help-0

[swift harbor]

yes

[harsh belfry]

I forgot I rewrote it it

Haha!

Sorry

[swift harbor]

ur good

did u do geometry yet

[polar mist]

Ah okay good

[harsh belfry]

I have but that was a long time ago

[swift harbor]

think u can help me

[cursive horizon]

Help please

[harsh belfry]

post the question, I most likely dont know the proper equations

[swift harbor]

this is the question

wait

I just realized

its right

I can check it

easy dubs

rolling thru the math homework in 10 minutes

[swift harbor]

37 |4/x-1|>2 is the problem

idek what im looking at

[cursive horizon]

|4/x-1|<=2. Solve for values of x

[harsh belfry]

so are you doing interval notation?

solve for x

[polar mist]

Separate into two situations. One where |f(x)|=f(x) and |f(x)|=-f(x). For the specific intervals of x

[cursive horizon]

So 4/x-1 = 2 and 4/x-1 = -2

[swift harbor]

ok one second

[polar mist]

So a simple example. |-3x|=-(-3x) for positive x, and -3x for negative x.

[swift harbor]

bueno

[cursive horizon]

Ok I got the values but how do I know the directions and stuff

[heavy gull]

Can someone break this down please

[urban dew]

no

[heavy gull]

Excuse me?

[dusk umbra]

my friends...if i have a system of equations represented by some matrices

and a determinant is given

How can I go about solving for my variables?

[heavy gull]

Hey christian sorry to be a jerk but this channel is in use rn

[dusk umbra]

OH

[heavy gull]

Please use a different one

[dusk umbra]

my bad, didnt realize thats how it worked

[heavy gull]

Thx

[rose parcel]

[dusk umbra]

by the way what are you confused about in your problem @heavy gull

[heavy gull]

How to get the answer

[dusk umbra]

is the answer you have written down the answer or just what youve got so far

[heavy gull]

<@&286206848099549185>

Its the answer from the back

[dusk umbra]

Well I can help you with the n part.

So what is n/n^2?

Do you know?

[heavy gull]

n^-1

[placid spire]

Or 1/n

[dusk umbra]

yes, thats right

so when you have something to an exponent, and that entire function is subject to another exponent, what happens?

[oak hound]

can u guys check questions 1?

[dusk umbra]

For exampe,(2^x)^y

[oak hound]

i need some urgent help

[heavy gull]

Thanks christian I think I found the answer so.ewhere else

I didnt know u could flip a fraction inside brackets to invert the exponent

[dusk umbra]

no problem glad you found it

let me know if you get stuck again

I dont know a lot but i think i understand this one

[final ferry]

can someone help me factorise this step by step 😀

[ivory gulch]

mayb i'm dumb but i don't think you can factor that brother

[small bear]

actually (a - 2 b + c) (a + 4 b + 2 c) but like good luck

[dusty oxide]

Can someone explain this step?

https://gyazo.com/14d0755413a3612b4612e296daa765ac

[alpine sable]

How do

[dusty oxide]

Anyone here? 😮

[alpine sable]

Learn your trig identities

[maiden mountain]

Hello, can someone help me with this

[dusty oxide]

What do you mean

I just dont understand the algebraic part of it

[dusty oxide]

How can we just move the 2

I mean its because its multiplication, but it doesnt click in my head

Or is it because you would take sin(x) times 2, and then sinx times cosX

Or do u first have to do 2*cos(x) and then take that times sin(x)

Can someone explain this step in more detail, I dont fully understand how it works.
https://gyazo.com/14d0755413a3612b4612e296daa765ac

<@&286206848099549185>

OH sorry for ping

I thought it was 10 mins

Fak, dont ban me please ❤️

[polar mist]

Don't worry. Also it's just factoring out the sin(x) and leaving the (2cos(x)-1)

[dusty oxide]

I kinda understand how its done, but I wouldnt be able to figure it out myself (its simple I know, but idk)

[maiden mountain]

when anyone is available let me know

[dusty oxide]

I just dont see how we would get back the 2Sin

Because I assume we first have to do 2*cos(x), or is that exactly what we dont have to do

[polar mist]

Well 2sin(x) cos(x) = 2cos(x) sin(x)= sin(x)cos(x)*2. Since it's all multiplication the order writing it does not matter

[frozen silo]

need help ;/

[polar mist]

Just the same as 2xy is the same as 2yx or even x2y

[dusty oxide]

But if we were to expand that again, how is it done, isnt it sinx * 2 + sinx * cos(x) + sin(x) * 1

or am I dumb

[buoyant kayak]

sin(x)*2cos(x) - sin(x)*1

[dusty oxide]

oh yeah I forgot the minus

[polar mist]

Yeah you just distribute the sin(x) back in

[dusty oxide]

Okay I guess that seems logical

So its not sinx * 2 + sinx * cos(x) - sin(x) * 1

or is that the same

[buoyant kayak]

you're multiplying 1 term into 2 terms and ending up with 3

so no

[dusty oxide]

Okay so u have to multiply sin with 2cos(x)

Because its a multiplication inside the parenthesis

So its prioritised?

[buoyant kayak]

2cos(x) is one term

2 is the coefficient of cos(x)

if you were to multiply 3(4x+6) what would you get

[dusty oxide]

Yeah so bascially 2 * cos(x)

Oh yeah

12x+18

Okay makes sense I guess

[buoyant kayak]

and you did that by multiplying 3*4x and 3*6

where 4 is the coefficient of x

[dusty oxide]

Yeah, thanks that clearified it

[buoyant kayak]

👍

[void herald]

Hey do any of you guys know how to do parametric equations by chance? (Sorry mid convo)

[buoyant kayak]

send the question

[void herald]

I’m doing some hw on it rn and I want to make sure I’m doing it right

[finite pecan]

😭 when all the question-# chats are being in use so u cant ask a question either lolol

[void herald]

@buoyant kayak here is the hw👆

[buoyant kayak]

looks good to me so far

[topaz scaffold]

#help-5 Is open, oof nvm

[void herald]

How would you find the starting location?

[buoyant kayak]

plug in 0 for t to find (x,y)

[void herald]

Ok

This is kinda off topic but like are you guys like teachers that help students like me on discord on math in general?

[buoyant kayak]

i'm a freshman in college lol

[void herald]

LMAO

[stray estuary]

any calc 1 people in here 👀

[void herald]

Pre calc💀

[stray estuary]

cuz like

im tryna do this

with just calc 1 techniques but i need integration by parts

[alpine sable]

im gonna cry inside if I have to take calc BC

[buoyant kayak]

what methods are you allowed to use?

[topaz scaffold]

You can easily get rid of the sin√x by expanding the sin(2√x) on the top

[stray estuary]

well im limiting myself to only calc 1 techniques

its not hard to simplify it, but im having trouble getting rid of this term

$$\int\frac{\sin(u)}{u}du$$

[ocean seal]

blanket

[stray estuary]

(after doing u=sqrt(x))

[topaz scaffold]

Ah, I don't think there's an indefinite integral for this one

[stray estuary]

yeah there isnt

[topaz scaffold]

I forgot what this is called

Shoot

[stray estuary]

and im just trying to get rid of it without integration by parts

[stray estuary]

Si(x)+C

the umm

[topaz scaffold]

Ah yes

[stray estuary]

dirichlet integral

is what it was called

[topaz scaffold]

Really?

I thought it was just called the sine integral

[stray estuary]

swear it was dirichlet

maybe im wrong

(to be fair, dirichlet integral would probably refer to a number of integrals that were unintegrable and this is just one of them)

[topaz scaffold]

Btw what's supposed to be inside the natural log?

[stray estuary]

ln(x)

[topaz scaffold]

Ah

I'm assuming it's sin(2√x)

[stray estuary]

ye

[alpine sable]

Can anyone please help me in the trigonometry section plz

[topaz scaffold]

How would you even do ∫ln(x)cos(x)dx without by parts?

@stray estuary ^^ ?

[topaz scaffold]

Well it's from Blanket's original question

Simplifying and using using the sub u =√x I got $$\int \qty( \frac{\sinu}{u} + \ln(u)\cos(u) )\dd{u}$$

[ocean seal]

RipeOrange

Simplifying and using using the sub u =√x I got $$\int \qty( \frac{\sinu}{u} + \ln(u)\cos(u) )\dd{u}$$
```Compilation error:```! Undefined control sequence.
<argument> \sinu 
                 
l.55 ...\qty( \frac{\sinu}{u} + \ln(u)\cos(u) )\dd
                                                  {u}$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.```

[topaz scaffold]

Trying to solve the integral without integration by parts ig

Nope

I don't know much calc 3

No idea, it's from blanket's question

Blanket the person

[topaz scaffold]

This question

[stray estuary]

oh hi

well its strictly using calculus 1 techniques

i dont believe IBP was a technique in calculus 1

at least not for my calc 1

is it?

[topaz scaffold]

^^ ?

Idk I've never taken calc 1

[stray estuary]

i've never taken a formal calc 1 course either

[topaz scaffold]

I've always thought it was calc 2 tho

[stray estuary]

i assumed it was complex enough that it was calc 2

and calc 1 was strictly substitution and algebraic manipulation of expressions

man

well

im going to try and stick to substitutions and see if i get anywhere

if not, ill give and use ibp

[topaz scaffold]

Ok, gl

[stray estuary]

most likely

i really just wanted to knock this out with ibp but oh well

a couple points loss is fine

i wish it was a bit more explicit in what constituted calc 1 techniques

[topaz scaffold]

Oh shoot

Will I get docked points for using stuff before it's taught?

This one

[stray estuary]

that's the thing

how does that help?

[buoyant ivy]

hegerty moment

[topaz scaffold]

$\qty(\int \frac{\sin(\sqrt{x})}{\sqrt{x}} \dd{x}) + \qty(\int \ln(x) \cos(x) ,dx )$ ?

[ocean seal]

RipeOrange

∫(Daman)dx

∫(Daman)dx

[topaz scaffold]

Wait, what happened to the natural log?

Ah

[alpine sable]

thats ugly

[stray estuary]

$$\int\frac{4x^{-1/2}\sin^2(\sqrt{x})}{4\sqrt{x}\sin(\sqrt{x})}dx$$

[ocean seal]

blanket

[stray estuary]

@alpine sable where is the conjugate here

yeah i was trying it iw as like

ok technically im in honors diff eq

we're doing integration review

and my professor's limiting us on techniques

its like extra work for honors on my transcript

yeah

idk i just call it honors de but its technically a program

[alpine sable]

Just a lil mistake :
Its
$$\int ln(\sqrt{x})cos(\sqrt{x}) dx$$
And just apply integration by parts for it and sinu/u gets cancelled

[ocean seal]

Spica

[topaz scaffold]

Yeah, it's a typo on my part, I got it right on my paper lol

[alpine sable]

Ohh then RIP its hard to solve without it then

[stray estuary]

i just feel okay

because i was able to do one of the problems

$$\int\frac{a\sin(x)+b\cos(x)}{c\sin(x)+d\cos(x)}dx$$

[ocean seal]

blanket

[stray estuary]

this was the first one i was able to do

math and biochem

dont ask why i put math, i just like the subject

i dont like it right now though

im just sad

na

[ocean seal]

∫(Daman)dx

[edgy bay]

Math trash

[woven echo]

yea p sure as long as they are factors they can be cancelled

i believe so

[stray estuary]

they can

[gray wind]

$\sum_{t=1}^{w}\frac{a_t}{(1-u^\frac{1}{2})^t} = 0$

[ocean seal]

BOuRNe_AGAIN

[gray wind]

Is it possible to somehow manipulate this into a polynomial in u? a_t is a function of t and w. Is there any info one could find out about the polynomial that could be formed by manipulation for a given w?

[humble tiger]

<@&286206848099549185>

[ocean seal]

∫(Daman)dx

∫(Daman)dx

[rich ivy]

how do I solve this

6x+12

I wrote it wrong

jesus

[woven echo]

u made that hella complicated

lol

[rich ivy]

uhhh

alright thanks

[glass lichen]

I mean, it's a wall of text

[alpine ledge]

Guys

Need help

?

Ya ik that

Wait how

Ohh ok..

Ya

[ocean seal]

∫(Daman)dx

∫(Daman)dx

[alpine ledge]

Oh

I know the answer now

Thanks a lot

I will try it by myself

[alpine sable]

how to calculate square root without calculator?

[alpine ledge]

I m weak at factorization

[alpine sable]

wym

[ocean seal]

∫(Daman)dx

[alpine sable]

what?

[woven echo]

i figure he means he needs to simplify it

[alpine sable]

so i just half the number i need to find the square root of?

[placid zinc]

Are you asking for your personal interest, or is your class telling you to find a specific square root?

[alpine sable]

it's for homework

121

[woven echo]

yea probs simplify it

[alpine sable]

Quick question that's a bit bizarre, if you get one B or C on an assessment but your other grades are high 80s and 90s will it affect your GPA at all?

[placid zinc]

The square root of 121 is 11.
That's because 11² = 121

[alpine sable]

but like i still dont understand how do i find square root without any help

like with any number

[woven echo]

you have to think of what perfect squares exist

[placid zinc]

With any number, you can't

[alpine ledge]

Its easy

Do it by prime factorization

[woven echo]

for some numbers, your only option is to turn it into perfect square factors

[alpine sable]

well your gpa is your average grade so any grade affects it

what abt

negative

numbers

[alpine ledge]

Omg

[woven echo]

since the negative is outside, you imagine its multiplying it by -1 in a sense

[long reef]

?

<@&286206848099549185>

[alpine sable]

oh it's the same if it were positive?

[woven echo]

if it was inside, it wouldn't be possible with real numbers

[placid zinc]

I think the best suggestion I could give would be "memorize some squares"

You'll memorize the common ones with practice

[long reef]

oh im new srry

[alpine sable]

what does this 3 mean

oh thanks

abt the -144 square root

Anyone good with spreadsheet programming?

[ocean seal]

∫(Daman)dx

[placid zinc]

Yes, but this channel is busy @alpine sable

[alpine sable]

pain

yeah

so -12 x -12 is -144?

or

[woven echo]

no the negative is being multiplied to the square root

-1( sqrt(144) )

[alpine sable]

yeah kind of

[woven echo]

for example, what do you think it would be if that - were say a 2 instead

yea

[alpine sable]

12 squared?

or

it'll

just be

12

[woven echo]

you are multiplying that 2 by the result of the square root

[alpine ledge]

Can anyone help me in the question

[alpine sable]

ohh so 24

[woven echo]

there u go

[alpine sable]

so what if it was that small 2

wait

nvm

[woven echo]

they usually wouldn't put it since its just assumed its square root of 2 without a number on the radical

but yea that little number determines what type of root you are getting

[alpine sable]

if it were a small 3 next to it i just have to find the cubed root of that number ?

[woven echo]

yes but what may confuse you is there could still be a value in front that it is multiplied by

that's saying take the cube root of 125, then multiply it by 3

which is why the - is multiplied after, you are just multiplying by -1

[alpine sable]

so 15?

[woven echo]

yep

[alpine sable]

thank u

[woven echo]

np

[alpine sable]

and thank u daman

[void herald]

<@&286206848099549185> can you see if I did my parametric equations right?

When do I ping them?

[woven echo]

i guess fwiw he posted it earlier in another channel but still

better to stick to 1

[void herald]

Ok I’ll do that next time

Understood

[woven echo]

this does not seem easy

[marble iron]

can anyone help me with 9th grade math

[jolly stone]

for real number solution, take cube root on both equations, then expand to quadratic equation

hold on, actually take the square root again and dont forget +-

[marble iron]

anyone?

i really need help

[jolly stone]

+-

[placid zinc]

In fact, use all 6 complex roots of unity, and you'll get all 6 solutions. ± are likely the only two real ones

[marble iron]

anyone help

[placid zinc]

@marble iron channel busy

[marble iron]

what?

[wispy junco]

OHH THANSK SM

[marble iron]

can u not help

[wispy junco]

i dont even know where to start here

[jolly stone]

every term there is a power of 2, so you can try write it out as 2^something = 2^other thing

[past ivy]

bro what is the question asking u for tho

nvm i didnt see x

[wispy junco]

i got 6/7 for the first one

where is 5/4 in it?

oh is there multiple solutions

OHH alright

i dont get that

[placid zinc]

Know your exponent rules, haha.
1/8 = 2^(-3)
See why?

To Colin

[wispy junco]

ohhh yes cuz 2^3 is 8 and to get rid of the negative exponent u do 1 over it right

[red carbon]

So ive integrated a function to get:

.5 x^2 + .5 y^2 + C = 0.

Then I moved C to the other side and multiplied everything by 2 to get C alone:

-2C = x^2 + y^2

I know that the "-2C term" can be rewritten as just C, aka:

C = x^2 +y^2

By what is the reason for this? I know it's a constant and it can be anything... but how would I justify that?

Would this suffice?

"Since C is any constant that is unknown, multiplying it by another number or negating it doesnt matter"

[valid wagon]

Anyone able to help with this?

It’s hw

I cant do the 1/e^(x-2)-1

It always goes to 1/0

Indeterminate

Are u not gonna help me bc u think it’s a test

Oh thanks

I’m from uk so it’s different it’s just a level maths

We do everything

I have tried l hopitals rule

I got stuck in a loop

[alpine sable]

@alpine sableCan I ask you a question about finding the range of the composite function?

[valid wagon]

Do I have to combine the fractions into one

Why differentiate though?

I cant just differentiate becuase it’s not in the form f/g where lim (f/g)=lim(f’/g’)

It can’t be

This is further maths a level

U cant just take deriv tho

There is no rule that says lim f = lim f’

Fuck

We cant use mc Laurin expansions bc x=2 is out of range

So l lhopitals must be only way

There must be some neat trick

But if u try differnecaiting top and bottom on that u get stuck in loop

This uses Taylor series as example but we haven’t done that yet

The thing is it must be using either mc laurin series , binomial series or lhopitals rule or just brute force algebra becuase that’s all the techniques we have Learned and my teacher wouldn’t give it something we haven’t learned yet

I have lesson tomorrow , I’ll ask my teacher and show you the solution once it get it

Yeah

I’ll send you the solution tomororw

[ocean glacier]

I need to find this point for collisions in my code, however I have no clue where to start

everything is in vectors though, so all I really need is an equation to find it's position on the x axis

it is

[jolly stone]

If you connect two centers of the objects together, you can find where it will collide

Two circles will tangent at the point where you connect the line between the center of two circles

[ocean glacier]

no

no that wont

[jolly stone]

Oh I misunderstood

You have a velocity also

Yeah my bad, that's gonna be a bit tedious

[valid wagon]

It does

Nah u keep differentiating

Until you get 2e^x-2

Which 2

Yeye

1/2

Lhopitals

Keep differnciating top and bottom

You end up with e^x-2/2e^x-2

Which is 1/2

Yeah after re writing as single fraction

Yeah

[ocean seal]

∫(Daman)dx

∫(Daman)dx

[jolly stone]

My thoughts are: find distance and direction of radius, then angle between that direction and the velocity, then law of sines to find out where exactly the obj1 will end up at collision

[valid wagon]

So after differentiating tøp and bottom twice

I get that

Sub in 2

You get 1/2

Not really

I mean I did

But like I just used l hospitals rule twice

Becuase we are differentiating top and bottom separately not treating it as one whole expression

We are using the fact that lim f/g=lim f’/g’

[jolly stone]

So then you can know what angle the obj1 does relative to the starting position and obj2

[smoky isle]

hello

listen here fella

s

can you please walk me through W=x+xyz for z?

what even is that

[alpine sable]

Hello, for the continuity tests, what does it mean by limit as x approaches c = f(c)?

so it makes sure that theres no removable discontinuity or jump?

it is confusing me a bit and i just need it better explained - forgot to write it in my notes.

[ocean glacier]

the problem is that to draw that you need to know the point it will hit on

also trig functions are slow and i would rather not run them every frame

[jolly stone]

Collision happens when distance between 2 centers is exactly radius1 + radius2

Wait so you're animating this every frame? Or you want exact value?

[ocean glacier]

Its to interpolate between frames

for continuous collision checking

[jolly stone]

If you're animating at every frame, you can detect if distance between 2 circles is less than the sum of radius

Collide when true

[ocean glacier]

well yes, but theres an issue with that system, that im trying to fix right now

[jolly stone]

What issue?

[ocean glacier]

which is if an object moves so fast it goes through an object between frames, it won't collide

[jolly stone]

Yep it does happen, can't be fixed

Alternatively you need some heavy math

[ocean glacier]

so i need to calculate the position that they would collide between frames

currently the idea is to transform 1 ball's position and velocity into the frame of reference of the other one, then check where they will collide, then transform that position back

[jolly stone]

Oh actually

You can trace out the line of trajectory, and detect if that line will intersect that circle or not

It won't give you exact location of collision, but it will definitely tell if it collides or not

Question is, do you actually need the point of collision

[ocean glacier]

yes

[jolly stone]

Or just want to check if it collides

[ocean glacier]

because I need to get the collision normal so i can bounce it

[jolly stone]

https://ericleong.me/research/circle-circle/

[ocean glacier]

that's just frame by frame calculating

https://www.shadertoy.com/view/7scGWM

I already have that

[jolly stone]

Wait I sent you the wrong link sorry

https://math.stackexchange.com/questions/913350/how-to-find-the-intersection-point-of-two-moving-circles this should include the math

Not exact formula but the general idea, which still involves trig

[red carbon]

Sorry, was someone able to answer my question? I got 2 notifications here but i cant find any answer to my question

[ocean seal]

∫(Daman)dx

[somber osprey]

hello

[next bridge]

i need to find the measures🥲

[tight locust]

x + (x+6) = 90

2x + 6 = 90

2x = 84

x = 42

x+6 = 48

Lol!

[next bridge]

why do this?

[tight locust]

it said you needed both angles

they are 42 and 48

[next bridge]

lol ya but i don’t understand why u did that equation

explain?

[glass lichen]

let the measure of the angle be x, what's the complement of x?

ie what angle is complementary to x

[ocean glacier]

I just thought of a way simpler way

but I do need the intersection points

wait i don't need the /2

i need the 2 intersection points between 2 circles (of equal size)

well yes, assuming point c is the one opposite to a

[simple stream]

question

The operator of a boat wishes to cross a 5km wide river that is flowing to the east at . He wants to reach the exact point on the opposite shore 15 min after starting. With what speed and in what direction should the boat travel?
my question is
wouldn't the direction be east of north?
my book says west of north

Agreed

the physics server is no where near as active as this server

ok

k

10 m/s

Lol

forgot to write that

I understand the velocity parts

but

it says the direction

is west of north

shouldn't it be east of north?

the direction

that is all I want

yes right?

but my book says west north

my theory is

?

so it would make you go to that exact opposite point right?/

ok that was my theory as to why it was west north

[ancient saddle]

Hello, what is the exact point?

[simple stream]

well the calculation part ik

I understand

just direction because my word problem understanding isn't so good

yes V=5.5m/s

then you use pythagorem theorem

5.5^2+10^2

and calculate the angle then ezzzz

x/t is velocity

yep angle and velocity

yes just inverse tan

d/t is speed

displacement/time is velocity

yeah I understand thanks

yes

it's because exact point on the opposite yes?

daman it's because the opposite exact point right?

is that why it's west north?

north west *

yeah ok that makes more sense

so let's say that piece of information was never there

would that mean it would be east north?

north west

yes okay you're missing one piece of information

question
The operator of a boat wishes to cross a 5km wide river that is flowing to the east at . He wants to reach the exact point on the opposite shore 15 min after starting. With what speed and in what direction should the boat travel?
my question is
wouldn't the direction be east of north?
my book says west of north

it says he wants to reach the exact point on the opposite shore

yes look I understand the unit circle

5.5m/s north

it says 10m/s east

which would mean 5.5m/s north is what I get

yes

@alpine sable

what would push you east?

yes

which is why the boat must go 10m/s west

for it to reach the exact opposite point

[simple stream]

that's my understanding of it

[alpine sable]

help

[simple stream]

yes that speed is 5.5m/s

cool physics word problems

need to be good at understanding

trying to get there lol

well thanks

I'll be going now

[woeful pulsar]

actually, that's usually how integrals are done analytically

[night geyser]

ty

#help-0 message

lmao they did this before

do they really think theres a demographic overlap

[solemn eagle]

Can someone help me with part b?

This is what I did

But the answer key says -47 m/s and I’m very confused on where I messed up

[rocky atlas]

I think your answer is correct. I tried average velocity as well but that doesn't give the answer -47 as well so m pretty much sure that the answer in your book is wrong or I might be wrong.

[solemn eagle]

I see

I’ll ask my teacher about that tomorrow then

Thank you!

[ocean seal]

∫(Daman)dx

[solemn eagle]

Wait why do you have -16(4)?

Shouldn’t it be -16(2) if we’re finding t=2

Hmm okay thank you for your help

I think my teacher messed up on the answer key

Since I got -15 and you and someone else got -15 too

Okie, thank you again!

Nope! I got the correct answers for the rest of them

Thanks for asking tho

[alpine sable]

How would I integrate sqrt(x^2+2x+1)?

what as u

tho

ik that

but what value of u

gotcha

k

[gray isle]

sqrt{a^2} = |a|
consider the positive and negative case

[alpine sable]

ok

can u even get it in one of those forms

[gray isle]

and the end result can be expressed nicely if you use the sign (not sine) function

no

[alpine sable]

ive never seen the sign stuff

[gray isle]

you're forgetting that
x^2+2x+1 = (x+1)^2

[alpine sable]

(x^2)/2 + x

i think this is meant to be done with a calc. ive never seen one this difficult in class

[gray isle]

there can be different forms

sqrt((x+1)^2) = |x+1|
and |x+1|/(x+1) = sgn(x+1)
for x \neq -1

[ocean seal]

∫(Daman)dx

[steep plover]

help pls

[alpine sable]

Point Q has coords (a, f(a+h)). See if you can use distance formula to find lengths of the sides

Is this NFA equivalent to $(ab)^(ba)^ \cup aa^*$

[ocean seal]

Manzareh

[steep plover]

ty

[alpine sable]

Np 😁

[mighty sinew]

What would be the easiest way of showing that if a,b are smaller than some prime p, then p can't divide ab without using the FTA?

[alpine sable]

Remember that primes can only divide numbers that have the prime in question as a factor (i.e. a and b are both not divisible by p essentially)

[orchid python]

hey, is there any site like Symbolab that I can use? thanks

[mighty sinew]

yeah good enough

tyy

[tender blade]

Why does this simplify to 6a^4b^5c? The bases are different so you can't add the powers right?

[onyx lodge]

how would one approach this question

[steep plover]

@alpine sable

[jagged imp]

this channel is taken but the idea is to get the general form of the tangent line in terms of the point of tangency first, and then find the x intercept of that and set it equal to -2

[alpine sable]

Did you plug each coordinate into this formula?

Point P is (a+h, f(a+h)), Point Q is (a, f(a+h))

[orchid python]

how can I differeniate this sqrt(x^2+(2x-3)^2)

[wanton crag]

is this only for maths or can i ask science too?

[orchid python]

when I need to use the chain rule @alpine sable ?

can you give me some

I don'

know where techinically I have to use it

ok

[alpine sable]

Given that sqrt of 4.5 = 2.121 and sqrt of 45 = 6.708, then sqrt of 4500 - sqrt of 450 = ?

[ocean seal]

∫(Daman)dx

[alpine sable]

Given that sqrt of 4.5 = 2.121 and sqrt of 45 = 6.708, then sqrt of 4500 - sqrt of 450 = ?
What's the pattern here

Okay

[orchid python]

thank you @alpine sable

[stray estuary]

i did haha

it was pain

trust

my god ive never done something so atrociously difficult

i wont HA

[wild kraken]

is the answer 2

the second person is trustworthy

[jagged raptor]

thanks you too

[wild kraken]

previous one is unresolved

[mellow tinsel]

Can someone tell me what this means?

[jagged imp]

Probably that the vector b is in R^m but this channel is taken

[mellow tinsel]

Whoops, my bad

[alpine sable]

hii can somebody explain how to solve these out

[next hatch]

?L = 1m^3

that'd probs be easier

[valid nexus]

If a + 1/a= 9 , then the value of a^3 +1/a^3 is is?

[orchid python]

hey

I have this function

y = tan^2 (x)

I want to apply the chain rule to it

but I am confused which value of the f(x) should be

here g(x) is tan(x)

[woeful pulsar]

can you express it as a composite function?

[orchid python]

and f(x) is x^2 or f(tanx)

[valid nexus]

this

[orchid python]

i am practicing on Khan academy

so f(x) here is x^2 and g(x) is tan(x) right

[woeful pulsar]

remember how to factor a^3+b^3

[valid nexus]

ye

[woeful pulsar]

you don't have to solve for a here

[orchid python]

I thought there are 2 functions

[mental bridge]

how do u solve this

[woeful pulsar]

try finding another channel

[mental bridge]

y

[orchid python]

if there is only one function, how can I apply the chain rule then?

[woeful pulsar]

tan is a function yeah

[orchid python]

yeah I meant tan(x) is a function

[woeful pulsar]

erm

[orchid python]

I got 2x*sec^2x

but this is not the answer

[woeful pulsar]

that doesn't look right hmm

[elfin fiber]

helpp

😭

[woeful pulsar]

essentially chain rule says the change in f(g(x)) depends on f'(g(x)) because that's how fast f changes but we have to scale it with how fast g changes

[orchid python]

i'm here

yeah I got this part

[alpine sable]

is x^-2 = -x^2

?

[orchid python]

yeah, but the f(x) is not x^2?

[rigid wind]

f(y) = y^2, y = tanx

[woeful pulsar]

erm

[orchid python]

yeah I got it

[woeful pulsar]

i think you might be a bit too strict on the notation here

because x, y all these are just variables

we can just say f(x)=x^2, it's the same as saying f(y)=y^2 or f(t)=t^2

[orchid python]

yeah

[woeful pulsar]

identifying the composite function is like the first step though

[rigid wind]

yea

you just write out the answer, not much showing what to solve

lol

[elfin fiber]

help plsss

what

[woeful pulsar]

which grade is this

[elfin fiber]

8

[woeful pulsar]

do you know how ratios work?

[elfin fiber]

yeah

[tight locust]

no.

[elfin fiber]

but i don't get ques 10

[orchid python]

hey

[orchid python]

why 2(tanx)^1

[woeful pulsar]

essentially they just want you to state if the ratios are the same

[fair osprey]

Literally just see if there equivalent ratios

[elfin fiber]

😭

[tight locust]

a proportional relation is something that can be modelled with the equation y=kx

[elfin fiber]

ohh

[tight locust]

in other words, the two variables will always differ by a constant factor

[elfin fiber]

i got it

for the first one

do i simplify?

[balmy patrol]

https://cdn.discordapp.com/attachments/373217754666500097/889362255983042560/unknown.png

can someone pls help me

i have no clue on how to figure thus out

[elfin fiber]

h

m

how do i figure it out??

[tight locust]

does 4/15 = 10/40 ?

[elfin fiber]

the first one isn't equivalent right?

[elfin fiber]

no?

[tight locust]

then do the variables differ by a constant factor?

[elfin fiber]

howww

ughh

[woeful pulsar]

hmm looks okay

[orchid python]

thank you @alpine sable

[woeful pulsar]

yeah they are not the same, therefore?

[elfin fiber]

i need to how

how

i

know

[orchid python]

one is with respect to x one is with respect to tanx

is this correct?

yeah

[woeful pulsar]

since it's not the same, it's not a proportional relationship

[elfin fiber]

ok

[woeful pulsar]

can you do the same with the other parts?

[elfin fiber]

ok

let me see

how do i like

make it into a ratio?

[woeful pulsar]

yeah

[elfin fiber]

14 on top 16 on bottom?

[woeful pulsar]

well up to you really

[elfin fiber]

ok

it's not the same right?

[orchid python]

I also can apply the chain rule in this function, right: d/dx tan(sqrt(x))

[elfin fiber]

@woeful pulsar

[elfin fiber]

broo

[woeful pulsar]

usually the ratios are written left and right
instead of as a fraction

[ocean seal]

marc

∫(Daman)dx

[silver relic]

let the whole thing be equal to x, then x = sqrt(6-x) because it contains itself

[ocean seal]

marc

[elfin fiber]

it's not equivalent right?

[woeful pulsar]

is this prove or disprove

[woeful pulsar]

usually the top and bottom 1/3 are fractions, not ratios

[elfin fiber]

okkk

but

[woeful pulsar]

are you sure p is an odd prime?

[rugged tide]

thank u bud

[woeful pulsar]

okay try proving for p=2 first

[elfin fiber]

it's not a proportional relationship right?

[woeful pulsar]

for the 15:4 and 40:10, it's not proportional

[orchid python]

,help

[ocean seal]

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

[abstract tapir]

yep thanks

[elfin fiber]

ye but b?

[elfin fiber]

it b??

[woeful pulsar]

try writing out the ratios, are they the same?

[elfin fiber]

no

they aren't

[abstract tapir]

by mistake

[ocean seal]

marc

[sacred aurora]

4

for a

then do the limit from left then limit from right

[woeful pulsar]

so is the statement true?

^^

[woeful pulsar]

so 14:16 is not the same as 210:240?

okay say you have an odd prime, then it's 2k+1 then...?

[ocean seal]

marc

marc

[woeful pulsar]

if p is 3 mod 4, what is p^2

[abstract tapir]

👍

[woeful pulsar]

if p is odd p is 2k+1

continue from there

where did you get -2 from

p^2 = 4k^2 + 4k + 1 yeah

[ocean seal]

marc

[woeful pulsar]

how did you get this

observe this

[abstract tapir]

anyone know how to solve it

[ocean seal]

marc

marc

marc

[woeful pulsar]

whoops

okay p is odd

so p=2k+1

so this

observe

[ocean seal]

marc

[elfin fiber]

it is it is

sorry

[woeful pulsar]

yeah so it's a proportional relation

[elfin fiber]

c is hard

idk

[woeful pulsar]

locate the ratios

[elfin fiber]

what

[woeful pulsar]

what are the ratios in part c?

[elfin fiber]

ok

1:5

[woeful pulsar]

yeah is the other ratio the same?

[elfin fiber]

no

@woeful pulsar

it's not

[woeful pulsar]

what's the other ratio?

[elfin fiber]

3.8:19?

[woeful pulsar]

yeah is it the same or different?

[elfin fiber]

uh

same?

ig

[woeful pulsar]

1 : 5
3.8 : 19
you can try multiplying by 3.8 to see?

[elfin fiber]

ok

times what?

[woeful pulsar]

1*3.8 : 5*3.8

[elfin fiber]

ok

lol

it is

what abt ques 11?

[somber osprey]

wsp

[elfin fiber]

nvm i got it

tysm for the help..

gn!

[mortal flame]

why cos + sin for this?

apparently it's the angle notation for quaternions, but not sure if I should know this trig

[blazing compass]

Can someone help with this??

[fallen sky]

choose a n b such that lets say for the first one f(2) is same when calculated both from equation 1 and 2

[somber osprey]

OK

[half frost]

Why is there a S under 2.0 m/s ?

Is it because it's 2.0 m/s squared?

[radiant niche]

no

basically the question given is acceleration unit which is 2.0 m/s^2

so as it is s^2 , one of the s is shifted down

thus leaving 2.0m/s^1

[half frost]

So, he wants the final units to be m/s . So he moves the "2 down

[radiant niche]

yes

the final answer should be m/s

the unit

[half frost]

if he wanted the units to be in m/s 2, then square the 5?

[radiant niche]

nope , 5.0 is as it is

the down s and the s which is in 4.0 s gets cancelled

which leaves 5.0 m/s + 2.0 m/s (4.0)

[half frost]

Yes, but it mean if I wanted the answer to be in m/s"2

[radiant niche]

they asked velocity

[half frost]

ahh, so the square is always acceleration ?

[radiant niche]

if they asked acceleration then we should get final answer in ms/^2

[alpine sable]

I'm looking at the solutions, why is it for AB^T the solution says to do A * B first and get the transpose of that, but for AA^T the solution does A * transpose of A?

[radiant niche]

yes , and without square is velocity

[half frost]

gotcha! Thank you very much!

[radiant niche]

welcome

[alpine sable]

.

Can someone help me with this? I am getting BigTetha(n^4) not O(n^3) I don't know if this is correct

also why it is O(n^3) in best case since in best case n=0 hence we get O(1)

[subtle nebula]

Find the sum of the geometric series 12 + 6 + 3 + ...

i have no idea what the last term is?

ok nvm i know now lol

inifinite gemoetric series

[barren jacinth]

can anyone help me what is this question even asking

[vale wigeon]

it's asking you to select which statement from your list must be true

[barren jacinth]

but i dont understand the statements 😫

[opal wyvern]

My professor just posted exam results, and it says the mean was 44.07, SD=13.2, and R=24-69

I got a 69, does that mean I scored highest in the class?

[alpine sable]

What's R? Range, then yes I think.

[opal wyvern]

Idk it just says R

I'm thinking range too but idk how tf i got highest score in the class

[alpine sable]

You are a good student. Taking help from others and learning.

[lucid aurora]

Is anyone able to help me with this?

[alpine sable]

what does $X_1,X_2 \sim Ber(p)$ mean? Is it a joint probability distribution?

[ocean seal]

faraday

[vale wigeon]

think it might just mean X1 and X2 both follow the same distribution

[nocturne saddle]

this maybe a bit advanced, but can anybody help me?

Still, dont have any ideas :(

[jolly stone]

p(2^(p-1)-1) = m^n
If p = 2, that thing becomes 2 = 2^1
Then we now only consider odd primes
It is clear that m must have a factor of p, so let m = kp for some positive integer k
(2^(p-1)-1) = k^n p^(n-1)
Here is my thought so far

[stray estuary]

hey all

i have another question

[alpine sable]

Yes

[stray estuary]

nvm i got it hee

[nocturne saddle]

erm...

actually

the exponent must be greater or equal 1

[vale wigeon]

are you sure you want to allow the exponent to be 1

because then your question becomes trivial, and i don't think that's what you intended

[alpine sable]

Is there a difference between writing $y = ax^2$ and $f(x)=ax^2$?

[ocean seal]

Etienne

[placid zinc]

That first one relates a variable called "y" to a variable called "x".

That second one defines a function called "f", which takes x as an input, and outputs ax²

[alpine sable]

But so if I was looking to take the derivative of y or f(x) I would get the same thing

[placid zinc]

Ye

[alpine sable]

Okay

Cool

Cheers mate

[proud apex]

https://i.vgy.me/pZSjtp.png

[obsidian crane]

9

[proud apex]

how do i do this

[obsidian crane]

1/5 multiplies with 10

[proud apex]

oh

ok

[obsidian crane]

It's the rule

[proud apex]

ohh

i get it

thanks

[radiant barn]

Hello

Oh

[vagrant frost]

Can somebody explain to me when using y = mx + c

0 = 2x - 1
x = 1/2

Why is it that x is 1/2?

[worldly island]

Decided to relearn integration for fun, struggling how to find the maximum point for this equation e^x=2x^2

How do I isolate the X

[radiant barn]

Oh sorry

[faint crane]

eh how did they find the range?

like the range is the maximum value that the function can take with every output right?

so like you can put anything in but the values will be between -2 and 2

like if you put for x = 8 in the equation

the value will be -126

[worldly island]

Since the function is modded the y values only exist between 2 and minus 2

[faint crane]

but how

again

if you put 8 in the equation

oh wait

ehhh

ahh

nvm

thgnxxz ❤️

[worldly island]

Nw lol can get confusing sometimes

How have they found the minimum point here

[undone dock]

The minimum can be found by solving y' = 0

[worldly island]

@undone dock phrased the question wrong lol lemme do it again

This is the question, part a how can I find out the max value algebraically without subbing in

[undone dock]

From what i know the only way to do that question is to sub in 1.48 and 1.49 for x

[worldly island]

Ah right no worries

Thought it was possible

[undone dock]

Not as far as i know, sorry

[alpine sable]

Hello, having a bit of trouble with this problem

Don't know how to find the limit as x approaches negative infinity

I already found the limit as x approaches infinity (1/2) but I'm not sure how to go about showing my work for finding the other imit

[small bear]

Well it is analogous to finding the limit as x approaches infinity you just need to be careful with the sign of x

What did you do to find the limit as x approaches positive infinity?

[alpine sable]

i divided the numerator and denominator by the largest power

so

let me write it out

[small bear]

alright

[alpine sable]

i did this

then i got sqrt 1 + 0 / 2 + 0

[small bear]

alright, that is good, except I want to retrace a bit because there is a vital step that is missed that will help us with the negative infinity scenario

[alpine sable]

mhm

[small bear]

let me also write it out

[ocean seal]

peaceGiant

[small bear]

now let us look at the top part

when you need to put the x inside the square root, you must make sure that x is positive

[alpine sable]

mhm

[small bear]

does that make sense?

[alpine sable]

yeah

[small bear]

because of that, a step we usually forget to do (and in the case of positive x values we don't need) is wrap that x in an absolute value

since |x|>=0

[alpine sable]

following so far

[ocean seal]

peaceGiant

[alpine sable]

god i should really learn latex

[small bear]

what do I mean about the sign, let's look at the case where x is negative, and for a concrete example lets take x=-5

[alpine sable]

also this might be dumb to ask but why is the x in the denominator squared now

[small bear]

when we have sqrt(smth) / (-5) we can't put the minus sign inside

[alpine sable]

if it wasnt inside of the square root in the previous step

[small bear]

we can put objects inside the square root by squaring them (they are inverse functions)
5 = sqrt(5^2)

as an example

however -5 doesn't equal sqrt( (-5)^2)

let me write it out step by step what actually is happening (since I might be confusing you

[ocean seal]

peaceGiant

[small bear]

so why am I telling you this?

well in your case you have x going to negative infinity