help-0

[slender marten]

$\frac{\dd{y}}{y - \frac{7}{3}} = -\frac{3}{2}\dd{t}$.

[ocean seal]

stabulo

[slender marten]

2 dy/dx = 7 - 3t = -3(t - 7/3). Rearranging to give the above differential.

[sacred steeple]

Geometry is really difficult for me

[slender marten]

You probably made a error simplifying a long the way.

[slender marten]

I don't know much geometry, so sorry about that.

Rearrange.

[vestal hawk]

@slender marten is e^(-3t/2) the same as e^(-t/2)/3

[slender marten]

(Note. You can only divide by y - 7/3 for y not equalling y = 7/3, this will be a lost solution you will need to include somehow to form a general solution.)

[vestal hawk]

S as it forms a Z

[slender marten]

You wrote (1/3)e^(-t/2).

[normal turtle]

@lone heart

its saying this is wrong i need help

[slender marten]

Looks correct.

[slender marten]

Each x in the table maps to one and only one real value of y. Looks like your answer is wrong.

It doesn't.

We require that each input x corresponds to one and only one real value.

[normal turtle]

anyone know where i messed up

[slender marten]

x = 3 corresponds to y = -8. This is one and only one real value

x = 2 corresponds to y = -3. This corresponds to one and only one real value.

You are saying that it is not a function.

?

Why?

You have it the wrong way around.

Every x value must map to one and only one y.

y(x) = 2 on the interval -2 <= x <= 2 is a function even though every x on that interval maps to the same output value.

You cannot have the same input value mapping to two y values.

x = 2 couldn't be allowed to map to both y = -4 and y = 4 for example.

Just read it again, very slowly.

I think so.

You are going in the wrong direction.

The domain is the x values.

There are 7 elements of the domain in this function.

The domain is the set {-3, -2, -1, 0, 1, 2, 3}.

Each of these map to a single output.

x = -3 maps to only y = -8 and so on.

If the question was x as a function of y then it would not work since a element of the domain y = -8 would map to both x = -3 and x = 3.

[feral flower]

mate i literally need help with my times tables

[slender marten]

I'm not sure how else I can describe it.

You can also think of it as a one-to-one graph. One input maps to one and only one output.

[vestal hawk]

guys how do i find general solution of this
dy/dt = 2y(100-y)

[slender marten]

The inputs are x = -3 and x = 3.

It doesn't matter if they map to the same y value as long as they map to one and only one.

Outputs mapping to outputs?

x = -3 maps to the same output as x = 3 which is the value -8.

x = y^2.

$y = \pm \sqrt{x}$.

[ocean seal]

stabulo

[slender marten]

x = 2 maps to both the values -sqrt(2) and sqrt(2).

Since the element in the domain x = 2 doesn't map to one and only one element image, since it maps to two elements in the image, is it not a function.

Just find a video, I cannot explain it in any other way.

Maybe someone else can. I just don't see the confusion at this time.

It is a function and answer C means it is not a function since that option starts with the word "No".

Where?

I wonder what came before that.

[alpine sable]

Is Question 12d not already a CNF?

[slender marten]

I'm only here to help you, so I wouldn't see the point in me trying to pull some weird mischaracterisations.

[alpine sable]

Also, why is not(Q) or P a labeled as a CNF according to the solutions to the book, is it not only a DNF? Maybe its both idk

[slender marten]

Hopefully someone else can aid you with the answer since it's the first time in three plus years someone has not eventually understood my explanation.

Never aggression, I've come to accept everyone is trying their best.

Yes. This is true.

This makes it a function.

[near cove]

Does anyone know the answer to this

[slender marten]

Hence in option C, the part "No" disqualifies this option.

[alpine sable]

Skewed Left
Min: 0
Q1: 13
Median: 16
Q3: 19
Max: 20

[near cove]

Thanks

[slender marten]

I think I misread the option C. I'm glad you got it in the end.

[wary stream]

Don't give out answers

[alpine sable]

Sorry 🥲

[pure frigate]

I have a question on Permutation and combination:

I have 6 Marvel character and 4 DC character.
I have to select 4 member such that there's at least one character from each group.
Given solution logic:
1M and 2D
or
2M and 2D
or
3M and 1D
= (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) = 194

_
My logic:

I select 1 from Marvel: 6 ways.
And 1 from DC: 4 ways
I select remaining two from the remaining 8: 8C2

= 6 x 4x 8C2 = 672

=
My another logic:

I select 1 from Marvel: 6 ways.
And 1 from DC: 4 ways
I select one from the remaining 8: 8C1
I select one from remaining 7: 7C1
= 6 x 4x 8 x 7= 1344

[wraith cairn]

second one has repeats.

I believe the first approach is right.

[pure frigate]

How it's repeats. I'm not understand

[proud bough]

multiplication rule

means order

so it'll count the orders

so it'll repeat

imagine you pick A from marvel, then pick B from the remaining which is also from marvel

next time you get to pick B first, then pick A again

so it has repeats

[dark granite]

answer isn't 186

should be 182

you can do this by cases. For case 1, consider when neither banana nor tuna is chosen. For case 2, consider when exactly one of banana and tuna is chosen. Then add up those cases.

you could also count the complement and subtract from the total

the complement would be when banana AND tuna is chosen

the total would be without any restrictions

I might be able to help...I'll take a look and see

[fringe token]

I need help in this question

[placid zinc]

x and y are the sides of a right triangle. 68 is the hypotenuse

[fringe token]

Yes I managed to got that far

I don’t know how section c is done

[placid zinc]

So you've written down:
y/x = 3/4
For part b

That implies y = 3x/4

Now, sub that into the first equation

[fringe token]

Uhu I have done that part

But I don’t know how to find an exact number

Like x is this y is that

[placid zinc]

After subbing, what are you looking at?

[placid zinc]

I suggest squaring 68 instead of putting a square root on your variables, haha. Just a bit easier that way

[fringe token]

Ok

[vale wigeon]

don't you know kaynex

[placid zinc]

It seems like you got x = 3y/4 which isn't correct

[vale wigeon]

making things easier for yourself is actually bad

[placid zinc]

I always forget. Pfft. Thanks Ann!

So make sure to get a cube root in there

[vale wigeon]

[crisp grove]

seems ok

[fringe token]

Alright thanks @placid zinc

[vivid fulcrum]

the only question ive had a problem with in arithmetic sequences

[vale wigeon]

you know the definition of an arithmetic sequence, right?

[vivid fulcrum]

yes

[vale wigeon]

can you state it for me?

[vivid fulcrum]

a sequence that works with addition/subtraction

ik the formulas too, but

[vale wigeon]

that's too vague.

[vivid fulcrum]

idk what im supposed to do here

[vale wigeon]

one way to do this would be to look at the differences between adjacent terms.

those differences are supposed to be the same

an arithmetic sequence is a sequence in which the difference between any two adjacent terms is the same

this difference is called the common difference

[vivid fulcrum]

yeah

[placid zinc]

Specifically, each term is the last term, except you add some predetermined number.

[vale wigeon]

thank you for this nearly useless rephrasing

[placid zinc]

👍

[warm tartan]

Can someone help me? Thanks

[vale wigeon]

@loud cedar do not give out answers.

[lone heart]

From

#❓how-to-get-help

Rule 7

When asking for help, do not insist on getting just the answer; we are here to help you learn, not cheat. Likewise, if you are providing help to others, try your best to explain and elaborate instead of simply giving away the answer.

[loud cedar]

(5/6+x * 180)-40 = x/6+x * 180

[loud cedar]

aight

therefore it's ||3||

[vale wigeon]

sure. a straight line coincides with any of its own tangents

[humble yoke]

What did I do wrong? the solution should be -5 and - 7

[gray isle]

@humble yokepretty much everything is wrong.
you did some suboptimal manipulation from line 1 → 2
and you didn't express stuff as a square properly

[lavish seal]

Is this true?

[crisp grove]

No

[lavish seal]

Ok thanks

[humble yoke]

Can you elaborate? I subtracted 3 and divided through 3 from both equations, in order to factorize it. And whats wrong with the square?
(x-6) * (x-6) = x^2+12x+35

[magic lodge]

sorry could I just check 3y + 1 = 4y right?

[gray isle]

$(x-6)(x-6) \not\equiv x^2+12x+35$

[ocean seal]

ℝamonov

[vale wigeon]

@magic lodge no

[safe vine]

this question is just for fun, but if an event has a 60% chance of it happening, how many times will that event have to happen so that you get the desired event?

did that make sense

[gray apex]

one time, assuming that the event happens :)

[humble yoke]

ups, you're right thank you very much :)

[safe vine]

._.

what if it doesnt happen

[humble yoke]

I think what you mean can be calculated with the expected value

[vale wigeon]

there is no number of trials you can make to guarantee that you succeed at least once.

[safe vine]

like

to get a 99% chance to get it

[safe vine]

i think thats it

[wispy olive]

No.

[woeful heath]

How do I get both 1 and 2?

[vale wigeon]

@woeful heath channel busy please move

@safe vine the probability of getting all failures in n trials is 0.4^n

so to be 99% sure you get at least one success, you need the fail probability to be 0.01

,calc log(0.01)/log(0.4)

[ocean seal]

Result:

5.0258831894641

[vale wigeon]

you need to conduct 5 trials

[lavish seal]

Is it -256/-81 or 256/81

[upbeat wyvern]

256/81 I think

[lavish seal]

Ok thanks

[alpine sable]

anything power even number is always positve

[safe vine]

thx

[vale wigeon]

@lavish seal as it happens, -256/-81 is the same as 256/81

but (-4)^4 = 256 unambiguously

[alpine sable]

@lavish seal u shud take -1 out of every -4 you did it only for 1

[tough coral]

idrk what the answer to C is

i feel like it's the variable bin widths but im pretty sure that's allowed

so what do the plots violate

[lavish seal]

Ohhh i get it so -1^4 is 1 so its positive

Right?

[alpine sable]

yes

[lavish seal]

Thanks for the help

[tough coral]

any1 who knows stats

[alpine sable]

thats true for any number , that is (any number)^(even number ) is always positive

[tough coral]

anyone

guess not

[vale wigeon]

http://dontasktoask.com/

[tough coral]

na

i posted the question

like 3 lines ago

so that is not applicable

[vale wigeon]

oh you did

my bad

[tough coral]

ye

[crisp grove]

anyyyuyu numberrrrr

[vale wigeon]

your gotcha is not appreciated

[crisp grove]

but gotta tell him somehow that's it's not true

0²=0

[forest swan]

i need help sorry

[tough coral]

that looks cancerous

i mean

just use pemdas

do the 12/6 first

then take 3/5 to the power of that

etc etc

[gray apex]

its not too bad if you write it out

[tough coral]

im p sure its just 4/5

i did it in my mind

so it might be wrong

[gray apex]

i got 4/5 as well

[tough coral]

(1-(9/25))/(8/10)

[gray apex]

16/20

[tough coral]

so ye

nice

bump

anyone know how to do C

[gray apex]

but i dunno if just straight up giving the answer is correct

[forest swan]

yeah its right ty

[tough coral]

do you know how to do it now though

[opal crest]

help pls😢 , I know here I need to use lim x->0 (sinx/x) = 1, but how to solve it idk

[tough coral]

god

limits

are cancer

worst part of calc

[opal crest]

[tough coral]

simplify it

cot(4y) = cos(4y)/sin(4y)

hm

[opal crest]

it only gets worse with every action

[forest swan]

yeah

[tough coral]

just use symbolab

tbh

[alpine sable]

Why is Sin(pi) = 0?

[tough sinew]

Memorize this

it'll save u in calc

[slim fog]

That’s why I use infinitesimals like a boss 😎

[sinful relic]

Because it has gone pi around the unit circle which is half the way. When it has gone pi around it, the y-coordinate will be 0

[alpine sable]

What if a have an angle in a triangle that is pi?

[sinful relic]

then it's 180 degrees

if it's pi radians, I think

[alpine sable]

But if it's pi degrees?

[sinful relic]

angles in pi radians, the circle arc, just pi

[sinful relic]

idk if it can be that

[tough coral]

because

if yout hink about it

pi = 180 degrees

so

the "triangle"

[steel oyster]

Sin is the y value

[tough coral]

is essentially a straight line

and

since sin = opposite/hypotenuse

and its a straight line

the height = 0

because it has no height

so 0/hypotenuse = 0

[alpine sable]

Oh right yeah

Yeah Wolfram though i was speaking in radians, so I got confused

Sorry

[steel zodiac]

in a right triangle, why is the hypotenuse always the longest?

[tough coral]

because

i mean

idk

how to explain it

isnt it common sense

[sinful relic]

@tough coral An angle is in pi radians? But the arc of the circle will just be pi, and the unit the radius is?

[steel zodiac]

how is it common sense

[tough coral]

wdym

pi = 180 degrees

[steel zodiac]

what?

[tough coral]

ok

well

[steel zodiac]

how do you prove that

[alpine sable]

Can't you look at it like the hypotenuse is the shortest path?

[tough coral]

think about it logically

if you walk

from a

ok

nvm

ill draw another pic

[sinful relic]

i'm saying if you have an unit circle an angle will be pi radians and the length of the circle arc will be pi and the unit of the radius

[tough coral]

sure

[sinful relic]

yes

?

[tough coral]

whats the point

of that?

[sinful relic]

what

im asking if its corrext

[lavish seal]

Isnt it because c² = a² + b²

[tough coral]

yea its right

but anyway

@steel zodiac there really isnt

an explanation

[steel zodiac]

that's the formula, but how do you prove that?

[tough coral]

you just have to use your brain

oh god

listen

[sinful relic]

is it right

[tough coral]

yes

[sinful relic]

k

[tough coral]

alva

lets say

ok bruh

why dont you just

draw a fucking right triangle

and measure it

and figure out why

the hypotenus is longest

[steel zodiac]

why don't you just suck a dick, because you clearly aren't helping

[tough coral]

dude

theres no explanation

for this

its literally common sense

i have no clue how to help you

which is longer?

the top one

[sinful relic]

a and b are the 2 small sides and the hypotenuse will always be longer

[tough coral]

if you look at it

the top one is longer

thats the explanation

it just is longer

[toxic bobcat]

I believe what she is asking for is a proof.

[tough coral]

there is no proof

its like asking

line a is 4 cm, line b is 5cm which is longer

[steel zodiac]

I am asking for a proof, that's not a proof

[tough coral]

well obviously line b

because its 5 cm

like

[sinful relic]

there's proof for calculation

[tough coral]

???

[alpine sable]

Is there a way to show that sqrt(a^2+b^2)/(a+b) is smaller than one?

[humble yoke]

you proof it by expanding the lines to a quadrat

[lavish seal]

Have you googled it I think there are some answers there

[humble yoke]

like this

you expand it

to a qudrat

[tough coral]

Yeah but the thing is

Alva wants you to prove

The Pythagorean theorem too

[toxic bobcat]

Just prove that the angle apposing the hypo. is the largest angle

[humble yoke]

thats the proof for Pythagorean theorem

you expand the lines to a quadrant

[tough coral]

Alvas asking why the hypotenuse is the longes

Not for the proof of the Pythagorean theorem

[sinful relic]

yesh you can expand it to a quadrat and you get

(ab)^2 =

[tough coral]

Yeah

Sure you can explain it that way

You can prove the Pythagorean theorem

And you can prove that the hypotenuse is the longest through that

But you don’t need to do that

Literally

The hypotenuse is the longest

[toxic bobcat]

I think it can be proved by basic proportionality

[tough coral]

Because in the human created object of a triangle

[alpine sable]

Yeah that's what I was trying to do

[tough coral]

That’s how it’s defined

There’s a reason why circles aren’t right angles

If they were the same length it wouldn’t be a right triangle

It would be an afc

Arc

[lavish seal]

Guys there is this question which is
"An irrational number times an irrational number is irrational" then I should answer: always true or sometimes true or never true

[tough coral]

Well

Square root 2 Times Square root two is not irrational

So it’s not never

But

[tough coral]

But

Square root 2 Times Square root 3

Is irrational

So it’s sometimes true I’m p sure

[steel zodiac]

AC and BC litterally look the same length,

[tough coral]

No

They are not

Measure it with a ruler

Or smth

Or with your fingers

One on c and one on A

[lavish seal]

It looks like but they arent

[toxic bobcat]

90 degrees is the largest angle possible in this triangle and the line opposite to the largest angle is the longest side, you can use a scale

[tough coral]

look

this is a circle

the two lines are equal in length

[sinful relic]

$(ab)^2 = 4ab \cdot 0.5 + c^2 \
(ab)(ab) = 2ab + c^2 \
a^2 + ab + ba + b^2 = 2ab + c^2 \
a^2 + b^2 + 2ab = 2ab + c^2 \
a^2 + b^2 + \cancel{2ab} = \cancel{2ab} + c^2 \
a^2 + b^2 = c^2$

[tough coral]

but

its not enough for a right triangle

so the hypotenuse must be longer

[ocean seal]

Lil Sachi

[alpine sable]

The circle is a really good explanation

[tough coral]

si

[alpine sable]

What’s 1+1 divided by 1,000 🤔

[tough coral]

idk

depends on how you group it

[alpine sable]

Oh k

[tough coral]

is it 1+1/1000

[alpine sable]

My teacher said I’m dumb 👀

[tough coral]

or (1+1)/1000

[alpine sable]

Oh

Thanks

[tough coral]

what

[alpine sable]

❤️

[tough coral]

ok

i didnt really answer anything

but sure

[alpine sable]

I appreciate you

[tough coral]

fr

[alpine sable]

Yes

[tough coral]

i appreciate you too

[alpine sable]

❤️❤️::

[tough coral]

we are all mutually appreciative

[alpine sable]

Yes

[tough coral]

<3

[sinful relic]

1+1/1000
1+0.001
0.002

[tough coral]

si

[alpine sable]

I haz a new friend

❤️

[sinful relic]

wait nvm

[lavish seal]

Isn't 1+0.001 = 1.001

[sinful relic]

yes

agree

[toxic bobcat]

different Grouping

[sinful relic]

0.001 + 0.001 is 0.002 and 0.001 + 1 is 1.0001 or what? 1.001?

[vale wigeon]

0.001 + 1 = 1.001, yes

[sinful relic]

you count the decimals after the 0. and add it to 1?

[alpine sable]

If 100x100=200 then what Is 200,000,000x2000,000,0000 divide 300 multiply 5000,0000,0000,00000,000 then Subtract 100,000,0000

[sinful relic]

bruh

[alpine sable]

Ikr

😭

[alpine sable]

100x100 = 200?

[sinful relic]

10000

[toxic bobcat]

genius

[alpine sable]

Don’t judge me I ain’t tryna do math In 5:23 In the morning

😭😭

[vale wigeon]

@alpine sable how old are you, eleven?

[alpine sable]

Nah

11 Year olds aren’t even allowed on discord 😭

I’m just asking random ass questions 😂

[lavish seal]

Quick question: any fraction is a rational number right?

[alpine sable]

yes

Yes

[vale wigeon]

any fraction with integers in the numerator and denominator is a rational number.

[tough coral]

i know

a 9 year old

who was on discord

its not like they hack into your computer to find out your age

[toxic bobcat]

is 0 an integer?

[alpine sable]

Wtf

[vale wigeon]

yes, but what does that have to do with the message i just replied to?

are you about to gotcha me with "you can't divide by zero"?

[sinful relic]

can't it also be an integer? 4/2 can be sinplified to 2

[vale wigeon]

all integers are rational yes

[toxic bobcat]

well I was going to try to

[lavish seal]

Wait so is there a irrational fraction?

[vale wigeon]

sqrt(2)/10

here's a fraction whose value is irrational

[toxic bobcat]

Its not rational though

[lavish seal]

Oh ok

Thx

[vale wigeon]

what's your point grandvizierwazir

[tough coral]

Ngl

Stats is harder than calc

Hot take

[toxic bobcat]

That the statement you made is not true for all

[sinful relic]

how do you calculate 1+0.001 in your head?

[marble saffron]

2 is the solution but how does one solve it

[vale wigeon]

@toxic bobcat

here's a fraction whose value is irrational

irrational. i said irrational.

@marble saffron channel busy please move

[toxic bobcat]

no no no

[toxic bobcat]

you said any fraction with integers in the numerator and denominator is a rational number.

[vale wigeon]

so you were trying to gotcha me with "bUt WhAt iF tHe DeNoMiNaToR iS ZeRo HuH?"

[toxic bobcat]

Well, zero is an integer and dividing by it doesn't give you a Real Number which is a superset of Rational Numbers

I am just suggesting that, that statement is not true for all.

[vale wigeon]

division by zero is undefined and your attempt to pointlessly gotcha me is unappreciated

[opal crest]

it is a trap? shouldn't there be 400 left?

[vale wigeon]

one would have thought it doesn't require explicit mention that you can't divide by zero

@opal crest this limit is 400, but you have to understand why it's 400

if x were approaching 400 from below instead the limit would be 399

[opal crest]

hm

because it won't reach 400? or what

[vale wigeon]

no

because floor(x) = 399 if x is slightly less than 400 but floor(x) = 400 if x is slightly bigger than 400

[toxic bobcat]

One can have different ways of thinking, I just thought thought it should be mentioned, I would leave this channel as our discussion might stop other from posting useful questions.

[opal crest]

ok, thx ❤️

[lavish seal]

The answer says it is undefined, but I thought it was -1. Why is it undefined?

The bottom question not the top one

[toxic bobcat]

Well 0^0 is undefined

[lavish seal]

I thought any number ^0 was 1

[toxic bobcat]

Yes it is for all reals except 0

[lavish seal]

Ok thx

[alpine sable]

Yes but the 0th root of 0^0 is the same as 0^0^(1/0), and 1/0 is undefined

Hi

How everyone doing

Oh this ain’t main chat my b

[lavish seal]

Guys thanks for the help for my homework, finally I can go to sleep

[alpine sable]

Where Is main chat?

#chill maybe?

[upper escarp]

how to do d?

[alpine sable]

can you show your work/answer on the previous ones?

[upper escarp]

i don’t have the answer sheet but this is my answer for previous question

oh nvm i got the method

my n value was wrong also

[golden badge]

what is the statistical probobility that i have pooped at the same time as kim kardashian?

[errant tangle]

why are you asking this??

[alpine sable]

I did this and got x = -3 and x = 2 so I worked out the area by doing integral of 7- x between -3 and 0 – integral x² + 1 between -3 and 0 but I got a negative area of -39/2 anyone know why

[rotund vector]

Guys

Help me

[alpine sable]

Bro I asked first use other channel

[rotund vector]

?

[alpine sable]

#rules

[jolly stone]

consider how long you poop = t_you, and how long kim kardashian poop = t_kim
assuming both you and kim kardashian poop once a day at a fixed time (if more than once the math gets ugly like your poop and kim kardashian's poop)
fix your time to 0 poop o'clock, probability of kim kardashian poop at the same time as you is when kim kardashian starts within time t = 0 and t = t_you, and then t = 24-t_kim and t = 24 (restart at midnight poop o'clock)

[rotund vector]

oh :((

ok

[jolly stone]

so the event you're interested is t_you + t_kim hours, so the probability of you pooping at the same time as kim kardashian is (t_you+t_kim)/24 (can exceed 1 if the sum is more than 24 hours so just say that probability is 100%)

enough internet for the day

[golden badge]

@jolly stone thank you 🙂 it makes my heart warm!

[alpine sable]

can someone please help!

[jolly stone]

but if you or kim kardashian poop more than once per day then it's gonna be messy, but you can approximate using proportion of time to poop

[jolly stone]

can you show your work?

and why between -3 and 0? you want to find the whole area or just R1 and R2 separately?

[jolly stone]

what have you done so far?

[rotund vector]

wdym

[jolly stone]

what did you try before?

or any ideas you think you want to try?

[rotund vector]

sin cos tan

trying to find ratio between line

[jolly stone]

im letting that point with right angle point D, and you can set the length CD as variable x

you can find out what BD is

[rotund vector]

yea i set it alr

[jolly stone]

in terms of x

and then also AD in terms of x, using the bigger triangle

[rotund vector]

ok lemme try

[alpine sable]

I want to split the part on both sides of 0 so I can use the right hand side to find r2 later on

I'll show my working but I got it wrong

[jolly stone]

oh interesting

R1 begins from -3 to 0

not 0 to -3

you will get negative term on 39/2

[alpine sable]

So -3 is the upper bound?

or lower bound

[jolly stone]

lower bound

[alpine sable]

Wait why?

[jolly stone]

-3 is smaller than 0

[alpine sable]

Oh

But then won't u still get same answer?

[jolly stone]

area of integration is defined as positive value when you start from left to right in 2d graph

you will get same answer but different sign

integral f(x) dx from a to b = - integral f(x) dx from b to a

[alpine sable]

Oh I see

because ill be subtracting the negative 39 / 2

which is + 39 / 2

[jolly stone]

yep

[alpine sable]

Ok great thank you

[jolly stone]

[alpine sable]

and doing this I should get correct answer?

[jolly stone]

i think, didnt check math

[alpine sable]

Ok

[flat vale]

lol i just came and did a lil quick math

is the ans 125/6 and 103/6? @alpine sable

[clear totem]

hello

[jolly stone]

i think you bugged the integration, answer R1 should be 125/6

[clear totem]

how can i find section when y is given

[jolly stone]

dont know how but something is wrong along the way

[flat vale]

u can't

completely diff way of finding r2

even if u split u can't use that ans to find r2

to find r2 u need to find area under the parabola from 0 to 2

and under the linear from 2 to 7

[jolly stone]

what they tried is split into -3 to 0 and 0 to 2, then to find R2 is the triangle minus that 0 to 2

[flat vale]

that's the easiest way

[alpine sable]

U guys got the right answer

I've gone wrong somewhere

[jolly stone]

did you integrate correctly? cant see your work there

[alpine sable]

Hang on i did it somewhere else

[flat vale]

that's really tedious

you are doing double the work

should still work tho

[jolly stone]

same work anyways

[flat vale]

no ur actually doing much more work

i'll show you hang on

[alpine sable]

leme write all my working out

give me 5 min

[jolly stone]

you need to integrate 2+1 times: first way is -3 to 0 for line over parabola, 0 to 2 for line over parabola, and the triangle 0 to 7 (which doesnt even count as integration)

your suggestion is: R1 as -3 to 2 for line over parabola, 0 to 2 for under parabola, and 2 to 7 for triangle (also doesnt count)

[rotund vector]

is x(CD) ≡ 66.11 ?

i using tan()

[jolly stone]

x = 162.75, can you show your work>

[rotund vector]

wait wot

[jolly stone]

what is your equation

sorry but i have to go right now, might need other helpers to continue from this

[rotund vector]

ok np

i just found my falut

[sinful relic]

A derived function is a function that expresses tangent slopes of another function?

[alpine sable]

I think I got it thanks guys

it was just a problem with my bounds and calculations I believe

[alpine sable]

https://cdn.discordapp.com/attachments/888126717246459914/889124160750637086/image0.jpg

,rotate

[alpine sable]

I know how to do simultaneous linear equations
Im doing the elimination method but
What do i do with 2y-ax = 2

can someone answer this?

[jolly stone]

when 2 lines are parallel together, they have the same slope

[alpine sable]

pls?

[woeful pulsar]

have you done calculus?

[alpine sable]

yupp

[woeful pulsar]

how does that help with finding local minima?

[alpine sable]

but im not gud in it

[alpine sable]

differentiatiion

[woeful pulsar]

so how do you do that?

[alpine sable]

first differentiate f(x) rite?

[woeful pulsar]

which gives you?

[alpine sable]

x^2-2x-3

then?

[woeful pulsar]

if x is a local minima, what can you say about the derivative of f

[alpine sable]

then f(x)=0?

am i rite @woeful pulsar ?

[woeful pulsar]

not accurate enough

f'(x)=0

[alpine sable]

ohhh yaa sorry

afterdat?

[woeful pulsar]

use that observation to continue

[alpine sable]

i differentiate f'(x) to find its double derivative?

[woeful pulsar]

why do you want to differentiate f'(x)

what is the aim here?

[alpine sable]

so to find wehter its the minma or the maxima?

bro um cud just tell me how to do it?

[woeful pulsar]

well, that's one way to try

[alpine sable]

ok

just telll me wt to do next?

[woeful pulsar]

try it out then, you're quite close already

[alpine sable]

i got x=3 and -1

then?

[woeful pulsar]

so those are what you get when you solve f'(x)=0

[alpine sable]

yupp

[woeful pulsar]

so they are candidates for the local minima

how do you check if they are?

[alpine sable]

by again differentiating?

[woeful pulsar]

can you try it out?

[alpine sable]

was this rite?

[woeful pulsar]

how will differentiating again help?

[alpine sable]

brooo im bad at this

pls tell me wt to do next

pls?

[woeful pulsar]

how would you check if f has a minimum at x=3?

[alpine sable]

idk

sorry but i genuinly dont know

[woeful pulsar]

have you heard of first derivative test / second derivative test

[alpine sable]

nope

pls help me no?

@woeful pulsar

[woeful pulsar]

https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new/ab-5-4/a/applying-the-first-derivative-test-to-find-extrema

^resource from khanacademy on first derivative test

[alpine sable]

bro but for now

can u just tell me how to solve this question?

@woeful pulsar

[woeful pulsar]

go learn it, I sent a resource

[alpine sable]

😭

pls?

[fast topaz]

a.

{(1,2),(1,3),(2,2)(2,3)}-{(1,3),(1,4),(2,3),(2,4)}

{(1,2),(2,2)}

I'm stuck here and dont know what to do next?

How do I get {(1,2)}x{2}

?

[woeful pulsar]

{1,2}x{2}

actually your set and the final answer are the same

[glass lichen]

this is just {1,2}x{2}

[fast topaz]

Can you explain how they are the same, because I do not understand

[woeful pulsar]

can you calculate {1,2}x{2}?

[fast topaz]

back to {(1,2),(2,2)}?

[glass lichen]

can you calculate that product?

[fast topaz]

hmm, no

[glass lichen]

ok... so how did you compute {1,2}x{2,3}?

[fast topaz]

Do the same with {(1,2),(2,2)}?

[glass lichen]

no

do the same with {1,2}x{2}

cause they're both cartesian products clearly

[fast topaz]

{(1,2),(2,2)}

[glass lichen]

yes

so there you go, they're equal

[fast topaz]

I don't understand how to do it "backwkards" tho

{(1,2),(2,2)} to {1,2}x{2}

[glass lichen]

just the reverse process of doing the product

$A\cross B={(a,b)|a\in A, b\in B}$

[ocean seal]

Mosh

[fast topaz]

Sorry, I'm not getting it... So frustrating

[woeful pulsar]

it should be pretty obvious when you can factor it, just consider the projection map $f$ such that $f((a,b))=a$.

i.e. just take all the first elements

and take all the second elements

[ocean seal]

Element118

[woeful pulsar]

and see if when you cartesian product those two sets together you get the original set

[stark viper]

hey guys morning, I'm studying combinations and I'm stuck in a question.

Could you guys help me with that?

[woeful pulsar]

given that 2 choose n is the same as 12 choose n, find n?

[stark viper]

I'm not used to the english terms in math, but choose would be like (C8, 12 = 12!/8!4!) ?

in that case, yes

[visual dew]

can i ask

can somebody check this, did i do it correct

[small cypress]

How do I do b

someone pls

iii)

[tame moss]

seems right

[junior wing]

May i know the solution?

[alpine sable]

So to find lim as x approaches 2 from the right and to find the lim as x approaches 2 is the same equation?

since its x => 2

[astral dagger]

the limit as x approaches 2 only exists if the side limits evaluate to the same value

so you'd calculate the limit from the left with x^2 and from the right with -4x + 12

[alpine sable]

But I thought you need to do 2 separately as well?

besides 2 from each side

[astral dagger]

well, I think that the question wants to show that f is continuous everywhere

and there is no problem doing it that way

[alpine sable]

But am I wrong in saying that since the equation -4x + 12 has x => 2, you use that equation for finding the limit as x approaches 2 and finding the limit as x approaches 2 from the right?

since it's greater than or equal to

[astral dagger]

as I've said, you cannot calculate the lim as x approaches 2 directly

you may need to do each side

[alpine sable]

I did each side and they're both 4, so would it be wrong to assume the limit as x approaches 2 is 4 unless stated otherwise?

[astral dagger]

it's correct

[alpine sable]

sometimes, for example, theyll have what the limit as x approaches 2 is right in the piecewise function, and it may be different from its one sided limits

[astral dagger]

if it's different, then you can't assume the value of the limit

[alpine sable]

but if they don't state otherwise, then it's correct?

[ocean seal]

SubGui

[astral dagger]

I don't think so, but let's see if someone with a different opinion shows up

[crisp grove]

what's the question?

[trim stump]

can u help me @crisp grove

[crisp grove]

ask

[trim stump]

its 1.3 im having problems with

[glass lichen]

,rotate

[trim stump]

does anybody know how to solve it

[trim stump]

can u help me

[deft geyser]

try to label each of the sides

give them variables and try to find expressions that give you their values

like let the sides of R be x, y, and try to find x and y in terms of the sides of other rectangles

[trim stump]

i just dont really understand it

@deft geyser i honestly dont know how to do it

[deft geyser]

ok this looks like ass but this is kinda what i mean

give each side a bariable

each of the rectangles at the top have a height of a

each of the rectangles in the middle layer have a height y

give the lengths of each rectangle a similar name

and find relations between them

[trim stump]

;-;

thx anyways

rip i cant solve it

[deft geyser]

does this make more sense?

_ _

the big rectangle has sides (a+y+b) and (c+d+x)

[deft geyser]

so take the top right rectangle it has area a*c, but we know that's just 5
ac = 5

write similar formulas for each rectangle

and use those to find x and y

and then use x and y to find x*y which is R

[trim stump]

i havent learnt fomulas before ;-;

im in p7

im dumb

[deft geyser]

huh, ok...
how old are you? idk what p7 is?

[trim stump]

nvm

but im dum

[subtle nebula]

can a radius be negative?

i solved this and got k = -36

tested it and it doesnt match the given r = 4

however when i tested with 36 instead of -36, i got r = 4

[glass lichen]

no, but k isnt the radius

[subtle nebula]

yea ik

[glass lichen]

you just complete the square then solve for the radius

[subtle nebula]

yes

thanks man

[rancid heath]

I’m doing a question on modelling with exponentials and I got the answer and I checked the mark scheme and it says the answer can’t be non integeric. What does that mean?

[vale wigeon]

"non integeric"? is that the exact word the mark scheme uses?

[rancid heath]

Yes

[vale wigeon]

they probably mean the answer can't be a non-integer, which may or may not be justified depending on what the problem is

[rancid heath]

On my calculator the answer was like 1644.464……

[devout sigil]

So u have to round off ur answer such that ur final answer would be an integer

[rancid heath]

The question doesn’t specify that so how would I know in an exam?

[devout sigil]

Do u have the full question?

It could depend on the context

[devout sigil]

So ur final answer is the population of bacteria

[rancid heath]

Yeah so I subbed in 7 and I got 1644.464

But according to the mark scheme that’s not acceptable

[devout sigil]

Shouldn’t the population be an integer? So u can round that off to 3sf or nearest integer

It would sound off if u were to say 1644.464 bacteria

[rancid heath]

Ohhh so I can’t have like 0.4 of a bacteria

So it depends on the context

[devout sigil]

Yea

[rancid heath]

Ohhh ok thanks that helped

[devout sigil]

Np, glad to help

[coral scroll]

Hello, if I flip a coin 10 000 times, and I want to know the probability of getting 4781 (random number) heads or less, do I have to sum up all probabilities (P(X=0) + P(x=1) + ... P(x=4781))or is there another way? Thank you

I looked up "cumulative distribution function for binomial" but I'm only finding techniques with the sum of all probabilities

[rancid heath]

Does it tell you the probability of landing on heads?

[coral scroll]

The probability is 0.5

a normal coin toss ^^

[rancid heath]

Can’t you use binomial cumulative distribution to find p(x ≤ 4781)

[coral scroll]

But the definition of the binomial cumulative distribution that I found has a sum

I want to know if there is another way without a sum

[rancid heath]

Does your calculator not have a function that lets you solve binomial cumulative distributions

[coral scroll]

I want an analytical expression

[alpine sable]

yes that is true

[rich crow]

i dont get how to simplify this!?

[sleek elbow]

3:2 maybe?

im not sure

[undone river]

Yea i think it’s 3/2

[dusty tree]

yea

[rugged lily]

Do I use a Poisson distrbution with X⁓Po(3)?

go to another question room pls

[opal crest]

um

[rugged lily]

<@&286206848099549185>

[livid jolt]

looks like a poisson to me too
and the question asks for assumptions
so maybe u can state that u assumed a poisson distribution and then solved

[rugged lily]

ok

also to find the no. of pages like in part i) do i just find P(X=0) and multiply that by 500

[wintry wolf]

Hi, i gotta factorize (2x-5)(7x+3x)-(4x²-20x+25) i keep finding (2x-5)(6+3x) but google says its false

Nvm

[sudden garden]

can ayone explain this to me?

[high crest]

Which term is confusing you?

[sudden garden]

|c|=RAD WHAT IS RAD?

[small bear]

radian?

[high crest]

Yes, c is the angle in radians.

It's not the absolute value function |x|, the brackets [x] are used in physics to "extract" the units of a variable

[orchid pollen]

Can someone help me with a question?

About limit

Have some working out but not all of it can't get it for the life of me

[sudden garden]

thank you every one!

[lime sage]

What does the "" in set "C{(0, 0)}" denote?

[noble vortex]

how do i get my full marks

[lime sage]

Yikes....I meant to ask what does the \ in set C\{(0, 0)} denote? Sorry for the trouble!

[next bridge]

whats the angel measure of <COD

[small bear]

You are given <AOD = 115.
Also <AOD = <AOC + <COD
You are given <AOC = 30
You have two of the angles, now do the algebra to find <COD

[alpine sable]

im pretty sure you can do 115 - 30 to get the answer

[magic warren]

i am confused it says 1/2d is not the right answer and i have no idea

[full fog]

The app might not recognise the first way thats why

[magic warren]

oh so that is correct?

[full fog]

Yeah it's correct

[high crest]

It means C without (0, 0)

[magic warren]

oh ok thanks ive never done kinematics before so i thought i could just be being stupid

[lime sage]

Ah...got it! Thank you!

[alpine sable]

I'm having a bit of trouble finding videos on how to graph equations like these by hand. Could anyone help me or point me to any resources that would help me?

[brave hornet]

someone can help me? i don't understand what is happening

[orchid pollen]

Can someone help me with a question?

[sick scaffold]

what does this mean and how is it different from f(x)?

[thick cypress]

nothing different

[harsh belfry]

t means that f is a function that takes the value x to the value y iirc

[orchid pollen]

Hey muffin

[thick cypress]

it just shows to what x is projected

[orchid pollen]

Could you help me?

[harsh belfry]

ah ok

[thick cypress]

need to go sorry for disturbing

[sick scaffold]

so are these to same thing?

[brave hornet]

but why if the third row of B is all 0
and third row of EB might not be 0
I cant imagine that matrix

[winter rock]

Hi, does anyone have a little of free time and could help me?

I got some exercises that I want to do but I would like to do em with someone so I could verify my answers at the same time, and fully understood the questions ect..

[tribal temple]

can any1 solve this

im in year 11 please help

[glass lichen]

yes, f maps x to 3 means f(x)=3

[tribal temple]

help me?

[glass lichen]

I dont help people that ping me

[tribal temple]

cool

[orchid pollen]

you’re such a bitch lollll

[glass lichen]

[tribal temple]

🤣

fr these ppls act like they prestige and think that they are albert einstein

[glass lichen]

Nah, I just don't like getting bugged to help. I help on my own accord, like everyone else.

[orchid pollen]

why you block me lol

[orchid pollen]

nah you a bitch you could just say nah sorry but you out here

acting like you the shit

saying you don't help ppl who ping you

ppl get pinged once and act like a celebrity

[buoyant kayak]

or maybe it's annoying

food for thought

[stoic oriole]

^

[orchid pollen]

Alr it's annoying sure well then say don't ping me? Rather than acting like some celebrity

[buoyant kayak]

whole point of this server is to post questions, and if someone wants to help, they will

[stoic oriole]

it's not acting like a celebrity, it's just not feeling like helping people that ping them

[orchid pollen]

I'm not saying you need to help but randomly getting rude to someone bc they innocently ping you is just stupid.

[glass lichen]

How exactly do you propose I tell someone not to ping me... without knowing who's going to ping me.

[stoic oriole]

it's not people's job to help you, people help others when they want to

[orchid pollen]

Why is that big of a deal? You check the ping, say no I can't help, sorry and then say you don't want to be pinged

Not that hard

[glass lichen]

I said no, and then you proceeded to cause an ordeal

[orchid pollen]

If someone in real life were to ask you for help would you randomly say 'No I don't help people who ask me'

[glass lichen]

Now stop misusing the channel

[stoic oriole]

all mosh person did was that and say why they weren't helping i don't see why it's such a big deal

[orchid pollen]

Sounds like a bitch, doesn't it? instead you say no I can't help

[tawny pulsar]

Is this channel busy?

[glass lichen]

Nope

[tawny pulsar]

ait

Use mathematical induction to prove the following:

a) 2n+1 <= 2^n for all integers n >= 4
b) n^2 <= 2^n for all integers n >= 4

In part (b), part (a) should be used. Both inductions start at n = 4

can anyone help me with part b

[glass lichen]

ok, where are you stuck?

[tawny pulsar]

i've proven for n = 4

[glass lichen]

ok so you did the base case

[tawny pulsar]

and im getting confused when im doing n + 1 when the task states that i should use part a

[glass lichen]

yes

so assume $n^2\leq 2^n$ then show $(n+1)^2\leq 2^{n+1}$

[ocean seal]

Mosh

[glass lichen]

$(n+1)^2=n^2+2n+1$

[ocean seal]

Mosh

[rustic rock]

nice identtity

[glass lichen]

Then you apply the IH and part a

[tawny pulsar]

IH?

i cant see what im supposed to do from here

[glass lichen]

Inductive hypothesis

$(n+1)^2=n^2+2n+1\leq 2^n\cdot 2^n$

[ocean seal]

Mosh

[past sundial]

Really random question but like which angle do you look at of a triangle to see if it’s obtuse or acute? Like there are several angles

[glass lichen]

a triangle is obtuse if it has an obtuse angle

if it has all acute angles, then it's acute

[past sundial]

? Like cause an obtuse triangle has 1 obtuse angle and 2 acute

[glass lichen]

yes

so it's obtuse..

[past sundial]

So like how do I classify triangles if they have like several angles like do I chose the angle that’s the one that’s not similar from both angles?

[glass lichen]

if it has an obtuse angle, it's obtuse

if all the angles are acute, it's acute

[stoic oriole]

just look at the largest angle - if it's larger than 90, it's obtuse, if it's 90, it's right, if it's less than 90, it's acute

[past sundial]

Oh ok

Thanks

[stoic oriole]

np!

[lean reef]

Hi I need help with this 🙂

[tight locust]

6+c = -3 + 2

6 + c = -1

c = -7

Lol!

[glass lichen]

what have you tried..?

[lean reef]

Omg I got -7 the second time I guess I forgot to add the -

The first time I got a positive 7

Thank you !

[fervent anchor]

Oh

[harsh belfry]

So I found my derivative and second (velocity and acceleration respectively) derivative for x(t)

I was told that I need to factor x'(t)

doing that I am given

Then I would take +1, and +3 and plug it into the interval notation.

I'm not sure what I did incorrectly

[tawny pulsar]

Thanks for trying to help mosh, i just dont get it

[polar mist]

So your outer interval limits are not infinity due to the fact that you've been limited in the question by a set of t between 0 and 10. Otherwise the 1 and 3 and correct. Then for c I am getting a different answer, try recalculating and if you still get wrong we'll figure out why

[harsh belfry]

@polar mist Thanks for part b

I managed to get 2 for x"(0)

then I plugged in 2 into the original equation

[polar mist]

x''(t)=0 just to clear

So the original equation is for the position

They're asking for velocity

[harsh belfry]

I have a poor understanding of how this works in application. So would I plug in 2 into x"

x"(2)

[polar mist]

So if x(t) is position, what is x'(t) and x''(t)

[harsh belfry]

x'(t) is the velocity

x"(t) is the acceleration

[polar mist]

So if you want to find velocity at t=2. You find x'(2)

[harsh belfry]

Oh ok!

Thanks

[oak hound]

yo

[polar mist]

No problem

[harsh belfry]

So when plugging in 2 into x' I still actually get -3

would it perhaps be a positive 3 since I cannot have negative velocity?

disregard if wrong^ (shot in the dark)

Channel currently in use

[oak hound]

can u help a 8th grade student?

[swift harbor]

3(2)^2-12(2)+9 -> 6^2-24+9 -> 12-15= -3

I think

I do da math

right

[polar mist]

nonono

[harsh belfry]

Yeah i still get -3 which is incorrect.

I am plugging it into the first derivative however.

Ah wait!

[swift harbor]

-3 is the answer I just verified it

[harsh belfry]

Im dumb I'm dumb!!! @swift harbor

It was the answer