help-0

[dark trail]

in my case i did

waitttt

i did -2x-3x2! which i multiply by 2x^2

as opposed to 4x^2/2!

[lone belfry]

i think if i remember right its (1+ax)^b=1+bax+b(b-1)/2! (ax)^2 + b(b-1)(b-2)/3! (ax)^3 ?

[dark trail]

yeah thats practically the way ive done it my issue is makign sure im calculating the numbers correctly

cuzz when i do them separately

i get different answers

like -2 x -3 = 6

then 6 x 2! = 12

12 times 4 = 48

but its different if i multiply all at once

[tired nova]

5x - 1
x - 2 x + 1

What would be the answer to this partial fraction?

[dark trail]

wrong channel

[tired nova]

What channel do I need to ask in?

[lone belfry]

i have the same formula as this

[dark trail]

whats ur answer?

[lone belfry]

1-4x+12x^2-32x^3+80x^4-192x^5 don't want to do the one in x^6

[dark trail]

hmmm

ok

ty

[lone belfry]

yw

[lone heart]

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[serene pilot]

52 i need help!!!

[lone heart]

@serene pilot Has your question been resolved?

[small panther]

@serene pilot did you write something ?

[serene pilot]

no

i have no idea

[small panther]

Ok

You want (1-4i)z real and z+6-i imaginary

So let z = a +ib

(1-4i)(a+ib) =a + ib-4ia +4b = a+4b + i(b-4a)

You want this to be real

So you want b-4a =0

That is the first condition

[serene pilot]

ok

[small panther]

Now your turn

Write the second condition using z+6-i imaginary

Its the same method

If you didn't understand you tell me

[serene pilot]

ok

[small panther]

Got anything ? @serene pilot

[serene pilot]

@small panther

[small panther]

Yes exactly

And you want it to be imaginary

So what equation do you get ?

@serene pilot

[lone heart]

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[serene pilot]

b-1=i?

[small panther]

.reopen

No

You want it to be imaginary only

[lone heart]

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[lone hatch]

The first expression makes sense but the second one is just confusing

[velvet cliff]

well look

the second one is with respect to a

so we treat a as the variable

and t as a constant

just imagine t is a constant

[lone hatch]

So I should only derivate (t^2 + t^3) ?

[alpine sable]

t is the constant, that's why it gave a different answer

[alpine sable]

u can apply sum/difference rule

d/da (at^2) + d/da t^3

[lone hatch]

thanxx

[lone heart]

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[acoustic thunder]

hello i just want some clarification for this question

i was doing proof of contradiction and this is the markscheme but

can i move the 3 to the other side and say an even number cannot be equal to an odd?

would that also be accepted as a correct answer

[lone heart]

@acoustic thunder Has your question been resolved?

[acoustic thunder]

<@&286206848099549185>

[quartz igloo]

Generally, no

For most questions, at least the way I've been taught, you've got to keep the LHS and the RHS completely seperate

Otherwise, you could do something ridiculous like times both sides by zero, which would mean zero=zero, which would imply everything is true

It's weird like that

[acoustic thunder]

i see

thanks

[acoustic thunder]

oo what if i keep it the same and just say left side is odd and right side is even

ljke 2(4p^3 + 3p^2 + 3p) + 3 must be odd

[lone heart]

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[humble plaza]

If you know the Result is a first class. How do you calculate the probability of the exam being multiple choice? Whats the calculation used?

[vale wigeon]

bayes' theorem

@dry igloo please open your own channel

[long axle]

#❓how-to-get-help @modest heart

[alpine sable]

Bruh

Are you given a value for x

What kind of math is that

The values dont even follow the pythagorean theorem

[hard patio]

Get your own channel

[humble plaza]

0.27 / (0.27 + (0.7 x0.8)) = 0.325

Is this correct

[humble plaza]

for this

<@&286206848099549185>

[lone heart]

@humble plaza Has your question been resolved?

[humble plaza]

Anyone help por favor

[lone heart]

@humble plaza Has your question been resolved?

[stiff root]

Hello, I am writing a thesis on autonomous driving. What exactly is the function of the camera on the B pillar in the car?

Thanks for the help.

[lone heart]

@humble plaza Has your question been resolved?

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[hardy geyser]

https://gyazo.com/9bd611e69ea11ce8298a58535a633bd8

[hardy geyser]

so im trying to find the concavities and i got my first and second derivative but whenever i plug my critical point into my 2nd derivative i got DNE cause its 0 in the denominator

https://gyazo.com/aa3526e7dfb7046a0647d765b42695f9

[lone heart]

@hardy geyser Has your question been resolved?

[lone heart]

@hardy geyser Has your question been resolved?

[lone heart]

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[quaint crown]

Found the values of x

[lone heart]

Please don't occupy multiple help channels.

[quaint crown]

Is it correct

Hey

@lone heart

[fluid pendant]

How u got from x-2sqrt(x)=1

To the next line

[quaint crown]

cane write in the paper please

[fluid pendant]

Ahh

Im stupid

But shouldnt it be +-sqrt(2)

[quaint crown]

ok

@lone heart

[lone heart]

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[round raven]

hI

How do I solve this

[serene junco]

Find the third angle of the triangle and then use the law of sines

@round raven

[lone heart]

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[tacit arch]

• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.

[carmine oxide]

well ik that i have to divide

[tacit arch]

use the formula for converting x and y to r and theta

[carmine oxide]

when i divide 0/10 and i get 0

[tacit arch]

correct

where does that appear in your formulas?

[carmine oxide]

the zero?

[tacit arch]

can you show the formulas you're using

[carmine oxide]

tanx=y/x

[tacit arch]

should be tan(theta) and not tan(x)

but yes that's right

so you have tan(theta) = y / x = 0 / 10 = 0

[carmine oxide]

thats what i meant to put

[carmine oxide]

correct

[tacit arch]

do you know when tan(theta) = 0 ?

[carmine oxide]

yes at 180 degrees and 0 degrees

[tacit arch]

which one of those matches your coordinate (10, 0)? plot it if you need to

theta is measured counterclockwise starting from the positive x axis

[lone heart]

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[alpine sable]

Can someone help me with finding some missing values in tables

[alpine sable]

<@&286206848099549185>

[south sentinel]

what is your table

[alpine sable]

sorry its sideways

@south sentinel

[south sentinel]

6,8,10,12,14,16,18

they are apart by the same values. so kind of equidistant. so if you divide 12-6=6 by 3 6/3=2 that is how much you increase at each step

a function form for this would be f(x)=6x+6, plug in x to get your desired function value

[alpine sable]

Is the 3 in 6/3 because there is 3 jumps between the 6 and 12?

@south sentinel would F(e) =2 and F(w)=6

[south sentinel]

yes

[south sentinel]

also yes

[alpine sable]

k

thx

.close

[lone heart]

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[winter ocean]

Was wondering how to answer the question and whether the given numbers were correct

[pallid scarab]

The given numbers can be anything from 0 to 1, so if they are given they are correct :)

As to how to answer the question

Let's write T the event of passing theory test, and P the event of passing the practical test

[winter ocean]

Ok

[pallid scarab]

Actually P is a very bad name

[winter ocean]

? P is ok?

Nvm continue

[pallid scarab]

Well if you understand P(P) we can continue like that

Dw

So

How do you write the event "passing only one of the two tests" in terms of the other events T and P ?

[winter ocean]

Ummmm

[pallid scarab]

You can tell me if you're stuck

[winter ocean]

Honestly im still reading. (Dyslexic sry)

Pass P fail T or fail P pass T?

[pallid scarab]

Yes !

[winter ocean]

Ok cool

[pallid scarab]

More precisely, we write it as $(P \cap T^c) \cup (P^c \cap T)$

[ocean seal]

rafilou2003

[pallid scarab]

Idk how you write the negation of an event, but we write it as ..^c

[winter ocean]

Why T^c

Whats T^c

[pallid scarab]

It's literally "not T"

[winter ocean]

Oh oh ok

[pallid scarab]

I can rewrite it for you

Out event is $(P \cap not(T)) \cup (not(P) \cap T)$

[ocean seal]

rafilou2003

[winter ocean]

Its ok thx

[pallid scarab]

So

Those two events from which we take the union, do we agree they are disjoint events ?

[winter ocean]

Yes

[pallid scarab]

So if we take the probability of the union

[winter ocean]

They do not have any effect on each other

[pallid scarab]

It's not that they don’t have an effect on each other, in fact they do

[winter ocean]

Oh

[pallid scarab]

Because you can't have both at the same time

[winter ocean]

Oh right

[pallid scarab]

But

Since those are disjoint events

When we take the probability of their union, it's equal to... ?

[winter ocean]

100/100

[pallid scarab]

?

[winter ocean]

75/100 and 15/100

Wait

[pallid scarab]

Don't get too hasty xd

[winter ocean]

25 mb

[pallid scarab]

We don't even have a value for the probability xd

[winter ocean]

Huh

[pallid scarab]

Remember we're looking for the probability of P xd

[winter ocean]

The probability of passing the theory test is 0.75

[pallid scarab]

I was trying to make you realize that we can use $P(A\cup B)$ for A and B disjoint events

[winter ocean]

The probability of passing just one is 0.36

[ocean seal]

rafilou2003

[pallid scarab]

Our event is $(P \cap not(T)) \cup (not(P) \cap T)$

[ocean seal]

rafilou2003

[pallid scarab]

And we just said those two are disjoint :)

[winter ocean]

But dont know p

[pallid scarab]

Yes, it doesnt matter yet

[winter ocean]

Oh ok

I

Ok

[pallid scarab]

Shit

Let's write P(P) = p

[winter ocean]

Oh not ok

[pallid scarab]

We so we want to find p

[winter ocean]

W8 too many P and p-s wich is wich

Why is the P(P) isnt that gona end up as P×P?

[pallid scarab]

I warned you :(

[winter ocean]

Oh mb

[pallid scarab]

So

Let's switch names

[winter ocean]

Fair

[pallid scarab]

"Pass theory" is event A

[winter ocean]

Yes

[pallid scarab]

"Pass practical" is event B

[winter ocean]

👍

[pallid scarab]

We know from the exercise that $P[(A \cap not(B)) \cup (not(A) \cap B)]$ = 0.36

[ocean seal]

rafilou2003

[winter ocean]

Yes

[pallid scarab]

But, since $A \cap not(B) $ and $ not(A) \cap B$ are disjoint events, we have that :

[winter ocean]

I understood the last one

[pallid scarab]

Edit part 10

Xd

[winter ocean]

Becasue they are disjointed they are...

[pallid scarab]

When we take disjoint events, the probability of their union is ?

[winter ocean]

They may sound dumb ehat wdym by union

[pallid scarab]

When we take the probability of "A or B"

When A and B are disjoint events

What do we get ?

[winter ocean]

100% of one of them happening?

[pallid scarab]

And what is "one of them happening" ?

[winter ocean]

Either A & not B or not A& B has to be an outcome

[pallid scarab]

Forget about those

[winter ocean]

Oh ok

[pallid scarab]

Let's say C and D are any disjoint events

What is $P(C \cup D) =$ ?

[ocean seal]

rafilou2003

[winter ocean]

PC and PD?

[pallid scarab]

If by "and" you mean "+", then yes !

[winter ocean]

Oh ok

PC + PD

[pallid scarab]

But, since $A \cap not(B)$ and $not(A) \cap B$ are disjoint events, we have that :

[ocean seal]

rafilou2003

[pallid scarab]

$P[(A \cap not(B)) \cup (not(A) \cap B)] = P(A \cap not(B)) + P(not(A) \cap B)$

[ocean seal]

rafilou2003

[pallid scarab]

This is, again, because the events are disjoint

[winter ocean]

Yes so the "OR" has turned into an + bc they are disjointed l?

[pallid scarab]

Yep

[winter ocean]

Ok cool

[pallid scarab]

So now

What else do we know about events A and B

[winter ocean]

The probability of failing one and passing one is 0.36

[pallid scarab]

Yes, we already said that

So $0.36= P(A \cap not(B)) + P(not(A) \cap B)$

[ocean seal]

rafilou2003

[winter ocean]

Yes

[pallid scarab]

What else do we know ?

[winter ocean]

0.18 = P(A & not B)
0.18 = P(not A & B)

[pallid scarab]

That is very wrong

[winter ocean]

Oh

[pallid scarab]

Just because 2 + 4 = 6 doesnt mean 2 = 3 and 4 = 3

[winter ocean]

Huh

Oh right

Yh

[pallid scarab]

So, what else can we use from the exercise ?

[winter ocean]

(PA + PnotB) + (PnotA + PB)

[pallid scarab]

We said this relation was true for what kind of events ?

[winter ocean]

Disjointed

[pallid scarab]

Are A and notB disjointed ?

[winter ocean]

Ummmmm

PC - PD

[pallid scarab]

Not that either

[winter ocean]

Multiply?

[pallid scarab]

What is something that is mentioned in the exercice ?

[pallid scarab]

And this works for which kind of events ?

[winter ocean]

Joint

[pallid scarab]

No, there's another condition

$P(C \cap D) = P(C) × P(D)$ is only true when C and D are... ?

[ocean seal]

rafilou2003

[pallid scarab]

The answer is somewhere here :)

[winter ocean]

0.75

[pallid scarab]

The relation is only true when C and D are 0.75 ?

[pallid scarab]

This relation

[pallid scarab]

We need a condition on the events C and D so that the relation here is true

And that condition is mentioned somewhere in your exercice...

[winter ocean]

I don know sry

Chances of passing theory is 0.75

Therefore chances of failing theory are 0.25

Chances of failing one and passing one are 0.36

So yh

Pass and fail or fail and pass

[pallid scarab]

Re-read all that is said in your exercise's statements

Dont omit any sentence

[winter ocean]

Idk waht is even going on anymore

What happened to drawing the probability tree

I swear thats how u do these q

[pallid scarab]

I mean there are many ways to do those questions

Let's draw the probability tree if you want

The first branches are A / not(A)

The next branches are B / not(B)

Write p = P(B) so you can actually write something for the branches with B

[winter ocean]

I dont understand why there is p and P if they are the same thing. Ik of them are probability. I also drew a tree but the banches were like
<
<
<

The letters are killin my brain

[pallid scarab]

. B
/ p
A
/ \ 1-p
/0.75 not(B)

\ 0.25 B
\ / p
not(A)
\ 1-p
not(B)

With p = P(B)

So P(not(B)) = 1 - p

Got it ?

[winter ocean]

Im drawing that out

Ive written it out but i dont understand what is capital P compared to lowercase p

[pallid scarab]

P(A) is the probability of the event A

and I introduced small p = P(B), the quantity we're searching

[winter ocean]

But isn't p also the probability

[pallid scarab]

Small p is nothing but P(B)

You could have named it any way you like

I could have said x = P(B)

Do you prefer using x ?

[winter ocean]

But is P = p bc this is very confusing

[pallid scarab]

Ok, forget about small p

Replace every small p by "x"

[winter ocean]

Ok

[pallid scarab]

x = P(B)

[winter ocean]

Yes

[pallid scarab]

So

Remember that we got $0.36= P(A \cap not(B)) + P(not(A) \cap B)$ from previously

[ocean seal]

rafilou2003

[pallid scarab]

And now, using the probability tree, what do we get ?

[winter ocean]

Hol up in calculating

[pallid scarab]

Alright, you may look at this when you're done to see if you were right

$0.36 = 0.75 × (1-x) + 0.25 × x$

[ocean seal]

rafilou2003

[winter ocean]

Ok i got everything apart from why its multiplyed 0.75*(1-x)

[pallid scarab]

And you got the 0.25 × x as well ?

[winter ocean]

Yes

But why multiply

[pallid scarab]

So, why do you think we made a probability tree ?

For which types of events is making the tree useful ?

[winter ocean]

Events that are not effecting each other

[pallid scarab]

Yes, the true name for those events is right here

"The two events are independent"

[winter ocean]

Yes

[pallid scarab]

And when events C and D are independent : $P(C\cap D) = P(C) × P(D)$

[ocean seal]

rafilou2003

[pallid scarab]

Thus why we multiply

[winter ocean]

Ok

Oh right

[pallid scarab]

I'm assuming that you can solve this

then you get the probability of passing practice is P(B) = x = ...

[winter ocean]

0.36 = 0.75 - 0.75x + 0.25x

Thx for ur time but my dad say i have to go to slep 😭 i cant read fast enough to comprehend what is going on w the letters.

0.78

.close

[lone heart]

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[graceful creek]

i need help on a study guide i have for algebra 2 my test is tomorrow

[graceful creek]

can anybody help me on this?

[solid swan]

On the absolute inequality treat it as multiplying by -1 to the left of the y axis and multiply by 1 when right on the other questions just multiply out brackets and get all terms of the same type on one side and divide to get the value for 1 term and for the questions like 8 cross multiply.

[graceful creek]

im gonna be honest i dont know what any of this means your going to need to dumb it down for me

[lone heart]

@graceful creek Has your question been resolved?

[lone heart]

@graceful creek Has your question been resolved?

[lone heart]

@graceful creek Has your question been resolved?

[woven spade]

what exact part do you need help with

[graceful creek]

all of it bruh i got a test tomorrow

[woven spade]

like what part of it do you have trouble with

[graceful creek]

all of it but compound inequalities is my weakest

[woven spade]

let's take 26. :
-24<= 2x-10<-6
add 10 on both sides
-14<=2x<4
-7<=x<2

you just basically isolate

x

you can basically do anything as long as you do it to everything

say +10

you can add 10 to 2x-10 but you need to also add 10 to -24 and -6 to get -14 and 4

[woven spade]

reversal of signs being an exception

then you have to change the inequality symbol

[lone heart]

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[vale sigil]

.close

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[lone heart]

@graceful musk Has your question been resolved?

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@graceful musk Has your question been resolved?

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[wicked geode]

is the answer for this just 1?

[vale wigeon]

surely not

[wicked geode]

because i got it down to tan(theta)/tan(theta)

[vale wigeon]

show your work.

[void solar]

its not

you shouldnt get a constant for an indefinite integral

[vale wigeon]

it's not 1

it's $\int 1 \dd{\theta}$

[ocean seal]

Ann

[wicked geode]

yea that

[wicked geode]

is just saying 1 not the same as that?

[vale wigeon]

no it is not

[wicked geode]

oh ok but it's the correct working out?

[vale wigeon]

appears as such, yes

[wicked geode]

ok thanks

[lone heart]

Channel closed

Closed due to the original message being deleted

[wicked geode]

oh oops

if not then anyone can dm me the right answer

[wicked geode]

so it would just be what Ann wrote at the top right?

[void solar]

probably

[random escarp]

are we supposed to send our questions here, im stupid :,).

[void solar]

#❓how-to-get-help

read that

[wicked geode]

#help-3 this is vacant

[lone heart]

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[random escarp]

thank you

[wicked geode]

oh nvm you can use this now

[random escarp]

o

[void solar]

@random escarp Whenever you see this that means its open. you just post your question and it pins the first message you send

[void solar]

In this case its pinned this lol

so this channel is now opened in your name

[random escarp]

mk !

[void solar]

.close (close the channel)
.reopen (reopen the channel)

those are the commands

[random escarp]

im probably the youngest here since im only in 8th grade and you guys seem much smarter and mature

[void solar]

Its all ranges of ages and questions here

dont worry about it

youngest i helped was a kid learning how to add fractions

[random escarp]

o-

[void solar]

im still in highschool as well. :D

send your question here and ill help

[random escarp]

woah

i needed help understanding what its asking for here

[void solar]

its asking you to convert celsius to fahreheit

[random escarp]

ou

so i was right the first time

[void solar]

Do you know how to do that?

[random escarp]

so its 68 fahrenheiht ?

[void solar]

yeah!

[random escarp]

kinda, im a bit new to the school im now in, i recently moved from brazil so they do math a bit different there

[void solar]

US?

[random escarp]

Yes

[void solar]

ah, have fun with the messy imperial units

[random escarp]

oh my

thats gonna be hard

[void solar]

Im not sure what the right column is,

Looks like a ratio / fraction of comparing the two

[random escarp]

yeah, its a bit similar to constant of proportionality i think?

[void solar]

Maybe

[random escarp]

there is no constant of proportionality in that ratio though, i believe '

[void solar]

yeah theres not

[random escarp]

yeah definitely not any constant of proportionality, the way to write the equation is similar though

i just don't get where they got the nine over 5 from in the sentence here

[void solar]

Thats just the conversion between the two

I dont think you would need to know why its that amount specifically

[random escarp]

hm okay!

i've gotten the temperatures down, im confused one what im supposed to do for the far right column

[void solar]

yeah me too lol

Looks like a fraction

So maybe its just

$\frac{Temp(F)}{Temp(C)}$

[ocean seal]

Xiszt

[random escarp]

ouhh i think i get it

you have to multiply it by 1.8 right?

like f= c*1.8

hm no wait thats wrong

[lone heart]

@random escarp Has your question been resolved?

[lone heart]

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[rain sundial]

How does 2e^2x = e^x become 2x + ln 2 = x? Im getting 2x * ln 2e = x

[rain sundial]

I used ln on both sides

[merry depot]

Check your rules again
ln(MN) = ln(M) + ln(N)

[lone heart]

@rain sundial Has your question been resolved?

[rain sundial]

okay

but still, then it become 2x * ln 2 + 1 = x if im not wrong

but its supposed to be what i said earlier

[merry depot]

Why would they be multiplied together?

[rain sundial]

because of log(a^b) which becomes b * (log a)

[merry depot]

2x isn’t an exponent on 2

[rain sundial]

ok give me a sex

sec*

so do i ln them seperately and then add them together

so i t become ln 2 + ln e^2x = x?

[merry depot]

Yes

[rain sundial]

okay thanks man

.close

[lone heart]

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[fallow zealot]

How can I find C without its X or Y coordinate

And what does “C is a point on the negative y-axis such that ABC is isosceles with AB=BC” mean

[small panther]

That means C is on the red part of the y axis and the triangle ABC is isosceles with AB = BC means AB=BC

[fallow zealot]

Yeah so I was trying to use the formula where AB=BC to find the coordinates but since I don’t have either the coordinates of x or Y there will be 2 unknowns and I will be stuck

[small panther]

No

try it

[small panther]

Because you will have 2 equations

[fallow zealot]

So like that?

[small panther]

Try using vectors

You know what i mean ?

[fallow zealot]

English isn’t my first language

So I don’t know what that means

[small panther]

Things like this

[fallow zealot]

We have never been taught such things before

[small panther]

Oh are you sure ?

[fallow zealot]

Are there any other things I could do to solve the problem without using vectors?

Yeah

[small panther]

You can draw it

You have the coordinates of A and B

So place A and B on a graph

[fallow zealot]

Done it

[small panther]

Next, you have to trace a circle with B as center

[fallow zealot]

C (1,-6)

[small panther]

Not possible

C has to be on the y axis

-y axis

[fallow zealot]

What makes -y axis and y axis different

Just the negative sign or what

[small panther]

Yes, -y axis means the negative part of y

I'd say that

(0,-5) or (0-6)

My graph isn't precise

But your graph has to be precise

[small panther]

With the radius = AB

[fallow zealot]

Can I just sub X = 0

[small panther]

Oh yes I didn't see that

That'll work

[fallow zealot]

I subbed X and turn it into 0

And got 3 = y

Since it’s negative Y axis

Does it mean it’s on -3

[small panther]

don't you have 2 solutions?

It's a quadratic equation

[small panther]

nono you can't do that

sqrt(a^2 + b^2) isn't a+b

Here you can start by removing the square roots

Then you'll have your equation

[small panther]

But not the way you did

[fallow zealot]

Do you have a pen and a paper

you demonstrating it would make it much more clear for me to understand

[small panther]

k

First I just squared the equation

[fallow zealot]

Ohh I see

[small panther]

Now you have to solve it

[fallow zealot]

So with the equation, now C can be found

[small panther]

You find 2 solutions : y=-5 or y=+3

But since C is on the -y axis

y has to be negative

So we found Y=-5

[fallow zealot]

I get it now

Thank u bro

[small panther]

Here is the graph @fallow zealot

As you can see AB = BC since they are the radius of the circle

And we do find -5

[fallow zealot]

seeing in on a graph makes things much clear to understand

[small panther]

Yes that's why I told you to draw it

It always helps

And as you can see, we also have the y=+3 solution

But it was the wrong one

[mental yacht]

Can anyone help me 😦

[alpine sable]

Please translate the exercises to English

[mental yacht]

Number 4: Calculate all zeros of the respective function

[alpine sable]

a) you can solve it by factorization
x^3-2x=x(x^2-2)=0

[mental yacht]

Number 3: which of the following functions are symmetric to the y-axis and which are point-symmetric to the origin

[alpine sable]

4b) if one of them is zero all of them will be equal zero, so either
x-2 = 0
x+1 = 0
1/2x-4 = 0

4c) you can let m=x^2, then use quadratic formula or completing the square to solve for m
then plug m back in (m=x^2) and then solve for x

remember to check the solutions because some of them can be extraneous solutions

[alpine sable]

it should be a), im not sure what do you mean by "point-symmetric to the origin"

[mental yacht]

I also have no idea what he means by that hahaha

[lone heart]

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[placid estuary]

how to do this

[placid estuary]

All I know is to make it into 6 (that long symbol) x/(x-5)^2

and I am stuck

I don't even know how to start this

[kindred anchor]

Hi again

Take (x-5)=t and substitute accordingly

[placid estuary]

what?

wait

a/t + b/t^2?

[void solar]

would u=(x-5)^2 be a better sub?

[placid estuary]

or something else

[kindred anchor]

Not like that.

[rapid tapir]

partial fractions?? idk

[kindred anchor]

Not partial fractions.

[rapid tapir]

partial fractions would work

[kindred anchor]

Taking t=(x-5), dt=dx

[placid estuary]

wait what?

[kindred anchor]

The integral would become, $$6 \cdot \int \frac{t+5}{t^2} \dd{t}$$

[ocean seal]

QuantumBee

[placid estuary]

I am still confuse

I don't get it

[vague coral]

they just did a u-sub, nothing crazy

t = x-5
so x = t+5

and dt = dx

you switch all that in the original integral

[placid estuary]

ah

that thing

[vague coral]

and you got this

yes

[placid estuary]

so

[vague coral]

now it is much easier to solve

[kindred anchor]

You can split and continue to work on this

Finally, substitute t everywhere, you would the get the answer in terms of x.

[placid estuary]

so

it should be

6 Ln Ix- 5I - 30 (x-5)^-1 + C ?

-> 6 Ln Ix- 5I - 30/(x-5) + C

?

[kindred anchor]

,w \int \frac{6x}{(x-5)^2} dx

[ocean seal]

Results provided by WolframAlpha

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

Requested by QuantumBee#7757

[kindred anchor]

@placid estuary ^

[placid estuary]

huh

[kindred anchor]

You are right

[placid estuary]

ah ok

so what is this?

[kindred anchor]

That's your answer

I was bored to do it myself, so I checked it with the bot.

[placid estuary]

ah

[lone heart]

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[worldly mountain]

2+2=5000

[empty cedar]

https://tenor.com/view/math-zack-galifianakis-thinking-calculating-gif-5120792

whats the question

[meager phoenix]

prove that 😱

[worldly mountain]

it's such a joke

[empty cedar]

2+2=5000
2=4998
2+4998=5000

2 is a variable they just chose a number as it

[worldly mountain]

no

2=2500

2+2=2500+2500=5000

https://tenor.com/view/easy-gif-22367924

[empty cedar]

Lets close the channel

[lone heart]

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[marsh quiver]

Proof by induction
can anyone help me?

[lone heart]

@marsh quiver Has your question been resolved?

[lone heart]

@marsh quiver Has your question been resolved?

[alpine sable]

what is the problem?

as in, what are you stuck on

[marsh quiver]

Idk how to start the last problem since i have never don’t prooof by induction for factorials

[alpine sable]

wait im confused are those two separate questions or

oh okay so you just want the last thing

was confused for a bit

anyways

[alpine sable]

take P(4) as your basis step

[marsh quiver]

What would be my induction step?

[alpine sable]

okay

so assume $n = k, on k \geq 4, 2^k \leq k!$ is true

[ocean seal]

♡LexQa♡

[alpine sable]

💀

okay

so we want to find it when n = k+1

so $2^{k+1} \leq (k+1)!$

[ocean seal]

♡LexQa♡

[alpine sable]

thats okay so far right? @marsh quiver

[marsh quiver]

So I have to show ?

$2^0 + 2^1 + 2^k + 2^{k+1} $

[alpine sable]

well, let's consider (k+1)! first

that is just (k+1)k! correct?

[alpine sable]

but if you remember, we defined $2^k \leq k!$

[ocean seal]

♡LexQa♡

[alpine sable]

this means

$2^k(k+1) \leq (k+1)k!$ is true as well

[ocean seal]

♡LexQa♡

[alpine sable]

this implies that the inequality holds for when both sides are multiplied by a number at least k+1 @marsh quiver

if that makes sense

[marsh quiver]

Yes I understand

[alpine sable]

so this implies that $2^1\cdot 2^k \leq (k+1)!$ is true, since $2 < k +1$ because we defined $k \geq 4$

[ocean seal]

♡LexQa♡

[alpine sable]

this means, that at the minimum k =4 which means 2 < 5 is true

this, the proof is finished with induction

are you confused by anything? @marsh quiver

[marsh quiver]

So we can use our assumptions to further our solutions Rt?

[alpine sable]

yes, it is a common question in induction

"Why do we assume the thing that we want to prove is true? Isn't that redundant?"

The thing is, you are not assuming anything, but you are actually just linking the dots on a more general level

[alpine sable]

it is all because of your basis step that students tend to overlook

if you can go from your basis step of P(1) to the second term P(2), then induction is definitely viable

because from there you can link P(2) to P(3), and P(3) to P(4), and P(k) to P(k+1)

this is also the reason that induction may fail

[marsh quiver]

Oh I see

[alpine sable]

if you cannot prove P(2) through P(1), then you have no basis to prove P(k+1) through P(k)

[alpine sable]

think of a hypothesis

such as "All flowers are black"

we want to prove that preposition with induction

if we take our basis step to be P(1), you have one flower in your hand which is black

you can safely assume that because it is one singular flower

but when we start considering P(2), we have no idea. Because why is the fact that I have one black flower imply that the second one should be black too?

Does that make sense? @marsh quiver

[marsh quiver]

Yes it makes sense

[marsh quiver]

So I started the first one can you take a look?

[alpine sable]

i have to go to class now, i am sorry

[alpine sable]

im sure <@&286206848099549185> can assist you here

[marsh quiver]

Ok thanks

[opaque spear]

Where can I get help with some game theory exercise?

[smoky vigil]

guys i need help with this please

[lone heart]

@marsh quiver Has your question been resolved?

[rotund forum]

I think it’s ok

[alpine sable]

okay im back @marsh quiver

are u here?

we can work on your second problem

[marsh quiver]

I am here lol

[alpine sable]

Question is Convert to a binomial:

[marsh quiver]

I think you have to factor not quite sure

[alpine sable]

Idk have next week a test

Asking tomorrow my teacher

[alpine sable]

sorry @marsh quiver

i didnt read ur message

you shoud've pinged me

do u still need help?

[lone heart]

@marsh quiver Has your question been resolved?

[lone heart]

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[alpine sable]

I don’t understand inverse functions and asymptotes, I don’t understand a lot to be fair

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[lone heart]

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[alpine sable]

.reopen

[lone heart]

✅

[alpine sable]

<@&286206848099549185>

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[thick flame]

Does anyone know in what year the factorial function was named?

[thick flame]

This is out of curiosity because I can't find it online (at least not easily)

[slate jolt]

https://en.wikipedia.org/wiki/Christian_Kramp

if you mean the notation

!

and it seems factorielle

which is french for factorial was introduced by https://en.wikipedia.org/wiki/Louis_François_Antoine_Arbogast

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[peak night]

81

[wary stream]

#❓how-to-get-help

This is where you should know your times table

[fallen verge]

i cant tell if you are trolling or not

how old are you my friend?

[wary stream]

Use a calculator

People are helping you

[fallen verge]

how old are you my friend?

[wary stream]

What is your age?

[vapid ice]

Classic. 110

[wary stream]

You seem to be underage

[last ether]

Bro

[wary stream]

Aka under 13

[last ether]

MF with the geometry dash pfp

Anyways are you gonna just yell at people or do you have a genuine question that the internet could not solve

[last ether]

Minor trolling

[last ether]

@high ether

[last ether]

Answer

[wary stream]

.

[last ether]

Because like

I'm perfectly fine with just closing the channel if you're gonna Shitpost or ask trivial questions

[wary stream]

.close

[lone heart]

Channel closed

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Use .reopen if this was a mistake.

✅

[last ether]

<@&268886789983436800> this guy keeps shitposting

Not today buckeroo

Stop abusing channels

.close

[lone heart]

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[calm gale]

Hello

[calm gale]

For this q

Im not sure how to prove vector addition in part a)

do i just make 2 randon vectors u and v with variables u1 v1

then add them

but im confused on how to prove how u + v still falls ujnder AD = DA

[lone heart]

@calm gale Has your question been resolved?

[orchid stump]

how do u solve this (2x)/(x-2)=(1)/(x+2)-2?

[calm gale]

use another help cahnnel

[lone heart]

@calm gale Has your question been resolved?

[calm gale]

wtf

how am i the only channel which gets no one

[calm gale]

💀

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[gentle solar]

Can someone help me write a formula for this? Addition is boring

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[alpine sable]

<@&286206848099549185>

[alpine sable]

Would the answer for the first one be the same numbers ?

Do I repeat 10,25,15

?

[serene junco]

Nope, on the right, you factored out a 5

What would have to go in those blanks, so that if you distributed the 5, it would be equal to the left side?

[alpine sable]

So I need to see what times 5 gives me 10? And then same for the 25 and 15?

[serene junco]

Not just 10, 10x

And not just 25, but 25y

etc

[alpine sable]

Ohhh okay

So would my first blank be 2x?

[serene junco]

Yep

[alpine sable]

Oh alright, I understand now! Thank you so much

[serene junco]

Sure thing 👍

[alpine sable]

.close

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[neat plank]

I'm trying to make my problem in a readable fashion, so bare with me:

I *need* 6 numbers, each number has 2 options to choose from, I need the max number possible combinations

Here's a visual representation
Number 1 | 2 | 3 | 4 | 5 | 6 |
Op1    4   6   8  10   1   4
Op2    3   7   1   9   11  8

What formula should I look for, cause I know

(n!)/(r!(n-r)!)

But that would only work if I'm looking for max combinations on 6 chosen out of 12 possible choices like

Number 1 | 2 | 3 | 4 | 5 | 6 |
Batch of to pick from
4   6  10  3   7   1   9   11  8

[prime badge]

ok, so what's the readable version?

the word "max" is throwing me off

what is being maximized?

if you have 6 one-in-two choices the total is 2^6

[neat plank]

Hm

I mean, it just seems too simple to be 2^6, but for now that's my only option so I guess I'll use Excel to verify lmao

Nvm, I changed the variables in my question and it matches, you got it lmao thanks

!close

!help

[alpine sable]

@neat plank .close

-_-

[neat plank]

.close

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[sour moat]

<@&286206848099549185>

[sour moat]

i need help please!!

<@&286206848099549185>

[tacit arch]

!15m

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[tacit arch]

Read

[sour moat]

sorry i didn't mean to do that but :
3:4 = 6 : ?

the missing ratio

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[icy violet]

How do I do tree diagrams

[void sun]

Well you first got to look at the highest percentage

Which is in this case 51%

That's more than half so thats our first option

[icy violet]

Yup

[void sun]

So the probability that they use it is 51 : 100 x 74

[icy violet]

@void sun

[void sun]

It's there

[icy violet]

Would that equal 37.73

37.74

But that means 3000%

Or is it 0.51 times 0.74

@void sun

.close

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[ember stag]

.close

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[rain topaz]

Solved the integration and
i am trying to compare two values together to find b,
4x^(b+1)/b+1 = 2x^2
Idk how to solve this

[ornate condor]

hi

well

when u int

$\int x^b= ax^{b+1}$

[ornate condor]

for a=1/b

anyway

[vale wigeon]

[ornate condor]

ull see that when u integrate u get 4 terms

[vale wigeon]

and bad wording

and also wrong

[ornate condor]

im so sad rn

ill just

[vale wigeon]

$\int x^b \dd{x} = \frac{1}{b+1}x^{b+1} + C \neq \frac{1}{b} x^{b+1} + C$

[ocean seal]

Ann

[ornate condor]

zoom out

o wait

LOL

smh

[rain topaz]

o yes i did get 4 terms
i am trying to compare one of the term with the other term in the other side of the equation
4x^(b+1)/b+1 = 2x^2

but im not sure how to get the value of b from here

[ornate condor]

u look at the powers

the other stuff gives u the other 3 terms

so thrs just 1 term that can b gotten by the ^b term

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[civic jasper]

Could someone explain to me why the left solution is incorrect?

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[void solar]

think its because since y can be -4

(4+y) = 0

and your not allowed to divide by zero

weird though idk

[velvet cliff]

yeah it's because of htat

y= -4 is a solution

[vague mirage]

See bro in the right side you get y=-4
And if you see here in the left side 2nd step you have divided (4+y) by (4+y) but y = - 4 then you have divided 0 by 0 which is undefined therefore you didn't get the solution@civic jasper

[civic jasper]

Ah thank you for the explanation everyone. I appreciate it!

Have an awesome day

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@tacit comet Has your question been resolved?

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[wheat isle]

i use quadratic formula on this?

[wheat isle]

so after expanding it would be x^2 + 2qx - px^2 + q^2?

[rustic ruin]

you can use vieta's formula here also i think

that would be faster

[wheat isle]

it wouldnt be confusing without expanding brackets first?

[rustic ruin]

why would you need to expand the bracket

just use x2-Sx+P=0 and vieta's formula
where S is the sum of roots and P is the product of roots

[wheat isle]

Sx?

or p

ohh

-b/a

and c/a

[rustic ruin]

yes yes

[wheat isle]

px/x^2 is sum and product is q/x^2

oops

-px/x^2

i meant

[rustic ruin]

no

-p/1 is the sum