help-26

[golden blade]

good job riemann

[thorny flame]

riemann

[topaz sinew]

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Send your question here to claim the channel.

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[pearl fog]

let n be an odd number thats greater than 1, A is an nxn symmetric matrix such that each row and column of A is made out of some permutation of (1,2,3,...,n). prove that all numbers (1,2,3,...,n) appear in the main diagonal

[topaz sinew]

@pearl fog Has your question been resolved?

[topaz sinew]

@pearl fog Has your question been resolved?

[topaz sinew]

@pearl fog Has your question been resolved?

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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[supple bay]

Could someone please help me with part a in the attached image?

[topaz sinew]

@supple bay Has your question been resolved?

[exotic mantle]

are you familiar with what a linear combination is?

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Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[neon iron]

Lemme claim this and write the questions after cause it's long lmfao

[neon iron]

Practice:

1. 2^x = ½
2. 4^x-1 = 16
3. 125^x-1 = 25^x+3
4. 9^x^2 = 3^x + 3
5. 9^2x = 27
6. 8^4x-12 = 16^5x-3
7. 4^5x-13 = ⅛^x <8^x for ⅛x>
8. 3^2x - 3^2x • 3^-1 = 18
9. 3^x+2 + 3^x = 10/81
10. 2^x2/2^5x = 1/6
11. 4^2x - 20.4^x + 64 = 0
12. 0.001^x = (1/10)^x-3
13. (2/5)^x-2 = (5/2)^3x+2

Let's begin!!

1. 2^x = 1/2
   2^x = 2^-1
   x = -1
   Correct? Please react each answers if correct or not.

2. 4^x-1 = 16
   2^2(x-1) = 2^4
   2(x-1) = 4
   2x - 2 = 4
   2x = 4 + 2
   2x = 6
   x = 3
   Correct? Please react each answers if correct or not.

[thick lily]

4^x-1 is not 4^(x-1)

[neon iron]

Huh?

Kindly bold the incorrect answer before you say so. I do not follow.

[thick lily]

I know that's probably what it is, just want to make sure they know

[hollow drum]

I think they are pointing out that you should have parentheses

[neon iron]

Where?

Kindly bold the incorrect answer before you say so. I do not follow.

I still do not follow. This is not making me understand unless you point out the incorrect answer.

[hollow drum]

It's the lack of parentheses when you type out problems

[neon iron]

Kindly bold the incorrect answer before you say so. I do not follow.

2. 4^x-1 = 16 <- Is this what you are talking about??
   2^2(x-1) = 2^4
   2(x-1) = 4
   2x - 2 = 4
   2x = 4 + 2
   2x = 6
   x = 3
   Correct? Please react each answers if correct or not.

[neon iron]

You cannot expect me to understand right away if you do not use this.

[thick lily]

as it's written it means this: $4^x-1=16$
what you've written means this: $4^{x-1}=16$

[thorny flame]

Merosity

[neon iron]

Please confirm

2. 4^x-1 = 16 <- Is this what you are talking about??
   2^2(x-1) = 2^4
   2(x-1) = 4
   2x - 2 = 4
   2x = 4 + 2
   2x = 6
   x = 3
   Correct? Please react each answers if correct or not.

[thick lily]

I'm not playing this game sorry

[neon iron]

This is literally pointing out on what you are saying.

I am pointing out which one you are referring to.

[neon iron]

If you do not like to help please do not chat in this channel. You are confusing me which frustrates you. You need to calm down.

[hollow drum]

In text, when you say 4^x-1 = 16, it reads as four to the x power .... minus one, not four to the x minus one

[hollow drum]

Like this

[thick lily]

I just told you I had left

try harder 😉

[storm garnet]

is this ragebait or something

[neon iron]

Why is this difficult for you people to understand

Is the question 4^x-1 = 16 the problem that you want to address??

[hollow drum]

4^(x-1) and 4^x - 1 have different meanings because of the lack of parentheses

[neon iron]

That is given to the teacher.

That question was given to the teacher.

[storm garnet]

ur supposed to do (4^x)-1 not 4^(x-1)

[neon iron]

Therefore, I cannot question it because he already explained that it was on purpose.

[storm garnet]

so ur teacher wants you to do the 2nd one?

[neon iron]

I have already ask the teacher about it. It is on purpose

[hollow drum]

There is a difference, you should type your problems clearly, and using parentheses

[neon iron]

I have already ask the teacher about it. It is on purpose

[storm garnet]

ABOUT WHAT

holy moly

what’s on purpose

elaborate

[hollow drum]

Is the problem printed on paper or from a textbook?

[neon iron]

The question 4^x-1 = 16

[hollow drum]

Or written down?

[neon iron]

He written it down on purpose.

[storm garnet]

what did he write it like

with x-1 in the exponent

or only x in the exponent

[neon iron]

I do not understand. Is your question "Why did he write it like that?"

[hollow drum]

4^(x-1) = 16 and 4^x-1 = 16 will result in two different answers based on what I showed above

[wooden osprey]

you are the one who need to calm down. you need to listen to other people, comprehend what people are saying and then answer relevantly

[storm garnet]

this gotta be like a failed chatgpt experiment

[wooden osprey]

cease this condescending attitude at once

[neon iron]

I am not even raising my tone?

It is depends on the person who thinks I am like that, correct? I am simply answering it.

[storm garnet]

it doesn’t seem like you’re trying o understand

[wooden osprey]

you are not, but you are too condescending to others

[neon iron]

Yet I still did not raise any negative action.

[storm garnet]

it’s not hard to understand

did the teacher write just the x in the exponent OR did he write the quantity x - 1 in the exponent

[neon iron]

Okay here.

To satisfy the answer, The teacher gave it like this

4^x-1 = 16.

^ indicate exponent
So x-1 is an exponent.

There is no parenthesis no separation no nothing. It is made like that.

[storm garnet]

could have said the last part first

[hollow drum]

No, when typed out, only the x is an exponent

[wooden osprey]

then your teacher is wrong

[storm garnet]

and made everything easier

[hollow drum]

Also, weren't you helped with this before? #help-3 message

[neon iron]

I wanted to practice again.

[hollow drum]

Then you can re read the messages?

[neon iron]

So you are saying I should have type it like
^x^-^1??

[hollow drum]

No you should have used parentheses

[neon iron]

I do not want to relook it. I want to practice it again.

[storm garnet]

it’s like

elementary math

[hollow drum]

Like 1/x + 1 means $\frac{1}{x} + 1$ but if you typed it like 1/(x + 1) then it is read as $\frac{1}{x+1}$

[storm garnet]

to use paranthesis

[neon iron]

That is not up to me to decide that since the teacher is the one who gave the question. All of our classmates ask the same thing including me, No parenthesis. It is on purpose that it does not have an parenthesis

[thorny flame]

CaptainNova22

[wooden osprey]

no, you should type it out as 4^(x-1)=16

[hollow drum]

.

[neon iron]

I type out what is on the board from my notebook.

[storm garnet]

if you’re just using ascii it’s harder to understand a math problem

[hollow drum]

Then send an image of your notebook

[storm garnet]

so parenthesis make it easier for people who don’t know to know

[neon iron]

I cannot since my Data is just text only. For American understanding, The Wifi only allows me to text and not send any videos or photos.

[wooden osprey]

very likely that on the board its written like this

am i correct?

[hollow drum]

By order of operations, if you typed something like 4^x - 1, you will read it as

[neon iron]

I cannot see photos.

I cannot satisfy your demands on adding on parenthesis because It was on purpose that the question itself does not have a parenthesis.

@pseudo sonnet Can you help me out instead?

I want to move on away from this

Just need to practice and get confirmation if I understand the topic or no.

[wooden osprey]

why is it that you are sticking to the question verbatim so much

[hollow drum]

When you transcribe something to text, you need to include parentheses for clarity

[wooden osprey]

like there is literally no difference between these

[hollow drum]

When you write it on paper, and send an image, then we understand it better that way too

[pseudo sonnet]

this is actually the reason why you should technically use parentheses when typing out your questions btw haha

[pseudo sonnet]

I'm unable to help at this very moment, because I have my own homework to get through

[neon iron]

I am just writing what is written. It is understandable either way that I am studying an Exponential Function.

[neon iron]

Ah okay thanks anyways

[pseudo sonnet]

I might come back later, but you're going to have listen to others for now

[neon iron]

How do we move on the conversation if these people can't move on either? They will have to keep asking me until they are annoyed, I do not want that to happen but they are just putting themselves up for that.

[hollow drum]

You aren't getting the point. Writing what is written in a notebook vs text, can be read completely different. When you are typing out problems via text, you need to be clear

[wooden osprey]

you should be able to think for yourself and recognize that you are asking for help, and if you are asked to provide more clarity, then you should do so

we cannot read your mind

[neon iron]

I am clarifying about my answer not the question.

[wooden osprey]

well if i dont understand the question then how am i supposed to verify if your answer is correct?

[neon iron]

I would like help but this is not the help I need. We are focusing on the question not the answer. We could never move on from this.

[neon iron]

This is literally Exponential Function surely everyone who first encounter it does the same thing.

[pseudo sonnet]

believe me, the others do know what they are saying (and they are unfortunately correct about the parentheses issue), so I encourage you to accept their thoughts at least a little bit

but... for the sake of moving this channel forwards, I feel like we should drop this parentheses stuff and just move on

this is clearly not a productive conversation, even if there is a reason we're having it

[hollow drum]

4^x - 1 = 16 and 4^(x - 1) = 16 results in two different answers
4^x - 1 = 16 results in x = 2.0437
4^(x - 1) = 16 results in x = 3

[neon iron]

Yes, I agree. This is getting too irritating.

[pseudo sonnet]

anyways, I'll take my leave now; please do your best to keep things civil

[neon iron]

This is literally Exponential function. There can't be 2 things that resolve to that answer because the you need to make 2 bases equal from the start?

2. 4^x-1 = 16
   2^2(x-1) = 2^4
   2(x-1) = 4
   2x - 2 = 4
   2x = 4 + 2
   2x = 6
   x = 3

Look at my answer. We can tell right away what supposedly matters. It is logical for Exponential Function that both bases needs to be the same.

[pseudo sonnet]

the answer is that you are correct btw

[neon iron]

Thank you omg finally.

[pseudo sonnet]

I confirmed this for you about 12 hours ago, did I not?

[neon iron]

Well I wanted to practice the solution rather than the answer

[pseudo sonnet]

sure

[neon iron]

I know its x = 3 but how did it come to that answer, you get what I'm saying?

And omg we are just at number 2 we are already starting a ridiculous argument over a question

I don't like this journey anymore but I have to face it in order to learn.

Practice:

1. 2^x = ½
2. 4^x-1 = 16
3. 125^x-1 = 25^x+3
4. 9^x^2 = 3^x + 3
5. 9^2x = 27
6. 8^4x-12 = 16^5x-3
7. 4^5x-13 = ⅛^x <8^x for ⅛x>
8. 3^2x - 3^2x • 3^-1 = 18
9. 3^x+2 + 3^x = 10/81
10. 2^x2/2^5x = 1/6
11. 4^2x - 20.4^x + 64 = 0
12. 0.001^x = (1/10)^x-3
13. (2/5)^x-2 = (5/2)^3x+2

Let's begin!!

3. 125^x-1 = 25^x+3
   5^3(x-1) = 5^2(x+3)
   3(x-1) = 2(x+3)
   3x - 3 = 2x + 6
   3x - 2x = 6 + 3
   x = 9
   Correct? Please reach each answers if correct or not.

4. 9^x² = 3^x+3
   3^2(x²) = x + 3
   2^x² = x + 3
   2^x² - x - 3
   a = 2
   b = -1
   c = -3

x = -(-1) + √(-1)² -4(2)(-3)/2(2)
x = 1 + √ 1 -4(-6)/4
x = 1 + √ 1 + 24/4
x = 1 + √25/4
x = 1 + 5/4
x = 6/4
x = 3/2

x = -(-1) - √(-1)² -4(2)(-3)/2(2)
x = 1 - √ 1 -4(-6)/4
x = 1 - √ 1 + 24/4
x = 1 - √25/4
x = 1 - 5/4
x = -4/4
x = -1

Correct? Please react each answers if correct or not.

5. 9^2x = 27
   3^2(2x) = 3^3
   2(2x) = 3
   4x = 3
   x = 3/4

Correct? Please react each answers if correct or not.

[pseudo sonnet]

9^x² = 3^x+3
3^2(x²) = x + 3
2^x² = x + 3

[neon iron]

Hm?

[pseudo sonnet]

you forgot the base

it's 3^(x + 3), not x + 3

[neon iron]

I removed the bases.

Because they are both the same

[pseudo sonnet]

but you left the base on the left hand side

3^2(x²) = x + 3

[neon iron]

NO WAIT

OMG THANK YOU

[pseudo sonnet]

2^x² = x + 3
2^x² - x - 3
a = 2
b = -1
c = -3

[neon iron]

4. 9^x² = 3^x+3
   3^2(x²) = 3^x + 3
   2^x² = x + 3
   2^x² - x - 3
   a = 2
   b = -1
   c = -3

x = -(-1) + √(-1)² -4(2)(-3)/2(2)
x = 1 + √ 1 -4(-6)/4
x = 1 + √ 1 + 24/4
x = 1 + √25/4
x = 1 + 5/4
x = 6/4
x = 3/2

x = -(-1) - √(-1)² -4(2)(-3)/2(2)
x = 1 - √ 1 -4(-6)/4
x = 1 - √ 1 + 24/4
x = 1 - √25/4
x = 1 - 5/4
x = -4/4
x = -1

Correct? Please react each answers if correct or not.

[pseudo sonnet]

you have another issue

[neon iron]

4. 9^x² = 3^x+3
   3^2(x²) = 3^x + 3
   2^x² = x + 3
   2^x² - x - 3 = 0
   a = 2
   b = -1
   c = -3

x = -(-1) + √(-1)² -4(2)(-3)/2(2)
x = 1 + √ 1 -4(-6)/4
x = 1 + √ 1 + 24/4
x = 1 + √25/4
x = 1 + 5/4
x = 6/4
x = 3/2

x = -(-1) - √(-1)² -4(2)(-3)/2(2)
x = 1 - √ 1 -4(-6)/4
x = 1 - √ 1 + 24/4
x = 1 - √25/4
x = 1 - 5/4
x = -4/4
x = -1

Correct? Please react each answers if correct or not.

Forgot the 0

Is that correct?

[pseudo sonnet]

seems good to me

[neon iron]

Okay

[pseudo sonnet]

good job!

[neon iron]

5. 9^2x = 27
   3^2(2x) = 3^3
   2(2x) = 3
   4x = 3
   x = 3/4

Correct? Please react each answers if correct or not.

[pseudo sonnet]

good

[pseudo jetty]

2^x² = x + 3

is there an extra ^ here

[pseudo sonnet]

oh good catch, I didn't even see that one

[neon iron]

6. 8^4x-12 = 16^5x-3
   4^2(4x-12) = 4^3(5x-3)
   2(4x-12) = 3(5x-3)
   8x - 24 = 15x -9
   15x - 8x = 24 - 9
   7x = 15
   x = 15/7

Correct? Please react each answers if correct or not.

[pseudo sonnet]

before I answer, make sure you see what snow said

there was something that I missed

[neon iron]

x² is suppose to be like that + x² itself is an exponential for 2.

So x is the Exponential for 2, ² is the exponential for x.

x is exponent for 2
² is exponent for x

x²

[pseudo sonnet]

uh oh

4^2 = 16, not 8, and 4^3 = 64, not 16

[neon iron]

2^x

[pseudo sonnet]

so your first step is unfortunately a mistake

[neon iron]

Ohhhh

6. 8^4x-12 = 16^5x-3
   2^3(4x-12) = 2^4(5x-3)
   3(4x-12) = 4(5x-3)
   12x - 36 = 20x - 12
   20 - 12x = 36 - 12
   8x = 24
   x = 3

Correct? Please react each answers if correct or not.

[pseudo sonnet]

12x - 36 = 20x - 12
20 - 12x = 36 - 12
8x = 24
x = 3

[neon iron]

OOPS

6. 8^4x-12 = 16^5x-3
   2^3(4x-12) = 2^4(5x-3)
   3(4x-12) = 4(5x-3)
   12x - 36 = 20x - 12
   -20x - 12x = 36 - 12
   -32x = 24
   x = 24/-32
   x = 3/-4
   x = -3/4

Correct? Please react each answers if correct or not.

[wintry jacinth]

This -12x should be positive:
-20x - 12x = 36 - 12

[neon iron]

7. 4^5x-13 = ⅛^x <8^x for ⅛x>
   2^2(5x-13) = 8^x-1
   doubting - help

[neon iron]

Okay

6. 8^4x-12 = 16^5x-3
   2^3(4x-12) = 2^4(5x-3)
   3(4x-12) = 4(5x-3)
   12x - 36 = 20x - 12
   -20x + 12x = 36 - 12
   -8x = 24
   x = 24/-8
   x = -3

Correct? Please react each answers if correct or not.

[wintry jacinth]

Looks good now

[wintry jacinth]

Exponent rule says 1/a^b = a^-b, here a = 2 (matching left side), 2^n = 8
Following the same steps as before, multiply by n instead of subtracting 1

[neon iron]

I don't get it

[wintry jacinth]

We start with 1/8 = 2^n (we want the same base on the left and on the right, so we replace 1/8 with 2^n)

Then, we use the exponent rules to find n

The exponent rule tells us: 1/a^n = a^-n
So we replace a with 2

[neon iron]

What

[wintry jacinth]

$$ {1 \over x}^n = x^{-n} $$

[thorny flame]

_nat_h_

[wintry jacinth]

$${1 \over 8} = {1 \over 2}^n = 2^{-n} $$

[thorny flame]

_nat_h_

[neon iron]

OHHHH

BECAUSE THERE'S X X IS EQUAL TO 1!!

I seee

7. 4^5x-13 = ⅛^x <8^x for ⅛x>
   2^2(5x-13) = 8^-1
   2(5x-13) = -1
   10x - 26 = -1
   10x = 26 - 1
   10x = 25
   x = 25/10
   x = 5/2

Correct? Please react each answers if correct or not.

[flint stump]

You used the negative exponent wrong

[neon iron]

Oh

[flint stump]

in second step

[neon iron]

Oops sorry

[flint stump]

1/8 = 8^-1

(1/8)^x = (8^-1)^x

[neon iron]

7. 4^5x-13 = ⅛^x <8^x for ⅛x>
   2^2(5x-13) = 8^-x
   2(5x-13) = -x
   10x - 26 = -x
   10x + x = 26
   10x² = 26
   x² = 26/10
   x² = 13/2

Correct? Please react each answers if correct or not.

[flint stump]

No still wrong

Before you cancel the bases, you need the bases to be equal

[neon iron]

OOPS SORRY

[flint stump]

On left side you have base 2, on right you have it 8

Also, here

10x + x = 26
10x² = 26

10x + x is not 10 x^2

[neon iron]

7. 4^5x-13 = ⅛^x <8^x for ⅛x>
   2^2(5x-13) = 2^3(-x)
   2(5x-13) = 3(-x)
   10x - 26 = -3x
   10x + 3x = 26
   13x² = 26
   x² = 26/13
   x² = 2

Correct? Please react each answers if correct or not.

[flint stump]

10x + 3x is also not 13x^2

its only 13x

[neon iron]

But it has x + x

[flint stump]

yes and x+x is 2x

[neon iron]

Ohhh

[flint stump]

x*x is multiplication

multiplication makes x*x = x^2

[neon iron]

7. 4^5x-13 = ⅛^x <8^x for ⅛x>
   2^2(5x-13) = 2^3(-x)
   2(5x-13) = 3(-x)
   10x - 26 = -3x
   10x + 3x = 26
   13x = 26
   x = 26/13
   x = 2

Correct? Please react each answers if correct or not.

[flint stump]

Yes

now you have it right

Also, I have a small suggestion for you. It would help you greatly if you can write which exact rule of exponents you have used in between your steps. It would help you familiarise yourself with what rule to use where, and also help you recall properly if you decide to read these problems again after a few days

You dont have to type it here, but if you copy the text you type here, on some notebook or whatever, if you write the names of the rules there, it would be good for you

[neon iron]

Okie

Practice:

1. 2^x = ½
2. 4^x-1 = 16
3. 125^x-1 = 25^x+3
4. 9^x^2 = 3^x + 3
5. 9^2x = 27
6. 8^4x-12 = 16^5x-3
7. 4^5x-13 = ⅛^x <8^x for ⅛x>
8. 3^2x - 3^2x • 3^-1 = 18
9. 3^x+2 + 3^x = 10/81
10. 2^x2/2^5x = 1/6
11. 4^2x - 20.4^x + 64 = 0
12. 0.001^x = (1/10)^x-3
13. (2/5)^x-2 = (5/2)^3x+2

Let's begin!!

8. 3^2x - 3^2x • 3^-1 = 18
   18
   /
   3 6
   /
   3 2
   3^2
   3^2x - 3^2x • 3^-1 = 3^2
   2x - 2x • -1 = 2
   x = 2 + 1
   x = 3

Correct? Please react each answers if correct or not.

[flint stump]

6 is not 3*3. It is 3*2

so 18 is not 3^3

[neon iron]

I used GCM

[flint stump]

Thats fine, but you got the wrong answer for 6

6 is sum of 3 and 3. Not the product

You need two numbers which on multiplication give you 6

[neon iron]

8. 3^2x - 3^2x • 3^-1 = 18
   18
   /
   3 6
   /
   3 2
   3^2
   3^2x - 3^2x • 3^-1 = 3^2
   2x - 2x • -1 = 2
   x = 2 + 1
   x = 3

Correct? Please react each answers if correct or not.

[flint stump]

Still no

18 becomes 2 * 3 * 3 right?

so thats 2 * 3^2

So the idea here is somewhat different

you have to take common factor on the left side

Your left side is 3^2x - 3^2x • 3^-1. It has two different terms
3^2x, and
3^2x • 3^-1

So, you need to make factors for this, and that should be the first step here

[neon iron]

I don't get it?

They are all the same bases why do I need to change it?

[flint stump]

18 has 2 * 3^2

so it has two bases, 2 and 3

you can write 2 * 3^2 as 2^1 * 3^2

so you see, theres two separate bases on right hand side

and that means you cant just cancel them out

[neon iron]

Oh okay

[flint stump]

So you have to write the numbers on left hand side as product of two numbers as well

those two numbers would be the factors

and then you match one factor with the 2 and the other with 3^2

After you do this, you can use the old method of cancelling bases, and solving for x

[neon iron]

I don't get itttt

[flint stump]

its fine, we can do it one step at a time

[pseudo sonnet]

I am back, but I'll watch this from afar for now

[flint stump]

You need to make factors for this of the left hand terms

[flint stump]

feel free to pop in

coz I gotta get breakfast in like 15 min

[pseudo sonnet]

sure thing

[neon iron]

Aren't they the same bases?

[flint stump]

Yes, but you need to factorise it

[flint stump]

because of all the reasons I explained here

[neon iron]

But They are the same bases? Meaning it's good and I need to factor the right side

[flint stump]

But you did factor the right side already

its 2 * 3^2

[neon iron]

I don't get it???

8. 3^2x - 3^2x • 3^-1 = 18
   3^2x - 3^2x • 3^-1 = 2 • 3^2?

Correct? Please react each answers if correct or not.

[wintry jacinth]

That part looks good

[flint stump]

Yeah, thats correct

[neon iron]

Then left..??

8. 3^2x - 3^2x • 3^-1 = 18
   3^2x² • 3^-1 = 2 • 3^2?

Correct? Please react each answers if correct or not.

[flint stump]

No, its not correct

[neon iron]

Oh

[pseudo sonnet]

[neon iron]

So how do I do it?-

[pseudo sonnet]

the product comes first

3^2x * 3^-1

because of the order of operations

there is a rule that allows you to combine products of exponentials

try to use that

[neon iron]

8. 3^2x - 3^2x • 3^-1 = 18
   3^2x • 3^-1 = 2 • 3^2?

Correct? Please react each answers if correct or not.

[pseudo sonnet]

ack, unfortunately not

we're not ignoring the 3^2x at the front, just focusing on the 3^2x * 3^-1 first

we need to combine them before we do anything else

[neon iron]

How do I combine them?-

Just.. 6^2x-1?

[wintry jacinth]

,tex .exp rules

[thorny flame]

higher!

[pseudo sonnet]

the first one is the one you want

[neon iron]

So.. 3^2x-1?

[wintry jacinth]

Yes

[neon iron]

OHHHH OKAY

[pseudo sonnet]

very well done!

[neon iron]

8. 3^2x - 3^2x • 3^-1 = 18
   3^2x - 3^2x-1 = 2 • 3^2
   what's next-

I HAVE AN IDEAAA

[pseudo sonnet]

‼️

[neon iron]

Nvm I don't know

[pseudo sonnet]

[pseudo sonnet]

there is a greatest common factor on the left hand side!

[neon iron]

Where-

[pseudo sonnet]

$3^{2x} - 3^{2x - 1} = 2 \cdot 3^2$

[thorny flame]

higher!

[neon iron]

Multiply 2 x 3??

[pseudo sonnet]

may I rewrite this a little?

it will be a hint

[neon iron]

Sure

[pseudo sonnet]

okay

$3^{2x} - 3^{2x - 1} = 2 \cdot 3^2 \implies 3 \cdot 3^{2x - 1} - 3^{2x - 1} = 2 \cdot 3^2$

[thorny flame]

higher!

[pseudo sonnet]

now do you see the common factor?

[neon iron]

I don't see it??

[pseudo sonnet]

[neon iron]

Like I don't understand it

[pseudo sonnet]

does this step make sense, before we move on?

if not, please tell me

[neon iron]

No it doesn't :(

[pseudo sonnet]

:c

well, I just used the property that 3^x * 3^y = 3^(x + y), but in reverse!

[neon iron]

I don't get it

[pseudo sonnet]

3^(2x) = 3^(2x - 1 + 1) = 3^1 * 3^(2x - 1)

this is what I did

,, 3^{2x} = 3^{2x - 1 + 1} = 3^1 \cdot 3^{2x - 1} = 3 \cdot 3^{2x - 1}

[thorny flame]

higher!

[pseudo sonnet]

is that better? :c

I just took the first 3^2x, and applied the product law of exponents backwards

[neon iron]

I still don't get it 😭😭😭

[pseudo sonnet]

[neon iron]

Can we just take it from the top

[pseudo sonnet]

oh no

sure

where are we at?

[neon iron]

Let's start like this

8. 3^2x - 3^2x • 3^-1 = 18

[pseudo sonnet]

okay

[neon iron]

8. 3^2x - 3^2x • 3^-1 = 18
   18
   /
   6 3
   /
   3 2
   3^2x - 3^2x • 3^-1 = 2 • 3^2

Then...

[pseudo sonnet]

then we combined the 3^2x and 3^-1

[wintry jacinth]

Would it be easier to convert 3^-1 to 1/3?

[pseudo sonnet]

I'm unsure if Kiomi finds that easier to understand or not

[neon iron]

8. 3^2x - 3^2x • 3^-1 = 18
   18
   /
   6 3
   /
   3 2
   3^2x - 3^2x • 3^-1 = 2 • 3^2
   3^2x - 3^2x-1 = 2 • 3^2
   then...

[pseudo sonnet]

then we're going to "uncombine" 3^2x into 3^1 • 3^2x-1

we're going to uncombine it like so

[neon iron]

Okay this is not working I still don't get it

[pseudo sonnet]

is the confusion lying in why we're doing this, or why my steps work?

[neon iron]

We combined 3^2x and 3^-1 then we combine them??

I don't get it

[pseudo sonnet]

we combined the second 3^2x with 3^-1; now we want to uncombine the first 3^2x into 3 * 3^2x-1

[neon iron]

OHHHHHHH

[pseudo sonnet]

3^2x - 3^2x-1 = 2 • 3^2

the one in bold is what we want to uncombine

[pseudo sonnet]

and we can uncombine it like this

[neon iron]

Wait I still don't get it

[pseudo sonnet]

where does your confusion lie?

[neon iron]

So like 3^2x... became... 3 • 3^x???

[pseudo sonnet]

nono

it became 3 • 3^(2x - 1)

[neon iron]

I DON'T GET ITTT 😭😭😭😭

[neon iron]

So we add 3???

[pseudo sonnet]

nono

I really want you to take a close look at what happened here

[neon iron]

Like 3^2x we add 3 and -1 so like
3 • 3^2x-1?

[pseudo sonnet]

we multiplied by 3, and subtracted 1 from the exponent

[pseudo sonnet]

the reason we can do that is because of this string of equalities

[neon iron]

So we add -1+1??

Then add another 3

THEN ADD ADD ADD ADD AAAAA THIS IS POINTLESS I STILL DON'T UNDERSTAND

[pseudo sonnet]

we're adding and subtracting 1 so we can apply the product law for exponents

we're doing it in reverse

3^(2x - 1 + 1) = 3^(2x - 1) * 3^1

sorry, made a mistake

[neon iron]

So... 3^2x1-1...

[pseudo sonnet]

3^(2x - 1 + 1)

[neon iron]

HUH!?!?!?????

I STILL DON'T GET IT

😭😭😭😭

[pseudo sonnet]

😭

[neon iron]

This is taking a long time to process 😭

[pseudo sonnet]

maybe I can try explaining this in a different way?

[neon iron]

Because like where did you get 1?

Why is the first one -1 from x?

[pseudo sonnet]

I added and subtracted 1 out of thin air

[neon iron]

Isn't it suppose to be 1 - 1

How did it happen?

[pseudo sonnet]

2x = 2x + 0 = 2x - 1 + 1

[neon iron]

Isn't -1+1 the same thing??

[pseudo sonnet]

I am adding 0

I'm adding 0 in the form of -1 + 1 so that I can apply the product law

[neon iron]

Then its suppose to be 2x^0

[pseudo sonnet]

this is a trick

[neon iron]

I DON'T GET ITTTT

[pseudo sonnet]

nono, the +1 and -1 do not go in the exponent of x

x has no exponent here

we are adding and subtracting 1 to 2x, that's it

[neon iron]

Let's just say -1+1 appeared

That's it

[pseudo sonnet]

yeah, it kind of does

I am casting magic!

[neon iron]

Okay

[pseudo sonnet]

allow me to rewrite it

,, 3^{2x} = 3^{2x - 1 + 1} = 3^1 \cdot 3^{2x - 1} = 3 \cdot 3^{2x - 1} \implies 3^{2x} = 3 \cdot 3^{2x - 1}

[thorny flame]

higher!

[pseudo sonnet]

do you understand why this = works

[neon iron]

8. 3^2x - 3^2x • 3^-1 = 18
   18
   /
   6 3
   /
   3 2
   3^2x - 3^2x • 3^-1 = 2 • 3^2
   3^2x - 3^2x-1 = 2 • 3^2
   3^2x-1+1 - 3^2-1 = 2 • 3^2
   3 • 2x^-1 - 3^2-1 = 2 • 3^2?

[neon iron]

No

AHHHH THIS IS TOO CONFUSING IM LTIERALLY FIDGETING

[pseudo sonnet]

because $3^{2x - 1 + 1} = 3^{1 + (2x -1)} = 3^1 \cdot 3^{2x - 1}$

[thorny flame]

higher!

[pseudo sonnet]

hang in there

we will get this, I promise

[neon iron]

It's pointless

[pseudo sonnet]

it is not pointless

keep some hope in your heart c:

[neon iron]

I still don't understand no matter how much you explain

[pseudo sonnet]

hm, maybe it would be better if I opt for a different explaination then

[neon iron]

It's hopeless

[pseudo sonnet]

I wasn't aware that this method was going to cause so much grief

I apologize

[neon iron]

I'm never going to pass

I don't understand anything

[pseudo sonnet]

hey now, hang in there

you're doing great

we will get this.

[neon iron]

Well I still don't understand!

[pseudo sonnet]

so we're at $3^{2x} - 3^{2x - 1} = 2 \cdot 3^2$?

[neon iron]

No matter how much you tried I still don't know how -1+1 exist!

[thorny flame]

higher!

[pseudo sonnet]

-1 + 1 = 0, so I'm really just adding 0 to the exponent in a clever way 😭

but let's move past that

maybe it's not the way to go

[neon iron]

I'm not going to succeed

Wait a moment..

[pseudo sonnet]

can we return to this?

[neon iron]

WAIT WAIT

3^2x = 0? Correct?

[pseudo sonnet]

no?

[neon iron]

Dang it...

I almost had it..

Its hopeless

[pseudo sonnet]

please, let's return to this

I want to do this in a different way

actually

let's take it from one step earlier

just follow my lead for a minute

$3^{2x} - 3^{2x} \cdot 3^{-1} = 18 \ 3^{2x} - 3^{2x} \cdot 3^{-1} = 2 \cdot 3^2$

[thorny flame]

higher!

[pseudo sonnet]

are we good so far?

[neon iron]

Yes

[pseudo sonnet]

okay

I am going to do a step

tell me if you understand

$3^{2x} - 3^{2x} \cdot 3^{-1} = 18 \ 3^{2x} - 3^{2x} \cdot 3^{-1} = 2 \cdot 3^2 \ 3^{2x} - 3^{2x} \cdot \frac{1}{3} = 2 \cdot 3^2$

[thorny flame]

higher!

[neon iron]

HUH!?

[pseudo sonnet]

negative exponent

it's just the negative exponent law

[neon iron]

I THOUGHT YOU SAID THAT WE COMBINE 3^2x and 3^-1

[pseudo sonnet]

I am going for a different approach

please forgive me

there is more than one method to doing this

the other method seems to have confused you greatly, so I want to go for this one

welcome back Bacter

maybe you'll have better odds at explaining this problem?

I'm pretty sad that my explainations don't seem to be as effective as I hoped

[flint stump]

$3^{2x} - 3^{2x} \cdot 3^{-1} = 2 \cdot 3^2
\
3^{2x} - 3^{2x} \cdot 3^{-1} = \left( 3-1 \right) \cdot 3^2
\
3^{2x} - 3^{2x} \cdot 3^{-1} = 3 \cdot 3^2 - 3^2
\
3^{2x} - 3^{2x} \cdot 3^{-1} = \left( 1 - 3^{-1} \right) \cdot 3^3$

[pseudo sonnet]

you missed the $

ah

I dunno if doing more steps in one go is better for Kiomi, or worse

I've been trying to go one step at a time, but it's not been going well

[neon iron]

https://tenor.com/view/esiledoodles-esiledoodles-cora-esile-esiledoodles-deadpan-anime-gif-15216314118662597519

[flint stump]

Im gonna cry.. How do I make a new line 😭

[thorny flame]

Bacter10Fr4g is not fr0g

[flint stump]

[neon iron]

I still don't get it

[flint stump]

So, can you tell me what steps do you understand in this? And where do you get lost?

[neon iron]

I SRSLY CAN WE LIKE CALL MAYBE ITS BETTER TO LIKE SPEAK IT OUT OF WHAT HAPPENED RATHER THAN TEXTING CAUSE ITS BEEN A LONG TIME NOW AND LIKE 😭😭

[flint stump]

sry, Im in a location with tons of noise and cant talk

[neon iron]

Hbu @pseudo sonnet ?

[pseudo sonnet]

$3^{2x} - 3^{2x} \cdot 3^{-1} = 18 \ 3^{2x} - 3^{2x} \cdot 3^{-1} = 2 \cdot 3^2 \ 3^{2x} - 3^{2x} \cdot \frac{1}{3} = 2 \cdot 3^2$

wait

$3^{2x} - 3^{2x} \cdot 3^{-1} = 18 \ 3^{2x} - 3^{2x} \cdot 3^{-1} = 2 \cdot 3^2 \ 3^{2x} - 3^{2x} \cdot \frac{1}{3} = 2 \cdot 3^2$

[thorny flame]

higher!

[pseudo sonnet]

is this good?

do we follow?

[neon iron]

YOU ALREADY SAID THAT WE COMBINE 3^2x • 3^-1 NOW THAT IT CHANGED IM NOW AS CONFUSED TO THE POINT MY MIND EXPLODES

I might have a stroke again

[pseudo sonnet]

I'M SORRY

I didn't know that that method was going to cause so much pain

I want to redo it now

[neon iron]

https://tenor.com/view/juvia-juvia-lockser-fairy-tail-water-mage-blushing-gif-491746434010845485

[pseudo sonnet]

https://tenor.com/view/pokemon-eevee-scared-gif-4780114

sad :c

I have no choice but to ask again: are we okay with this?

[thick lily]

it's not your fault, you've been patient

I think @neon iron needs to take a break

[pseudo sonnet]

perhaps

[neon iron]

NO

I'm fine!!!

[pseudo sonnet]

okay, then I am pleading you to answer me

[pseudo sonnet]

can you follow this or not?

I still don't know

[flint stump]

you should tell the exact step where you do not understand

or at least say you get overwhelmed if we put in too many steps at a time in a single picture

[neon iron]

You said combine!
So 3^2x • 3^-1
I already understand that its
3^2x - 1

IM CONFUSED WHY IS THERE A FRACTION HOW DID THAT HAPPENED

[pseudo sonnet]

it is the negative exponent law, as I said before

3^-1 = 1/3^1 = 1/3

that is all

there is nothing deeper to this, I promise

[neon iron]

IM ALREADY HAVING A STROKE IM SHAKING, MY HEART IS RAISING AND I FEEL LIKE IM ABOUT TO HAVE A HEART ATTACK FROM TOO MUCH PRESSURE IN MY CHEST

[pseudo sonnet]

are you sure you don't need a break?

[thick lily]

you definitely need a break

[neon iron]

NO IM FINE ITS NORMAL I PROMISE IDK??

[pseudo sonnet]

take some deep breaths

[flint stump]

you sound like you do need a break and thats def not normal

[pseudo sonnet]

you sound quite tense atm

have glass of water

breathe

[flint stump]

you dont have to stress out on the problem. We can skip this one for now and get back to it later

Lets do 12 for now

[pseudo sonnet]

there is no point in having a mental breakdown over a math problem

we can skip this one yeah

[neon iron]

Okay fine just let me get my heart rate down my friends literally saw me and hold me to calm down

[flint stump]

You have to take care of yourself first.

[pseudo sonnet]

math is not worth stressing this much over, I promise

[flint stump]

Not being able to solve a problem today wont change the world for you, but not being able to take care of yourself for a day definitely would chang the world for you, your friends and family

[pseudo sonnet]

you will be okay

[topaz sinew]

@neon iron Has your question been resolved?

[pseudo sonnet]

to Kiomi: I apologize for not being able to assist you with that question earlier. I'll try to think of better approaches to help you in the future.

I will be going to bed now, since it's 1:16am here. I hope you have a great day, and don't forget to take care of yourself! ❤️

good luck with the rest of the problems!

[topaz sinew]

@neon iron Has your question been resolved?

[topaz sinew]

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[errant flume]

okay so i understand how to find the derivative and all, but im confused about the part i circled in red

[errant flume]

when solving for the horizontal tangent

how did 2sin2x become 2*2sinx cosx

this is the teacher answer key btw

[topaz sinew]

@errant flume Has your question been resolved?

[errant flume]

its because of double angle therom

[topaz sinew]

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[indigo estuary]

How do I integrate this

[indigo estuary]

I have no idea where do begin

[merry hill]

let acos^2x + bsin^2x = t

[indigo estuary]

Ok

2sinxcosx/t

Or just sin2x/t

[merry hill]

none

do you know substitution?

[indigo estuary]

U substitution?

[merry hill]

yes

[indigo estuary]

Yea

[merry hill]

so do that

[indigo estuary]

So I let the whole denominator equal u and solve from there?

[merry hill]

yes

[indigo estuary]

Aight gimme a sec

[indigo estuary]

Aight thx I got the answer also how do I integrate this

Also if I have to use u sub again can u hint to me as to what I make u

[keen raptor]

u = x-a seems like it would work

[merry hill]

cos(x) can be written as cos((x-a)+a), then cos(a+b) formula

[indigo estuary]

Uhh I’m kinda stuck now

[merry hill]

how do you still have cos(x-a) here

[indigo estuary]

Oh right

[indigo estuary]

Is this right

,rccw

[merry hill]

why is that cos inside log

also why + between the two terms

[indigo estuary]

Oh yeah it’s meant to be minus

[indigo estuary]

Wdym

[merry hill]

ln|cos(x-a)|

why cos

integration of tanx isnt ln|cosx|

its ln|secx|

[indigo estuary]

Yes but -lnsecx = lncosx

[merry hill]

what minus

thats already outside, isnt it?

[indigo estuary]

Ok lemme put it in an integral calculator rq

[merry hill]

,w int cosx/cos(x-a)

[thorny flame]

Results provided by WolframAlpha

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

Requested by astar777

[indigo estuary]

Yea

[merry hill]

but you said the outside plus is supposed to be minus

also yes, your original answer is correct, i nitpicked two things different and didnt see why, my bad

a-x tho

not x-a

[indigo estuary]

Wait I’m getting different answers from the wolfram alpha one and this integral calculator

Wait no nvm im stupid

I put cos(x+a) as the deno instead of cos(x-a)

[indigo estuary]

Yea but cos is even so it’s alr right?

[merry hill]

oh yeah that works

its the same thing

[indigo estuary]

Yea thanks for your help

[indigo estuary]

Also do u have any advice on finding out which suitable entity in a question to make u

[merry hill]

when the derivative of what you substitute u for is there in the function and can simplify the integral

like for example cos(x)/sin(x)

if you do sin(x) = u

cos(x)dx = du, and your integral becomes 1/u du

[indigo estuary]

Ohk

I get it

Is it possible to use u sub for x(x+2)^1/2

@merry hill

[merry hill]

yes

u = x+1

[indigo estuary]

you mean u= x+2 or did u actually mean x+1

[merry hill]

yeah, 2

both are constant

doesnt matter if its 1 or 2 or 10

(in this context)

[indigo estuary]

ohk

[merry hill]

to be clear, what i mean by this is the u-sub will work

answer will ofcourse be different

[indigo estuary]

Ohk

[indigo estuary]

When u said to use x+2 instead of 1, how did u know that 2 would work better?

[merry hill]

wdym

[merry hill]

i just misread, i thought it was (x+1), so said u=x+1

[indigo estuary]

oh

ok

Thank you for your help

.close

[topaz sinew]

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[topaz sinew]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[final hollow]

help

[final hollow]

im very confused

when i solve for x using sin law it gives a different answer then when i use the cosine law

i dont understand how

[restive inlet]

values given are inconsistent and/or major rounding issues in the diagram

[vernal matrix]

(can you show what you did for both?)

[final hollow]

wait

how do i make desmos use degrees instead of radians?

[vernal matrix]

Spanner and choose degrees, radians is automatically selected iirc

[final hollow]

cuz what i did was $ x=\frac{10\sin30}{\sin40} and for cosine i did x=\sqrt{10^{2}+12^{2}-2\left(10\right)\left(12\right)\left(\cos30\right)} $

...

the robot aint workin

$x=\frac{10\sin30}{\sin40}$

[thorny flame]

element

[final hollow]

$x=\sqrt{10^{2}+12^{2}-2\left(10\right)\left(12\right)\left(\cos30\right)}$

[thorny flame]

element

[final hollow]

i dont understand how i got two different answers depending on whether i used the cosin law or sin law $x=\frac{10\sin30}{\sin40}$ and for cosine i did $x=\sqrt{10^{2}+12^{2}-2\left(10\right)\left(12\right)\left(\cos30\right)}$

[thorny flame]

element

[vernal matrix]

Probably inconsistent then, in particular-

That top angle should be 110 degrees, but...

,w 10/sin(40 degrees)

[final hollow]

but the diagram doesnt matter, its already given the values

[thorny flame]

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[vernal matrix]

,w 12/sin(110 degrees)

[thorny flame]

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[vernal matrix]

Well, the values must be ordered wrong, because it doesn't satisfy the sine rule

The above two should be equal but they're not

[final hollow]

... so in summary the triangle is just nonsensical?

wait...

but if you ignore the diagram and only look at the values, doesnt it follow all the triangle inequallity laws though?

[vernal matrix]

How do you mean? The order you pick them in is important - do you have any more context?

[final hollow]

oh, are you saying that the triangles values are mixed up?

[vernal matrix]

That may be the case, but the values may not work as they are

[final hollow]

so if i were to solve for x, no matter what i do, it will always be ambigious?

[vernal matrix]

Not too sure actually

[final hollow]

bruh what is wrong with that triangle

im so confused

well anyways ima leave this.

i got a second question though

how do you prove this identity

$\left(\sin x+\cos x\right)^{2}-1=\ \frac{2\tan x}{1+\tan^{2}x}$

[thorny flame]

element

[final hollow]

I tried a lot but i cant do it...

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@final hollow Has your question been resolved?

[final hollow]

@knotty finch

.closw

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[dense plover]

Let $C$ be an abelian category that has enough injectives. Let $S$ be a (possibly infinite) index set. For every $s \in S$, let $A_s$ be an object of $C$ and choose an injective resolution $0 \rightarrow A_s \rightarrow I_{s, 0} \rightarrow I_{s, 1} \rightarrow ...$.

Is $0 \rightarrow \oplus_{s \in S} A_s \rightarrow \oplus_{s \in S} I_{s, 0} \rightarrow \oplus_{s \in S} I_{s, 1} \rightarrow ...$ an injective resolution of $\oplus_{s \in S} A_s$?

[thorny flame]

DavidL1450

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[gentle night]

How to approach this problem?

What I did so far

[odd pagoda]

roughly speaking, you would like to connect $\int_0^1 f(x) f(1-x) dx$ and $\int_0^1 f(x) dx$. do you know some way to do that?

[thorny flame]

Denascite

[gentle night]

Hmmm
Won't we substitute f(x)f(1-x) by 1

[odd pagoda]

yes which is why thats a good integral to consider

but I think I made a mistake in my head, my idea doesnt quite work out the way I wanted to

ok I think you can save it

do you know any formulas/identities/... for an integral of a product of functions

[gentle night]

I think there is no simple form for that

Except for the integration by parts formula

[odd pagoda]

do you know an inequality involving a product of functions

[gentle night]

No

[merry hill]

am gm

[odd pagoda]

hmm am gm could also work, I was thinking of cauchy schwarz

[merry hill]

ah

[odd pagoda]

do you know either of those

[gentle night]

Yes I know am gm

But how would that help
I got
$$\frac{f(x)^2 +2 + f(1-x)^2}{4} \geq 1$$

[thorny flame]

Sherif Player

[odd pagoda]

from where did you get that

[gentle night]

I over complicated it
I took the square of (a+b)/2

$$\frac{f(x)+f(1-x)}{2} \geq 1$$ should work too

[thorny flame]

Sherif Player

[odd pagoda]

and now integrate both sides

[gentle night]

Wow
That worked

Thanks

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[muted delta]

Bit stuck how to approach it, I tried to go fully algebraic but I couldn't get an answer

[shy pivot]

Start with the fact both projections have equal magnitude

Witht this kind of question you first have to find the direction then the magnitude

Thats how i did it at least

[muted delta]

I've set up my equation such |3x+4y|/25 = |12x-5y|/169

[shy pivot]

No need for that

[muted delta]

really? what's the different approach

[shy pivot]

Thats not the way youll do algebra when doing exercises wih more abstraction

[muted delta]

how do I go about it then?

[shy pivot]

Make a simple drawing

[neon iron]

So u and v have same mag

[shy pivot]

No need to scale it correctly

[muted delta]

yeah I've got a rough one and I put the vector x through the middle

and tried to rougly draw the projections out

[shy pivot]

Exactly

When "building" x with u and v you should add "as much" of u as v

Idk if thats clear

Then the first quadrant thing tells you you should add positive quantities of both

Now you can do equations

[muted delta]

I'm a bit lost icl

[shy pivot]

So

When you have 2 vectors u and v that are not parallel

Adding au+bv where a and b are real can give you any vector you want right ?

[muted delta]

yeah

[shy pivot]

So here we are looking for the correct a and b

[muted delta]

ok

[shy pivot]

Since both projections have same value

You know xu=xv

Hold on i think itll be simpler if you just use equations

[shy pivot]

Just correct thar

Because its in the first quadrant you.know evrything will be positive

So remove absolute values

[muted delta]

there aren't any real solutions with that equation

[shy pivot]

Sorry for offering a bad method, it works for me but im bad at exolaining

[muted delta]

you're good

I just got really stuck with the expansion, doesn

the projection of x onto v become negative tho?

because it gets shorter?

[shy pivot]

U think you forgot some square roots ?

[muted delta]

I don['t think so, I expanded out adn simplified down

[shy pivot]

So its 5 and 13 instead of 25 and 169

[muted delta]

yeah the scalar projection

[shy pivot]

What you do is u•v/|u| right?

[muted delta]

yeah

[shy pivot]

Why do you divide by 25 and 169@muted delta

[muted delta]

it should be scalar not the vector prok

so 5 and 13 like you said Im pretty sure

[shy pivot]

Yes

Then we get the norm

Magnitude

What youll do is look at magnitudes squared

This way you dont get square roots

You can do that itll be long but i dont see a reason it wouldnt work

[muted delta]

I finished the equation out, I got y = 10.52 and x = 4.4

I want to check if the projections are equal

then hopefully this question is done

[shy pivot]

Sure

[muted delta]

it did not work lol

[shy pivot]

The other way would have been

[muted delta]

found the issue

[shy pivot]

Normalise u and v

So they both have magnitude 1

Now you know x =a(±u ±v)

[muted delta]

y = 3, x = 11

all done

[shy pivot]

And a is sqrt 130

[muted delta]

works perfet

121+9 = 130

and works for the values

thanks for your help

[shy pivot]

Gj you did it fast

[muted delta]

yeah, idk why I didn't get that the first time lol

its to late where I am now

[shy pivot]

Thats faster for me

[muted delta]

probably should've stopped haha

[shy pivot]

But its math so whatever works best for you

Ye np

[muted delta]

yeah exactly, thank you very much

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[neon iron]

Anyone know why khan acadmey says this is wrong?

[golden blade]

I think you were not meant to simplify it

Since it says to use the table

[neon iron]

If I try it unsimplified

[ruby tree]

That 4 looks suspicious

[golden blade]

You think there is a syntax error?

[hallow depot]

Hi Nel!

[golden blade]

Indeed

[golden blade]

This 4 looks "appropriate"

I think you gave the answers with your phone

[neon iron]

24x^4 - 36x^3 + 12x^3 - 18x^2

[golden blade]

x^4 and x⁴

So by that your original one was actually correct, but syntax error

[neon iron]

Retyped it still getting this

[golden blade]

I meant this, by original one

[neon iron]

oh

um that 4 seems low

[golden blade]

yes

[golden blade]

I assume you did this

the latter one instead former

[neon iron]

Yeah that was the issue

why tf do they got a lower 4

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[golden blade]

I need help with my proof

[golden blade]

I am trying to show the uniqueness of the gcd

[thorny flame]

bacc (unhelpful)

[chilly walrus]

why?

elaborate

oh i see why

i feel like it could be elaborated a bit more

[golden blade]

I was afraid, I would say too much, but basically it contradicts because we defined the gcd to be the greatest common divisor, but if d > d~ that means d~ cannot be the greatest common divisor

[chilly walrus]

yep

[chilly walrus]

this still feels weird

why do we need the arbitrary a_j?

[golden blade]

For d to be the gcd of these numbers, then d must divide every number, so what I wanted to do basically is generalize this idea by considering an arbitrary element a_j that d divides.

Man this is mentally so challenging for me what am I doing

I think I could leave out the picking an arbitrary element part

[topaz sinew]

@golden blade Has your question been resolved?

[thorny flame]

bacc (unhelpful)

[golden blade]

Any opinions?

[vernal matrix]

I'm happy

Alternatively if you e.g. know that any other common divisor is divisible by the gcd, then each gcd divides each other and they're both positive integers, so must be equal

[golden blade]

Ok thank you for your feedback.
The last thing you wrote, I just can't grasp it haha, can you elaborate a bit more with an example, please?

I just get lost very quickly, Algebra is just so abstract for my mind haha

[vernal matrix]

As in, if you have two strictly positive integers a and b that divide each other, then, say, there's an integer n (which needs to be positive) so a = nb, and there's an integer m such that b = ma, so a = nb = nma, and nm = 1 (you can divide by a as it's strictly positive)

The fact that a and b are positive makes n and m positive, so then the only way you can have nm being 1 is if n and m are both 1

That then leads you that both divisor statements say that a = b, so they have to be the same

[golden blade]

Thank you very very much

[vernal matrix]

Hopefully that makes it clear

[golden blade]

It does it all makes sense

Thanks chartbit

.solved

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[noble nest]

for f(x,y) = x * e^y

[noble nest]

$f_y = x e^y$ ?

[thorny flame]

Chuti | Argentina

[noble nest]

just like that?

[fallow heart]

Yep

[noble nest]

lol

okay cool

thanks 😄

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[spark rain]

Hey I need help in question 32 and DE's equation is y = -4x+31 and I could easily understand that AB is -1/ 4 and I also got the equation for AB and it's y = -1/4x +5 and the equation of AB is wrong and the M of AB is 1/4 and not -1/4, I found out it is wrong bc I looked in the answers to check my self, I will really appreciate it if you will take your time to help me.

[spark rain]

HELP ME!

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[frank lodge]

how do i start question 11

😭

maybe like a hint

[sweet shard]

chain rule or implicit differentiation

or solve for y first

[frank lodge]

ok nvm hints r not helping…i tried something stupid and it’s not gonna get me anywhere 😭 could u work it out

[buoyant horizon]

$x=\left(\arccos y\right)^2\implies y=\cos\sqrt{x}$

[thorny flame]

@buoyant horizon

[frank lodge]

i did. this

😭

do i continue

[buoyant horizon]

well

yes

that seems correct

wait what even is dt/dy

[frank lodge]

okay thanks, i’ll see if i get to the ans

[buoyant horizon]

Don't you use chain rule like this:

$[f(g(x))]^\prime=f^\prime(g(x))\cdot g^\prime(x)$

[thorny flame]

@buoyant horizon

[frank lodge]

huhh

[buoyant horizon]

uh

its like opening a box

if you have a function inside of a function and you want the derivative of the whole thing

[frank lodge]

it’s inverse cos so like isn’t there a diff method for solving those

[buoyant horizon]

you first find the derivative of the outer function, with the inside as is

[buoyant horizon]

method?

you mean cos-ing both sides?

like

y = arccos x
=> x = cos y

[buoyant horizon]

oh

if you wanna go that way, sure

[frank lodge]

i’m following the steps in my book cuz i’m new to the topic 😭

[buoyant horizon]

you'll get dx/dy = 2arccos(y) * dy/dx

[buoyant horizon]

hm

okay so,

i think by those steps you refer to the chain rule

in simple terms

if you want the diff of something that looks like two different things nested into one another

like you know, a box packed inside another box like thing

you use the chain rule

essentially, you "open the outer box" first, then "open the inner box"

by that i mean

lets take the example one: arcsin(x^2)

you see 2 different things: arcsin and x^2

i can diff both of them if they're separate

but since they're "nested"

[buoyant horizon]

i'll use this

I'll diff arcsin(x^2) by treating x^2 as if its just like x (this is why they do t = x^2 first)

This gives you $\frac{1}{\sqrt{1-(x^2)^2}}=\frac{1}{\sqrt{1-x^4}}$

[thorny flame]

@buoyant horizon

[buoyant horizon]

Now, you "open the inner box"

[buoyant horizon]

that is, multiply this result by diff of x^2

the thing you "assumed" to be just x

or t, as per the book

this would give you

$\frac{2x}{\sqrt{1-x^4}}$

[thorny flame]

@buoyant horizon

[buoyant horizon]

this is the example one in the pic you sent

now try the same thing for the given one

[frank lodge]

ik how to solve this one

i did it like this

but idk how to solve the one i sent

idk i found it weird

😭

can u solve it pls

[buoyant horizon]

alright

i'll do it the book way

[frank lodge]

thanks a lot 😭

[buoyant horizon]

@frank lodge First, do you understand this step?

$x=\left(\arccos y\right)^2\implies y=\cos{\sqrt{x}}$

[thorny flame]

@buoyant horizon
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[buoyant horizon]

what errror

well

[frank lodge]

yes

[buoyant horizon]

alright

so

as per the book

we let

$t=\sqrt{x}$

[thorny flame]

@buoyant horizon

[frank lodge]

yea

[buoyant horizon]

So that $\frac{\dd{t}}{\dd{x}}=\frac{1}{2\sqrt{x}}$

[thorny flame]

@buoyant horizon

[buoyant horizon]

does this make sense?

[frank lodge]

no i don’t get this one 😭

[buoyant horizon]

okay

so

$\sqrt{x}=x^{\frac{1}{2}}$, right?

sorry not the minus]

[frank lodge]

yes

[thorny flame]

@buoyant horizon

[buoyant horizon]

alright, so

This is like the formula for x^n

[frank lodge]

wait let me understand this i think i get it

ohh yeah

same as this right?

[buoyant horizon]

$\frac{\dd{t}}{\dd{x}}=\frac{\mathrm{d}\left(x^{\frac{1}{2}}\right)}{\dd{x}}=\frac{1}{2}x^{\frac{1}{2}-1}=\frac{1}{2}x^{-\frac{1}{2}}=\frac{1}{2x^{\frac{1}{2}}}=\frac{1}{2\sqrt{x}}$

[thorny flame]

@buoyant horizon

[buoyant horizon]

does this make sense?

[frank lodge]

yeah i just realized it’s the same as this

thanks

[buoyant horizon]

ah, yes

So

now according to the textbook, you do dy/dt

[frank lodge]

yeah

[buoyant horizon]

$\frac{\dd{y}}{\dd{t}}=\frac{\mathrm{d}\left(\cos t\right)}{\dd{t}}$

[thorny flame]

@buoyant horizon

[buoyant horizon]

right?

[frank lodge]

yes

[buoyant horizon]

this is just

$-\sin t=-\sin{\sqrt{x}}$

[thorny flame]

@buoyant horizon

[frank lodge]

now i’m confused again 🥲

[buoyant horizon]

alright

[frank lodge]

oh wait yes

nvm

[buoyant horizon]

lol

alright, so