help-0

[icy gyro]

I think if u can get the result in the form of t

[jovial forum]

I'll see if I can

better be able to or else I'm in trouble XD

[icy gyro]

just sub the p for 500 and u should be getting the result in the form of t

u can solve it in the form of numbers if u have the t

[jovial forum]

hmm sorry not sure what you mean

English is my second language, could you show an example (not 500 so I can try and do 500 on my own?)

[tranquil rock]

why is it m-n and not m+n?

[vale wigeon]

because e^{niε} is being conjugated

thus $\overline{e^{ni\ep}} = e^{-ni\ep}$

[ocean seal]

Ann

[native temple]

In my acellus lecture it says to derives rotation matrix by applying rotation to base vectors (0,1) and (1, 0) how is this done?

[tranquil rock]

makes sense, thank! but - do you know why it is being conjugated?

[native temple]

this was active?

sorry i’ll wait

[jovial forum]

following on from this, how do I find the value of t for P(t) = 500?

[peak kite]

Guyd

81 raise to power minus -1

What does it mean

Bruh i suck

Omg

81 -¹

Is

Anybody

Gon tell me

[icy gyro]

just 1/81

[peak kite]

Oh

I see

Ty

[quick violet]

when you integrate have the lower limit of dp as p(0) this is the initial condition, and upper limit as p(t). in the dt side of the integration it should be 0 to time t.

after this integration you can easily substitute value for t

[jovial forum]

Sorry, could you just step through it for me?

I'm so lost

I'm not sure what you mean

[gray isle]

what's the original question

[jovial forum]

Starting with dP/dt = 0.0005P(2000-P), find P(t) and find the value of t when P(t) = 500

So I need to find when the population is 500

[gray isle]

$\dv{P}{t} = 0.0005P(2000-P)$

[ocean seal]

ℝamonov

[gray isle]

that?

[jovial forum]

yeah

[quick tulip]

do i ask a question here

[gray isle]

this channel is in use

[quick tulip]

alr

[gray isle]

what did you have after integrating?

it looks like you made a mistake when looking at the logs

[jovial forum]

oh

Probably have

[quick tulip]

im just tryna get the sequence for 0, 3, 7, 12, 18 (this is summation notation)

where do i ask

[gray isle]

you have a separable differential equation here

[jovial forum]

So I start by multiplying both sides by dt?

[gray isle]

start by separating your variables P and t

[jovial forum]

1/(0.0005P)(2000-P) dP = dt?

[gray isle]

missing a pair of parentheses to clearly indicate the denominator

[quick violet]

Did they give P(0) ? in the question

[jovial forum]

oops, sorry, P(0) = 100

[gray isle]

1/((0.0005P)(2000P)) dP = dt

$\frac{1}{(0.0005P)(2000-P)} \dd{P} = \dd{t}$

[jovial forum]

Oh

I think I see where I've gone wrong

[ocean seal]

ℝamonov

[gray isle]

then you'll probably need to use something like pfd to integrate the left side

[jovial forum]

I'll do it manually shortly, just trying to understand where to go after this, so wolfram gives: log(P)-log(P-2000) = t + c

So I can just plug the values of P in here that I want to find the value of t for?

[gray isle]

P(0) = 100
indicates that when t=0, P=100

use that to determine the value of c

[quick violet]

Try solving it, integrals are pretty awesome 🙂

[jovial forum]

but I get a negative ln?

[jovial forum]

Thanks, I will. I've done some already I'm just stumped on this particular question, nothing I do is coming out right

even using Wolfram Alpha I can't get it right so I think I'm fundamentally not understanding it

[gray isle]

you should use |argument| for your logs instead of normal parentheses from integrating

[jovial forum]

Not sure I get that?

[gray isle]

get what

[jovial forum]

Say P = 500, then ln|500| - ln|500-2000| is a negative? How can it be negative time?

I'm so confused

is log(P) - log(P-2000) right or not?

[gray isle]

log|P| - log|P-2000|

who's saying time is negative

[jovial forum]

so t(0) = 100, then ln|100| - ln|100-2000| = ?

[gray isle]

where's t(0) coming from

[jovial forum]

When t(0), P=100

[gray isle]

that's not what t(0) means

[jovial forum]

oh

[gray isle]

also you mentioned P(0) earlier

[jovial forum]

yeah I meant P(t)

[gray isle]

P(0) = 100
indicates that when t=0, P=100
use that to determine the value of c

[jovial forum]

so P(0)

[gray isle]

(c is the constant of integration)

[jovial forum]

so ln|100|-ln|100-2000| = 0 + c

[gray isle]

yes

[jovial forum]

the answer still doesn't make sense though?

[gray isle]

how so?

[alpine sable]

help

pls

[jovial forum]

The answer is -2.9444

[alpine sable]

wait rly?

[jovial forum]

So the population is 100 at negative 2.9444 time?

yeah

that's why I'm confused

[alpine sable]

my answer right

[jovial forum]

no, not for your question, for mine

[alpine sable]

o

how about this

[jovial forum]

Please use another channel, this one is in use

[alpine sable]

help pls :(

[quick violet]

PART 2 SOLUTION

[jovial forum]

Wait so is ln(P) - ln(P-2000) wrong or not?

[gray isle]

| |

[jovial forum]

?

[gray isle]

abs val signs not ()

[jovial forum]

right, so ln|500| - ln|100-1900| = ln(500) - ln(1900) = -2.944

[gray isle]

wheres 500 coming froom

[jovial forum]

the value of P when t = 0

[gray isle]

and the 1900

i thought you said P(0) = 100

[jovial forum]

oops, 100-2000*

[gray isle]

and the 500?

[jovial forum]

sorry, 500 was a later question

either way I don't know what I'm doing

[gray isle]

sub in the initial condition to determine the value of c

ln|100|-ln|100-2000| = 0 + c
you had that earlier which was fine

[jovial forum]

So c is -2.9444

[gray isle]

keep the values exact

[quick violet]

Final part, Solve for P(t) may be ?

[gray isle]

the part:

ln|100|-ln|100-2000|
can be simplified applying basic log rules

(specifically difference to quotient)

[jovial forum]

ln|19|?

[gray isle]

no

what law/calculations are you applying to get that

[jovial forum]

I thought you could do ln(x) - ln(y) = ln(x/y)?

[gray isle]

you can

[jovial forum]

so ln(100/1900) = ln|19|?

[gray isle]

last i checked 100/1900 wasn't 19

[jovial forum]

oops

ln(1/19)

so c = ln(1/19)

[gray isle]

you could express that as **-**ln(19) if you want

[jovial forum]

log(P)-log(P-2000) = t + ln|1/19|

cool

log(P)-log(P-2000) = t + -ln(19)

thanks

[gray isle]

| | not just basic ()

[quick violet]

now i am confused how did log|P-2000| show up

[jovial forum]

So to solve for t we can say log(P)-log(P-2000) + ln(1/19) = t and sub in for P now?

[jovial forum]

I don't get this bit either tbh, why can we just start using absolute values?

[gray isle]

you're supposed to have abs values when integrating stuff in that form to begin with

$\int \frac 1x \dd{x} = \ln|x| + c$

[native temple]

In my acellus lecture it says to derives rotation matrix by applying rotation to base vectors (0,1) and (1, 0) how is this done?

[ocean seal]

ℝamonov

[quick violet]

See abs is just how integration works, You integrate 1 over x you get ln|x|

[jovial forum]

oh yeah

ffs

ok cool

So to solve for t we can say log|P|-log|P-2000| + ln(1/19) = t and sub in for P now?

[gray isle]

wdym sub in for P

[jovial forum]

What is the value of t when P reaches 500

[gray isle]

you fked up your signs when you manipulated the constant

[jovial forum]

I need to find the time when the population reaches 500

lol

[quick violet]

@gray isle Dont you think every single question should be made a thread? Then there is no need of multiple Q channels

[gray isle]

no bot support for threads atm.
they may be introduced when that happens

[quick violet]

Take this equation for T and sub p(t) = 500

[gray isle]

fix your signs with the manipulation of ln(1/19) first

[jovial forum]

log(P)-log(P-2000) = t - ln(19)?

log(P)-log(P-2000) +ln(19) = t

[gray isle]

yes

that works

and then you can sub in P=500 to determine the time t when that occurs

[jovial forum]

so t = 1.84582669?

[gray isle]

sounds about right

[jovial forum]

Does this give the same answer?

[gray isle]

well there's no point to isolate P

unless the question asks for it

[quick violet]

i am not sure about the eqn after integration in this statement though

[quick violet]

Yeah step 2 of the final part is enough to get the solution in this case

[jovial forum]

Does that look right?

[quick violet]

Oh i solved for the wrong question, i replaced 2000 with 0.0005 and vice versa

[jovial forum]

haha all good

[quick violet]

yeah then your solution is perfect 🙂

[jovial forum]

This is doing my head in, going to do as many practice q's as I can tomorrow

thanks for your help all

[quick violet]

🙂

[native temple]

In my acellus lecture it says to derives rotation matrix by applying rotation to base vectors (0,1) and (1, 0) how is this done?

like if multiplimg matric [1, 2, 3]

by 2

you would multiply 0,1 and 1,0 by 2

you would get 2, 0 and 0,2

how does that work?

[mint helm]

guys what does g(x,y) = {mod((x),) > 0, -1} mean

[native temple]

#help-1

bye

[glass lichen]

You rotate them... and make note of where they land in the output space

Also everything you said after what I replied to is nonsense

[tranquil turtle]

What is y=x

[glass lichen]

A line

An equation

A function

[native temple]

Couldn’t see that online or in paul’s linear algebra notes

[zinc hearth]

In the graphic, i need find X

please

[thin kayak]

can someone help w b

[gray isle]

what have you tried?

[thin kayak]

squaring both sides

but then i got a rly long equation

[gray isle]

you're making this more complicated than needed

you have a quadratic equation

[thin kayak]

oh

yes

[gray isle]

and just because there are complex numbers here, doesn't really stop you from applying something like the quadratic formula

[thin kayak]

should i do that?

[gray isle]

try and see what you get

[thin kayak]

ok i'll do that now

i got that

[wary badge]

Please explain me this proof?

[thin kayak]

@gray isle

[zinc hearth]

ñ

[gray isle]

you're not applying the QF properly

[thin kayak]

where did i go wrong?

[gray isle]

why is there z under your radical

[thin kayak]

whats a radical?

oh wait yeah sry my bad

[flint notch]

hello can you posst pictures for math

how dod you ssolve this

[thin kayak]

please use another channel this one's already taken @flint notch

@gray isle

[flint notch]

okok

[limpid maple]

hi

[gray isle]

you're still not applying the QF properly

[severe halo]

Someone knows it

[sage bronze]

is this a test

[severe halo]

Yes

[sage bronze]

Do not ask for help on tests

[wide raven]

please help me solving this question

[severe halo]

I just finished I had all good

[wide raven]

please can you translate

[split oriole]

Just expand

[wide raven]

i know that

i needed a shorter way

[wary badge]

X = 140°

[split oriole]

Hint subtact R1---> R1-(R2+R3) this will help

[wary badge]

@split oriole can I have ur help?

[wide raven]

ok i will try

[wide raven]

@split oriole It does'nt seem to help

[cosmic maple]

its 140 degree bro, Vertically opposite Angles!

[wide raven]

@split oriole sorry I was doing the operation on columns.......but tbh have already done that but stuck on the very next step

[split oriole]

On which point you are stuck?

[alpine sable]

Can you help me ;w;

[split oriole]

I can try

[alpine sable]

I need help studying

Indices polynomials and my girlfriend says it easy and proceeds to mock me

[alpine sable]

By answering 2 of the hardest questions in my paper pls help me study

[split oriole]

Post in group ,

[alpine sable]

Can you help me in DM I don't want to look dumb

I am afraid and very shy and no cus I will look stupid

I am afraid to look stupid

Can we do in DM

[split oriole]

Ok

[unkempt hatch]

how did we go from line 1 to line 2?

[gray isle]

long division and/or clever manipulation applying the same principle

[unkempt hatch]

is that the only way? the book simply says after simplifying. does simplifying imply long division?

[gray isle]

simplicity is subjective here

depending on the question, the final form they reach may be more useful for following parts

[unkempt hatch]

oh ok. was just wondering if there was anything else which is simpler than long division because the question is not at all related to long division. It is a question of mathematical induction

[gray isle]

if you're up to mathematical induction anything previously learned may be applied

[unkempt hatch]

yeah fair enough. thanks for the answer!

[fierce scroll]

Hello i would like some help with this question

[ancient saddle]

Hello, try raising both sides of the first equation to the 2nd power

[gray isle]

that's not how squareing works

[peak cloud]

Couldn't this be done without removing the decimal?

[gray isle]

yes, the division can be done without shifting the dp two places

[fierce scroll]

i mean isnt it the same?

[gray isle]

$(a-b)^n \neq a^n - b^n$

[ocean seal]

ℝamonov

[peak cloud]

Weird enough,the answer in my textbook for this question is 3 1/11

[vale wigeon]

you can use your logic to prove that 7 = 1

[gray isle]

,calc 33.92/11

[ocean seal]

Result:

3.0836363636364

[fierce scroll]

what

[peak cloud]

I know they haven't done the question with decimal and just wrote it in fraction form but that still looks wrong.

Here is the remainder one.

3 92/11

[gray isle]

3 92/1100

[molten bramble]

Can someone help me with all of these

[peak cloud]

My textbook probably got it wrong.

Not unusual unfortunately.

[gray isle]

what's the actual original question and what is the textbook saying

[peak cloud]

Find the positive square root of:9 67/121
Textbook's answer:3 1/11

[gray isle]

oh the textbook is correct then

what's leading you to do 33.92/11

[exotic mortar]

Can someone help me please?

^using binomial theorem

[vale wigeon]

what values can n even take for there to be an x^5 term?

[exotic mortar]

I think it'll have to be 1 or 3

or 5

[peak cloud]

I first convert it into improper faction then find out the square root of both the denominator and numerator (1151 and 121)then I get 33.92 and 11.Then,I divide them both.

[vale wigeon]

@peak cloud channel busy please move

[gray isle]

shah was here first

[vale wigeon]

@exotic mortar two of these are possible while another is not

oh they were

my bad

...

[gray isle]

wheres 1151 coming from

[vale wigeon]

the curse of questions-zero

[exotic mortar]

Sorry ill move

[peak cloud]

Oh I messed up in addition.

Thanks Ramonov,I got it right.

[winter salmon]

i keep getting sqrt of 2/3

and its wrong :( i can't think of another way to solve it

[gray isle]

can you show your work

do you mean $\sqrt{\frac23}$

[ocean seal]

ℝamonov

[winter salmon]

yes

[gray isle]

well the value is correct, but may not be as simplified as they want

they probably want a rational denominator

[winter salmon]

they said the answer was sqrt6 over 3 but i dont know how they got that

[sage bronze]

rationalise the denominator

[unique latch]

How do u guys keep track of this server

[topaz scaffold]

Wdym?

[winter salmon]

oh omg how did i not think of that

[unique latch]

Like theres so many channels and its so active

[winter salmon]

thanks

[unique latch]

Dum

[topaz scaffold]

I only look at the math help channels lol

[unique latch]

Jk

[topaz scaffold]

[unique latch]

K

[winter salmon]

[unique latch]

Jk

Jk

Mk

Jk

[sly mantle]

refrain from making comments like these

[unique latch]

Ok sorry

[dense blaze]

im trying to find
$\lim_{x \rightarrow -\infty} \frac{cosx}{3x}$ \
\
so i showed \
\
$-1 \leq cosx \leq 1 - line 1$ \
\
$\frac{-1 }{3x} \leq \frac{cosx }{3x} \leq \frac{1}{3x}$ - line 2 \
\
then afterwards, i would use squeeze theorem to find the limit of $\lim_{x \rightarrow -\infty} \frac{cosx}{3x}$ \
\
for line 2, do i have to reverse $\leq$ signs since the limits is $\rightarrow - \infty$ ?

[ocean seal]

sevenseas

[topaz scaffold]

No

It still holds on the negative side

[warped phoenix]

hey quick question, sin/cos/tan is used for finding a missing side, and arc sin/cos/tan is used to find a missing angle, right?

[topaz scaffold]

Yep

[warped phoenix]

great, ty

[jolly stone]

yes you need to reverse the sign

[topaz scaffold]

I am in confusion apparently

Oh right

Sorry

[jolly stone]

-1/(3x) still -> 0 from positive side as x -> -infty

[dense blaze]

ohh yeah

[sly mantle]

@dense blaze as x->-infty it’s enough to consider what happens for x<0, in which case dividing by x flips inequalities

[dense blaze]

ya i see thanks!!

[runic obsidian]

can someone help me with this question?

[topaz scaffold]

One question at a time lol

[alpine sable]

what

[runic obsidian]

^

[topaz scaffold]

So if you put in $\frac{x-2}{2}$ into f(x) you'll get 5x-10

[ocean seal]

RipeOrange

[runic obsidian]

wait how

[topaz scaffold]

Is this an ACT/SAT question btw?

[runic obsidian]

yeah]

[topaz scaffold]

Ah

So what you want to do is just plug in then

For example for answer choice A

f(x) = 10x-5

That means $f(\frac{x-2}{2}) = 10(\frac{x-2}{2}) -5$

[ocean seal]

RipeOrange

[runic obsidian]

ohhh

i understand it now

i was confused with how it was phrased

[topaz scaffold]

Ah

[runic obsidian]

thanks for helping clearing that up 🤣

[topaz scaffold]

Np

[topaz scaffold]

Recall that if an angle is in radians

Doing θ*r would give you the arc length

[alpine sable]

the answer is 1.5 radians right

[topaz scaffold]

With θ being the angle in radians and r being the radius

[topaz scaffold]

Yep

[alpine sable]

can you help me with b)

[topaz scaffold]

Hmmm

3 radians would be a little less then π

So it'll be a little less then half the circle or 180 degrees

Not sure what it means by radius of the angle tho

[oak chasm]

@gaunt magnet What does a derivative tell you about the function?

[gaunt magnet]

fx is increasing on interval x>4 and f(x) is decreasing on the interval x<4

[oak chasm]

No, in general, what does a derivative of a function tell you about the function?

[warped phoenix]

can i use a ti 84 + ce to solve for x or do i need one of those cas calculators?

[oak chasm]

@warped phoenix Looks like it can solve some equations: https://sciencing.com/solve-texas-instruments-ti84-calculator-8074871.html.

[oak chasm]

@alpine sable How many degrees are in a circle?

[alpine sable]

360

[oak chasm]

How many radians are in a circle?

[alpine sable]

um

idk

i forgot everything

[oak chasm]

There are 2π radians in a circle.

So, 360 degrees is equal to 2π radians.

So, multiply the degrees by 2π/360 degrees.

The degrees will cancel, leaving radians.

Does that make sense?

[alpine sable]

ok so i multiply 10 by that?

[ocean seal]

Chai T. Rex

[oak chasm]

The degrees cancel.

[alpine sable]

what would that be

[oak chasm]

Well, what's 10 times 2 divided by 360?

[alpine sable]

20 divided by 360

idk

[oak chasm]

Which is what fraction?

[alpine sable]

1/12

i think

[oak chasm]

No, try again.

[alpine sable]

i mean 1/18

[ocean seal]

Chai T. Rex

[alpine sable]

thanks for babysitting me through the question

[oak chasm]

No problem.

OK, expand those.

Use the distributive property on 2(x - 3) and 3(x - 1).

OK, so a(b + c) = ab + ac.

Have you seen that before?

OK, that's called the distributive property.

If you have a number in front of parentheses and an addition inside parentheses, here's what you do.

You multiply the number in front of the parentheses with each number you're adding inside the parentheses.

8(2 + 3)

8 · 2 + 8 · 3

See how I multiplied the number in front of the parentheses with each number I'm adding inside the parentheses?

No, multiply each by 8.

So, let's do it with your problem.

You have two of those things.

Let's do the first one.

2(x - 3)

We multiply 2 by each thing inside the parentheses.

2 · x - 2 · 3

Don't forget the - that was there between them.

Does that make sense?

OK, so 2(x - 3) = 2 · x - 2 · 3 = 2x - 6.

Does that last part make sense?

[alpine sable]

@oak chasm would i dvide by 2 pi/360

[oak chasm]

Is this a graded test or homework?

Sorry, we can't help with tests.

<@&268886789983436800>

[sly mantle]

b&

[oak chasm]

@alpine sable For that one, you want the radians to cancel out.

[ivory sky]

Dose someone know why
(x ^1/2 )^5 equals 5/2 and not 1/2

[oak chasm]

So, you have 360 degrees and 2 π radians.

You put the radians on bottom.

[alpine sable]

what do you mean

[oak chasm]

Well, when you have the same thing on both sides of the fraction, you can cancel, right?

[ocean seal]

Chai T. Rex

[oak chasm]

See how the 2s cancel?

[alpine sable]

yea

[oak chasm]

Units do that too.

So, you want radians to cancel.

[alpine sable]

how would i wwrite this one out

like

[oak chasm]

So, you put radians on the bottom to cancel your radians from the problem, which will be on top.

[alpine sable]

so will it be

[oak chasm]

So, 360 degrees/2 π radians has radians on the bottom.

So that's what you use.

[alpine sable]

omg im so confused

[oak chasm]

(\frac{\pi}5 \cdot \frac{360^\circ}{2\pi})

[ocean seal]

Chai T. Rex

[alpine sable]

oh

[oak chasm]

You use what you unit you want to cancel out to get what unit to put on the bottom of the conversion fraction.

[alpine sable]

what does that eual

equal

[oak chasm]

You want radians to cancel out and be left with degrees? Put radians on the bottom.

[alpine sable]

and then i do the same for the question below it

[oak chasm]

Well, do the multiplication.

What do you get?

[alpine sable]

around 35 is that wrong

[oak chasm]

It's almost right.

What's the exact fraction?

[alpine sable]

i got 35.96

not a fracion

[oak chasm]

No.

Do the multiplication directly.

Leave π as π.

[alpine sable]

ok

um

1130.9724/62.8318

idk

[oak chasm]

No, leave π as π.

What is the top when you multiply?

[alpine sable]

its 1130

[oak chasm]

No, it isn't.

[alpine sable]

360 pi

[oak chasm]

Right.

[alpine sable]

OHH

[oak chasm]

What is the bottom when you multiply?

[alpine sable]

and then 10

pi

[oak chasm]

Right.

πs cancel.

[alpine sable]

so 36

[oak chasm]

Right, 36 degrees.

[alpine sable]

omg thanks

[oak chasm]

You're welcome.

[ivory sky]

Dose someone know why (x^1/2)^5 equals 5/2 and not 1/2.

[oak chasm]

What do you mean by equalling 5/2?

Where is the x?

[ivory sky]

I mean the exponets multiplyinv

[oak chasm]

Well, 5 times 1/2 is 5/2.

[ivory sky]

Oh

How would I find a number multiplied by its self 4 times equals 9

[oak chasm]

OK, how do you write a number multiplied by itself four times?

[ivory sky]

X^4

[oak chasm]

OK, so write the equation for your problem.

[ivory sky]

(9^1/4)^2

[oak chasm]

That's not an equation.

The problem has an equation.

[ivory sky]

Uh

I don't know what you mean

[oak chasm]

See where it says equals in the problem?

[ivory sky]

No

[oak chasm]

Read the problem.

[ivory sky]

I don't see it

[oak chasm]

Read this ^

Do you see equals there?

[ivory sky]

Ye

[oak chasm]

OK, so when you write the equation, the equals will be replaced by an equal sign.

What's on the left side of equals in the sentence there?

[ivory sky]

Oh you meant make an equation

X^4 = 9 mabey

[oak chasm]

Right.

Now what can you multiply the exponent by to make it 1?

[ivory sky]

1/4

[oak chasm]

Right, so take both sides to the power 1/4.

Also, when you take a number to the 4th power, the sign disappears, right?

[ivory sky]

X = 9^1/4

Ye

[oak chasm]

OK, so you need a plus-minus symbol on one side.

That's because the sign disappeared, so we need to add it back.

It could be positive sign or negative sign.

So, we add both back.

[ocean seal]

Chai T. Rex

[oak chasm]

Does that make sense?

[ivory sky]

Ok

But I don't know what 9^1/4 is

[oak chasm]

OK, so factor 4.

What do you get?

[ivory sky]

2x2

[ocean seal]

Chai T. Rex

[oak chasm]

Does that make sense, since you multiply the powers?

[ivory sky]

Yes

[oak chasm]

What's the square root of 9?

[ivory sky]

3

[ocean seal]

Chai T. Rex

[ivory sky]

And I Don't tinck their is a 3^1/2 because it's prime

[ocean seal]

Chai T. Rex

[ivory sky]

Ok

Ty

[ocean seal]

Chai T. Rex

[oak chasm]

No problem.

If you want to check, fill in both values of x into your original equation.

[ivory sky]

Ok

[ocean seal]

Chai T. Rex

[oak chasm]

Calculate the left side. See if it comes out to 9.

[ocean seal]

Chai T. Rex

[oak chasm]

Same thing.

[ivory sky]

Ye I got 9

[oak chasm]

How about for the negative version?

[ivory sky]

9 again

[oak chasm]

OK, and do you need just real number answers or have you started complex numbers?

[ivory sky]

I just need real numbers

[oak chasm]

Oh, OK, then those are the answers.

[ivory sky]

Ty

[oak chasm]

You're welcome.

[buoyant meadow]

I'm stugled

[alpine sable]

what are you asked to do?

simplify?

[buoyant meadow]

No, they just ask to solve

But..

I don't know very well with these negative numbers

[alpine sable]

it's okay

it looks like you have done an attempt to solve this, can i see it?

if you haven't let me know, and we can start this together.

[buoyant meadow]

My.. rascunho?

Okay..

I will show you

[alpine sable]

what is rascunho?

okay.

[buoyant meadow]

I dont know the word in english

But is when we try to solve

But is just a try

[gaunt magnet]

hehe.

[alpine sable]

it's okay, let me see if possible.

[alpine sable]

@gaunt magnet please read #❓how-to-get-help , this channel is occupied.

[gaunt magnet]

i have

over 100 timesd

[alpine sable]

okay, well, again, this channel is occupied and it goes under #❓how-to-get-help not to post in an occupied channel, please use a free one.

[gaunt magnet]

this not free

[alpine sable]

no, it's not free.

[gaunt magnet]

[alpine sable]

@buoyant meadow do you not need help anymore?

[buoyant meadow]

I did solve first the terms 3² and 2² and take the denominator

After i did the fraction and the result is : 81/9

I multiply the terms 3²/1 × 2²/1 × (-9)²/(-3)² = 2916/9

And the denominator in the botton
(-3)² = 9

But..

I dont know if i'm rigth

And what to do now

[buoyant meadow]

Oh.. Okay

[alpine sable]

no, that wasn't directed to you

it was directed to Usman.

[buoyant meadow]

Can you help me?

[alpine sable]

okay

[alpine sable]

so what i'm seeing here is fine

but i'm unsure whether you've ended up with a final result

all you have there is broken up parts of calculations, which are fine but still not have a result gathering everything

[buoyant meadow]

So.. can i continue the problem?

[alpine sable]

yes, you are pretty much almost done

so, you have done the upper part $$\frac{3^2\cdot 2^2\cdot \frac{(-9)^2}{(-3)^2}}{(-3)^2}=\frac{\frac{2916}{9}}{9}$$

[ocean seal]

Al𝟛dium

[buoyant meadow]

If i flip this, can i make a multiplication?

[alpine sable]

this is what you've told me, which is correct so far

[alpine sable]

this is a little ambigue

[buoyant meadow]

I dont know if have more thing to do here

[alpine sable]

whenever you have these fractions, you can always do the following $\frac{\frac{2916}{9}}{9}=\frac{2916}{9}:9$

[buoyant meadow]

9/1?

Oh.. Okay

[alpine sable]

what is this supposed to mean?

9/1 isn't the answer to this problem

[buoyant meadow]

9
_
1

You have write

1
_
9

[alpine sable]

yes, that's good now

$\frac{\frac{2916}{9}}{9}=\frac{2916}{9}:9$

[ocean seal]

Al𝟛dium

[buoyant meadow]

@alpine sable thanks

[alpine sable]

okay, now do you know how to finish this?

[buoyant meadow]

No

[alpine sable]

okay.

do you know how to deal with simpler examples like $\frac{2}{3}:\frac{2}{1}$?

[ocean seal]

Al𝟛dium

[alpine sable]

or do you need a refresh on how to divide fractions?

[buoyant meadow]

Maybe fliping

[alpine sable]

okay, yeah we can do it that way as well, it is true that we can "flip" the second fraction and multiply the 2 fractions: $$\frac23 {\color{green}{:}}\frac21 =\frac23 {\color{green}{\cdot}} {\color{blue}{\frac12}}$$

[ocean seal]

Al𝟛dium

[alpine sable]

does this make sense?

[buoyant meadow]

Yeah

But i have thinking that need flip both fractions

[alpine sable]

no, you don't flip both fractions, that'd be incorrect

[buoyant meadow]

Thanks

[astral dagger]

qualquer coisa posso te ajudar

quando precisar falar em pt

anyways

[alpine sable]

so are you able to finish now?

[buoyant meadow]

Tá de boa cara, eu vou tentar

I'm..

Como dizer confiante? @astral dagger

[astral dagger]

I think "confident" will fit

[buoyant meadow]

I'm confident

[alpine sable]

okay, you're welcome

[prime zodiac]

Hope this channel was free. I need some assistance figuring out how to solve this differential equation and get an implicit general solution. Let me first show the question:

https://i.imgur.com/QESExmf.png

Now, my plan of attack was:

1. separate
2. integrate
3. clean up and set equal to C (that's what it wants, I guess)

Here's my steps (going to type latex so the bot gets it just a sec)...

$$\frac{3y^6-y}{y^9}dy = \frac{x-6}{x^2}dx$$

[ocean seal]

simple

[prime zodiac]

$$\int{\frac{3}{y^3}-\frac{1}{y^8}dy} = \int{\frac{1}{x}-\frac{6}{x^2}dx}$$

[ocean seal]

simple

[prime zodiac]

$$\frac{-3}{2y^2}+\frac{1}{7y^7} = ln(x)+\frac{6}{x}+C$$

[ocean seal]

simple

[prime zodiac]

simplified left side $$\frac{-21y^5}{14y^7}+\frac{2}{14y^7} \equiv \frac{2-21y^5}{14y^7}$$

[ocean seal]

simple

[prime zodiac]

$$\frac{2-21y^5}{14y^7} = ln(x) + \frac{6}{x} + C$$

[ocean seal]

simple

[prime zodiac]

then finished with $$\frac{2-21y^5}{14y^7}-ln(x)-\frac{6}{x} = C$$

[ocean seal]

simple

[prime zodiac]

but my homework system is marking me wrong and now I'm stuck :p

It wants it in this =C format https://i.imgur.com/fRYtMED.png

Oh my god

It wanted $$ln|x|$$ instead of $$ln(x)$$

Channel free.

[ocean seal]

simple

[placid zinc]

Good presentation, I enjoyed

[prime zodiac]

[oak chasm]

@prime zodiac The first step is wrong.

Oh, never mind.

I misread.

[prime zodiac]

Eh? The homework system accepted it anyway

[wheat condor]

anyone knowing calc ?

<@&286206848099549185>

[alpine sable]

https://www.dontasktoask.com

[ashen agate]

is the correct way to answer a question like , In how many ways can the letters in the following words be arranged? by multypling the number of letters like 5x4x3x2x1?

[wheat condor]

Any Calc experts around who are willing to commit into looking into my problem, whatever that may turn out to be, even if it's not actually related to Calc or if someone who doesn't know anything about Calc could actually answer my question?

[ashen agate]

https://www.dontasktoask.com/

[alpine sable]

try #calculus

I dont understand why we factor to solve quadratic equations

I understand how, you find two numbers that multiply to give C and add to give B, but I dont understand why

it's just a formula, I have no idea how it works.

[austere bridge]

If you factor as $(x+r_1)(x+r_2)$, you expand to get $x^2+(r_1+r_2)x+r_1r_2$. If you match terms with $x^2+bx+c$, you see that $r_1+r_2=b$ and $r_1r_2=c$

[ocean seal]

cgodfrey

[austere bridge]

(assuming a=1)

[placid zinc]

If you expand, I'm sure you have no problem saying:
(x - a)(x - b) = x² - (a + b)x + ab

Factoring is simply using this relationship in reverse.

[alpine sable]

What does expand mean

[austere bridge]

FOIL

is what I know it as

multiplying each pair of terms

[alpine sable]

I dont see why the middle term has to be a+b

[placid zinc]

If you don't know how to multiply two binomials, take a second to look it over, googling "FOIL method" will get you lots on it.

Because factoring is doing this, but in reverse

[alpine sable]

I've googled FOIL, I've memorized the rule

but again, these are just rules to me

I want it to intuitively click in my mind

not more formulas

[placid zinc]

FOIL is actually the distributive property, but applied a lot

[alpine sable]

Yeah I understand foil more

[placid zinc]

So by applying FOIL:
(x - a)(x - b) = x² - (a + b)x + ab

Which means, if we write our polynomial in that form on the right, we can easily write it in factored form

[alpine sable]

I dont get how (x-a)(x-b) is coming from x^2 - (a+b)x + ab

I also don't know why it's (a+b)x +ab

[placid zinc]

Do you understand how to apply FOIL on
(x - a)(x - b)?

[alpine sable]

Yes but I dont know why that is coming up

[placid zinc]

We like writing polynomials in that form, so knowing more about it is a good thing

[alpine sable]

I am not getting how they are equivalent forms

[placid zinc]

Let's try on this:
(x - 2)(x - 4)
What is that, when expanded?

[alpine sable]

x^2 -4x -2x +8

[placid zinc]

Yaya. That is, x² - 6x + 8

[alpine sable]

6x?

oh

gotcha

[placid zinc]

Note that -6 is the sum of -2 and -4
And 8 is the product of -2 and -4

[alpine sable]

that last part seems like a coincidence

why must 8 be a product of -2 and -4

[placid zinc]

You could call it a coincidence haha

Just, FOIL makes sure that this always happens

If we drop the numbers and do the general form again:
(x - a)(x - b) = x² - (a + b)x + ab

You see that the product, ab, always ends up there

[alpine sable]

6^2 + 12x -8

what is the first step here

[placid zinc]

Haha so this one isn't the same as I was just focusing on when the first coefficient = 1

Here's an example:
x² - 5x + 6

Can be written as:
x² + (-2 - 3)x + (-2)(-3)

Which we already know can be written as:
(x - 2)(x - 3)

And if you'd like to check, you could expand that, to get the original problem back

[ashen agate]

How many digits greater than 200,000 are there using only the digits 1, 1,
1, 2, 2, 3?

how do i solve this

<@&286206848099549185>

anyone

<@&286206848099549185>

[wary stream]

First, you needed to wait 15 minutes before pinging helpers, and second you don't need to ping multiple times

[jovial forum]

Just a quick question, I know how to multiply two matrices together, so if I have A and B I can find AB, but I don't know what this arrow above them means. Is this just asking to find AB like I normally would or am I meant to do something else?

So is the answer (15,0,2)?

[tiny ledge]

That arrow indicates to find the vector AB, so the vector B - vector A

So it would be (5-3,2-0,1-2) = (2,2,-1)

[jovial forum]

Thanks, simple as that?

[tiny ledge]

Yep

[jovial forum]

Thanks!

[ashen agate]

There are 5 speakers scheduled for a seminar on careers. How many
different orders of speaking are possible if there are no special conditions

is it 120?

[tiny ledge]

5! different orders, so yeah 120

[gaunt magnet]

hey

channel free

?

ok

i think im stuck on 1 part

ill show my steps

i start off like
$\ (x^{2} -5)^{4}\frac{d}{dx}(\frac{3}{2x}+9)^{3} + \frac{d}{dx}(x^{2}-5)^{4}(\frac{3}{2x}+9)^{3}$

[ocean seal]

Usman

[topaz scaffold]

Can you find another channel please?

That's not in use?

[rocky geyser]

k sorry

[gaunt magnet]

$$\frac{d}{dx}\left(\frac{3}{2x}+9\right)^3$$
$$= 3\left(\frac{3}{2x}+9\right)^2 \cdot \frac{d}{dx}\left(\frac{3}{2x}+9\right) \ [\text{using chain rule}]$$
$$= 3\left(\frac{3}{2x}+9\right)^2 \cdot \left(\frac{-3}{2x^2}\right)$$

[ocean seal]

Usman

[gaunt magnet]

i differentiated the (3/2x+9)^3 part

now

[tiny ledge]

That's correct so far

[gaunt magnet]

ok so now i Do the same thing for the derivative of (x^2-5)^4

thats where i may go wrong

[prime zodiac]

follow same steps for power rule, should be ok, give it a try

[gaunt magnet]

ye did the same steps and got 4(x^2-5)^3 . 2x

[prime zodiac]

yes sir, looks right

[gaunt magnet]

Now plug everything in and i got

$(x^2-5)^4\cdot 3(\frac{3}{2x}+9)^2(-\frac{3}{2x^2})+4(x^2-5)^3\cdot 2x(\frac{3}{2x}+9)^3$

[ocean seal]

Usman

[prime zodiac]

that looks good, now just simplify it

[gaunt magnet]

Oh can it get simplified?

[tiny ledge]

I don’t think you can simplify if it’s just the derivative, can only really collect like terms

Multiples and such

[prime zodiac]

4 and 2x can combine to 8x

that's all i meant

otherwise looks right

[gaunt magnet]

i think it can get factored

[limpid maple]

this is very confusing for me :/

[prime zodiac]

channel is in use, plz find another put.... p v q's truth table is T, T, T, F whereas p -> ~q has F, T, T, T so that's already not quite correct

edit: my b, forgot v is inclusive lol

[prime zodiac]

Which part?

[gaunt magnet]

,w factor (x^2-5)^4\cdot 3(\frac{3}{2x}+9)^2(-\frac{3}{2x^2})+4(x^2-5)^3\cdot 2x(\frac{3}{2x}+9)^3

[ocean seal]

Results provided by WolframAlpha

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

Requested by Usman#0988

[prime zodiac]

Oh you mean factor out the top and stuff. You can but it's not strictly necessary (unless your teacher wants that)

[gaunt magnet]

well i think i dont need to factor its good how it is

[rocky geyser]

Can someone help me in channel three

[prime zodiac]

be patient.

[rocky geyser]

Have been for the past 25 minutes

[prime zodiac]

Ok.

sorry not sure how to help with that -- please grab another free channel and ask again, explain the exact question and so on. This one is still in use by @gaunt magnet I believe

[untold warren]

got a quick q

how would I turn this equation

into this one

ive isolated the x in the orignial equation, do I just apply the derivative, square, etc?

[ripe remnant]

If u get a 10/12 in a math quiz

Is that a B

Or A

[prime zodiac]

depends on the professor/school grade scale but it's an 83% which is typically a B.

[ripe remnant]

Oh ok

[prime zodiac]

take the derivative of x with respect to y, then you can plug that in and square the whole thing (FOIL)

[untold warren]

yeah just having troubles with it

[prime zodiac]

what have you got now

[untold warren]

the sqrt is confusing me

[prime zodiac]

sqrt(1-2y) is the same as (1-2y)^(1/2). Does that help you differentiate?

[untold warren]

ah i think i see?

[prime zodiac]

Give it a go and see where you get

[untold warren]

sorta like this?

then I guess this?

ah wait not 1/4, just 1

[ripe remnant]

How do u solve this

[ionic jewel]

define solve?

it's just a constant, you can look up the value

[ripe remnant]

Ok thx

[ripe remnant]

What if it comes up in a math quiz

[ionic jewel]

it's the Euler–Mascheroni constant

[ripe remnant]

Ok

Thx

[ionic jewel]

there's no better way to express it afaik

[ripe remnant]

Ok thx for ur time

[eternal shadow]

I guessed and I was correct with C.

Can someone explain it anyways?

[ancient saddle]

The length of the square's diagonal is equal to the radius r, so it's area is r^2/2. The shaded area is the circle's area minus the square's area: πr^2 - r^2/2 = 36π - 18

[surreal meadow]

i call it the Mascheroni constant, Euler has enough things named after him 😤

[peak kite]

Guys my old school teachers told me to teach 8 th year old so my teachwr gonna give me questions i will give to them and rhen i havw to tell if the answeer is ok

Anybody

[ionic jewel]

You know they started naming things after the first person that discovered them after Euler at some point

so its even more than you would expect

[surreal meadow]

what

[peak kite]

I will get questions i need answers

Not now tho

[ionic jewel]

dont use every channel

just ask when you hav equestions

[peak kite]

Idk what i hhave to ask

I will get questions after

2 and half hours

[surreal meadow]

i'm confused

[peak kite]

I need answers asap

Basically its a meeting with lil jids

Of 8th

Lil kids

[surreal meadow]

well i'm assuming you'll be able to answer the questions yourself

otherwise you wouldn't be put in this position no?

[peak kite]

I don't wanna be

My teachers told could you maybe have an online meeting my the kids of your schiol and teach em stuff

[surreal meadow]

ok so are they 8 years old

or are they in 8th grade

[peak kite]

8th gade

Grade

[surreal meadow]

and what grade are you in?

[peak kite]

I am in 11th grade

But i don't do maths

Atm

Maths ain't my subject

[surreal meadow]

they're not going to be learning what you'd learn

[peak kite]

Other subjects i can do

[surreal meadow]

did they tell you what type of math they are learning?

[peak kite]

They sended me ss of their book

[surreal meadow]

can we see 1

[peak kite]

I only have one

[surreal meadow]

this looks like pre-algebra

[peak kite]

No

Exponents and power

And percentage

[surreal meadow]

i see

yeah it's algebra

[peak kite]

Would you be able to do questions like this

[surreal meadow]

you should be able to

you're in 11th grade no?

[peak kite]

I don't do maths

I failed in 10th grade

[surreal meadow]

then tell your teacher that?

[peak kite]

I did not tell her earlier

Hwo do i tell her noq

[surreal meadow]

email?

[ripe remnant]

Oof don’t worry I’m not that great at math aswell but I pass when I study

[peak kite]

No

[peak kite]

So will ya help me in 8th grade work

[surreal meadow]

shrwan what math did you fail in 10th grade?

was it algebra?

[ripe remnant]

I’m in yr 7

[peak kite]

Yeah

[peak kite]

Oh nvm

[ripe remnant]

Sorry

[peak kite]

No i mean

[surreal meadow]

so if i gave you 10x + 5 and told you x = 2

would you be able to solve that?

[peak kite]

I can do that

[candid nova]

Anyone know how to figure out what the method is to solving how many equivalence classes there are for the relation R on F

[surreal meadow]

that's one of the questions in the page

[peak kite]

No its just one question

There are tough one

Most probably i will do em all

But still need someone that can help if smthn goes wrong

@surreal meadow

[surreal meadow]

there's no guarantee someone will be readily available to help you

[peak kite]

CaN you

After

[surreal meadow]

no

[peak kite]

2 hours

Ok

[surreal meadow]

do you know what

[peak kite]

<@&286206848099549185> help

Me

[surreal meadow]

(a + b)(a + b) = ?

[peak kite]

Screw it

Guys my old school teachers told me to teach 8 th year old so my teachwr gonna give me questions i will give to them and rhen i havw to tell if the answeer is ok

My teachers told could you maybe have an online meeting my the kids of your schiol and teach em stuff

<@&286206848099549185>

[surreal meadow]

don't ping helpers multiple times

[candid nova]

what is going on lol...

[peak kite]

I nsed help

Need helo

Need help

[surreal meadow]

shrwan its not that deep

[peak kite]

Ik

[surreal meadow]

they are in 8th grade

[peak kite]

But

[candid nova]

same bro but u gotta wait for the helpers

[peak kite]

Idk

[surreal meadow]

it's not that big a deal

[peak kite]

If smthn goes wrong

[surreal meadow]

just go review algebra for 10 minutes

[peak kite]

I need someone that can help

[surreal meadow]

what would go wrong???

[peak kite]

Idk

No one gonna help me

[candid thistle]

It's a math test

[peak kite]

No

[candid thistle]

I don't think we are allowed to help with that

[peak kite]

There qill be above 120 studenta

Ah no one gonna help

[candid thistle]

Yes, the number of students don't decide whether it is a test.

Just review algebra

[peak kite]

I have to give em questions

[candid thistle]

You make questions or do you solve em?

[peak kite]

My tecaher gojna give me sheet

I send en

They solve em

Then i tell em

Whats the mistake

[candid thistle]

Ohh ok

Then you should know, yes?

[peak kite]

I falield maths in 10th grade

I need help with grade 8th

[candid thistle]

ok ig we can help

[short sonnet]

Can i dm someone my math hw

[candid thistle]

cuz it aint you whos getting graded

[peak kite]

Yeah

Afyer 2 hours ok

You be online please

[candid thistle]

I won't be here after two hours but someone else most likely will

[peak kite]

Omg

No one else is helpinh me

[candid thistle]

well i cant be online discord at that time :(

[peak kite]

Omg

[surreal meadow]

@peak kite it's your job to inform the teacher if you're not up to a task

you failed to do that, and now there's no guarantee someone will be able to help you

[candid thistle]

try doing the problems beforehand if you have problems

[candid thistle]

grammer

[surreal meadow]

just accept the fact that you're in an uncomfortable position and do your best to help those 8th graders

go review some basic algebra while you can

[candid thistle]

Springboard mathematics 😢 I greatly dislike that curriculum

Yet our school uses it :/

[candid nova]

<@&286206848099549185>

[surreal meadow]

@candid nova #❓how-to-get-help

[candid thistle]

Don't ping da helpers but what is your problem?

[candid nova]

i posted it above

let me do it again

[surreal meadow]

@candid nova next time try posting in an unoccupied channel so your question doesn't get written over

[candid nova]

ah mb

just need help on b

[wanton beacon]

How would I go about solving this?

<@&286206848099549185>

[stoic cloud]

For this would domain be just (-2)? or [-2,-5]?

[candid thistle]

The domain is an interval