help-42

[wind bane]

im just trying to understand the derivative

[rigid scaffold]

theta/t is not angular velocity

theta is the angular displacement

t is time

since linear velocity is rate of change of displacement with respect to time

does it make sense that angular velocity is rate of change of angular displacement (theta) with respect to time

[wind bane]

...

isnt theta/t angular velocity

[rigid scaffold]

change in angle means d theta

since d means small change

very small change

so its like this

[wind bane]

wait. so d(theta)/dt is the instantaneous angular velocity.

right?

[rigid scaffold]

in a way yes

[wind bane]

in a way?

[rigid scaffold]

d theta/dt is used when angular velocity is variable

but if its constant u can use theta/t

its like suvat and dv/dt

[wind bane]

yeha

this makes sense

so lemme just understand this..

so d(theta)/dt is the instantaneous angular velocity meaning that. it gives you the change in angular velocity at a specific moment in time. agree?

so it acts like a variable kinda

[rigid scaffold]

yes

like finding a tangent to f(x) at a point

where f(x) is a curve

[wind bane]

but theta/t is a constant

[rigid scaffold]

we can treat it like a straight line, hence, we can use the simple division theta/t to find the gradient

[wind bane]

then what is linear velocity

[swift laurel]

if dθ/dt is constant then θ/t is constant

[rigid scaffold]

essentially theres no small change, the ds just cancel out

[swift laurel]

linear velocity is the velocity you are used to

ds/dt

[wind bane]

okay thanks a lot guys

.close

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[tidal vale]

help

[tidal vale]

pls answer this then show me what to put on my calculator

[jagged agate]

What have you tried

[velvet osprey]

!noans

[calm coral]

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

[jagged agate]

Hi ann

[velvet osprey]

first and foremost you should make a diagram here

[jagged agate]

Have you tried drawing a diagram?

[velvet osprey]

sniped lol

[tidal vale]

one sec

[jagged agate]

U cooked

[velvet osprey]

i might need to go to sleep any minute now tho

[jagged agate]

I think i got this

😂 cookin w trigo

looks simple.

[tidal vale]

its annoying

maybe for u

[jagged agate]

Have you drawn the diag?

[tidal vale]

tan(8.3
∘
)=
66.5
h
​
⇒h=66.5×tan(8.3
∘
)

hold on that didnt help and no

65x tan83

[jagged agate]

Well, i’m pretty certain you would need a diagram but assuming you don’t really want to draw a disgram

What is the distance travelled by the plane?

[tidal vale]

i need to know how to do it on my calculator

133 miles per hour

[jagged agate]

It travels for 30 mins before being directly over the landmark.

So you need to know the distance, no?

[tidal vale]

no the hight

[jagged agate]

Yes, you’re looking for the height.

[tidal vale]

distance of the hight idk

[jagged agate]

You’re given angle of depression

You could use one of the 3 basic trigo sin, cos, tan.

[tidal vale]

thats what im supposed to use

[jagged agate]

Which you already did here.

[jagged agate]

^

[tidal vale]

i keep getting it wrong

[jagged agate]

But you don’t have the opposite, adjacent or hypotenuse.

So i’d suggest drawing a diagram to help you find one of the three

And with any one of it, you could use the angle of depression to find the height.

[tidal vale]

51249feet?

[jagged agate]

Is this the distance?

[tidal vale]

the hight yes

is it right ?

[jagged agate]

Its close to my solution

Did you use the correct conversion?

[tidal vale]

1 mile=5280 feet

[jagged agate]

Whats your height in miles

[tidal vale]

9.707

[jagged agate]

interesting

You could try using 9.7 miles

But yes your solution is right

$tan(8.3\degrees) = \frac{Height}{66.5}$

[potent lotus]

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

[tidal vale]

?

ohh

try that

[jagged agate]

As long as you got this step, you’re on the right track.

And i saw your previous step so you’re fine

[jagged agate]

You should get somewhere between

[tidal vale]

yeah i did that

[jagged agate]

,calc 9.707*5280

[potent lotus]

Result:

51252.96

[jagged agate]

Or

,calc 9.7 * 5280

[potent lotus]

Result:

51216

[jagged agate]

It’s really the rounding

[tidal vale]

my teacher fucked me when it came to that at the beginning of the year

since it doesnt say to round she says dont round carry your answers on the calculator

[jagged agate]

As a STEM student! I only use 3 s.f or 1 dp!

[tidal vale]

so which answer has no rounding the top one ?

[jagged agate]

The bottom…..

Did it work?

[tidal vale]

yes

[jagged agate]

Okay

[tidal vale]

life savor over here

[jagged agate]

Nah

You did everything rigjt from the beginning

It’s just rounding error.

[tidal vale]

i have a iep so sometimes this online shit screws me up

and yeah my teacher screwed me with that at the begging

i got more questions

[jagged agate]

😂

[tidal vale]

yep

[jagged agate]

Working?

[tidal vale]

wdym

[jagged agate]

Show me ur steps

[tidal vale]

tan(42
∘
)=
427
h
1
​

​
⇒h
1
​
=427×tan(42
∘
)≈427×0.9004=384.47 ft

top of tower

tan(24
∘
)=
427
h
2
​

​
⇒h
2
​
=427×tan(24
∘
)≈427×0.4452=190.10 ft

bottom of tower

then add

am i wrong

sorry i type on word then copy paste

[jagged agate]

😭

I genuinely cannot read this

[tidal vale]

hang on

tan(42∘)=427h1⇒h1=427×tan(42∘)≈427×0.9004=384.47 ft

that better

tan(24∘)=427h2⇒h2=427×tan(24∘)≈427×0.4452=190.10 ft

first top then bottom

[edgy lava]

tan(42) would be h1/427 not the other way around

[tidal vale]

rewrite my eqaution to what it shoud be

[jagged agate]

What she said.

Remember, Tan = Opp/Adj

[edgy lava]

????

do it urself lmao

[tidal vale]

sorry i just relized my copy paste went wrong i did do it that way

h1 divided by 427

and i was just tryna see where its wrong

574.57 is what i got for h

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[wanton grove]

I’m trying to show this, but I’m not sure how

I was able to show that the volume of the solid bounded above by sphere and below by cone defined on board

[calm coral]

@wanton grove Has your question been resolved?

[remote mural]

Ohno my question before this wasn't resolved but I went to sleep

Wait what's going on tho I wanna try

[remote mural]

Wait show what let me comprehend this

[remote mural]

Sorry I don't think I have the knowledge to understand the usage of phi in your work TAT

[wanton grove]

Most of my confusion is actually coming from that

[calm coral]

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[analog plinth]

determine whether f(x)=|x-5| is differentiable at x=-5. if it is, find the derivative, if it is not, prove it.

[analog plinth]

how would I approach this?

[mossy geode]

its not

modulus function is non diff at zero

nvm

its is

it is no diff at 5

[winter elbow]

The result isn’t zero

[civic dirge]

I see what you did haha

[mossy geode]

it is diff at -5

u can use derivative definition to check or draw the graph

[analog plinth]

gpt says it's not differnetiable

[mossy geode]

gpt is not good at math

it hallucinates sometimes

[civic dirge]

Nice, another example of GPT failing questions

[mossy geode]

i was solving a comvinatorics question one day and it said as C occurs ahead of A

[analog plinth]

can someone please give me the full layout of how to solve like the steps?

[mossy geode]

😔

[analog plinth]

like gpt does

[mossy geode]

check continuity and then differentiavility

[winter elbow]

Afraid not

[mossy geode]

use lhl rhl= fx for cont and for diff use rhd =lhd check

if its non cont its non diff not vice versa

[analog plinth]

okay

and if continuous and rhd=lhd then its differnetiable

[mossy geode]

then its diff

[analog plinth]

okay

and what does the question mean "prove it"

[mossy geode]

u find it and see it justifies the claim

[analog plinth]

for this example it is dfiferntialble right?

[mossy geode]

what do you think

[analog plinth]

is that not a corner

[mossy geode]

thats at 5

-5 is a straight line

its diff

[analog plinth]

wouldnt derifgviative be a vertical line

I thought straihgt vertical line was no deriviative?

[mossy geode]

it isnt vertical

is it

all polynomials are diff in their domain

straight line is a polynomial of deg 1

[analog plinth]

can you put it into laymans terms why it's differentialble

like one coherent sentence

im kinda slow sorry

[mossy geode]

u need to revisit

this topic

[analog plinth]

alright

what topics exactly?

[mossy geode]

i laid it out in multiple simple points

differentiavility continuity limits functions

[analog plinth]

okay bet

ima just use what u said and learn it more

thanks for the help

.close

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[cunning reef]

A "magical birthday" is a birthday in which our age is equal to the sum of the digits in which we were born. For example, people born in 1899 will have a magical birthday in 1926. Similarly, people born in 1908 will have a magical birthday in 1926 as well. Find the first year after 1926 (the first year) that there exists people born on different years that will have a magical birthday in that year.

[cunning reef]

so heres what im thinking

a person born in year $x$ will have a magical birthday in year $y$ if $\$ $x - y = \sigma(y)$

[potent lotus]

Copter

[cunning reef]

wait what denotes sum of digits again..

[glass heart]

sigma is fine

[cunning reef]

oh okay

[glass heart]

doesnt matter

[cunning reef]

then there's two y values where this is true

how do i go about figuring that out?

[glass heart]

I dont think there is something better than just straight up brute force

the sum of digits function is not nice mathematically speaking

[cunning reef]

awh hell nah💔

[glass heart]

for each year y compute y+sigma(y)

computing consecutive sums of digits is easy

so this is not too much work

generally you will always add 2 in each step, one from increasing y and one from increasing sigma(y)

[cunning reef]

1935 i think?

[glass heart]

dunno I wont do the calcs

[cunning reef]

lmao

thanks anyways

.close

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[barren token]

how

[native fox]

^real

[barren token]

i was able to find the independent of (2x^2-3/x)^6 which was like -4860 but idk how to get the constant in the first function: (x+1/x)^5

[velvet osprey]

you won't actually want to do that here

the constant terms from each bracket will not help you much

bc you would have to also think about how you could get x^n from one bracket times x^-n from the other...

which is difficult

[barren token]

mhm

[velvet osprey]

do this instead

[calm coral]

@barren token Has your question been resolved?

[barren token]

sorry ive been trying to expand the first function and the second function and mulitply them together to get x^11 ? am i on the right track ?

@velvet osprey

[velvet osprey]

yes

there are only two ways to get x^11

either x^2 * x^9 or x^8 * x^3

[barren token]

I SOLVED IT AFT ER SO LONG

i got -36180

.close

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[obsidian shale]

help, how do I solve this if neither the frequency of conversion (m) or the nominal rate (i^m) of the other one is not given? tried using the simple interest formula P = F(1 + rt) but got 1.004%. The answer key in the book says it should be 2.015% but how do I come up with that 😭😭

[obsidian shale]

<@&286206848099549185>

[calm coral]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[obsidian shale]

okay, simple and compound interest formula came up w the same ans as well

[polar bison]

Don't ping helpers

Wait for 15 minutes then

[obsidian shale]

yeah sorry

[unkempt drift]

,calc (1 + 0.01/4)^4

[potent lotus]

Result:

1.0100375625391

[unkempt drift]

,calc (1 + 0.01)^4

[potent lotus]

Result:

1.04060401

[unkempt drift]

yep, the book is wrong

should be 1.0038% as you said

[obsidian shale]

ohh really 😮

okay thank you

[swift dragon]

<@&268886789983436800>

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[sturdy edge]

hello

[sturdy edge]

may anyone help me to figure out this question ?

I am trying to apply NAND-AND but I cant get them both together

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@sturdy edge Has your question been resolved?

[calm coral]

@sturdy edge Has your question been resolved?

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@sturdy edge Has your question been resolved?

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[calm coral]

Please don't occupy multiple help channels.

[unreal rose]

how did this happen?

[spare beacon]

I don't want to do any calculation to verify it, but I expect it's because the MGF series starts at x = 1 and its a consequence of reindexing.

[unreal rose]

what does reindexing mean

[spare beacon]

Like changing the sum from x = 1 to infinity to x = 0 to infinity

[unreal rose]

when x=0 this thing = 2 so i still dont understand

[spare beacon]

What I am saying is that they are using a geometric series to evaluate the infinite sum and you cannot just replace that without accounting for the missing first term.

And that I assume that is where it comes from

[unreal rose]

oh geometric sum

[spare beacon]

Just add and subtract the missing term of the geometric series, absorb one into the series, evaluate the geometric series and simplify

[unreal rose]

i didnt even see that im not in the right mind for this

[spare beacon]

Then see if that matches or not

[unreal rose]

alr thx

.close

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[short salmon]

I'm a little curious

did you ghost ping me here?

I got a ping and it was deleted when I checked this channel

[polar bison]

The harder the problem is the more you need to wait

[short salmon]

me when I asked abt an annoying probability theory question :(

[polar bison]

So wait for a postgraduate

[short salmon]

uhhh, this is definitely not necessary

unless i am going crazy, i think this question would fall more into the pre-university math category

[polar bison]

..

[short salmon]

the wording is just a little confusing

which is why I think people aren't answering

by "value of the income stream," do they mean how much you'll be making in t years or how much money you'll have in total?

also, does "interest" here just mean gaining interest on the money you have stored away?

I really hate that they can't ask their question more clearly 😅 i haven't done word problems in so long since all my college classes never really touch on applied math

what's the said formula you're meant to use?

I have one in mind but.... if you're taught something in a certain way, it's prob best to do it that way to please your professor

can you send it here?

oh, it's an integral

oh this one is going to be annoying to integrate because e^negative something

i'd just wolfram alpha it if i were u lol

-_-

i mean, i could i guess but

you should probably do it yourself for pedagogical reasons

oh yeah, they probably would not approve of me plugging the integral into wolfram for you

well ok, let's uh, plug in the terms and then we can stick it into wolfram

so, for part a, T=4 and r=0.0371, right?

because, well, it's sort of good to understand this formula more intuitively

which means looking at what e represents

which is uh... for you to read on your own. I refer you to https://en.wikipedia.org/wiki/E_(mathematical_constant)#Definitions

well, sure, but it has a really important interpretation when it comes to computing interest with integrals

because it's a limit of an expression useful for such tasks

and also, it integrates and differentiates nicely

ok ummm

I would like to ask you to think closely about why e is useful here, since I think it'll help u better understand the problem

look at the limit definition and see what happens if you rewrite it with $\frac 1n=r$

[potent lotus]

00100000

[short salmon]

wait wait

I'm trying to help you understand the math here a bit more

not just give the answer

but it will benefit you in the long run to properly understand the math...

well, alright, if you say so

uh, well, sure I guess, but like...

ok fine. I suppose I will wolfram it for you :P

no, because I didn't compute the integral

I had integrals in mind for both

I'm getting a different number for future value

no

however, I'm plugging in the exact same integrals as you just wrote out

so it might be a calculator issue on your end

or a mistake on my end

uhhhhhh

sure

FV: 5517.53
PV: 1248.87

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[short salmon]

were those values correct?

oh. well, I'm glad to help

hopefully, you can figure out what was causing you to get incorrect values for your integrals

I'll be happy to answer your questions if you have spare time

however, I don't really have the time to directly teach you, unfortunately

seeing as you're an undergraduate, I have some great books I can recommend you, however

yeah. I don't really mind

it's just that if I'm particularly busy, I may not be able to respond

it's my spring break right now tho

of course.

well, which books to recommend really depends on what you're interested in learning i guess.

hmmm... the unfortunate thing about calculus is that it's mostly taught through heuristics, so it's important to have a strong "intuitive" sense of the principles behind each concept. thankfully, it's definitely something buildable and not innate

I'd recommend you read AOPS calculus. It's definitely my favorite single-variable calculus book

full disclosure: i learned single variable calc mostly from high school and not through that book, but I did skim a good chunk afterwards

💀 not the tea and coffee

on a related note, I drank way too much coffee last afternoon, and couldn't sleep well at all as a result

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[exotic bane]

What is the least multiple of 2016 whose sum of digits is 2016 ?

[exotic bane]

somebody help me pls

[leaden thunder]

did you try finding a pattern for sum of digits for multiples of 2016

2 + 1 + 6 = 9

4 + 3 + 2 = 9

[potent smelt]

999...999, with 224 digits is the smallest number whose sum is 2016, this is not divisible by 2016 though.

[exotic bane]

yeah ive proved the number we're looking for has exactly 225 dfigits

[potent smelt]

So I would approach this with divisibility rules

We know that 2016 = 32 * 7 * 9

[exotic bane]

yes

so the last 5 digits of our numner must be divisible by 32

[potent smelt]

The 9 divisibility we can take care of by just ensuring that our sum is 2016

[exotic bane]

yup

[potent smelt]

The 7 one is a little trickier, and I'm not sure of a good way to approach it tbqh, as the method is remove the last digit from the number, double it, and subtract it from the leftover part

We also want to make the leading digit as small as possible

That vs the 32 divisibility seem to be in tension

[exotic bane]

but how would that be feasible for 225 digits

[potent smelt]

It's not. I'm not actually entirely sure how to do this by hand

This feels like an Olympiad question, so I am assuming no calculators

[exotic bane]

yup

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[potent garnet]

Bro

That's not a question.

So you instead claimed it with a non-question so I couldn't ask. Quite rude.

[plush pulsar]

Hi

[potent garnet]

Absolute state of the internet.

[plush pulsar]

I’ll stop trolling, close it if you’re not asking a maths related question

What is it?

[elder pawn]

-.-

[tender coral]

11

[elder pawn]

dont ask if we can help

[golden lily]

Dude, people are probably gonna be able to help, so just type it out already

[elder pawn]

just ask ur q

[golden lily]

Do you understand how to multiply exponents with the same base and how negative powers work

Ok, I gotchu

Basically imagine I have 2^2 x 2^3

This is just 2x2x2x2x2

Or 2^5

We can generalize this though

If I have a^b times a^c it equals a^(b+c)

Does that make sense?

Ok, so now negative exponents

Imagine we have 2^2, what operation can we do to go back to 2^1?

Like doing fractional exponents in general?

Not quite

Sooooooo

Imagine I take 2^3 how do I go back to 2^2?

This will help, trust me

Think simpler

You could multiply by 2^-1

Or you could just divide by 2

They're the same

So 2^-1 must equal 1/2

2^-2 equals 1/(2^2)

And so on and so forth

Ypu can also reverse it tho

1/(2^-a) equals 2^a

These are the same principles behind every problem

Try again by combining exponents

[calm coral]

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[dreamy lance]

We can see the messages you delete in the logs. It's sort of shitty to spam ping users and delete your messages. Don't do that.

[calm coral]

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[glacial nacelle]

The equation
[\frac{ax^2 - 24x + b}{x - 1} = x^2 + x]holds for exactly two real values of $x,$ and their sum is $12$. Find $a - b.$

[potent lotus]

Dork9399

[glacial nacelle]

I cross-mulitplied and simplified, and got this

$x^3 - ax^2 + 23x - b = 0, x \neq 1$

[potent lotus]

Dork9399

[glacial nacelle]

Since the equation only holds for 2 real values, we can assume that x^3 - ax^2 + 23x - b has a root at x=1

which implies that 24 - a - b = 0

also since the other two roots add to 12, we can assume that a = 13, by vieta's formulae

that implies that b = 11

But, if we plug the numbers in and factor

$x^3 - 13x^2 + 23x - 11 = (x-1)^2(x-11)$

[potent lotus]

Dork9399

[bold bear]

Why can you assume that?

[glacial nacelle]

which means it only satisfies for one real x

what else could the roots be?

oh wait

[bold bear]

Well if two of them are the same

[glacial nacelle]

oops

bruh

so uh

assume we have (x-r)(x-r)(x-(12-r))

then a = 12+r

23 = r^2 + 2(12-r)r

23 = -r^2 + 24r

so r = -1

and 12-r = 13

a = 11, b = 13

uh

so its

$x^3 - 11x^2 + 23x - 13$

[potent lotus]

Dork9399

[glacial nacelle]

,w factor x^3 - 11x^2 + 23x - 13

[potent lotus]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by dork9399

[glacial nacelle]

oh

,w expand (x+1)(x+1)(x-13)

[potent lotus]

Results provided by WolframAlpha

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

Requested by dork9399

[glacial nacelle]

.clso

.close

[calm coral]

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[calm coral]

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[glacial nacelle]

Find the solutions to
[\frac{x(x^2 - 56)}{4 - 7x} - \frac{21x + 22}{x^3 + 2} = 4.]Enter all the solutions, separated by commas.

[potent lotus]

Dork9399

[calm coral]

@glacial nacelle Has your question been resolved?

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[chrome plume]

I have to calculate the area that is made by two function

[chrome plume]

x=y^2-4 and x=y-2

here is the plot for them

i will explain now

when i rotate

this what i get

so i want to calulate the red area - blue area right?

then why when i integrate this

i get the negative number of the area

-1 and 2 is where the function are even

why?

isn't the red area the integral of y^2-4

okey then

this

right so i made the mistake on plot

but

why is it negative though

i want the blue

okey but what do you mean

ohhh

right so the area is negative because of that

so i just multipy this by -1

or is there another method

i mean the integral is negative

but i conclude it is supposed to be area and multiply right?

okey th

thx now i see

i didn't notice the y axis

.close

[calm coral]

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[calm coral]

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[gusty lance]

how do i do this with u sub

or regularly integrate it

[glad parrot]

Multiply top and bot by e^x before

And then u = exp will be a cool way

And for b) try to write it as exp(ln(7^x)) and then simplify

[tulip spear]

$\int a^xdx=\frac{a^x}{\ln(a)}+C$

[potent lotus]

ooaa

[gusty lance]

i dont want to use the fomrula tho

[tulip spear]

Ok

Then just do $\int a^xdx=\int e^{x\ln(a)}dx$

[potent lotus]

ooaa

[tulip spear]

u=xln(a)

[gusty lance]

what

why not js

ln u = xln7

can you do it like this

with logairthmic diff

[tulip spear]

this is integration

[gusty lance]

ya but for u sub method

cant we say u = 7^x

lnu = xln7

[tulip spear]

ig?

[gusty lance]

ok so then du/udx = ln7 + x/7

[tulip spear]

?

[gusty lance]

$\frac{1}{u} \cdot\frac{du}{dx} = ln7 + \frac{x}{7}$

[potent lotus]

gamer75431

[gusty lance]

is this right

[tulip spear]

no

[gusty lance]

whats wrong with ti

[tulip spear]

$\frac1u\cdot\frac{du}{dx}=\ln(7)$

[potent lotus]

ooaa

[gusty lance]

isn't it product rule

xln7

f'xgx + fxg'x

[tulip spear]

ln(7) is a constant

[gusty lance]

oh true

yes

but now i am getting du/dx = uln7

$\frac{du}{ln7} = 7^x dx$

[potent lotus]

gamer75431

[gusty lance]

idk if this right tho

if its right then i have no clue where to go from here

cuz isn't that the whole integrand

theres no U that were integrating

[calm coral]

@gusty lance Has your question been resolved?

[gusty lance]

.close

[calm coral]

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[calm coral]

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[crimson swift]

how can i know that myself?

[velvet osprey]

black magic tbh

[royal ingot]

using delta

but too much calculations

[velvet osprey]

or rawdog the 5 digit number that the discriminant probably is

[crimson swift]

?

[crimson swift]

how much is too much?

[royal ingot]

depends in how much your brain can support

[pure kayak]

if you can use just a standard calculator, then its not much effort
if you want to do it solely by mind and body, you might get a tad sad

[crimson swift]

how can i use a calculator to find that?

mode 53?

[pure kayak]

quad formula

calc will deal with the big numbers

[royal ingot]

125 is 5^3
404 = 101* 4
308 = 154 * 2 = 77 * 4

[crimson swift]

?

[royal ingot]

I guess keep factoring until it becomes easier to calculate

there is a mistake there

[crimson swift]

i can use a calculator

[crimson swift]

i just dont know how to get to that with it

[royal ingot]

oh ok

what about the discriminant ?

[crimson swift]

its nice

but again, i just dont know how to get to that with it

mode 53 on the discriminant ?

[pure kayak]

(we dont know what mode 53 is)

[royal ingot]

honestly I don't use a calculator to solve second degree equations

[crimson swift]

idk whats the quad formula

[royal ingot]

you can write the discriminat in your paper calculate it and then write the solution for x and calculate it

[pure kayak]

$\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

[potent lotus]

AℤØ

[pure kayak]

that

[crimson swift]

ok so mode 53 solves that in my calc, the answers to that are 2, 154\125,

[pure kayak]

so (x-2)(x-154/125) has the same roots as your quadratic

you multiply by 125 since thats your x^2 coefficient
(x-2)(125x-154) is your factored form

[crimson swift]

thanks

.close

[calm coral]

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[calm coral]

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[potent lotus]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[frank jungle]

you need to enclose your latex in $$

[potent lotus]

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

[frank jungle]

just one dollar sign

$\LaTeX$

[potent lotus]

dyxn

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

[calm coral]

@split quest Has your question been resolved?

[calm coral]

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@split quest Has your question been resolved?

[royal ingot]

whats the problem ?

[calm coral]

@split quest Has your question been resolved?

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@split quest Has your question been resolved?

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[wicked arch]

need help woth question. “A tire with a diameter of 38cm rotates 10 times in 5 seconds.” a) What is the angle that the tire rotates through, in radians from 0s to 5s?

[bold bear]

What have you tried?

[wicked arch]

i have no idea where to start

please help😭😭 what does this question even mean? its about angular velocity

[bold bear]

Part a isn't about angular velocity, it's just the raw angle

Okay here's an easier question

Say the tire rotates once

[wicked arch]

yup

[bold bear]

How many radians is that?

[wicked arch]

2pi

[bold bear]

Great

[wicked arch]

because thats 360!! heck yeah

[bold bear]

So how about if the tire rotates 5 times?

[wicked arch]

oh 360 x 5

[bold bear]

Sorry 10 times I misread the question

[wicked arch]

so 1800

[bold bear]

But yeah

Except that's degrees

Not radians

[wicked arch]

wait so it should be 3600

in degrees

[bold bear]

Yeah

[wicked arch]

and into radians its like that times pi over 180

[bold bear]

Eventually you just learn to think in radians but for now it's okay to convert everything to degrees, if you find that easier

Yeah exactly

Which is?

[wicked arch]

so 20 pi?

[bold bear]

Yep

[wicked arch]

so 20 pi is the answer?

[bold bear]

Yeah

2 pi is one rotation

[wicked arch]

ohhh

[bold bear]

so 20 pi is 10 rotatins

[wicked arch]

so the angle the tire rotates through is 20 pi

woah what the heck thats actually easy

[bold bear]

I reckon you just panicked bc you saw radians

[wicked arch]

thank you!!🙏

[bold bear]

It's not too bad

[wicked arch]

yeah😭💔

tysm!! good bye depression😭

[bold bear]

np

[wicked arch]

also how to close this chat

is it .close

.close

[calm coral]

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[grizzled coral]

what is meant by linear factor

as in like

imaginary and real

so a complex root

[civic dirge]

The FToA is often stated as "has at least one root" yes

In your book, they're just saying (x - a) can be factored out of any polynomial

Which is really the same thing

[grizzled coral]

so its justt asying that a polynomial of degree "n" can be simplified into multiple factors?

😭

[civic dirge]

They're just saying (x - a) can be factored out of any polynomial

(x - a) is linear, and since it can be factored out, we call it a factor

It's a linear factor

[grizzled coral]

ahh okay

that makes sense

[velvet halo]

or (z - a) in accordance with that screenshot

where a is a complex number

[grizzled coral]

ok ty

.close

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[bright wraith]

how is the limit of this 0

[bright wraith]

so what i thought

i thought u plug in 0 for x

so that would be 1/ 1+(1/0)

but 1/0 is undefined

[twin raptor]

you can't necessarily plug in 0

[drifting seal]

what does 1/x approach as x -> 0^+

[twin raptor]

think about what happens as x gets really small but is >0

[blazing coyote]

Hint: Write this as $\lim_{x \to 0^+} \frac{x}{1+x}$

[potent lotus]

What a wonderful world !

[civic dirge]

I'd try plugging in things like 0.01, 0.0001, 0.000001... and seeing what happens

[bright wraith]

o

wait

what does approaching x->0+

mean

like its approaches 0 as y is positive or sum

[bright wraith]

I want to think of it graphically

[bright wraith]

After you plug 0 into this u get 0

[strange spindle]

X/(1+x) when u put x=0 it becomes 0/1=0

[bright wraith]

k but why is it when u just plug in 0 for the orignal equation its undefined

[wet urchin]

cause 1/0 isnt defined

[bright wraith]

exactly?

[wet urchin]

what

[bright wraith]

wont that mean the limit would be undefined?

[wet urchin]

approaching 0

and being 0

are 2 different things

[bright wraith]

Ok

ok i have a equation

if the question asked

[wet urchin]

hence why you have to take the limit

[bright wraith]

lim x->0 without the positive, what would it be

[wet urchin]

uh

[drifting seal]

how’d you do on your physics final

[bright wraith]

bro are we real

there is a general for a reason

[wet urchin]

like a 70% got a C in the class but gotta retake anyway cause i need a C+ for a prereq of next class

so basically it was pointless

[drifting seal]

tough

[wet urchin]

fr

[wet urchin]

does like

anything even change

am i missing smth

[bright wraith]

wait

im so confused

[wet urchin]

about?

[bright wraith]

wait so as x goes to 0

right

it goes to infinity

and to negative infiinity

[wet urchin]

no

approaches 0

[bright wraith]

wait this shi aint right

[wet urchin]

what are you specifically not understanding

like where do you get confused

[bright wraith]

the whole thing

like what is the limit represent

how did they get 0

where it clearly intersects on the graph

at 0,0

[wet urchin]

do you know what a limit does?

[bright wraith]

huh

not rly

[wet urchin]

if your like not really sure how limits work at all id watch a quick youtubve videe explaining them

would help u wayy more trust me

just search calc 1 limits tutorial or smth on youtube

https://www.youtube.com/watch?v=YNstP0ESndU

this probably is a good one

you can even watch in like 1.5x speed cause he lokey talks kinda slow

[calm coral]

@bright wraith Has your question been resolved?

[calm coral]

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[wild marten]

Hi, I wanted to prove that every every subgroup of a abilian group is normal, and I kinda did it in this form: (H is the subgroup of G)

assume $g \in G$ We need to show $gHg^{-1}=H$. $\forall h \in H$ we can show that $ghg^{-1}=gg^{-1}h=eh=h$ thus you would get back the entire group and they are normal

[limber nacelle]

so what have you tried

[wild marten]

sorry i pressed enter too eraly

my book does it completely differently so

I was curious

would by proof still be correct

[potent lotus]

BOSS

[twin raptor]

yes it's correct

[wild marten]

ok in that case

any clue what was done here?

[twin raptor]

it's the same thing

just written differently

[wild marten]

why is he using gh=hg

i mean its true but whats the reason for it

[twin raptor]

he is starting with gh = hg and right-multiplying both sides by g^{-1}

[elder pawn]

these are equivalent

[wild marten]

Ok wait so when proving that a subset is normal

we only need to prove one of them right

as they mean the same thing

[elder pawn]

yes

[wild marten]

ok i was curious why he wrote both

just making sure we only needed to prove/show one

[twin raptor]

he is using gh = hg to prove ghg^-1 = h

he isn't proving both

[wild marten]

i mean why

isnt gh = hg enough

[twin raptor]

yeah sure

[wild marten]

whats the latex command for iff btw

[twin raptor]

$\iff$

[potent lotus]

flying_fly

[wild marten]

ah cool

ok so

[wild marten]

why did he do this

because if $gHg{-1} = H \iff gH=Hg$ then we only need to show either or right

[potent lotus]

BOSS

[elder pawn]

i might be a dumb reader

[twin raptor]

yeah

[elder pawn]

but ill read gh=hg and say thats clear bc abelian, then i understand the proof

[twin raptor]

he just chose to show gHg^-1 = H

[wild marten]

hmm

he says since tho

oh

[elder pawn]

do u get what i mean

[wild marten]

gh=hg is the def of commutative

ah

[twin raptor]

gh = hg because the group is abelian

[wild marten]

yeah

[twin raptor]

that is what he is using

[wild marten]

yeah

not to show it is normal

alr

he could just stop there tho

just making sure

[twin raptor]

yeah he could

[elder pawn]

i think he did this to make it easier for a dumber reader to understand 🙂

[wild marten]

it would just be shitty if he stopped there because it doesnt really form the connection between abelian to normal

but yeah

@twin raptor @elder pawn if ur still here

should this not be $r^{i}H=Hr^{i}$

[potent lotus]

BOSS

[twin raptor]

i think it is saying r^iH and Hr^i are both equal to H

[wild marten]

wait

why

oh

oh

OHHH

its because the last one

would go

if i is 1

then i+n-1 wiuld go to e

its jsut shifting the rotations by a factor of i

thats so cool

unless im wrong

also

i never understood

why the reflections are written as s

and then a factor of r

[twin raptor]

sorry what do you mean by this

[wild marten]

like the way he discribes s

[civic dirge]

s comes after r, I can only imagine that's why s is used

s and r are common in dihedral groups

[elder pawn]

@wild marten its good to look at the wiki example

try to convince urself every reflection is s (reflect horizontal) then a power of r (rotate pi/4 ccw)

[calm coral]

@wild marten Has your question been resolved?

[wild marten]

@elder pawn ohh

so every reflection is just

a reflextion on the x axis with a rotation?

[elder pawn]

every reflection is s (reflect horizontal) then a power of r (rotate pi/4 ccw)

[wild marten]

@elder pawn how did he move it at the bottom:

Like where did he make it so rs = sr^{-1}

[civic dirge]

rs = sr^{-1} is true in every dihedral group

You can swap s and r. If you do, take the inverse of r (inverse of s is just s itself)

[wild marten]

ok so if u look

at the srs=r^-1

how would this get translated to $rs = sr^{-1}$

[potent lotus]

BOSS

[civic dirge]

srs = r^(-1)

Left-multiply both sides by s:
ssrs = sr^(-1)

ers = sr^(-1)

rs = sr^(-1)

Where e is the identity

[wild marten]

OHH

ok yeah

that makes sense

[civic dirge]

I would think you'd want to go the other way though

[wild marten]

s has order 2

and r has order n

[civic dirge]

rs = sr^(-1) is the common fact

srs = r^(-1) shows the rotations are fixed under conjugation by s

[wild marten]

Yeah

For all dihedral groups right

@civic dirge

also also also also

if ur still here

$D_4$ would be on a square right

not a rectangle

[civic dirge]

That's a triangle

[potent lotus]

BOSS

[wild marten]

whoops typo

but yeah

because all the angles and line

would have their own reflection

[civic dirge]

All dihedral groups are on equilateral shapes

[wild marten]

goat

and last clarifying question

if u have time i feel bad lmao

[civic dirge]

Huh? I am here because I am bored at home lol

[wild marten]

W lmao

okok so

[civic dirge]

No need to feel bad

[wild marten]

whats the latex command for subgroup

lets say H is a subgroup of $S_3$ where its just {e,(12)}

[elder pawn]

many ppl use $\le$

[potent lotus]

BOSS

ロケットジャンプ

[wild marten]

ok so

lets say H \le $S_3$ where its just {e,(12)}

[potent lotus]

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

[elder pawn]

wrap $ around all latex

[wild marten]

yeah

i got lazy

ok but with that

if i wanted to show its not normal

do i need ot find the entire coset

[elder pawn]

no

[wild marten]

or just show that (12) does not commute with say (123)

its element spesific right

like each element has the saem coset

same*

like is there a case where i get like

[elder pawn]

normal is $ghg\inv\in H$

[potent lotus]

ロケットジャンプ

[wild marten]

gH = {z,y} and then Hg = {y,z}

[elder pawn]

to show not normal, show its false for one g and h

[wild marten]

(12)(123)(21) = (132)

which $\notin H$

[potent lotus]

BOSS

[elder pawn]

ya

[wild marten]

but just to understand

you can have the same coset

with different elements of H times g

as long as u get all of h for gH and Hg its fine

like

for an indivisual element, gh does not need to be hg for a spesific h

does that make sense

[elder pawn]

ya

gh=hg only holds in abelian G so if ur trying to impose that itd be damn hard to find normal subgroups in general haha

[wild marten]

@elder pawn yeah thats what i was thinking lmao

.close

[calm coral]

Channel closed

Closed by @wild marten

Use .reopen if this was a mistake.

[wild marten]

.reopen

[calm coral]

✅

[wild marten]

uno sec

@civic dirge twin

u still alive

[twin raptor]

do you have another question

[wild marten]

yes

im trying to understand this

have the same determanant does not make it the same matrix rifght

[twin raptor]

correct

[wild marten]

ok i dont understand this proof then

[twin raptor]

because ghg^-1 has determinant 1, it is still in SL2(R)

even if it's different from h

it's similar to what you were saying above

[wild marten]

ok let me break this down

oh

OH

OHHHHHHHHH

so no matter what u get the entire subgroup again

im so stupid

alr ty

:D

essensically

gHg-1 means that u just get back all matricies with det 1

how do u know u get all of H tho

[twin raptor]

this is a good question

suppose h is in H

you want to find h' in H such that gh'g-1 = h

and solving this yields h' = g-1hg

and h' is in H by the same determinants argument

[wild marten]

wait im walking back to my dorm ill follow up when i reach