help-0

[warped phoenix]

channel in use

[bleak vapor]

Oh sorry

[warped phoenix]

so i cant take the sqrt of both sides here?

[vague coral]

you can but you will have $\sqrt{sin²x + cos²x} = 1$

[warped phoenix]

ah...

so you cant take a sqrt of sin or cos

got it

[ocean seal]

Herels

[warped phoenix]

but then i still dont understand how sin^2(x) + cos^2(x) = 1

like

what value is x

for us to know it's 1

or are we meant to solve for 1

[vague coral]

for all values of x

[alpine sable]

Can someone help me?

ok

This is my question

,rcw

[alpine sable]

whats this thick bar mean

Such that?

or parallel to?

Parallel

ok

Yup

hm wait I see you already done work

and i don't see an issue with it

[bleak vapor]

Lol

[alpine sable]

so whats the issue?

[bleak vapor]

I need help

[alpine sable]

Plz I’m so bad at math

Your supposed to get 180 for it to be a triangle right? So would you add those two and find it?

[alpine sable]

We all need help : (

[fair sentinel]

Is it the middle on we are looking at

[alpine sable]

yeah

[ocean seal]

Πολλά άτομα είναι

[alpine sable]

Alright thanks!

[pseudo citrus]

Question: Given x = cosec 5y
a) Find dy/dx in terms of y
b) Hence find dy/dx in terms of x

I got part a correct as -1/(5cosec(5y)cot(5y))

For the second part Im not sure how you get rid of the cot 5y

because ofc you can just sub cosec 5y =x for the cosec part

[ember ether]

it's easy to prove that sin(x)²+cos²(x)=1

[warped phoenix]

how?

[ember ether]

look

[fair sentinel]

Pythagorean theorem

[ember ether]

yes

[fair sentinel]

Ayyy

[ember ether]

give me a sec im gonna draw u something so you can understand

[fair sentinel]

X would be the internal angle of a right angle triangle?

[ember ether]

look

this a trigonometric circle

so the radius R=1

so you can do the Pythagorean theorem

and you will habe cos(x)² + sin²(x)=1

did you understand ?

[fair sentinel]

I did

Sorta

lol

[ember ether]

so i just took this x as an example

you can do the same thing with every angle u want

wich means for all the angles their cos² + sin ²=1

or u can prove it with vectors

[warped phoenix]

sorry i was busy

[ember ether]

did you understand ?

[warped phoenix]

so sin^2(x) and cos^2(x) are both the sides that are not the hypotenuse right?

[ember ether]

yes the radius is the hypotenuse

[warped phoenix]

ohh

right

sin^2(x) + cos^2(x) = c^2

and since it's a unit circle, c = 1 (radius = 1) ?

[ember ether]

and cos(x) is the horizontal one and sin the vertical

yes

[warped phoenix]

OHHHHHHHHHHHHHHHHHHHHHH

I GET IT

thank you!!!!!

[ember ether]

nice

no problem

[warped phoenix]

i wasnt thinking in terms of unit circle so that's probably why i wasn't understanding it initally hahaha 😅

[ember ether]

it's ok you can use vectors too

[thin berry]

I got a stroke reading this

[upper pebble]

2(2/3k - 3) = 1/3k + 10

[ionic jewel]

yeah i dislike problems like that

its literally reading comprehension not math

[thin berry]

Ummm

[thin berry]

Can you explain ?

[upper pebble]

"Three is subtracted from two thirds of the number k..."
2/3k - 3

"...and the difference is doubled."
2(2/3k - 3)

"If the result is ten more than one third of the number..."
1/3k + 10

so 2(2/3k - 3) = 1/3k + 10

[thin berry]

Ooh

I thought the difference is the value doubled

Tysm

[warped phoenix]

The amplitude is -30, and the period is 5.2, right?

[upper pebble]

the amplitude is the distance from the midline to the peak or trough

[ionic jewel]

(its also the number at the front of the eqn)

[upper pebble]

true

[warped phoenix]

wait

but i was told the aplitude is the distance from the x axis

[upper pebble]

i believe you were told incorrectly then

also distance is always positive so it would be 30 if that were the case

[warped phoenix]

the midline is -20 right

so then the amplitude is 10?

ok that makes sense

[upper pebble]

yes

[warped phoenix]

but then the period still is 5.2 right?

[upper pebble]

i'm not sure about the period

need to brush up on my trigonometry

[warped phoenix]

anyone else have any idea?

[toxic prairie]

from that equation right there?

the period is 4

[warped phoenix]

yeah

😦

how?

[toxic prairie]

see that $\pi/2$ in the sin function

woops

but either way

[ocean seal]

holazach

[warped phoenix]

yeah..that means a horizontal stretch by pi right

[toxic prairie]

yeah, so in essence you have the normal period that is $2\pi$ and this gets scaled to $2\pi/(\pi/2)$ which is $4$

[ocean seal]

holazach

[upper pebble]

ah i remember that now, nice

you can also tell that the period is 4 by looking at the graph

it completes one cycle in 4 units

[toxic prairie]

yeah I mean some graphs are harder to read but yeh

[upper pebble]

true

[toxic prairie]

best way with graphs is to measure the distance between the peaks

[faint patrol]

I'm trying to help my daughter with math. Is this how you do it?

[upper pebble]

5^2 = 25
sqrt(5^2) = sqrt(25) = 5
so it's the same thing as 25/5, which equals 5

[faint patrol]

Thanks!

My daughter also typed this out. Is this correct?

[upper pebble]

[jagged imp]

no :)

[upper pebble]

yes 2 = 1

[jagged imp]

you divided by 0

[faint patrol]

I'm not following.

[upper pebble]

same

[arctic wren]

[faint patrol]

<@&286206848099549185> Can anyone walk me through?

[glass lichen]

stop trolling

[faint patrol]

Sorry. Do I go to a different channel?

[jagged imp]

i didnt really want to call it out on the tiny tiny chance they werent

but the first image is

[glass lichen]

No, you just post actual questions, not obvious trolls

[dark granite]

this isn't true because $2(a-x)=a-x$ doesn't imply $2=1$ since you assumed $a-x=0$ by assuming $a=x$.

[ocean seal]

logician_pdx

[glass lichen]

no crap, it's a common proof for 2=1

[faint patrol]

Thanks!

[dark granite]

you're welcome

[glass lichen]

and that's the common flaw, any amount of googling will say that

[faint patrol]

Oh, I understand now.

Thank you.

[dark granite]

You're welcome

[faint patrol]

Do you know any website I can google for help? I couldn't find any after a couple searches.

[dark granite]

take it easy. it's totally possible that @faint patrol looked this up on google already and didn't understand what was being said there on google

[glass lichen]

literally google the question like any other query

[glass lichen]

they are clearly a troll.

[dark granite]

but how do you know that they are?

[warped phoenix]

[upper pebble]

[glacial hedge]

Is this channel being used?

[upper pebble]

currently, no

[glacial hedge]

How does symmetry help here?

for the second surface integral of x^2+y^2+z^2

thats 4pi becaues its on a unit sphere correct?\

Im really confusion

<@&286206848099549185> ?

[dark granite]

well so what do you know about what x^2+y^2+z^2 equals?

[glacial hedge]

1

[dark granite]

@glacial hedge

right

[glacial hedge]

what does this say about x^2 though?

[dark granite]

and so what does that double integral with essentially 1 calculate

?

[glacial hedge]

its surface area

which is 4pi

OH

WAIt

Is it because you can split x^2+y^2+z^2

into 3 integrals because of symetry

so its 4pi/3

?

[dark granite]

yes

[glacial hedge]

tyy

[dark granite]

you're welcome!

[alpine sable]

I need help

what is 20 ^-27

@coral sail

or anyone

[junior blaze]

I need help

[dark granite]

@glacial hedge You get that problem, right? It's been a while since I've done vector calc

[glacial hedge]

uhh idk but im pretty confident that's correct

i havent turned it in yet

[dark granite]

okay gotcha

I'd suggest working out that problem the long way @glacial hedge just to be sure

by the long way, I mean parameterizing, taking partial derivatives, finding the magnitude of the relevant normal vector etc, then integrating

[glacial hedge]

i would but knowing that homework usually wants u to use a certain observation when it gives you a "hint" in the problem

🙂

[dark granite]

yeah I'm just talking about as a for sure way of checking your answer

[glacial hedge]

ye ye ty

[dark granite]

you're welcome

[glacial hedge]

Ayyy i was right!

*you were right

[dark granite]

nice!!

We works

[sinful monolith]

how do i do this?

[subtle sun]

B = 20, C = A =100

[vague coral]

a = 90

[sinful monolith]

right

a =90 cuz its a right angle

[jagged imp]

where does it say its a right angle

[solar shell]

you don’t know it’s a right angle

[sinful monolith]

its not?

[solar shell]

it’s 100 degrees

[sinful monolith]

looked like 90 lol

why is it 100?

[solar shell]

On a straight line, all angles add to 180

20 + 60 + A = 180

[sinful monolith]

oh

so is it E?

180+100?

[solar shell]

100 + 100 + 20 I believe

hol up

Yeah 220

C + b does not equal 180

C + b + the angle between them = 180

[sinful monolith]

100 is a and c?

[solar shell]

Yes that

They are equivalent

[sinful monolith]

aw i see now

[keen wasp]

answer is B, could someone please explain the formula

and also would the answer be 1 - (0.99)^100 if the question is asking the probability that it will happen at least once

i thought the answer would be B but without the 100 c 1 but that obviously is way too low

i kinda get what they did but need more explanation

[cinder lily]

Apply this formula

[keen wasp]

thanks but i figured out the formula, i just dont get why u have to multiply by the number of combinations

[ocean seal]

Elonmosqito96

[glacial hedge]

there we go

[upper pebble]

@lyric wadi did you find the answer to the question you deleted

i was curious

[grizzled ember]

Why is that true and how do I know it to be true?

[lyric wadi]

yes yes am good now

[upper bridge]

does anyone know how you would answer this

[tranquil pelican]

Could you explain what you do think you understand so that I know where to start please

[minor heath]

<@&268886789983436800> look up

[sly mantle]

b&

[minor heath]

pog

[tranquil pelican]

I've never seen a question like this before so here's how I am thinking about it. Lines are of the form y= mx+b or the point coordinate formula. Well, if they both go through the origin then it's line 1, "y_1 = m_1 x" and line 2, "y_2 = m_2 x"

Then x = y_1/m_1 = y_2/m_2 => y_1 = (m_1/m_2)y_2 , so they're related by a constant. Proportional.

@grizzled ember

[oak matrix]

Pls help I can’t even understand the question lol

[tranquil pelican]

Its asking what that expression converges to, given A < B. Which might just be to avoid any /0 problems

[ocean seal]

Callaway

[oak matrix]

Why does it have the 1/ab in the beginning?

[tranquil pelican]

Its saying its also equal to that expression

[teal epoch]

The first part is already a hint to answering your question.
It asks to evaluate the expression.

[oak matrix]

OMG wait so the dots are a symbol not the multiplication sign

[teal epoch]

Hint:
$\frac{1}{a \cdot b} = \frac{1}{a} -\frac{1}{b}$.

[ocean seal]

Callaway

[teal epoch]

no
they're multiplication signs

[oak matrix]

Aghhhhhh

[teal epoch]

Okay let me clear things up.

[teal epoch]

channel busy.

[tranquil pelican]

it looks like 1/ab = 1/(b-a) * (1/a - 1/b) * 1/(1*2) + ...

[ocean seal]

Callaway

[minor heath]

you mean $\frac{1}{ab}=\frac{1}{b-a}(\frac{1}{a}-\frac{1}{b})$

[ocean seal]

G3oG0dly

[teal epoch]

wait, it does?

[minor heath]

,w \frac{1}{ab}=\frac{1}{b-a}(\frac{1}{a}-\frac{1}{b})

[ocean seal]

Results provided by WolframAlpha

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

Requested by G3oG0dly#8680

[teal epoch]

oh.

[tranquil pelican]

woah

based

[teal epoch]

hmm i see. my mistake.

[oak matrix]

So 1/1x2=1/2-1 (1/1-1/2)

[teal epoch]

,w \frac{1}{a}-\frac{1}{a+1}

[ocean seal]

Results provided by WolframAlpha

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

Requested by Callaway#0634

[teal epoch]

???

[minor heath]

$\frac{1}{(1)(2)}=\frac{1}{2-1}(\frac{1}{1}-\frac{1}{2})$

[ocean seal]

G3oG0dly

[minor heath]

do it with the other terms

and try to see the pattern

[oak matrix]

This is probably really simple but I just cannot comprehend anything rn lol

Ok

Wait omg I think I get it

A lot of it cancels out

[teal epoch]

this seems more like a telescoping series.

[oak matrix]

Tysm<33

[alpine sable]

Can there exist at least one plane which is tangential to 3 ovoid in any position in space and of any size?

[charred flint]

jesus christ

[thorn kindle]

y^2 = 3x or y^2 = 4x

This question doesnt make sense

We are not given the value of x

[harsh acorn]

"if x is even and negative"

doesn't it mean it is 0 (Just forget what I said lol)

[charred flint]

@alpine sable yes, just get a plane that's tangent to 2 and rotate it around till it hits the 3rd ovoid

[thorn kindle]

-2

But the question makes 0 sense

[harsh acorn]

Yeah, I thought even means positive sorry lmao

[thorn kindle]

We are not given the value of star

[charred flint]

it took me 10 minutes to understand the question

[thorn kindle]

Nor can we solve for it

[charred flint]

all of the formatting is wrong lmao

[true maple]

i still dont get it

[charred flint]

[star (number) star] gives you 4*number if it's odd

it's a single input operation like (number)^2 or something

[true maple]

star sqaured = 3x?

-22 star = 3x?

idk

[charred flint]

uh ignore the square thing I said

it's stars surrounding the number -23

and -23 is odd so you use the -4x formula

[harsh acorn]

is star equals to 6?

,calc 6-23*6

[ocean seal]

Result:

-132

[harsh acorn]

nah

oh, It says negative

[charred flint]

star isn't a number or anything

the 2 stars make up a function that's applied to -23

[true maple]

-23*4=-92?

[charred flint]

yup

[true maple]

omfg

🤣 such a dumb question

i thought the star was a variable

not a fx

ty

[harsh acorn]

yeah same lmao

[true maple]

bro

the x inbetween stars

looks like multiply sign

not x as in variable

[charred flint]

yea it's a funny typo

[ionic jewel]

that is the single most cursed notation ive ever seen

and what happens if its a positive even?

that might actually just be the most cursed question ive seen

[alpine sable]

Yep i think that'll work

[inner sequoia]

|6/(x-3)|=2

what is x

,calc |6/(x-3)|=2

[ocean seal]

The following error occured while calculating:
Error: Value expected (char 1)

[ionic jewel]

,w abs(6/(x-3)) = 2

[ocean seal]

Results provided by WolframAlpha

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

Requested by 兔子#6562

[alpine sable]

@pliant bear

[teal epoch]

(Day 2)
Hello everyone!
I just want to know how intelligible is the question to other people.
If there are some parts you don't understand, or suggestions that seem to improve this question please let me know.

Question (V4):
You are given a picture of a 12-hour clock where the minute hand and the hour hand have the same length. That means when only looking at it you have no way to figure out which one of them is which, but you can still tell the time of it by using logic.
How many different times are there in which one cannot guarantee what time it is?

The answer here is 132. You can verify if you want.

[lethal stump]

the question is great, i just think a diagram explaining the situation would make it crystal clear

[thorn kindle]

What do you mean by logic

Do you remember the time?

[dark granite]

@teal epoch The question is nice; I'd recommend describing instances when the hour and minute hands can't be overlapping completely. Also, explain what you mean by "times" because one might argue that if the minute hand is halfway between two minute markers on a clock, then some might still count that as representing a time. Unless one knows exactly where the hands could overlap and what you mean by "time", your question is quite vague and lacks some clarity.

[ionic jewel]

^

and some clocks have hands that go between numbers, and some jump to the next number when it gets to that time

[dark granite]

@teal epoch You've also seemed to implicitly assume that there is no second hand. Maybe explicitly state that assumption.

[thorn kindle]

12 * 11

At every multiple of 5 min i think

,calc 132*5

[ocean seal]

Result:

660

Result:

55

[teal epoch]

it's actually $12^2-12$

[ocean seal]

Callaway

[alpine sable]

one question

[teal epoch]

the -12 represents those overlapping things

[teal epoch]

channel busy

[thorn kindle]

144-12 = 132 = 12*11

[alpine sable]

1+2=x find x

[teal epoch]

the times well represent how many times or something

[dark granite]

I won't answer this as this channel is busy like @teal epoch stated. Please go elsewhere

[teal epoch]

is there anything that can rephrase so that it makes a lil bit clear

[teal epoch]

wdym?

[thorn kindle]

Huh no it should be 12*12

[dark granite]

I just don't think people know that much about analog clocks.

[thorn kindle]

Unless you remove overlaps? Was that stated in the problem

[dark granite]

I didn't hear anything about a second hand....I only heard about a minute hand and an hour hand

[teal epoch]

well i've considered overlaps but you can still determine the time so it doesn't matter

[thorn kindle]

Its about when you cant determine the time

[teal epoch]

yeah
that's why i subtract 12 from it

[thorn kindle]

Every multiple of 5 minus overlaps

Yeah you did it good job

[teal epoch]

One example is when one hand is pointing at 12 and the other at 3
The time is either 12:15 or 3:00
The time 12:15 is invalid, since the hour hand should have been between 12 and 1 instead of pointing directly at 12
Therefore, one can conclude the time of that configuration is 3:00

[dark granite]

Some analog clocks don't even have a second hand....by leaving out details about the second hand, we're left to wonder about whether that is involved in how you'd define a "different time"

[thorn kindle]

Does the hour hand move continously or discretely

[teal epoch]

you are given a picture so it doesn't move

[thorn kindle]

But does it move discretely or continously

Some clocks are like that where the hour will be on 5 exactly until its 6 o clock

[teal epoch]

oh something like when the hour hand is at 5 and when the minute hand is at 12 it goes to 6 all at once?

[thorn kindle]

Yeah

[teal epoch]

wait there are clocks like that

huh

[dark granite]

there are some strange clocks out there

prolly best to detail what clock you're talking about, in your problem statement

[teal epoch]

for that it's continously
i've never seen a clock with its hour hand move discretely
i'll consider that

what do you call a clock that moves continuously
a continuous clock???
lol

[dark granite]

an atomic clock lmao

[teal epoch]

how bout for discrete ones

[thorn kindle]

It already gave you the answer though

132

Which is what we got so i dont see the confusion

[vale wigeon]

never seen one of those

ive seen ones where the minute hand moves discretely but the hour hand moves smoothly on all clocks iirc

[dark granite]

same

[ionic jewel]

Ive seen a handful so i can confirm they exist

[rich basin]

Sorry, this is for both parts of it

I think my answer for the first part is 7 C 4 using the dividers

[teal epoch]

this channel is occupied for now
can I kindly ask to please move your question to an unoccupied channel

[rich basin]

Okay sure

[teal epoch]

(Day 2)
Hello everyone!
I just want to know how intelligible is the question to other people.
If there are some parts you don't understand, or suggestions that seem to improve this question please let me know.

Question (V4.5):
You are given a picture of an atomic 12-hour analog clock where the minute hand and the hour hand have the same length. That means when only looking at it you have no way to figure out which one of them is which, but you can still tell the time of it by using logic.
How many moments are there in which one cannot guarantee what time it is?

Notes:
• Assume that we are reading time at infinite precision.
• There is no second hand on the clock.
• A.M and P.M doesn’t matter.
• No loopholes are allowed.

• “You can still tell the time of it by using logic.”
One example is when one hand is pointing at 12 and the other at 3.
Then the time is either 12:15 or 3:00.
The time 12:15 is invalid, since the hour hand should have been between 12 and 1 instead of pointing directly at 12.
Therefore, one can can say that the time is 3:00.

• “How many moments are there in which one cannot guarantee what time it is?”
One example is this one time that looks like 12:50 and 10:04 at once.
Both of them are valid, and therefore cannot tell the time of it.
This only count once.

how can i put those notes on the question but at the same time it doesn't make it lengthy?

[ionic jewel]

sin is the name of the operator/function

$\sin\theta$ is that function operating on the variable theta

[ocean seal]

bunny

[vale wigeon]

||it's the difference between "to fuck" and "i fucked your mom"||

no, you're misspelling things wildly and the "and" leaves much room for doubt about your understanding

sin is the name of the trig function itself

don't call me bro.

you want to know where the name sin came from?

okay, nevermind

have you been introduced to the concept of functions?

...

[vale wigeon]

i asked this question, you answered unhelpfully

you're wasting your what?

can you please stop screaming every ten seconds

okay so you don't know what a function is

[upper pebble]

you're probably wasting both your time and Ann's time in general

[vale wigeon]

then it will be impossible to tell you what sine is, as opposed to sin(θ)

there is so much wrong with what you said.

[livid pier]

sin is opposite/hypotenuse

SohCahToa

[vale wigeon]

and you're butchering the spelling of everything you write. and you're using this "and" seemingly to indicate division.

it feels as if you're not here to learn

[ionic jewel]

it's a miracle this guy's shift key still works

[vale wigeon]

DON'T FUCKING HAY ME

[livid pier]

._.

whats going on lol

[upper pebble]

[vale wigeon]

yikes

why do i even bother...

[alpine sable]

@cobalt breach sine is a trigonometry function, that takes an angle as its input, its equivalent to opposite divided by hypotenuse (of a triangle with the same angle), sine is the name of the function, sin(theta) is just inputing theta to the sine function

[ionic jewel]

yo Ann take a break, it's ur time, only help people who want your help

you aren't paid to be here don't deal with his bs

[ember ether]

does anyone know the definition of an angle here

[ionic jewel]

we all know what angles are yes

[alpine sable]

If you want to learn more about sine, look into the unit circle (https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:trig/x2ec2f6f830c9fb89:unit-circle/v/unit-circle-definition-of-trig-functions-1)

[vale wigeon]

good point

[ember ether]

@cobalt breach look Sin is a function but it has a period it repeat it self its like for every x (angle) it will give sinx ( image ) so we can do a graph and draw the function

[alpine sable]

im guessing you are just doing basic trig, ie finding angles and sides on a right angle triangle? If so you dont need to worry about what sine is or does, just know its opposite / hypotenuse and use your calculator

that depends

[ember ether]

and we know that sin(x+2pi)=sin(x) knowing that x belongs to the Set R

so the period of Sin is 2pi

[alpine sable]

if you really want to know what it does, given an angle on a unit circle, sine of that angle is the y coordinate around a circle with a radius of 1, that probably doesn't make a lot of sense, you would need to listen to someone explain it with diagrams, so dont be worried if it confuses you

idm

[livid pier]

yeah

[alpine sable]

if you know enough trig there are alot of angles you dont need a calculator for

but generally, and especially for what you are doing you use a calculator

im only in yr 11

[livid pier]

youngsters

[alpine sable]

most people here are likely graduated

[livid pier]

ur in middle school?

and ur doing trig wtf

thats pretty advanced imo

[alpine sable]

are you learning proper trig, or just trig related to what you would do in your Pythagoras topic with right angle triangles

[livid pier]

i dont think i touched trig until junior year

[alpine sable]

you should try khan academy

[livid pier]

yea khan academy is pretty good

they have free courses

[alpine sable]

I use to a lot, and still do occasionally

[livid pier]

i'm using it for calc 2 right now

[ionic jewel]

minimum age for discord is 13 so I'd recommend being 13 if you don't want to be banned

but yes, Khan academy is a good place to learn trig, but there's a million tutorials out there

[sudden tulip]

Hi how do I solve this

I tried using the factorisation of $x^2$ thing

[ocean seal]

Team Bayern

[mossy geyser]

try rational root theorem

and hint: ||there’s a small solution||

[sudden tulip]

How do I do that ?

[cinder lily]

there can only be integer roots that divide 48

so try those

[sick moss]

Did you get your solution? Can I ask my question?

[jagged imp]

you can use another channel if you're not sure if this one is available. #help-5 is defo free

[sick moss]

ok. tx

[sudden tulip]

im still unsure

[acoustic abyss]

hi i have a doubt

anyone?

help plz

hellow?

[teal epoch]

1.) Simplify the expression $8w^4 \cdot 5w^5 \cdot w^4$.

Is the rephrase right?

[acoustic abyss]

yep

tysmm

[ocean seal]

Callaway

[acoustic abyss]

yep

[teal epoch]

Have you tried solving this problem?

[acoustic abyss]

how do i do it

[acoustic abyss]

just tell me how to do it ill try on my own

dont tell the answer

[teal epoch]

I'll tell you how to do it but in an example

[acoustic abyss]

alr sure

ty

[teal epoch]

Example: Simplify $2x^2 \cdot 3x^3$

[ocean seal]

Callaway

[acoustic abyss]

ohh

ok

then

[teal epoch]

To make things clear, we'll make $2x^2 \cdot 3x^3$ as $2 \cdot x^2 \cdot 3 \cdot x^3$.
Don't worry, they're the same

[acoustic abyss]

alr

[ocean seal]

Callaway

[teal epoch]

(in any order)
First, multiply the (whole) numbers.
In this case, it's 2 and 3.
$2 \cdot 3=6$

[ocean seal]

Callaway

[teal epoch]

Next are the variables.
We're going to use the exponent identity $x^a \cdot x^b=x^{a+b$.
Therefore, $x^2 \cdot x^3=x^{2+3}=x^5$

[acoustic abyss]

alr

[ocean seal]

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

[teal epoch]

Lastly, multiply those together and you'll get $6x^{5}$.

[acoustic abyss]

ohh thats it?

ok tysmm

one more thing

[ocean seal]

Callaway

[acoustic abyss]

yea got it tysmm

[teal epoch]

yeah only for this case

[acoustic abyss]

im rlly confused

[teal epoch]

What are we going to do here?

[acoustic abyss]

so this will be 40⁹⁶?

[acoustic abyss]

make y the subject

[acoustic abyss]

the y to the side

[teal epoch]

you mean $40^{98}$?
no

[ocean seal]

Callaway

[acoustic abyss]

then

.

[teal epoch]

where did the $w$ go?

[ocean seal]

Callaway

[acoustic abyss]

oh yea

40w⁹⁶

[acoustic abyss]

this is correct?

[teal epoch]

You're wrong, but you're close
Can you tell us where do you get the 96?

[acoustic abyss]

4 x 4 x 6

[low gorge]

40w^{14}

[acoustic abyss]

ohh

u have to add?

[teal epoch]

no, that's not how it goes

[teal epoch]

yeah

[acoustic abyss]

ohhh i thought we have to multiplyy

ohh tysmm

[teal epoch]

$x^a \cdot x^b=x^{a+b}$

[ocean seal]

Callaway

[acoustic abyss]

ohhh alr

[acoustic abyss]

yep ik this

so the numbers has to be multiplied

while adding the exponents?

[low gorge]

Yes

[acoustic abyss]

ohh ok

[acoustic abyss]

this one?

[teal epoch]

I can't put to words on what to do, but i'll put examples here

[acoustic abyss]

alr

[teal epoch]

1.) Express $x+2=y$ in terms of x.

[ocean seal]

Callaway

[teal epoch]

Just subtract 2 to both sides.
$x+2=y \implies (x+2)-2=(y)-2 \implies x=y-2$

[ocean seal]

Callaway

[acoustic abyss]

ohh

[teal epoch]

2.) Express $x=3yz$ in terms of z.

[ocean seal]

Callaway

[teal epoch]

Just divide both sides by $3y$.
$x=3yz \implies \frac{(x)}{3y}=\frac{3yz}{3y} \implies z=\frac{x}{3y}$

[acoustic abyss]

ok

ohhh

[ocean seal]

Callaway

[teal epoch]

3.) Express $y=2x+1$ in terms of $x$.

[ocean seal]

Callaway

[acoustic abyss]

alr

[teal epoch]

First, subtract 1 from both sides.
$(y)-1=(2x+1)-1 \implies y-1=2x$

[ocean seal]

Callaway

[teal epoch]

Lastly, divide both sides by 2.
$\frac{(y-1)}{2}=\frac{2x}{2} \implies x=\frac{y-1}{2}$

[ocean seal]

Callaway

[teal epoch]

The Target

[acoustic abyss]

ohhh

ok tysmm

[alpine sable]

some nudges? don't know where to begin

need help

Let P1 be the linear space of real polynomials of degree at most one, so a typical element
is p(x) := a + bx, where a and b are real numbers. The derivative, D : P1 → P1 is,
as you should expect, the map DP(x) = b = b + 0x. Using the basis e1(x) := 1,
e2(x) := x for P1 , we have p(x) = ae1(x) + be2(x) so Dp = be1 .
Using this basis, find the 2 × 2 matrix M for D. Note the obvious property D2p = 0
for any polynomial p of degree at most 1. Does M also satisfy M2 = 0? Why should
you have expected this?

[analog locust]

guys

why is the euclidean distance between an average and a point is (x-xi)^2?

explanation to it? :/

[alpine sable]

Jus a sec

Anyone kno this

2+1=x find x

[upper pebble]

try adding 1 and 2

[versed hazel]

lol

[upper pebble]

i think that might work

a bit daring but yeah

i like your ditto pfp

[versed hazel]

yo can any1 help me solve this????

[thorn kindle]

@versed hazel all the factors that appear in the numerator of the first expression are those that appear in the denominator of the second expression and vice versa

Albeit with each term having their signs flipped

[versed hazel]

hmmm

[thorn kindle]

So 1 = (-1)/(-1)

Wait no i read that wrong sorry

[versed hazel]

"numerator of the first expression are those that appear in the denominator" i dont think this is true

[thorn kindle]

Yeah just realized that lmao

[versed hazel]

lol its fine

[thorn kindle]

Just clear the denominators

[versed hazel]

i tried that u cant just clear it

[thorn kindle]

Multiply both sides by the denominator it works

Then distribute and compare

[versed hazel]

can u show the steps i dont think it works

[thorn kindle]

(a-b)(c-d)(e-f)=(c-b)(e-d)(a-f)

Expand both sides

Then

(b-c)(a-e)(f-d)=(a-c)(f-e)(b-d)

[versed hazel]

hmmm

[thorn kindle]

Expand that out

[teal epoch]

not related, but how do you get the @ helpers role?
do you ask to the mods

[versed hazel]

lmao

[thorn kindle]

You dont want it

[versed hazel]

help me solve this then u can get the role

[teal epoch]

no i don't want to have that role I'm just curious of how do you guys got those

[versed hazel]

lmao

[thorn kindle]

Not worth it

[alpine sable]

rubber bands

[versed hazel]

guys

can we get back to the topic pls

[alpine sable]

wait has anyone solved my question

[versed hazel]

ikd i think that was long time ago

[alpine sable]

oh i just checked it was left unsolved ,do u understand the topic well enought to help me

[versed hazel]

@thorn kindle still there bro i think i know what to do

[alpine sable]

Hello. I'm doing trying to solve a system of equations, but my result doesn't really make sense to me. Would someone mind cross checking my work?

[versed hazel]

sorry bro we are tryin to solev smthin in tjis channel

[noble sinew]

The only thing you can do is put stuff on a single fraction and see what cancels and compare

So have you tried that

[noble sinew]

You isolated m correctly from 1st equation. Now plug in the expression you have from m in 2nd equation and solve that equation (will only have 1 variable now)

[alpine sable]

I just picked the first equation. I figured it doesnt matter which you pick?

[noble sinew]

Yes step 1 was correct

Everything after wrong

Isolate m was correct - now do what I said

[alpine sable]

Alright, I will try

I don't feel like this is correct

[noble sinew]

You left out a 1 when subbing

It is equal to 1100 not 100

[alpine sable]

oooops, let me try again

[noble sinew]

Yes

[alpine sable]

There we go. I think this is right

Thanks

So when I solve a variable in the first equation in the system, I always gotta substitute that variable in the second equation?

Like: I guess the thing I tried before was solving for m in the equation (200m+300w=1200), and then I just plugged m in that same equation.

[noble sinew]

Yes isolate a variable in either equation then use the expression you have in the other one and that equation will now have 1 less variable

This also works for 3 equations with 3 variables or even n equations with n variables

[alpine sable]

Right, thanks. Never got the part where you gotta plug it in the second equation. Makes sense. Also kind of makes sense why i ended up with just 'm', when trying to do it with the same equation. (I guess)

[solemn lily]

Can someone help me with this permutations exercise?

I calculated this if need

And σ^(-1)=σ^4

[arctic wren]

Idk how to prove it, but can you create a matrix with letters and symbol's T that multiplies the other one and make the multiplication ?

[solemn lily]

Those are permutations and the product is not matrix product

[arctic wren]

So T is the permutation matrix ?

[solemn lily]

Yes

Or no, it's just a permutation

[little wadi]

oops

[solemn lily]

<@&286206848099549185>

[alpine sable]

Guys

<@&286206848099549185>

<@&286206848099549185>

pls i dont really understand

@pliant bear

@pliant bear

[manic quail]

[crisp grail]

Dude you can ping 15 mins after you send ur question and not twice

[manic quail]

What don't you understand?

[alpine sable]

the question

the whole question

[crisp grail]

a, b, c or d

[solemn lily]

Any solution on my problem?

[crisp grail]

Not that I know

[crisp grail]

Prolly ask ur question again in another channel

[glass lichen]

Or Kai can move channels

since they posted most recently when the channel was being used

[strong smelt]

quick question, can 100^100 be expressed as (10·10)^100, or is it 10·10^99

I think it's the second one

[spring harbor]

10.10^99

[strong smelt]

aight, ty :)

[spring harbor]

Cause when you multiply two same numbers, you add up their exponents

10^1 * 10^99 = 10^(99+1)

[strong smelt]

and 10=10^1

[spring harbor]

yup

[strong smelt]

yeahh

thank you

[gray isle]

its the first one

[teal epoch]

uh-

isn't $10^{200}$?

[ocean seal]

Callaway

[spring harbor]

Ohhhh wait

it's 100^100

I thought 10^100

I even used 10s here

[teal epoch]

$100^{100} \implies (10^2)^{100} \implies 10^{200}$

[ocean seal]

Callaway

[spring harbor]

yeah this @strong smelt ^

[gray isle]

100^100 = (10 * 10)^100
10^200 would also be valid

10*10^99 = 10^100 (which isn't what you wanted)

[golden wharf]

Can someone help me with this question, my answer right now is 7.4% but I’m not too confident because I only learned this stuff yesterday

[sharp sail]

what is 1/(1/0)

0/1 or undefined

[lost cairn]

Snuggles, a toy company's train, is 1000 metres long. It is travelling at a uniform speed, and a 3000m tunnels awaits. Thirty seconds pass from the time the last car has just completely entered the tunnel until the time when the front of the engine emerges from the other end. Determine the speed of the Snuggles, in km/h.

[timid summit]

there's two things to fix: you've got the probability of getting red then purple, but you could also get them in the other order. Also, once you've taken one out, there's only 8 options not 9

[lost cairn]

Please

[timid summit]

undefined.

[timid summit]

draw a digram, and figure out the distance it travels (in km) divided by the time it took (in hours)

[sharp sail]

Well I once had this question like
sin 90 (in degrees) is 1
cos 90 is 0
tan 90 is 1/0 which ik is undefined
But cot 90 then should be 1/(1/0) which is undefined like u said, but it is taken 0 from the perspective cot = cos/sin = 0/1 = 0

[lost cairn]

k ig

[sharp sail]

it is like indirectly taking 1/(1/0) to be 0/1 = 0

[sterile gale]

Done?

How to do this

[lost cairn]

Berta’s teacher, Ms. Rose Harper tells her class that when sixty consecutive odd integers are added together, their sum is 4800 and asks the class to determine the largest of the sixty integers. Help Berta get the answer!

@timid summit

[sterile gale]

Hmm

When mine can get the answer

[sharp sail]

well take every integer to be x x+2, x+4 and so on

[lost cairn]

k

[sharp sail]

or its better that u take first one to be x-30 then x-28, x-26 etc @lost cairn

[timid summit]

cot(x)=1/tan(x) only when tan(x) is defined 🙂

[sharp sail]

So cot 90 is undefined

?

[timid summit]

it's defined, it's 0. It just isn't 1/tan(x). 🙂 Using cot(x)=cos(x)/sin(x) works better.

[sharp sail]

lmao from the view cot = 1/tan its undefined

from cot = cos/sin it is defiend

defined*

xD

[vague coral]

math is weird af

[lofty abyss]

Does anybody know an equation for the function f(x)= x^4 that I'd compressed horizontally by a factor of 1/2, vertically stretched by a factor of 7, reflected in regards x x axis, vertically translated 2 units down and horizontally translated 3 unit right .

I can't think any one of them

[lost cairn]

@sharp sail it says 60 consecutive so shouldnt it be x+x+2...... x+120?

[sharp sail]

yea but aren't x-60, x-58, x-56.. consecutive odd

They are

and it'll be easy to add all those together cuz minus and plus will cancel out

[lost cairn]

but 60 is an even number

[gray isle]

whether something like x-60 is odd or even depends on the value of x

[sharp sail]

bruh, if x is odd and 60 is even it'll give odd

just solve nd dont question me lmao jk

:)

[granite silo]

Someone help me with 3 trigonometric limits?

[sharp sail]

@lost cairn

[granite silo]

Someone help me with 3 trigonometric limits

[late tundra]

a).
cos(1/0) is cos(somehugenumber)
and cos(0)=1
so a= not determinable

[lost cairn]

k thx

[sharp sail]

welcome

[late tundra]

i helped u in this channel

[granite silo]

OOH Thanks sorry

Sorry I hadn't seen it friend

[late tundra]

did u understand

[granite silo]

Well, yes, but if it is an indeterminacy, shouldn't we do more calculation?

[lofty abyss]

<@&286206848099549185> it's already 15 minutes and I still haven't got the answer, need help

[strong smelt]

ohh I see, ty

[alpine sable]

For part (b), how can I plot the corresponding graph?

I would have to integrate, to get v = k/2 t^2, but how would I get that from just looking at the graph of acceleration?

[alpine sable]

You build one.

[lofty abyss]

I'm not sure am I right

[alpine sable]

What?

[lofty abyss]

I said is f(x)= -1/2x^4 (x+7)-3

I haven't submit it yet

[acoustic abyss]

plz help

[sharp sail]

6(4+r)

@acoustic abyss

[alpine sable]

Go through each of the requirements and think if it satisfies each one.

[lofty abyss]

OK

[acoustic abyss]

tysm

[sharp sail]

welcome

[acoustic abyss]

why is there a minus after r?

[sharp sail]

lmao idk maybe a typo

[acoustic abyss]

lol yea

thats what i thought

ty tho

[sharp sail]

Lol ok

[acoustic abyss]

this is (x-8)5 right?

[sinful monolith]

how do i find AD

[acoustic abyss]

anyone

[upper pebble]

yes

assuming said number is x

[acoustic abyss]

yep

soo (x-8)5 ?

[upper pebble]

yes

[candid bolt]

Sorry is this chat free?

[acoustic abyss]

yep

go ahead

[candid bolt]

Pog

[acoustic abyss]

its blurr

quetion no.?

[candid bolt]

I am a bit confused on how to simplify 5b.

Sorry I can take a screen shot if that is better

[acoustic abyss]

yep

[candid bolt]

Ok word BRB then

I can for sure tell that step one is using the distributive property on the left most term. But past that it just becomes a mess of statements

[upper pebble]

area of a triangle = 1/2bh, where b = base, h = height

you are given the area and the height, so you can substitute the information into that formula and solve for the base

you can solve for the length of AD by using the Pythagorean theorem on the left triangle, and then you can subtract the result from the total measure of the base to find the length of DB

[harsh acorn]

Use phytogras+trigonometry area formula

[candid bolt]

Is there like a nested distributive property for logical statements?

[upper pebble]

Pythagoras

[teal epoch]

Probably knowing the area of a triangle and the Pythagoras theorem is enough to solve this problem.

[harsh acorn]

determine ADB line by area of triangle formula, use pythogras to find AD line, and subtract ADB-AD so you can get DB

[alpine sable]

need full process i'm so confused

[harsh acorn]

long division?

[alpine sable]

yes

it can be done in factor theorem too but i keep getting wrong ans so yh

[harsh acorn]

divide it, you will get another polynomial, and let x=5 in this polynomial

you will get the value

[upper pebble]

what are crores

[harsh acorn]

what

[upper pebble]

it says when x = 5 crores

[harsh acorn]

Probably a mistake

I am sure last sentence means "when x equals 5"

[candid bolt]

Would it be cool if I asked a quick question?

I am still confused on that logical expression :/

[acoustic abyss]

heyy is this free?

Five-sixths of the sum of d and 9 plus the product of 7 and b (im really confused)

[acoustic abyss]

i have to write it as a form of expression

5/6 (d+9) + (7+b)

is that correct

no right

[upper pebble]

7+b is not the product of 7 and b

[acoustic abyss]

ohh yeaaa

[upper pebble]

that would be the sum of 7 and b

[acoustic abyss]

yea

so what will it be?

[pseudo summit]

I have a quite dumb question, and idk how to google it, how can I convert like 1,5 milion to an actual milion?

How can I know the equivalence?

[upper pebble]

what's the product of 7 and b?

[acoustic abyss]

7 +b

u cant add it right

[upper pebble]

a product is the result of multiplication

[upper pebble]

i don't know what you mean

[pseudo summit]

me neither, holy moly

[upper pebble]

[pseudo summit]

Im brazilian so my english is bad

[upper pebble]

it's okay

[acoustic abyss]

ohhhhhh

im so dumb ok tysmm

5/6 (d+9) + (7b)

[upper pebble]

no you're smart, and correct

[acoustic abyss]

tysmm

[pseudo summit]

like, 1,5 milion is the same thing that 1.500.000

but 1,5 is like a simplified form

[upper pebble]

1.5 million = 1,500,000 yes

[pseudo summit]

yeah but whats the actual math for doing that conversion?

[upper pebble]

well i suppose one way would be to multiply 1.5 by "million" (1.5 * 1,000,000)

[wet fulcrum]

did you get it?

[alpine sable]

not really
like i can solve in process but i keep getting wrong ans

[wet fulcrum]

what is the right answer?

[alpine sable]

idk 😩✌️

[pseudo summit]

hm

[alpine sable]

it was from random practice set

[wet fulcrum]

breh moment

[upper pebble]

[wet fulcrum]

how do you know that what youre doing is wrong

[alpine sable]

coz ppl said

[wet fulcrum]

sheeeeeeesh

[alpine sable]

that i did wrong in some steps

[wet fulcrum]

ok lemme try gimme a sec

[alpine sable]

alrighty

[acoustic abyss]

(i) 3n + 𝑚2(m – n) when m = -3 and n = 5

[upper pebble]

substitute accordingly and solve

[acoustic abyss]

i did it, is the answer 7?

[acoustic abyss]

?

[upper pebble]

it isn't 7

[wet fulcrum]

@alpine sable is the answer 4675?

[alpine sable]

it'll be 4525

but idk process

[wet fulcrum]

im getting 4725 for some god foraken reason

[alpine sable]

;-;

[wet fulcrum]

what equation did you get?

[alpine sable]

idk...i asked my teach and he said the ans 4525

[wet fulcrum]

ahh

[alpine sable]

can u send that process of 4725? i might as well see if u don't mind @wet fulcrum

I have a question.
I can't solve the equation. Can someone help me, please? 🙂

1.5^(x) - 1.25^(x) = 1

Please ping me ^^

lemme give it a try

[sleek elbow]

1.5^(x) - 1.25^(x) = 1 | sqrt()
1.5 - 1.25 = 1

Am I allowed to do this? Or can that not be done?

[gray isle]

hell no

[sleek elbow]

ok 😄

would feel good tho

[alpine sable]

xD

Me too

[sleek elbow]

nice pfp @alpine sable :))

[alpine sable]

i saw tesla

thanks xD

x should equal 2.488

But i dont know how to go on

:c

[alpine sable]

x≈2.487...
if I'm not wrong the question is 1.5^x - 1.25^x=1 right?

yes

But how?

by graph

[river hearth]

Im stuck on this on my homework

[alpine sable]

My calculator says me also 2.488, but i want to calculate it

so calculation steps

[wet fulcrum]

sure

wait lemme crab my phone

[upper pebble]

🦀

[alpine sable]

look at the degree and sign of the first coefficient

[alpine sable]

oh well after u construct the graph you'll see that the solution of x value of the point of intersection

[alpine sable]

thx

yeah sure but i want to do it with calculating steps

mhmm

and not graphically

Here I have stopped

oh

[wet fulcrum]

@alpine sable

the addition at the end is wrong i did -50 at the end instead of +50

[alpine sable]

ow

[wet fulcrum]

oh wait not that i look at it its a shit angle

[upper pebble]

i was thinking there could be a way to do 1.5^x - 1.25^x = 1 using logarithms but idk

[gray isle]

1.5^(x) - 1.25^(x) = 1
doesn't seem to be a nice way to solve that

[alpine sable]

seems correct to me
gotta ask my teach if he made a mistake or smtg

[alpine sable]

idk

[wet fulcrum]

ay okay

[alpine sable]

But i must :/

[gray isle]

do you have the exact instuctions given?

[alpine sable]

the instructions are to solve it step by step

[gray isle]

literally "solve it step by step" nothing else?

[alpine sable]

no

[gray isle]

nothing about approximations? graphing?

[alpine sable]

I mustn't do it graphically

No, just step by step

Until x = ...

[gray isle]

do you have a pic of the problem?

as written

because i suspect you're omitting something

[alpine sable]

no

At school i was only given this equation

[wet fulcrum]

x comes around 2.5 not sure how you would do that without a graph

[gray isle]

are you sure you copied it down correctly?

what class is this part of?

[alpine sable]

Yes

13. class, Bavaria

[gray isle]

what topic of math are you doing?

[alpine sable]

revision

[gray isle]

be less vague

basic algebra? calculus?

[wet fulcrum]

revision of WHAT

[keen sundial]

algebra, logs etc etc

[alpine sable]

logs

potencies

and so on

[wet fulcrum]

are you allowed calculators?

[alpine sable]

Yes sure. But we should calculate step by step

We can use it to calculate only

Not to solve the whole equation

[wet fulcrum]

ahh

[gray isle]

whelp there's definitely something wrong somewhere

even wolfram resorts to graphing

[alpine sable]

idk this are the instructions

[wet fulcrum]

yea

[wet fulcrum]

these*

[alpine sable]

yeah sry

[wet fulcrum]

ntg to be sorry about

[keen sundial]

wolfram doesnt give me anything when i enter it

[wet fulcrum]

now watch people call me grammar nazi

[alpine sable]

?

[keen sundial]

grammar nazi!

[wet fulcrum]

seeeeee

[keen sundial]

anyways i think something's up with dis equation

[wet fulcrum]

• thought

[keen sundial]

no

[alpine sable]

@wet fulcrum omg that's the correct ans
thx!

[proud sentinel]

Can we write big-O(n^(n+3)) as big-O(n^n) only?

Does +3 matter?

[wet fulcrum]

🙂

ew

better

[silver idol]

I don’t know how to come up with a function for this

If you have .05cents you multiply it by 1.2 every day and you do it for 20 days how much will you have.

wait is it just

.05*1.2^days

I think it is

[upper pebble]

i think so

[fallow geyser]

could somebody walk me through this? the videos aren't helping much..

[jagged trout]

first of all, make it so that you only have the x or y on one side and the rest on the other side

[teal epoch]

Ah, the substitution method.

[upper pebble]

but what about the elimination method

[rapid pagoda]

both can be used