help-38

[wraith hinge]

Can someone HELP

With 5part b

I dont understand how the answer is 19

For no(5 part b)

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@wraith hinge Has your question been resolved?

[zinc ginkgo]

Did you find the mean and standard deviation

[wraith hinge]

Ye

10.22

1.35

[zinc ginkgo]

What's mean + std dev =?

[wraith hinge]

11.57

@zinc ginkgo

[zinc ginkgo]

Yea I'm not sure why it's not 20

Are you supposed to assume the 15 people in the 11 OMR column follow some distribution

[wraith hinge]

well

[wraith hinge]

I tried doing unitary method

like even distribution

but I dont get 19

[zinc ginkgo]

Uniform distribution wouldn't give you 19 either

Yea sorry don't know

[wraith hinge]

it's okay

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[humble thistle]

how to factor like this

I tried factoring y to get x-1/y(x-1)-2x+2

but I cant cancel

[main sigil]

that's correct

try x instead

maybe you will have better luck

[humble thistle]

I tried that first but I dont know what i can do with that

[fleet bear]

Factor the -2x+2 as well

[humble thistle]

x-1/x(y-2)-y+2

[main sigil]

this works too actually

[humble thistle]

oh I see

[main sigil]

notice that -y+2 = -(y-2)

[fleet bear]

I legitimately did not notice that at first

[humble thistle]

x-1/y(x-1)-2(x+1)

x-1/(y-2)(x-1)

[main sigil]

And I legitimately didn't notice this would work lol

[main sigil]

yep, and now just cancel

[humble thistle]

thank you two, its done

thanks

.clos

.closee

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[humble thistle]

jesus

thanks

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[rotund grove]

find the cuberoot of (2+root5)
also of (2-root5)

[wraith stream]

what do you mean find

like find the first digits or

[rotund grove]

wait

[lusty delta]

no they mean take the cube root of those expressions

[rotund grove]

find:
the cuberoot of [[[[[[(2+root5) ]]]]]]] + the cube root of [[[[[[[[(2-root5)]]]]]]

[lusty delta]

go figure

[wraith stream]

yeah I know but there's no variables or anything that's just basic arithmetic you can plug into a calculator

[zinc ginkgo]

Why are there so many brackets here

[rotund grove]

to be clear

[zinc ginkgo]

That's less clear

[wraith stream]

are you supposed to like approximate them without the use of a calculator or something

[rotund grove]

sorry but the answer is 1

[wraith stream]

or like simplify it

[wraith stream]

???

ok wait I see

[rotund grove]

don't talk if u don't know

[lusty delta]

the solution i tell students for this problem is to begin let this expression = x

then find x^3 in terms of x

[wraith stream]

earlier you said to solve both roots which are irrational numbers, so I assumed you meant you were trying to approximate them

[rotund grove]

are uu a teacher?

[wraith stream]

now you're saying you need to add them

[rotund grove]

sorry

[rotund grove]

this

[wraith stream]

it's alr

[lusty delta]

no but this is very common exercise

[lusty delta]

btw it does not have very nice or simple solution but this way is best in my opinion

[rotund grove]

ok got it

math is interestng

[lusty delta]

u figured out how to see answer is 1?

[rotund grove]

What

how to see the answer?

u figured?

[lusty delta]

i am asking if you were able to deduce that the answer is 1

using the solution method i suggested

[rotund grove]

yeah express in terms of x the RHS and solve the cubic

[lusty delta]

okay good

[rotund grove]

One more

I was humbled today

Ignore the 'what is q here?' and just find the value of theta.

hery

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[west pine]

is this correct?

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[west pine]

.close

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[cinder lark]

!step

!help

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[cinder lark]

.help

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.help >step>

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[cinder lark]

there's a command that shows what step you are on

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gr

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[cinder lark]

.help commands

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What step are you on?
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[wind cloak]

!status

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[cinder lark]

THANKS

[pearl lotus]

Just type it out

[pearl lotus]

Pro

[cinder lark]

!status

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[cinder lark]

Four

I believe the function is one to one..

Here is why:

The function has a linear slope of -5

So it is decreasing

Meaning that the two values will be different and function wont have same outputs to two different inputs

Which is what a one to one function is

[cinder lark]

Can someone verify my logic

[pearl lotus]

Strictly decreasing*
Seems correct

[cinder lark]

alr

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[cinder lark]

thanks

oh

@pearl lotus

would this be the right inverse?

[pearl lotus]

Yes

[cinder lark]

they want me to sketch the graph of function and its inverse here

obv the function has 25 but the graph doesn't go to 25 im not sure what to do

@pearl lotus

[pearl lotus]

Draw the graph from 25 in your notebook and then see it's value at 20 and distance from y axis and we know that the slope is -5

[cinder lark]

could i just

do that in desmos

[pearl lotus]

that's cheating but since it's a linear function u can

[cinder lark]

well i dont understand what u mean by 20 and distance from y axis

This is what I have

Just not sure how to input that here:

[cinder lark]

ah

so basically (1,20)

ic

[pearl lotus]

yes

[cinder lark]

does that look right

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[tulip gyro]

what am i doing wrong here?

[zinc ginkgo]

it's not fully simplified yet

factor both 360 and 150

[rancid nebula]

egg!

[tulip gyro]

ohh i see thank you! I thought it had something to do with the simplification

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[urban copper]

\textbf{Let } (\mathbf{L}) : (\lambda (5, 0, -4) + (-9, 2, 8)), \quad (P = (4, 4, -5)) \quad \textbf{and} \quad (\mathbf{\Pi}) : (2x + y - 2z = 4).

\textbf{All the points on } (\mathbf{L}) \text{ that are at the same distance from } (\mathbf{\Pi}) \text{ as the point } (P) \text{ are:}
\begin{enumerate}[label = \Alph*)]
\item ((16, 2, -12)) and ((-14, 2, 12))
\item ((6, 2, -4)) and ((-4, 2, 4))
\item ((16, 2, -12))
\item ((6, 2, -4))
\end{enumerate}

[solid kiln]

ඞඞඞ

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[urban copper]

<@&286206848099549185>

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[urban copper]

<@&286206848099549185>

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[urban copper]

.close

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[wet shard]

I love ur username

Also close what

This channel isn't closed

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[hollow apex]

Hello everyone

[hollow apex]

Just a quick question about factoring

[solid kiln]

ルミナ

[hollow apex]

This cannot be factorized any further right?

[cosmic meadow]

Not over integers

[hollow apex]

ok ty!

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[icy hedge]

Can someone check this

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[lusty delta]

looks pretty good

[round relic]

it feels weird

[lusty delta]

they correctly set up a system of equations, correctly solved the system of equations, and arrived at a correct conclusion

i guess they could delete all the text they wrote at the start, but i don't really see what's weird about this

[round relic]

The hours can't be negative, can they?

Also he didn't really calculate the time

And T,C are probably intergers.

[lusty delta]

negative hours are indicated nowhere on this paper

[round relic]

If you push C way high then T would have to be negative. That satisfies the equations but definitely not the questions.

So 0≤T≤4; 0≤C≤6

And if you assume the hours have to be integers than there are only 3 different solutions.

(T,C) ∈ {(4,0);(3,3);(0,6)}

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[covert wolf]

What is area of line AD when there's triangle ABC while AB=AC and point D is over line AB while BD =5 ,FC=13

[stray drum]

!occupied

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[vivid glade]

where is F?

[covert wolf]

It is at highest height of □FEC when BD=5

[vivid glade]

triangle FEC, but where is E?

[covert wolf]

Over the line BC

[vivid glade]

so we're placing D on the line AB so that BD = 5, and we're placing E arbitrarily on the line BC. I don't follow where F goes

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[untold drum]

Or just show a sketch with the labels

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[covert wolf]

I had no idea how could I could explain exactly like the picture

[keen orchid]

@covert wolf

[covert wolf]

?

[keen orchid]

F가 어디 있다는건가요?

[covert wolf]

BE의 수직선에서 AC의 연장선과 만나는점

[keen orchid]

번역하시면서 중요한 정보를 많이 빼먹으신 것 같은데
원문 보내주시면 풀어볼게요

[keen orchid]

Problem)
For an isosceles triangle ABC with AB=AC, let D be the point on AB such that BD=5cm.
The line perpendicular to BC and passing through the point D intersects with the lines BC and AC at points E and F, respectively.
Given that FC=13cm, the length of AD.

[wraith hinge]

got the same

[wraith hinge]

한국인 이세요?

여기에 한국인이 있다니 ㄷㄷ

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[jagged light]

hi can someone help me with this:

[jagged light]

the task is to simplify this rational algebraic expression

it's my 1st time seeing 2 different variables used

i tried using polynomial division:

is this simplified enough

[lusty delta]

that seems good

[jagged light]

tbh now that i look at it

it looks like x is supposed to be y

if x is y:

im able to factor cleanly

thanks ill close this

.close

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[golden peak]

I don't understand how the total displacement for this is -200 m. I come up with -1400 m.

[carmine mauve]

So, he travels at a speed of 50 m/s for 50 s, and later -30 m/s for 120-80 s.

• How many metres did he travel forwards?
• How many metres did he later travel backwards?
• So, what's his total displacement?

[golden peak]

He traveled forward 1000 m then to get to -30 he would have had to travel another 1500 m (-1500)?

Would it not be (50s)(20 m/s) + (50s)(-30 m/s) ?

That gives me -500 but it's supposed to be -200

[marble nimbus]

120-80 isn’t 50

[golden peak]

Oh shit I didn't realize I typed 50. That would be why it's coming out -500

I thought I put 40, mb, thanks

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[misty night]

In the second line of this, what happens to the -1/2?

[vagrant marsh]

it gets factored

[left gazelle]

It's the common term basically

Take a look at the brackets

[misty night]

Thanks a bunch. Just lulled it over after being hella confused. Thanks again

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[shy valley]

How do u do this

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[zinc ginkgo]

Draw a triangle with one angle equal to sec inverse of x

sec(angle) = 1/cos(angle)

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[coral sedge]

Hello, does anyone know how to solve this second question?

[coral sedge]

This is the equations from the first

And this is what my teacher did, but i just though, if we do the same thing with the equation that has the cosine then the answer will be different, why's that?

@wraith hinge sorry for pinging but this is the question from yesterday if you're intersted

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[tired dust]

sorry, second question

recognize that sin can only be values of 0 to 1

as the value of sin get closer to 0, the value of Fb will get super high

when sin = 1, then Fb will just be 1

sin is 1 at 90°

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[naive nimbus]

(arrow over a + arrow over b) . arrow over C = bird0, -1,0 bird

@urban copper

[urban copper]

bird?

tf?

[naive nimbus]

the v

the v then

mb

the sideways v

looks like an arrow but its different

i solved it for u lol

[naive nimbus]

now u have to figure out how to solve it with what i gave u

lets see if u can do that

[urban copper]

<@&286206848099549185>

wdym

I need more handhold

[urban copper]

<@&286206848099549185>

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[quiet turret]

$f(x)=2sin(x)-2 \quad \quad \quad \quad 0 \leq x \leq \pi$

[solid kiln]

pixel

[quiet turret]

what would be the increments

when sketchinng this

like each poinnt

[full dock]

what do u think

[quiet turret]

uh

💀

im asking

so

idk

so since the period is 2pi

with that domainn

we'd draw only up to pi

but idk in whatincremennts

idk how that would work

[restive rose]

See what you get when x = 0, pi/2, pi

With 2sin(x), you would just be streaching it vertically, so that it goes between -2 and 2. With 2sin(x) - 2, you're translating it down by 2.

[quiet turret]

ok ya

we reach peak at pi/2

and then intercept at pi

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[sage anvil]

guys is this good?

appareantly its not

f) 35.714

was correct answer

:3

not b) 30.000

[strange ice]

can u post the original queation pls

[sage anvil]

ok 1 second

[strange ice]

from what i see u worked that out correctly

but something couldve gone wrong before

[sage anvil]

So 40,000 money is inserted as the (pi) which is profits

profits must be minimally 40,000 for dividends to be paid 40000

and q(pc-tv) tv- variable cost and pc-price of unit sold q - volume of bussines activity

-50000 is fixed costs

[strange ice]

hmmmmm

what is pi? is that a variable?!

[sage anvil]

it is profits

which must be 40,000 money in order for 40,000 dividends to be paid

[strange ice]

damn i have never seen pi used as a variable

[sage anvil]

in economics its often used

[strange ice]

oh eco

i dont do that so pls edscribe what the question means

[sage anvil]

i might have forgot tax

i try calculate now

[strange ice]

ah

[sage anvil]

yes tax

.close

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@blissful helm Has your question been resolved?

[trim jolt]

@blissful helm Has your question been resolved?

[obsidian pine]

i think it might be because row 4 is all zeros, thus no matter what column 4 has (its 75% all zeros too), the multiplication doesnt contribute anything to the final numbers in the matrix B, so you can just ignore them

welp i havent touched matrices for a while, so it might have to do with how you found the two matrices, like specifically looking for matrices with zeros in row 4 or column 4

but in general no you cant do this to most matrices

unless the zeros are there

[trim jolt]

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[quiet turret]

$\frac{cos(2x)}{sin(2x)}=cot(x)$

[solid kiln]

pixel

[quiet turret]

i have to prove LHS = RHS

how do i do it

[wraith hinge]

https://www.mathematics-online.org/inhalt/aussage/aussage101/

[split chasm]

you can't
because that isn't true for all x

[quiet turret]

wdym

[queen dew]

It is not an identity

[quiet turret]

really?

the question tells me to prove the identity

[split chasm]

can you take a pic?

[quiet turret]

sure but theres legit no other info

[split chasm]

did you copy it down correctly?

[quiet turret]

es

[somber ginkgo]

if that's what the question says, probs best to ignore it cus the identity isn't true

[quiet turret]

ok then

thank u

what about

sin(x+y)= sin(x)cos()+cos(x)sin(y)

oh this one is easy lol

one ste

step

[lone saffron]

the proof is geometric

[quiet turret]

what does that mean

[quiet turret]

ah ok makes sense

[lone saffron]

you need to prove the identity geometrically

or maybe you can use induction

[split chasm]

were you being asked to prove the identity for that

sin(x+y)= sin(x)cos()+cos(x)sin(y)
or just state it

[quiet turret]

Use angle sum formulas

Prove using angle sum formulas:

and then it stated the question

what are these questions lol

[split chasm]

can you take a pic of what's going on?

[split chasm]

cause that's mega cyclic
using the angle sum identity to prove the angle sum identity

[somber ginkgo]

ahaha what a sheet

the last question is legit

[quiet turret]

dude i need practice for trig identities so badly

like proving them

and these are the papers that my teacher is providinng

like?

😭

[split chasm]

i'd recommend finding a trig identities worksheet online or from a book

[lone saffron]

only 1 f**king step and it's done

[quiet turret]

so what do u want me to do for the questionn

[quiet turret]

lol

[split chasm]

state what i said

[quiet turret]

whats mega cyclic

using the angle sum identity, prove the angle sum identity

😭

[somber ginkgo]

*2!

which is slightly more than 1!

[quiet turret]

ya numerator can be simplified

[split chasm]

circular logic is better terminology

[lone saffron]

stop using factorials😭

[somber ginkgo]

still works even with factorials!

[lone saffron]

yeah that's that

[quiet turret]

well yeah im done with this paper now

time to do literature quote analysis

fun!

😔

save me

[split chasm]

mistyped earlier

[quiet turret]

allg

thank u for the help guys

.close

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[fallen sphinx]

Hi! I'm kinda stuck on this logarithm question-

[fallen sphinx]

Is this step correct? Or-

[whole coral]

Does that ${^{2}\log 5}$ mean log base 2 (of 5)?

[solid kiln]

@whole coral

[fallen sphinx]

Yep

[whole coral]

In that case, no, this becomes $(2^{-1})^3$, bear in mind you can e.g. move and put things in brackets

[solid kiln]

@whole coral

[fallen sphinx]

Ohh

Icic

Lemme just fix that rq

[cinder badge]

i forgot this notation and thought it was tetration

[whole coral]

It's somewhat less common, but I've seen it before for logs

Of course, the one time you assume it's log base 2, it's actually tetration

[cinder badge]

yea me too i saw it back like 3 4 yrs

[fallen sphinx]

Finally found the answer 😭😭
Tyyy

.close

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[fallen sphinx]

I'm back--

[fallen sphinx]

That I think I butchered

That's my process so far

[still rose]

are the numbers on top of the log the base?

[fallen sphinx]

Yep

[still rose]

alright

[vagrant marsh]

you want y/x

[fallen sphinx]

Oh

I messed that one yp

Up

[vagrant marsh]

you got the right answer, just flipped

[fallen sphinx]

😭😭

[fallen sphinx]

Wait right answer?

[vagrant marsh]

yeah, what is log(1) in any base?

[fallen sphinx]

Oh yeahh

Ohhh

Oml I'm so dum

Excuse me while I close this 😭😭

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[remote ingot]

$\int\limits^{\frac\pi2}_{\frac\pi3}\frac{dx}{\sqrt{1+\sin x}}=$

[solid kiln]

mooN boY

[remote ingot]

I'm not sure where to even begin with this one

when i input it to some free step by step calculators it seems to be somewhat above my level yet it's from one of my exams

[trim jolt]

@remote ingot Has your question been resolved?

[charred trail]

maybe try rewriting sin(x) as 2sin(x/2)cos(x/2) and use the pythagorean identity?

see where it takes you i suppose!

or u=1+sin(x) and some other trig identity

[remote ingot]

nothing comes to my mind really

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[remote ingot]

.reopen

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✅

[remote ingot]

umm... <@&286206848099549185> preety please...

[wraith hinge]

what do you need help with?

[remote ingot]

this integral

[bronze ibex]

try multiplying num and denom with root of 1 + sin x and then try to make denom cos^2x form and split up num

[remote ingot]

i'll try that

what exactly do you mean by cos^2x form?

[hollow panther]

hello

i am really struggling with a maht problem

[limpid dawn]

open a channel

[hollow panther]

alr thanks

[trim jolt]

@remote ingot Has your question been resolved?

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@remote ingot Has your question been resolved?

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[sage anvil]

guys does it matter when choosing which sets of y1,x1 and y2,x2 will be in this formula?

[sage anvil]

for example value y1 = 20% gives me 500 something which is x1

value y2=21% gives me 550 something which is x2

does it matter if i choose y2 to be 20% and y1=21%

would y = change

for me sometimes it change sometimes not idk if mistake

and for x some constant number

[zinc ginkgo]

it doesn't matter

[sage anvil]

😮

[zinc ginkgo]

just kidding yes it matters

[sage anvil]

😮

😮

[zinc ginkgo]

i thought you meant swapping (x1, y1) and (x2, y2)

[sage anvil]

so y1 always has to be smaller?

the smaller % value

i give picture 1 second

I calculated this as 27,61%

however its not that

its actually 21,28%

[zinc ginkgo]

what is "this"

[sage anvil]

IRR = 27,61% from the formula you see down right

and left to it is input variables

from the formula

when i put y1 to be 21% and x1 to be 2,540 and y2=22% and so on...

then i got correct 21,28% = IRR

the unknown

[zinc ginkgo]

probably just rounding error

[sage anvil]

hmmm

[zinc ginkgo]

keep all dcimals

[sage anvil]

oh now i got it right

idk why error i did 3 times got wrong

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[west jacinth]

This is more of a conceptual thing but this proof isnt computing

[west jacinth]

I dont understand how they reduce the fractions down to zero

• why they do that

[prime lynx]

Divide top and bottom by highest power

[west jacinth]

i got that

I dont understand the ending

how does this follow

[prime lynx]

1/100000000000000

If we continue increasing the denominator

What do you think the expression will approach

[west jacinth]

0?

[prime lynx]

Yup

[west jacinth]

But it will never get there?

So how do you so confidently still just say "0"

[prime lynx]

But that's its limit(extreme)

[west jacinth]

so it will approach zero

thats the jump

showing that as the denom increases it will approach zero?

[prime lynx]

Yes

[west jacinth]

and that tells us the limit approaches zero?

[prime lynx]

Yes

[west jacinth]

cool

thanks

infinity is weird

sorry about that

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[prime lynx]

Lol

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[trim jolt]

@urban copper Has your question been resolved?

[left oriole]

so you want Ab1 + Bb2 + Cb3 = 2Ae1 + 2Be2 + 2Ce3, yes?

where b1,b2,b3 are the three vectors in B

and e1,e2,e3 is the canonical basis

[urban copper]

how so?

[left oriole]

A,B,C are the coordinates w.r.t basis B, and 2A,2B,2C are the coordinates w.r.t the canonical basis

(sorry, I re-used the letter B but hopefully it's clear anyway)

[urban copper]

okay and how do I find the coordinates with respect to basis B

[left oriole]

well the only unknowns here are A,B,C

you know b1,b2,b3,e1,e2,e3

so you should be able to express this in the form Mx = y

where M is some matrix and x = (A,B,C) (column vector)

and y is a vector

then see if you can solve for x

[trim jolt]

@urban copper Has your question been resolved?

[urban copper]

okay

how do I do that

[urban copper]

.close

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[finite lynx]

I was wondering if the values were pi/6 11pi/6

[finite lynx]

and I wasn't sure how to solve for the negative values

do I just make pi/6 negative and call it a day?

I understand how to get here

[quasi sorrel]

yes the negative values should be the same

[finite lynx]

oh ok

so just confirming my answers are right

[hearty plank]

Yes because cos of -x is cos x for all real x

[finite lynx]

what about if it was sin or tan?

would it always be the same?

[finite lynx]

also do you have any tips for trig

[hearty plank]

No

[finite lynx]

😦

[hearty plank]

I'm beat in it too

[finite lynx]

was I right at least?

[hearty plank]

Yes

[finite lynx]

and what about for sin

is sin x = - sin x?

[hearty plank]

Yes

-x

[finite lynx]

so both are teh same?

wait what is that supposed to mean?

[hearty plank]

But yeah for sine it's not the same

So you know the unit circle?

[finite lynx]

kinda not really

[hearty plank]

Or the circle of teaching trigonometric

[finite lynx]

whats the trick for sin

if this situation

was sin

what happens?

[hearty plank]

I use the unit circle for it

[finite lynx]

how exactly?

[hearty plank]

So do you know the quadrants where each function is positive?

[finite lynx]

I know about cast

[hearty plank]

Cast, okay

So sin in positive in both quadrants 1 and 2 yes?

And sine means height by radius yes?

So just taking equal height on both sides you get sin (180 -x) = sin x

Honestly the circle will get everything solved

[finite lynx]

so do I just make a circle and everythings good?

I just don't understand hwo to do it with negative pi

[finite lynx]

sorry to ping you but I want to confirm that my answer is. correct

[hearty plank]

Can you draw the circle for sine

And the angles where they equal ✓3/2

If so, then there's a method to go around it in circular form. I'm unsure how to explain in typing.

[finite lynx]

I did go around it but when I don't understand what happens between the ranges of 0 to -2pi

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[marsh forum]

Now I feel this is $[0,\infty)$

[solid kiln]

Veni, vidi, perii

[marsh forum]

now to prove this trivial fact

We first attempt to prove that $\bigcup_{i\in \N} [0,i+1] \subseteq [0,\infty)$

[solid kiln]

Veni, vidi, perii

[marsh forum]

hnn

Any interval [a,b] , a,b \in \W are contained between any two real numbers

so this fact is true

is this fine?

.close

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[grim sparrow]

I don't understand what you're saying

any interval is contained b/w any two real numbers?

.reopen

[trim jolt]

✅

[grim sparrow]

@marsh forum sorry for the reopen, but I suggest just proving it how you would prove any set inclusion

to show A \subseteq B, take x \in A and show that x \in B

[marsh forum]

Yeah, will try.

As I haven't done many such problems before, Ill post it on MSE so that I have a ready reference

sorry

I get what you mean

[grim sparrow]

well...

[marsh forum]

but hope you understand

As in discord is great for most problems

but I can't loo up problems randomly

when I want to

[grim sparrow]

I really do think that you can prove this inclusion right here and right now, but I will respect it if you don't want to do it rn

it's quite literally a 2-liner

[marsh forum]

I know how to do it, I think

[grim sparrow]

would you like to try rn?

[marsh forum]

Okay

let $x\in \bigcup_{i\in\mathbb{N}}[0,i+1]$

[solid kiln]

Veni, vidi, perii

[marsh forum]

so $x$ is of the form $[0,a]$, $a\in \N$

[solid kiln]

Veni, vidi, perii

[grim sparrow]

x is not an interval

x is a real number

[marsh forum]

mhm

okay

What's wrong with me

[grim sparrow]

nothing is wrong with you

[marsh forum]

okay, so $x>0$

[grim sparrow]

well...

x is not going to be negative

it's in the union of all those closed intervals

[solid kiln]

Veni, vidi, perii

[grim sparrow]

none of which is negative

but this isn't really the important thing about x

[marsh forum]

Yeah

but I'm coming to the important point now

any positive number lies between 0 and a natural number

[whole coral]

(hint: you can add a few words here that will make the statement correct )

[marsh forum]

so this proves inclusion in one direction, I suppose

[grim sparrow]

you haven't told me why

so what if x is in between 0 and a natural number?

me dumb, dunno what that tells me

explain it to me like idk what's going on

[marsh forum]

so x>0

and for any positive real number, you can always find one number geq 0 and another whole number greater than it

[grim sparrow]

I think I know what you're trying to say, but the wording isn't great

[marsh forum]

I mean I don't have to prove these thoerms

as in there's a number between any..

[grim sparrow]

you probably don't, yeah

[marsh forum]

I think this is somewhat like the archemedian property

[grim sparrow]

but your wording has not told me enough yet

Let $x\in \bigcup_{i\in\mathbb{N}}[0,i+1]$. Then $x \in$ ?

[solid kiln]

higher!

[grim sparrow]

this is good btw (if you're saying what I think you're saying )

it'll tell you what x \in

[marsh forum]

some interval [0,i+1]

[grim sparrow]

yes

more specifically, there exists a natural number a such that 0 <= x <= a

so x \in [0, a]

then the next thing is to show that x \in [0. infty)

[marsh forum]

x is a real number, right

[grim sparrow]

yes

[marsh forum]

any for any real number, one can find a natural number less than it, and one greater than it

[grim sparrow]

less than or equal to, and greater than or equal to :p

but yes

[marsh forum]

hmm

now to prove the backward inclusion

right

[grim sparrow]

huh, you finished one side of the proof?

[marsh forum]

I think so

[grim sparrow]

you didn't state the last line here

[marsh forum]

I also think I'm going really slowly

3 problems in 3 hours is really bad

[marsh forum]

Which is?

[grim sparrow]

why is x \in [0, infty)?

[marsh forum]

$\bigcup_{i\in\mathbb{N}}[0,i+1] \subseteq [0,\infty)$

[solid kiln]

Veni, vidi, perii

[grim sparrow]

you know that x \in [0, a] for some natural number a

so why is x \in [0, infty)?

[marsh forum]

uh

Not sure

I think I'm having a brain fart

[grim sparrow]

well, think set inclusions again

[marsh forum]

for any given natural number, one can find a real number less than it, and one more than it

[grim sparrow]

this doesn't tell me anything

it just tells me that x \in [a - 1, a]

[marsh forum]

Then I'm not sure

[grim sparrow]

but we already know that x \in [0, a]

[grim sparrow]

well, [0, a] \subseteq [0, \infty), do you agree?

[marsh forum]

Yes

[grim sparrow]

then since x \in [0, a], and [0, a] \subseteq [0, \infty), we have x \in [0, infty)

[marsh forum]

Well, I'll have to prove that first,no?

[grim sparrow]

what is there to prove?

okay, fine

if x \in [0, a], then 0 <= x <= a

and y being in [0, infty) means that 0 <= y

this just implies immediately that x \in [0, infty), because it satisfies the condition of being in [0, infty), so [0, a] \subseteq [0, infty)

[marsh forum]

Yup

okay

[marsh forum]

How's this related to the problem though

oh

okay

[grim sparrow]

mhm

[marsh forum]

so this concludes the foward proof?

I'll close this for now

the lure spivak is too hard to resist

I'll do this in the evening for sure. no calc then!

LA and proof writing

.locs

.close

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[twin yoke]

One message removed from a suspended account.

[twin yoke]

One message removed from a suspended account.

[exotic pine]

$$(\frac{1}{2^n+1})\cdot\frac{1}{2}$$
$$(\frac{1}{2^{n+1}})\cdot\frac{1}{2}$$
$$(\frac{1}{2^n}+1)\cdot\frac{1}{2}$$

[solid kiln]

Skill_Issue

[exotic pine]

which one of these do you mean?

[twin yoke]

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[exotic pine]

whst do you want to do with it?

simplify?

[twin yoke]

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[exotic pine]

actually, just multiply the fractions like normal

$\frac{1}{2^{n+1}\cdot2}$

[solid kiln]

Skill_Issue

[twin yoke]

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[exotic pine]

remember 2=2^1

and remember your exponentiation rules

[twin yoke]

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[quasi sorrel]

what's $2^2\cdot 2$

[exotic pine]

no

[twin yoke]

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[solid kiln]

Carter

[twin yoke]

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[quasi sorrel]

review your exponent rules

[twin yoke]

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[peak ridge]

How do I guess the instantaneos velocity for 19??

[peak ridge]

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[opaque sleet]

Is this correct? I just need confirmation if my Cross Product is correct

[left oriole]

i found one mistake

[opaque sleet]

what is it?

[left oriole]

double check your result for the first determinant

actually check all three

[opaque sleet]

38i?

[left oriole]

you seem to be doing ad + bc instead of ad - bc

[opaque sleet]

hmmm

I see

welp that solves my problem, thanks @left oriole

[left oriole]

np, cheers

[opaque sleet]

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[versed crypt]

for cii, i did 5! * 6P4 why is that wrong?

[hearty plank]

What answer is given?

[versed crypt]

5! * 4!

[unique minnow]

This is very specific to this problem, but the idea is that if you put the 5 consonants in a bag and place them in some order, you get 5! different configurations. I think you got that right.

Since there is exactly one less vowel, the only way you can separate the consonants is if you place the vowels in the 4 spaces between the consonants. There are 4 choices for the first space, 3 for the second and so on, yielding 4! ways of choosing the vowels.

You can see it as choosing the word made up of the 5 consonants (5!) and choosing a word made of the 4 vowels (4!), and then weaving the vowel in between the consonants, if that helps visualizing.

[versed crypt]

ohh that make sense ty

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[zenith oriole]

can someone explain to me why the answer to this isn't 0? (second week taking calc, I might've overlooked something obvious, sorry)

[swift ice]

how you approached?

[split chasm]

you're not supposed to evaluate the limit for the denominator yet

[ancient edge]

from the left you need to use one of the formulas from the piecewise

[zenith oriole]

... oh my god so I'm not stupid, just rushed lmao

sorry for bothering y'all

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[zinc wagon]

what is the approach for this? I don't have any idea where to begin

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[zinc wagon]

sorry guys i closed it by mistake

[zinc wagon]

.

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[zinc wagon]

<@&286206848099549185>

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[zinc wagon]

ok i will close this i suppose don't wanna keep it occupied

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[zealous sigil]

Hi, would anyone know how to find the derivative of this without using the chain rule or a formula

[zealous sigil]

I got this so far but I am not sure where to go from here

[marble wharf]

why would you want to do this without the chain rule

[zealous sigil]

It's a homework problem. Since they were showing us the 'proof' for inverse trig functions like arcsin and arccos, and now they want us to extend that to this one

[marble wharf]

so they also did arcsin(x^3) or something like that?

[zealous sigil]

No

They only did arcsin and arccos

and arctan

[marble wharf]

are you sure that you arent just supposed to find the derivative of arctan with those tools?

and then combine it with the chain rule?

[zealous sigil]

Yes, unfortunately it says we will get no marks if we use the chain rule

[marble wharf]

yikes

[near quiver]

you got a demon instead of a teacher

btw it is an interesting question (i also don't have an idea)

[zealous sigil]

Haha, he's pretty good but this question is pretty tricky

[wraith hinge]

I wonder how they did arcsin without chain rule? Can you show us here, maybe we'll have some idea

[marble wharf]

well doing the inverse is doable

there is the inverse function theorem which basically tells you the derivative

but the x^3 is quite a yikes

[marble wharf]

(and presumably what was shown in class is essentially the proof applied to this specific case)

[wraith hinge]

isn't inverse function theorem basically chain rule?

[marble wharf]

oh fuck is it? i dont remember the proof that well

now that you say it, yeah probably

[zealous sigil]

Hi, they did something like this for arcsin

[marble wharf]

thats basically chain rule but hidden

chain rule allows to treat dy/dx as a fraction like that

[zealous sigil]

Yeah, honestly it's all pretty confusing and I don't even know why they asked something like this

I just got this and I'll put it down and whatever happens happens I guess

[marble wharf]

but I mean, you definitely can't replicate that for your thing

ah well I guess you can

that works

probably what they want to hear

[zealous sigil]

Ah well that's good. I'll just put this down then.

Thanks so much for the help, have a great day.

.close

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[vestal summit]

In the original limit of n we want the limit at n -> inf?

[vague walrus]

0

it said find f(0)

and that fn is continous

and that defined on all r and gave that definition

[vestal summit]

Wait so we're solving this, right?

[vague walrus]

yeah

for f(0)

i made f(n)

[vestal summit]

f(0) is when n = inf

[vague walrus]

i am not sure if i can put inifnity in the function parameter can we?

[vestal summit]

Well, I meant that $\lim_{n \rightarrow \infty} \frac{1}{4^n} = 0$

[solid kiln]

EQUENOS

[vestal summit]

So $f(0) = \lim_{n \rightarrow \infty} (\sin e^n)e^{-n^2} + \frac{n^2}{n^2 + 1} = 1$

[solid kiln]

EQUENOS

[vague walrus]

hmm we can do that

ohh since it is a cont fn

right

😭 not sure

[vestal summit]

Well it's just a sequence limit

Idk if that's what the task asked to do but yeah

[vague walrus]

not sure if i understand

[vestal summit]

First term vanishes to 0 and the second term approaches 1

[vague walrus]

i know how to eval the limit

[vestal summit]

oh

[vague walrus]

im not sure how u can

do that

since the function isnt even defined for n

and is the limit applied inside the function parameter

f(lim here)= lim here?

any recommended reading?

[vestal summit]

Yeah it's related to the properties of limits

If f is continuous then lim f(a_n) = f(lim a_n)

[vague walrus]

oh right right

that thing

we do for 1^ infintiy

[vestal summit]

Oh I see what they wanted you to do