help-39

[midnight haven]

maybe something like this?

Let $A={|x|\leq1\mid x\in\mathbb{R}^2}\subset\mathbb{R}^2$ the unit circle. Consider the sets $B_i={x\in A\mid \mathrm{arg}(x)<2^{-i}}$. What is the limit $\lim_{i\to\infty} B_i$?

[jolly parrot]

Toby

[narrow salmon]

o___O I wish I could understand that lmao

[midnight haven]

have you done (real) analysis or topology before?

[narrow salmon]

No. I am not a classically trained mathematician.

[midnight haven]

which means?

[narrow salmon]

My level of education never went past college Algebra II, which I failed, and I cheated my way through high school calculus because young me couldn't comprehend any of it. >___>

so yeah that lol

[midnight haven]

all good

so basically, we are making the circle smaller and smaller when we keep cutting it in half

so taking limits (since we assume we are talking about a nice space, like the numbers we learn about in school), the limit of the area goes to 0

one way to see this is using euclidean geometry: the area of a slice of angle $\theta$ of circle of radius 1 is $\theta/2$, and every time we halve $\theta$, it gets smaller and we can write $\frac{\theta}{2^i}$ for some $i$, the amount we are halving. So taking limits $\lim_{i\to\infty}\frac{\theta}{2^{i+1}}=0$

[jolly parrot]

Toby

[pearl pond]

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[pearl pond]

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[mighty marten]

what part is confusing about it?

yes

ok, well it says what is the probability that a nine is rolled

not saying a nine is rolled

so if you were to roll a 6 sided dice, what are the chances that you will get a 9?

yes so it would go on 0 on the number line, cause you cant roll a 9

[pearl pond]

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[foggy dawn]

i need help on number 1

[foggy dawn]

i’m stuck trying to find the values

without a calculator

[plush bramble]

use sum and difference identities and express all the sec/cot/tan/csc in terms of cos and sin

[pearl pond]

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[vital wasp]

Why did I get the wrong vertex?

[fossil harbor]

you only found when y=0, if I understand what you mean, then you have to differentiate it before solving?

[vital wasp]

Wdym

I got 0 because 4(0)^2 - (0)^4 is 0

Does it matter if the y is 0?

[fossil harbor]

I'm not too good in maths in english haha, are you trying to find the maxium value?

[vital wasp]

yeah the vertex

[fossil harbor]

then you need to check when the derivative is equal to 0 right, not the function itself?

otherwise you just find the when the graph crosses the x axis

[vital wasp]

sorry i don’t know what derivative means

@fossil harbor

[fossil harbor]

ehhh its the rate of change in each point, like if you draw a tangent in each point of the graph

[vital wasp]

how do i find it?

for this graph

[fossil harbor]

to find the derivative of x^a its a*x^(a-1)

[vital wasp]

why find x^a in particular?

[fossil harbor]

so you take the exponent down and raise to the power of the exponent minus one

its just a general rule that fits your graph

so 4x^2 would mean the derivative is 8x

or 2*4x^1

[vital wasp]

Wait but isn’t -1 = a instead of 4?

[fossil harbor]

a is just the power thatx is raised to

so in x^3 its 3 and x^2 its 2

[vital wasp]

What is x then?

[fossil harbor]

x is what you have in your function

but yeah if you find the derivative and solve for when its = 0, then you will get the square root of 2

which is 1.4141... and so on

[pearl pond]

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[vagrant current]

How would i solve 3b

[pearl pond]

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[pearl pond]

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[jade tiger]

is there a proof to say that sen²(x)+cos²(x)=1???

[jade tiger]

am very lost at tryg, only need a little bit of orientation :c

[midnight haven]

sen?

[jade tiger]

i mean sin

[midnight haven]

oh yea

[jade tiger]

here in chile we use sen and write it as seno

[midnight haven]

just look at the unit circle wait

[jade tiger]

i'll wait :p

XKJSKAJFKAS

what was that

[midnight haven]

My uncle Penjayo

My fault og

[jade tiger]

he handsome

[jade tiger]

OHHH

[midnight haven]

yep

pythagorean

[jade tiger]

i think that was all i need it to understand it 😮

thx

.close

[midnight haven]

npp

[pearl pond]

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[crisp cloak]

the answer to this is 0.5 according to Microsoft math. How do you calculate this? I can't find any resources on how to calculate roots of negative indexes

[proven moon]

negative essentially means "reciprocal"

writing this out in indicies form would be $4^{-{\frac{1}{2}}$

[jolly parrot]

Doug Judy
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[proven moon]

there we go

and the negative in the power means

$4^{-{\frac{1}{2}}} = \frac{1}{4^\frac{1}{2}}$

[jolly parrot]

Doug Judy

[proven moon]

and we know what 4^(1/2) is

it's 2

so

$4^{-{\frac{1}{2}}} = \frac{1}{4^\frac{1}{2}} = \frac{1}{2} = 0.5$

[jolly parrot]

Doug Judy

[crisp cloak]

Hmm alright thank you, I'll keep re reading over it and try and make it click

[pearl pond]

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[formal pond]

I am having trouble with this one

[formal pond]

how would i find it by inspection

[pearl pond]

@formal pond Has your question been resolved?

[formal pond]

No

[pearl pond]

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[wind mantle]

Guys like it seems so simple and I graphed it cus desmos but I'm not too sure where to go from here

[wind mantle]

Like idk what to do now and the quiz is tomorrow 😭

[feral sedge]

well you have the partial function for |2x-14|

if you divide it by -4x+28

what does that look like on the inside

[wind mantle]

I can like factor out

[feral sedge]

like how does that change these

[wind mantle]

right? I could factor out -2 or am I going in the wrong direction

actually I got it, thanks king

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[midnight haven]

Can someone help? I can’t figure this out and I’m getting stressed out

[grim patrol]

dang

[midnight haven]

chill gang

[grim patrol]

i cant read that venn diag

[midnight haven]

no need to stress over sets

u know what intersection and union is right

[grim patrol]

whys there 3 numbers lol

[midnight haven]

Yes but I get confused on them

[midnight haven]

basically

union is the combination of two sets

so if set A is 1, 2, and 3 and set B is 2, 3, and 4, then the union between them is 1, 2, 3, and 4

[light helm]

<@&268886789983436800> slight concern whether this is a test or pre-test

[midnight haven]

notice how the elements of the set do not duplicate as sets are collections of unique leements

[midnight haven]

its online bruh

[honest bough]

Online tests are still tests

[midnight haven]

plus u can see a window behind the scroll bar which means that its not locked

[midnight haven]

Him and some other guy have been accusing me that it’s a test just cause I blocked off my personal information

[opal lantern]

this doesnt mean anything.

[midnight haven]

Cause I didn’t want ppl to see my name

[midnight haven]

i mean even if it is a test me telling u what a intersection and union is isnt very different from googling it

[opal lantern]

most of my university exams were take-home with no restrictions on sources used; still 0 collaboration/asking the internet allowed

[midnight haven]

It’s not timed and I have unlimited retakes I can show a picture after my test is over but I’m not showing my other stuff on my computer.

[opal lantern]

this particular assessment also seems to be timed

it isnt timed? then what is this

[midnight haven]

Pre test

[midnight haven]

just take a picture of the tab bruh

and if it comes to it just google it bruh

imo cheating is okay when u learn from it

cheating and learning beats just getting shit wrong on tests and never leraning what you didnt know ever

[honest bough]

Academic dishonesty is explicitly forbidden in this server and in most academic institutions

[midnight haven]

thats fair

just my two cents

.close

[pearl pond]

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[hollow lily]

Hello, I have a statistics question; is it possible to do a a fit to a set of data points that look like a poisson distribution but that aren't normalized?

[hollow lily]

I know one way to fit a curve to this is to normalize it and then fit a poisson for the theoretical mu=8.74, however is there a way to fit this with the given y-axis scale?

im mainly doing this in order to figure out the residuals which i believe you cannot do with a normalized graph such as this one

[pearl pond]

@hollow lily Has your question been resolved?

[pearl pond]

@hollow lily Has your question been resolved?

[west galleon]

Yes

A probability is occurance / total amount of tries

The first one is occurance

The second one is probability

So devide the y axis by the total amount of tries and you will fit probability

@hollow lily

[pearl pond]

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[river idol]

Can someone please help me with 6,7, and 8 I just can’t figure it out I’ve been stuck forever!

[golden bolt]

can you just.... screenshot?

[pearl pond]

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[pearl pond]

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[river idol]

.reopen

[pearl pond]

✅

[river idol]

I can’t take a screenshot I’m not on my MacBook I’m on my phone

[earnest stratus]

In any case, average rate of change is the slope of secant line.

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[woven gate]

@plush bramble @slate thicket heyy

[woven gate]

I made a mistake lol

it's

,rotate

[woven gate]

,w integral x/(a+ x cos theta )

[jolly parrot]

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[plush bramble]

well shit i didn't sign up for this

[woven gate]

??

[plush bramble]

i just mean i have no idea

[woven gate]

okk

[plush bramble]

it's probably worth differentiating the right hand side and recover the integrand

[slate thicket]

just try some u sub

i’m just guessing btw

[woven gate]

I'm almost reaching

[slate thicket]

a + rcos(theta) =u

oh

[woven gate]

@slate thicket

@plush bramble is this correct

[plush bramble]

oh that's easier than i thought

[plush bramble]

get your answer into this form

[slate thicket]

something not quite right i feel

[woven gate]

yea me too

sus

[slate thicket]

the log term in WA is not matching

[woven gate]

ohhhh

1 min

[slate thicket]

oh okay i see it now

[woven gate]

but that cos theta?

,w integral r/((a/cos theta) + r)

[jolly parrot]

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[woven gate]

hmm

I missed something

[pearl pond]

@woven gate Has your question been resolved?

[woven gate]

<@&286206848099549185>

ohh

@plush bramble @slate thicket i got it

I'm so dumb lol

you guys want to know???

ok nevermind

.close

[pearl pond]

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[woven gate]

just ping

[pearl pond]

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[quaint nacelle]

how do i answer this q

[quaint nacelle]

1. Jennifer buys a very large box of mixed-colour drawing pins. 25% are blue, 15% are red, and the
   remainder are brown. Jennifer selects 6 drawing pins at random from the box.
   Find the probabilities that: (i) all 6 drawing pins selected are brown

the methids im thinking of

are tree diagrams

but im not sure how to go about it

[brave mason]

first whats the chance of getting brown on the first pick

[quaint nacelle]

60%

since its the first event right

@brave mason

[brave mason]

yeah do they replace the pins

[quaint nacelle]

i would assume no

[brave mason]

hmm i would think yes tho

cause then the probability is variable with n number of pins

[quaint nacelle]

oh my bad i read tht wrong

uhhh ok

so

wait a min

[brave mason]

so do yk if they replace or not

[quaint nacelle]

imma go with no they arent replaced?

[brave mason]

u sure?

[quaint nacelle]

i have no idea ibr

what are the implications of either

option

[brave mason]

well if they replace the chance will be 60% each time

[quaint nacelle]

if they'e not replaced its cond prob?

[feral pewter]

Probably use the fact they said “very large” to imply that the change in probability from a selection is marginal

[brave mason]

i guess so

[quaint nacelle]

wdym by marginal

[feral pewter]

Like it won’t make a difference

[quaint nacelle]

ok so independent probability is this case?

what method do i use to ans thus tho

[feral pewter]

You are assuming each pick is Independent event

[quaint nacelle]

so how do i prove eitheror

like what do i do

[feral pewter]

First pick is 60%, second is still 60% etc

[quaint nacelle]

yes

[feral pewter]

And you are multiplying each

[quaint nacelle]

so

0.6^6

or 0.6 x 6

for 6 instances

[feral pewter]

Yeah ^6

[quaint nacelle]

3 of the drawing pins are blue and 3 are not blue

so for this ne

one*

i multiply prob of blue by 3

and prob of not blue by 3

amd add the answers together?

@feral pewter

[feral pewter]

You multiply

And also arrange

[quaint nacelle]

can u explain fully please

wdym by arrange

[feral pewter]

Like 6c3*(0.25)^3*(0.75)^3

[quaint nacelle]

and why is it like this exactly

are u multiplying the .25 and its coefficients by .75 and its coeffs

or are you putting .75 to the power of .25

[feral pewter]

6c3 is arranging the picks, it is the difference between like brbbrr and brrrbr for example

[quaint nacelle]

ok

[feral pewter]

Do you know this?

[quaint nacelle]

no

[feral pewter]

0.25 is probability of blue

[quaint nacelle]

yes

[feral pewter]

And you ^3 for three picks

[quaint nacelle]

okay

[feral pewter]

And 0.75 is probability of not blue

And same ^3

[quaint nacelle]

yes

and so how do i connect those 2 probabilities

[feral pewter]

Multiplication sorry

[quaint nacelle]

could u pls edit it to the correct option?

i dont want to enter the wrong values

i assume just multiply (.75)^3 by (.25)^3

[feral pewter]

That is correct, but if ur class is meant to consider arrangements then you need to multiply it aswell by 6c3=20

Like this
20 * (0.75)^3 * (0.25)^3

[quaint nacelle]

so 20(.75)^3 times (.25)^4

oh ok

ty

imma try this

@feral pewter

how would i answer this last one

at least one drawing pin is red

wd it mean by at least 1

is this a probabilit distribution

[feral pewter]

The trick with questions that are “at least 1” is to realise that
P(“At least 1”) = 1 - p(none)

[quaint nacelle]

so prob of none being selected in 6 instances issss

1-.15^6

error on calc

so

[feral pewter]

Prob of none being selected is (1-0.15)^6

[quaint nacelle]

yeah just did it

.85

[feral pewter]

So prob of at least 1 is 1-(1-0.15)^6

[quaint nacelle]

= .62

thanks so much bro

what type of probability is this

so im not confused in the future

[feral pewter]

This one is binomial distribution

[quaint nacelle]

okayy and what were the key words that let u know that ws the case?

[feral pewter]

Binomial is probability of n success in a two outcome scenario, here u have multiple colours but in this case it was asking blue and not blue which is only two outcomes, blue is treated as the success and n in this case is 3

[feral pewter]

This one is just a common probability trick

[quaint nacelle]

awesome thank u

imma write tht down

[feral pewter]

Ok nws gl

[quaint nacelle]

thank you so much

.close

[pearl pond]

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[quaint nacelle]

have a great da

[pearl pond]

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[outer prawn]

The slope and y-intercept of a straight line are -1 and 5. The aera bounded by this straight line with x-axis between x=0 and x=1, is

[outer prawn]

,w The slope and y-intercept of a straight line are -1 and 5. The aera bounded by this straight line with x-axis between x=0 and x=1, is

[jolly parrot]

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[scarlet radish]

Have you tried drawing a diagram

[outer prawn]

yes

ig they are

asking this aera

[scarlet radish]

Y intercept is the intersection of the line with the vertical axis

And since the slope is negative, the line is going downwards

So the line that you have drawn is not correct

[outer prawn]

oh

what will the equation of line be?

of the y- intercet at -1 and 5

[golden bolt]

The slope is -1*

[outer prawn]

oh

how

i m not getting

[scarlet radish]

You substitute the values of the slope and the y intercept into this equation

c represents the y intercept, since when you substitute x = 0 into that, you get y = c

and m represents the slope

So what is the equation of the line?

[outer prawn]

y=c

[scarlet radish]

Nope, the slope is -1, and the y intercept is +5

So y = -x+5

[outer prawn]

oh

its like this

[scarlet radish]

Yep that’s good

[outer prawn]

so it will be

the integral lower limit=1 upper limit=5 (-x+5)dy

no

its not

[scarlet radish]

Yep it’s not

What would it be?

[pearl pond]

@outer prawn Has your question been resolved?

[outer prawn]

i dont know

can you tell

@scarlet radish

[pearl pond]

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[midnight haven]

how do i simply the definition for the nth term

[midnight haven]

in a practice problem i found the nth term was S(n)=4+3(n-1) for n > 1 but would the simplified version be S(n) = 1+3n for n>1

[hollow cobalt]

4 + 3(n - 1) = 4 + 3n - 3 = (4 - 3) + 3n

[midnight haven]

wait how do you do that though

[pearl pond]

@midnight haven Has your question been resolved?

[autumn narwhal]

@midnight haven What's your question exactly?

The nth term is

$a_1 + (n - 1)d$

[jolly parrot]

RedstonePlayz09

[autumn narwhal]

where a_1 is the first term in the sequence, and d is the difference.

Note that this only applies to arithmetic sequences.

Are you asking how they got from
4 + 3(n - 1)
to
1 + 3n
?

[tall tangle]

^multiplication for geometric and d-->r

i concur with hunter 🤩

[pearl pond]

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[pearl pond]

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[feral gust]

thank you i guess

https://tenor.com/view/i-need-your-help-bear-grylls-you-vs-wild-out-cold-help-stranded-gif-23429832

[pearl pond]

@feral gust Has your question been resolved?

[pearl pond]

@feral gust Has your question been resolved?

[feral sedge]

My guess is you don't know which ones positive

Both possibilities probably yield the same answer in the end

[feral gust]

in my book it say's -1 but when i use the identity of (cosa\sina)^2 = 1 \ 1+(tan\cot)^2 i get wrong answer. i guess i should use another identity? and thank you so much for your help!!!

[feral sedge]

division is forward slash /

Idk how you're applying that identity

I don't see either side here

One thing you could do is just find both possible values of sin/cos and plug in

but if you wanted to solve it without doing that

first step I recommend is to split the fraction up into 2 fractions

[feral gust]

thank you! i will try again

[feral sedge]

Np!

[feral gust]

Boom solved. You were right, just to put sin and cos as they are with one of them negative

Appreciate it mate. Best of health's

[feral sedge]

np!

if you wanted to prove it you'd just swap them as well and do both

if you just want the answer do one

[pearl pond]

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[strange hill]

Why is the first derivative of e^2x 2e^2x? Shouldn’t it just be e^2x due to the Exponent rule?

[plush bramble]

you're applying the exponent rule without (2x) in the exponent

$\frac{d}{dx}(e^x) = e^x$ ONLY has x in the exponent

[jolly parrot]

riemann

[plush bramble]

$e^{2x}$ has 2x in the exponent

[jolly parrot]

riemann

[strange hill]

I thought that when you apply the rule you’d get e^x ln e

@plush bramble?

[plush bramble]

,calc log(e)

[jolly parrot]

Result:

1

[strange hill]

Yeah so wouldn’t it just multiply out to e^2x?

[plush bramble]

no

you're confusing two rules together

and forgetting chain rule

,w differentiate 2^x

[jolly parrot]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by riemann#2529

[plush bramble]

,w differentiate e^(2x)

[jolly parrot]

Results provided by WolframAlpha

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Requested by riemann#2529

[strange hill]

Oh you have to use the chain rule for this?

[pearl pond]

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[ocean cloud]

This is the first time im seeing this type of question

[wind fox]

sin^-1 is just 1/sin

[pearl pond]

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[olive lantern]

how do i find domain and range for this

rational function

[grim patrol]

domain is just trivially when we have the denom as 0

[wind fox]

if you graphed it what would it look like

[grim patrol]

omg why do i keep saying =0

i mean when denom is non zero

[wind fox]

so thats what the equation looks like, but if you didnt have a graphing calculator, how would you find where those asymptotes are

[olive lantern]

x=2

y=3

im think

[wind fox]

yeah, but how would you find that without the graph

[olive lantern]

u sub in ur notation

-1/4(x)+2

-3(y)+3

is that right

[pearl pond]

@olive lantern Has your question been resolved?

[pearl pond]

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[spice rampart]

Help 🆘

[pearl pond]

Please don't occupy multiple help channels.

[spice rampart]

Hi y'all I have this question not sure why I am getting the wrong answer

This is my work

The answer is coming up as 17,484.44

<@&286206848099549185>

[tall tangle]

e^

[spice rampart]

Yea that is what I have used in a simpler way

I think 😆

For r/n I have done 0.043/4 as the interest compounds 4 times

[pearl pond]

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[pearl pond]

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[chrome ferry]

Where’d I go wrong

That one negative should be there

🤔

[real scarab]

antiderivative of cos is -sin

[chrome ferry]

Think I messed up first line when rewriting the second integral by parts

[real scarab]

oh my bad

its the other way around

yeah you forgot a -

in the second integral by parts

there are 3 of them

[chrome ferry]

Like this ? Not done yet but

[real scarab]

if you add brackets yes

[real scarab]

no

if you go back

you had - integral of sinx (2x+x)

then - [ integral by parts]

[chrome ferry]

I finally got it

Ty

🙏

[pearl pond]

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[pearl pond]

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[pearl pond]

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[lunar temple]

Write the vector equation for the line
a) passing through the points A(-4, 3, 0) and B(1, 1, 2)
b) passing through the point Q(1, 2, 4) and parallel to the z-axis

[lunar temple]

just need help with b

[slate thicket]

what have you tried?

[lunar temple]

well parallel means scalar muilpile

multiple

[slate thicket]

it’d help if you first try to find general point on a line

yes

[lunar temple]

yea its (5,-2,2)

[slate thicket]

so if it is parallel to z axis x coordinates will always be 1 y will always be 2 and z will vary

[slate thicket]

hm?

[lunar temple]

huh

[slate thicket]

i mean like parametric form

x= 1
y=2
z= 4+t

[lunar temple]

ok

[slate thicket]

will this be ur line?

[lunar temple]

i can use A or B from question one right

or i have to use AB?

AB= t(5,-2,2), tER

[slate thicket]

uhh? idts they are related

[lunar temple]

can you just tell me how to do it?

[slate thicket]

hmm 🤔

[lunar temple]

this is vector equation

[slate thicket]

okay vector equation is of the form p + tq

[lunar temple]

tea

ya

[slate thicket]

where t is parameter

cool

p is the point which we know

that is

(1,2,4)

correct?

uh do youget it?

[lunar temple]

correct

[slate thicket]

oh okay

[lunar temple]

now

[slate thicket]

now for the q part

[lunar temple]

ok

[slate thicket]

we know

line parallel to

z axis must be of the form

(0,0,t) for all t in reals

[lunar temple]

t can be anything?

[slate thicket]

yes

[lunar temple]

and why you put 0 0?

[slate thicket]

like (0,0,6) is a point on z axis

so is (0,0,2)

[lunar temple]

because we want only z axis

[slate thicket]

yes

[lunar temple]

ohhhh ok ]

thanks

[slate thicket]

so can we write it as

t(0,0,1)

[lunar temple]

) 𝑟⃗ = (1 , 2, 4) + t(0, 0, 1), tR

[slate thicket]

yes

[lunar temple]

thanks

.close

[pearl pond]

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[slate thicket]

[pearl pond]

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[copper kestrel]

I feel like it's E just because f'(x) seems like it hits 0 for C

is that right? I'm unsure how to consider f''(x) (or if I even need to)

[real scarab]

f'' tells you about the acceleration

is the slope growing or decreasing?

[copper kestrel]

for E it's growing I think?

ohhhh

[real scarab]

yeah

but for C

after 0 the slope is more and more steep downhill

so its decreasing

so yeah its E

[copper kestrel]

I see

thanks

.close

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[willow ermine]

does this look correct? i’m confused if i’m switching the functions by mistake

[pearl pond]

Please don't occupy multiple help channels.

@willow ermine Has your question been resolved?

[willow ermine]

<@&286206848099549185>

[severe quartz]

24 is false yes but ur reasoning is wrong

Oh yes its not false

25 is not correct as well

26 its true that it dne but im not sure what 16 and 3 have to do with it

Ah wtf i keep forgetting its -2

[willow ermine]

so for the top two i did switch them because of the negative and positive?

and for 26 since my two answers weren’t equal i put dne im not sure if that’s the right thinking

[severe quartz]

For 24 x approaches -2 from the left side

So u have to use the last definition

[severe quartz]

It is the right thinking, but neither of those answers should be 3

[willow ermine]

my bad i meant to put 4

[severe quartz]

Do u get 24 now

[willow ermine]

yea i got it now thank you!

.close

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[crude rune]

Can someone please help me graph this in desmos

<@&286206848099549185>

[pearl pond]

@crude rune Has your question been resolved?

[graceful cloud]

fit some curve to them datapoints i guess

[pearl pond]

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[crude rune]

.close

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[tropic saddle]

$e^{\ln^2(n)} = e^{\ln(n)\cdot \ln(n)} = \left(e^{\ln(n)}\right)^{\ln(n)} = n^{\ln(n)}$

[jolly parrot]

Denascite

[pearl pond]

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[tropic saddle]

yes

(a^b)^c = a^(bc)

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[pearl pond]

Please don't occupy multiple help channels.

[spare citrus]

<@&286206848099549185>

How about this one

[midnight haven]

That’s the thing, it’s a class of 60. I think it may be a error

Or I may be thinking of it wrong 🤔

Right my fault thinking of it wrong then for sure

[spare citrus]

Bago can u solve the second one?

Thank you very much my guy have a great day

[pearl pond]

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[lyric lintel]

Need help with integration

[lyric lintel]

I am studying classical mechanics and am having a hard time understanding volume and surface integrals

If someone can please explain them properly

[midnight haven]

would this be volume of revolution?

[lyric lintel]

#2

Like how did he change the integrations from -l/2 to 0

[pearl pond]

@lyric lintel Has your question been resolved?

[pearl pond]

@lyric lintel Has your question been resolved?

[pearl pond]

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[upper violet]

need help with this

[feral sedge]

are there any angles you can find now?

with the ones you already have

[upper violet]

F?

cause it’s congruent

[cosmic widget]

im sorry to bother but how can i create my own channel for help?

[upper violet]

scroll to the top

Channels

there is math help available channels

do u see it?

[cosmic widget]

is it help-2?

[upper violet]

yeah any one of those

just ask your question

[cosmic widget]

thankss

[upper violet]

np

@feral sedge

u there?

[feral sedge]

ye

[upper violet]

is it f?

[feral sedge]

which F

[upper violet]

d is 107

is f also 107

cause it’s congruent

[feral sedge]

there's like 3 angle Fs

do you mean DFB?

[upper violet]

yeah

[feral sedge]

Nah you don't know that triangle EDF is isosceles

look at the two angles you do have

are they part of the same triangle?

[upper violet]

it says be is congruent to bc

[feral sedge]

yeah but how does that make angle DFB equal to CDF

[upper violet]

so what angles are equal?

[feral sedge]

well

what triangle is isosceles

[upper violet]

DAC

[feral sedge]

It is?

What 2 sides are the same?

[barren hill]

@upper violet <AFB is 73 degrees

73*

[upper violet]

uhh

[barren hill]

bc

when u look at the triangle

[upper violet]

yeah

[feral sedge]

???

[barren hill]

just gonna move that down here

according to klue

[feral sedge]

no it isn't

[barren hill]

klu

[upper violet]

what

[feral sedge]

oh

[barren hill]

according to klu

angle DFB is 107 degrees

[upper violet]

yh

[barren hill]

which means that the angle of AFB is 180 - DFB

because its a straight line

which means the two angles need to add up to 180

[feral sedge]

he did say that angle DFB was 107 degrees

but it's not true

[barren hill]

oh was he wrong

[upper violet]

it’s not 73 though

yeah I just entered that

[barren hill]

if DFB was 107 then itd be 73

[upper violet]

it’s not right

[barren hill]

yea ok

sorry i thought DFB was 107

[upper violet]

no it’s adc

that’s 107

[barren hill]

ohhhhh

yeah yeah

ok gimme a min imma try to solve it

[upper violet]

I need to finish this

can you help me again @feral sedge

[feral sedge]

yes

[upper violet]

I’ll bring it down again

[feral sedge]

the 2 angles you have

are they part of the same triangle?

[upper violet]

no

I mean yeah

[barren hill]

klu

[upper violet]

adc

yeah?

[barren hill]

are ADE and DFE congruent

[upper violet]

no

[barren hill]

okay

[upper violet]

BE and BC are

[barren hill]

well yeah but we dont know either of em

[upper violet]

yeah

[feral sedge]

ok so

they're part of the same triangle

what does that tell us about the third angle

[upper violet]

all add up to 180

[barren hill]

oh

klu

i solved it

basically

@upper violet

[upper violet]

you did?

[barren hill]

yes

so

AFB and ADC are 2 angles in a triangle

so now we subtract 151 from 180

because we need that to find the 3rd angle

which is 29

which means that ACD is 29 degrees

which also means that FED is 29 degrees

and we know that ADC is 107

which means that FDE is 180 - 107

which means FDE IS 73

so now we know that FDE is 73 and FED IS 29

[feral sedge]

yeah

nice

[barren hill]

so to find EFD

we subtract 73

• 29 from 180

which is 78

bc 73 plus 29 is 102

plus 78 is 180

[feral sedge]

ye

[barren hill]

and we know that AFB and EFD are the same angles

[upper violet]

yeah

[barren hill]

which therefore means that AFB equals 78

and thats pretty much it

bc when u look at the problem

[feral sedge]

oh didn't realize the person writing switched lol

[barren hill]

u can make out ab 2 or 3 different triangles

[barren hill]

lol ive been working on the prob

so theres ur answer klu

[upper violet]

ty so much guys

[barren hill]

idk if i explained that well enough

[upper violet]

really appreciate it

[barren hill]

yeah i just took geo last year

[upper violet]

you did ofc lol

[barren hill]

ofc ofc

[feral sedge]

np

[barren hill]

do u have any more problems

[upper violet]

no that’s it for today

gonna go finish the rest of my hw

but ty again

[barren hill]

okay dm me if u need help w anything im bored asf

[barren hill]

fsfs

do u understand how i solved the problem though

[upper violet]

yeah I do

[barren hill]

okay!

[upper violet]

I read everything so I get it now

[barren hill]

okay cool cool

good luck w the rest

[upper violet]

ty

[feral sedge]

i have a geo problem if u want lol

[barren hill]

sure

what are u tryna find

[feral sedge]

show these 3 angles sum to 90 degrees

not a problem for hw or anything but just a fun one

[barren hill]

sure

well doesnt each angle equal 90/3

if all 3 are congruent and add up to 90 degrees

[feral sedge]

they're not congruent

[barren hill]

isnt each angle 30 degrees

OOP

[feral sedge]

it's just 3 squares

[barren hill]

i thought those were congruent signs

so u wanna find d f and e?

[feral sedge]

just the indicators for which ones to add

yeah

[barren hill]

ok one sec

[feral sedge]

it shows <EFB is congruent to <BDF but that's not originally given

it might be a hint

[barren hill]

alr i got this

[feral sedge]

seems like the hardest part is to show that actually

[barren hill]

u mean EBF?

[feral sedge]

yea

[barren hill]

ok well angle E is 45 degrees

[feral sedge]

this is the original

[barren hill]

hm

well angle e is 45 degrees

[feral sedge]

ye

[barren hill]

which means

the angle to the left of e is 135 degrees

[feral sedge]

i think this problem is really difficult

idk how i'd solve it without trig

[barren hill]

im not going to bed till id solve it

[barren hill]

facts i could probably use law of sines

[feral sedge]

the solution is really crazy if you want a hint

[barren hill]

sure

[feral sedge]

1 sec gotta make a good diagram

drawing 3 more squares on top and doing this should help some

also giving the angles names

[barren hill]

ohhhh

[pearl pond]

@upper violet Has your question been resolved?

[feral sedge]

ah did u find the solution lol

i can post further if u want

.close

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[midnight haven]

A metal alloy is 25% copper. Another
metal alloy is 50% copper. How much of
each should be used to make 500 g of an
alloy that is 45% copper?

[midnight haven]

Im so confused

I just need 2 equations

but i dont get it..

probably convert the % to decimal point

but like still how do I make 2 equations out of that

[fierce oxide]

let amount of 25% alloy be x, where amount of copper is 0.25x grams
amount of 50% alloy as 500-x , where amount of copper is 0.5(1000-x)=500-0.5x grams

can start from here

[midnight haven]

ummmm

[pearl pond]

@midnight haven Has your question been resolved?

[grim patrol]

magic

hm

then also uk the amt of copper in the final alloy is

.45*500

so

.45*500=.25x+(500-x).5

[pearl pond]

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[cobalt valve]

how would i re write this?

e^-2-x?

[vague basin]

When it's asking to find the domain, what is it asking you to do?

[cobalt valve]

(-oo, oo)?

thats it, right?

its finding where the function can be

left and right

but, dont i need to convert this to be an exponential?

[vague basin]

Is $ln$ defined for all $x$ values?

[jolly parrot]

beeswax

[vague basin]

I don't see why you would in this example

[cobalt valve]

ln cant be less than zero, right?

[vague basin]

If you have ln(x), x can't be less than 0, correct

Can x be 0?

[proven swift]

x > 0 for lnx to exist I think

[cobalt valve]

non inclusive... right

[proven swift]

no ln0 is undefined

[vague basin]

Okay, so going back to our problem, how can we figure out where our function isn't defined?

We just established that the input for ln has to be strictly greater than 0

[proven swift]

firse you have to put the condition that -2 - x > 0 for the function to exist

[cobalt valve]

By funding what would make it zero

[proven swift]

which then suggests that x < -2

[vague basin]

bingo

[cobalt valve]

So (-oo,

-2?

[vague basin]

Including -2?

[proven swift]

(-oo, -2)

[vague basin]

Nice

[proven swift]

no excluding it

yeah

bc if u inlcude -2 then it'd become ln0

[cobalt valve]

Sick

So when would i have to convert it to an exponential??

Or never?

[proven swift]

yeah, but it's gonna get a hell lot more complicated in higher studies

[cobalt valve]

Hahahaha 😂

[proven swift]

why do u have to

it wont be necessary

[vague basin]

I don't see how the exponential plays a role in finding the domain

[cobalt valve]

Well, i just remember that the teacher today kept saying that know how to convert these into exponentials was super important

For future problems

[proven swift]

not sure abt that tho but u don't need to convert it into exponential for this question

[cobalt valve]

Right ok, thanks m8

[proven swift]

no worries

[cobalt valve]

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[pearl pond]

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[pearl pond]

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[round temple]

Hint: ADC + ADB = 180

[karmic swallow]

ty

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[terse aspen]

What is the ratio of the sides of a rectangle whose lengths are a and b if its perimeter is o=36cm and the length of b is 2cm longer than the length of a?

[hollow cobalt]

Plug in b = a + 2 into 2(a + b) = 36

And solve for a

[pearl pond]

@terse aspen Has your question been resolved?

[terse aspen]

would it be 6?

[hollow cobalt]

a = 8

Because 2(a + b) = 2(a + a + 2) = 2(2a + 2) = 36
2a + 2 = 18
a + 1 = 9
a = 8

[terse aspen]

oh

how is it 18 tho?

[hollow cobalt]

36/2 = 18

[terse aspen]

Thanks

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[gentle ingot]

Pls explain how integration of v becomes v instead of v^2/2

[hollow cobalt]

Because we're integrating with respect to t

[gentle ingot]

Yeah but

Integration of x should be x^2/2 right?

[hollow cobalt]

Integration of x with respect to x*

[gentle ingot]

Wdym

[hollow cobalt]

Integral of x with respect to x is x²/2 + c for some constant c
If we integrated with respect to some other independent variable, let's say with respect to a, then the integral would be ax + c for constant c

[gentle ingot]

So if we are integrating with other variables we need to multiply?

[hollow cobalt]

Would be more correct to say that we treat other variables as constants

[gentle ingot]

So like integration of h^2 from 0 to x would be h^2x

?

[hollow cobalt]

As long as it's with respect to x, yeah

[gentle ingot]

I see

Ty

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[amber basin]

hello!

[amber basin]

how can i prove that x^(5)-7x - 1 = 0 has a solution in [-1,1]

[tropic saddle]

IVT probably

[merry python]

try plugging in -1 and 1

and notice it's a continuous function

[amber basin]

f(-1) = 6
f(1) = -7
like this?