help-0

[worldly path]

should i drive like an arrow sign

[slate jolt]

write it like this first

then replace the values at 4 and 0

[worldly path]

ohhh

put that for the last line

wait

like this?

(writing)

[slate jolt]

yeah so now replace

and you forgot the e

after 15

oh actually i didnt see your second line im getting tired

your previous answer was right then

my bad sorry

[worldly path]

No it's okay you've helped me a lot

I didn't know that I could show my work with the box thingy

Thank you very much !!

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[alpine sable]

Because interest compounds, I did the following, manually

1: 0.002x$776,801.52 = $1,553.60304. $776,801.52 + $1,553.60304 = $778,355.12304.
2: 0.002x$778,355.12304 = 1,556.71024608. $1,556.71024608 + $778,355.12304 = $779,911.83328608

Is the the most effecient and accurate approach? Or am I to use a future value calculator?

[runic trench]

Imagine being named Jojo klum

Fuuuuck no

[alpine sable]

everytime i see it im reminded of joji

[runic trench]

Worked it out the ans is 38,554,545

[alpine sable]

wait so it grew by that much in 2 weeks? surely not...

[carmine reef]

,w 10.4/52

[ocean seal]

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[carmine reef]

,w 1251.002^(5225)

[ocean seal]

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[carmine reef]

,w 1.002^1300

[ocean seal]

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[carmine reef]

,w 1.002^21678.603033500*12.428824/13.428824

[ocean seal]

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[carmine reef]

yeah looks about right

fastest approach is using sum of geometric series

[alpine sable]

@carmine reef ty!

[carmine reef]

np!

[alpine sable]

@carmine reef what's a geometric series?

[alpine sable]

is it the way the formula here is constructed?

[carmine reef]

geometric series is when you have a sequence like 1,2,4,8,16,...

well that's a geometric sequence anywayd

[alpine sable]

uhh okay, gotchya

[carmine reef]

the terms have to differ by a constant ratio

the general form is a, ar, ar², ar³, ...

[alpine sable]

okay thanks, got it, super appreciated @carmine reef 🙂

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[carmine reef]

no problem!

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[neon harness]

Kind of a dumb question but how do unitary matrices preserve inner product?

[neon harness]

For instance, the matrix

1 1

-1 1

it's action on the vector [1 0] is [1 -1]

but the inner product of [1 0] with itself is not equal to the inner product of [1 -1] with itself?

[slate jolt]

well its not unitary

[neon harness]

How? isn't that an orthogonal matrix?

[slate jolt]

maybe i messed up the calculations in my head

[near coral]

isn't AA^T 2 times identity

[slate jolt]

youd have to normalize it

[near coral]

if all the entries had /sqrt2

it would be orthogonal

rotation by pi/4?

or something, idk

[slate jolt]

and also you could tell its not orthogonal because of this

[near coral]

-pi/4 *

[neon harness]

Ok I see

Yea I forgot an orthogonal matrix must be expressed in a normal basis

And it's not actually unitary for its inverse isn't its transpose

Thanks for the input

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[loud ridge]

hi! can anyone point me to the right direction with this?

[loud ridge]

Rephrased 😄

[harsh girder]

if the two vectors are parallel, then you can find a constant m that u=m v

so $\frac{2}{1}=\frac{-k}{-6}$

[ocean seal]

秋水

[loud ridge]

I think I understand 😅 Thank you so much!

Can I close this with a command or?

.close

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[lavish oyster]

hello, can someone please explain to me how?

[alpine sable]

how what?

[lavish oyster]

how 10x^2-5x+6 can be 10(x-1/4)^2+43/8?

[alpine sable]

(x-1/4)^2=?

[velvet sundial]

hello can someone teach me adding and subtracting fractions with unlike denominators?

[alpine sable]

find another channel this one is occupied

[lavish oyster]

is that clear enough?

[inner path]

developp ur expression (x-1/4)² and u find 10(x² + 1/16 -x/2) +43/8

so 10x² +10/16 -10x/2 +43/8

so with simplification we find 10x² -5x + 6

[lavish oyster]

oh ok, but I mean the opposite

So 10x² -5x + 6 to 10(x-1/4)²+43/8

[harsh girder]

$$\begin{align}
10x^2-5x+6 & = 10(x^2-\frac{1}{2}x)+6 \
&=10((x-\frac{1}{4})^2-\frac{1}{16})+6 \
&=10(x-\frac{1}{4})^2-\frac{10}{16}+6 \
&=10(x-\frac{1}{4})^2+\frac{43}{8}
\end{align}$$

[ocean seal]

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

[lavish oyster]

ooo okay thanks👍

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[stable field]

Need help for real life situations on the following for rational functions

Have for health already but unsure with physics and chemistry

[lone heart]

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[cunning raven]

Actually have no idea why autograder is marking d) wrong

[lone heart]

@cunning raven Has your question been resolved?

[cunning raven]

<@&286206848099549185>

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@cunning raven Has your question been resolved?

[cunning raven]

<@&286206848099549185>

[fluid basin]

what do you think the correct answer to d) is and why

also, why would your answer to d be different than your answer to a

[cunning raven]

I massaged d) to have non-negative d value

idk why I was allowed to massage a) and not d)

[fluid basin]

the thing is, the plane in a and the plane in d are obviously parallel to one another

so if it's perp to a, it has to be perp to d as well

[cunning raven]

my problem with this whole thing is why was I allowed to move the numbers around for a)

[fluid basin]

i'm not sure what you mean by 'd value'

[cunning raven]

if I can't od the same for d)

ax + by + cz = d (d value)

[fluid basin]

you can always multiply an equation for a plane by a non-zero number and still have an equation for the same plane

[cunning raven]

so a) was just deliberate manipulation?

[fluid basin]

if you multiply the eqn in d by, um (10/-7.5) i think, you get the eqn in a except that the constant is difefrent

and if you have two equations for planes that are the same except for the constant, those two planes are parallel

so the plane in d is parallel to the plane in a, and thus if a is perpendicular ,so is d

[cunning raven]

I'm confused why I'm alllowed to have negative distance

in the planes formula

[fluid basin]

it's a "displacement", which is essnetially signed distance

ther'es no reason why d has to be positive, not sure why you've been taught that tbh

[cunning raven]

so for a) I just multiplied entire plane by -1 in order for it to be parallel with the direction vector?

[fluid basin]

well, it's paralle to the direction vector whether or not you multiply by -1

[woeful moat]

Hello, does anyone know how to solve this problem

[fluid basin]

this channel is occupied, please ask your question in an open channel

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@cunning raven Has your question been resolved?

[graceful verge]

help me plss ineed solution

ineed right noew plss help

[lone heart]

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[grizzled mulch]

I got this as homework and I’m confused on how to do it

[grizzled mulch]

Idk how to find x without an area

[pastel swift]

hi

[autumn pasture]

make an equation

[pastel swift]

yeah

[autumn pasture]

also which is the shaded area?

[pastel swift]

i think the shaded area would be the smaller rectangle

[autumn pasture]

ohh I see it

HAHA

[pastel swift]

oh its you

hi

[autumn pasture]

[pastel swift]

The area of the smaller rectangle would be 2(12-x) = 24-2x

[autumn pasture]

should be $2(12-x) = \frac{1}{4}\cdot{12(x+2)}$

[ocean seal]

duckiescute!

[autumn pasture]

then just need to solve for x ya :)

[pastel swift]

where did you learn latex from?

i want to learn it, it seems cool

[tall topaz]

Learn the basics from YouTube

If you just want to write simple expressions

[pastel swift]

thanks

[autumn pasture]

yea I just learned from seeing people type it hahaha

then I practiced a little in #latex-testing

[lone heart]

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[grizzled mulch]

Thanks

[lone heart]

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[swift flame]

how do i solve this

<@&286206848099549185>

[neon scarab]

Try simplify the expression by the given f(x) equation.

[swift flame]

what do you mean simplify it's still f(x)=x^2-x

[hybrid zenith]

put f(x) into the equation

then u can simplify

[swift flame]

so is it going to be f(x^2-x + h) - f(x^2-x) / h

[hybrid zenith]

add h to each x as its f(x+h)

[neon scarab]

Given f(x), ask yourself,
0. What is f(x)?

1. What is f(x + h)
2. How to simplify f(x + h) - f(x), in a way no more f(…) but only x is needed in final expression?
3. Then how should you simplify that giant fraction you want to know about?

[swift flame]

okay thank you so much

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[violet idol]

Hi guys

[violet idol]

If I have the following function f(x) = 2x+1 how can I build its graph?

[echo socket]

Pick any pair of points that lie on that graph and just connect them with a line

Since the function is just of the form kx + b

[violet idol]

what do you mean any pair?

[echo socket]

Any two points

[violet idol]

so I would choose any x

[echo socket]

For example (0, 1) is a point lying on the graph

[violet idol]

and then I replace inside 2x+1

[echo socket]

Yes

[violet idol]

so the y

would be the result

[echo socket]

Yes, pick some x, calculate its y and you'll have a point

But you need two different points

[violet idol]

but the y

is the result of 2x+1

right?

[echo socket]

Yes

For each x, y is 2x + 1

[violet idol]

So like
x y
1 3
3 7
-2 -3

etc

[echo socket]

Yeah, just pick 2 out of them

Then draw them on a plane and connect them

[violet idol]

So if I have f(x) = 1/x

would be
x y
2 0,5
4 0,25
-3 -0,33

etc? these results are righty?

[echo socket]

Yes, but you wouldn't be able to connect them with a single straight line

[violet idol]

got it

ty ❤️

[violet idol]

why XD

[echo socket]

Because y = 1/x isn't a straight line, unlike y = ax + b

[violet idol]

I have this graph on my book so yeah, exactly

ty for the help ❤️

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[unborn mica]

/open

[unborn mica]

.open

i need help

[mortal trellis]

then ask a question

[unborn mica]

v

[night geyser]

.close

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[haughty valve]

is there any other better way than doing it like (x-4-3sqrt(6)) (x-4+3sqrt(6)) ?

or is that the only way to get the quadratic equation

[lone heart]

@haughty valve Has your question been resolved?

[harsh girder]

you can use Vieta's formulas

[haughty valve]

thanks

i guess

.thanks

.cklsoe

.clseo

.close

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[late jay]

Help, I've been looking at how to solve this problem for a long time and I haven't been able to think of any way to approach it. Could you help me?

[plain flame]

honestly its just using a lot of substitutions and using a lot of algebra

i dont see any neat tricks you could use tbh

but there might be idk

[late jay]

But do you have any idea how it can be done?

[plain flame]

well i hate to say just work it out

but thats it essentially

you might want to turn it into 1 fraction

thats how i would probably start

[late jay]

Ok, if I get stuck, do I create another channel again?

[plain flame]

yeah sure

[late jay]

ok, thanks

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[neon elm]

q. 36

I dont know how to factorize and the pencil work is the solution done by my friend

I dont underdstand how ot works ?

it

Please

Btw, please pin me when u are ready, thx so much !

this is how i think to do, i am not really sure how to work on

[astral ruin]

take x-4=t

[neon elm]

Oh , i need to find the root of the equation and the ans will be like

I am so so so sorry for not adding this at first

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[neon elm]

@astral ruin Hello, i figured out the ans , thx for ur help

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[neon elm]

Emm is just like i missed some part, i am really sorry for interrupt ur time and effort and i really thank you for u to help me deal with this

[astral ruin]

no problem
i am glad you figured it out

[neon elm]

thx so much

nice person

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[wet tangle]

!search

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[timber wigeon]

I have 'x' identical items of mass 'm'. I randomly pick a batch of some of these items and weigh them. Batches must have at least 1 item but cannot have more than 'x' items.
I conduct this random weighing 'n' times. What is the probability that the weights of any two batches differ by mass 'm'?

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@timber wigeon Has your question been resolved?

[timber wigeon]

<@&286206848099549185>

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@timber wigeon Has your question been resolved?

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[keen bolt]

I understand it’s most likely quotient of chains but applying it is making my brain do cartwheels

[plain flame]

quotient of chains?

it just asks when the derivative is 0

[keen bolt]

yeah

so first you would use the quotient rule which would involve the chain rule to find the derivative right?

[alpine sable]

I'm new to this server but do you guys also help with physics or just mathematics?

[plain flame]

lots of people in here also know physics so youll be just fine

[keen bolt]

yeah

[alpine sable]

thanks

[plain flame]

there is a physics dedicated discord as well though

perhaps for the more advanced questions its better to go there

[alpine sable]

alright

[plain flame]

yeah you need the chain rule for the derivative of sqrt(3t-2)

so yeah you have the right idea

now just work it out 🙂

[keen bolt]

I got to the one where I set it to 0

I also replaced t with x to make it easier

[plain flame]

,w solve d/dt sqrt(3t-2)/t = 0

[ocean seal]

Results provided by WolframAlpha

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

Requested by Gijs#0201

[plain flame]

there is always derivative-calculator.com

to check the steps

[keen bolt]

yeah how did we get that though

[plain flame]

i could tell you but that website tells you in 2 seconds and is always right

im just not as good as a computer program lol

[ancient meteor]

0 multiplied by x^2 equals to 0

[keen bolt]

OOHHHHH

wow basic algebra has eluded me

[keen bolt]

also thank you I’ll probably check it out if I’m really stuck

.close

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[lone heart]

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[coarse socket]

hello can somebody explain the solution to me?

[coarse socket]

solution:

the above part was just A is true, which i got

but i don’t get B,C,D

[trim wagon]

wow

what a clever question

really best use of inertia theorem

which i haven’t seen any yet

okay so

B)

lets start with it

the first line in explanation for B

means there is always some point x_1 such that f’(x_1)<0 no matter how small you choose delta

which ig you already understand?

do you?

@coarse socket

[coarse socket]

wait what’s inertia theorem

[trim wagon]

the momentum theorem as they’ve mentioned

[coarse socket]

oh

[coarse socket]

wait no i don’t understand this

wait i get it

[trim wagon]

hmm okay then onto next line?

[coarse socket]

yes

[trim wagon]

do you know momentum theorem?

[coarse socket]

i have forgotten some part of it, can you tell?

[trim wagon]

yea

so it goes something like: if the limit of a function is non-zero then there exists a delta>0 such that f(x) doesn’t change sign in that nbh

[coarse socket]

yes

[trim wagon]

okay so do you get the line 0<x_1 - δ’<x_1 < x_1 + δ’

which comes from theorem

[coarse socket]

yes

[trim wagon]

so there exists a x_2 between x_1 + δ’ such that f(x_1) > f(x_2) which we get from the derivative <0 fact

uhh do you get it?

[trim wagon]

well this you can also see from the graph of the derivative if you want

,w plot 1+ 4xsin(1/x) -2cos(1/x)

[ocean seal]

Results provided by WolframAlpha

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Requested by Deep.#0001

[trim wagon]

as you can see there are infinitely many points where derivative is <0 for some very small nbh of 0

[coarse socket]

what is nbh

[trim wagon]

hm neighbourhood

[coarse socket]

ohh

yes i think i grt it now after the graph

[trim wagon]

oh cool so do you get B) ?

[coarse socket]

let me think, wait

[trim wagon]

sure

[coarse socket]

i get it now @trim wagon

[trim wagon]

oh okay, so can you apply similar analogy to C)?

[coarse socket]

yes

[trim wagon]

great

now let me see D)

oh okay well

now that you got B) and C)

we know that for some x_1 and x_2

f’(x_1) <0 and f’(x_2)>0

so yes there will be two points where their derivatives product at that point will be <0

its like multiplying +ve and -ve which will be -ve

uhhh do i make sense to you?

[coarse socket]

yes i think i get it now

omg you are so smart

thanks

[trim wagon]

np

[coarse socket]

i was really confused before

[trim wagon]

hm

[coarse socket]

hey how are you not green yet?

[trim wagon]

idk, maybe the mods select who they feel are helpful? anyways i don’t really care much about that

anyways i’m glad i could help you

[coarse socket]

what you are very helpful

i’ve seen you quite a few times

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@coarse socket Has your question been resolved?

[lone heart]

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[alpine sable]

Not particularly a math question, but I was wondering how are you suppose to practice physics

[alpine sable]

Because, I’m beginning to learn Quantum physics/mechanics, and beginning to use Scott H. Young’s ultralearning book, and he recommends practicing what you are learning, but how would I practice physics?
Would I just do then mathematics for physics or is there some sort of other way

[strange sleet]

use QM problem books, solve problems, read solutions.
have a look at Qiskit see if you can apply what you've learned in QC. that is an application.

also have a look at Sympy's notebooks on QC https://github.com/sympy/quantum_notebooks/tree/master/notebooks
and docs https://docs.sympy.org/latest/modules/physics/quantum/index.html

see if you can transition some of your problem solutions in SymPy.

these are just some ideas. Disclaimer: idk QM/QC, but that's what I would do

[alpine sable]

Hmm, thanks I’ll look into it

.close

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[alpine sable]

Hello very simple question, does anyone know the slope intercept form of the standard form 2x-2y=4? If so, can you please explain how you solved the equation?

[plain flame]

wdym slope intercept form?

[trim valley]

help

[plain flame]

please make your own channel @trim valley

[trim valley]

sry

[gray isle]

perform algebraic manipulation and work towards isolating y

[trim valley]

im new

[alpine sable]

slope intercept form or y=mx+b

[plain flame]

just solve for y

[alpine sable]

thats what im asking how?

how do you solve for y?

[plain flame]

well if 2x-2y = 4, what is y?

you subtract 2x from both sides

so you get -2y = 4 - 2x

then multiply by -1 to flip the sign

2y = -4 + 2x

y = -2 + x

y = x -2

[alpine sable]

Thank you for your help, I get it now

[plain flame]

np

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[brave stone]

can someone explain to me the directing of this question

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[brave stone]

.close

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[worldly path]

https://cdn.discordapp.com/attachments/1011751524743000074/1026241387403956284/unknown.png

[worldly path]

How are there two more critical points for part d?

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[brave stone]

can someone lead me into the direction this question is asking

[carmine reef]

ok well you should be able to find csch right away

by it's definition

[brave stone]

i got it now sorry, i dont understand it at all tho i used a calculator

i understand you set sinh(x) =8/15 and solve

.close

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[steel aurora]

Any topology enjoyers to help me out with this one?

[steel aurora]

So my first instinct was to think of the circle as parametrized t from 0 to 1 (counter)clockwise, and think of the projective line as the half circle, so the map is just from whatever value in the parametrization of the point to the point corresponding half of the same

dunno if that makes sense

but then I don’t know how to describe very well this parametrization, as intuitive as it is.

maybe I’m not thinking of the projective line correctly?

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@steel aurora Has your question been resolved?

[alpine sable]

Consider the map $z\mapsto z^2$ in the complex plane

[ocean seal]

Blitz

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[edgy scroll]

How do I solve question 1b?

[sly breach]

(n+6j)3 Something like this I presume

n being a number and j being another number

[edgy scroll]

Ok, thank you!

[sly breach]

Also when doing brackets, try make them look less like C's

It was a little confusing

[edgy scroll]

Oh I see, thanks again

[sly breach]

❤️

[edgy scroll]

.close

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[sage wadi]

Find the equation of the line that passes through (1,2) and is perpendicular to
y

2
x
+
3
.
Leave your answer in the form
y

m
x
+
c

[sage wadi]

really need help withh this one question

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[alpine sable]

What does it mean for two lines to be perpendicular to each other?

[lone heart]

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[abstract fractal]

What have you tried

[alpine sable]

& for a function to be continuous at a point, what criteria must be met?

There’s 3 conditions

No, there’s 3 rules that must be met for a function to be continuous at a certain point

I’ll give you one, the limit of the right hand side that is approaching a point must be equal to the limit of the left hand side approaching the same point

[alpine sable]

#❓how-to-get-help

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[fierce linden]

This seems like its a quartic

and the derivative of a quartic is a cubic

its also a negative quartic

so we would get a negative cubic

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[fierce linden]

<@&286206848099549185>

[storm topaz]

Yrr

[fierce linden]

I got it

[vestal imp]

You just need to mark the turning points

[fierce linden]

I acc just did it

[vestal imp]

and associate +ve and -ve

[fierce linden]

thanks tho

I do have another question

@vestal imp

[vestal imp]

I can't help u with that XD I don't know

[fierce linden]

oh

ok nw

[vestal imp]

GL tho, someone able to should come soon

[fierce linden]

<@&286206848099549185>

@violet hemlock Sorry for pinigng you, but would you be able to help me?

@rapid thistle

Sorry for pinging you

can you help?

[fluid basin]

don't ping individual users for help

[fierce linden]

sorry

i have been sitting here for 30 mins

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@fierce linden Has your question been resolved?

[fierce linden]

I got it!!!!!

.close

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[lone heart]

Please don't occupy multiple help channels.

[flat elbow]

please help x2

[wary stream]

Don't open multiple channels even if you have different questions

.close

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[normal holly]

how to solve #5.

[sour dove]

have you tried drawing a tree diagram? 🙂

it makes it easy to see how many!

otherwise we can do it the way you had it so far:
Write down all possible combinations:
If Shelby picks A, then Ray can choose between O, B, or P (so you can do AO, AB, AP, 3 possible combinations if Shelby chooses an apple). So far we have 3 possibilities
If Shelby picks O, then Ray can choose between A, B, or P (so you can do OA, OB, OP, 3 possible combinations if Shelby chooses an orange). So far we have 3 + 3 = 6 possibilities

can you finish the pattern?

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[alpine sable]

How do i rewrite 6k with the help of dinominators

[trim wagon]

hey its you

[alpine sable]

Aye

Deep

Good morning bruv

[trim wagon]

hmm

[trim wagon]

not so good

anyways

[alpine sable]

😟

Whats up

[trim wagon]

did you try 6= 3*2?

[alpine sable]

🤔🤔

Hmm

[trim wagon]

get to some telescope

[alpine sable]

Telescope 👁️👄👁️

What is that

[trim wagon]

eh

telescopic series

…

https://en.m.wikipedia.org/wiki/Telescoping_series

[alpine sable]

Hmm

Oh

This

[trim wagon]

,w partial fraction of xy/((x-y)(3x-2y))

[trim wagon]

yes ig

[ocean seal]

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[trim wagon]

there u go

[alpine sable]

🤔

[trim wagon]

x=3^k

y=2^k

[alpine sable]

OHH

Makes sense

But

[trim wagon]

[alpine sable]

How do i know which term to break

And how to break

[trim wagon]

https://youtu.be/QKkdYW77xNI

i mean

u do this

only if u know

it will be telescopic

i mean

if it isn’t

telescopic

[alpine sable]

Then

[trim wagon]

then we’re in trouble

but here it is

[alpine sable]

😟

I see

So i just

Kinda expand

[trim wagon]

so here we get

[alpine sable]

The numerator

Into denominator

[trim wagon]

$\frac{3^{k+1}}{2^{k+1}-3^{k+1}} - \frac{3^{k}}{2^{k}-3^{k}}$

which is telescopic

ig

lemme see

[alpine sable]

Hmm

[trim wagon]

yes u get telescopic smh

😌

[alpine sable]

[novel cairn]

I have question can i ask

[trim wagon]

#❓how-to-get-help ?

[novel cairn]

Ok

Sorry

[trim wagon]

uhh @alpine sable u got it?

[alpine sable]

Hmm

HMMMM

HMMMMMMM

[trim wagon]

[alpine sable]

Why are the terms of the denominator flipped

[trim wagon]

well wolfram is weird

x-y = -(y-x) smh

[novel cairn]

We do these types of questions in 5 grade

You guys are so dump

[trim wagon]

uh?

[alpine sable]

Hmmm

[novel cairn]

What?

[alpine sable]

Sus

[wary stream]

First

● Respect that other people might be at a different stage in their education than you, what is obvious to you might not be obvious to them.
That's in #rules

[trim wagon]

,w dump

[ocean seal]

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[trim wagon]

what?

what does it even mean

lol

[alpine sable]

Bruh

[lone heart]

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[wooden mantle]

If I use U substitution in this what would du be?

[wooden mantle]

the entire thing or?

actually wait du is -3x^2 right?

[vague coral]

du is -3x^2 dx

[wooden mantle]

aight, thanks

.close

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[solar bridge]

.close

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[severe wyvern]

f(x) = 4x-3 x greater or equal to 4 find range of f(x)

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[severe wyvern]

.reopen

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✅

[surreal meadow]

what’s giving you trouble @severe wyvern

[severe wyvern]

f(x) = 4x-3 x greater or equal to 4 find range of f(x)

[tall topaz]

What have you tried

[severe wyvern]

i dont if this is right byut ive put 4 into eqaution and got that the range is f(x) greater or equal to 13

[tall topaz]

Yeah that correct

,w plot y=4x-3

[severe wyvern]

oh ok thank you

[ocean seal]

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[tall topaz]

It’s strictly increasing so the range y>=13

[severe wyvern]

ok

.close

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[radiant jewel]

i dont get how to find limit. ik the making a table way but is there not a way to do it faster?
The limit is the top image and if you use lhopitals rule it should be 0 cause derivative 1 is 0. But symbolab says its -infinity and that is correct. that checks out with the table method and graphing it too.
I'm confident there is a way to solve this faster than making a table of values of x as it gets closer but I dont know how.

[radiant jewel]

<@&286206848099549185>

[neon scarab]

LH rule is only applicable in limited cases

1. 0/0
2. infinity / infinity
3. infinity - infinity
   And so on

[radiant jewel]

it is 0/0

[neon scarab]

Your limit is none of that, so the rule does not applies.

[radiant jewel]

wydm

wdym

[radiant jewel]

ohh

im so dumb

[radiant jewel]

but how would you solve the limit then?

without making a table?

[neon scarab]

Simple, you have 1 in numerator and 0 in denominator by “blindly” substituting x, which means your limit is constant / 0 case

Then it has to be diverging to positive or negative infinity

[radiant jewel]

is there a name for this rule

[neon scarab]

Nahhh, i dont think so(?) If you are in elementary calculus class, this is just a thing-to-know that you will have to apply in assignment or exam 🙂

[radiant jewel]

this is from bc 😢

I have to make up a limits quiz tmrw cause i was sick and i didnt learn this in class 😦

.close

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[gilded osprey]

how do I solve this?

[ornate condor]

...

#❓how-to-get-help

[alpine sable]

hhhh

[trim wagon]

uh?

[ornate condor]

ppl ocassionally del their msgs

[trim wagon]

oh i c my b

[gray isle]

first simplify the given expression

[gilded osprey]

alr

[lone heart]

@gilded osprey Has your question been resolved?

[gilded osprey]

?

<@&286206848099549185>

[gray isle]

did you make any attempt at simplifying the given expression?

[gilded osprey]

... idk how

[gray isle]

are you able to get f(x+h)

[gilded osprey]

x²-x?

[gray isle]

no

f(x) = x^2 - x
was given

how are you getting x^2-x for f(x+h)

[gilded osprey]

man irdk..

[gray isle]

do you understand basic function notation

[gilded osprey]

ngl no

[gray isle]

so are you implying you are unable to evaluate
f(5)?

[gilded osprey]

yeah

[gray isle]

f(x) = x^2 + x
to get f(5) simply sub x=5 into the equation

[gilded osprey]

ohh

what do I do next

[gray isle]

were you able to evaluate f(5) here?

[gilded osprey]

x=5?

[gray isle]

no

[gilded osprey]

oh

[gray isle]

f(5) is not the equation x=5

[gilded osprey]

f (5) = 5² + 5

?

[gray isle]

yes

[gilded osprey]

oh nice

[gray isle]

which can be simplified

similarly, to get f(x+h)
replace all the xs in f(x) = x^2 + x
with (x+h)

[gilded osprey]

f (x+h) = x+h² + x+h

[gray isle]

no

you're missing ()

[gilded osprey]

f (x+h) = (x+h²) + (x+h)

[gray isle]

no

parentheses in wrong place

[gilded osprey]

f (x+h) = (x+h²) + x+h ??

[gray isle]

no

f (x+h) = (x+h)^2 + x+h
you want that ^2 on the outside of the parentheses
to represent that whole (x+h) being squared

[gilded osprey]

oh

ok

f (x+h) = (x+h)² + x+h / h

[gilded osprey]

<@&286206848099549185>

[lone heart]

@gilded osprey Has your question been resolved?

[gray isle]

f (x+h) = (x+h)² + x+h / h
no

sry, copied down the wrong sign earlier. though it was + instead of -
anyway using f(x) = x^2 - x
f(x+h) = (x+h)^2 - (x+h)

f(x+h) is not the same as f(x+h)/h

$f(x) = x^2 - x$
$$\frac{\overbrace{f(x+h)}^{ (x+h)^2 - (x+h)} - \overbrace{f(x)}^{(x^2-x)}}{h}$$

[ocean seal]

ℝamonov

[lone heart]

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[unkempt iron]

hello

[unkempt iron]

jsut wanted to check my ven diagram question

for b i got 24/92

is this correct?

and for c i got 20/108

just wondering if my answer is correct

note -> b is Nz Males

[lone heart]

@unkempt iron Has your question been resolved?

[unkempt iron]

<@&286206848099549185>

[lone heart]

@unkempt iron Has your question been resolved?

[unkempt iron]

ah nvm i got 50

[unkempt iron]

54/35

.close

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[dense compass]

I struggling to understand what Jucys-Murphy elements definition and what they do, could anyone elaborate on it please?

[dense compass]

Is it a scalar that's assigned to an element of the group algebra kS_n?

<@&286206848099549185>

[fluid basin]

you may want to ask for help in #groups-rings-fields

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@dense compass Has your question been resolved?

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[alpine sable]

How can one get started here?

[lone heart]

@alpine sable Has your question been resolved?

[vale wigeon]

@alpine sable do you know what a borel set is?

[alpine sable]

Yes

A set of the sigma algebra generated by open sets.

I started decomposing A into open and closed sets, but then showing that each of the components sets was either open or closed got me stuck.

[mortal trellis]

you could try writing it as the preimage of a measurable set of a measurable function. assuming you are allowed to use that certain functions are measurable

[alpine sable]

I don't know whether I'm allowed to do so, but finding such a function also seems quite difficult. I think I'll just try both and see whether I can find any form of solution.

[mortal trellis]

do you know that continuous functions are measurable?

[alpine sable]

Yes

[mortal trellis]

oh wait I made a mistake in my head. nvm

[lone heart]

@alpine sable Has your question been resolved?

[noble sinew]

0<x<=1 can be written as intersection between 0<x and x<=1 and similar for 0<y^2+z^2<=x can be written as intersection between 0<y^2+z^2 and y^2+z^2<=x

[alpine sable]

Oh, and then one can say that since those are measurable functions, the preimages of the sets must be borel sets?

[noble sinew]

si

[alpine sable]

I see. Thank you.

.close

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[crisp geode]

someone explain this notation

[crisp geode]

dark mode users have difficulty reading it?

[half epoch]

Yes, but it’s not completely unreadable

Without any context, it’s just dividing both the numerator and the denominator by \delta v

However, I have a feeling you are looking for a more specific answer. Maybe it’s a demonstration of the chain rule?

[chilly pike]

delta u/delta x = delta u/delta v times delta v/delta x

[crisp geode]

it's generally a notation used for derivates which i don't understand

this specific example is from wikipedia article of the chain rule

$\frac{\Delta u}{\Delta x}=\frac{\Delta u}{\Delta v} \cdot \frac{\Delta v}{\Delta x}$

how do i use this bot

my question is more about what this notation (especially the delta) means in the context of derivates

so generally the delta divided by something

,tex $\frac{\Delta u}{\Delta x}=\frac{\Delta u}{\Delta v} \cdot \frac{\Delta v}{\Delta x}$

[ocean seal]

conjurer

[crisp geode]

my question: generally what does delta something divided by delta something mean in terms of derivatives

or should i go somewhere else if i want to get raw theory explained to me?

[half epoch]

Delta denotes “change”, usually when we evaluate this changes over infinitesimal changes (e.g. in the limit) these delta’s are replaced with d

So it’s technically illustrating that a change in u due to a change in x can also be expressed in terms of a change in an intermediary “property” v.

Evaluated in the limiting case with infinitesimal changes you get the usual chain rule

[crisp geode]

and i think there is some delta notation that is said to replace/be more modern then the notation of f'(x)

what is that?

[half epoch]

There are a couple different notations out there for derivatives

They are all used and are equivalent, depends on the context usually. E.g. physicists enjoy the dot notation

$f’(x) = \frac{, df}{, dx} = \dot{f} = \frac{, d}{, dx}f$

The dot one is usually used when the variable is time though

[ocean seal]

Learath2

[lone heart]

@crisp geode Has your question been resolved?

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[waxen jungle]

I understand that the purpose of solving this equation is to find the x-intercepts to determine the shape of the graph using their multiplicities

however, I skipped a year in math and I don't understand why or how to change these types of equations to find the zeros

I believe that the first zero is -1

but I'm unsure if I have to do something to the (2x-3)^2 before deciding its zero

[cursive wharf]

Unless I’m misunderstanding you, nope, the other zero is just 3/2

[waxen jungle]

wouldn't the other zero just be 0?

[alpine sable]

just solve the 1/2 (x+1)(2x-3)^2=0

so x+1=0 or 2x-3=0

[waxen jungle]

so 2*?=3?

[alpine sable]

then u get the x

[waxen jungle]

okay I think I see what you mean

[alpine sable]

maybe i's misunderstanding u but i think it's much much more easier than u think

[waxen jungle]

.5 is the other zero

1.5*

[alpine sable]

if u want to see, this is the graph

[waxen jungle]

so there is no factoring involved?

that's a relief

yeah I know I can easily plug in the graph but he doesn't want us to

but I see how the graph correlates now!

thank you

.close

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[alpine sable]

HLEP

[alpine sable]

easy

14 ,
x= 80
y=70

15,
y=110
x=70

[paper merlin]

Can u also do we are friends btw

[alpine sable]

16,
x+y = 150
x-2y = 30
''''''''''''''''''''
y= 120
x= 30

19,
x= 97

,rotate

[alpine sable]

20,
x= 21

[alpine sable]

kk

[paper merlin]

Ty

[alpine sable]

omg thank uu

18,
m< UVW = 81

[alpine sable]

THX DADDY

[paper merlin]

How do u get 18

[alpine sable]

17,
x=16
y=11

[alpine sable]

my pleasure

[alpine sable]

here buddy its it

[paper merlin]

Oh

[alpine sable]

got it ?

that was easy af

[alpine sable]

which class u both ?>

[alpine sable]

in geometry

in a confsuing topic..

[alpine sable]

nah thats not even close ....

[alpine sable]

age ?

[alpine sable]

i was helpin my friend, i already did geo

[alpine sable]

im 18

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

Ohhh ....

[alpine sable]

Still u were unable to do that ?

[lone heart]

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[alpine sable]

what is 2.6 cos 12degrees rounded to 2dp

[alpine sable]

.close

[lone heart]

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[alpine sable]

.reopen

[lone heart]

✅

[alpine sable]

work out tan 6degrees =f/2.3 give answer to 2dp

any1 can help?

[tall topaz]

What have you tried?

[alpine sable]

mate idk

how do i get f

[tall topaz]

Wel you can multiply both sides by 2.3

Tell me what that gets you to

[alpine sable]

so 2.3tan 6=f

[tall topaz]

Yeah

Now plug that into your calculator

[alpine sable]

0.24

ahh ok ty

[tall topaz]

,w 2.3*tan(6 degrees)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Pure#9389

[tall topaz]

Alright

[alpine sable]

uhhhhh

do i do the same

[tall topaz]

You just plug in into your calculator

[alpine sable]

put what

[tall topaz]

The thing you’re trying to calculate

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[sour dove]

Hello, need some help with some Abstract Algebra:

[sour dove]

I'm stuck towards the end (I think)

Here's what I have

[sour dove]

@fiery chasm Hi this channel is occupied.

[fiery chasm]

Can you solve this

[sour dove]

no I'm asking on my own problem

head to #❓how-to-get-help

and open a free channel please

[ocean seal]

MellowDramaLlama

MellowDramaLlama

MellowDramaLlama

[sour dove]

So that's what I have so far

Then I tried this, but it didn't go anywhere:

[ocean seal]

MellowDramaLlama

[sour dove]

Buuuuut I'm not sure where to go from there

[lone heart]

@sour dove Has your question been resolved?

[sour dove]

.close

[lone heart]

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[native nebula]

help

[native nebula]

can you explain me what is happening in the solution?

[rough crown]

is the 2nd pic ur workings or solution

[native nebula]

my professor's

[rough crown]

wait lemme think abit

okay so do you know the sum of first n intergers (1+2+3+4+...+n)?

using summation of arithmeitc sequence it is n(n+1)/2

[native nebula]

yeah this I know

[rough crown]

lets call the sequence in the question T, sum of the first n terms in sequence T Gn, and the sum for first n integgers Sn
we can see that
G1 = 1 = S1
G2= 1+(2+3)= S(1+2)
G3= 1+(2+3)+(4+5+6)=S(1+2+3)
G4=1+(2+3)+(4+5+6)+(7+8+9+10)=S(1+2+3+4)
and so on
thus Gn = S(1+2+3+...+n)= S(n(n+1)/2)

Gn is the final answer

basically each term in the sequence T, we add an increasing number of integers

T1 we add 1 integer, T2 add 2 integer and so on

Adding them all up ie Gn , has (1+2+3+...n) integers in total, which is n(n+1)/2 terms
and so Gn is the sum of first n(n+1)/2 integers

[native nebula]

what is Gn?

[rough crown]

Gn is the sum of the first n terms in sequence T, which is the one in ur question

and expanding it would give us the sum of first n(n+1)/2 integers

which u can find easily

[native nebula]

Gn has (1+2+3+...+n) integers in total?

[rough crown]

yeah

first term has 1 int, 2nd term has 2, 3rd term has 3 and so on

add them all up and u have 1+2+3+…+n int

[native nebula]

terms is okay

but not integers

[rough crown]

?

[native nebula]

Gn has n terms

ohh

[rough crown]

yeah

[native nebula]

okay

[rough crown]

each term adds n integers to the sum