help-0

[tiny finch]

@tacit arch

[tacit arch]

do you know what derivatives are yet

if not give this a skim
https://tutorial.math.lamar.edu/classes/calci/tangents_rates.aspx

[lone heart]

@tiny finch Has your question been resolved?

[tacit arch]

@tiny finch

[tiny finch]

no not really

@tacit arch

[tacit arch]

did you read this yet

[alpine sable]

should I learn calculus 2 and 3 first or linear algebra

[tacit arch]

this channel's occupied. Ask someone in #discussion

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@tiny finch Has your question been resolved?

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[lilac imp]

how to get at that circled step from the last one

[worn fox]

https://www.examsolutions.net/tutorials/harmonic-identities/#:~:text=The Harmonic Identities%3A,≡ Rsin(x %2B α)

[lilac imp]

#precalculus

[lilac imp]

but what is " R "here ?

[worn fox]

tells you on the page

[lilac imp]

ya ya ty , my bad i overlooked

@worn fox is there any simpler way , like without using this indentity we can solve it ?

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[alpine sable]

Can someone explain me how the characteristic of a ring works?

[alpine sable]

Why is it useful?

I know that a ring A has char(A)=t means t is the smallest number such that 1+1+1+...+1 t times =0

But that means when I have something like t×a where a is an element from A it means that t×a=0?

Because it is a new concept for me

And it is confusing

Should I think about the characteristic of a ring like the order of 1 in the group (A,+)?

[mortal trellis]

well if that helps you

the easiest examples are just Z/nZ

[alpine sable]

This is true so?

[mortal trellis]

yes

[alpine sable]

And the characteristic of Z/nZ is just n right?

[mortal trellis]

yes

[alpine sable]

Thanks

But

What are the applications

Of the characteristic

[mortal trellis]

well its just good to know what you are dealing with

rings with characteristic 2 and 3 can have wildly different properties

especially 2

[alpine sable]

Lets call char(A)=t and a an element from A. So that means a^t is 1?

[mortal trellis]

no

[alpine sable]

but a^t=a^(1+1+1+...+1) t times why?

Can you explain me please

[mortal trellis]

and?

the 1 there is an exponent, an integer

not the 1 of the ring

[alpine sable]

Oh

Right

I understand

I need to get comfortable with the 0,1 notation

Thank you

.close

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[alpine sable]

Oh my

[alpine sable]

[robust geode]

Ow an arithmetic problem !

What's the latest maths chapter you have done so far ?

@alpine sable

[alpine sable]

Hcf and lcm

[alpine sable]

^*

Lol

[robust geode]

Nice

So

[alpine sable]

Ye

[robust geode]

12 cakes cost £2.5
8 sausage rolls cost £1.2

We want more than 60 cakes and more than 60 sausage rolls

But we want to pay the same price

And the minimum amount as well

Here I wrote a concise version of the problem

What's the price of 24 cakes ?

[alpine sable]

Internet is acting up so uh i may not get ur messages (hope this mssg delivers)

[robust geode]

It delivers

[alpine sable]

Okay, internet is working now

Lemme read ur mssg

[alpine sable]

£5

[robust geode]

Right, now I'll be asking in general

If I let k be a positive integer

Then what's the price of 12*k cakes ?

[alpine sable]

12 cskes cost 2.5 so 12k cakes will cost 2.5xk

[robust geode]

Right

The exercise states that we want more than 60 cakes, so what would be the something you could do based of this ?

[alpine sable]

Im confused on how to use hcf and lcm here

So ill just forget bout them

Anyway so

[robust geode]

Good thing, discovering where to use it is always a great way to approach a concept !

[alpine sable]

Um well 60 cakes cost 12.5

[robust geode]

Nice

What about sausage rolls ?

[alpine sable]

Um im getting 9

[robust geode]

Can you show your work ?

[alpine sable]

Wait nvm 11.25

[robust geode]

Can you show your work ?

[alpine sable]

Hai

Lo

[robust geode]

It was 1.2 pounds, per sausage box

Not 1.5

12 cakes cost £2.5
8 sausage rolls cost £1.2
We want more than 60 cakes and more than 60 sausage rolls
But we want to pay the same price
And the minimum amount as well

[alpine sable]

Sorry oof its 5amhere idk wats happening

Imma do it again

[robust geode]

I copypasted the concised version

[alpine sable]

60/8= 7.5 and 7,5x1.2 is 9

Nvm

I cant

Imma sleep

[robust geode]

Thanks, yup it was 9, I just wondered how you dealt with it

[alpine sable]

Wait

Can we still continue

If u want

[robust geode]

Of course

[alpine sable]

oh

[robust geode]

If you don't give up already of course

[alpine sable]

Ye

So 9 ye

[robust geode]

Nice, warrior

[alpine sable]

)-: thank you

[robust geode]

There was something fishy about that

Not that it was wrong

But do you see what the 7.5 represents ?

It was the result of 60 (sausage rolls) by 8 (sausage rolls per box), so it represents a number of ?

Boxes

Though, 0.5 boxes is ...

Meh

If they are bought per box, it's because these sausage rolls can't be separated from their box

8, 16, 24, 32, 40, 48, 56, ... 64 !

64 is the integer which is after 60 and is a multiple of 8

Remember, we want to pay the same price

Here is a representation which could help you

You want to figure out when a multiple of 2.5 is the same than a multiple of 1.2, when you simplify the exercise

An other thing I'll indicate to you is

We are comparing decimals here, but you use the lcm function for two integers

So I suggest you to make the problem be between integers

The problem becomes, indeed, about calculating the lowest common multiple between two integers. What are these two integers ? That should be the question you would ask yourself

Since you compare prices between each other, then let's multiply the prices by 10 in order to be able to compare their multiple as integers

£2.5*10=£25 and £1.2*10=£12

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[alpine sable]

😭 ok so, 12 cakes in 1 box which costs 2.50 pounds and so 60 cakes will be in 12.5 boxes and 1 box costs 2,50 so 12.5 will cost 31.25 and now 8 sausage rolls in each pack which cost 1.20 and so for 60 rolls, there will be 7.5 packs and 7.5 x 1.20 = £9

[alpine sable]

Message wont deliver coz internets bad again

Ugh

Lol

Omg 😂

.close

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[dark spade]

Hi, why are these graphs different if the bottom two equations should be equal to the top one?

[dark spade]

My work:

[fallen verge]

(2x/3)^(3/2) is not the same as (2/3)(x^(3/2))

[dark spade]

ah

one second

Lmao thank you @fallen verge

I should have kept the parenthesis

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[steep mantle]

this is what i have so far
is my graph correct and am i on the right direction

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@steep mantle Has your question been resolved?

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[wise jewel]

i need help

[wise jewel]

here's my work

I’m stuck at the last line

Do I just distribute now?

Or is that my final answer

[red sinew]

why dont you try multiplying everything in the parentheses by 2x^(1/3) first

and then calculating the derivative

its so much easier that way

[lone heart]

@wise jewel Has your question been resolved?

[robust geode]

I agree with that champ

🤌

[red sinew]

ayyyy i didn't know you were here too :D

[robust geode]

Of course I am! I knew you were there at the first place u know

Just came to be that you were at a place I looked at and boom

[wise jewel]

ohhhh

its just 12...

isnt it

g'(x) = 12 ?

[red sinew]

yepp

[red sinew]

noice

[robust geode]

That means g(x) = 12x+cst

That's when you know simplifying g would have been so much easier

Indeed if you were to use power rules, you would have got g(x) = 12x-8

[wise jewel]

i went through all that for nothing

gosh, thanks yall

[robust geode]

Hey

At least you'll remember to look for simplification first!

And you are welcome

By the way

[robust geode]

That's what kernel was explaining to you there

Basically we're trying to tell you to... Go smort smort about it

Does that make sense?

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[vale lichen]

hey, why is it wrong to just mulitply the two matrices that are given

so why is (AB)^-1 not A^-1*B^-1

it doesnt work right

so would the best route to take be inversing the matrices A^-1 and B^-1 then mulitplying them then inversing the result

[tardy stag]

the opposite of "putting on your socks and shoes" is "taking off your shoes and socks"

[vale lichen]

oh wait

[tardy stag]

$(AB)\inv = B\inv A\inv$

[ocean seal]

hayley!

[vale lichen]

ohhh

okay great

wait why is this the case

is it similar to how when finding the solutions using matrix equation you do

[tardy stag]

you can prove it fairly easily

[vale lichen]

AX=B ---> X=A^-1B

is it kinda similar to this

[tardy stag]

yeah

like

imagine you had uh

[vale lichen]

okay I guess Ill try it eventually

[tardy stag]

$ABx = c$

[ocean seal]

hayley!

[vale lichen]

mhmm

[tardy stag]

solve for x

sure, you could multiply both sides by $(AB)\inv$

[ocean seal]

hayley!

[vale lichen]

ahh

[tardy stag]

but do each one individually

[vale lichen]

but then yeah

youd get like matrix C

and then it would be the inverse of C mulitplied by c

is that what youre getting at?

[tardy stag]

not quite

starting with ABx = c

we can multiply by à on both sides

[vale lichen]

whats that fancy A

inverse of A?

[tardy stag]

A inverse

[vale lichen]

ok cool good to know

AHHH

[tardy stag]

(that's not really standard but would be understood)

[vale lichen]

So then itd be Bx = A^-1c

then x=B^-1A^-1c

[tardy stag]

yeah

[vale lichen]

so like it shows (AB)^-1 = B^-1A^-1

[tardy stag]

yep

[vale lichen]

okok greatness

amazing

thanks

whats the proof called

the actual legit proof for it

[tardy stag]

uh good question

[vale lichen]

np ill just somehow find it

should be easy enough

ok thanks for the help

.close

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[tardy stag]

https://proofwiki.org/wiki/Inverse_of_Matrix_Product

[vale lichen]

awesome

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[unborn geyser]

Help

[maiden glen]

|x+4| is always non-negative; at the very smallest, it is 0

so how small can the left side be?

[lone heart]

@unborn geyser Has your question been resolved?

[unborn geyser]

0?

[maiden glen]

it's 6|x+4| + 8

|x+4| can be zero

so the left is at least 6 * 0 + 8 = 8

which is greater than 7

[unborn geyser]

so what do i have to do

[maiden glen]

we've just found that the left side is always at least 8

regardless of what x is

so it's >7, regardless of what x is

[unborn geyser]

wait i just realize after the > is -

i thought that means no solution

@maiden glen

[maiden glen]

I don't see a minus anywhere

[unborn geyser]

i minus 8 to the right

[maiden glen]

so if you subtract 8 from both sides, you get 6|x+4| > -1

6 is positive, and |x+4| is zero or positive, so the left side is zero or positive, which is greater than -1

so the inequality holds, regardless of x

[unborn geyser]

oh yeah its only if equal sign

[unborn geyser]

dont i also divided both sides by 6

[maiden glen]

you can do that if you want

but the product of two positive numbers is positive

and the product of anything with zero is zero

so the left is zero, or positive

[unborn geyser]

x+4>-1/6

[maiden glen]

and the right is negative

don't drop the absolute value bars

it's |x+4|>-1/6

[unborn geyser]

i thought u drop it and make the right side also positive

[maiden glen]

you're trying to find for which x the inequality holds

|x+4| is >= 0 for all x

almost by definition

-1/6 is negative

so |x+4|, which is >= 0, is certainly greater than -1/6

for all x

so the original inequality holds for all x

[unborn geyser]

so whats the inequality

[maiden glen]

this is the question

[unborn geyser]

yeah

i mean the inequality equatio n thing

[maiden glen]

what are you asking

[unborn geyser]

Interval notation

@maiden glen so is the answer -inf +inf

[maiden glen]

yes, it holds for all real x

which is the same as x in (-inf, inf)

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[alpine sable]

Hey I'm taking AP Pre-Calculus this year as a Junior in High School. I was wondering which text book I should get to self-study, cause it's an AP class I don't know if I should get an AP Pre Calculus book or just a Pre Calculus textbook for self-study

[barren portal]

James Stewart, Mathematics for Calculus will be a good pick

He is also authored the famous calculus book

[alpine sable]

Ooh thank you

[alpine sable]

THATS EXPENSIVEE

WHAT THE HECKK

[onyx ingot]

Do any of you know how to do geometry 😭

[barren portal]

magbe get a used copy?

[tardy stag]

I'm curious what makes you think you need to self-study instead of just using the material (and book!) your school provides you?

[alpine sable]

I struggle to follow along with school

I have the notes and everything

But I would like to strengthen my knowledge before the exam

It's not that I'm self-studying

[winter shadow]

to be fair sometimes external resources teach better than schools

[alpine sable]

I'm just trying to understand more

Than what the school teaches

[tardy stag]

books are good if you think you can learn from them; there are also a billion videos available talking about all of the concepts you'll see, if that's your style. Either way, you probably want to do practice problems with solutions

[alpine sable]

@tardy stag Do you know what AP Pre-calc is?

[barren portal]

textbooks are great, as they contains tons of excercise to try

[tardy stag]

i have opinions about AP pre-calc (that it's weird since colleges don't offer credit for it, and that's kind of the whole point of AP classes) but I don't know the material in it

[alpine sable]

Do you know where I can get one online

[barren portal]

Yes, but I can’t disclose here

[alpine sable]

Right, it was either AP or traditional this year

So I picked AP

[alpine sable]

Can you send me in dms

[barren portal]

I perfer not to

See if you can find yourself

[alpine sable]

Alright

[barren portal]

mb

I have a moral standpoint in sharing pdf of textbooks with people

[alpine sable]

morals morals morals

np

Thanks for helping

[barren portal]

Wait

You mean used book online?

i thought you mentioning about pirated pdf?

[alpine sable]

Oh no

I was thinking of buying a used

[barren portal]

maybe try amazon idk

[alpine sable]

I mean I found the pdf

But I don't want to get arrested

So I'm not gonna use it

[barren portal]

did you find it in google search?

[alpine sable]

Yah

[barren portal]

All cool with that

Start studying have fun

[alpine sable]

YUHH

@barren portal

Also

[barren portal]

yes

[alpine sable]

Do you think it matters if I get an AP Pre calc book

Or just a pre calc book that you sent

Cause AP Pre Calc books are specifically for the exam

[barren portal]

well, precalc is all about practice

[alpine sable]

Yes

But AP Pre calc

Is about understanding the concepts and putting it into words

I thought AP books would help with that

On the exam

[barren portal]

In my opnion, this book is best on precalc so far

It’s written specifically so to excel in calculus other than the usual pre-requisite for calc

I suppose it will work for AP too

Stewart Calc for AP calculus works so does this i hope

[alpine sable]

Okk

I’m gonna go look for books at my local library

@barren portal I made a 68 on my first stat test

https://tenor.com/view/toddlers-and-tiaras-big-grin-excited-girl-giddy-smile-gif-25584914

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[drowsy charm]

I'm confused on how to set up the linear function, and which information is relevant and if there is any irrelevant information.

[tacit bobcat]

If there are 0 maintenance calls, what is the cost?

If there is 1 maintenance call, what is the cost?

[drowsy charm]

0

35, right?

[tacit bobcat]

No...

[drowsy charm]

How so?

[tacit bobcat]

Even if there are 0 maintenance calls, the cost is not 0.

[drowsy charm]

Ah

It's 600 then?

and then each call adds $35

[tacit bobcat]

Yes

Yes

[drowsy charm]

Ahhh i see

y=35x+600

[tacit bobcat]

Yes

You write it as C(x) = ...

No need to introduce a new variable y

When they tell you to write it as a function C of input x

[drowsy charm]

ahh okay

thank you!

[tacit bobcat]

Revenue is what you get when you charge customers

[drowsy charm]

I have R(x)=50x but what about the fact that the max amount of calls is 90 per month

is that irrelevant in this question

[tacit bobcat]

It's not

If you want to include that information

You can write something like
[R(x)=\begin{cases}50x &\text{if } 0 \le x \le 90 \ 0 &\text{otherwise}\end{cases}]

[ocean seal]

Watson

[tacit bobcat]

or even just 'undefined' otherwise

Or some other placeholder like (-\infty)

[ocean seal]

Watson

[drowsy charm]

okay

Would the same apply for this question like this?

or is it not needed in this case

[tacit bobcat]

Yes

You can write it in

[drowsy charm]

okay, sick

[tacit bobcat]

The profit is not 50x - 600 though

even within that interval

[drowsy charm]

15x-600?

50-35 to account for the cost per lawn

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@drowsy charm Has your question been resolved?

[drowsy charm]

<@&286206848099549185>

.close

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[torn patio]

Last Part

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@torn patio Has your question been resolved?

[quick halo]

What are you confused about?

[lone heart]

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[spare fern]

How would I find the equation whose roots are three times those of:

[spare fern]

$$x^2-14x+45=0$$

[ocean seal]

Lex1729

[quick halo]

Do you know Vieta’s formulas?

[spare fern]

No

[quick halo]

You could solve this equation first

[spare fern]

Okay so the roots are x=5, and x=9

[subtle birch]

do you know the roots coefficients relation?
Like x1 and x2 being roots of the equation x^2-14x+45 satisfy x1+x2=14 and x1x2=45

[quiet kindle]

Those are Vieta's formulas

[subtle birch]

yes I know

But I have seen cases where people just don't know the name they know the formulas

[quiet kindle]

Lex doesnt know the formulas, I am clarifying that those are the ones (:

[spare fern]

Oh yeah

wait but shouldn't a + b = -14?

[quiet kindle]

yes, the answers are -9 and -5 if I am not mistaken

(The roots)

[gray isle]

depends on what your variables represent

also ideally don't use a,b here as those are usually used to represent the coefficients and constant in general form

[spare fern]

That's strange cause my calculator says that the roots are x = 5 and x = 9

[quick halo]

Have you substituted back in to check your answers

[vale wigeon]

mistaken you are

[spare fern]

Yeah it should be x = 9 and x = 5

[subtle birch]

x^2-14x+45 can be factored as (x-5)(x-9). Here x=5 and x=5 satisfy x^2-14x+45=0

[quiet kindle]

Yes, if the roots are -9 and -5 then to get the answers you multiply by negative one

[quick halo]

the roots are the solutions, which are the answers

[gray isle]

if you want to factorise by splitting
then many would be more comfortable finding the pair that multiply to c=45 and sum to b=-14
(note that in this route, these pair of values don't actually represent the roots)

[quiet kindle]

In that case I apologise for the misunderstanding

[spare fern]

Alright so what would I do now after getting the roots?

[quick halo]

Your goal is to find the equation with roots three times that of the original one

So the new roots have to be 3(x_1) and 3(x_2), or 3*5 and 3*9, since you found them

[spare fern]

What should I use?

[quick halo]

Do you know how to find a quadratic with these roots?

[quick halo]

you could use m and n

or p and q

[spare fern]

alright so m + n = -14

and mn = 45

Oh I see since my solutions are x = 5 and x = 9

can't I just multiply both solutions by three then factorise

like this

(x-15)(x-27) = 0

[tardy stag]

yeah

[quick halo]

Yes, that way happens to be easy in this case, but if you were to use vieta’s formulas, that would also work

[spare fern]

Oh ok

[quick halo]

You’ve solved it

[spare fern]

And alternatively If I were to use Vietas formula how would that work?

[quick halo]

Suppose that the roots are x_1 and x_2. Then, x_1 + x_2 = 14 and x_1 x_2 = 45. The required coefficients of the new equation can be found like this:

new roots are 3x_1 and 3x_2, then 3x_1 + 3x_2 and 3x_1 * 3x_2 are the new coefficients

[spare fern]

hold on

[quick halo]

which are just 3(x_1 + x_2) and 9x_1 x_2

and you already know those

[spare fern]

why is it x_1 + x_2 = 14 and not x_1 + x_2 = -14?

[quick halo]

x_1 and x_2 are the solutions

In this case, 5 and 9

[quick halo]

It comes from how you multiply out (x - r)(x - s) = 0

[gray isle]

sum of roots = -b
(for monic quadratic, or more generally -b/a)

[spare fern]

Oh I see

[quick halo]

Oh, I’ve used a and b

It’s r and s now

better?

[spare fern]

So using Vieta's formula It would be like this:

m + n = 14

mn = 45

then multiplying both sides by 3 on each equation

3m + 3n = 42

(3n)(3m) = 405

[quick halo]

yes

[spare fern]

so x^2 + 42x + 405

that gives me roots of x = -27 and x = -15 though...

[quick halo]

not quite

[quick halo]

from this, you get x^2 - (r + s)x + rs = 0

so you have to subtract the sum of the roots

[spare fern]

Oh so x^2 -42x + 405

[quick halo]

Yes

You should find it has the correct roots

[alpine sable]

x²-14x+45=0
Or, x²-9x-5x+45=0
Or, x(x-9)-5(x-9)=0
Or, (x-5) (x-9)=0
Or, x-5=0
Or, x=5 ...(i)
Or, x-9=0
Or, x=9 ...(ii)

[quick halo]

Yes, he already found the roots

[spare fern]

Thanks for helping out 👍

[quick halo]

no problem

[spare fern]

.close

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[cerulean talon]

ignore the crosses on 10

forgot to remove those

okay so i’m unsure on how to find the amplitude and wavelength, considering i don’t have frequency

also unsure as to how i find amplitude

[strange meadow]

Are you meant to measure the amplitude

[cerulean talon]

well it’s digital..

let’s suppose i did

one moment

okay yeah it’s 1.3cm

[quick halo]

you can calculate the wavelength from the information given

[cerulean talon]

how do i do that?

[quick halo]

notice that the wave repeats

[cerulean talon]

yep

[quick halo]

so you can measure the length of the wave over one period

[cerulean talon]

oh right

6

[quick halo]

Including units is helpful

[cerulean talon]

in the table it’s left blank so i was going off that lol

[quick halo]

It’s written at the top

[cerulean talon]

okay

question 10

frequency = 3.3 recurring

correct?

1/0.3

@quick halo

[quick halo]

How did you get this?

[cerulean talon]

i did this

1/T

[quick halo]

How did you get the period?

[cerulean talon]

it says 0.6s of time

for the full thing

so half is 0.3 since there’s 2 waves

right?

[quick halo]

Yes

[quick halo]

You’re right

[cerulean talon]

but

when i times that by 6, it doesn’t equal velocity, or at least what it shows

it gives 20

[quick halo]

consider the units

it’s like with that question about the momentum of the ball you did

the units had to be converted

so it’s best to get used to writing the units always when doing physics

[cerulean talon]

oh, 0.06

okay i see, i’m dumb

sorry lol

thank you for the help

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[uneven isle]

I solved this question but quite tediously

i solved it by expressing the internal hexagon's area as a function of x

and then chain ruled d(area)/dt

as da/dx * dx/dt

which is just da/dx * 3

i was wondering if there are more convenient solutions than what i have done here

and paardon for bad formatting

[cinder sundial]

is this a high school math question

[uneven isle]

yep

[quick halo]

Observe that the area of the hexagon is at a minimum after 10 seconds

[mellow grail]

Can't u just do final-initial/10?

Is calculus necessary

[quick halo]

Because it is 3*10 = 30 cm along the perimeter of the hexagon

[quick halo]

It is asking for the instantaneous rate of change of the area after 10 seconds

[quick halo]

Which means it is exactly halfway along the edge

[uneven isle]

yep thats what i had done

[quick halo]

and the hexagon is just between growing and shrinking

[mellow grail]

Instantaneous isn't mentioned

[quick halo]

therefore the rate of change is 0

[uneven isle]

i mean i can understand that logically

but i have to prove it mathematically if that makes sense

[quick halo]

You can prove it mathematically by saying that it is at a minimum, and the derivative at a minimum is always 0

[uneven isle]

ah fair

i guess teachers probably wont care enough to make me prove that area is minimum when half way

[quick halo]

but that is identical to the explanation

[quick halo]

you could say the side length is least

or appeal to symmetry?

[uneven isle]

mhm yeah ig

well i just wanted to see if theres any other big brain ways to do it

thats all, thx for the help

.close

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[barren portal]

Here they used tree diagram to do so, can you help to figure out alternatively and also help me with the reasoning of it?

[quick halo]

can you show the tree diagram?

[vale wigeon]

there is a very slightly better method

[barren portal]

can you motivate me ?

hopefully I can scribble a bit and see with that help

[vale wigeon]

basically make a diagram of all possible intermediate scores

[barren portal]

Is the quantity 5 choose 3 useful?

[vale wigeon]

dunno

i did it without

make a diagram of all possible intermediate scores during the playoff and count the number of ways to get to each

like this

[barren portal]

Let me try

Is the answer being 2* 5 choose 2 a coincidence ?

[vale wigeon]

could probably come up with a way to say why it isnt

but i cbf

[barren portal]

alr

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[median vessel]

why does this approach negative infinity?

[echo socket]

The top can be factored as (x^2 - 1)(x + 1), which is negative near 0

[median vessel]

Ok thank you!

[echo socket]

Close the channel if you have no other questions

[median vessel]

how do i do that

[echo socket]

Type .close

[median vessel]

.close

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[mellow skiff]

e^1+lnx

[ember trail]

What is the question ?

[alpine sable]

e^1+lnx duh /s

@mellow skiff Bit more info wouldn't hurt

[white crater]

also do you mean e^(1 + lnx)

or actually (e^1) + lnx

[alpine sable]

Probably the first since no Reason to specify ^1

In that former case it at least simplifies a bit nicely

[white crater]

ye

but never hurts to make sure

[opal jolt]

there's no question here

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[high palm]

I don't know how to start

[atomic harbor]

What's the slope of a line that makes 45° with the x-axis?

[opal jolt]

they are giving you data for 3 slopes.
You need to find the points where in the curve given, the tangent has that slope

[high palm]

1

[atomic harbor]

Yeah right

So when does the slope of a line tangent to the curve y=x^2-5x+6 equals 1 ?

[high palm]

When x = 3

do I differentiate it

f'(x) = 2x-5

[atomic harbor]

Yes

What point that corresponds to on the curve y = x^2-5x+6 ?

[high palm]

what?

i dont understand

[high palm]

but how

[atomic harbor]

I mean x coordinate is 3 but the point is (x,y) so writr it in that form

[high palm]

oh

(3,1)

[atomic harbor]

Yes

For b
Just note that parallel lines have ____ slope?

[high palm]

-3

[atomic harbor]

Yep

[opal jolt]

on the first one they gave you slope data in the angle with horizontal
on the second one, with the implicit function of another line
on the third, with another line and the "perpendicular" condition.

having the slope, as you've done in (a), you can compute where it happens

[high palm]

ok so for the second

the gradient is -3

for wherever this point lies on the curve

[opal jolt]

correct

you'd call it slope because it's for a tangent line, but yes

[high palm]

how do i go about calcualting it

i dont undersatnd why i even differentiuate it

why cant i use the original equation

[opal jolt]

The derivative gives you the slope of the tangent at each point

[high palm]

how so?

[opal jolt]

if you have the slope of the tangent, you can calculate the point

[high palm]

say in this e.g.

y = x^2-5x+6

ill differentiate it

[opal jolt]

it's the definition of derivative, the slope of the tangent to a curve

[high palm]

y = 2x - 5

how is the slope of the tangent at each point

is it not the slope of the tangent at A point?

this is where i am confused

becuase y = 2x-5 doesnt move

its a single line

[opal jolt]

okay, what's the value of the derivative for x=0?

[high palm]

y = -5

[opal jolt]

,w graph x^2-5x+6

[ocean seal]

Results provided by WolframAlpha

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

Requested by lordfelix

[opal jolt]

does it look like the tangent at 0 has slope -5?

[high palm]

yes

i can believe that

[opal jolt]

repeat at x=2.5. What's the value of the derivative?

[high palm]

y = -0.5

or somethign

[opal jolt]

you had it right before

[high palm]

0?

i know thats the derivative

but its not the y value is it

[opal jolt]

y=2x-5, so for x=2.5, y=0

does it look like the tangent at 2.5 has no slope (is horizontal)?

[high palm]

oh

i see

[high palm]

so when i do this with the derivative equation

the tangent equation

y gives me the slope

[opal jolt]

the derivative gives you the slope of the tangent wherever you want

[high palm]

not hte actual value

[opal jolt]

but only the slope of the tangent, not the actual tangent

[alpine sable]

y'=0

[high palm]

ah ic

makes senes

[opal jolt]

now, when they say something along the lines "the tangent is parallel to THIS", it means it has the same slope

so you know what the result of the derivative has to be, and have to compute where it happens

[high palm]

ic

[opal jolt]

instead of you saying "i want the slope at x=3", you do "my slope is y'=78, what x gives me that?"

[high palm]

ic

make ssen

eses

sense

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[upbeat eagle]

Hi

[upbeat eagle]

---

If the question said for
4.A x^2 +3x -4

B.i) y=1/2 x^2 +3/2x +2

.

What would the transformation be?

y= 1/2 f(x)

^ Is what I think it is

[tepid drum]

do you mean $y=\frac{1}{2x^2}+\frac{3}{2x}+2$

[ocean seal]

calculus is fun

[upbeat eagle]

Yes

Its the same thing no?

[tepid drum]

and the one below it is $y=\frac{1}{2f(x)}$

[ocean seal]

calculus is fun

[tepid drum]

?

[upbeat eagle]

The one bellow y = 1/2 f(x)

[tepid drum]

oh so $y=\frac{f}{2}$

[ocean seal]

calculus is fun

[upbeat eagle]

This

[tepid drum]

ok wrong

[upbeat eagle]

This

Y = 1/2 f (x)

[tepid drum]

yea wrong

[upbeat eagle]

Would it be then f (x/2)

But that doesnt make sense in my head because the 4 goes to the 2

and there is no x with 2

So it has to be
? f(x)

[tepid drum]

$f(x)=x^2+3x-4 \implies \frac{f(x)}{2}=\frac{x^2}{2}+\frac{3x}{2}-2$

[ocean seal]

calculus is fun

[tepid drum]

what i just typed is this

[tepid drum]

this is another story

[upbeat eagle]

ok

.

Isnt this the same?

[tepid drum]

here did you by any chance mean $y=\frac{x^2}{2}+\frac{3x}{2}+2$

[ocean seal]

calculus is fun

[tepid drum]

yes it is

[upbeat eagle]

Yes

I meant that

[tepid drum]

ok this is slightly wrong

the mistake is the sign of 2

[upbeat eagle]

Oh right yes sorry

I mean -4

to -2 not +2

[tepid drum]

it was -4 you divided by a positive number so sign doesnt change

[tepid drum]

yes exactly

[upbeat eagle]

Yes my bad

[tepid drum]

now f(x/2) is just f(x) but with every x replaced by x/2

[upbeat eagle]

.
Another question if you dont mind

So for the 2f(x)

Would it just be
2 x^2 + 6x - 8

.

For the -f (x)

Would it just be
-x^2 - 3x + 4

.

Is it possible to do

2 x^2 + 6x - 4 With somekind of y= f(x)

UWU SEMAPIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

[brave kayak]

2f(x) - f(x) = f(x) =x^2+3x-4

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[upbeat eagle]

It is?

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[upbeat eagle]

Oi

[upbeat eagle]

Thats smart thank you sry for ping

< 3

nvm

Doesnt work

Ill try and figure it out

Idk

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[upbeat eagle]

Hello

[upbeat eagle]

So for the 2f(x)

Would it just be
2 x^2 + 6x - 8
.

For the -f (x)

Would it just be
-x^2 - 3x + 4
.

Is it possible to do

2 x^2 + 6x +4 With somekind of y= f(x)

[proven leaf]

you're attempt is correct, yes but I don't understand what this part is asking?

2 x^2 + 6x - 4 With somekind of y= f(x)

[upbeat eagle]

Is it possible to change the x values

Only and leaving the 4 alone

If that makes sense

[proven leaf]

well that would be a whole different function then

f(2x) will get the closest but that'd be 4x2+6x-4

[upbeat eagle]

If you dont mind how do

f(2x) work

[proven leaf]

put 2x in for every x :)

[upbeat eagle]

Im a bit stuck on functions tehe

[proven leaf]

$(\textcolor{red}{2x})^2+3\cdot\textcolor{red}{2x}+4$

[ocean seal]

MrFancy

[proven leaf]

that make sense? :)

[upbeat eagle]

It would be for ? x^2 +4x +4

Oh yes makes sense

Bro 1.20h on functions fk me

Thank you

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[alpine sable]

What kind of rule of pattern did this use

[alpine sable]

.close

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[vapid stratus]

How do I find conditional probability of Y given X

[vapid stratus]

I cannot find any references or formulas online to do it so im confused how to proceed

<@&286206848099549185> anyone around 😢

[atomic turtle]

Yes

[vapid stratus]

phew can ya help a bit on this @atomic turtle 😢

[small ridge]

hi

[vapid stratus]

hello

any help anyone?

if someone from statistics

[vapid stratus]

. I cant proceed

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[hybrid meadow]

when do we need to calculate two eigenvectors for a repeated eigenvalue and when not

[hybrid meadow]

example being this case:

where we only have one eigenvector

but some repeated eigenvalues have two eigenvectors

[worn fox]

you just need to find all of them, whatever that amount might be

there can be at most n eigenvectors for an eigenvalue, where n is the n that appears in (x-lambda)^n, the biggest power of (x-lambda) that appears in the char poly

[hybrid meadow]

but by that account (lambda -5)^2 should have two eigenvectors but in the answer sheet theres only 1 eigenvector given namely (1,-2)

[worn fox]

"can be at most"

[hybrid meadow]

and how do you know if there are more you need to calculate?

[worn fox]

theres no way in general to figure out how many there might be other than to solve the system and see how many linearly independent solutions you get

[hybrid meadow]

would you happen to have any pro and contra examples just to get a feel for it

[pallid scarab]

You only "know" you're gonna get at least 1 eigenvector, and AT most "n" linearly independent eigenvectors for a given eigenvalue of degree n

Here I already know that without calculating the eigenvectors, there's only gonna be 1

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@hybrid meadow Has your question been resolved?

[hybrid meadow]

alright wait ill give it more of a try to figure this out and then come back, because im still not sure how you "know"

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[eager anvil]

does this have no domain?

[jagged cobalt]

it can take negative inputs, but the output would then be imaginary, so if working purely in the reals, then it has no domain i guess

[eager anvil]

oh alright, thanks

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[vital brook]

Hi can someone help me with this

[vague coral]

let z = a+ib

[vital brook]

yea

[vague coral]

the rest of the work is just algebra

[vital brook]

like i know im trying

to show that z isimaginary or 0

but like how do i do that

[olive iris]

I dont know but i will try to make two eqatuions

One i will assign it to 0 (equation = 0)

And the second i will assign it to i

[vague coral]

just write z/(z-i) in the form x+iy
and show that y = 0

[olive iris]

And again idk that much

It migt be wrong

[vital brook]

I think in a "show" question you cant really start off with what you're trying to prove

[vital brook]

okk

lol gimme a sec i did smth wroin ggotta redo

[olive iris]

I got an answer from chatGPT

Here it is:

To show that z is either imaginary or 0 when z/(z - i) is real, we can start by writing out the expression for z/(z - i) and simplifying it:

Let z = a + ib, where a and b are real numbers.

Now, z - i = (a + ib) - i = a + (b - 1)i.

Now, let's calculate z/(z - i):

z/(z - i) = (a + ib) / (a + (b - 1)i)

To make this expression real, the imaginary part of the denominator (b - 1) must cancel out. This means b - 1 = 0, or b = 1.

If b = 1, then z = a + i. In this case, z is imaginary.

If b ≠ 1, then b - 1 ≠ 0, and z/(z - i) will have a non-zero imaginary part, so z is not imaginary.

Therefore, z is either imaginary (if b = 1) or 0 (if b ≠ 1 and a = 0).

Idk if it is true or not

[pallid scarab]

!nosols

[lone heart]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[pallid scarab]

Also NEVER ask ChatGPT math solutions

They're bad and not useful

What it wrote here is completely wrong

[vital brook]

how can i get the other solution that it can be imagineary?

[pallid scarab]

This is one way to do it

[vital brook]

but

how do i get the other solution

of z bneing imaginary

[pallid scarab]

You've shown a = 0

So z = bi

[vital phoenix]

it's an or question

[pallid scarab]

Is imaginary

[vital phoenix]

^^

[pallid scarab]

Also 0 is technically imaginary

[vital brook]

ooo yea

i forgot it said the other equation was real i thoughnt it was z

okay

thxxx

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[alpine sable]

My working is on the left

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[tall talon]

Is this statement true?

$\mathbb{N}=\left{n:n\ge 0\wedge 1\left|n\right}$

[ocean seal]

themathboi #2137
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

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[jagged cobalt]

is that 0 and 1 divided by n?

[echo socket]

It says "n >= 0 and 1 divides n"

[jagged cobalt]

ah okay

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[dense lily]

i need to do the following binomial = 2x^2 + 2x - 12

[dense lily]

basically i have to simplify them into binomials

i cant think of two things that multiply to get -24 but subtract to get 2

like how bro

6 - 4?

[winter shadow]

6-4 does indeed work

6-4 is 2 and 6*-4 is -24

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[rotund plank]

has this problem been answered correctly?

what I don’t understand is that it seems like (from the way they took moments about A) that they have assumed that the line of action of the weight, and the ladder are in the same vertical plane

I think it makes sense that the ladder should be perpendicular to the edge but I don’t understand why it should touch the box at the midpoint of the edge

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@rotund plank Has your question been resolved?

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@rotund plank Has your question been resolved?

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@rotund plank Has your question been resolved?

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@rotund plank Has your question been resolved?

[ancient saddle]

Hello. That's because the weight goes across the center of mass. In this case, the box is assumed to be homogeneous, so it's center if mass is at its middle point

This is 2D dynamics, so you can assume that all forces are in the same plane of action unless otherwise is specified

[rotund plank]

it’s a 3D box though?

a cuboid

[ancient saddle]

You can think of it as a wide homogeneous ladder on the upper side of the box

[rotund plank]

oh right

[ancient saddle]

Or also you can think that the ladder is exactly at the middle of the side

Anyway, at this level you should assume that I guess

[rotund plank]

I was imagining the ladder to have zero width, but yep it definitely makes sense that it has width

[ancient saddle]

I'm not sure what you mean by this 🤔. The reaction force is what is perpendicular to the ladder