help-36

[thorn stump]

no i mean i get that

[cyan kayak]

Let's work through it

[thorn stump]

in the first one, im "withdrawing" P and then starting from there

but whats going on in this situation?

thats what my original question was

[cyan kayak]

We start with 0

And at first our increase comes almost entirely linearly

Because we have a slope of D

Due to our deposits

And then eventually compound interest takes over

[thorn stump]

from what im getting is, theres like a "starting ground" in this one
while over on the other there isnt?
and hence the D term comes in here

theres no depositing in the first one

but here we do

but then we also are withdrawing in the first case
so why should the 2 be totally different
cuz essentially we do have a starting amount here as well

[cyan kayak]

\begin{align*}
\dv{A}{t} &= D + kA \
\frac1{D+kA} \dv{A}{t} &= 1 \
\int \frac1{D+kA} \dv{A}{t} , \dd{t} &= \int 1 , \dd{t} \
\frac{\log(D + kA)}{k} &= t + C \
\log(D+kA) &= kt + C \
D + kA &= \exp(kt + C) \
A &= C \exp(kt) - \frac{D}{k}
\end{align*}

Now we find C by using our initial condition:

\begin{align*}
A(0) &= 0 \
A(t) &= C \exp(kt) - \frac{D}{k} \
0 &= C \exp(k \cdot 0) - \frac{D}{k} \
C &= \frac{D}{k} \
A(t) &= \frac{D}{k} (\exp(kt) - 1)
\end{align*}

[soft zealot]

OmnipotentEntity

[cyan kayak]

@thorn stump ^

Does this make sense?

[thorn stump]

no no, i got this

but im just saying that like
A' = Pke^kt
and A' = D + kA
why are these 2 different
cuz in the case of A' = Pke^kt, im depositing P, and im getting A = Pe^kt back
and in the case of A' = D + kA, im ALSO depositing D, but im getting a different result?

is this cuz im depositing D continuously?

[cyan kayak]

Yes

[thorn stump]

aahhh okay

so that is like a one time deposti

and this is being continuous

okay i got i now
THANK YOU THO!

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[grave lichen]

What’s wrong with my answer?

[grave lichen]

!status

[final saddle]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[grave lichen]

3

[limpid egret]

is D the answer ?

[hushed saffron]

B

[white sphinx]

how?

[hushed saffron]

They have given the correct answer is bhaven't they?

[grave lichen]

Yes B is the right answer

[white sphinx]

well ig you have to pick the closest to the price u got

it doesnt matter if its more or less

[hushed saffron]

Accurate

[white sphinx]

i was thinking if the max chair price is $160.7407, how will you buy chairs worth $161 but thats not what its asking

which is what OP probably thought too and ticked A

[hushed saffron]

*closest to the maximum possible price of per chair

[white sphinx]

i interpreted that as "closest price you can buy the chair at, which is the closest to the maximum price"

[grave lichen]

Here’s how but i don’t get why they made it 1.07 shouldn’t be 0.07 ????

[limpid egret]

x + 0.07x = 14000

1.07x = 14000

[grave lichen]

What is x?

[hushed saffron]

The actual amount excluding taxes

Ig

Well you see this amount that is 14000=x+x*7/100?

That's what he has written ig

[grave lichen]

But what’s wrong with my answer ?

[limpid egret]

orginal price + tax = total budget

[hushed saffron]

Well you have found the sales tax for 14000 which is incorrect, 14000 is the total budget

[limpid egret]

you took 7 percent of total and subtracted it froom total

[hushed saffron]

14000 is the amount including tax

[hushed saffron]

Did you understand how this came?

[limpid egret]

@grave lichen

[hushed saffron]

Bro is solving the problem ig

[limpid egret]

all good then

[hushed saffron]

Yup

[grave lichen]

Yes sorry

Thhx it all clear

[hushed saffron]

Nice

Close the channel then

[grave lichen]

I was about to close it but i saw u texting😅

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[soft zealot]

Alin

[surreal owl]

help me understand it pls

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[vernal flicker]

VENDE_SE CONTA!!! NV:790. FRUTA:KITSUNE E DOUGH PERME VALOR:175,86 R$

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[shy edge]

hi

[shy edge]

hello

[wind glen]

👋

[shy edge]

is number 26

the ans is 78

@wind glen

@wind glen

[south whale]

Its -3 raised to the power 4

Not -3 multiplied by 4

U need to multiply -3 with itself 4 times

-3*-3*-3*-3=-3⁴

[shy edge]

is it 78

@south whale

[south whale]

Yes

-3⁴

Is 81

[shy edge]

what

WHATY

is it 78 or is it 81

HOLY LORDS MY BRAINS GONNA EXPLODE THE OTHER GUY SAYS IT POSITIVE 78

WHEN I TOLD HIM IT 81

[tall sierra]

it is 81

why would it be 78?

[shy edge]

HUH

the other guy said it positive

[tall sierra]

it is positive

beacuse you are multiplying an even nubmer of negative numbers

[shy edge]

not negetive so 81 -3 is 78

so is the final answer 78

[shy edge]

thos

number 26

[south whale]

Final ans is 78

[tall sierra]

oh final answer

[south whale]

-3⁴ is 81

[tall sierra]

i didnt see the whole picture i am sorry

[shy edge]

oh

[south whale]

How u gon be stupid and confident at the same time bro

[tall sierra]

i am telling u, all i seen was -3^4

[south whale]

All good bro

[shy edge]

the other other guy star throwing up random formula and i got confuse

[south whale]

Holy shit ur jacked

A jacked nerd

[shy edge]

damn

[tall sierra]

not even close to a nerd

failing like half my classes

what am i doing here idk

[south whale]

What classes u take?

[shy edge]

the 34

is it correct

[south whale]

Whats the question

U wrote on it

[shy edge]

34

[south whale]

I cant see clearly

[tall sierra]

cant type it out cause on kbm

but, negative number cant be under an even root

so NR would be correct

[shy edge]

basically -6 root Nr

[tall sierra]

nope

just NR

beacuse its not real

[shy edge]

yea i dont understand nr

need more explaination

[tall sierra]

it means that specific math problem is unidentified

not possible

just like you cant divide with 0

beacuse it would break math

[shy edge]

help me do num 35 pls

[tall sierra]

now you see, that is not an even root

so there can be a negative number under it

looking for the number which if you put to the power of 3 you get -27

you see already that its gonna be a negative number

[shy edge]

3 X 9 is 27

[tall sierra]

it is but not what we looking for

x times x times x = -27

(its soo hard to type out math stuff on keaboard lol)

can you see which number would make that true?

[south whale]

Essa brooo

Nooo

Y u teaching him incorrect stuff

[tall sierra]

wdym

[south whale]

His answer is correct

[shy edge]

number 35

i dont have answ

[tall sierra]

was just about to say that he was almost spot on

[south whale]

Im talking bout 34

[south whale]

..

[tall sierra]

alright now how on earth would that be wrong?

[south whale]

Nr is iota

iota is √-1

So √(36*-1)= 6√-1

And √-1 is nr

So ans should be 6 nr

And there is a negative sign

So final ans -6 nr

[tall sierra]

what kinda answer is that, if we have something like that we just give up on solving it since a part of the problem is not real

thats how i was taught

[south whale]

Yes it has an entire different approach

Used in coding

[shy edge]

man help me with 35 alr i got a exam tmr 😭

[south whale]

I apologise

[tall sierra]

it states say NR if problem not real in the task

[tall sierra]

its -3

[south whale]

No

Negative in root

Not real

If u going with essa approach then ans is nr

If my approach then ans is 3i

I is iota

[tall sierra]

wait what is an iota

isnt i an imaginary number

[south whale]

Yes

i is √-1

[shy edge]

so what is number 35

is it -3

[tall sierra]

it is

[south whale]

What is the answer in solutions

[tall sierra]

do you understand why? cause thats whats improtant

also what grade math is this?

[shy edge]

grade seven

[tall sierra]

see @south whale, this guy really doesnt need to know about imaginary numbers, i didnt even know about that stuff untill grade 10

you might be overcomplicating it for him in my opinion

[south whale]

Yeah u correct big guy

[tall sierra]

now thats what i like to hear lol : )

[shy edge]

how abt 37

38

[tall sierra]

someone else gotta help you with that, i dont understand what the task says since i dont learn math in english, sorry

[shy edge]

what

[south whale]

Lemme cook wait

[shy edge]

ok ok

[south whale]

Send the image again

Its too far up

Ans for 37 is 3 and 4

And for 38 is -4 and -5

[shy edge]

how is there two anws

per each

[south whale]

We have to find the 2 consecutive numbers the root lie between

So there are 2 consecutive numbers for one answer

[south whale]

.

[tall sierra]

oh so thats what that means

[shy edge]

how is 11 lie between 3 and 4

that impossiblke

11 is hight that 3 and4

it 5 that lie between 34

[south whale]

Hih

Huh

Its root 11

Not 11

[tall sierra]

yep

[south whale]

U dont have to find till the decimals

Just use hit and trial

[shy edge]

how u get 4

[south whale]

Square of 4

Is the closest

To 11

Out of any integer

[tall sierra]

its beacuse root 11, which is around 3.3 as shown in the picture, 3.3 is between 3 and 4

[south whale]

But he cant use calc in an exam

U have to solve it widout calc

[tall sierra]

just using it to explain why the answers are that

once you see why the answer is why, then you get is usually

[shy edge]

ok

that it

let skip this aight

[tall sierra]

you need anything else?

[shy edge]

page 105 to 106

numer 18

i jus need a clarify

[tall sierra]

so smol cant see

lemme get phone

cant understand task in english : (

[shy edge]

wahty

@south whale

[tall sierra]

real sorry about being useless, but i learn math in hungarian so dont know the terms in english

[shy edge]

ur hurygain

what

i never knew

does it snow

[tall sierra]

nah

and thats the worst way i ever seen hungary spelld xd

its cool tho

[shy edge]

oh ok

well bye bye

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[candid ember]

Im supposed to solve for the trigonometric fourier series and the answer looks like this im not quite sure how they got f(t) to 3/2-3/2 t

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[candid ember]

im supposed to solve for the trigonometric fourer series my answer sheet says that we can see in the figure that a0/2 is -1/2 which i didnt understand and also it looks like f(t) is 3/2-3/2t and im not sure how i can find these values by looking at the figure.

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[lament vale]

It looks like f(t) = 1 - 3/2 t, in [0, 2], because f(0) = 1

Anyways, the coefficients are still 3 / (nπ)

f(1) = -1/2, while the series at t=1 equal to a0 + 0 (because sin(πn)=0)
So we have -1/2 = a0 + 0
Hence a0 = -1/2

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[tranquil pine]

anyone here?

[tranquil pine]

.close

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[mental root]

I have the following pair of equations:
[ x_k\sin\theta + y_k\cos\theta = \sin(\phi_k - \phi_c)] and
[x_k\cos\theta - y_0\sin\theta = \cos(\phi_k - \phi_c)\sin(\lambda_k-\lambda_c)]

[soft zealot]

The د

[mental root]

I have two sets of points where $(x_k, y_k, \phi_k, \lambda_k)$ satisfy the equations , leading to four equations

[soft zealot]

The د

[mental root]

how can I solve for the constants $\theta, \phi_c$ and $\lambda_c$?

[soft zealot]

The د

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[pearl bane]

prove | |a| - |b| | <= | a - b |

[pearl bane]

how to use minkowski's inequality to solve this?

[wary copper]

is that just triangle inequality

if so, you can just do the classical proof for it assuming the standard form

consider |a| = |a-b+b| and |b| = |b-a+a|

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[clever solstice]

Nine people board a train with three carriages. Each person chooses a carriage at random and independently of the other people. Under appropriate Laplace assumptions, what is the probability that

a) exactly three people get into the first carriage,

b) three people get into each carriage,

[clever solstice]

to come back to this carriage problem

its number of favorable outcomes/ total outcomes?

total outcomes in the first example is 3^9

we want 9C3

and rest outcomes is 2^6 ?

cuz we want exactly 3

so 9C3 * 2^6 / 3^9

?

now for b(

9c3 6c3 3c3

84 * 20

/3^9

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[clever solstice]

what is the probability for 9 people split into groups of 2, 3 and 4 people

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[fringe salmon]

idk what to do here

[vital crag]

Write it as a^b = exp(b * log(a))

Then pass the limit into the exponential

[fringe salmon]

u mean sth like this ?

[vital crag]

Right

[fringe salmon]

ok so i got

ln(2-x) - 1/2ln(3x^2+4)

all multiplied by 1/x ofc but im splitting them

what do i do now

<@&286206848099549185> plws

[tranquil pine]

That's easy bro js buy an scientific calculator

[fringe salmon]

this

that was an example for sth else

[fringe salmon]

this is the one

[tranquil pine]

That's easy too bro

Js study in ur school

[fringe salmon]

then help bruh

wdym

might gbe easy for u

[tranquil pine]

It's easy bro just put 0 in the X and tadaaa

[fringe salmon]

bruv

its 0^infinite are u serious

1 srry

[tranquil pine]

U don't need to include that 0•infinite js do it old school

[fringe salmon]

wdym

its indefinite form

indeterminate*

[tranquil pine]

No idea

Ask an expert on the server

[tranquil pine]

<@&286206848099549185> this hoe

[fringe salmon]

how are u helper u dk indeterminate form tf

[glad harbor]

that role is self assigned

[glad harbor]

are you allowed to use L'Hopitas?

I forgot how to spell it

[fringe salmon]

no cant use it

[glad harbor]

hmm, not sure then
I'll come back if I solved it

[fringe salmon]

alr

[winter mesa]

Have you tried changing the variable?

Put t=1/x

Then calculate the limite when x->0+ and 0-

I think you'll get 1 in both cases

[winter mesa]

You'll get the limite for t->+infinity and t-> - infinity

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[past bronze]

why this is not a function

[boreal timber]

post original question

[past bronze]

it asks to find domain range and determine if its a function or not

[boreal timber]

inequalities arent functions

so no

[past bronze]

what do you mean

also why this is not a function

[boreal timber]

this is an inequality

[boreal timber]

that one is afunction

[rare urchin]

No?

[boreal timber]

"A function requires a unique y value for each x value."

[boreal timber]

if u limit range

[past bronze]

wait is ^sqrt x the same as y^6?

[boreal timber]

range*

[boreal timber]

?

[past bronze]

why they are not the same

y^6 and 6sqrtx

ignore the + 1

[rare urchin]

Yeah but it doesn’t ask that, it just says if it’s a function or not?

[boreal timber]

this

u limit the range

[dire narwhal]

they're not the same because one of them maps 2 y values to 1 x value

and is thus not a function

[boreal timber]

for it to be a function

[rare urchin]

^

[past bronze]

so if y is to the power of anything except 1, its not a function?

[boreal timber]

no

odd powers are ok

without limiting range at all

[dire narwhal]

y=x^anything is a function of x onto y.

it is not, at least not generally, a function of y onto x.

[boreal timber]

but he means y^anthing = x

right?

[past bronze]

so y^3 = x is a function?

[boreal timber]

yes

[past bronze]

why

[past bronze]

i mean its apparent why graphically

but i want to know why reasonally

[dire narwhal]

that's a bijective function even

[boreal timber]

well

wdym reasonally

[dire narwhal]

f: R->R, f(x)=x³ maps precisely one f(x) to each x.
its inverse also does the same.

it's bijective

[dire narwhal]

hence why this works

[past bronze]

oh ok thanks

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[short cypress]

how do I find vert asymtote of this

[silent phoenix]

set the denominator equal to 0

[short cypress]

Divide by -2?

oh no

-2x+6=0

-2x=-6

[short cypress]

-6/-2

3

yeah

what about this one?

so hard to think

[silent phoenix]

set one side equal to 0

[short cypress]

right

I did that

[rare urchin]

Then just solve it

You know

Rational equations

LCD and allat

[short cypress]

no -5

right

@rare urchin

[rare urchin]

Yeah that’s the condition of existence

[rare urchin]

Did you solve it first

[short cypress]

No I just assumed it was -5 based on the denominator

and cuz I kinda forgot how

I’m sorry I’m so stupid rn

[rare urchin]

Well yeah that’s how you do it

But now you have to solve it

[short cypress]

What does the process looks like

Unless I already have the answer

Like this? @rare urchin

[rare urchin]

That looks confusing

[rare urchin]

I don’t know what method y’all use but

Then Just multiply both sides by X + 5

[short cypress]

Where did the x-5

Come from

[rare urchin]

That’s a plus

I lied 💀

Do not use that

[rare urchin]

Yeah that should be the answer you provided

[short cypress]

What would be the answer

I have a lot of numbers on there

[rare urchin]

Are you supposed to use that method or can you use the parabola method

@short cypress

[short cypress]

I don’t know

As long as we get something that is in internal notation

[final saddle]

@short cypress Has your question been resolved?

[short cypress]

<@&286206848099549185>

[viral ermine]

What is uppp

Uh

Lemme scroll up

6x<36/x+5?

[short cypress]

What

[viral ermine]

Yea

Uh what

[short cypress]

Where

[viral ermine]

Idk

[viral ermine]

This

[short cypress]

What abt it

[viral ermine]

Do you help or

Like

[short cypress]

What

[viral ermine]

Ok wait what lmao

Wait just tell me what u need help on

I’ll try my best

[short cypress]

I need help solving

😭

[viral ermine]

Solving…?

[short cypress]

Solving the rational inequality

Yes

[viral ermine]

Ok

[short cypress]

That’s what the prompt is asking

[viral ermine]

Ok 🙂

Uh

My great great great great great grandfather always told me

Pretend it’s a normal equation with a normal equal sign 👍

And simply get x’s one sign numbers another

[short cypress]

that’s what I did

[viral ermine]

And what did you get?

[short cypress]

36/x+5-6x

[viral ermine]

Hmmm

Ok

Wait what lemme

Oh ok

Ok wait brb 😭

Ok so

What next would be to times everything by the denominator

So you’d get some like like

-6x^2 -30x +36

Does that look familiar at all

[short cypress]

yes cuz I wrote it down

I have that already

[viral ermine]

Oh

Good 👍

But also

It’s a quadratic yayyyyyy!!!!!!!

Aka ax^2 + bx + c

And not only that the other side is a 0

So we can use the quadratic formula

Because we treat the inequality as a normal equation

Ok

[short cypress]

can’t we just do a times c

and b

method

[viral ermine]

Im either living under a rock or I’m stupid because I haven’t heard of this

[short cypress]

You do a times c

-6 times 36

[viral ermine]

Oh oh

YESS

There’s that one too

[short cypress]

And B

[viral ermine]

Yea and you gotta find factors right?

[short cypress]

Maybe

Idk what u mean by factors

[viral ermine]

Like stuff divisible by something is a factor

For example factors of 9 are 1, 3, and 9

[short cypress]

Yah that

[viral ermine]

Ok

So uh

-6 x 36

Is

[short cypress]

-216

[viral ermine]

(You got this!)

Nice

And we have to find factors of -216 that equal to -30…

Hi aspect!!!!!!!!

[short cypress]

6 and -36

[viral ermine]

Idk who u are but hi

[short cypress]

ez

[viral ermine]

Good

👍👍👍

Ok

So

It would be like

(x+6)(x-36)

And the whole thing rn is

(x+6)(x-36)>0

Do you know what now?

Unless you aren’t there

Then

Well

We make it a normal equation

Like (x+6)(x-36)=0

Surely you know what now right

Unless you arnt there

Since anything times 0 is 0

[short cypress]

No what

[viral ermine]

Oh

Hey

[short cypress]

I was watching the fight

but

[viral ermine]

What fight

[short cypress]

Wouldn’t it be

-6x^2-6x+36x+36

no?

[viral ermine]

Oh yea

That’s the step before what I did

I forgot that oops

[short cypress]

ngannou ferreira

ez

[viral ermine]

Lmao what.

Ok so you get your bunch of numbers

And you know what next?

[short cypress]

bro what does this have to do with math bro

[viral ermine]

Idk

[short cypress]

Factor

right

[viral ermine]

Yesssssss

Can you do it by yourslef

Even tho I have the answer somewhere

[short cypress]

bam

[viral ermine]

Hey that’s not nice

[viral ermine]

Uh

Wait what

Oh

You got a miswrite

Remember it’s -30x

So instead of 36x and -6x it’s reversed

[short cypress]

Bro who even are you

right

[viral ermine]

Can I see ur revised equation

Nvm I’ll do it

So it’s -6x^2 +6x -36x +36

[short cypress]

Right

[viral ermine]

And then you get the stuff out to make it become

6x(-x+1) +36(-x+1)

And that becomes…

[short cypress]

yup

6x+36

[viral ermine]

Nuce

Nice

-6(x-1)(x+6)

[short cypress]

How

[viral ermine]

Uh to make it simple

If there’s more factors you can take them out

For example the (6x+36) can be 6(x+6)

Oh

I found a mistake

[viral ermine]

You get this

And do you know what to do now?

[short cypress]

Idk

[viral ermine]

Ok so

Rn it’s

-6(x-1)(x+6)>0 right?

Ok

What you do

Is

Still pretend > is a =

-6(x-1)(x+6)=0

And what X 0 is 0

What times 0 is 0

[short cypress]

0

[viral ermine]

Yea

Well anything times 0 is 0

So we make either x-1 or x+6 a 0 to make the whole thing 0

Does it make sense?

???

[short cypress]

uhhh no

[viral ermine]

So you know how it’s (x-1)(x+6) = 0?

If we make the (x-1) a 0

Then it would be 0(x+6)=0

Then the whole thing is 0

I have to eat my lunch now

Uh

I’ll just explain the rest

[short cypress]

huh

[viral ermine]

To make either x-1 or x+6 0

You make x 1 or -6

[short cypress]

wouldn’t the things be x=1 and x=-6

[viral ermine]

Yes

[short cypress]

and x=-5

[viral ermine]

But since it’s an inequality

[viral ermine]

No

It would just be something like x<1 and x>6

Try it in the original inequality

I’ll go now

Sorry

But hope you learnt something

[short cypress]

bruh

<@&286206848099549185>

still need help…

[vital crag]

There's a lot to read. Where are you stuck now

[short cypress]

Well I’m right here rn

@ the bottom

[viral ermine]

Ok well I’m back

Let’s start where we left if I stead

Instead

Ok

-6(x-1)(x+6)>0

Pretend this is a normal equation

-6(x-1)(x+6)=0

Make either term equal 0

Because anything times 0 is 0

Let’s make the (x-1) 0 by making x=1

-6(1-1)(1+6)=0

-6(0)(7)=0

0=0

So one of our “anchors” is 1

Now we try with -6

(This also results in 0)

[short cypress]

ok

[viral ermine]

Now we know the numbers we need is 1 and -6

So either between -6 and 1 or outside that domain makes the equation greater than 0

Let’s try using -3

-6(-3-1)(-3+6)>0

-6(-4)(3)>0

72>0

Nice

And if we used something outside of that domain (expansion)

Let’s use like

2

-6(2-1)(2+6)>0

-6(1)(8)>0

-48>0 (not true)

[short cypress]

I have no idea why we’re doing any of this

[viral ermine]

So

[viral ermine]

It will make sense

So now we know to make

The first equation

All the way back

Try using a value between -6 and 1

Or -6<x<1

[short cypress]

You could’ve said that at the beginning

[viral ermine]

Uh

Yea

I should’ve

[short cypress]

What’s the function that we have rn

-6(x-1)(x+6)/x+5 right?

[viral ermine]

???

-6(x-1)(x+6)>0

[short cypress]

what happened to the x+5

[viral ermine]

It got multiples

Multiplied

Into -6x^2 -30x +36

👍

Ping my user if u need anything else

I’m gonna do other stuff

[short cypress]

ohhh I see

So we sub in numbers into -6(x-1)(x+6)

@viral ermine

<@&286206848099549185>

[short cypress]

<@&286206848099549185>

[viral ermine]

What my dnd was off

[viral ermine]

Sorry man

Sub it into the original equation

The fraction one

[short cypress]

This one?

@viral ermine

[viral ermine]

No

The very first one

Use numbers -6<x<1

[short cypress]

Oh

[short cypress]

Wym

[viral ermine]

Use numbers between -6 and 1one

And see if it works

[short cypress]

So -5

So yes it works

also works with -4

[viral ermine]

Ok

So it probably is the answer

I’m gonna go offline for a while

[short cypress]

so what’s the answer

(-6,1)

cuz it’s any number between those

.close

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[quiet otter]

someone help

[quiet otter]

i don't know how to do this question

[distant sleet]

what have you tried so far?

[quiet otter]

idek how to approach it can you help me

[distant sleet]

So we know the formula for acceleration is f=ma

Or a=f/m

As m=5 we want to find the sum force on the cube to find the acceleration

So how would we find

[quiet otter]

wait nvm i figured it out

sorry

.close

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[sonic crystal]

i need help with starting

[pliant shore]

Pythagoras gives $AT = \sqrt{R^2 - x^2}$

[soft zealot]

south's secret twin brother

[pliant shore]

now use the 45-90-45 triangle ratios to find the length of the square base

[sonic crystal]

whats R in this question

[pliant shore]

the radius of the sphere

[sonic crystal]

o ok

[sonic crystal]

which triangle are we looking at here ATO?

[pliant shore]

ah no, look at ATD now

[sonic crystal]

ATD is a right angle triangle?

is it cuz like

[sonic crystal]

T is in the middle of the square is that why its a right angle

[pliant shore]

yep!

[sonic crystal]

o okay

hold on

[sonic crystal]

im confused how we get the x though because isnt x the length of OT but we are looking at triangle ATD

unless OT = TD?

[pliant shore]

nearly

right, OT = OT and OA = OD (radii)

so by RHS congruence that means AT = TD

[sonic crystal]

wait if AT = TD that means TD is also length R?

[pliant shore]

nope, cause OAT is not an isosceles right triangle

[sonic crystal]

but AT length R no?

[pliant shore]

no!

R = OA = OB = OC = OD = OS

all those points are on the surface of the sphere (and O is the centre)

T is not on the surface of the sphere

[sonic crystal]

Ohhhhhhhhhhhhh

[sonic crystal]

i was thinking R was the radius of the circle not the sphere

@tulip coyote I SUMMON U

MY TEST IS TOMORROW

I NEED ALLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL THE HELP

[tulip coyote]

,ti @sonic crystal

[soft zealot]

The current time for waterrbeam is 01:29 PM (AEDT) on Sun, 20/10/2024.
chartbit is 10 hours behind, at 03:29 AM (BST) on Sun, 20/10/2024.

[sonic crystal]

WHY ARE U 3AMM

WHY ARE U AWAKE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[tulip coyote]

Don't ask why, ask why not

[sonic crystal]

are u sure ur in the math mindset to help me

🤣

[tulip coyote]

When am I sure

[sonic crystal]

REEEEEEEEEEEEEEEE

ok

ok

so i dont get whats going on here

like im trying to find

the sides of the triangle

or something

[tulip coyote]

[pliant shore]

read the fricking question moment

[pliant shore]

.

[sonic crystal]

https://tenor.com/view/dead-to-me-gif-24361182

yo

likewtf is goijng on 😭

[pliant shore]

basically we have this

and we have AT = TD

so now you can find AD, the side length of the square base

[sonic crystal]

ok nvm i got it

.close

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[timber rivet]

How can I find the n-th derivative of this function?

[final saddle]

@timber rivet Has your question been resolved?

[wary copper]

there probably is an easier way but u can try patterns

u may try logging both sides

diffing

rearrange from that so that f'(x) is the subject

and repeat for another iteration to see if u can find a pattern

[timber rivet]

For only f', this method works, but it's too complicated to repeat for iteration to find f^(n) (x)

[final saddle]

@timber rivet Has your question been resolved?

[modest kindle]

what is $\tan\frac\pi4$ ?

[soft zealot]

0_א

[stone wagon]

is it tan(pi/4 x) or tan(pi/4)x ?

[soft zealot]

Nethuja-Gunawardane

[stone wagon]

oh that's much better lol

[timber rivet]

former

misread

[stone wagon]

oh.

here's what the function looks like btw

the red blobs are just ridiculously fact oscillations up and down

[stone wagon]

is there any restriction on the domain

of x

[timber rivet]

no, they didnt give😿

[final saddle]

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[autumn slate]

I'm hardstuck on a log/exp problem and I want to see if I'm understanding it correctly.

So I have to come up with a one-variable exp/log equation with two specific solutions, and the equation has to include a specific number.

My steps thus far are:

• Create an equation with a log and exp function that are inverse of each other
• I have the two specific solutions as the points where they intersect
• I thought that if they are inverse functions, that their curves will have inverse relationship and they will be able to intersect neatly
• Then I tried assigning the specific number to either the coefficient or the d or c transformation parameters
• This is where things started to go wrong - the functions are no longer inverses of each other even if I gave both of them the same c parameter or the same a value
• In the end I found two functions that intersect on those points through trial and error on Desmos

[runic tulip]

can you share the question too?

[autumn slate]

the question has the specific solutions x=1 and x=2, and the equation has to include -12 and not include 3

[final saddle]

@autumn slate Has your question been resolved?

[autumn slate]

Is there anyone who can help me with this?

[final saddle]

@autumn slate Has your question been resolved?

[autumn slate]

.close

[final saddle]

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[tranquil pine]

is this correct?

[runic tulip]

!show

[final saddle]

Show your work, and if possible, explain where you are stuck.

[runic tulip]

show your work

[tranquil pine]

Aight one sec

[tranquil pine]

It may not look well here

5 * 6 = 30
5 * -3i = -15i
-2i * 6 = -12i
-2i * -3i = 6i²

then I combined l ike terms and simplified

30 - 15i - 12i + 6(-1)
30 - 27i - 6
24 - 27i

[runic tulip]

its correct

[tranquil pine]

k

thanks

[runic tulip]

you should do such thing on paper

and send pic

[tranquil pine]

I dont got paper

[runic tulip]

💀

https://tenor.com/view/skill-issue-gif-24176277

[tranquil pine]

Atleast I was right I guess

When will I use this in the real world

[runic tulip]

it is imaginary lmao

[tranquil pine]

i guess

.close

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[vagrant wraith]

Im having trouble seeing how theorem 3.4(iii) gives us that Q(\sqrt(D))=T

I could see how they would be isomorphic but im not sure about the equality

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[vernal bloom]

Each side of a sqaure is increasing at a rate of 6cm/s. At what rate is the area of teh sqaure increasing when teh area o fthe sqaure is 16cm^2

[vernal bloom]

would 6cm/s

be

wait

let me search up area sqaure

skull

i think its a^2

let me doubel ccheck

caus eim dumn

would it be

dA/dt = 2a(ds/dt)

ds/dt being

6

,calc 7*8

[soft zealot]

Result:

56

[vernal bloom]

.close

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[drowsy epoch]

you are the best

[vernal bloom]

yes

[drowsy epoch]

.close

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[runic tulip]

double check area of square?

[vernal bloom]

yea i got it

dw

[runic tulip]

kk

[runic tulip]

wouldnt it be 8*6?

2a = 8

ds/dt = 6

?

.reopen

[final saddle]

✅

[vernal bloom]

uhhhhh

let me see

[vernal bloom]

I don’t think so

[drowsy epoch]

pro

:blood:

.close

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[pseudo coral]

Two armies are launching missiles at their enemies. One has the high ground with an elevation of h = 400 m. Both weapons were purchased from the same manufacturer so the have the same initial speed for the projectile of 420 m/s. Both have an initial speed for the projectile of 420 m/s Both have initial launch velocities with the same launch angle of 60 degrees relative to the horizontal. Calculate the maximum horiztonal distance that each army can shoot their missles

[inland kettle]

"two armies are launching missiles at their enemies"
perfect start to a question

[pseudo coral]

exactly

so how do we get started

[inland kettle]

try drawing a diagram and using the eqs of motion

that'll help quite a bit

[pseudo coral]

I did and the book has a very weird way of solving it

[inland kettle]

show

[pseudo coral]

Question ^^

Answer

[inland kettle]

no clue where they got half of that from

[pseudo coral]

thats exactly what im saying

theyre pulling it out of their ass

i get finding the components

thats all i get

[inland kettle]

rip

[final saddle]

@pseudo coral Has your question been resolved?

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[granite grove]

Hi i was watching professor leonard but he did this, inside the square root it is 1-x^2, so how does square root and square cancel each other out? I thought it was only for multiplying and dividing

[vital crag]

That's almost the definition of square root

[granite grove]

so it cancels out even though we're substracting and adding in a sqaure root?

im confused

[vital crag]

$\sqrt{x}^2 = x$ for all nonnegative x

[soft zealot]

riemann

[granite grove]

Oh okay so when you cancel it out x=1 in the image so we can do it?

no wait

i dont get it

[granite grove]

but how do we know that x is nonnegative? do we solve for x for eq 1-x^2 and see if x is nonnegative to check if sqaure and sqaure root cancel?

[coral prawn]

If x is negative then you're doing something very illegal in the first place

A professor would never write sqrt(1-x^2) if 1-x^2 could be negative

Of course there's usually a good reason for why what you have inside the square root is nonnegative and this is something that's always good to verify

[vital crag]

He explained it earlier in the video. Pay attention to x

[coral prawn]

My guess in this case would be that -1 <= x <= 1, and therefore x^2 is at most 1, and thus 1-x^2 is nonnegative

but I haven't seen the original video

[granite grove]

where?

[granite grove]

so how do we verify if x is nonnegative sqrt(1-x^2) so do we solve 1-x^2 for x?

[coral prawn]

maybe this helps?

[vital crag]

Watch the video