#help-23 | Mathematics | Page 469

broken ether Apr 5, 2022, 4:38 PM

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ok

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now that ive got this where do i go further ?

winter pivot Apr 5, 2022, 4:39 PM

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What is -2 + 2

broken ether Apr 5, 2022, 4:39 PM

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0

winter pivot Apr 5, 2022, 4:40 PM

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Yep

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And what is 0+2

broken ether Apr 5, 2022, 4:40 PM

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2

winter pivot Apr 5, 2022, 4:40 PM

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So then we have:

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2x = 2

broken ether Apr 5, 2022, 4:40 PM

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yes

winter pivot Apr 5, 2022, 4:40 PM

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What can we do now?

broken ether Apr 5, 2022, 4:40 PM

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uh

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i do not know

lean otter Apr 5, 2022, 4:40 PM

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you are learning calculus even though you cant solve simple equations? 🤔

winter pivot Apr 5, 2022, 4:41 PM

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Could you write the equation in words?

broken ether Apr 5, 2022, 4:41 PM

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lean otter you are learning calculus even though you cant solve simple equations? 🤔

dude please don’t judge me

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i have really bad difficulties with math

winter pivot Apr 5, 2022, 4:41 PM

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winter pivot Could you write the equation in words?

Ignore him, do this

broken ether Apr 5, 2022, 4:41 PM

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winter pivot Could you write the equation in words?

what do u mean by that?

winter pivot Apr 5, 2022, 4:41 PM

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If you had to say that equation out loud

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How would you say it

broken ether Apr 5, 2022, 4:42 PM

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two x equals two

winter pivot Apr 5, 2022, 4:42 PM

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Alright that's a good start!

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But what exactly do we mean by "two x"?

broken ether Apr 5, 2022, 4:43 PM

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uhhh

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yea no idea

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we have

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2 and an unknown

winter pivot Apr 5, 2022, 4:43 PM

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What sort of operation is that?

broken ether Apr 5, 2022, 4:43 PM

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i wouldnt know

winter pivot Apr 5, 2022, 4:44 PM

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What are we doing with the numbers 2 and x?

broken ether Apr 5, 2022, 4:44 PM

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they equal 2

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so x is 0

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because 2 =2?

winter pivot Apr 5, 2022, 4:44 PM

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Not quite

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Let's step back a bit

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I want you to read this equation out loud:

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3(5) = 15

broken ether Apr 5, 2022, 4:45 PM

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three times five equals fifteen

winter pivot Apr 5, 2022, 4:45 PM

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Yes

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There is a specific word you used there

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It is very important

broken ether Apr 5, 2022, 4:45 PM

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times ?

winter pivot Apr 5, 2022, 4:45 PM

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"times"

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Yes

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What does that mean?

broken ether Apr 5, 2022, 4:46 PM

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you multiply

winter pivot Apr 5, 2022, 4:46 PM

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Yes!

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So what does "2x" mean?

broken ether Apr 5, 2022, 4:46 PM

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we multiply 2 by x?

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2(x)?

winter pivot Apr 5, 2022, 4:46 PM

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Yes!

broken ether Apr 5, 2022, 4:47 PM

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so it’s 1?

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2 • 1 = 2

winter pivot Apr 5, 2022, 4:47 PM

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Yeah x is 1

broken ether Apr 5, 2022, 4:47 PM

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ohhhhh ok

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i see

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and so my final answer would be

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2(1)=2?

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or

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something like that?

winter pivot Apr 5, 2022, 4:48 PM

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So we had that f'(x) = 2x - 2.
And 2x-2=0 when x=1

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So far so good?

broken ether Apr 5, 2022, 4:49 PM

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hang on

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wait i don’t understand one part

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2x-2 = 0 but 2•1 is 2

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so why 0

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oh wait

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i think i see

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no wait h

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hang on i am confusing myself one second

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ahhh ok

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i get it now

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ok so far so good

winter pivot Apr 5, 2022, 4:52 PM

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Yes. Now when is 2x-2 greater than 0?

broken ether Apr 5, 2022, 4:53 PM

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when x id higher than 2?

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is*

winter pivot Apr 5, 2022, 4:54 PM

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If 2x-2 = 0, then x = 1

broken ether Apr 5, 2022, 4:54 PM

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yes

winter pivot Apr 5, 2022, 4:54 PM

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So then if 2x - 2 > 0, then?

broken ether Apr 5, 2022, 4:54 PM

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wouldn’t that be equal to zero though?

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2x-2=0?

winter pivot Apr 5, 2022, 4:55 PM

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Yeah we already solved that. We know when 2x-2 is 0. But now we want to find when it's greater than 0

broken ether Apr 5, 2022, 4:56 PM

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ah ok

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i think i see now

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so since it’s greater than 0 what does it mean?

winter pivot Apr 5, 2022, 4:59 PM

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2x - 2 > 0

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add 2 to both sides

broken ether Apr 5, 2022, 5:00 PM

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winter pivot add 2 to both sides

2x - 2 + 2 > 0 + 2?

broken ether Apr 5, 2022, 5:06 PM

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winter pivot 2x - 2 > 0

times? you there? 🥲

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anyone else who can help?

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<@&286206848099549185> any one of you guys? 😅🥲

sudden briar Apr 5, 2022, 5:28 PM

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broken ether 2x - 2 + 2 > 0 + 2?

you are correct

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continue

safe radishBOT Apr 5, 2022, 5:33 PM

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@broken ether Has your question been resolved?

broken ether Apr 5, 2022, 5:45 PM

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sudden briar continue

idk how to continue

sudden briar Apr 5, 2022, 5:45 PM

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2x>2

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so???????????????????/

broken ether Apr 5, 2022, 5:45 PM

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ok

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uhhh

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i don’t know

sudden briar Apr 5, 2022, 5:46 PM

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multiply by a positive number

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do what to the inequality

broken ether Apr 5, 2022, 5:46 PM

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yes

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häääh im confused by what u mean by that

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ok so

sudden briar Apr 5, 2022, 5:46 PM

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so basically

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say we have a>b

broken ether Apr 5, 2022, 5:46 PM

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2(1)

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for example

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2=2

sudden briar Apr 5, 2022, 5:47 PM

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we multiply by a POSITIVE real c

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we have that a>b is equivalent to ac>bc

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here 2x>2

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we multiply by the positive number 1/2

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we get x>1

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o oops

broken ether Apr 5, 2022, 5:48 PM

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this is so confusing

safe radishBOT Apr 5, 2022, 5:48 PM

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Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

broken ether Apr 5, 2022, 5:48 PM

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.reopen

safe radishBOT Apr 5, 2022, 5:48 PM

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✅

sudden briar Apr 5, 2022, 5:49 PM

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$2x>2 \iff 2(1/2)x>2(1/2) \iff x>1$

broken ether Apr 5, 2022, 5:49 PM

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HUUH

flat frigateBOT Apr 5, 2022, 5:50 PM

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Hwai

broken ether Apr 5, 2022, 5:50 PM

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i don’t understand so completely why we do 1/2

sudden briar Apr 5, 2022, 5:50 PM

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to cancel the 2?

bronze prism Apr 5, 2022, 5:50 PM

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Because knowing things about 2x is weird, it's much more convenient to know things about just x

broken ether Apr 5, 2022, 5:51 PM

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ok wait

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back track for a second im still completely lost

sudden briar Apr 5, 2022, 5:51 PM

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wait how come the original question equality

broken ether Apr 5, 2022, 5:51 PM

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is that a question

sudden briar Apr 5, 2022, 5:52 PM

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yes

broken ether Apr 5, 2022, 5:52 PM

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idk what u are asking

sudden briar Apr 5, 2022, 5:52 PM

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oh

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nvm

bronze prism Apr 5, 2022, 5:52 PM

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Let's take it from the start

broken ether Apr 5, 2022, 5:53 PM

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kk

bronze prism Apr 5, 2022, 5:53 PM

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We know that f(x) is increasing if and only if f'(x) ≥ 0

sudden briar Apr 5, 2022, 5:53 PM

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well anyway f(x) is monotonically increasing on the interval [1,+inf)

bronze prism Apr 5, 2022, 5:53 PM

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(the equality case isn't really relevant here, but let's include it for completeness's sake)

broken ether Apr 5, 2022, 5:53 PM

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okay

bronze prism Apr 5, 2022, 5:54 PM

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However f'(x)=2x-2, so we want to know for which x (and not for which 2x or 3x or whatever) we have 2x-2 ≥ 0

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When 2x-2 ≥ 0, f'(x) ≥ 0 so f is increasing

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When 2x-2 ≤ 0, f'(x) ≤ 0 so f is decreasing

broken ether Apr 5, 2022, 5:54 PM

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ok i understand that

bronze prism Apr 5, 2022, 5:55 PM

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So then the question is : for which x do we have 2x-2 ≥ 0

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Now, the first golden rule is that you can add anything to both sides of an inequality

broken ether Apr 5, 2022, 5:55 PM

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what’s an inequality?

bronze prism Apr 5, 2022, 5:56 PM

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a ≤ b is an "inequality", it's a way of saying how a and b compare to one another

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In this case "a ≤ b" means that "a is less than or equal to b"

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For example, 1 ≤ 3 because 1 is less than 3

broken ether Apr 5, 2022, 5:56 PM

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Ah ok

bronze prism Apr 5, 2022, 5:56 PM

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But it's also true that 1 ≤ 1, because the definition is "less than or equal to"

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If we write a < b, we remove that "or equal to" part

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It's called a strict inequality

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When the symbols go the other way, so does the relation

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a ≥ b means "a is greater than or equal to b"

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a > b means "a is greater than b (and not equal)"

broken ether Apr 5, 2022, 5:57 PM

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I see

bronze prism Apr 5, 2022, 5:58 PM

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perhaps a better word for "inequality" would be "comparison", because that's really what we're doing here

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Now, let's use a simple example to make obvious the various transformations you can do to an inequality

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Let's compare my amount of money (written a) with my neighbor's (written b)

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Think of them as bank balances, so they can actually go negative

broken ether Apr 5, 2022, 6:00 PM

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kk

bronze prism Apr 5, 2022, 6:00 PM

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I have strictly more money than my neighbour (written a ≥ b), then that won't change as long as we both receive (or lose) the same amount of money

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If we both receive a million bucks (it's our lucky day), I will still have more money than him (it's a bit less flagrant, but it is still true, and that's all we care about)

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If we both lose 100 (an unluckier day), the same will be true

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Now, to put this everyday obviousness in mathematical terms

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If a ≥ b, then it stays true as long as we add the same amount to a and b

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If we write that added quantity c (which may be negative, like when we lose money instead of gaining it), then we can write this as a+c ≥ b+c

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Follow so far?

broken ether Apr 5, 2022, 6:03 PM

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Yes

bronze prism Apr 5, 2022, 6:05 PM

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This property is sometimes pompously called "translation invariance" or "shift invariance"

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Because as long as you shift or translate both quantities by the same amount, inequalities stay the same

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(note that this is also true of equalities)

broken ether Apr 5, 2022, 6:06 PM

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Ah

bronze prism Apr 5, 2022, 6:07 PM

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and it's even more trivial in that case

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If two things are the same, they stay the same as long as you do the same operations to each of them, because, well... they're... the same.

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Although it would be nice, the same thing isn't true of inequalities, and as such we have to be a bit more precise

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Now, in a very similar fashion to solving equalities/equations where we have a quantity that we don't know

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A good rule of thumb is to isolate that quantity on one side of the inequality

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Hence, suppose you know 2x-2 ≥ 0 and you want to only have x on the left side : what do you need to add to both sides to achieve that?

broken ether Apr 5, 2022, 6:11 PM

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2?

broken ether Apr 5, 2022, 6:11 PM

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bronze prism Hence, suppose you know 2x-2 ≥ 0 and you want to only have x on the left side : ...

wait can you add negatives

bronze prism Apr 5, 2022, 6:12 PM

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Yes

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but in case you feel confused with what you heard before, they were talking about multiplying by negatives, not adding them

broken ether Apr 5, 2022, 6:12 PM

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ah wait

bronze prism Apr 5, 2022, 6:12 PM

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And yes, 2 is the right answer

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You get 2x-2+2 ≥ 0+2, which simplifies to 2x ≥ 2

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Now we're getting somewhere

broken ether Apr 5, 2022, 6:13 PM

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ah ok

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so now with 2x >_ 2

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where do we go further?

bronze prism Apr 5, 2022, 6:14 PM

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Right, so now we'll discuss multiplication with inequalities

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(by the way, if you can't type ≤ and ≥, the standard way to write them on keyboards is <= and >= )

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Now, let's also make some obvious observations and deduce mathematical generality

broken ether Apr 5, 2022, 6:15 PM

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bronze prism (by the way, if you can't type ≤ and ≥, the standard way to write them on keyboa...

ah ok

bronze prism Apr 5, 2022, 6:16 PM

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I still have more money than my neighbour in this scenario. If both me and my neighbour's bank accounts get doubled, then I will still have more money than them.

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Mathematically, if a ≥ b then 2a ≥ 2b

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But it's also true in the other direction. If both of our accounts get halved, I still have more money than them.

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(you can see it as the "reverse" step of doubling, which conserved the inequality)

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So a/2 ≥ b/2

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In fact, this is true for any positive constant

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No matter how small or how big

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if c > 0, then ac ≥ bc

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In our case, from 2x ≥ 2 we want to really isolate the x, so we want to get rid of that pesky factor of 2

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So we multiply by 1/2 because 2*1/2=1

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Thus, (1/2)*2*x ≥ (1/2)*2. Simplifying, we get x ≥ 1.

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But before i go (gotta eat), a final remark about negative factors

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if the multiplicative constant is 0, it's kinda boring

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because a*0=b*0=0

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But if it's negative, things get flipped around

broken ether Apr 5, 2022, 6:20 PM

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ahh

bronze prism Apr 5, 2022, 6:20 PM

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If i have 1000 and my neighbor has 900, and somehow our accounts get turned into negatives (i.e multiplied by -1), then I have -1000 and my neighbour has -900

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But notice, -1000 is less than -900

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Because it's further out in the negatives

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Here, the general rule is that if c < 0 (negative !!) and a ≥ b, then ca ≤ cb (crucial ! notice how the inequality sign has been flipped !)

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In other words, multiplying by negative numbers flips inequalities.

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Right, now I have to go, I'll let this sink in

broken ether Apr 5, 2022, 6:23 PM

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Thanks so much system :D

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I think I’m getting a better understanding

bronze prism Apr 5, 2022, 6:35 PM

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I'm back, if you have any questions don't hesitate

safe radishBOT Apr 5, 2022, 6:40 PM

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@broken ether Has your question been resolved?

safe radishBOT Apr 5, 2022, 6:55 PM

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devout frigate Apr 5, 2022, 7:09 PM

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can anyone confirm my answer of 19/12

safe radishBOT Apr 5, 2022, 7:09 PM

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devout frigate can anyone confirm my answer of 19/12

devout frigate Apr 5, 2022, 7:19 PM

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if its right id like help with this too

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<@&286206848099549185>

safe radishBOT Apr 5, 2022, 7:41 PM

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@devout frigate Has your question been resolved?

devout frigate Apr 5, 2022, 7:42 PM

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no

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<@&286206848099549185>

safe radishBOT Apr 5, 2022, 8:12 PM

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@devout frigate Has your question been resolved?

devout frigate Apr 5, 2022, 8:12 PM

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.close

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covert fiber Apr 5, 2022, 8:20 PM

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How I can do integral for this 1 ??

safe radishBOT Apr 5, 2022, 8:20 PM

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covert fiber How I can do integral for this 1 ??

ancient escarp Apr 5, 2022, 8:21 PM

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,rotate

flat frigateBOT Apr 5, 2022, 8:21 PM

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covert fiber Apr 5, 2022, 8:21 PM

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Wt is this xd

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Oh k

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Nice bot ;-;

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Can u tell me step by step cuz I actually forgot how to do integral for this

tall bough Apr 5, 2022, 8:26 PM

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sub sqrt(1-2x)

covert fiber Apr 5, 2022, 8:28 PM

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?

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Can u be more clear pls xd

safe radishBOT Apr 5, 2022, 8:43 PM

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@covert fiber Has your question been resolved?

covert fiber Apr 5, 2022, 8:45 PM

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<@&286206848099549185>

mossy bramble Apr 5, 2022, 8:48 PM

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its just a u sub

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u=sqrt(1-2x)

covert fiber Apr 5, 2022, 8:48 PM

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What is u sub

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What is sub xd

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My English isn’t that good xd

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pls don’t go 🥲

inland rune Apr 5, 2022, 8:50 PM

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substitution

covert fiber Apr 5, 2022, 8:50 PM

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I don’t think I learned that

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Or know it

covert fiber Apr 5, 2022, 8:51 PM

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tall bough sub sqrt(1-2x)

Is that the result or wt ?

inland rune Apr 5, 2022, 8:51 PM

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u=sqrt(1-2x)

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you replace sqrt(1-2x) with u

covert fiber Apr 5, 2022, 8:52 PM

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What is “u” xd

inland rune Apr 5, 2022, 8:52 PM

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you just make it as a temporary variable

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https://www.youtube.com/watch?v=sdYdnpYn-1o

YouTube

The Organic Chemistry Tutor

How To Integrate Using U-Substitution

This calculus video tutorial provides a basic introduction into u-substitution. It explains how to integrate using u-substitution. You need to determine which part of the function to set equal to the u variable and you to find the derivative of u to get du and solve for dx. After replacing all x variables with u variables, find the antideriva...

▶ Play video

covert fiber Apr 5, 2022, 8:52 PM

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There is other way right ?

safe radishBOT Apr 5, 2022, 9:22 PM

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devout frigate Apr 5, 2022, 10:02 PM

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need help with the parametrization

safe radishBOT Apr 5, 2022, 10:02 PM

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devout frigate need help with the parametrization

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@devout frigate Has your question been resolved?

devout frigate Apr 5, 2022, 10:36 PM

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<@&286206848099549185>

safe radishBOT Apr 5, 2022, 11:06 PM

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@devout frigate Has your question been resolved?

devout frigate Apr 5, 2022, 11:06 PM

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still waiting

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<@&286206848099549185>

safe radishBOT Apr 6, 2022, 12:06 AM

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@devout frigate Has your question been resolved?

devout frigate Apr 6, 2022, 12:10 AM

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.colose

safe radishBOT Apr 6, 2022, 2:10 AM

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devout frigate Apr 6, 2022, 2:14 AM

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.close

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safe radishBOT Apr 6, 2022, 2:45 AM

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winter fern Apr 6, 2022, 3:13 AM

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Why is the answer E? As far as I can recall, the derivative should be $e^{x+x^2}(2x)$, and so at $x=1$ we get $2e^2$

safe radishBOT Apr 6, 2022, 3:13 AM

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winter fern Why is the answer E? As far as I can recall, the derivative should be $e^{x+x^2}...

flat frigateBOT Apr 6, 2022, 3:13 AM

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cgodfrey

winter fern Apr 6, 2022, 3:14 AM

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My recollection is that $\frac{\mathrm d}{\mathrm dx}\left(\int_{f(x)}^{g(x)}h(t),\mathrm dt\right)=h(g(x))g'(x)-h(f(x))f'(x)$

flat frigateBOT Apr 6, 2022, 3:14 AM

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cgodfrey

safe radishBOT Apr 6, 2022, 3:29 AM

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@winter fern Has your question been resolved?

winter fern Apr 6, 2022, 3:30 AM

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<@&286206848099549185>

plucky elk Apr 6, 2022, 3:51 AM

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flat frigate **cgodfrey**

You missed product rule

safe radishBOT Apr 6, 2022, 4:01 AM

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@winter fern Has your question been resolved?

winter fern Apr 6, 2022, 4:05 AM

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plucky elk You missed product rule

Where is the product rule coming from? Isn't it just $e^{x+x^2}$ times the derivative of $x^2$?

flat frigateBOT Apr 6, 2022, 4:05 AM

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cgodfrey

plucky elk Apr 6, 2022, 4:15 AM

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winter fern Where is the product rule coming from? Isn't it just $e^{x+x^2}$ times the deriv...

Nope. Factor out an e^x from the integrand outside the integral

winter fern Apr 6, 2022, 4:15 AM

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ooh I see

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.close

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safe radishBOT Apr 6, 2022, 5:56 AM

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safe radishBOT Apr 6, 2022, 6:26 AM

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@lean otter Has your question been resolved?

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gilded delta Apr 6, 2022, 6:30 AM

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are those two linear mappings surjective?

safe radishBOT Apr 6, 2022, 6:30 AM

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gilded delta are those two linear mappings surjective?

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@gilded delta Has your question been resolved?

safe radishBOT Apr 6, 2022, 7:00 AM

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safe radishBOT Apr 6, 2022, 4:39 PM

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tribal cove Apr 6, 2022, 4:43 PM

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safe radishBOT Apr 6, 2022, 4:43 PM

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tribal cove

tribal cove Apr 6, 2022, 4:44 PM

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can anyone tell me what should I do next
Idk how to compute the partial 4n times thing
And I am not sure am I on the right track

shy temple Apr 6, 2022, 4:52 PM

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tribal cove can anyone tell me what should I do next Idk how to compute the partial 4n times...

Use the hint. The coefficient of $x^{2n} y^{2n}$ in the Taylor expansion about $0$ of $f$ is given by that partial derivative times $\dfrac{1}{(2n)!^2}$

flat frigateBOT Apr 6, 2022, 4:53 PM

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1345631

safe radishBOT Apr 6, 2022, 4:59 PM

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@tribal cove Has your question been resolved?

safe radishBOT Apr 6, 2022, 5:14 PM

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warm niche Apr 6, 2022, 5:20 PM

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i dont get how the first asymptote is -3pi/4

safe radishBOT Apr 6, 2022, 5:20 PM

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warm niche i dont get how the first asymptote is -3pi/4

warm niche Apr 6, 2022, 5:21 PM

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the answer sheet showed that the first one is -3pi/4

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but i dont get how that is -3pi/4

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it looks like -pi/4

woven kiln Apr 6, 2022, 5:22 PM

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warm niche i dont get how the first asymptote is -3pi/4

range?

warm niche Apr 6, 2022, 5:22 PM

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i dont get it

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i just started trigonometry

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so

woven kiln Apr 6, 2022, 5:22 PM

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warm niche i dont get how the first asymptote is -3pi/4

what is the domain of that

warm niche Apr 6, 2022, 5:23 PM

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i didnt learn how to find the domain from the function sry

woven kiln Apr 6, 2022, 5:23 PM

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otherwise there are infinitely many asymptotes

warm niche Apr 6, 2022, 5:23 PM

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this is the answer

woven kiln Apr 6, 2022, 5:23 PM

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so what you’re saying isn’t much,

warm niche Apr 6, 2022, 5:23 PM

#

#

i dont get how the first line is at -3pi/4

woven kiln Apr 6, 2022, 5:23 PM

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this is just a graph transformation question

warm niche Apr 6, 2022, 5:24 PM

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yes

woven kiln Apr 6, 2022, 5:24 PM

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yeah

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so what’s the domain of x

warm niche Apr 6, 2022, 5:24 PM

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umm

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what x cannot be right

woven kiln Apr 6, 2022, 5:24 PM

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pi is the translation, and 2x is the stretch of 1/2 on the x

woven kiln Apr 6, 2022, 5:24 PM

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woven kiln so what’s the domain of x

*of f(x)

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so range of x values

warm niche Apr 6, 2022, 5:25 PM

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i dont get anything u say sorry

woven kiln Apr 6, 2022, 5:25 PM

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not range of f(x)

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ok

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wait

warm niche Apr 6, 2022, 5:26 PM

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ok

woven kiln Apr 6, 2022, 5:27 PM

#

#

see that

warm niche Apr 6, 2022, 5:27 PM

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yes

woven kiln Apr 6, 2022, 5:28 PM

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It’s got infinitely many asymptotes

warm niche Apr 6, 2022, 5:28 PM

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yeah

woven kiln Apr 6, 2022, 5:28 PM

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yeah,

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so you can only find them within a region

warm niche Apr 6, 2022, 5:28 PM

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but for this function the period is pi/2

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i think

woven kiln Apr 6, 2022, 5:28 PM

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warm niche but for this function the period is pi/2

so!

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*?

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there is still not first or last

warm niche Apr 6, 2022, 5:29 PM

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oh wait

woven kiln Apr 6, 2022, 5:29 PM

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woven kiln

look

warm niche Apr 6, 2022, 5:29 PM

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that doesnt do anything

woven kiln Apr 6, 2022, 5:29 PM

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exactly

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you have half a question kid

warm niche Apr 6, 2022, 5:29 PM

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lol ok

woven kiln Apr 6, 2022, 5:29 PM

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you need a domain

warm niche Apr 6, 2022, 5:29 PM

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ok

woven kiln Apr 6, 2022, 5:29 PM

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do you get why

warm niche Apr 6, 2022, 5:30 PM

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yes

woven kiln Apr 6, 2022, 5:30 PM

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anyways,

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general cases

warm niche Apr 6, 2022, 5:30 PM

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it doesnt specify

woven kiln Apr 6, 2022, 5:30 PM

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warm niche it doesnt specify

it should in theory

warm niche Apr 6, 2022, 5:30 PM

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ok

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imma leave the question black

woven kiln Apr 6, 2022, 5:30 PM

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anyways, back to what I was saying

warm niche Apr 6, 2022, 5:30 PM

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blank

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ok

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yes

woven kiln Apr 6, 2022, 5:30 PM

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you can do general case

warm niche Apr 6, 2022, 5:30 PM

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i dont know what that is

woven kiln Apr 6, 2022, 5:30 PM

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whenever cos(x) = 0

warm niche Apr 6, 2022, 5:30 PM

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ok

woven kiln Apr 6, 2022, 5:31 PM

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tan(x) has an asymptote

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yes?

warm niche Apr 6, 2022, 5:31 PM

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yes

woven kiln Apr 6, 2022, 5:31 PM

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so if cos(2x+pi) = 0

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you’ll have an asymptote

warm niche Apr 6, 2022, 5:31 PM

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ok

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i get it

woven kiln Apr 6, 2022, 5:31 PM

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yeah

woven kiln Apr 6, 2022, 5:31 PM

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woven kiln so if cos(2x+pi) = 0

solve that

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you’ll get it

warm niche Apr 6, 2022, 5:32 PM

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ok thanks

woven kiln Apr 6, 2022, 5:32 PM

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and it repeats every pi

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no worries man

woven kiln Apr 6, 2022, 5:32 PM

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woven kiln and it repeats every pi

pi/2 even

warm niche Apr 6, 2022, 5:32 PM

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ok

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got u

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i can close this now right

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i think i know what am doing now

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.close

safe radishBOT Apr 6, 2022, 5:34 PM

#

Channel closed

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crystal rampart Apr 6, 2022, 5:40 PM

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hi guys I need help, I'm French and I have a hot exercise. The question of the exercise is: For what value x is the area of rectangle 1 equal to the area of rectangle 2? ( solve this problem using an equation ) , rectangle 1 has a width of 5 and the length is 3 x + 1 and rectangle 2 has a width of 4 x and a length of 6, thank you for helping me as soon as possible I have difficulties in mathematics 🙂

safe radishBOT Apr 6, 2022, 5:40 PM

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crystal rampart hi guys I need help, I'm French and I have a hot exercise. ...

warm niche Apr 6, 2022, 5:53 PM

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we can show the area for the first one as this

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5(3x+1)

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and that is equal to the rectangle 2 area

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which is 6(4x)

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so we can show this equation like this

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5(3x+1)=6(4x)

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and you can solve that right?

crystal rampart Apr 6, 2022, 5:56 PM

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ah okay thanks but suddenly for part 5 (3x + 1) we have to perform the double distributivity?

warm niche Apr 6, 2022, 5:56 PM

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yep

crystal rampart Apr 6, 2022, 5:56 PM

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okay

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rlly thx

warm niche Apr 6, 2022, 5:56 PM

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yw

crystal rampart Apr 6, 2022, 5:57 PM

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A = (3x+1)×5=4x×6
A = 5 x 3x + 5 x 1 = 4x x 6
A = 15x + 5 = 24x
A = 15x + 5 - 15x = 24x - 15x
A= 5 = 9x
A= x = 9/5
is that the result?

warm niche Apr 6, 2022, 6:00 PM

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very well done

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yep

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if u want to check just substitute x into the equation

crystal rampart Apr 6, 2022, 6:03 PM

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okay

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good day

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English > French

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x)

warm niche Apr 6, 2022, 6:04 PM

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u too

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🙂

safe radishBOT Apr 6, 2022, 6:18 PM

#

@crystal rampart Has your question been resolved?

#

Channel closed

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boreal haven Apr 6, 2022, 6:25 PM

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Prove the identity 1/cosθ - cosθ/1+sinθ = tanθ

safe radishBOT Apr 6, 2022, 6:25 PM

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boreal haven Prove the identity 1/cosθ - cosθ/1+sinθ = tanθ

boreal haven Apr 6, 2022, 6:25 PM

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Prove the identity 1/cosθ - cosθ/1+sinθ = tanθ

#

#

Can you help

limber patio Apr 6, 2022, 6:28 PM

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boreal haven Can you help

Take LCM

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And use the identity, Sin²x +Cos²x=1

boreal haven Apr 6, 2022, 6:28 PM

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cosθ?

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LCM

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or 1

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because i know at some point tanθ= sinθ/cosθ will help

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but if you say i should use Sin²x +Cos²x=1

limber patio Apr 6, 2022, 6:30 PM

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boreal haven because i know at some point tanθ= sinθ/cosθ will help

Yup, for the final step but let's go step by step for now

boreal haven Apr 6, 2022, 6:31 PM

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so i take lowest common multiple first

limber patio Apr 6, 2022, 6:31 PM

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First take the LCM

limber patio Apr 6, 2022, 6:31 PM

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boreal haven so i take lowest common multiple first

Yup

limber patio Apr 6, 2022, 6:31 PM

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boreal haven so i take lowest common multiple first

And tell me what's the numerator you get

boreal haven Apr 6, 2022, 6:33 PM

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i just don't understand how you use lcm here to be honest

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1-cos²(θ) +sin (θ) / (1+sin(θ)) cos(θ)

limber patio Apr 6, 2022, 6:36 PM

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boreal haven 1-cos²(θ) +sin (θ) / (1+sin(θ)) cos(θ)

Yup you're right

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Now in the numerator, instead of writing 1
Change it to sin²θ + cos²θ

boreal haven Apr 6, 2022, 6:37 PM

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sin(θ) / cos (θ)

limber patio Apr 6, 2022, 6:38 PM

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boreal haven sin(θ) / cos (θ)

Got it?

boreal haven Apr 6, 2022, 6:38 PM

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this is step by step?

limber patio Apr 6, 2022, 6:38 PM

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boreal haven this is step by step?

What do you mean?

limber patio Apr 6, 2022, 6:38 PM

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boreal haven 1-cos²(θ) +sin (θ) / (1+sin(θ)) cos(θ)

Replace 1 by what I wrote and you'll see your answer

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Be back in 10 mins

boreal haven Apr 6, 2022, 6:39 PM

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ok

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sin²θ + cos²θ-cos²(θ) +sin (θ) / ( sin²θ + cos²θ+sin(θ)) cos(θ)

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@limber patio

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<@&286206848099549185>

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i think my man just has better shit to do

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it's understandable though

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thank you for the help up until now

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i shall patiently wait for your return

#

.close

safe radishBOT Apr 6, 2022, 7:05 PM

#

Channel closed

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radiant latch Apr 6, 2022, 7:18 PM

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Hello guys, i have a problem :

safe radishBOT Apr 6, 2022, 7:18 PM

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radiant latch Hello guys, i have a problem :

radiant latch Apr 6, 2022, 7:18 PM

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I have : (u - a.idE) ° (u - b.idE) = 0 (L(E)), u is linear

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With a =/ b

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And my first question is to prove that a or b is a eigenvalues

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It was easy

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But the second one is to proove that

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If u is not a homotheties, a and b are eigen values of u

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I don’t know how to process

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(I don’t speak fluently English, so sry for the potential error)

#

So i have to demonstrate this :

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u is a homothety => a and b are not eigen values of u

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$(u - a.Id_E) \circ (u - b.Id_E) = 0_{L(E)}$

flat frigateBOT Apr 6, 2022, 7:24 PM

#

Pako

radiant latch Apr 6, 2022, 7:27 PM

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I don’t know if i have to post in advanced math or not

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<@&268886789983436800> could you guide me pls

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Is it the appropriate channel ?

timber valve Apr 6, 2022, 7:27 PM

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#linear-algebra might be better

radiant latch Apr 6, 2022, 7:28 PM

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timber valve <#540211747613704221> might be better

Thx, but i can’t write

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Oh sry, i can

safe radishBOT Apr 6, 2022, 7:44 PM

#

@radiant latch Has your question been resolved?

#

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• Be polite and have a nice day!

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gray plaza Apr 6, 2022, 8:27 PM

#

safe radishBOT Apr 6, 2022, 8:27 PM

#

gray plaza

gray plaza Apr 6, 2022, 8:28 PM

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Would someone please tell me what I have done wrong? 😀

covert yoke Apr 6, 2022, 8:29 PM

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@gray plaza can't. Don't actually know what you're supposed to be doing

#

Read #❓how-to-get-help for further information on how to ask a good question.

gray plaza Apr 6, 2022, 8:34 PM

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I have to do integration of that function.

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But the answer I received doesn't match with the correct answer.

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So, I am wondering what I have done wrong.

tall bough Apr 6, 2022, 8:49 PM

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nothing wrong

safe radishBOT Apr 6, 2022, 8:54 PM

#

@gray plaza Has your question been resolved?

gray plaza Apr 6, 2022, 8:54 PM

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tall bough nothing wrong

In video the answer is shown as :

gray plaza Apr 6, 2022, 8:55 PM

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tall bough nothing wrong

tall bough Apr 6, 2022, 9:01 PM

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HAHAHAHA

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you made it way more complicated like doing ibp for xe^(x^2)

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normally

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your answer should be equal to that

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check it by a calculator

gray plaza Apr 6, 2022, 9:03 PM

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Haha

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Gotcha

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Thank you ❤️

#

.close

safe radishBOT Apr 6, 2022, 9:04 PM

#

Channel closed

Closed by @gray plaza

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queen parcel Apr 6, 2022, 9:14 PM

#

safe radishBOT Apr 6, 2022, 9:14 PM

#

queen parcel

#

@queen parcel Has your question been resolved?

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somber hazel Apr 6, 2022, 10:20 PM

#

my online school has very outdated videos to "explain" equations and i don't understand how to do this

safe radishBOT Apr 6, 2022, 10:20 PM

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somber hazel my online school has **very** outdated videos to "explain" equations and i don't...

latent sage Apr 6, 2022, 10:21 PM

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Do you know the inscribed angle thereom and understand how it works?

somber hazel Apr 6, 2022, 10:22 PM

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not at all

latent sage Apr 6, 2022, 10:22 PM

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somber hazel not at all

Ah

somber hazel Apr 6, 2022, 10:22 PM

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yeah idk how to find c for example

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if i find angle c i get b

latent sage Apr 6, 2022, 10:23 PM

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I see

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Hint:

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Isn't angle ECD an inscribed angle?

somber hazel Apr 6, 2022, 10:23 PM

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yes i believe so

latent sage Apr 6, 2022, 10:24 PM

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And you know the measure of arc ED :)

somber hazel Apr 6, 2022, 10:24 PM

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ED is 52*

latent sage Apr 6, 2022, 10:24 PM

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So, the inscribed angle thereom states...

somber hazel Apr 6, 2022, 10:25 PM

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idk the thereom

latent sage Apr 6, 2022, 10:26 PM

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Ah

somber hazel Apr 6, 2022, 10:26 PM

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yeah...

latent sage Apr 6, 2022, 10:26 PM

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Draw a diagram of an inscribed angle then :)

somber hazel Apr 6, 2022, 10:27 PM

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oh wait isn't the arc 2x the angle so c is 26?

latent sage Apr 6, 2022, 10:27 PM

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Yep :D

somber hazel Apr 6, 2022, 10:27 PM

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so

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c and b are 26*

latent sage Apr 6, 2022, 10:27 PM

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Mhm!

somber hazel Apr 6, 2022, 10:27 PM

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how about fiunding BSD?

latent sage Apr 6, 2022, 10:28 PM

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Instead of directly finding BSD...

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What other angle can we find that helps with the problem?

somber hazel Apr 6, 2022, 10:28 PM

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uhhhhh

#

d = 57*
b = 26*
s = x*

latent sage Apr 6, 2022, 10:29 PM

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Ah I missed that LOL

somber hazel Apr 6, 2022, 10:29 PM

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lol

latent sage Apr 6, 2022, 10:29 PM

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I found it by using another thereom

somber hazel Apr 6, 2022, 10:30 PM

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what formula can i use to get s?

latent sage Apr 6, 2022, 10:31 PM

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Like the one that says CSB = 57 x 2 + 52 / 2

somber hazel Apr 6, 2022, 10:31 PM

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for triangle BSD

latent sage Apr 6, 2022, 10:31 PM

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somber hazel for triangle BSD

Well the sum of the angles of a triangle are 180

#

So you're basically done with the problem! :D

somber hazel Apr 6, 2022, 10:31 PM

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oml how did i forget that

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57+26=83
180-83=97

latent sage Apr 6, 2022, 10:32 PM

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somber hazel oml how did i forget that

Yeah it can be difficult sometimes :D

somber hazel Apr 6, 2022, 10:32 PM

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s=97

latent sage Apr 6, 2022, 10:32 PM

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somber hazel 57+26=83 180-83=97

Yep!

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Nice job :D

somber hazel Apr 6, 2022, 10:33 PM

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ty for the help!

latent sage Apr 6, 2022, 10:33 PM

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yw!

somber hazel Apr 6, 2022, 10:33 PM

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how do i close this?

latent sage Apr 6, 2022, 10:33 PM

#

.close?

somber hazel Apr 6, 2022, 10:33 PM

#

.close

safe radishBOT Apr 6, 2022, 10:33 PM

#

Channel closed

Closed by @somber hazel

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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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urban shore Apr 6, 2022, 11:00 PM

#

How can i make *1 summation skip the term when k = *2

safe radishBOT Apr 6, 2022, 11:00 PM

#

urban shore How can i make *1 summation skip the term when k = *2

#

@urban shore Has your question been resolved?

crisp oxide Apr 6, 2022, 11:16 PM

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for this problem it'll probably be easier to just write out every term

#

but https://tex.stackexchange.com/questions/80460/expression-under-summation-on-multiple-lines shows how to do it

TeX - LaTeX Stack Exchange

Expression under summation on multiple lines

Possible Duplicate:
Separate long math text under sum symbol into different lines?
I want to write expression \sum_{i=0}^n i with i\neq 4 under the
summation symbol. How can I write this?

safe radishBOT Apr 6, 2022, 11:45 PM

#

@urban shore Has your question been resolved?

covert yoke Apr 6, 2022, 11:57 PM

#

urban shore How can i make *1 summation skip the term when k = *2

You can use a (1 - delta_k2) where delta is the dirac delta function.

#

This will give you 1 on all k not equal to do, and 0 when it does.

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$\sum_{k=1}^4 (1 - \delta_{k2}) \left(k - \left(\frac1{2}k - 1 \right) \right)$

flat frigateBOT Apr 6, 2022, 11:58 PM

#

OmnipotentEntity

covert yoke Apr 6, 2022, 11:59 PM

#

sorry, not dirac delta, that's the kronecker delta. https://en.wikipedia.org/wiki/Kronecker_delta

Kronecker delta

In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers. The function is 1 if the variables are equal, and 0 otherwise:

or with use of Iverson brackets:

where the Kronecker delta δij is a piecewise function of variables i and j. For example, δ1 2 = 0, whereas δ3 3 =...

safe radishBOT Apr 7, 2022, 12:15 AM

#

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frosty ridge Apr 7, 2022, 12:38 AM

#

I need help to show that $\frac{2n+1}{(2n+2)^2}<\frac{1}{2n+3}$ for all n≥1

safe radishBOT Apr 7, 2022, 12:38 AM

#

frosty ridge I need help to show that $\frac{2n+1}{(2n+2)^2}<\frac{1}{2n+3}$ for all n≥1

flat frigateBOT Apr 7, 2022, 12:38 AM

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Goose on a Moose

drowsy moss Apr 7, 2022, 12:42 AM

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what have you tried, what is the method you want to use?

frosty ridge Apr 7, 2022, 12:45 AM

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Besides graphing it on desmos to convince myself that it is true, I'm stuck on the first step haha

simple radish Apr 7, 2022, 12:45 AM

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Here's a hint: maybe it is easier to show that $\frac{1}{(2n+2)^2}<\frac{1}{(2n+1)(2n+3)}$

flat frigateBOT Apr 7, 2022, 12:45 AM

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dackid

drowsy moss Apr 7, 2022, 12:45 AM

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frosty ridge Besides graphing it on desmos to convince myself that it is true, I'm stuck on t...

try showing $\frac{1}{2n+3}-\frac{2n+1}{(2n+2)^2}$ is positive

flat frigateBOT Apr 7, 2022, 12:46 AM

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Zybikron

frosty ridge Apr 7, 2022, 12:46 AM

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thanks for the hints peeps. Ill give this problem another go.

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.close

safe radishBOT Apr 7, 2022, 12:46 AM

#

Channel closed

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simple radish Apr 7, 2022, 12:47 AM

#

Good luck goose

safe radishBOT Apr 7, 2022, 12:48 AM

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runic socket Apr 7, 2022, 12:52 AM

#

i am 99% sure that both b and c needs to have the angle but i cant seem to find it

safe radishBOT Apr 7, 2022, 12:52 AM

#

runic socket i am 99% sure that both b and c needs to have the angle but i cant seem to find ...

runic socket Apr 7, 2022, 12:53 AM

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like the equation is supposed to be 1/2sin^-1((gx)/v^2) or something like that

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but then i get this which isnt even an answer choice

safe radishBOT Apr 7, 2022, 1:09 AM

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@runic socket Has your question been resolved?

runic socket Apr 7, 2022, 1:09 AM

#

<@&286206848099549185>

runic socket Apr 7, 2022, 1:33 AM

#

<@&286206848099549185>

safe radishBOT Apr 7, 2022, 2:03 AM

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@runic socket Has your question been resolved?

runic socket Apr 7, 2022, 2:03 AM

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bruh

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.close

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true zodiac Apr 7, 2022, 2:16 AM

#

safe radishBOT Apr 7, 2022, 2:16 AM

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true zodiac

true zodiac Apr 7, 2022, 2:16 AM

#

#

I literally just dont get it

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.close

safe radishBOT Apr 7, 2022, 2:18 AM

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floral wasp Apr 7, 2022, 2:37 AM

#

how do you determine if a function is continious on a given value of X

safe radishBOT Apr 7, 2022, 2:37 AM

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floral wasp how do you determine if a function is continious on a given value of X

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@floral wasp Has your question been resolved?

plucky elk Apr 7, 2022, 3:05 AM

#

floral wasp how do you determine if a function is continious on a given value of X

take the limit of the function at both sides.

#

https://tutorial.math.lamar.edu/classes/calci/continuity.aspx

Calculus I - Continuity

In this section we will introduce the concept of continuity and how it relates to limits. We will also see the Intermediate Value Theorem in this section and how it can be used to determine if functions have solutions in a given interval.

safe radishBOT Apr 7, 2022, 3:07 AM

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wraith root Apr 7, 2022, 3:18 AM

#

safe radishBOT Apr 7, 2022, 3:18 AM

#

wraith root

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@wraith root Has your question been resolved?

normal wharf Apr 7, 2022, 3:38 AM

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wraith root

This is a binary operation right?

#

You are asking in terms of group theory?

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If yes then operate A-¹ on both sides

safe radishBOT Apr 7, 2022, 3:48 AM

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safe radishBOT Apr 7, 2022, 2:00 PM

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lean otter Apr 7, 2022, 2:01 PM

#

hey what’s newton’s method for

safe radishBOT Apr 7, 2022, 2:01 PM

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lean otter hey what’s newton’s method for

valid grove Apr 7, 2022, 2:02 PM

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By newton’s method I assume you mean newton’s method of approximation

lean otter Apr 7, 2022, 2:08 PM

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ig? what’s that

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how does it work, why does it work and what do i need it for :>

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okay maybe one at the time

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What do i need Newtons method of approximation for?

queen parcel Apr 7, 2022, 2:21 PM

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You can look it up on Wikipedia - that page is pretty helpful @lean otter

safe radishBOT Apr 7, 2022, 2:31 PM

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dreamy dagger Apr 7, 2022, 3:15 PM

#

How long will it take for an investment of 1100 dollars to grow to 6900 dollars, if the effective rate of interest is 6.2 percent? (Assume compound interest at all times.)

safe radishBOT Apr 7, 2022, 3:15 PM

#

dreamy dagger How long will it take for an investment of 1100 dollars to grow to 6900 dollars,...

dreamy dagger Apr 7, 2022, 3:15 PM

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Anwer in years

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I originally got 29.6 years as I used the monthly compound formula but I am not sure if that's correct

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buoyant shadow Apr 7, 2022, 3:20 PM

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can you show how you got it?

dreamy dagger Apr 7, 2022, 3:29 PM

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Yeah sure

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!close

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.close

safe radishBOT Apr 7, 2022, 3:30 PM

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worthy owl Apr 7, 2022, 3:36 PM

#

Can anybody help me on this question

safe radishBOT Apr 7, 2022, 3:36 PM

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worthy owl Can anybody help me on this question

valid grove Apr 7, 2022, 3:39 PM

#

$\frac {x-6}{y-6} =\frac 1 2$

flat frigateBOT Apr 7, 2022, 3:39 PM

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Deep.

valid grove Apr 7, 2022, 3:40 PM

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$\frac {x-14}{y-14} =\frac 2 5$

flat frigateBOT Apr 7, 2022, 3:40 PM

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Deep.

spice grove Apr 7, 2022, 3:44 PM

#

@valid grove

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Why are you doing their work?

grave flint Apr 7, 2022, 3:45 PM

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they just showed how to express the ratios with the variables

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they didnt solve it

valid grove Apr 7, 2022, 3:45 PM

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spice grove Why are you doing their work?

Ohh

next crater Apr 7, 2022, 3:45 PM

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you should guide them

spice grove Apr 7, 2022, 3:45 PM

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Right.

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They legit gave the answer away.

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Bu forming equations.

valid grove Apr 7, 2022, 3:46 PM

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Sorry

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NervousSweat

safe radishBOT Apr 7, 2022, 3:51 PM

#

@worthy owl Has your question been resolved?

safe radishBOT Apr 7, 2022, 4:06 PM

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viral current Apr 7, 2022, 4:16 PM

#

how do i solve this?

safe radishBOT Apr 7, 2022, 4:16 PM

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viral current how do i solve this?

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@viral current Has your question been resolved?

thin bridge Apr 7, 2022, 4:38 PM

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you are told that this is an arithmetic sequence

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can you determine the common difference between consecutive terms?

covert yoke Apr 7, 2022, 4:44 PM

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viral current how do i solve this?

An "arithmetic sequence" is a sequence that has a common difference. You wrote down a sequence with a common ratio, which is a "geometric sequence."

safe radishBOT Apr 7, 2022, 4:46 PM

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viral current Apr 7, 2022, 4:46 PM

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.reopen

safe radishBOT Apr 7, 2022, 4:46 PM

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✅

viral current Apr 7, 2022, 4:47 PM

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covert yoke An "arithmetic sequence" is a sequence that has a common difference. You wrote d...

i tried n-9 and n+9 but its still wrong

#

is there a way to approach these type of problems

covert yoke Apr 7, 2022, 4:48 PM

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Try -18-9n

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Or -9-9n depending on the indexing (starting from 0 or 1)

viral current Apr 7, 2022, 4:49 PM

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ok -18-9n did not work but -9-9n did

covert yoke Apr 7, 2022, 4:49 PM

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Think about what happens when you replace n=1,2,3 etc

viral current Apr 7, 2022, 4:49 PM

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so u used index 1 instead of 0?

covert yoke Apr 7, 2022, 4:49 PM

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If you have n-9, you'll get (-8, -7, -6, -5...)

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Clearly this isn't the sequence you see.

viral current Apr 7, 2022, 4:50 PM

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oh right

covert yoke Apr 7, 2022, 4:51 PM

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A good way to approach arithmetic sequences is to see what the common difference is, then use that difference with an offset

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In this case the common difference is -9

viral current Apr 7, 2022, 4:51 PM

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how did u get the offset?

covert yoke Apr 7, 2022, 4:51 PM

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Which is why it was a-9n

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For the offset, because it's one indexed, you have -18 = a - 9n = a - 9(1)

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Solve for a to get the offfset

viral current Apr 7, 2022, 4:56 PM

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gotcha tysm

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wait uh wdym by "one indexed"

covert yoke Apr 7, 2022, 4:59 PM

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viral current wait uh wdym by "one indexed"

Meaning that counting for n starts at 1.

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In math you generally, but not always start at 1. In computers you generally, but not always start at 0. Because there's a lot of overlap between math and computers, there has been a lot of starting at 0. I find it's nicer in general to start at 0.

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Alas, not everyone agrees.

safe radishBOT Apr 7, 2022, 5:12 PM

#

@viral current Has your question been resolved?

safe radishBOT Apr 7, 2022, 5:27 PM

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warped fulcrum Apr 7, 2022, 5:37 PM

#

this question has to do with statistics.

I am told to find population mean from this X ~ N(μ; σ2 = 625) and I have no idea how to do it. I get that 625 is standard deviation squared, but how do I find the mean?

safe radishBOT Apr 7, 2022, 5:37 PM

#

warped fulcrum this question has to do with statistics. I am told to find population mean fro...

#

@warped fulcrum Has your question been resolved?

plucky elk Apr 7, 2022, 5:56 PM

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warped fulcrum this question has to do with statistics. I am told to find population mean fro...

not enough information given

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show the original problem

warped fulcrum Apr 7, 2022, 5:56 PM

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ok let me translate it real quick

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We know that X ~ N(μ; σ2 = 625),

What is the number of subjects so that the width of the 99% confidence interval for measuring blood cholesterol does not exceed: (a) 11; b) 3?

plucky elk Apr 7, 2022, 6:00 PM

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you don't need the mean to calculate width

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take mu to be 0 and you'll still get the right answer

warped fulcrum Apr 7, 2022, 6:15 PM

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ok so the question asks me to find the number of subjects when blood cholesterol <=11, when confidence interval is 99% and population variance is 625.

So if I get this straight, I need to find sample size right?

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but don't I need margin of error to find it?

safe radishBOT Apr 7, 2022, 6:47 PM

#

@warped fulcrum Has your question been resolved?

warped fulcrum Apr 7, 2022, 7:34 PM

#

I've tried to use this site to help me find the answer(https://www.statisticshowto.com/probability-and-statistics/find-sample-size/) But even though it has an example of finding a Sample Size Given a Confidence Level and Width (known population standard deviation)

I don't see the width being used in the example.

Statistics How To

Stephanie

Sample Size in Statistics (How to Find it): Excel, Cochran's Formul...

Sample size definition and how to find one in easy steps Hundreds of statistics videos, how-to articles, experimental design tips, and more!

#

'Example question: Suppose we want to know the average age of an Florida State College student, plus or minus 0.5 years. We’d like to be 99% confident about our result. From a previous study, we know that the standard deviation for the population is 2.9.'

Where is the confidence level width?

warped fulcrum Apr 7, 2022, 8:34 PM

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eh whatever, I'll skip this one

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.close

safe radishBOT Apr 7, 2022, 8:36 PM

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dusk solar Apr 7, 2022, 8:39 PM

#

safe radishBOT Apr 7, 2022, 8:39 PM

#

dusk solar

dusk solar Apr 7, 2022, 8:39 PM

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i am just so confused on how to even begin to solve this

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the way i did it before was completely wrong

bronze prism Apr 7, 2022, 8:48 PM

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First of all, the derivative of g is just f

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That's the fundamental theorem of calculus

#

Put another way, the fundamental theorem of calculus states that for any antiderivative F of f (i.e F'=f), then $\int_a^b f(t)\mathrm{d}t = F(b)-F(a)$

flat frigateBOT Apr 7, 2022, 8:50 PM

#

Syst3ms

bronze prism Apr 7, 2022, 8:51 PM

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In this case, $g(x) = \int_{-1}^x f(t)\mathrm{d}t = F(x)-F(-1)$.

flat frigateBOT Apr 7, 2022, 8:51 PM

#

Syst3ms

bronze prism Apr 7, 2022, 8:52 PM

#

When you take the derivative you indeed get g' = f

crisp linden Apr 7, 2022, 8:53 PM

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A very fun theorem to prove

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(actually fun that is)

bronze prism Apr 7, 2022, 8:54 PM

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For the first two questions, it's just calculating the area with some good old geometry formulas

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But remember, the area is signed. If it's under the curve it counts as negative

dusk solar Apr 7, 2022, 8:59 PM

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okay so when im finding the first two, i am finding the area between the axis and the function, correct?

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wait actually

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im still confused

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cuz isnt the graph showing f(x) and i need to find g(1)?

#

oh

safe radishBOT Apr 7, 2022, 9:17 PM

#

@dusk solar Has your question been resolved?

dusk solar Apr 7, 2022, 9:18 PM

#

.close

safe radishBOT Apr 7, 2022, 9:18 PM

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bleak orchid Apr 7, 2022, 9:31 PM

#

How’s is lim x-> infinity [(a+2)x+b+c/x+d+3/x*2] equal to 4?

safe radishBOT Apr 7, 2022, 9:31 PM

#

bleak orchid How’s is lim x-> infinity [(a+2)x+b+c/x+d+3/x*2] equal to 4?

#

@bleak orchid Has your question been resolved?

lean thorn Apr 7, 2022, 9:52 PM

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hmmm

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yeah that limit should be diverging or be infinity

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Unless there's some information above that was not part of the picture

bleak orchid Apr 7, 2022, 10:13 PM

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This is the whole sheet

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@lean thorn

bleak orchid Apr 7, 2022, 10:31 PM

#

<@&286206848099549185>

#

.close

safe radishBOT Apr 7, 2022, 10:41 PM

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long magnet Apr 7, 2022, 10:51 PM

#

Can someone please help me solve and understand this? I wasnt at school for the unit and it's homework for tomorrow

safe radishBOT Apr 7, 2022, 10:51 PM

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long magnet Can someone please help me solve and understand this? I wasnt at school for the ...

long magnet Apr 7, 2022, 10:51 PM

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why is it sidewaysss

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sharp crane Apr 7, 2022, 10:57 PM

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@long magnet oddly worded problem. is x = width and y = girth or the other way around?

long magnet Apr 7, 2022, 10:58 PM

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idkkk he didn't specify

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does it matter?

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<@&286206848099549185>

safe radishBOT Apr 7, 2022, 11:22 PM

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@long magnet Has your question been resolved?

long magnet Apr 7, 2022, 11:31 PM

#

.close

safe radishBOT Apr 7, 2022, 11:31 PM

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safe radishBOT Apr 8, 2022, 12:06 AM

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light frigate Apr 8, 2022, 12:41 AM

#

Screen_Shot_2022-04-08_at_8.40.17_AM.png

safe radishBOT Apr 8, 2022, 12:41 AM

#

light frigate

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Please don't occupy multiple help channels.

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low nest Apr 8, 2022, 1:24 AM

#

so if $G$ (with $|G|=p^n m$ and $p$ does not divide $m$) has more than $1$ Sylow $p$-subgroup, then are these subgroups always disjoint (other than the identity)?

safe radishBOT Apr 8, 2022, 1:24 AM

#

low nest so if $G$ (with $|G|=p^n m$ and $p$ does not divide $m$) has more than $1$ Sylow...

flat frigateBOT Apr 8, 2022, 1:24 AM

#

Beous

low nest Apr 8, 2022, 1:24 AM

#

i know if n=1 then they are disjoint, but what if n>1?

safe radishBOT Apr 8, 2022, 1:39 AM

#

@low nest Has your question been resolved?

low nest Apr 8, 2022, 2:08 AM

#

<@&286206848099549185>

safe radishBOT Apr 8, 2022, 2:38 AM

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@low nest Has your question been resolved?

low nest Apr 8, 2022, 2:53 AM

#

.close

safe radishBOT Apr 8, 2022, 2:53 AM

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ionic patio Apr 8, 2022, 3:07 AM

#

safe radishBOT Apr 8, 2022, 3:07 AM

#

ionic patio

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@ionic patio Has your question been resolved?

ionic patio Apr 8, 2022, 3:30 AM

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.close

safe radishBOT Apr 8, 2022, 3:30 AM

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rotund prairie Apr 8, 2022, 4:38 AM

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Can someone help or guide me in the right direction to do the first question? I have no clue how to start

safe radishBOT Apr 8, 2022, 4:38 AM

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rotund prairie Can someone help or guide me in the right direction to do the first question? I ...

upper badge Apr 8, 2022, 4:39 AM

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you can use identity cos^2(x) + sin^2(x) = 1

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once you find the values of trig ratios, be sure to give the appropriate sign

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depending on which quadrant theta is located in

rotund prairie Apr 8, 2022, 4:41 AM

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since im just given cos(x) is cos^2(x) just the value squared?

upper badge Apr 8, 2022, 4:41 AM

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so, for the 28th ques... when you find cos(theta) youll get a positive value from (-0.886)^2 + cos^2(x) = 1, but you need to add a negative sign

upper badge Apr 8, 2022, 4:42 AM

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rotund prairie since im just given cos(x) is cos^2(x) just the value squared?

yes

rotund prairie Apr 8, 2022, 4:44 AM

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upper badge yes

Thats question 27. Does that look right? If so what do I do now?

upper badge Apr 8, 2022, 4:44 AM

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looks good

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find sqrt

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and let the sign remain positive since its in the 1st quadrant

rotund prairie Apr 8, 2022, 4:46 AM

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upper badge and let the sign remain positive since its in the 1st quadrant

Ty so is this it?

upper badge Apr 8, 2022, 4:47 AM

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yes

rotund prairie Apr 8, 2022, 4:47 AM

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ty ty. Also is there any shortcut to seeing that sin(x) and cos(x) will be the same or do u have to just do it?

upper badge Apr 8, 2022, 4:49 AM

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not sure

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they will be same only when equal to 1/√2 ~ 0.707

rotund prairie Apr 8, 2022, 4:50 AM

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oh ok tu so much for the help

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.close

safe radishBOT Apr 8, 2022, 4:50 AM

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timber atlas Apr 8, 2022, 5:03 AM

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safe radishBOT Apr 8, 2022, 5:03 AM

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timber atlas

timber atlas Apr 8, 2022, 5:04 AM

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I’m confused on the x-int’s

plucky elk Apr 8, 2022, 5:09 AM

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timber atlas I’m confused on the x-int’s

plot them?

timber atlas Apr 8, 2022, 5:10 AM

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Mm.

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,tex y=$x^2-2x-3$

flat frigateBOT Apr 8, 2022, 5:11 AM

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Jun♾

lilac patio Apr 8, 2022, 5:11 AM

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-3=a(x-3)(x+1)

timber atlas Apr 8, 2022, 5:11 AM

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So the answer says this

timber atlas Apr 8, 2022, 5:12 AM

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lilac patio -3=a(x-3)(x+1)

Ok i see

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Where did the -2 come from here?

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That’s what I’m confused at

lilac patio Apr 8, 2022, 5:13 AM

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factor it out

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x times x

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x times 1

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-3 times x

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-3 times 1

plucky elk Apr 8, 2022, 5:13 AM

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lilac patio -3=a(x-3)(x+1)

this is smarter

timber atlas Apr 8, 2022, 5:14 AM

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lilac patio factor it out

Still confused here

lilac patio Apr 8, 2022, 5:14 AM

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.

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x times x

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Is x^2

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x times 1 is x

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-3 times x is -3x

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x-3x=-2x

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-3 times 1 is -3

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add it all together

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x^2-2x-3

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there's no a value aka stretch factor

timber atlas Apr 8, 2022, 5:16 AM

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So basically (x-3)(x+1) and just multiply together

lilac patio Apr 8, 2022, 5:17 AM

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yes but you have to multiply every component together

timber atlas Apr 8, 2022, 5:17 AM

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Yh

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Ok I get how you did it

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Thanks

lilac patio Apr 8, 2022, 5:17 AM

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np

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good luck

timber atlas Apr 8, 2022, 5:17 AM

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Thks

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.close

safe radishBOT Apr 8, 2022, 5:18 AM

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safe radishBOT Apr 8, 2022, 5:49 AM

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candid grove Apr 8, 2022, 6:14 AM

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Can someone explain this question?

safe radishBOT Apr 8, 2022, 6:14 AM

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candid grove Can someone explain this question?

mighty dew Apr 8, 2022, 6:15 AM

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example 3?

candid grove Apr 8, 2022, 6:15 AM

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Yes

mighty dew Apr 8, 2022, 6:17 AM

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ok well what part of the solution dont u understand

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i feel it would be better for me to explain that

void cosmos Apr 8, 2022, 6:18 AM

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mighty dew Apr 8, 2022, 6:18 AM

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um

void cosmos Apr 8, 2022, 6:18 AM

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Hello there I am trying to punch in this equation in my calculator

mighty dew Apr 8, 2022, 6:18 AM

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let me finish explaining to reet pkls

void cosmos Apr 8, 2022, 6:18 AM

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and the answer should be 4.6, however I am doing aomething wrong

candid grove Apr 8, 2022, 6:19 AM

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How did they find out the ways letter can be arranged?

void cosmos Apr 8, 2022, 6:19 AM

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I see that tour helping Reet, however I feel like that would take a fair bit of time

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so if you don’t mind sorting out my issue rq that would be nice with all due respect

candid grove Apr 8, 2022, 6:20 AM

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I don't understand the underlined part

mighty dew Apr 8, 2022, 6:20 AM

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yep reets will takle 30 seconds i understand the concept - but thanks

vocal sun Apr 8, 2022, 6:20 AM

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Oh there is a formula

void cosmos Apr 8, 2022, 6:20 AM

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alright

mighty dew Apr 8, 2022, 6:20 AM

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so reet when you have a question like that the vowels are considered one letter

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so without the vowels there are 7 letters

vocal sun Apr 8, 2022, 6:21 AM

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n!/(d1! * d2! * d3!...) where nis the total number of letters in the word and d1, d2, d3, etc. are letters that repeat more than once in the word

mighty dew Apr 8, 2022, 6:21 AM

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thats not the same as what reet is asking?

vocal sun Apr 8, 2022, 6:21 AM

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Thats for any permutation of letters

candid grove Apr 8, 2022, 6:21 AM

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Okay yes they have put the formula

mighty dew Apr 8, 2022, 6:21 AM

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he has a group of letters to be next to each other

vocal sun Apr 8, 2022, 6:21 AM

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I know

candid grove Apr 8, 2022, 6:22 AM

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I don't understand the last sentance

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Total number of arrangements in which vowels are always together

mighty dew Apr 8, 2022, 6:22 AM

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yes

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so thats the total number of ways that the letters can be rearranged while having the letters together in one way or another

vocal sun Apr 8, 2022, 6:23 AM

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For the combination of vowels, you have 4 vowels, which can be arranged in a line 4! times. I believe the 2! comes from the places in the string of characters where 4 vowels can go but I may be wrong

mighty dew Apr 8, 2022, 6:23 AM

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the 2! is for repeats

vocal sun Apr 8, 2022, 6:23 AM

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Ahhh

mighty dew Apr 8, 2022, 6:23 AM

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so you do the 8!/2! for the original

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then multiply by arrangements for vowels

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which also has reapeats as established

candid grove Apr 8, 2022, 6:24 AM

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Why did we multiply?

mighty dew Apr 8, 2022, 6:24 AM

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bc it can go anywhere in the group of letters (constanants)

vocal sun Apr 8, 2022, 6:24 AM

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In 8!/2!2! you did not include the 4 vowels

mighty dew Apr 8, 2022, 6:25 AM

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yep^

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so u must inlclude the arrangements of the 4 vowels by multiplying

candid grove Apr 8, 2022, 6:25 AM

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Okay

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Got it

mighty dew Apr 8, 2022, 6:25 AM

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vocal sun In 8!/2!2! you did not include the 4 vowels

thanks for the help bro

vocal sun Apr 8, 2022, 6:25 AM

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mighty dew thanks for the help bro

no problem

mighty dew Apr 8, 2022, 6:26 AM

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hey u cant help me again rq?

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u dont know much about logger pro?

vocal sun Apr 8, 2022, 6:26 AM

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unfortunately I don't, sorry man ☹️

mighty dew Apr 8, 2022, 6:26 AM

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eesh ok all good

safe radishBOT Apr 8, 2022, 6:40 AM

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@candid grove Has your question been resolved?

safe radishBOT Apr 8, 2022, 6:55 AM

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void cosmos Apr 8, 2022, 7:02 AM

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mighty dew eesh ok all good

jimmy

safe radishBOT Apr 8, 2022, 7:02 AM

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void cosmos jimmy

void cosmos Apr 8, 2022, 7:02 AM

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how does this work

mighty dew Apr 8, 2022, 7:02 AM

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ye

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which part

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or do u mean how do u get that answer

safe radishBOT Apr 8, 2022, 7:17 AM

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@void cosmos Has your question been resolved?

void cosmos Apr 8, 2022, 7:22 AM

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mighty dew or do u mean how do u get that answer

how do u get the answer

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like the way they went from step 2 to 3

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multiplying

mighty dew Apr 8, 2022, 7:23 AM

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it looks wrong to me

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they should multiply brackets by 7/8

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then take that from 1

void cosmos Apr 8, 2022, 7:24 AM

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hmm?

mighty dew Apr 8, 2022, 7:25 AM

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yep i got -1.37

void cosmos Apr 8, 2022, 7:25 AM

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how did u solve it

mighty dew Apr 8, 2022, 7:25 AM

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so are u using calc

void cosmos Apr 8, 2022, 7:25 AM

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yea

mighty dew Apr 8, 2022, 7:25 AM

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ok so put 7/8(71+root3505/48)

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then 1 - ans for above

void cosmos Apr 8, 2022, 7:26 AM

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\

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no

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I want to understand

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how did they get

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that 113

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and - 7

mighty dew Apr 8, 2022, 7:26 AM

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oh ok lol

void cosmos Apr 8, 2022, 7:26 AM

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ye

mighty dew Apr 8, 2022, 7:28 AM

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bro i have no idea

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the 7 obv multiplies to the root3505

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but the 113 no idea

void cosmos Apr 8, 2022, 7:30 AM

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same

mighty dew Apr 8, 2022, 7:30 AM

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do u understand my othr working tho

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like how to do it

safe radishBOT Apr 8, 2022, 7:32 AM

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bronze moth Apr 8, 2022, 10:35 AM

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safe radishBOT Apr 8, 2022, 10:35 AM

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bronze moth

quasi bison Apr 8, 2022, 10:36 AM

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well you've highlighted the leading entries

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now you just need to tick the checkboxes for their coordinates

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is that something that's giving you trouble?

bronze moth Apr 8, 2022, 10:37 AM

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lmao

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i am dumb

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@quasi bison Thanks

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https://tenor.com/view/pump-pump-it-pump-it-up-gif-22218192

Tenor

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.close

safe radishBOT Apr 8, 2022, 10:39 AM

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lean otter Apr 8, 2022, 11:09 AM

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what are geometric means

safe radishBOT Apr 8, 2022, 11:09 AM

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lean otter what are geometric means

lean otter Apr 8, 2022, 11:20 AM

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<@&286206848099549185>

safe radishBOT Apr 8, 2022, 11:35 AM

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@lean otter Has your question been resolved?

safe radishBOT Apr 8, 2022, 12:05 PM

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@lean otter Has your question been resolved?

mortal meteor Apr 8, 2022, 12:36 PM

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@lean otter the geometric mean of two numbers a and b is $\sqrt{a \cdot b}$

flat frigateBOT Apr 8, 2022, 12:36 PM

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Alexander42

lean otter Apr 8, 2022, 12:36 PM

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oh

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ty

simple radish Apr 8, 2022, 12:39 PM

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I'm not entirely sure that is helpful in this problem

tidal imp Apr 8, 2022, 12:41 PM

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lean otter what are geometric means

If you don’t know the Geometric Mean Theorem for right triangles, I would go back to proportions of similar triangles

lean otter Apr 8, 2022, 12:43 PM

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an hour and a half pasted, I figured everything out

tidal imp Apr 8, 2022, 12:43 PM

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oh ok good

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What’s your answer

lean otter Apr 8, 2022, 12:44 PM

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b

tidal imp Apr 8, 2022, 12:44 PM

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That’s right

lean otter Apr 8, 2022, 12:44 PM

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yup

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now

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how do I find the perimeter of a triangle with 1 side and 3 angles given

mortal meteor Apr 8, 2022, 12:54 PM

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use that the angles are very special. You might think about ||how you can fit it into an equilateral triangle||

safe radishBOT Apr 8, 2022, 1:51 PM

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@lean otter Has your question been resolved?

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maiden tartan Apr 8, 2022, 2:17 PM

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Hello, I have a theory question. Is it possible for a formula to exist that for any complex function will yield all derivatives of that function?

safe radishBOT Apr 8, 2022, 2:17 PM

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maiden tartan Hello, I have a theory question. Is it possible for a formula to exist that for ...

maiden tartan Apr 8, 2022, 2:22 PM

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Or maybe better stated, can a function exist for any coords (x,y,z) that can yield (x,y,z,t) where t = z if you can bound it to another function that contains all possible paths for (x,y,z)?

potent bay Apr 8, 2022, 2:26 PM

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all derivatives?

maiden tartan Apr 8, 2022, 2:32 PM

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position and momentum.

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Is how I'm thinking about it anyway, I don't know the math speak equivalent.

potent bay Apr 8, 2022, 2:33 PM

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i dont rly understand ur Q, but im pretty sure the answer is no

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i mean that A formula exists for ANY function seems surreal

maiden tartan Apr 8, 2022, 2:35 PM

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I'm sorry I don't know how to ask it better. Perhaps not a single formula, but a formula that will give you all potential formulas is a better way to say it.

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Is it possible for me to post an image to help illustrate?

potent bay Apr 8, 2022, 2:37 PM

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i dont know if its possible to you, but the option is given to anyone 😄

maiden tartan Apr 8, 2022, 2:38 PM

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d'oh -- sorry I'm a discord newb, I thought it was restricted.

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For any complex function can I draw another version of it that yields more information about that shape in polynomial time?

Screen_Shot_2022-04-08_at_9.40.27_AM.png

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Then, using this magically function, turn that image, into it's derivatives:

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would be the derivatives of the smoothest line in the first picture.

Screen_Shot_2022-04-08_at_9.44.21_AM.png

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If I can ensure that every point is bound to some other know it all function:

Screen_Shot_2022-04-08_at_9.49.09_AM.png

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<@&286206848099549185>

safe radishBOT Apr 8, 2022, 3:08 PM

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@maiden tartan Has your question been resolved?

safe radishBOT Apr 8, 2022, 3:23 PM

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