help-13

[harsh nova]

can someone please explain why this is the case?

The thing I marked

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[cedar kiln]

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[weak mountain]

Let $f:\Omega\to R^n$, $\Omega$ open in $R^m$. Show that the frechet derivative, if it exists at $a\in\Omega$ is independent of the norm on $R^n$ or $R^m$

[wraith dagger]

Mirinim

[weak mountain]

What is this asking me to show? We’ve already proven the equivalency of norms on finite dimensional space a while back

[crimson sedge]

(it might be worth asking in one of the analysis channels too)

[cedar kiln]

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[main jetty]

are they doing matrix multiplication on the matrixes?

I'm getting a different answer

[cedar kiln]

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[manic pumice]

help

[slow thicket]

Plug in f(x) and just simplify

What do you have so far

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[sleek yoke]

hi

okay so to get a i did dy = 3ydt

1/ydy = 3dt

integrate

lny + c = 3t + c

etc etc

[chrome zinc]

why are you not just integrating this?

in terms of t

maybe i'm misreading smth

dy/dt is the first derivative

integration of that would give you y(t)+C and then u have to solve for C

[sleek yoke]

oh shit i see so ive just gone about this wrong

[soft zealot]

Well those cs are two separate constants added in, but they reduce to that K constant symbol

You know what it’s gotta look like, and K*f(2)=400

Find K

[sleek yoke]

K*f(2) = 400 yeah but

wait

thats what i been doing

i probably simplified wrong or something ill try that again

[soft zealot]

K = 400/f(2) right?

[sleek yoke]

yes

[soft zealot]

So what’s f(2)

[sleek yoke]

e^6

[soft zealot]

So K=400/e^6

What’s Kf

[sleek yoke]

ffs

i kept puttign in

400/e^6

and didnt multiply by the original f(t)

i just put K in alone

[soft zealot]

[sleek yoke]

i was like

theres no way my K is wrong

completely forgetting about the rest of the function

appreciate it man

or woman

or person my fault

nonetheless appreciate it

lmao

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[cedar kiln]

@plain carbon Has your question been resolved?

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[sonic patrol]

Anyone here familiar with vectorized python functions? I'm currently stuck in a runtime error

[crimson sedge]

sorry i just wanna vent how fucking annoying sinusodial functions are like god damn my mistakes are always so small and accidental its pissing me off

[sonic patrol]

lol i feel ya

[lethal jackal]

probably should ask a different server or at least post your error

[sonic patrol]

you recommend any servers? this is the best place i know of lol

[lethal jackal]

idk maybe some programming servers or the cs server in #old-network

but certainly nobody's going to be able to help you if you just say "my code is stuck in a runtime error"

[cedar kiln]

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[balmy crag]

I was wondering how to use this capture recapture method

[cedar kiln]

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[magic coral]

How do I solve this

[tame wraith]

what?

wdym solve

theres no variable to solve

[magic coral]

I have to prove that lhs = rhs

[tame wraith]

@magic coral cant you use these identities

[magic coral]

Nope I can’t use those

The teacher hasn’t taught us that

Well the answer comes but ig it can be solved in another way as wel

[cedar kiln]

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[soft loom]

DONT UNDERSTAND THE QUESTION

TRIED MANY WAYS BUT MY ANSWER IS DIFFRENT

[lethal jackal]

where do they get these questions

[soft loom]

MY TEXTBOOK

[lethal jackal]

im curious what textbook is it

also you should probably show what you tried

[soft loom]

ITS NELSON TEXT BOOK

AND FOR A)

[lethal jackal]

wait what's the textbook called

[soft loom]

nelson calculus and vector i think

I USED THE FOMULA lim h->0 f(a+h)-f(a)/h for the whole question a

[lethal jackal]

yeah no

can you think about what "average velocity" means?

how would you find your average speed if you drove 2500 miles in 5 hours?

[soft loom]

2500/5

[lethal jackal]

so in general, how might you find the average velocity of something over a time period?

[soft loom]

for 8 sec?

i mean for 0 and 8?

[lethal jackal]

let's say from the time period t = 0 to t = 1

[soft loom]

oh

i see

tysm

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[sturdy bloom]

I'm just not sure if my area equation is right

[copper crest]

Area is just LW ryt

Where l is length of large rectangle

[sturdy bloom]

huh

what

[vague rapids]

See, you can find general value of l and w

[sturdy bloom]

So does it even matter that there'd a border in the middle?

can't I just do l×w

[vague rapids]

yeah that'll work the same

[sturdy bloom]

so why did I even need the perimeter

[vague rapids]

Maybe to find general value of l and w

Like this

We got both l and w in terms of k

Which may help to find the max area

[sturdy bloom]

uhm

Now im confused

Should I just continue solving like that?

[vague rapids]

I am unclear ahout the atea function

Could you give a clue about it

[sturdy bloom]

what?

[vague rapids]

Lile what is an area function in your terms?

[sturdy bloom]

length x width?

[cedar kiln]

@sturdy bloom Has your question been resolved?

[vague rapids]

Okay I have got it

[vague rapids]

This just gives area in terms of either length or breadth which as far as I know won't help to find the function for maximum area

[obsidian coral]

Don't give out answers or do the work for people

[vague rapids]

He won't understand in text form

[cedar kiln]

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As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[cedar kiln]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

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[hollow terrace]

How To Solve Simultaneous Linear Equations Through Substitution Method?

[dire geode]

Do you have an actual problem

[hollow terrace]

Yeah, One Second

3x - 2y = -2y
2x - y = -8

Solve To Find the value Of x And y Via Substitution

[royal loom]

solve an equation for either y or x (in terms of the other variable)

and then substitute that into the other equation

[hollow terrace]

Can You, Give Me An Example With The Question Above

I Know The Elimination One, I Need To Learn Substitution Method...

[vague rapids]

Find the value of x in terms of y

In equation 1

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[crimson sedge]

I don't know how to determine if a function is continuous let alone the values of x.

can somebody help me out with this please?

[wide lintel]

The function is not continuous where the denominator is equal to zero

[crimson sedge]

does the denominator matter at all?

[crimson sedge]

how do I find that for example for question a)?

[wide lintel]

X^2 + 1 = 0

Solve that

That is where there will be a hole in the graph because the function cannot exist if there is a divide by 0

[crimson sedge]

negative and positive square root of 1?

you can't take the square root of a negative number though right?

[crimson sedge]

mhm.

[wide lintel]

Yes unless you include imaginary numbers which don’t matter for this particular question

[crimson sedge]

okay

so how would I write that down?

[wide lintel]

Usually in interval notation

[crimson sedge]

so it really doesn't matter what is in the numerator

so long as you find what makes the denominator = to 0?

[wide lintel]

This, or vertical asymptotes

[crimson sedge]

how to find those?

does C have a vertical asymptote?

[wide lintel]

I know there is a way, I forgot how to do it algebraically. You can usually tell if you just graph it

[crimson sedge]

okay

ty sm for explaining it

I will try and do c on my own then and I'll come back if I can't figure it out!

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[versed yacht]

hey, shouldn't the numerator be negative here too, making the whole thing positive?

[versed yacht]

its just limits using l'hopital

checked many online solutions and they all seem to say otherwise, am i tripping

[upbeat lotus]

It should but they have cancelled two negatives

$\frac{\frac{-1}{2\sqrt{5+x}}}{\frac{-1}{-2\sqrt{5-x}}}$

[wraith dagger]

Offline due to exams

[vague rapids]

what

[upbeat lotus]

Notice there's -x in the denominator inside the sqrt function

When you would use the chain rule to differentiate that

You will get a extra -

In this question they cancelled that

,w d/dx(-√(5-x))

[wraith dagger]

Results provided by WolframAlpha

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

Requested by 𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛#6985

[upbeat lotus]

See it gives the same result

Then the numerator would be negative if you do it this way

[upbeat lotus]

I'm ignoring the 1 cause it is useless here

[versed yacht]

oh i get it now, forgot about using chain rule for the -x

that makes sense

tysm!

[upbeat lotus]

Welcome

[versed yacht]

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[lapis basin]

Need help proving this

[cedar kiln]

@lapis basin Has your question been resolved?

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[cedar kiln]

Channel closed

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[lapis basin]

.reopen

[vague rapids]

What is even the question?

[cedar kiln]

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[solemn bronze]

I'm struggling with the set notation in the 2nd definition

[solemn bronze]

https://i.imgur.com/VBr97Zu.png

https://i.imgur.com/0OPnzVH.png

that part

what exactly does $t_{i-1} \le x \le t_i$ mean?

[wraith dagger]

math

[solemn bronze]

I know t_0 to t_n are the points in the partition

but they start at 0 and go to n

where is i defined and why are we taking i-1

[burnt vapor]

i goes from 1 to n

So m_1 = inf {f(x) : t_0 ≤ x ≤ t_1}

Et cetera

t_0, t_1, t_2, ... , t_n are points in the interval

[solemn bronze]

wait so m_1 would be the infimum of f(x) from f(0) to f(1)?

[burnt vapor]

No

[solemn bronze]

well the infimum of the set of results of f(x) evaluated from f(0) to f(1)?

[burnt vapor]

From f(t_0) to f(t_1)

[solemn bronze]

a rightr

the way t_0 ... t_n is defined, there are infinitely many ts right? it's "n" aren't natural numbers or anything

[burnt vapor]

No, there are finitely many

There are exactly n+1

n is a positive integer

[solemn bronze]

but isn't it all points from "a to b"

[burnt vapor]

No

You are trying to approximate the area

So you pick a finite number of points

[solemn bronze]

oh it says it right in the first defn "is a finite collection of points" 😅

I guess I'm lost on how you pick the number of points now

I mean I guess we never do need to pick the number of points

at least not to understand the rest of it

[burnt vapor]

You pick an arbitrary number of points

Lates you'll want to take limit when n → ∞

[solemn bronze]

ok I wanna confirm one more thing on this part that for sure I'm getting right

this part here, before we take th einf/sup of it https://i.imgur.com/L4XaPvw.png

let's say we're evaluating for i = 1

the set is defined as the outputs of all values of f(x) where x is between t_0 and t_1 (inclusive)

I'm having a little trouble forming this question

what I'm trying to say is t_0 and t_1 are just 2 points arbitrarily far away based on how large n is

so even though n is finite

aren't there still infinitely many points between t_0 and t_1 itself?

I'm just trying to get a better understanding of what exactly is in that set defined there, and if it's the outputs of a function between 2 x values then it seems like it should be infinite

even if we define [a, b] as [0, 100] and set n = 100 so that t_0 = 0 and t_1 = 1, there are infinitely many points between 0 and 1 right?

[burnt vapor]

Right

[burnt vapor]

This set is infinite

Well not always, f might be a constant function

[solemn bronze]

right

[burnt vapor]

But I'm quite sure that if f is continuous that set will always be an interval

[solemn bronze]

wdym by interval?

[burnt vapor]

[c,d]

[burnt vapor]

The point is that when n becomes larger, we expect this set to be smaller, in the sense that its infimum and its supremum get closer

[solemn bronze]

right

[near jolt]

How do you describe the language for the RE baba ? 1star0star1star0star .

I know what it can consist of... But cannot describe it with rambling on

[burnt vapor]

Please read #❓how-to-get-help

[solemn bronze]

ok I think I got this enough to keep reading

thanks

.close

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[hidden osprey]

How do I find the dimensions of the triangle

[crimson sedge]

you can find CO using the ratio

and DC using trig

[hidden osprey]

CO = 3r/5

How do I find DC

[vague rapids]

Which triangle

[hidden osprey]

OCD

[half forge]

Tan(theta)

[hidden osprey]

5tan(theta)/3r?

[vague rapids]

Yeah you just wrote it

[half forge]

Tan(theta)=DC/OC
DC=tan(theta) × OC

[hidden osprey]

ohhh DC/OC

now i see

thanks

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[cedar kiln]

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[twilit star]

Hello i have issue with understanding if this statement is true or false

[gilded elm]

what do you think

recall the definition of a subset

[twilit star]

I get mixed answers from many students from true to false. Everyome says false. Yet nothing exists in every group

[steep meadow]

Alright think about the following

What are the elements in the right set?

[twilit star]

1, a group with 1 element of nothing.

[steep meadow]

Well it's not a group but a set

But yes

A set with 1 element of empty set

Which is just {{}}

Now on the left hand side. What are the elements of that set?

[twilit star]

But on the left side is a group of nothing. Which always exists in every group

Nothing always exists no?

[steep meadow]

Not quite

Since it's not a set of nothing

[gilded elm]

its a set containing the element "emptyset"

[steep meadow]

It's a set containing a set of nothing

[gilded elm]

now think again

[steep meadow]

You can always think about {∅} as {{}} if that helps

[twilit star]

It only made it more confusing because it will make the answer to true

Since it does exist in the right side

{{}}

[steep meadow]

EHHH no I think you're more confusing yourself

The left side is the set {{}}

Meaning the only element in it is {}

[gilded elm]

is the element {} an element of the right side?

[steep meadow]

The right side is the set {1, {{}}}

[gilded elm]

think about that

[twilit star]

Ohhhh

[steep meadow]

Meaning 1 and {{}} are the elements

[twilit star]

I see why it doesnt exist. Because on the roght side there are no set of nothing

[steep meadow]

Exactly!

But there is a set of a set of nothing

[gilded elm]

be precise

[twilit star]

It would be true if in the roght group was {1,{}}

[steep meadow]

Right

[gilded elm]

the right side does not contain the empty set as an element

[twilit star]

Thank you all ❤️

[gilded elm]

please do not use the word "group"

it has a mathematical meaning

[steep meadow]

Yes a group is something completely different

[gilded elm]

you need to be careful and precise with terminology

[twilit star]

Ok , i just started my degree so i am a newbie

I will use correct terms

[gilded elm]

good to ensure you stay precise then

[steep meadow]

Also mentioned it earlier haha

[twilit star]

Thank you all

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[gilded elm]

we can technically give any set a group structure but thats offtopic lmao

[cedar kiln]

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[livid needle]

I know that the points (k,-5) (2k+1,7) (4,3) are all on the same linear function and I need to find k. because the slope of any pair of these points is equal I came to the following equation

$ \frac {-5-3}{k-4} = \frac{7-3}{2k-3}$

[livid needle]

But I have forgot how to solve these problems

$ \frac {-5-3}{k-4} = \frac{7-3}{2k-3}$

Why does latex not work?

[long swan]

Yeah looks good

Solve the proportion

[livid needle]

Wdym?

[long swan]

Wdym?

What part of what i said is confusing?

[livid needle]

What does solving for a proportion mean?

[long swan]

You have an equation relating two fractions

Can you solve this equation

[livid needle]

I don't belive I really know how

[long swan]

Oh ok now I see your confusion

[livid needle]

I think it has something to do with equalizing the numerators

[long swan]

Not quite.

It has to do with the ratio between the numerator and denominator being the same on both sides.

How about this:
1/2 = x/10

How would you solve this?

(Just as an example)

[livid needle]

Multiply both sides by 10

[long swan]

Great!

And we also know that 1 is half of 2, so 5 is half of 10, meaning x = 5 here, right?

[livid needle]

Yes

[long swan]

Alr

And we know that 5 is five times 1, and 10 is 5 times 2

So 1/2 = 5/10 because:
1/2 × 5/5 = 5/10

Point being that there are multiple ways to view these equalities

[livid needle]

I see

[long swan]

Now let's take a look at your problem

Would you agree that we have:

-8/(k-4) = 4/(2k-3)

[livid needle]

Yes

[long swan]

Alright. What can we multiply 4 by to get -8?

4 times something = -8

[livid needle]

-2

[long swan]

Great.

So that means:

-2(2k-3) = k-4

[livid needle]

Oh

[long swan]

Do you see what I did there?

[livid needle]

Yeah

Thx

It really did help

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[lilac chasm]

Is sqrt-576 no real roots?

[cedar kiln]

@lilac chasm Has your question been resolved?

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[indigo marsh]

What kind of statement would I need to give for this

[livid hound]

amgm

[buoyant latch]

Something to show that expression is at least 2+ some positive number

[indigo marsh]

Hmm

If k>0 then k+1> 0? Lol

[quartz marlin]

derivative, equate to zero

[indigo marsh]

Because it says ‘least value’?

[quartz marlin]

yeah

[sage forge]

Or try to slipt it into two fractions and do LHS > 2. You can also substitute sqrt(k) = a. We had to do this in a (unmarked) analysis exam

It goes rather fast this way

[indigo marsh]

Right

Yeah they haven’t differentiated it what they’ve done is weird

Ughhh

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[upbeat lotus]

Seems fine to me

[cedar kiln]

@solemn dune Has your question been resolved?

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[delicate patio]

Can I asume that f'(x) is always greater than zero?

[carmine whale]

Yes ig

[latent bloom]

Hmm

[half forge]

greater or equal

[delicate patio]

hmmm

[latent bloom]

So like

[carmine whale]

Not always greater tho

[delicate patio]

This problem's gonna be hard then

[carmine whale]

It's ≥0

[delicate patio]

:/

[latent bloom]

xf(x) >-2

[delicate patio]

please don't give any hints

I'll work my way around

[latent bloom]

Admirable

[delicate patio]

yes like I did prove that f(x) is always less than -1 for x < sqrt(2)

but I proved this on the assumption that f'(x) > 0

😢

[half forge]

f'(x) can be 0 even if f(x) is an increasing fuction

[latent bloom]

Yep

[carmine whale]

Do u have to find all possible functions f(x)

[half forge]

e.g. f(x)=x^3 is an increasing function but f'(x)=0 at x=0

[delicate patio]

yea

this is the whole question, if you guys are interested maybe

[cedar kiln]

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[eager kiln]

why does the function e^|x-b| switch from decreasing to increasing at y=1 specifically.

[eager kiln]

i dont get it

[lyric narwhal]

because

you have selected a b value of 1

the graph of e^x intersects the y axis at y=1

[eager kiln]

nah b just shifts the graph left and right. if i take b=4.3, it looks like this?

[lyric narwhal]

yes

whenever you have an absolute value, you can say that the zeroes of the expression inside the absolute value are where the graph has turning points

so since you have |x-b|, it is at x=b where the graph changes shape

[eager kiln]

oh right i get it.

[eager kiln]

ah ok that makes sense yes

thanks

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[eager kiln]

.reopen

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✅

[eager kiln]

wait im a bit confused about how |x| works. so suppose x= -4.2, what would be |x|

[lyric narwhal]

it would be 4.2

you can think of it as just removing the sign of the value

[eager kiln]

oh ok i assumed thats how it works yes

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[rigid wolf]

Someone help I been having trouble with it at 3

[rigid wolf]

Why tf did a bot pin it

[latent bloom]

Because you now claimed this channel

Sometimes the chat is too much to read and to scroll through

So pinning the first message in the help channel helps

[rigid wolf]

Oh ok

[lyric narwhal]

do you know what middle term splitting is?

[latent bloom]

Okay are you familiar with factoring?

[lyric narwhal]

ah

ok

[rigid wolf]

Yes#

[lyric narwhal]

try to factor the expression

that is given

using middle term splitting

[rigid wolf]

Okay that makes more sense.

[lyric narwhal]

you should end up with one of the options

[rigid wolf]

Okay thank you

Close

•close

Yeah no I don’t get it

.close

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[tall quiver]

@dry heart hi you helped me with that differential question

[tall quiver]

can u elaborate mr.deep?

[dry heart]

do uk leibniz rule

[tall quiver]

mr can u clarify what is leebnith law?

oh sorry

leibniz rule

[tall quiver]

no sir

where can i study that?

[dry heart]

https://en.m.wikipedia.org/wiki/Leibniz_integral_rule

[tall quiver]

thank you sir

ill study this and if i have further question contacting you

bye sir for now

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[wary blade]

how do i do this

what does it mean for an integral of a function over a small range to be zero

the graph is both above and below the axis?

something like this?

i mean, yes but

how does it matter for a subspace

[crimson delta]

what is always in a subspace

[wary blade]

0

right

or 0(x)

[long swan]

right!

so what is your "zero vector"?

(your vectors are functions)

[wary blade]

f(0)? i guess??

uh

or is it some other function z(x) = 0

some random function in the interval which is just 0

all the time

i got it, thanks

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[white trail]

how would i do this? i haven't been taught this concept yet :,)

[dusk finch]

To find inverse of y=something, you have to get x on one side of the equation and everything else on the other

[white trail]

how would i deal with ln?

i kinda understood log but i haven't learned ln yet

[dusk finch]

ln is inverse of exponentiation base e

[white trail]

ohh thank you!!

i got it thanks!!

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[dusk finch]

Once you get x to one side and everything else to other side, swap x and y back

Here is worked example

[vernal solar]

For inverse functions, one thing I find useful is it's just the opposite of the original function.
The variables x and y are switched
So say y = x+1
The inverse would be
x = y+1
So inverse y = x-1

[white trail]

.close

did i do the close thing wrong 😭

/close

close

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[cedar kiln]

@onyx axle Has your question been resolved?

[onyx axle]

<@&286206848099549185>

[onyx axle]

Im not able to do the question

Plz help

[nimble veldt]

NSQ and MTR are congruent. this says something about the angles. eg. angles at Q an R.

[onyx axle]

Yes ang q=r

I got that part

So pq=pr

[nimble veldt]

thats all you need.

[onyx axle]

Confused

[nimble veldt]

angle at P in PST = angle at P in PQR.

[onyx axle]

But ang 1 not = q

Or 2 not = p

[nimble veldt]

yes of course

[onyx axle]

Similarity requires 2 angles min right?

[nimble veldt]

angle 1 = angle 2 = ((180-P)/2

[onyx axle]

Oh coz its isoceles and an angle is common?

[nimble veldt]

angle at Q = angle at R = (180-P)/2

[onyx axle]

Oooh ok got it thanks a lot

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[crimson sedge]

can i get help on b (ii)

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

nope

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[sudden escarp]

wasnt integration easy?

[sudden escarp]

what is this

[south tundra]

It is called u-sub

[sudden escarp]

yes, i know it

[long arrow]

wdym

[sudden escarp]

but it was never as complex as this

[long arrow]

by what's this

[sudden escarp]

how did that answer come to be

[long arrow]

what step exactly don't you understand above

[south tundra]

This is only the beginning, trust me

[sudden escarp]

last one

[long arrow]

notice that if u = x - 1
then we have:
x = u + 1

[south tundra]

Just plug in x = u + 1

[sudden escarp]

can you believe how easy this became

thats the essence of math

its always hard until its easy

[long arrow]

like everything

[sudden escarp]

thank you both so much, especially you modus thats like the third question you answered for me!

hopefully there wont be more

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[lean cave]

hey, im struggling with understanding how this works.

[lean cave]

i dont understand how you can use x = sec(u)

to me, i cant see any indication that you would use it

[long arrow]

that's because of identity

sec^2(x) - 1 = tan^2(x)

this lets simplify (x^2 - 1)^3/2 nicely

[lean cave]

how would you know to use sec instead of another trig function?

[long arrow]

https://blogs.adelaide.edu.au/maths-learning/2016/11/08/how-i-choose-which-trig-substitution-to-do/

[lean cave]

ah i see

[long arrow]

have a look, but it's rather about practicing integrals like that than studying them by heart

I mean u-subs

[lean cave]

is there anywhere you'd recommend finding practice questions?

[long arrow]

sort of intuition after getting experience

[lean cave]

any good websites u know of?

[long arrow]

KhanAcademy, OrganicChemistryTutor, YouTube etc.

[lean cave]

thanks, i appreciate it 🙏

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[upper rose]

Can someone help me finding the Equation of the Circle?

[upper rose]

A(?,0)
B(-3,0)
C(0,-6)

[long arrow]

to find radius you can use

|AB| = |AC|

and you'll find A also

so it's all you need

[upper rose]

I got 4.1666666 Idk if it's true tbh

[upper rose]

by doing this

[long arrow]

,w (x+3)^2=x^2 + 6^2

[wraith dagger]

Results provided by WolframAlpha

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

Requested by Modus#7591

[long arrow]

so A = (9/2, 0)

[upper rose]

Wiat what

Did I calculate incorrectly?

4.5 is the right answer thanks man

[upper rose]

I mean, x=4.5 is the right answer

But why did I get 4.166666 then?

Did I do something wrong here?

[dire geode]

,rotate

[upper rose]

,w (x+3)^2=x^2 + 6^2

[wraith dagger]

Results provided by WolframAlpha

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

Requested by Rektus#0945

[upper rose]

ohhhhhhh

I did 36-11 instead of 9

[dire geode]

,calc 36-9

[wraith dagger]

Result:

27

[upper rose]

lmao

I can't believe I was stuck on it for so long because of that without noticinglol

At least I got help here I guess

Thanks for the help

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[rare snow]

Hi

[quartz frost]

hello 🙂

[rare snow]

could I just get the name of this exercise?

[long arrow]

system of inequalities? idk

[cedar kiln]

@rare snow Has your question been resolved?

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[jade stag]

why is y on top, how did they get there

[dusk finch]

ln is inverse of exponentiation

[dire geode]

https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-intro/v/plotting-exponential-logarithm

[dusk finch]

When you are stating y=ln(x) you are stating that e^y=x

[upbeat lotus]

Do you know what is log?

[dusk finch]

That's the definition of log

[obsidian coral]

Applying rule 7

Both sides have the base of e

[dusk finch]

||Rule 7 is probably derived from the identity||

[obsidian coral]

True

[wraith dagger]

MathIsAlwaysRight

[jade stag]

e i guess?

i understand the rules, but like i dont understand e and ln

even though theyre the same as log base 10 or log base e?

[obsidian coral]

$log_e$ is ln

[wraith dagger]

dldh06

[upbeat lotus]

Do you know the definition of e

$\lim_{n\to \infty} (1+\frac{1}{n})^n$

[wraith dagger]

𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛

[upbeat lotus]

=e

[obsidian coral]

Probably way too advance, if doug doesn't know limits yet

[upbeat lotus]

Oh you don't know limits @jade stag

[dusk finch]

e is a complicated number, for now just accept that it's really important constant. You will hear about it soon

[jade stag]

are you telling me that when u use e to "cancel out" ln, you raise ln x as an exponent and you do this y aswell?

[upbeat lotus]

Yes

Like $e^{\ln(69)}=69$

[wraith dagger]

𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛

[upbeat lotus]

But sometimes we use e or ln for solving problems not always this

It is used literally everywhere

In complex number

like Euler's Identity
$e^{i\theta}=\cos(\theta)+i\sin(\theta)$

e is widely used every where

[jade stag]

like tis?

[wraith dagger]

𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛

[obsidian coral]

You are going down an unnecessary rabbit hole

[upbeat lotus]

I have experience to fall for a hole so you could say that

[upbeat lotus]

Yes

[obsidian coral]

Yes, e is like pi, where leaving it in terms of e is more exact unless it states to round, at least that's my opinion

[upbeat lotus]

Solve this ln(f)=69 solve for f

@jade stag

[jade stag]

f=e^69

[jade stag]

make sure to pull out

[upbeat lotus]

Very good very good

Remember in ln(x) function x can't be negative

Other wise it would be complex

Like her

And for solving it

It will break you (pen + is +good - good)

Solve for this
$\log_{10}(x)=6699$

[wraith dagger]

𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛

[upbeat lotus]

My mobile is at 3% solve it now

I will chew your meat @jade stag

Otherwise

[dusk finch]

That's ||10^6699 + 2pi*sqrt(-1)*log(e)||

[upbeat lotus]

Ok my mobile is dead I'm going good night

[jade stag]

yooooooooooo 😂 😂

[jade stag]

gn bro

[dusk finch]

Fun fact: It's actually correct

[jade stag]

hm really

so 2 pies and a squirt = 6699?

[dusk finch]

Wait its not

There is damn 10

not e

[jade stag]

isnt log _e

same as log _10?

ik log e = ln

[dusk finch]

Nope

log_10 is log base 10

log_e is log base e

and e=2.71828...

which is definitely not 10

[jade stag]

what does

a base mean

i dont understand this tbh

ik regular e = 2.7

but log_e idk

log_e same as e?

[dusk finch]

Check this

log stands for "to what power do I have to raise base to get the argument"

[jade stag]

there is nothing infront

of log_10 though or log_e

do we assume its >1

or = 1

or x?

log_10 x = 25 -> 10^25 = x?

for example

does e have a base

does ln have a base

left side i understand right side not so much

well tbh dont understand it cause why would u find lnM/lnb, if u could do logM/Logb?

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[plain totem]

OH nvm

.close

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[oblique lynx]

Can somebody please explain to me how this is 5?

[long arrow]

sin^2(t) + cos^2(t) = 1

and you're done

[oblique lynx]

oh yes, thats what i thought, but wouldnt that left me with sqrt(-3)^2+3^2+4^2?

[long arrow]

nope

[obsidian coral]

You should expand (-3sin)^2 and (3cos)^2

And then you'll see that you can factor out a gcf

And get left with sin^2(t) + cos^2(t) times that gcf

[wraith dagger]

Modus

[oblique lynx]

oooh, i see it now, thank you! also thanks for blazingly fast reply man

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[long radish]

In an isosceles trapezoid ABCD, X is the midpoint of the lateral side AB, BX=1 and CXD = 90º. Find the perimeter of the trapezoid ABCD.

[long radish]

I have 0 idea

please help me

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[long radish]

<@&286206848099549185>

[dull oxide]

what is an isosceles trapezoid

[errant chasm]

It's symmetrical basically

Oh it's a hint, nvm I'm dumb

[silent finch]

coord bash is really easy

but drawing a line parallel to the height passing through x will probably lead to a sol

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[crimson sedge]

quick question regarding formatting

[crimson sedge]

if i have the progression

wait sec

just typing

$t_n=\frac{1}{\left(1+n\right)^2}\left(1^3+2^3+3^3+...+n^3\right)$

[wraith dagger]

Caleb.

[crimson sedge]

how do i represent the second part in terms of n

for example the second term is thios

$t_2=\frac{1}{\left(1+2\right)^2}\left(1^3+2^3\right)$

[wraith dagger]

Caleb.

[dire geode]

$\sum_{k=1}^n k^3 = 1^3 + \ldots + n^3$

[wraith dagger]

riemann

[dire geode]

https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-3/v/sigma-notation-sum

there's also a closed formula for sum of first n cubes if you're interested

[crimson sedge]

yes im interested

[crimson sedge]

ah i see now, i just overlooked that haha, thank you

[dire geode]

https://www.cuemath.com/algebra/sum-of-cubes-of-n-natural-numbers/

[crimson sedge]

oh

so its the square of the sum of an arithmetic sequence?

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[austere silo]

why can i use reverse chain rule on the right equation but not the left ?

[dire geode]

what is "reverse chain rule"

and what are you even doing on the left?

for integrals, that's called u-substitution
https://tutorial.math.lamar.edu/classes/calci/substitutionruleindefinite.aspx

[austere silo]

idk what americans call it but we just say reverse chain rule in the UK

and its different from u-sub & integration by parts

[dire geode]

it's probably just u-sub

[dire geode]

read this

[cedar kiln]

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[hollow osprey]

what even is the expression on the right?

$y = \sin(x)^3$?

[wraith dagger]

Geopchad

[hollow osprey]

how would you even apply reverse chain rule to something that's not an integral?

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[eternal jewel]

Hello, I am confused with question a in terms of how exactly I have to find the amount of sand removed. I know I have to find the integral of both functions but if I need to find how much that’s going to be removed don’t I just need to integrate s(t)?

[eternal jewel]

In the packet I did the lesson with I had to subtract one integrated function with another to find a rate or quantity

But I’m not sure if I have to do it here

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[marsh pond]

is this notation good?

or does it break down near the bottom

the question:

am I suppose to include "lim t-> 0" even on the last 3 lines?

[violet night]

I would say after you substitute the limit notation thingy mabobby on the left drops

[modern compass]

you dropped parenthesis in the denominator, which makes it confusing. But otherwise it's fine.

[marsh pond]

Yeah, I thought about this too but realized the parentheses are optional

[obsidian coral]

realized the parentheses are optional
Not always

[marsh pond]

in this case I think so?

[modern compass]

i mean..... not really

[marsh pond]

can't really use commutative property

the 1 + single term is gonna stay on the right side

[modern compass]

a * b + c is not the same as a * (b+c)
This time the answer might have worked out the same, but only because the limit was to 0

[obsidian coral]

Based on order of ops taht could be (sqrt(1 + t) * 1) + sqrt(1 + t)

[obsidian coral]

So no

[marsh pond]

oh

I got lucky here

ya you're right

ty

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[turbid spoke]

factor theorem is x-r = 0?

[royal loom]

no

What the factor theorem is saying is that

if r is a root of the function

meaning that when you put in r, you get out 0

meaning also, f(r)=0

then a factor of the function is (x-r)

and you can see that this is true, imagine you have two factors, (x-r) and (x-a)

so your function would then be (x-r) * (x-a)

try plugging in r to this function

replace x with r

(r-r)*(r-a)

well r-r is 0

and you get 0*(r-a)

which you know will be 0

because multiplication by 0 is 0

so therefore putting in r, when you have a factor of (x-r) means that r is a root

and vice versa

[turbid spoke]

like this?

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[high kernel]

Anyone know if I did this right

[buoyant latch]

That looks wrong

That error measurement should have units of unit²

And it should be a percentage of s right?

[high kernel]

Honestly

No clue

[buoyant latch]

As the tree gets larger

[high kernel]

I asked another helper he said he’s never seen a question like this before

[buoyant latch]

The 5% error is greater numerically

And thus should have a higher numerical error margin

Like the number should be higher

So the error should be dependent on s

Your answer isn’t

[high kernel]

How would I solve it?

[buoyant latch]

Well we want a percentage

That’s what the question is asking

% of area

[high kernel]

Honestly I have no idea

[buoyant latch]

Ok can you rephrase the question

See if you understand the question before you try to solve it

[high kernel]

We wanna find the error percentage when the error measuring the stem is at 5% max

[buoyant latch]

Ok

Close

Error percentage of what

[high kernel]

Of the calculated area

[buoyant latch]

Ok so how does the area change when your s is increased by 5%

[high kernel]

Constant increases when the proportions become larger

[buoyant latch]

Replace s with something that represents a 5% error in measurement

[high kernel]

I don’t know

[buoyant latch]

What does a 5% error in measurement mean?

[high kernel]

the actual value could be either 5% higher or 5% lower than the measured value.

[buoyant latch]

Ok let’s say you measured s

What does 5% higher mean

How does that affect s

[high kernel]

S is 5% lower

[buoyant latch]

No no no

If you measured s 100% more than it should be

You’d measure s+s = 2s

Instead of just s

So how about 5% more

[high kernel]

Let me get this straight

So If its 100% it’s s+s

So if its 5% it would be

S+0.05s

[buoyant latch]

Yes

Now factor the s

[high kernel]

1.05s

[high kernel]

This?

[buoyant latch]

Yes

So if you put 1.05s into the function

What do you get

[high kernel]

Like into the equation I had before

[buoyant latch]

So instead of A(s) we do A(1.05s)

And what is the percentage difference between these 2?

[high kernel]

Like this

[buoyant latch]

What happened to the s

[high kernel]

I replaced it with 1.05