

Popescu V2

[misty frost]

@uneven kiln mai ai idei?

[uneven kiln]

sincer e prima data cand vad cv de genu si sunt la matematica la facultate

dar i-as da valori sa vad cum se comporta

gen 1, 2 etc.

si dupa as arata ca e la fel ca si functia ai f(x) = x^2

Gen alta varianta nu vad @misty frost

[misty frost]

Mersi

[uneven kiln]

imi poti da mesaj oricand

poate pot sa te ajut

[cedar kiln]

@misty frost Has your question been resolved?

[obtuse mango]

where is the problem from?

[obtuse mango]

anyway notice that the LHS is not symmetric but the RHS is

so we'll get something if we do x -> y, y -> x

[sharp lotus]

nu am nici o sugestie dar va doresc succes : )

[obtuse mango]

wait actually this immediately kills the problem

unfortunately i don't speak romanian but i hope my hints helped

[cedar kiln]

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[fresh rock]

hiiii

[fresh rock]

how i get proability in measures of central tendency

i dont unnderstand

[dire geode]

if you're working on an actual problem or reading something just show it

[cedar kiln]

@fresh rock Has your question been resolved?

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[fresh rock]

oke

[fresh rock]

its vasicalli

measures of central tendency

[manic swan]

Median is lowest number to highest, and the middle one is median

[fresh rock]

o tannkkkk

[manic swan]

Average all numbers summed and divided by the amount of numbers

[fresh rock]

and in grouped data

how

[manic swan]

Moda is the number being most quantity

5,5,5,6,6,6,6,6,7,7

6+6/2= 6

!done

[cedar kiln]

If you are done with this channel, please mark your problem as solved by typing .close

[drowsy isle]

what is the launguage at all?

[fresh rock]

SPANISH

[drowsy isle]

okay okay.i'm uable to read.

[cedar kiln]

@fresh rock Has your question been resolved?

[cedar kiln]

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[potent echo]

How to solve this differential equation

[dire geode]

that looks separable?