help-0

[naive valley]

yep

hint:

you don't need to calculate this one

just think

how does it relate to R B R B R

[cosmic orbit]

one more black

1 less red

[naive valley]

but in terms of probabilities

[cosmic orbit]

it will be the same

[naive valley]

in both cases you have 26 of each color to start with

and you choose three of one color and 2 of the other

yep

same probability

[cosmic orbit]

Ok cool

[naive valley]

and then to get your final answer, what do you do?

[cosmic orbit]

325/4998

I got this question wrong and im wondering why

[naive valley]

325/4998 should be correct

hmm, when in doubt start with the definition of conditional probability

P(both gold | both the same color)

[cosmic orbit]

ye i just did that

Im going to work out the Prob that 2 balls r the sasme colour

[naive valley]

this one can again be done by just thinking without really calculating

P(both the same color) = P(BB) + P(RR) + P(GG) and those three are all the same since there are three balls of each color

[cosmic orbit]

So i worked out the caradinality of them both being the same colour is 3

[naive valley]

and you want P(GG) / (P(BB) + P(RR) + P(GG))

which is just P(GG) / (3P(GG)) by the above reasoning

so it's 1/3, you don't even need to calculate P(GG) !

[cosmic orbit]

did u get 3 P(GG) by saying all 3 have the same probability

[naive valley]

yea, P(BB) = P(RR) = P(GG)

so their sum is just 3 times one of them

(doesn't matter which one since they're all the same)

[cosmic orbit]

Cool cool

Thanks

!

[lone heart]

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[tired star]

its asking for a differential equation and i did everything its just the last question asks how much time do you need to read 20000 bacteria's and it takes t = 8.54 h

however my issue is that in the question it says t = [0,8]

so does that mean there are no answers?

[lone heart]

@tired star Has your question been resolved?

[limpid turret]

It's not t=

It's t is an element of the interval between 0 and 8 inclusive

That is, t can be any value from 0 to 8

Oh I see your question now

What's up with part c

Seems to be asking for population after 5 hours, but isn't that given?

[lone heart]

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[hollow thicket]

how do I solve for c?

[lone heart]

@hollow thicket Has your question been resolved?

[lone heart]

@hollow thicket Has your question been resolved?

[lone heart]

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[unique salmon]

Need to solve the longest side of the triangle to get the area of the rectangle

a/sin alpha = b/sin beta?

[hazy ferry]

yeah

[unique salmon]

weird tho, it doesnt come out right in my calculator

i tried doing

50/sin 50

[hazy ferry]

what did you get

[unique salmon]

i got 70.71

then did x sin 100

got 70.71

Is it supposed to be the same answer?

[hazy ferry]

uhmm

for 50 / sin 50 I get 65.27

[unique salmon]

weird

[hazy ferry]

but you are right, you get the longest side by doing: (50/sin50) * sin100

[unique salmon]

weird

[hazy ferry]

try it again

[unique salmon]

well okay thank you

.close

[lone heart]

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[unique salmon]

17. Express the deviation of the straight line p from the 15. problem from the x-coordinate axis

15. m = 1/3
    y = 1/3x + 2

I don't understand the 17th problem tho

[tired star]

Yeah idk why they did that

Im guessing you need to justify it

[unique salmon]

<@&286206848099549185> does anyone have an idea

[last ether]

The deviation?

Like the distance?

|f(x)| lol

[unique salmon]

I dont understand myself

like the only problem i didnt understand

[last ether]

Like is it the distance between the line, f(x), and the x axis?

Then it's legit just |f(x) - 0|

[unique salmon]

like is that supposed to be some answer

cause i myself don't understand what the teacher is asking there 💀

[last ether]

Well yeah. Think about it

The deviancy is just the distance

[unique salmon]

ye

[last ether]

But distance increases as |f(x)| approaches infinity

[unique salmon]

thats why its - 0

[last ether]

Assuming a vertical line as distance, then the distance is |f(x) - 0| = |f(x)|

Perpendicular distance would be different but I don't think the problem is asking for perpendicular distance

[unique salmon]

well thank you, i think i kind of understand it a little

i got one question tho

sin x = 1

is there a way to solve this

[unique salmon]

@last ether

[last ether]

Yes

Unit circle

Or take the arcsine of both sides

Although you can use logic

[unique salmon]

you mean this thing?

[last ether]

I mean yeah

If you wanna use a graph

Or just use your unit circle

[unique salmon]

wow

They never showed us this

This looks amazing

[last ether]

It's ass I don't memorize that. I just use 45-45-90 and 30-60-90 theorem

[unique salmon]

so the answer is 360?

[last ether]

The coordinate points in the unit circle are (cos(θ), sin(θ))

No

You just gotta find the point (0, 1)

[unique salmon]

90?

[last ether]

90 degrees, yeah

[unique salmon]

sin x = 90?

[last ether]

No

x = 90

,w Sin[Pi/2]

[ocean seal]

Results provided by WolframAlpha

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

Requested by Umbraleviathan#3607

[last ether]

pi/2 rad = 90°

[unique salmon]

well yes that 180/2

but what do we do with that

[last ether]

You're asking to solve sin(x) = 1

So x = 90 + 360n, where n is an interger

[unique salmon]

hold up there

things escalated quickly, i know x is 90 which is pi/2

but where did you get 360n

was that like the first 1?

[unique salmon]

this

[last ether]

That only accounts for 0 to 360 degrees. There an infinite number of coterminal angles

And therefore an infinite number of answers if unbounded

The 360n accounts for that infinite number of answers

[unique salmon]

so 360n will always be added

[last ether]

Well yeah

[unique salmon]

so 2 pi n

[last ether]

$x = 90 + 360n, n\in \bZ$

[ocean seal]

Umbraleviathan

[last ether]

Yeah

[unique salmon]

damn bruh

thats insane

i feel like ive seen this million times before, but forgot about it

[lone heart]

@unique salmon Has your question been resolved?

[rocky grove]

Hey

Do you still have questions or?

[unique salmon]

hmm well

im just writing everything important from here

ill let you know if i need something

if not, ill close it

[rocky grove]

There are always help channels available so

If you feel like you answered all your questions now, then it's better to close it and return later when you have other questions.

[unique salmon]

alright

also

i just found something

i already solved it which is problem 6

x = 27

but problem 7 is related

[rocky grove]

Yeah we solved it together yesterday

What does problem 7 translate to?

[unique salmon]

yeah i learned logarithms, and one sec ill translate

Establish the conditions for the solvability of the equation

[rocky grove]

Ooo that's like the domain and range

[unique salmon]

so something in the brackets

[rocky grove]

Yep

[unique salmon]

like (x to infinity)

just an example

[rocky grove]

$x \in (0, \infty)$

[ocean seal]

VulcanOne

[rocky grove]

Yeah

Something like that

[unique salmon]

mhm, but what does the range come from

the x result?

or the log

[rocky grove]

The log

[unique salmon]

i see

[unique salmon]

so we use the 3x

from the log

[rocky grove]

Range: $\mathbb{R}$

[ocean seal]

VulcanOne

[rocky grove]

Yeah

[unique salmon]

3x > 0

[rocky grove]

Mhm

[unique salmon]

but what do we do next with this

we can't leave it just like that?

[rocky grove]

Well if 3x should be greater than 0, then x itself should be greater than 0

If you divided both sides by 3

[unique salmon]

true

yeah

i was first doubting

that dividing it with 3 would make sense

i guess it does

so 3x > 0 and x > 0

[rocky grove]

What if it was 3x + 1 > 0?

[unique salmon]

hmm

[rocky grove]

What would you do here?

[unique salmon]

3x > -1
x > -1/3

[rocky grove]

Yepp

[unique salmon]

so basically doing this based of the logarithm i see

[rocky grove]

Yeah

[unique salmon]

mhm ty

[rocky grove]

Last trick I have for you

What if it was log(|3x + 1|)?

[unique salmon]

im back

hmm

ok first

|3x + 1| i would change this to -3x -1

log(-3x - 1)

[rocky grove]

Why?

[unique salmon]

is it not the same as in absolute equation?

hmm

[rocky grove]

The absolute value function takes your input and makes it positive

All the time

So basically it safe guarded the log function

Except for 1 point

The absolute value function still has a 0

[unique salmon]

where is that 0?

[rocky grove]

Solve for 3x+1 = 0

[unique salmon]

x = -1/3

[rocky grove]

And thus

[unique salmon]

is it because it's less than 0 so it's kind of 0?!

[rocky grove]

$x \in \mathbb{R} -{ -\frac{1}{3} }$

[ocean seal]

VulcanOne

[unique salmon]

ill write that down

[unique salmon]

the result for this right

[rocky grove]

No it's because the absolute value function isn't fully above 0. It has a an x-value that makes it 0. And log doesn't like 0. So you find the x-value that makes 3x+1 = 0.

[rocky grove]

Yep

[unique salmon]

i see

so if it was |-3x-1| then then it would be okay to change to 3x+1

[rocky grove]

Yeah

[unique salmon]

awesome

[rocky grove]

No wait

It would be safe to make it like this

[unique salmon]

👁️

[rocky grove]

$|3x+1| = \sqrt{(3x+1)^2}$

[ocean seal]

VulcanOne

[unique salmon]

oh

you basically get rid of the ||

this way

[rocky grove]

Yeah

[unique salmon]

ill write this too

okay

ty

[rocky grove]

[unique salmon]

For a ∈ R {-5, 5}, simplify the expression

[rocky grove]

[unique salmon]

ok so

(5+a) (5-a)

[rocky grove]

I'm having a hard time looking at the image

[unique salmon]

5a 10a^2

---

5-a 25-a^2

[rocky grove]

Ooo okay

$\frac{5a}{5-a} - \frac{10a^2}{25-a^2}$

[ocean seal]

VulcanOne

[rocky grove]

Okay you started nicely

(5-a)(5+a)

[unique salmon]

im at

25a - 5a^2

(5 - a)(5 + a)

[rocky grove]

Yepp

Common factor

[unique salmon]

5a (5-a)

top

[rocky grove]

Yee

[unique salmon]

5a

5+a

should be answer

[rocky grove]

Yeee

[unique salmon]

and i would like to add

shouldnt we have those things after solving this

like

idk what they are called in any language 💀

shouldnt we get something from these

after solving it

a = -5;

[rocky grove]

Difference of 2 squares

[unique salmon]

oh

this?

[rocky grove]

Yep

[unique salmon]

which would be a = +and- 5

or just +?

[rocky grove]

Yeah but

[rocky grove]

This is true

But you aren't supposed to find the zeros

[unique salmon]

oh

so only anything above 0

so just a = 5

[unique salmon]

wait then

isnt this in the range

why can't it be both

[unique salmon]

like this

[rocky grove]

No that's the domain

[unique salmon]

oh

then that means none of these are correct?

[rocky grove]

a is allowed to be any number so long it isn't +5 and -5

[rocky grove]

Wdym?

[unique salmon]

because a is +5 and -5

[unique salmon]

just like what you said here

[rocky grove]

The question tells you to simplify under the condition that a will be any number so long it is not +5 or -5.

It already tells you the domain

And you work under that assumption

[unique salmon]

then a = +and- 5 is correct?

[rocky grove]

[unique salmon]

im confusedddd

[rocky grove]

Lemme read the question

Ok so

The original question what does it say?

[unique salmon]

well

lets just skip this

[rocky grove]

No please

I wanna know

[unique salmon]

BRO I DONT EVEN KNOW WHAT IT MEANS IN MY LANGUAGE 💀

[rocky grove]

[unique salmon]

💀

[rocky grove]

It tells you it will never get to -5 and 5

[unique salmon]

well

it didnt

[rocky grove]

And you simplified it

And that's it

[unique salmon]

i think i did it right

so there was no need for the stuff

[rocky grove]

Yep

[unique salmon]

yeh

we didnt get to finish this

[rocky grove]

$(a^b)^c = a^{b\cdot c}$

[ocean seal]

VulcanOne

[rocky grove]

And

[unique salmon]

2²n⁵•½ • 3²n⁵•½

[rocky grove]

$a^m \cdot a^n = a^{m + n}$

[ocean seal]

VulcanOne

[rocky grove]

So

$n^5 \cdot n^5 = n^{10}$

[ocean seal]

VulcanOne

[unique salmon]

so

[unique salmon]

do we do

the thing

[rocky grove]

Before distributing your 1/2 power

[unique salmon]

Oh

Should I have made it

6²n⁵?

Or that doesn't make sense

[rocky grove]

It does but why is n^5?

Did you apply 1/2 power?

[unique salmon]

because thats how it was from the start

[unique salmon]

i didnt apply it in this case

yet

[rocky grove]

$4n^5 \cdot 9n^5$

[ocean seal]

VulcanOne

[rocky grove]

Can we do this?

$4 \cdot 9 \cdot n^5 \cdot n^5$

[unique salmon]

(4n⁵ • 9n⁵)½

[rocky grove]

?

[unique salmon]

Is that possible

[rocky grove]

Yeah

$abc = bca =cab$

[ocean seal]

VulcanOne

[unique salmon]

Damn

Ight

Now we can apply ½

[rocky grove]

Commutative property

[rocky grove]

Before we do

[unique salmon]

4 x 5?

[ocean seal]

VulcanOne

[rocky grove]

Mistyped it sorry

[unique salmon]

Oh yeah we make it 36 • n⁵ • n⁵

Right

[rocky grove]

Yeah

And can we do this?

$n^5 \cdot n^5 = n^{5+5} = n^{10}$

[ocean seal]

VulcanOne

[unique salmon]

yes

thats possible

[rocky grove]

Ok so

$36n^{10}$

[ocean seal]

VulcanOne

[rocky grove]

Agree?

[unique salmon]

yes

[rocky grove]

Now we apply

[unique salmon]

36n⁵

or

we can

√36n¹⁰

[rocky grove]

Yep

[unique salmon]

which one though

is it possible to have 2 different answers

[rocky grove]

The second one is correct

[unique salmon]

i see

[rocky grove]

The first one is wrong

[unique salmon]

6n¹⁰

[rocky grove]

Hmm

[unique salmon]

I assume this is the final answer unless we can actually do something about the n¹⁰

Wait

Nvm, idk

[rocky grove]

$(a^b m^n)^c = a^{bc} \cdot m^{nc}$

[ocean seal]

VulcanOne

[unique salmon]

Hmm

I can't imagine this oof

[rocky grove]

So your final answer = 6n^5

[unique salmon]

What happened to the n¹⁰

[rocky grove]

It got the 1/2 power

[rocky grove]

Through this rule

[unique salmon]

Oh I see

But

Didn't we lose the ½

After doing √36n¹⁰

[rocky grove]

The 1/2 power goes out on the entire 36 x n^10

[unique salmon]

si n¹⁰•½ happened

[rocky grove]

Multiplied*

Yes

[unique salmon]

Yeah because of the rule

I see now

This was one was quite difficult ngl

It's not hard once you learn it

Tho

[rocky grove]

Yeah you need to know your exponent rules

[unique salmon]

I'll write them all down

ty thats all

take care

.close

[lone heart]

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[vague coral]

[last ether]

No

[plain flame]

[rose sigil]

then do it 🙂

[tacit arch]

.close

[lone heart]

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[alpine sable]

I need help with solving my equation. I made it myself and I need help solving it to understand what I'm doing.

[lone heart]

Please don't occupy multiple help channels.

[tacit arch]

i closed your other channel

You're solving for what values of N that the inequality is true?

[alpine sable]

Okay thankyou because I didn't know what I was doing at first 💀 and yes

I'm having a test soon and I'm studying by making inequality equations

So I made my own to test my limits

And I'm stuck..

On it..

..

[vale wigeon]

you are stuck not knowing how to begin?

[alpine sable]

Well see.....not rlly but here's what I did first

I subtracted 3 from both sides

[vale wigeon]

that is good

what did you get after subtracting 3 from both sides?

[alpine sable]

Sooo 3 minus -7 = 10

[vale wigeon]

...

[alpine sable]

Im writing everything on papers give me one sec 😭😭

[vale wigeon]

you should have written everything on paper to begin with

[alpine sable]

yah...

2 - minus 3 = -1

[vale wigeon]

...

[alpine sable]

....noo other way around?

[vale wigeon]

when you subtract the same thing from both sides of an inequality,

you should get another inequality

you should not just blurt out disjointed arithmetic statements

[alpine sable]

Okay thankyou, I will try agn☠️

So..

-7 minus 3 = -10. 3 - 2 = 1

And don't we have to multiply?

[vale wigeon]

what part of

you should not just blurt out disjointed arithmetic statements
do you not understand?

[alpine sable]

Disjointed...what do you mean ma'am those number are apart of the equation

I'm solving for n

N > ( The answer). N < ( The answer)

[vale wigeon]

$\frac{N}{-7} + 3 > 2 \ \frac{N}{-7} + 3 - 3 > 2 - 3$

[ocean seal]

Ann

[vale wigeon]

this is what i expected you to write

[alpine sable]

oh okay so I will explain what I identify here

[vale wigeon]

no need to explain

just do

[alpine sable]

Yes ma'am-

[vale wigeon]

simplify things in context

not just go "45 minus 22 is 23"

[alpine sable]

Yes ma'am

My answer is -23.

Tell me what I did wrong if I am

Can I explain to you how I solved this?

[tacit arch]

your answer should be an inequality

like $N < -23$ or something

[ocean seal]

riemann

[alpine sable]

Yes I know sir but I was just working it out for myself to get the answer, than I put everything in it's place, Including the variable and etc.

Thankyou tho.

WAIT so I'm correct?

With my answer

[tacit arch]

this, specifically is incorrect

[tacit arch]

type out equations of what you mean here

[alpine sable]

Okay what did I do wrong sir...

[alpine sable]

Yessir

Soo

[tacit arch]

it should look very similar to what ann sent

[tacit arch]

in this message

[alpine sable]

yessir I made that equation myself, I'm studying for a test soon and I was testing my limits.

I'm online schooled.

Okay so I first subtracted -7 minus - 3. Then I've learned that the greater the sign meaning " >" is a sign to mutiply. And the " <" Is to divide.

[vale wigeon]

what you did wrong is how you are formatting your work right now. it is messy in the extreme.
it does not matter whether the problem came from your own composition or from a textbook,
and it does not matter whether you are online-schooled or not,
you must learn to format your work properly

Then I've learned that the greater the sign meaning " >" is a sign to mutiply. And the " <" Is to divide.
you have learned bad and misleading info, at best.

at worst you have been set up for failure, perhaps even deliberately.

[alpine sable]

Hmmmm

I figured it out

The answer is positive 7

Let me show you how I got it.

[vale wigeon]

no, the answer is not just "positive 7".

the answer isn't a number.

the answer is an inequality.

[alpine sable]

Huh

I knoww

[vale wigeon]

and in saying "The answer is positive 7" you have conflated the two very different potential answers N > 7 and N < 7, and we cannot tell which you meant.

[alpine sable]

I know that's why I said I'm going to show you how I got it by using the inequality and variables.

I'm saying it to you right now because I'm talking to you

What my answer was

Now I'm going to show you how I got it

So N > 7. N/7 + 3 > 2.

We are going to reverse those numbers.

3 * 2 = 6. N / -7 > 2 - 3.

N / - 7 > -1 * 7.

N > 7.

N < 7 *

What I did here was mutiply 3 * 2 = 6

-7 + 6 = 1

-1*

omg my pc is slow sorry

Then reveresed the numbers putting 3 > 2 over to 2 - 3.

[vale wigeon]

your presentation is getting better but it's still kind of lacking

[alpine sable]

Thankyou ma'am.

Then mutiplying -1 and -7 which equals to the sum 7.

So N < 7.

That's all thankyou for breaking it down for me a little bit, I'm starting to understand

I'm going to highschool next yr and this is the only thing I'm struggling with

I have almost a c in math It is at a 82. The rest of my subjects I have all a's and b's

is it okay if you can give me another equation of your own?

[vale wigeon]

an equation or an inequality?

[alpine sable]

Both

[lone heart]

@alpine sable Has your question been resolved?

[tacit arch]

N / 5 + 6 < -3

[lone heart]

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[fallow wadi]

How many numbered graphs are there on n vertices (that is, the vertices are distinguishable and we are not interested in isomorphisms) that have all degrees even and nonzero?

[fallow wadi]

Does this have any solution?

[lone heart]

@fallow wadi Has your question been resolved?

[lone heart]

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[steel dagger]

number 38

i have no idea how to start

i got 2^3y

but i doubt that does anything

[rocky grove]

Well this is a good start

[jade hollow]

k/8^y = 8^y/2^x
k=2^6y/2^x = 2^6y-x

[jade hollow]

ratio of successive terms in a GP is equal

[steel dagger]

oh yeah related ratios

[rocky grove]

A. $2^{6y-x} = \frac{(2^{3y})^2}{2^x}$

[ocean seal]

VulcanOne

[ornate ginkgo]

For 39 you just have to differentiate the function and get 6x using nx^n-1 for xⁿ

[lone heart]

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[lone heart]

@cosmic orbit Has your question been resolved?

[lone heart]

@cosmic orbit Has your question been resolved?

[royal plank]

the superscript c means opposite chance?

[cosmic orbit]

yes

well it's the compliment

so 1-Probability

[lone heart]

@cosmic orbit Has your question been resolved?

[lone heart]

@cosmic orbit Has your question been resolved?

[lone heart]

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[lyric fable]

need help

[lone heart]

@lyric fable Has your question been resolved?

[finite flax]

read the drop-down options and tell me what you think is the correct option.

Also, read the statement that precedes the figure. That will provide the reason for statement 1

[lone heart]

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[alpine sable]

,rotate

[tribal haven]

you don't have to necessarily open a new one for every question

[alpine sable]

Oh I thought you went to bed

My bad

[tribal haven]

that was vulcan

in Q4 you kind of try to do the reverse and put everything back together

[alpine sable]

Oh ok

[tribal haven]

how do you put the 2 back into the log in $2\log_3(x)$

[ocean seal]

IV

[alpine sable]

Log3 x²/(x+2)⁵

Is that it

[tribal haven]

ye

[alpine sable]

Is ln special?

[ocean seal]

IV

[tribal haven]

yes in the sense that you'll see it a lot, no in the sense that it's just the log of some random base

[alpine sable]

ln2 is loge 2

[tribal haven]

yes

you can just keep it as ln

[alpine sable]

OK bet thanks

ln2(5-x)^⅓/x

Not dividing the ⅓ dividing the whole thing

@tribal haven

[tribal haven]

looks good

[alpine sable]

OK thank you

I have another problem

,rotate

[tribal haven]

tl;dr shove it into a calculator

you have $Q=A_0e^{\frac{-t\ln 2 }{29.3}}$

and are given relevant quantities

[ocean seal]

IV

[alpine sable]

Is 430 A

[tribal haven]

ye
it's just reading comprehension

[alpine sable]

430oe^((-69.1ln2)/29.3)

What does tiny o do

[tribal haven]

it's part of the symbol, $A_0$ is the unknown quantity

[ocean seal]

IV

[alpine sable]

Don't need it

And is that up there right

[alpine sable]

How do I solve this

[tribal haven]

by plugging it into a calculator
there are no unknowns, it's just a number

[alpine sable]

OK

What goes on left

Log5 x^(3/2)/y³

@tribal haven

[tribal haven]

how do you bring 3 back inside $3\log_5 (\frac{\sqrt{x}}{y})$

[ocean seal]

IV

[alpine sable]

Cube it

[tribal haven]

yes, now write it out

[alpine sable]

Log5 (sqrtx^3/y^3

Is that it

[tribal haven]

yes

[alpine sable]

Does 3 go outside of sqrt or in

Are they same equations

[tribal haven]

that does not matter

[ocean seal]

IV

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

<@&286206848099549185>

[tribal haven]

what problem do you still have

[alpine sable]

Sorry my dad was being annoying

Are they the same

[tribal haven]

i answered that 15 minutes ago, yes

[alpine sable]

Oh OK

Yes

So x^2/3 is sqrtx^3

They are

Thank yalls gn

.close

[lone heart]

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[native temple]

https://media.discordapp.net/attachments/486841085210132490/1053641414866632785/IMG_0139.png?width=518&height=412
I'm trying to handle problem B
https://i.imgur.com/Uxl5BpU.png Here are the answers path to them?
The work I did was https://i.imgur.com/HZw11Wr.png. I honestly have little idea on what to do so help me please.
Please give me a step by step process on how to solve this and what I fundamentally don’t understand I truly can’t do this on my own.

[lone heart]

@native temple Has your question been resolved?

[lone heart]

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[alpine sable]

how do i input for third term@

[placid zinc]

Sub in n = 3:
a3 = a2 + 3

[alpine sable]

ive been up for way too long

thank u

[placid zinc]

I hear that haha. Feel free to ask if you have anything else

[outer lark]

#❓how-to-get-help

[jade canyon]

ty

[lone heart]

@alpine sable Has your question been resolved?

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[fickle pawn]

how can i solve this ? using complex no

[lone heart]

@fickle pawn Has your question been resolved?

[fickle pawn]

<@&286206848099549185>

i solved it this much

but i think i am completely wrong

[wild trail]

$cos^{-1}x = \frac{\pi}{2} + \iota log(1 + \sqrt 2 )$

[ocean seal]

numbpy

[fickle pawn]

ya this one

[wild trail]

Then i = cos(pi/2 + i log(1 + sqrt(2)) cause cos-1 is invertible and cos is it's inverse

[fickle pawn]

right

[wild trail]

RHS = $cos(\frac{\pi}{2} + \iota \log(1 + \sqrt 2)) = -\iota \sin\frac{\pi}{2} \sin (\log(1 + \sqrt 2))$

[fickle pawn]

further ?

[ocean seal]

numbpy

[wild trail]

Now sin(pi/2) = 1, so we are left with -i sin(log(1+ sqrt(2))

[fickle pawn]

but can't wee take it as

i = cos(x+iy)

[wild trail]

as what?

[fickle pawn]

i mean it is similar to z = x+iy

[wild trail]

Yeah, here x was pi/2

[fickle pawn]

ya

but ig i did some mistake in solving

at some step

[wild trail]

recheck it then

[fickle pawn]

thats what i am doing from last 30 minutes

[tacit arch]

Use the definitions of cosh and sinh in terms of exp

[wild trail]

where did you get h from here

It's a direct application of cos(x + iy) formula where x = pi/2 and y = log(stuff)

[fickle pawn]

using this formula

just got reply from my batch mate

this is how he solved

[wild trail]

I see, I think I might have made a mistake somewhere then. Lemme recheck

okay, so $cos(\frac{\pi}{2} + \iota \log(1 + \sqrt 2)) = \cos(\frac{\pi}{2}) \cosh (\log(1 + \sqrt 2)) -\iota \sin\frac{\pi}{2} \sinh (\log(1 + \sqrt 2))$

[ocean seal]

numbpy

[fickle pawn]

yah

[wild trail]

Now, cos(pi/2)=0 and sin(pi/2)=1 so, we get

$cos(\frac{\pi}{2} + \iota \log(1 + \sqrt 2)) = -\iota \sinh (\log(1 + \sqrt 2))$

[ocean seal]

numbpy

[wild trail]

Now, sinh(x) = (e^x - e^(-x))/2

e^(log(1 + root(2)) = 1 + root(2) and e^-(log(1 + root(2)) = 1/(1 + root(2)) = root(2) - 1

[fickle pawn]

this is the actual question bank and i am Fked up rn

[wild trail]

thus, $\sinh (\log(1 + \sqrt 2)) = \frac{(1 + \sqrt 2) - (\sqrt 2 - 1)}{2} = 1$

[ocean seal]

numbpy

[wild trail]

That's why finally we have -i

[fickle pawn]

ya i think so

[wild trail]

You'll need a lot of practise ngl

[fickle pawn]

ya maam, really a lot a lot of practice

but tomorrow is my test 1

ngl i am gonna fail in that

[wild trail]

Btw we were supposed to get i right not -i

[fickle pawn]

yah

[wild trail]

This is a much better proof and slick proof

[fickle pawn]

ya correct

its easy, but still at first i was not even able to understand it

[wild trail]

I just find it weird that sinh^(-1)(-1) = log(1 + sqrt(2)). So, we should be able to get a -1 somewhere but nope

I rechecked my calculation many times

[fickle pawn]

bro being frank what you just said is out oy my league, i really didnt understood a thing in that

well i appreciate all your help bro, thanks a lot

still i am here

[wild trail]

Frankly even I don't have much idea, I barely passed my complex class

[lone heart]

@fickle pawn Has your question been resolved?

[fickle pawn]

.close

[lone heart]

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[wheat crystal]

what is the interpretation of this problem saying to do

find inverse of F and then plug the inverse of F into the inverse of G?

[gilded vessel]

do whats inside the brackets first

#❓how-to-get-help

[wheat crystal]

so find uhh

g of f?

is

Plugging f into g right

then finding the inverse of that?

[gilded vessel]

yeah

[wheat crystal]

oooo kay

Ty

.close

[lone heart]

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[nocturne robin]

find Min A
i tried to find the solution but can't

[vale wigeon]

as stated, max A is +infty

[nocturne robin]

thank you

[raven haven]

what on earth is A+infty

[nocturne robin]

;-;

sorry

my english isn't good

[vale wigeon]

A can be as big as you want

[nocturne robin]

can u help me fix it?

[vale wigeon]

no

[raven haven]

could you post the question

[vale wigeon]

i think you have missed a key part of the question

[nocturne robin]

hm;v

sorry

all I can translate is find 'Min A'
apologize about this

[vale wigeon]

show the original untranslated problem in full

[nocturne robin]

i mean

Min A;vv

okay my bad i'm stupid, forgive me

[edgy walrus]

The maximum value for A is positive infinity so it can be as big as possible

[nocturne robin]

i see

[nocturne robin]

okay

in other words, find x so that A has the smallest value

[lone heart]

@nocturne robin Has your question been resolved?

[nocturne robin]

can anyone help me plsss

[raven haven]

is y fixed?

if theyre asking for min A

then you wanna differentiate

[nocturne robin]

i want to find Min A and find x so that A has the smallest value

[keen plinth]

is y fixed

[nocturne robin]

no

[keen plinth]

so then you're not just finding x

you're finding both x and y which minimise A

[nocturne robin]

yes

[keen plinth]

well

if you just want to algebra bash

[keen plinth]

and then

[nocturne robin]

okay i see

what about x and y?

[keen plinth]

you select x, y to minimise this sum of squares

i.e. make both squares 0

[nocturne robin]

okay thank you

.close

[lone heart]

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[tiny lintel]

Pls suggest me some methods to solve this problem. Thx a lot

[tribal haven]

aren't you the IVT guy

[tiny lintel]

oh

hello

[tribal haven]

so use IVT again :p

[tiny lintel]

:o

but I don't know where to start

[tribal haven]

er

i think IVT by itself is sufficient enough to get you started

i'll let you think for a couple minutes

[tiny lintel]

okay

Maybe we may start by taking the derivatives?

[tribal haven]

that's not necessary (and only helps with finding the turning opints)

answer this: if x=a is a root for the polynomial, what's the value of f(x) at x=a?

[tiny lintel]

f(a)

[tribal haven]

but a is a root

so f(a)=?

[tiny lintel]

lmao

a

wait

welp

[tribal haven]

waits in anticipation

[tiny lintel]

the value of f(x)

we just substitute a into f(x)

right??

[tribal haven]

i uh

google roots of a function

[tiny lintel]

what makes f(x) = 0

[tribal haven]

the fact that x-a is a root of f(x) means f(x) at x=a is equal to 0

i wonder if i worded that wrong

actually might've

but now you should be able to figure out what to look for to use IVT

[tiny lintel]

how could x-a make f(x) = 0 at x=a
may u give me an example

so now, to begin, I need to find the values that make the polynomial equals 0?

[tribal haven]

let g(x) = x²-3x+2 = (x-2)(x-1)

so x=1, x=2 are roots and at those two x values you have g(x) = 0

similarly whichever roots you may have you'll also have these properties

so now start trying x values and see if you can get something to work with IVT

[tiny lintel]

oh

I see

okay

I have found out 2 real roots and 2 unreal roots

but in the 2 reals, just a root makes the f(x) equals 0

[tribal haven]

that doesn't seem like something you can do with IVT

but i guess that'll also answer the question if you factor the whole thing

[tiny lintel]

hmm

welp

maybe factoring seems to be daunting for this problem

[tribal haven]

i mean the question is intended for IVT, if it's easy to factorise it's probably not gonna get solved via IVT

i'll give one final hint then leave you alone because it's about as close as i can get you to the correct idea without telling you what to do

||evaluate f(0)||

[tiny lintel]

Nice

I was focusing on evaluate the value of f(x), including f(0) until now and I see your hints

I think I'm doing right

.close

[lone heart]

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[half sable]

project where im trying to reach the moon

[half sable]

anyone want to find out more?

[strange meadow]

?

whats the math question?

[sonic egret]

.close

[lone heart]

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[heavy rover]

.reopen

[distant cove]

If
P(A) n P(B) = {emptyset}
so
AnB=emptyset

[distant cove]

Is it true?
and if so, how can i prove it

[tribal haven]

how do you get an intersection between two real numbers

[distant cove]

A,B are sets
P is the power set

[strange meadow]

its not true no?

[tribal haven]

but P(A) is a number between 0 and 1 regardless of how you define A

[distant cove]

P isn't prob, its power set

[tribal haven]

oh, now it makes more sense

[strange meadow]

OH

P IS POWER SET

RIGHT

um

let me think then

[distant cove]

maybe, i need to prove or disprove

[strange meadow]

yes

its true

use proof by contradiction

or use contrapositive

probably contrapositive is easier

[distant cove]

p-->q
nq-->np
?

n is not

[strange meadow]

yes

use that

[distant cove]

@strange meadow
how can i continue from here

$A\cap B\neq\phi\Rightarrow P(A)\cap P(B)\neq\phi$

[ocean seal]

Kingo

[distant cove]

sorry im new in this

[strange meadow]

ok so it follows that there exists an element x which is an element of A and B right

because the intersection is not the empty set

[distant cove]

correct

[strange meadow]

go from there

[distant cove]

it means that

B is subset of A? @strange meadow

[strange meadow]

no it doesn't

[distant cove]

well

im lost

idk how to do that

[strange meadow]

bro

ok we want to prove this statement

[distant cove]

yes

so there's x which is in A,B

[strange meadow]

A intersection B is not the empty set so there exists an element x which is an element of A and B. thus x is a subset of A and a subset of B and so x is also an element of their powersets. Thus P(A) intersection P(B) cannot be the empty set because it contains x. QED

@distant cove

[distant cove]

Bro

you're a genius

and

$A\Delta B=A\Delta C$

[ocean seal]

Kingo

[distant cove]

this is obv not true

what's the best counterexample for this statement?

[strange meadow]

whats the delta

[distant cove]

symmetric difference

[strange meadow]

you know i dont even know set theory

i only know basic set theory

let me google it

oh ok

wait so the statement is for all sets A, B, C that is true

and you want a counterexample?

[distant cove]

i already found one

but sadly i need to formal disprove

[strange meadow]

dont you set A to be the empty set?

and then require B and C to be different sets and then you're done

i have to sleep soon

so quickly respond

[distant cove]

but that's not a formal disprove

i need to show both sides

subsets

[strange meadow]

why not?

if the statement is a for all statement

all you need is one example

[distant cove]

imo, it is
but my professor doesn't want counterexample

specific in here

[strange meadow]

is the statement for all?

[distant cove]

yes

[strange meadow]

is it for all A, B, C this is true

thats weird

[distant cove]

its obv false

[strange meadow]

counterexample is like the easiest thing here

[distant cove]

that's why he doesnt want it

hahaha

[lone heart]

@distant cove Has your question been resolved?

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[rustic light]

I dont really understand why the red angle is equal to 2 theta (this is about a parabolic mirror)

[pliant cedar]

because those two vertical lines are parallel

[ornate condor]

um

[pliant cedar]

or because the exterior angle = sum of two interior angles thing

[ornate condor]

the triangle n the line

yes that thing lol

[rustic light]

ah ok thx

.close

[lone heart]

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[mossy laurel]

What have you tried so far?

[lone heart]

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[swift sky]

I need help

[swift sky]

Let $L_1$ be a straight line in $R^3$ which is defined by (x, y, z) = (2, 2, 0) + t(3, 0, 2) a) Determine the plane containing the line $L_1$ and the point A = (8, 2, 3)
(b) The line $L_2$ is defined by (x, y, z) = (5, 1, 0) + t(2, 1, 1). Determine an equation for that line which passes through the point A = (8, 2, 3) and intersects both $L_1$ and $L_2$

[molten pivot]

ok

then what

[swift sky]

Okay so I've already answered a and I'm struggling with b

[karmic rapids]

"for that line"?

[ocean seal]

afeAlway

[swift sky]

it should be the

or a

[karmic rapids]

I assume you mean "for a line"?

yes

so

the equation for the line will be u + v + tw where u,v,w are the vectors you gotta find

you know that A is on the line

[swift sky]

the plane's equation is

[karmic rapids]

and that L1 and the line have a shared point

and L2 and the line

[swift sky]

(8, 2, 3) + t(6, 0, 3) + s(3, 0, 2)

Wait I don't get it

L3 is on the plane like L1 right? That is cuz L3 got go through 2 different points on the plane

[lone heart]

@swift sky Has your question been resolved?