help-17

[lime gorge]

$y’ = n \left (\frac {1 + \sin x}{\cos x} \right)^{n-1} \cdot \dv {y}{x} \left (\frac {1 + \sin x}{\cos x} \right)$

[lime gorge]

Is this what u got

[lyric moon]

Wait

No

It should be cosx*2

[lime gorge]

What does * represent

[lyric moon]

U mean the 2?

It's an exponent

But not for the the x

(cosx) *2

[lime gorge]

Use ^ for exponent

Not *

[lyric moon]

Oh mb

[lime gorge]

Ok so

How did u get (cosx )^2

[lyric moon]

Using the quotient rule

[lime gorge]

Ok so, upon using quotient rule, I get:

$\frac {(\cos x)^2 - (1+\sin x)(-\sin x)}{(\cos x)^2} = \frac {\sin x + 1}{\cos ^2 (x)}$

[lyric moon]

Mhm

So

[lime gorge]

And simplifying gets me

[lyric moon]

(cosx) ^2+sin^2x = 1

1+sinx/(cosx)^2

[lime gorge]

Ok good

[lyric moon]

Yeh

So what I've tried is

[lime gorge]

$y’ = n \left (\frac {1 + \sin x}{\cos x} \right)^{n-1} \cdot \dv {y}{x} \left (\frac {1 + \sin x}{\cos x} \right) = n \left (\frac {1 + \sin x}{\cos x} \right)^{n-1} \cdot \frac {\sin x + 1}{\cos ^2 (x)}$

[lime gorge]

Yes?

[lyric moon]

Simplifying it to sec^2xtanxsecx

Btw it's a multiple choice

[lime gorge]

I simplified it to this

[lyric moon]

Ok

[lime gorge]

I’m not seeing any answer choice look like this lol

There’s not even any exponent to the power of n

[lyric moon]

Ik that's why I stayed for like an hour

[lime gorge]

Can you show where u got this from

[lyric moon]

Im tryna find a question like that but I really can't

The professor wrote it out

[lime gorge]

Yea the most I’m getting is

$\frac {n(1+\sin x)^n}{(\cos x)^{n+1}}$

[lyric moon]

Isn't 1+sinx -cos^2x

[lime gorge]

Show me how u got that

[lyric moon]

So

Cos^2x+sin^2x=1

Oh wait nvm

That's 1+sin^2x

[lime gorge]

U gotta show me ur work

[lyric moon]

It's really all over the place so u wouldn't understand anything

[lime gorge]

Ok then just write it out clearly

[lyric moon]

y = n(secx + tanx)^n-1 * (sec^2 x * secx * tanx)

[lime gorge]

Sec^2 x + secxtanx

Not *

Yes

Now what

[lyric moon]

That's the most I got

[lime gorge]

Use exponent rules on the n-1

[lyric moon]

Wdym

It's not -n

[lime gorge]

a^(n-1) = a^n / a

Use that

[lyric moon]

U sure that's the only way?

We won't get to any of the final answers this way

[lime gorge]

Why do you say that

None of the answer choices have exponent anyway, what’s the point

[lyric moon]

Cuz then we would end up with a denominator with a ^n+1

[lyric moon]

Yea im tryna figure out how to get rid of it

[lime gorge]

U can’t get rid of exponent

The answer choices are wrong

[lyric moon]

U sure?

[lime gorge]

Ye, doesn’t make sense that there’s no exponent

[lyric moon]

I think some way some how the exponent moved to y

Ima just go to the next question and leave this one for last so i don't end up late

[lyric moon]

Alright so do you any clue?

[lime gorge]

About what?

[lime gorge]

This is it

The answer choices are wrong

[lyric moon]

I doubt it tho

[lime gorge]

🤷‍♂️idk what to tell u

[lyric moon]

Cuz these questions are from a previous test

From last year I think so it's mostly right

[vocal sleet]

@lyric moon Has your question been resolved?

[vocal sleet]

@lyric moon Has your question been resolved?

[lyric moon]

Yo brotha

I think I figured it out

Just want to make sure

So what I did

Is I simplified it before derivation

As in y = (secx + tanx) ^n

So no quotient rule here

Then n(secx + tanx) ^n-1 (sec^2 x + secx tanx)

After that u factor out a secant which is secx on the second part so it becomes (secx + tanx)

(secx + tanx)^{n-1} * (secx + tanx) = (secx + tanx)^n

Now we have n secx (secx + tanx) ^n

And as u can see the y = (1+sinx/cosx)^n which is the same as (secx +tanx) ^n

So it becomes n secx y

Which is b) ny secx

Thanks for ur time brotha I really appreciate it, may u have a good day/night

[lime gorge]

omg

i didnt even realize the answer had a 'y'

yikes

good catch

[vocal sleet]

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[trim portal]

can anyone tell me what i did wrong pls i dont get it

[trim portal]

thats the soltuion btw

[wary granite]

In your last step, when you multiply both sides by x(x-2)(x-3) to get rid of the bottom, 2x/(x-2)(x-3) turns into 2x^2

And also -(x^2 - 4) = ?

[trim portal]

do i have to to multiply by x-3 here?

[wary granite]

Can you tell me what you did in the last step to get 2x - x² - 4 = x² -9

[trim portal]

just collected all the info i had

but in the solution he has x'2+4

i think i had to do this for the 2nd task?

[wary granite]

One way to approach questions like this, is to see what you have in the denominator, in your case it's x, (x-3) and (x-2)

If we multiply both sides of the equation by them, you'll get rid of the denominators and get a cleaner equation

[trim portal]

so i have to do this?

[wary granite]

Sorry I'm not quite sure what you mean by "doing" that, u mean multiply that to the equation?

[trim portal]

yes

[wary granite]

u don't have (x+2) in the denominator though

[trim portal]

but above i have

dont i have to multiple the above with the one down

[wary granite]

We're trying to multiply something to the equation to cancel out the denominators

[trim portal]

yeah so this is rigth than no?

[wary granite]

Multiplying (x+2) won't cancel out anything though

[trim portal]

but x-2 x-3 is the divider no?

[wary granite]

Yep, and also x

[trim portal]

x too?

sec let me try it rq again

[wary granite]

Yea x is in the denominator as well

[trim portal]

like this?

[wary granite]

uhhh.. sorry no, let's do an example rq

[trim portal]

can you go call

[wary granite]

I can't sorry

[trim portal]

k

[wary granite]

For the example though, do you agree that
1/3 + 2/3 = 1

[trim portal]

ye

[wary granite]

Can you write what happens if we multiply both sides of that by 3

[trim portal]

3/3+6/3?

[wary granite]

Yep

And that turns into 1 + 2 = 3

[trim portal]

yep

[wary granite]

So imagine if we take the 3rd line you've written here, and multiply it by the things we have in the denominator

x, (x-2) and (x-3)

[wary granite]

That way you can cancel out the denominators, just like 3/3 and 6/3 got simplified to 1/1 and 2/1 here

[trim portal]

yeah

[wary granite]

So $\frac{(2x)(x)(x-2)(x-3)}{(x-2)(x-3)} cancels out to (2x)(x)$

[twin meteor]

nima

[trim portal]

yeah i think i got it now

[wary granite]

And the same thing goes for all the other ones

[wary granite]

Awesome give it a try

[trim portal]

yeah just a sec

ok so now i dont know what i did wrong again xD

[wary granite]

Fine till the 3rd line, after that -x² on the left and the x² on the right vanish

And uhh, they shouldn't vanish

[trim portal]

but i have 2x'2 and -x'2 and on right site x'2

so one stays

i think the solutions are wrong no?

[wary granite]

2x² - x² = x²

[trim portal]

oh fuck

im retardet

[wary granite]

Naaa everyone's been there

[trim portal]

thanks a lot for all the help im gonna sleep now gn

[wary granite]

Cheers, have a good night

[vocal sleet]

@trim portal Has your question been resolved?

[vocal sleet]

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[craggy mango]

So, Im just confused how to go about this after using the avg value formula

I have 1/12 * the integral f(x) dx with bounds [-5,7]

Idk what to do after that though

[vocal sleet]

@craggy mango Has your question been resolved?

[craggy mango]

<@&286206848099549185>

[uneven summit]

ok, you're allowed to use integrals

first thing i see with this graph is that it is made up of 3 different graphs

so break up the problem into 3 problem

[-5,-1] [-1, 5] [5,7]

[craggy mango]

as in, [-5,-1], [-1, 5], [5,7]

yeah

[uneven summit]

figure out f(x) for each one of those ranges

integrate f(x) over each one of those ranges

add them together, then divide by the total range

[craggy mango]

well

thats what im stuck on

idk how to figure out f(x)

[uneven summit]

yea... the graph isnt the clearest

[craggy mango]

unfortunately

[uneven summit]

like im assuming for [-5, -1] f(x)=4

[craggy mango]

i understand that part

but the rest i have no clue

[uneven summit]

[-1,5] looks like f(x) = -x+3.5

[craggy mango]

bc the lines arent even whole numbers

they're decimals

[uneven summit]

whats wrong with decimals

unless they actually give you f(x), your best estimate is all i can say

[craggy mango]

nothing if the lines were correct

but notice

the lines arent going by .5

so its not 3.5

nor by 1

theres 5 lines between 0 and 5

xDD

so its more like

idk

2.75?

like idek

[uneven summit]

ok fine, use (-1, 4) and ( 5,-2) as the 2 points

[craggy mango]

but

wait

see this is why im confused

[uneven summit]

determine the slope, use point slope formula

[craggy mango]

the points are wrong

f(x) = 4 is also wrong

[uneven summit]

well, im assuming that teh graph just sucks and is off by a couple pixels

otherwise its impossible

[craggy mango]

that line isnt even y = 4

also its like slightly under the line

if you zoom in

this question is aids

i mean i can tell you the answer bc my prof gave us the answer key

but i cant tell you how they got there

[uneven summit]

welp, then all you can do at this point is complain to the prof

what does the answer key define f(x) as?

[craggy mango]

it doesnt

it just says the avg value is 5/3

[craggy mango]

idk if this helps

[vocal sleet]

@craggy mango Has your question been resolved?

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[craggy mango]

.reopen

[vocal sleet]

✅

[craggy mango]

<@&286206848099549185>

[craggy mango]

bruh

ive been needing help for over 2 hrs ;/

.close

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[vocal sleet]

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[leaden jacinth]

any thoughts, diff eq

[runic harbor]

UGH

[dense orbit]

UGH

[runic harbor]

😭

[dense orbit]

QUE VENGUENZA!

[leaden jacinth]

SLOW

TOO SLOW

[dense orbit]

I don't think that's possible to solve for y in terms of x

explicitely

[leaden jacinth]

wondering if its possible in terms of x

try to get x' + x = something

[dense orbit]

wdym

[leaden jacinth]

ah i think i got it

(x - siny)dy = tanxdx

divide by dy and subtract x you git

siny = tanx*x' - x

and i think that might be solvable

[dense orbit]

yep there you go

[leaden jacinth]

im simply him

gg

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[dense plover]

!help

[vocal sleet]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[inner osprey]

do you know what an integrating factor is

[leaden jacinth]

yeah i just needed to get it setup first

i kept trying to solve for dy/dx,

but solving for dx/dy seems easier

and i think dy/dx is impossible to solve for

[inner osprey]

for non-exact differential equation

then,

in this case it does happen one of these is a valid integrating factor

[leaden jacinth]

ive never seen this thm of the integrating factor before

can you link where you got this from

[inner osprey]

search this term

[leaden jacinth]

ok cool i see, thats a very neat trick

i dont think thats even in our book

[vocal sleet]

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[coral notch]

i need help on part c

[coral notch]

this is a geometry/algebra class, is there any approach/solution to this that doesnt use calculus?

[vocal sleet]

@coral notch Has your question been resolved?

[lavish river]

u can easily tell that the optimal path would be to travel from A to X to P where X is on NP

let NX = x and form equations on x

[coral notch]

yeah i did that but idk where to go on from there, i got three equations: sqrt(10^2 + x^2) and x, and 25-x

nvm i got it

.close

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[civic scarab]

I am in 9th grade and i am struggling with basic co-ordinate geometry can somebody explain basic chapters like locus,section formula,equation of a straight line to help me get a better understanding in co-ordinate geometry

[civic scarab]

<@&286206848099549185>

[lavish river]

do u have a textbook?

[civic scarab]

Yes

I dont understand anytttthing of my freaking teacher

failed the first exam

[lavish river]

read the textbook and come back with specific things u do not understand about it

[civic scarab]

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[crisp zenith]

if we have a vector space of 4 dimensions

[crisp zenith]

and we have two vectors of that vector space

are there any two vectors we can choose such that it spans the vector space

it would be no right

yeah

we need atleast 4 vectors to span the vector space

was asking this for part c

if the rank is 2

then the nullity is 4

so the dimension of the null space is 4

meaning we need 4 basis vectors to span the null space

we only have X1 and X2, so those two alone can’t span it

is what I believe, s that right?

[heavy yoke]

if you have a space of dimension 4, then 2 vectors can't span it, yes

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@crisp zenith Has your question been resolved?

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[spice ingot]

I need help on question 7

[wary granite]

If we represent coins of annabelle, betty, cynthia and dora with a, b, c and d, u can write the info given to you in terms of a,b,c,d

[vocal sleet]

@spice ingot Has your question been resolved?

[sullen shoal]

Hello

@spice ingot u there?

[spice ingot]

yes

[sullen shoal]

Ok so

First consider a,b,c,d

These are the unknowns u have

For 1st line

He said c = (a+b)/2

Agreed?

[spice ingot]

yes

[sullen shoal]

Mhm 2nd line

What would the equation be?

Hm?

[spice ingot]

a = b*2?

[sullen shoal]

They said "half"

[spice ingot]

a = b/2

[sullen shoal]

Yes

And 3rd?

[spice ingot]

b = d

[sullen shoal]

And the last one?

[spice ingot]

d = c+10

[sullen shoal]

Yes

Now solve these 4 equations

Ull get right

[spice ingot]

130?

[sullen shoal]

What is 130?

[spice ingot]

the answer

[sullen shoal]

Yes correct

[spice ingot]

thx

[sullen shoal]

Anytime

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@spice ingot Has your question been resolved?

[spice ingot]

Yes

[vocal sleet]

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[pallid flume]

need to prove that p^2 - 8q - 11 doesn't equal 0 for any integers p and q

[pallid flume]

p^2 = 8q + 11

since p is an integer, p^2 is a perfect square

how do i prov e that 8q+11 isn't

[distant eagle]

Do you know about integers modulo n?

[pallid flume]

nope

[distant eagle]

Then try dividing each side by 4 and finding what the remainder could be, depending on p and q

[pallid flume]

p^2/4

= 2q + 11/4

remainder

as in

3?

[distant eagle]

I mean euclidean division

p^2 = 4c + r for 0 <= r <= 3

For example 8q + 11 = 4(2q+2) + 3

So the remainder is 3

What about the left hand side?

[pallid flume]

the left hand side

the remainder is either 0 or 1

[distant eagle]

So the remainder is different in both cases

[pallid flume]

yeah

it depends on

whether r is 0,1,2 or 3

[distant eagle]

Thus they can't be the same number

[pallid flume]

righttt

if they were they same number then

dividing them by 4 would give the same remainder?

[distant eagle]

Yes

[pallid flume]

ok tysm

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[prisma wyvern]

hi my friend is asking me if she is right and i dont know cuz we dont have a topic like this

[hybrid flicker]

uh

I'm guessing the middle columns are the ones that reflect the actual statement

[prisma wyvern]

yess

i dont know this topic my friend asked me if its right or no ,-,

[hybrid flicker]

cause rn I'm having a hard time reading this

[prisma wyvern]

same

[hybrid flicker]

so say table for P Q R is:
P : T T T T F F F F
Q : T T F F T T F F
R : T F T F T F T F

[dark kiln]

looks right

[hybrid flicker]

Q must be false for the first one to be possibly true

so 5th value doesn't add up

can only be false

[prisma wyvern]

im sry but i cant understand anything im just sending screenshots to her XD

[hybrid flicker]

alr

in any case table on the left is F F ? ? F F ? ?

so now suppose q is false

[prisma wyvern]

uh she said

[hybrid flicker]

this thing is now true under those conditions so disregard it

[prisma wyvern]

p is true q is false

[hybrid flicker]

uh

p isn't necessarily true on the left expression

[prisma wyvern]

she said not me ,-,

[dark kiln]

yeah number 5 is wrong

[hybrid flicker]

left expression is equivalent to $\neg q \wedge (p \Delta r)$

[twin meteor]

rafilou2003

[hybrid flicker]

so

either p true r false

or p false r true

F F F T F F T F

is the left statement

[prisma wyvern]

okkk

[hybrid flicker]

now right statement

when is "p or q" the same thing as "not q and r"

either both are true or both are false

if both are true, then it's p and not q and r

if both are false, then it's not p and not q and not r

[prisma wyvern]

im sending screenshots to her xD sry if im not understanding anything rn

[hybrid flicker]

so

p and not q and r is number 3

not p and not q and not r is number 8

F F T F F F F T

F F F T F F T F not equivalent to F F T F F F F T

@dark kiln if you're interested in checking my correction just to make sure

[prisma wyvern]

she get it now

is she wrong tho?

[hybrid flicker]

any correct answer without the correct justification is wrong

[prisma wyvern]

Ooooo thankss

tyyyy for the help

ill be closing the help thingy now byee

thxx

.close

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[hollow thorn]

Hey, can someone help me take a look which row did i went wrong at this prove thing?

[edgy gulch]

i think you can switch everything to sin and cos after the 4th line

[hollow thorn]

how bout i change it initially ?

[edgy gulch]

i guess you can try

[hollow thorn]

Uhhmmm what to do next cuh?

[edgy gulch]

holy this looks horrible lol

bad idea

[hollow thorn]

Yea 😂

[edgy gulch]

its easier if you change it after the 4th line

tanAsec²A / (1-tan²A)

change this to all sin and cos

[hollow thorn]

Lemme try

[fast warren]

hey, change ur sin2A too

and u will see the answer

cuz it cancels

[vocal sleet]

@hollow thorn Has your question been resolved?

[hollow thorn]

Yea cool i did it

How bout this question?

How cos theta turns that form ?

[warm turtle]

I simplified it a little, you can change cos(2A) to whatever you need to solve it

[hollow thorn]

Wow... Definitely a good idea tbh thank you so much @warm turtle

Appreciate it

[warm turtle]

Just remember, don't try to solve everything at once, brake the problem in small little ones, solve them, and then combine them to solve it. It will make all your problems much easier

[hollow thorn]

Alright

Thanks for tips

[hollow thorn]

How bout this part ? @warm turtle

[warm turtle]

you have solve it

sin(2A) = 2sin(A)cos(A)

that is a known trigonometric identity

[warm turtle]

this might help you on your studies

[hollow thorn]

Owhhh that's the thing

Thanks again bro

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[sacred plank]

why does it turn positive

[full ferry]

they added 1.889 to both sides, which cancels the -1.889

[sacred plank]

they did that?

oh

ncn thanks

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[untold ermine]

I need help wiith this equation:

[untold ermine]

I got definitions for r and s (following) and have to brint the equation to a form like
a*x1 + b*x2 + c*x3 = d and need the definitions for a, b and c.

my solution looks like this, but i'm pretty sure it's wrong. i tested it with an example. the left side of final equation was correct there, but the right side wasn't

here are my calculations:

[vast shale]

can you send the original question?

[untold ermine]

the question was to find a way to convert a plane in space from the parameter-form (not sure i'm translated this correctly) to the line coordinates.

[vast shale]

wdym by line coordinates? do you mean in terms of x y z?

[untold ermine]

yes like a*x1 + b*x2 + c*x3 = d

[vast shale]

did they give a particular plane to convert?

[vast shale]

do you know how to find the equation for the normal ?

in terms of i just k

[untold ermine]

no. but i tested the final equation with one, i choose. as i said

[vast shale]

if yes then you can find it by doing r.ncap=distance from origin

where r is a vector on the plane

you can call it xi+yj+zk

[untold ermine]

what then is r.ncap

[vast shale]

then take dot pdt with n cap

[vast shale]

unit vector in direction of normal is n cap

r is a vector on the plane

[untold ermine]

yeah, i do know about the way to do this with the equation for the normal.
i just figured out in 2-dimensional space, that it's possible to convert it directly, by writing down the equation for x and y of the result. then solve the first equation for the parameter and use it to replace the parameter in the second equation. finally you just have to transform the term to look like a*x + b*y = c and you are done. i tried to use that for three-dimensional space, which is what you see here.

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[vocal comet]

Anybody know this?

[vocal comet]

<@&286206848099549185>

[jovial patrol]

Easy

@vocal comet x=variable & other number

[vocal comet]

Ok

[jovial patrol]

I think now u can solve

[shrewd depot]

@vocal comet What class is this for? What do they mean by modeling in this context?

[vocal comet]

8th math and idk what they mean by modeling 🤷‍♀️

[shrewd depot]

I think I understand. Hold on.

[vocal comet]

Ok

[shrewd depot]

Start off with something like this. The circles are the "x" variables and the squares are the regular numbers. Green means regular positive values and red means negative values.

First, take away 3 green circles from each side. Now you have 2 green circles on the left and none on the right.

Then, add 4 green squares to each side. Now you have 4 red squares and 4 green squares on the left. On the right, you have 12 green squares.

Now, red squares and green squares 'cancel' each other out, meaning one pair of red and green squares is equal to zero. So the four green squares on the left cancel out the four red squares on the left.

[vocal comet]

Thank u

[shrewd depot]

So now the left side only has 2 green squares and the right side only has 12 green squares. Thus, 2x=12

Now divide each side in half. Now you have one green circle on the left and 6 green squares on the right. Final answer, x=6.

Does that make sense?

[vocal comet]

Yes

Thank you

[shrewd depot]

No problem, good luck

[vocal sleet]

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[dusky trellis]

Can someone give a easy proof

[merry python]

(1+1)^n

[full ferry]

the amount of subsets in a set is 2^n, you can also write it as that sum

[dense eagle]

induction also works too lol

[rare swift]

Hmm here's a combinatorial proof
Take a set s of first n natural numbers the total of subsets of that set will be equal to nC0 + nC1 .....+nCn
Well that's one way of counting another way of counting would be to denote the subsets by strings of 0 and 1 where 0 - when a no is not present in the subset
1 - when the number is present in the subset
Then my claim is that total no of binary strings would denote the total subsets and since each bit has two choices 0 or 1 we have total binary strings = 2ⁿ

[dusky trellis]

Yes, I proof it by induction. I am looking for some other ways to proof it

[rare swift]

Otherwise there's a boring method of binomial expansion or induction

[dusky trellis]

thanks

good point

[rare swift]

[dusky trellis]

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[heavy palm]

no. 5 how am I suppose to tell when it’s not differentiable without looking at a graph?

[heavy palm]

I’m just given the function

[dawn kestrel]

the derivative function f'(x) might not be valid for every x value, hence not differentiable at those points

take the derivative and see what happens

[heavy palm]

Ok

Give me a bit

[dawn kestrel]

take ur time

[merry python]

aman to the rescue

[dawn kestrel]

🙂

[heavy palm]

@dawn kestrel can I simplify this

Or is that my answer

[dawn kestrel]

i think your exponent is wrong, recall the power rule: d/dx [x^n] = nx^(n-1)

[heavy palm]

Oh right I meant -2/3

[dawn kestrel]

yes, and a^(-n) = 1/a^n, so I would suggest that you write it in fractional form

[heavy palm]

Oh right

[dawn kestrel]

its not required for every question, but here it is important imo

[heavy palm]

Right?

[dawn kestrel]

looks okay

okay so now, where are the x-values where f'(x) may not be defined

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@heavy palm Has your question been resolved?

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[north relic]

What is the highest value of infinite tetrations of x? x^x^x^x^x^x^x^x... (That isn't infinity)

[inner osprey]

there is no highest value

[molten anchor]

what does that q even mean 😭

[north relic]

Oh, well is there a highest value of x that makes it finite though?

[molten anchor]

OHHHH

i get the q

[molten anchor]

1 is clearly a value

which makes it finite right?

if i haven't misunderstood?

[halcyon ice]

he asked for the highest though wihch doesnt exist

[north relic]

Ok, then one last question, is there a range of numbers that it could be? [2 obviously doesn't work, but 1 definitely works] (How small can you make the range)?

[inner osprey]

e^(1/e) i believe

[molten anchor]

you're asking about the radius of convergence??

[halcyon ice]

wait i think i get yoru question

[molten anchor]

yh exactly

good edit

cos you can work it out

lower bound being e^-1/e??

check my math

yh @north relic here's a math stack exchange article that talks about exactly what you want: https://math.stackexchange.com/questions/108288/infinite-tetration-convergence-radius

[north relic]

Wait, then couldn't you just infinite tetrate at the highest # of the range to get the highest converging value?

[molten anchor]

yes

exactly

that value is e

[north relic]

Idk, in desmos, I got around 2.63 after pasting it at the highest range about 100 times.

[molten anchor]

which honestly is shocking that e comes out of nowhere

[north relic]

Ok, I think I understand enough it now.

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[bold kayak]

is the answer t = 1x+c

or

is this the answer

or am i twaeking and its the same thing

[flat whale]

yes your work is correct

[bold kayak]

yeah

but is y = 1x+c

also correct?

[flat whale]

no wtf is c

[bold kayak]

0?

[flat whale]

y=x is the answer

[bold kayak]

ok yk what thanks for the info

[flat whale]

y = x and y = x + 0 is the same

[bold kayak]

so

t : y=1x

is wrong

or like

well ik u cant put 1 before

an x

but like it cant be that wrong

[flat whale]

y = 1x and y=x are also the same

[bold kayak]

so then

t : 1x + c

is also correc then

since c is 0#

[bold kayak]

or should i just use this as my answer

[flat whale]

.

[bold kayak]

alright fine

also need ur advice on one other thing

number c

A function has derivative 0 in a point if and only if it is a stationary point of the function, aka not increasing nor decreasing. We can see graphically that the function has such a point at x=-1, and we also see that f is decreasing for all x<-1 and increasing for all x>-1. We thus conclude that x=-1 is the only x such that f'(x)=0.

is this the perfect answer?

[tall vessel]

instead of stationary point, just say horizontal tangent line at that point

[bold kayak]

alright bet thanks

[tall vessel]

make sure to say graph is contiuous and differentiable

[dull bear]

(I will say that it sounds a bit susly written, for what it's worth...)

[bold kayak]

what does that mean

am i doing to much?

[dull bear]

At least in my opinion

[tall vessel]

some words can be summed up

but good thing you note the key points on the graph!

[bold kayak]

about to get 10/10 on this fr

alright well thanks

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[toxic coral]

How do i do this can someone explain

[warm vine]

vertex of absolute function is at (0,0)

both x and y values zero

so here try to make the them zero

y+3 = 2|x+4| so y+3=0 and x+4=0

[toxic coral]

im cooked

wht do you mean

[elfin palm]

Ohh

Absolute value questions

[warm vine]

make the x part equal to zero

x+4 = 0

so x is -4

now put this back into the equation to get the y value

this is the vertex

[elfin palm]

Don’t forget there’s 2 cases

[warm vine]

its for finding vertex

[elfin palm]

Oh mb

[toxic coral]

so its y=-3?

or

[warm vine]

yes

[toxic coral]

So what do i do next

[warm vine]

thats it

the vertex is (-4,-3)

and you also have the axis of symmetry (x =-4)

[toxic coral]

ngl idk what that is

what's an axnis of syummtery

I plotted the two points but what does that do

and what about the 2 infront of the absolute value

[warm vine]

axis of symmetry is a line that divides a shape into two identical parts, creating one part as a mirror image of the other part

[toxic coral]

Ohh

Thank you

I get it now

[toxic coral]

Ohhhh

Thank you

What about the 2

though

[warm vine]

that doesnt affect the vertex

[toxic coral]

What does it do

[warm vine]

multiplying the input variable (here x) with a constant greater than 1 just stretches the graph vertically

if the constant is between 0 and 1 then you get vertical compression

pink is y = |x| and green is y = 2|x|

[toxic coral]

thank you

i get it now

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[turbid bronze]

How do i read this PDE?

[turbid bronze]

derivative u/t + constant b * differential u = 0?

[cyan talon]

you mean read as in understand what the objects in this equation are ?

or read as in say that equation orally ?

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[fading swift]

How do I rewrite this as 1 radical expression?

[dire torrent]

Recall that sqrt (f(x)/g(x))=sqrt(f(x))/sqrt(g(x))

That should be all you need for this problem, honestly

[fading swift]

oh thank you! I didn't remember that rule

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[vast shale]

Guys in algebra any variable if it is negative in x^2 will be positive right because x=-2 is (-x)^2 the negative is within the paranthases

[vast shale]

making sure

[hidden bramble]

yes

[twin horizon]

Yes

[vast shale]

ty

im done

someone confused me before lol

irl that is

[dire torrent]

If x is real, then yeah

I assume that's the case?

[twin horizon]

Well just know -(x)² is not always=(-x)²

[vast shale]

yes

[dire torrent]

Pretty sure that they're never equal unless x is 0 though?

[twin horizon]

0 is why I said that

[dire torrent]

Shouldn't you have said that those are equal for only one case instead?

Regardless, I may be confusing the guy, imma just drop it

[twin horizon]

I won't like to assume there's only one case

[loud walrus]

This is incorrect

First of all, if the variable is negative is negative, not positive.

Second

If x=-2 then (-x)^2 is not what you have to check

You have to check for x^2

Which would be (-2)^2

It would be clearer if you just say that squaring a negative real number results in a positive number

[dire torrent]

Pretty sure that's what the guy meant

Even if his wording was strange

[twin horizon]

Lol

[loud walrus]

And that’s why I point that out

[vast shale]

being able to articulate things properly is important for logic

i see you there

ah there is a difference between a "negative variable" and a "variable that equals a negative number"

youre pointing out my weird wording

[loud walrus]

No problem, saying things is not always easy

[vast shale]

ok

[loud walrus]

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[vast shale]

!done

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[candid tinsel]

What am I supposed to sketch in b?

[flat whale]

just plot like the first 3 terms

[candid tinsel]

Ah ok

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[bright kernel]

Calculate the line integral of that field, through the curve composed of the following curves

[bright kernel]

So is there any trick here I can use, the integral looks horrible

[heavy yoke]

see if it is conservative

[bright kernel]

Yeeep thanksss

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[sour pollen]

made it all the way to (sin(a) +cos(a)*tan(62)) -55/37=0 but calculator keeps screwing up my calcs and gives me nonsense

[sour pollen]

only need to calculate that expression and then convert from radians to degrees but my ti-nspire is acting up

[clear cedar]

-55 / 37 isnt necessary

[sour pollen]

yeah but i graphed it so it was needed then

i couldve left it as 55/37 on the other side

[clear cedar]

why do you need to graph it

[sour pollen]

to find the zeros of the graph

i could go the nsolve route and just do it in the calculator sheet but that game me some wack shit

[clear cedar]

solving algebraically is gennerally the easiest tbh

[sour pollen]

yeah i forgot everything about algebra after taking 3 classes of calc

how would i begin

[clear cedar]

just get rid of 55N for now and you get

37sin(alpha) = F2 * cos(62)

F2 = 37sin(alpha) / cos(62)

also why you get 37cos(alpha) = F2 * cos(62) is because the two forces are acting upon an equalibrium

this means that the force is negligable

[sour pollen]

here imma send you a explanation of a similar question and you tell me if its normal

[clear cedar]

what am i supposed to do?

sorry

[sour pollen]

just review the thing and compare it to what you are doing

[clear cedar]

alright gimme 5

[sour pollen]

last step of this is where i fuck up

[clear cedar]

@sour pollen i got this for the first part

And the solution checks as true

So yes its relevant to what we’re solving here

[sour pollen]

you forgot |f2|sin66

[clear cedar]

its not relevant 😛

it simplifies away

or maybe youre thinking of something else

[sour pollen]

here im bouta send my work

its the same i think you just didnt write the tan62 but went for a fraction of sin and cos

[clear cedar]

oh, this is for this #help-17 message

[sour pollen]

yeah the example

i did my work for the actual problem

[clear cedar]

ok i see

we're back to square 1

so as i stated before, both sides are acting on an equilibrium on the force

therefore its irrelevant for the calculation for the measures

it spreads out, it evens out

on both sides it ends up the same, therefore 55N is negligable. its = 0

do you understand what i mean

and this is important to understand for solving the problem

[sour pollen]

take a look at the drawing on top right, is that what you are trying to get at

[clear cedar]

lemme just ask real quick, do you have the answer to this problem

i get about 1.3 radians

or 73.74 degrees

[sour pollen]

just graphed it, found the zero and yeah 73.74

[clear cedar]

ok so

do you want to follow my solution or continue on your own

because idk any other solution

[sour pollen]

ok rq i want you to look at the last line of my work and the last line of your work

they are the same arent they

yours equals w while mine just goes to divide w by |f1| and move it to the left side to make the expression = to 0

so whats different

[clear cedar]

when you say it this stubbornly i have to calculate it xD

im sorry really

imma be back

[sour pollen]

Man this makes me realize I need to make my work look prettier so others can follow along

Fuck

[clear cedar]

@sour pollen

Yeah youre right

i feel dumb and mean

ok but you have this equation now

mine and yours

[sour pollen]

Nah man fuck calc

Stupid ass notations and shit got me confused

Thanks for the help dude shit got me spiraling

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[granite sandal]

could someone solve this for me and show the steps please

[jagged cargo]

what is the instruction

[granite sandal]

simplify, express each answer with postivie exponents

[jagged cargo]

do you know the law of indices?

[granite sandal]

no

[jagged cargo]

,tex .exp rules

[jagged cargo]

not even these?

[granite sandal]

ah these yes

[jagged cargo]

they are called laws of indices

[granite sandal]

i thought i could just flip the exponents but i end up with the wrong answer

[jagged cargo]

first, turn that -2 exponent into a positive one

[jagged cargo]

can you fill in the blank?

[granite sandal]

how would i turn the -2 to a postive?

i would have to flip the entire equation no?

[jagged cargo]

can you look at these rules and determine for yourself which rule is the most applicable to turn a negative exponent into a positive?

[granite sandal]

the negitive expoent where you put 1 over the negitive a

[jagged cargo]

correct

[jagged cargo]

in other words, you are correct

can you write it out?

[granite sandal]

(-3y^4 / x^3)^1/2

[jagged cargo]

where the hell did the 1/2 come from

[granite sandal]

flipping the exponent

[jagged cargo]

i want you to not blitz through it and do the problem step by step

$\left(\frac a b\right)^{-x} =\left(\frac b a\right)^x$

[jagged cargo]

try again

[granite sandal]

(-3y^4 / 2x^3)

[jagged cargo]

wrong

look closely

-2 is not the only negative exponent

but we are not gonna touch them, we will leave it as it be

[granite sandal]

so it would be (-2y^-4/ 3x^-3) cause i just flip the x and y around?

[worthy canopy]

Wouldn’t the exponents turn positive?

[vocal sleet]

@granite sandal Has your question been resolved?

[vocal sleet]

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[sinful pollen]

Consider the function $f(x) = \frac 1 x$

Find: $\frac {f(x + h) - f(x)} h$

[sinful pollen]

bruh

[twin meteor]

Devil Wears Prada

[sinful pollen]

so far i got

$$\frac {(\frac 1 x + h) - (\frac 1 x)} h$$

[twin meteor]

Devil Wears Prada

[sinful pollen]

did i do this right?

[sharp lynx]

not quite

[bold hound]

almost

[sharp lynx]

the first term in the numerator should be $\frac{1}{x+h}$

[twin meteor]

Steakanator

[sharp lynx]

get sniped

[bold hound]

😭

[sharp lynx]

sorry that was toxic

[sinful pollen]

why?

[bold hound]

the plus h applies directly to the x

it is f(x+h), not f(x)+h

[sinful pollen]

ok

is that it?

[bold hound]

so if you know how f(x) looks, to get f(x+h), just replace every x with x+h

[sinful pollen]

$$\frac {(\frac 1 {x + h}) - (\frac 1 x)} h$$

[bold hound]

and then the next step is to simplify

[twin meteor]

Devil Wears Prada

[bold hound]

👍

[sinful pollen]

i dont really know how to simplify this tho

[bold hound]

on the top you have two fractions

do you know how you can add them together?

[sinful pollen]

do i make them even

so theb

then

[bold hound]

yeah you want to make their denominators the same

[sinful pollen]

$$\frac {(\frac x {x(x + h)}} - (\frac 1 {x + h} {x + h(x))} h$$

fuck

oh

[twin meteor]

Devil Wears Prada

[sinful pollen]

omg

[bold hound]

$\frac{\frac{x}{x(x+h)}-\frac{x+h}{x(x+h)}}{h}$

[twin meteor]

Martin

[sinful pollen]

yeah thanks

so then the numerator

is just h

over

x(x + h)

[bold hound]

minus h, yes

[sinful pollen]

?

minus

h

what

[bold hound]

$\frac{\frac{-h}{x(x+h)}}{h}$

[twin meteor]

Martin

[sinful pollen]

oh word

taht turns into

[bold hound]

here we have two fractions which we can combine

[blazing wigeon]

$-\frac{1}{x^2+xh}$

[sinful pollen]

$-\frac 1 {x(x+h)}$

[twin meteor]

Devil Wears Prada

[bold hound]

$\frac{\frac{a}{b}}{c}=\frac{a}{b\cdot c}$

[twin meteor]

Martin

[sinful pollen]

what

[twin meteor]

mari

[sinful pollen]

yeah

[bold hound]

👍

[sinful pollen]

this is the final answer?

[bold hound]

yes

do you also have to take a limit?

[sinful pollen]

no thankfully

not a tangent line

[bold hound]

ah alright 👍

[sinful pollen]

thanks tho

.close

[vocal sleet]

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[vocal sleet]

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• Show your work, and if possible, explain where you are stuck.
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[violet moth]

Hey I need help finding an appropriate stability condition to keep my 2nd order pde stable during numerical analysis can someone guide me towards ressources on that?

[cunning basin]

2+2=5

[violet moth]

thank you

[vocal sleet]

@violet moth Has your question been resolved?

[cunning basin]

your welcome

[vocal sleet]

@violet moth Has your question been resolved?

[vocal sleet]

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[sinful magnet]

Why cant i calculate this matrice

[sinful magnet]

Why is it undefined

[bitter pilot]

There is no multiplication for vectors

[sinful magnet]

isnt that a dot product

?

[bitter pilot]

If it is you get a scalar