help-23

[night oxide]

im thinking the resultant sum is max when they are parallel, and cancel each other out when anti parallel

so both 3 and 4 would be wrong in this case

[dusk nova]

yeah that's good enough

"cancel each other" is not the right description though

parallel doesn't imply they have the same magnitude

but your idea of "canceling" is correct

[dusk nova]

[night oxide]

thx!

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[dense wadi]

im not too sure about the top part of C

[glacial sonnet]

it's just one less than the denominator

also

your part a and b are wrong

a should be $\frac{1}{36\cdot 6^n}$

[flat frigate]

chebyshev's infinite pee norm

[glacial sonnet]

and for b, the signs are alternating which is represented by (-1)^n, but it starts positive so we offset with (-1)^(n+1)

[glacial sonnet]

oops sorry it should be a 6^(n-1) since n starts at 1

[dense wadi]

ah yeah i forgot to add exponents oops

[dense wadi]

ah okay okay

[dense wadi]

isnt it n-1

if im not mistaken

[glacial sonnet]

they're the same

[dense wadi]

oh right

[dense wadi]

oh bruh

im blind asf

[glacial sonnet]

$(-1)^{n+1} = (-1)^{n-1 + 2} = (-1)^2(-1)^{n - 1} = (-1)^{n-1}$

[flat frigate]

chebyshev's infinite pee norm

[glacial sonnet]

[dense wadi]

tyty!

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[sudden sparrow]

can someone help me solve this

[sudden sparrow]

do i just need to find the missing side?

or find all angles?

[versed wave]

wdym? the question only asks you to find 1 specific angle

this angle can be found using

,tex .law of cosine

[flat frigate]

your local hot fungus

[sudden sparrow]

which angle

thats what i mean

i just dont understand what the question wants

[versed wave]

read the question out loud

[sudden sparrow]

so they want angle T?

[versed wave]

yes

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[sudden sparrow]

how would i find angle t?

[sudden sparrow]

using this?

this is cos law right?

[versed wave]

yes

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[shadow folio]

.occupy

Find the greatest number of 6 digits exactly divisible by 24,15 and 36

[shadow folio]

So, I know that 3 is divisible as it is the hcf but how can I find greatest 6 digit number

[hazy elbow]

hint:||largest 6 digit number divisible by all three of them must be divisible by their LCM||

[shadow folio]

480 is the LCM

It ain't 6 digits...

Do I just take the largest 6 digit number divisible by 3

[hazy elbow]

well, you misunderstood me

can you find the largest 6 digit number divisible by 480?

[shadow folio]

Oh

I got 998400

[hazy elbow]

well

999999-required number < 480

just divide 999999 by 480 and tell me the rem

[shadow folio]

So,

I did some trial and error

And found 999000 is the number

But don't know how to represent

@hazy elbow

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[dense wadi]

so this gives 1^inf

which is indeterminate

but after every LH attempt i get 1

is it normal

[lean otter]

by what do u mean "is normal"?

if u mean ur answer of 1 is correct, then no, it is not

Also, I wouldn't recommend L'H for this problem as id say it greatly overcomplicates the situation

[dense wadi]

is there another way i could?

[lean otter]

yeah

there is

so

,, e^x = \lim_{n\to\infty} \8{1+\4xn}^n

[lean otter]

this is called the limit definition of e, and is taken as fact if you do not know any other definition of e

are you familiar with it?

[dense wadi]

uh ive never seen it no

[lean otter]

well the gist of the story is that this is how you define what e is, and e^x by extension. Its really something you should remember in my opinion

[lean otter]

anyhow, what u have here is pretty much exactly that limit, but slightly modified

the + 2 in the denominator can be ignored as its effect is negligble at infinity

[dense wadi]

idk if its that i hevant learned it yet but

wait then

x+n is

basically going to 0

still right?

[dense wadi]

from here

[lean otter]

x + n?

[dense wadi]

x/n sorry

so bascially my thing is e^-7

[lean otter]

yeah

exactly

[dense wadi]

uhm wtf ive never learned it

maybe i skipped something

anyway tysm!

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[lean otter]

if you see any limit that is of the form (some rational function inserted here)^(some polynomial here) then the limit of e can probably be applied with some substitutions

so like, L'H and differentiating the thing can be entirely skipped

whether thats simpler or not is up to you i guess

(here it clearly was though)

[dense wadi]

ahhh anyway

tyty!

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[mossy rover]

Probability

[mossy rover]

The last part

I’m not sure of the way

Don’t mind the answer I know it’s wrong but the way is it right?

<@&268886789983436800>

<@&286206848099549185>

[warped roost]

please do not ping moderators for math help

[mossy rover]

Mb

[rigid jetty]

find the probability of picking a red then blue and add the probability of finding blue then red

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[cloud rock]

How do I find x int

[cloud rock]

So I could graph it

idk if im doing it wrong but im stuck at 2^x+1 = 1 when looking for x int

[ember sphinx]

the only way any power of any number can be 1 is if that power is 0

ie x^0 = 0 for any x (apart from like 0)

SO

2^(x+1) = 1

x+1 = 0

x = -1

[cloud rock]

im a little confused

wait

oh nvm

i dont get it

[cloud rock]

for this are u just getting out x+1?

and solving it?

[ember sphinx]

The only way

[cloud rock]

oh

[ember sphinx]

for any exponant

to equal 1

is to have the power

equal 0

[cloud rock]

ok i get it now

i was confused where the 2 and 1 went in 2^(x+1) = 1 but i got it now

thanks

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[lean otter]

Hello

[lean otter]

I Need help understanding what im being hold to do

give me a second to post

I'm being asked to find what jan's error is and find the correct volume and surface area of the cone.

Is that correct?

[tranquil ore]

Yes

[lean otter]

Im having issues finding what the error is

Looks like 22M and 22m

or 22 for base

and 22 on left and right

Im unsure

It's half a circle I guess

However Thats not right

I think it may be 22m for the circle

so 22m + 22m

semicircle

that just seperates it

a line

I am unsure what you mean

diameter

where's jans error?

Yeah I see 22 m x 2 on bottom

22

yeah but the slant height is 22

so she thought it was 11M?

So they want me to find what her error is

then include the surface area and volume?

Her error was check used the height instead of the slant,

How can I find the surface area

11 is the radius of the base, 22 is the height. so we

so we got to 2x that?

so we do 2x?

So the L would be 2 right?

Im confused, im sorry

So what do I do to find the surface area if I got 11 as the base and 22 as the height

I am unsure what hypotenuse is

im confused how to get a number out of that

Her error was check used the height instead of the slant, We can find the surface area by doing 11 m base + 22 m height = 33m?

Why ^2

Her error was check used the height instead of the slant, base = 11m height = 22m We can find the surface area by doing 11^2 + 22^2 = 11^2 = 121 + 22^2 = 484 = 121 + 484 is 605. So we got sqrt(605) for slant height

so 605 is the surface?

[flat frigate]

faiyrose

faiyrose

faiyrose

[lean otter]

I don't understand these forms

so find the square root of 605?

base = 11m height = 22m We can find the surface area by doing 11^2 + 22^2 = 11^2 = 121 + 22^2 = 484 = 121 + 484 is 605. So we got sqrt(605) for slant height. Square roof of 605 is 24.6 rounded

[lean otter]

Can you make this more readable?

or less long

[flat frigate]

faiyrose

faiyrose

[lean otter]

So it's still 1210?

I thought that wasnt right

[flat frigate]

faiyrose

Result:

1230.2476831458

[lean otter]

I don't understand it

How can I put the surface into this

Because im not getting 1230

[flat frigate]

faiyrose

faiyrose

[lean otter]

How can I find the volume

[flat frigate]

faiyrose

faiyrose

[lean otter]

⅓ x pi x 11^2 x 22 = 2787.26 rounded

[flat frigate]

Result:

2787.6398812853

Result:

2787.6398812853

[lean otter]

So this seems right now?

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[crisp gyro]

how would i finish doing part b, i p-sure i have to solve for x but idk how to do it with k

[pseudo scroll]

determinant > 0

that will give you two values of x and thus two intersection points

[crisp gyro]

oh ye the b^2 -4ac

so do i do a = 5, b = (2k-4), c = (1+2k) and then sub into b^2 - 4ac > 0 to get 4k^2 - 56k -4 > 0?

hold on, i forgot +7, i ended up getting 4k^2 - 56k -144> 0 so k< -2.22 and k>16.22

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[prime mason]

how did x^8 become u^2?

[desert pasture]

let x^4=u

[prime mason]

oh is it becuz if we squared (u)^2= (x^4)^2 on both sides we get x^8?

[mortal pawn]

yes

[desert pasture]

yeah

[prime mason]

Dam that was easier than I expected well thanks guys

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[sleek wigeon]

How do I do this question? I thought you had to see what variable the Lagrangian does not depend on, but here both r and rdot are in the equation

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@sleek wigeon Has your question been resolved?

[sleek wigeon]

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[raven heart]

@sleek wigeon you should try the physics server or one of the advanced channels here

[sleek wigeon]

Okay, I do maths at uni that's why I asked here sorry 😭

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[vapid bramble]

can someone help me with this one

[vapid bramble]

i tried putting it into parametric form and finding t and then plugging that in but that didnt work

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@vapid bramble Has your question been resolved?

[empty gyro]

yeah that won't work, as you're only finding where the t are equal, but that doesn't really tell you anything

[empty gyro]

solve for y and z in terms of x, then find the x where L1 and L2 would cross

[vapid bramble]

oh OK that makes sense

thanks!

I have another problem where it gives me the x y and z intercepts of a plane and says to find the equation of the plane

it says the x intercept is 9, the y intercept is 1, and the z intercept is -3

does this mean there's 3 points: (9,0,0), (0,1,0), and (0,0,-3)?

[empty gyro]

yes

[vapid bramble]

very good very good

follow up question

should I do like ab x bc to find the plane

where a is the x, b is the y, and c is the z

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[vapid bramble]

.reopen

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✅

[vapid bramble]

.close

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[north plinth]

I don't know why the part x^2 + 2x^2 + x^2 exists.

[dense grove]

i need help with this, im in highschool im so bad at maths and if someone could explain me how to solve this id be very gratefull

[steel stag]

to get x^2, 2x, and 1 to a similar form, they're saying x and 1 are both smaller than x^2 and replacing them with that

[north plinth]

Thank you!

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[lament river]

help

[lament river]

this screenshot includes question 1 and

1a and 1b

but i need help for 1c

[thin bridge]

because for the product you're considering
10x^2 * 60x^2 gives a term with x^4

they're asking for the coefficient of x^2 in the final expansion
not the product of coefficients of x^2 in each factor

$(1+5x+10x^2)(1-12x+60x^2) = ax^4 + bx^3 + \blue{c}x^2 + dx + e$

[flat frigate]

ℝαμΩℕωⅤ

[lament river]

ohh alright got it

hanks man really appreciate it

i mean thanks

btw i’ve another question

where did i go wrong? the answer key says that x = 2.5 and 0.5

ooh w air

wait*

i got it

where i went wrong was that i didn’t do the plus minus sign

damn

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[torn cave]

Hey sorry, i wont be able to ask it in a concise manner since i am not a math guy. The problem is more conceptul/abstract, it sounds like this:
Imagine event A with a chance of occurence 5% and event B with a change of occurence 50%. I can trigger a random event according to their chances for example by snapping my fingers. So in a long run obviously event B most likely will trigger 10 times more frequently. However in a short run it could be that on my first 11 snaps, event A will trigger 10 and event B only once, which is very unlikely but possible. If i will stop and look at the outcome i can come to a conclusion at this point that Event B is 10 times more 'rarer' than Event A. So the question is, if i calculate this rarity based on the final number of triggered events, what is the point of knowing the initial chances of any event triggering? I mean this information is useless , because it doesnt come into calculation. But why? I feel like here is something wrong about it, because it feels like Event A is by its nature more rarer because of its occurance rate of 5%. And it feels for me that it doesnt matter how many times i would trigger A more times than B, A will always be rarer anyway, why do i feel like that, is it because im stoopid, or is there something more about it?

[jaunty light]

so you are asking about the experimental probability, am I right?

[torn cave]

I am asking more like what defines the rarity of something, a probability of occurance or the number of occurances at the moment of measurement? Also I wish I would know what expiremental probability is, lemme look into it

[jaunty light]

I guess the definition of rarity is its probability of occurrence, but in the real world it is almost impossible to know exactly what the probability of occurrence is

that is why we calculate the 'experimental probability' to try and figure it out, though it is almost never 100% accurate

[torn cave]

when u say 'it is almost impossible to know exactly what the probability of occurrence is

[jaunty light]

consider a coin

it has a 50:50 chance of coming up heads

but say we did not know that

to figure out the chance that it comes up heads we would flip the coin a lot of times

then we could calculate the probability that it comes up heads by dividing the total number of heads counted, by how many times we flipped the coin

this is the 'experimental probability'

and if we flip the coin 100,000 times there could be exactly half of them coming up heads to give and experimental probability of 50,000/100,000 = 1/2

[empty gyro]

An ideal coin has this. Real coins are never ideal

[jaunty light]

but it is much more likely for it to be approximately 1/2 say 50,251/100,000

[empty gyro]

Probability is a funny thing

[jaunty light]

https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-probability-statistics/cc-7th-basic-prob/v/experimental-probability#:~:text=Experimental probability is the actual,be 47 heads%2C 53 tails.

[buoyant shadow]

if i understand correctly you're asking how these models apply to real life

they basically never do, so no one knows or thinks about this

so it's a hard question

[safe radish]

@torn cave Has your question been resolved?

[torn cave]

yes , i understand it, but i also understand that from 2 coin flips, the calculated expirimental probability is not precise, it gets more precise with more coin flips. What i try to point out is that for instance at the end of ur experiment '50,000/100,000 = 1/2' u understand that it is ~ 50/50, however u stopped at 100000 flips, but why? This is a good question if u will think about it, most likely u will stop because u will see that the chances do not tilt more towards one side or another after a certain period, it is almost always 50:50, however how would u know that if you will continue flipping the coins for 1 million years continously, at some point, the chances may start tilting towards the tails and eventually ratio could become 99:1 for instance, who knows. U can not prove that this is impossible, because u can not perform so much flips, therefore u can not say that the chance of getting a tails is 50/50 or 99/1, u dont know the true probability because, i now believe while writing this that all probabilities are true, depending, on when u measure, so even on the first 2 flips, if u get 2 tails in a row and stop the probability is 100:0, and this is true, does it make sense? So this also makes me conclude that the initial probability of an event doesnt matter, it only matters if such event occured despite how rare or not it is.Does it make any sense? Sry i am not rly a math guy 🙂

[buoyant shadow]

the proportion you measured is useful for predicting things about the experiments you made

so like, you use the past to predict the past

the "true probability" describes all future experiments

and you can't tell what it is by observing the past

it's more useful not less

but it's less useful to talk about it i guess, if we can;t even know it

[torn cave]

thanks for answer, but like in case with a coin, if we will consider the initial probability '50:50' to be true statement in a long run, can we say that this probability is a 'pseudo true probability'? Because i really want to believe that this probability came into people minds long before it was really measured, because it just feels natural that its 50:50, isnt?

[buoyant shadow]

i don't understand

now you're talking about what truth means

the answer to that can't come from outside

[torn cave]

sry i deviated from the topic, but thanks anyway , very interesting discussion

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[safe radish]

@formal zenith Has your question been resolved?

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[trim thicket]

How do i solve this?

[pseudo scroll]

the capacitive and inductive impedances must be equal

[trim thicket]

Can u show it to me? Thank you

Sorry i am quite new to this

[pseudo scroll]

Sure

do you understand what impedance is?

[trim thicket]

Nope

[pseudo scroll]

hmm

[flat frigate]

Sadie Carnot (η > 1)

[pseudo scroll]

does this look familiar

[trim thicket]

ohh

How do i apply this to the eqn to solve for w?

[pseudo scroll]

do you know what capacitive impedance is

[pseudo scroll]

it's similar but not exactly

[trim thicket]

not really, this was initially a chapter on complex numbers

and i was just doing practice qns till i stumble on this qn

[pseudo scroll]

is this from your unit?

[trim thicket]

Yea

[pseudo scroll]

because this is more physics than complex numbers

[trim thicket]

its weird aint it

[pseudo scroll]

oh is that what j is

the square root of -1

[trim thicket]

Yea

[pseudo scroll]

interesting I've never seen Z been represented as a complex number

[trim thicket]

Because rn i am doing engineering and the syllabus use j as the imaginary unit

[pseudo scroll]

and you haven't been taught about AC circuits in this unit?

Yeah fair

[trim thicket]

nope its just purely engineering mathematics

For this unit

how do i solve this qn though, have been stucked on it for quite a while now

[flat frigate]

Sadie Carnot (η > 1)

[trim thicket]

The answer is sqrt 3 / 2

[pseudo scroll]

yeah I think this only applies to series circuits

yours does say parallel

[trim thicket]

Yup

[pseudo scroll]

@trim thicket have you just tried isolating omega

[trim thicket]

Err idk how to begin except for conjugating the fraction on the lhs

[pseudo scroll]

,w 1/Z = 1/(1 + 2ix) + ix/2

[flat frigate]

Results provided by WolframAlpha

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

Requested by neonperseus

[pseudo scroll]

yeah that works

[pseudo scroll]

yeah it was literally that

[trim thicket]

Ohhh

Thanks

I'll try it out first

Wait i am confused on how do i go on?

Need a little help here

<@&286206848099549185>

[safe radish]

@trim thicket Has your question been resolved?

[trim thicket]

<@&286206848099549185>

[trim thicket]

<@&286206848099549185>

How do i solve this qn?

.close

[safe radish]

Channel closed

Closed by @trim thicket

Use .reopen if this was a mistake.

[trim thicket]

.reopen

[safe radish]

✅

[trim thicket]

How do i solve for this?

<@&286206848099549185>

[safe radish]

@trim thicket Has your question been resolved?

[trim thicket]

<@&286206848099549185>

[mental abyss]

Is this a physics question?

[trim thicket]

Nah mathematics complex number qn

The j is the imaginary unit

[radiant phoenix]

can you frame it more with math

idk half these units

[trim thicket]

Can you sub in the units and solve for w?

Idk how to continue from here

[oak tangle]

you can simplify it to a single fraction

then multiply the numerator and denominator by the complex conjugate of R+jwL

after that, just set the imaginary part to be 0

[trim thicket]

Ohh

Let me try it

[trim thicket]

Can you work it out to me too?

[oak tangle]

where have you reached?

[oak tangle]

yeah now just multiply by the conjugate

substituting the values first would make it easier

[trim thicket]

alright

Where do i go from here?

[oak tangle]

expand it

and keep substituting j^2=-1 where you see it

[trim thicket]

Okay

How do i expand the numerator?

[oak tangle]

multiply

(1+2jw-w^2)(1-2jw)=1(1-2jw)+2jw(1-2jw)-w^2(1-2jw)

[trim thicket]

Ohh

Whats next?

[oak tangle]

wait you made a mistake

[trim thicket]

Oooh

[oak tangle]

here you substituted c as 2 i think

[trim thicket]

Oooh

Lemme try again

Where do i go from here?

[oak tangle]

you changed the sign from + to - here

also this would be + too

[trim thicket]

Ohhh dangggg

[oak tangle]

yes its correct now

for Z to be real, Im(1/Z)=0

[trim thicket]

Ohhh

[oak tangle]

so j(2w^3-1.5w)=0

[trim thicket]

Thank you

Wait how do i present this

On paper

I dont know how to go from that to the real answer

Did i do smtg wrong

The answer is supposed to be sqrt 3 /2

<@&286206848099549185>

[oak tangle]

factor it and find the solutions

[trim thicket]

How does it become sqrt 3 /2

[oak tangle]

transpose 3/2 to the other side

2w^2=3/2

w^2=3/4

[trim thicket]

Ohhhh

Okay thank you

.close

[safe radish]

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[safe radish]

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[sharp dagger]

change the function so that it is continous at x=1

[ember girder]

just find lim x to 1 f(x)

=2

so A

[sharp dagger]

but isnt it undefined at x=1

a is correct tho

so ur right

[ember girder]

yes, that why we need to define it to make it continous

[sharp dagger]

where do u plug the 1 into

[ember girder]

it's 2 at x=1

[sharp dagger]

did u plug 1 into x+1?

to get 2

[ember girder]

2 is limit x to 1 f(x)

but it equals to x+1

[sharp dagger]

but when f(x) = x+1 , x cannot be 1 so how do u plug it in

apologies if i sound stupid

[ember girder]

i mean the origional function (x^2-1)(x-1)

sorry, (x^2-1)/(x-1)

[sharp dagger]

i think i understnd

i understand the bottom

but how did u get the first part

x+1 x cannot = 1

[ember girder]

simplify f(x)

[merry pelican]

Remember that x² - 1 = (x + 1)(x - 1)

[sharp dagger]

yeah

and ur left with f(x) = x+1

[obsidian oracle]

yes, and so f(x) = x+1 for x different from 1
you now want to CHANGE the function so that it is defined and continuous at x=1

so you are asked to define f(1) such that the resulting function is continuous at x=1

so what value of f(1) makes f continuous?

[safe radish]

@sharp dagger Has your question been resolved?

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[twin solar]

How do I solve o) using substitution?

[sharp tiger]

by parts

[ember girder]

use t replace 1/x

$\int e^tt^3d\frac{1}{t}$

[flat frigate]

pubuyun

[ember girder]

=$-\int e^tt^3t^{-2}dt$

[flat frigate]

pubuyun

[ember girder]

=$e^t(t-1)+C$

[flat frigate]

pubuyun

[twin solar]

I am not allowes to do it by parts

I have to use substitution

[twin solar]

Okey I did manage to może to -t*e^t but I do not know what tlthen sińce I can't do it by parts

[ember girder]

e^(t)=k

$\int k \ln k\space d\ln k$

[flat frigate]

pubuyun

[ember girder]

$\int \ln k\space dk$

[flat frigate]

pubuyun

[twin solar]

What did you substitute as k?

[ember girder]

e^(t)=k

[twin solar]

But then what did you do with times t

[ember girder]

d lnk = 1/k d k

t = lnk

[safe radish]

@twin solar Has your question been resolved?

[safe radish]

@twin solar Has your question been resolved?

[lean otter]

bruh

1/x = t

[twin solar]

i have already tired it

and it doesn't workj

[lean otter]

it does work

[twin solar]

nah one x will keep remaining

or

u will achive t*e^t

which won't then be solved wihtout parting formula

[lean otter]

yes

now apply parting formula

why dont you want to appl it

[twin solar]

it wab't introduced in this part of the book

so there must be another solution

which i am looking rof

for*

[lean otter]

hmm

[twin solar]

any thoughts?

[lean otter]

nope

i was thinking about some comples substitution but nah it wont work

[safe radish]

@twin solar Has your question been resolved?

[safe radish]

@twin solar Has your question been resolved?

[safe radish]

@twin solar Has your question been resolved?

[safe radish]

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[worn nimbus]

hey guys i'm just learning set theory and have to do the following proof. was wondering if i just prove this by using the set identities/logical equivalences

[worn nimbus]

this is the only real sort of example that we've gone over in the lectures

was mainly just wondering if for the question i presume that the sets are subsets of the universal set

<@&286206848099549185>

sorry for the ping

[worn nimbus]

i think it should be proven with the element method but just not sure how to interpret it

i presume we suppose that the hypothesis is true then prove that the conclusion is true

[safe radish]

@worn nimbus Has your question been resolved?

[safe radish]

@worn nimbus Has your question been resolved?

[wheat pawn]

I’d use proof by contradiction. Suppose there is an element in the set. Then it must be in (A-D), (B-D), and (C-D). Then go from there to get a contradiction

[worn nimbus]

hmm okay i'll give that a go thak you

i'm not really understanding the conditional

i seem to be alright with proving stuff using the set identities but i presume that's not applicable here and i'd be using an element proof

[wheat pawn]

The idea is to suppose the set is non empty (so hence contains an element). Then show that the element violates some of the initial conditions of the problem

[worn nimbus]

yeah that makes sense

which set are we talking about though

i was going to prove by contradiction by supposing the statement is false, hence assuming the negation is true, then showing that it's a contradiction

but i'm not sure how to apply that to the question

[wheat pawn]

Suppose $S=(A-D) \cap (B-D) \cap (C-D) \neq \emptyset$

[flat frigate]

Owen

[wheat pawn]

Then there exists an element $s\in S$

[flat frigate]

Owen

[worn nimbus]

ok i think i understand

so we're proving that s doesn't exist

in S

that leads to a contradiction

[wheat pawn]

Yes

[worn nimbus]

gotcha

alright let me try work this out

how does that relate to the hypothesis though?

[wheat pawn]

Use the hypothesis to get your contradiction

[worn nimbus]

okok

sorry for the confusion i've only done proofs where the sets are in some universal set before

[worn nimbus]

wouldn't it be curly brace notation for this since S is a set?

[wheat pawn]

Since A,B,C, and D are also sets it isn’t necessary. It’s clear S is also a set. But notation is somewhat subjective on what is the clearest to you

But your professor may prefer some notation. So use that

[worn nimbus]

gotcha

so for the hypothesis

is that saying the intersections of A and B and C are subsets of D

the order of operation is confusing me

so we're assuming that the green parts are in set D?

[wheat pawn]

Not quite

[worn nimbus]

gotcha

could i just let x be an element of D

then take the conclusion

[safe radish]

Channel closed

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[worn nimbus]

.reopen

[safe radish]

✅

[wheat pawn]

In your drawing $A \cap B \cap C$ is empty. Your shaded regions are $A \cap B$ and $B \cap C$

[flat frigate]

Owen

[worn nimbus]

hmmm okok

i understand

[wheat pawn]

Can you explain this more?

[worn nimbus]

using the set differene law i can transform the conclusion into this

then because x is an element of D, it is not an element of D complement

therefore it's empty

that feels wrong

[wheat pawn]

You can a,ways assume all the sets are subsets of some universal set

[worn nimbus]

ahhh ok

yea that was kind of my original question lol

would that be helpful with this question though because we're considering everything in the context of being a subset of D

[wheat pawn]

It is wrong. You did the case where x is an element of D. You also need the case where x is not an element of D. Since there is no reason x has to be in D by the initial assumption.

[wheat pawn]

This isn’t true. A,B, and C are not necessarily subsets of D. Just the intersection

[worn nimbus]

ahhh okay gotcha

that's more clear now

[wheat pawn]

For instance D could be the shaded blue set.

[worn nimbus]

yeah i get that

how would i go about proving that S is empty based on the hypothesis

[wheat pawn]

Use this and the fact that set intersection is distributive.

[worn nimbus]

what does that mean

because D^c is intersecting each set

[wheat pawn]

$(X \cap Y) \cap Z = (X \cap Z) \cap (Y \cap Z)$

[flat frigate]

Owen

[worn nimbus]

is that the distributive laws?

would be nice if that was included on here lol

[wheat pawn]

I don’t think it’s officially distributive law. But it is very similar

[worn nimbus]

i see how it works but i've only ever seen it with alternating signs

wait

i feel like that shouldn't work because of the associative laws

wait nvm

how does this look

i'm pretty sure it's wrong but i'm just trying to understand where i went wrong

i presume proving that x isn't an element of S doesn't prove that it's empty?

[safe radish]

@worn nimbus Has your question been resolved?

[safe radish]

@worn nimbus Has your question been resolved?

[safe radish]

@worn nimbus Has your question been resolved?

[worn nimbus]

howso?

[grizzled fossil]

Oh sorry

I mean you can just write S subset of D \cap D^c=\emptyset from where you stopped

No reason to even introduce an element

[placid flower]

Honestly if you keep remembering this it's not effective

just apply logic and use VENN diagrams

[worn nimbus]

i'm familiar with most of them because they're similar to the logical laws of equivalence which i'm familiar with

it's on the formula sheet 🤷‍♂️

[worn nimbus]

could you explain

[grizzled fossil]

$(A \cap B \cap C)\subseteq D$, so
$$S=D^c \cap (A \cap B \cap C)\subseteq D^c \cap D$$

[flat frigate]

ScapeProf

[worn nimbus]

i don't understand

oh wait

not really

[grizzled fossil]

you have S a subset of D^c \cap D=\emptyset

So if S is a subset of the emptyset, it must also be the emptyset

[worn nimbus]

oh wait

sorry i just realised this isn't the latest one

one second

this is what i have

i got my friend to look over it and he said it looks fine but i just want to check

[grizzled fossil]

Sets aren't in other sets

they can be subsets

And just next line when you stopped type $\subseteq D^c \cap D=\emptyset$

[flat frigate]

ScapeProf

[grizzled fossil]

No reason to write ... and unclear how you reach that conclusion

[worn nimbus]

ok gotcha

wait which line

[grizzled fossil]

\begin{align*}
S&=\dots \
&\subseteq D^c \cap D
\end{align*}

[flat frigate]

ScapeProf

[grizzled fossil]

And remove all your $\in$'s.

[flat frigate]

ScapeProf

[worn nimbus]

how am i proving that S is a subset of D^c n D though

[grizzled fossil]

if you take intersection of something larger

[worn nimbus]

is that better?

sorry i've been doing this shit all day my brain is fried

[grizzled fossil]

No reason to add since ... just continue
and then write hence S=\emptyset or smth.

Since you use S is a subset of the emptyset so it must be equal

[worn nimbus]

so i shouldn't restate it

[grizzled fossil]

Can do it after or to the side if you want to

But it just makes it harder to read if you add it in the middle

[worn nimbus]

hmm ok i gotcha

but other than notation is the proof solid?

i always second guess myself with proofs lol

[grizzled fossil]

si

[safe radish]

@worn nimbus Has your question been resolved?

[safe radish]

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[rustic grail]

Just need the answer. Thanks.

[safe radish]

@rustic grail Has your question been resolved?

[safe radish]

@rustic grail Has your question been resolved?

[rustic grail]

<@&286206848099549185>

[young nexus]

!noans

[safe radish]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[rustic grail]

Sorry, wasn't aware. I am actually interested in learning the steps but I thought I would get a prompter answer without the hassle.

I would be open to seeing the steps to the solution.

[young nexus]

can you formulate the question in your own words?

[rustic grail]

Yeah. I can tell that the intervening years are irrelevant. Since the rate is to be calculated in absolute terms, the calculation pertains exclusively to the entries for 2005-06 and 09-10.

Therefore, flowers gets immediately relegated since even without putting pen to paper, I know that the increase in percentage there is twofold (i.e. 200%).

[young nexus]

calculate the rate for each crop

[rustic grail]

And also, I can reject Total Horticulture by similar estimation.

[young nexus]

whats the rate for total?

[rustic grail]

As I say, I do that by estimation alone without putting pen to paper. Same for Flowers though it's a bit easier to get to 200%.

Essentially, I have 60-70 seconds to solve a question like this in my exam and I need a fool-proof procedure.

[safe radish]

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[safe radish]

@rustic grail Has your question been resolved?

[safe radish]

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[eager kestrel]

working on a review guide and lost my notes, forgot the next step

do i distribute the x to bx+c?

[icy lance]

you can if you feel a need to

but you could just begin comparing coefficients

[eager kestrel]

i kinda remember that

not exactly how but

theres no x values on the other side

[icy lance]

so the coefficients of x and x^2 must be 0

on the right

[eager kestrel]

bx + c = 0?

[icy lance]

nono, C is the only x coefficient on the right

you dont need to expand the brackets but still keep them in mind

when comparing

B is of x^2

[eager kestrel]

oh like if i distribute it

[icy lance]

yeah

[eager kestrel]

A wouldnt be 0 bc theres a +1 in the bracket right

[icy lance]

yup, your A=1 is fine

[eager kestrel]

so if b and c are both zero

how do i express the answer

[icy lance]

is B 0?

[eager kestrel]

theres no x^2 value on the left side?

[icy lance]

on the right you have (A+B)x^2

A+B=0

but A=1

so...

[eager kestrel]

what

[icy lance]

B cant then be 0

otherwise A=0

[eager kestrel]

where did you get the (A+B)x^2

would this bc easier if i just expanded everything

[icy lance]

if it helps you then it may be so

doesnt make things harder in any case

[icy lance]

yup

constants: 1=A
x : 0=C
x^2 : 0=A+B

[eager kestrel]

ohh i see

alr ill prolly be back in a few

.close

[safe radish]

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[eager kestrel]

to be clear thats
x+4 = Ax(x^2+4) + B(x^2+4) + (Cx+D)(x^2)

im not sure how i can start comparing coefficients here

.close

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[delicate birch]

how can we have the right side guys

[steel stag]

since you have thing + 7/100*thing, it turns into (1+7/100) thing and that gives you the extra part to make it squared

[delicate birch]

oh okay

i got it

thank you so muchhh

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[lean otter]

Is this by hand?

Def u sub

[winter fern]

what do you mean by hand?

[trim swan]

or, recognize sqrt(4-x^2) as the top half of a circle with radius 2

[winter fern]

Am I supposed to use trigonometry substitution

[white swallow]

Yes

[trim swan]

Since you know what that is, probably yeah lol

[white swallow]

x=sin(t)

[winter fern]

I really dont know what that is or how to do it. I just know thats what im supposed to do

Ive been trying to learn it for the past 2 hours but ive never even taken trig before lol

[neat fable]

If you recognize that it represents the area of a semicircle with radius 2,
area of semicircle is 1/2 pi r^2

so 1/2 pi (2)^2 = 2 pi

there is your answer, value of the integral is 2 pi

[trim swan]

the trig sub would be x = 2sin(t), wouldn't it?

[neat fable]

alternatively just solve with trigonometric sub

[winter fern]

I think thats how my professor expects us to solve it on the test

[white swallow]

Oh yea that

[winter fern]

How do I know what to put in there though

[trim swan]

generally if you have something involving the form
a^2 - x^2
you want to do
x = a*sin(theta)

if you have something with the form
x^2 - a^2
you probably want
x = a*sec(theta)

and if you have something with the form
x^2 + a^2
you probably want
x = a*tan(theta)

In this case you have 2^2 - x^2, so it's a good idea to try x = 2sin(theta)

[winter fern]

So I would have sqrt of 4-2sin(theta)

[trim swan]

No, that isn't what you should get if you substitute x=2sin(theta)

you don't have 4-x, you have 4-x^2

[winter fern]

it would be squared

[trim swan]

Yeah

[winter fern]

so can I remove the square root and write it like 2-2sin(theta)

<@&286206848099549185>

[civic pollen]

u can also use the formula of underroot asquare-xsquare

[winter fern]

what is underroot?

[neat fable]

no!

[civic pollen]

anything to the power 1/2

[flat frigate]

misha

[winter fern]

how did you simplify that?

[neat fable]

huh

[winter fern]

like how did you turn 4-2sin0^2 into 4-1-sin^20

[flat frigate]

misha

[civic pollen]

this is the general formula . It was given in our textbook . u can write 4 as square of 2 and use this formula

did it help?

[safe radish]

@winter fern Has your question been resolved?

[safe radish]

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[calm kraken]

How do I find out the answer to this question

[calm kraken]

So confused

[shadow tapir]

the solution will be the intersection between the two graphs

you dont actually need to solve for x there

just look at the graph

[safe radish]

@calm kraken Has your question been resolved?

[calm kraken]

Yeah I understand that

Now

But how do I find out which one is the answer lol

[shadow tapir]

A is showing the point (0,4)

but (0,4) isnt the intersection of the two graphs

B shows (0,2.83) which again isnt an intersection

D also doesnt

however C shows the intersection, which is (-1,3)

[calm kraken]

Okay

I see

Thanks

Could you explain what it means by “find the zeroes”?

Are they meaning the x intercepts?

[unique citrus]

Most likely, yes

[calm kraken]

Okay

[safe radish]

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[calm kraken]

Do I find x intercepts on the simplified equation ?or on the original

.reopen

[safe radish]

✅

[unique citrus]

It should be the same either way but it depends on whether you are expected to derive them by hand or if you can just put it in a graphing calculator

[calm kraken]

Meant to derive them by hand

[calm kraken]

But I did it in the simplified equation and got it right

Would you be able to teach me how to solve this question, I am so confused don’t even know where to start..

@unique citrus

[unique citrus]

You're just filling in values

into the table

Do you know what an asymptote is

[calm kraken]

Yeah a non permissible value.. it can’t be on the graph

[unique citrus]

Do you know what happens to a function as it approaches an asymptote generally speaking

[calm kraken]

It gets really really close to it but never touches the asymptote

[unique citrus]

So, I'm confused then as to what the issue is, you seem to understand what an asymptote is

It's basically just saying "fill in these tables and explain how they relate to the asymptote"

[calm kraken]

Idk what to do

How do I fill in the table

With which values

[unique citrus]

You would just plug in the x values into the function

f(x) is a function which takes x in and spits out a value

In fact if you use Desmos you can do this

(getting a video rq)

https://desmos.com/scientific

saves you a lot of time

@calm kraken

[calm kraken]

I can’t use desmos on a test tho

Ok so plug those x values into the equation get the f(x) values then what

[unique citrus]

then use a normal calculator

It doesn't need magic features it just needs to be able to compute the result of plugging in a value

[unique citrus]

yes

and then talk about what it shows you

in regard to asymptotes

[calm kraken]

Okay

I see

Thanks

[unique citrus]

👍

[calm kraken]

@unique citrus one last question

How do I do these

@unique citrus

[safe radish]

@calm kraken Has your question been resolved?

[unique citrus]

I am going to bed

These are just graph transformations you will need to memorize what they look like or you can kind of figure it out in your head

I can’t help you with the problem without just doing it for you but just learn these shapes and what the functions that produce them are

[safe radish]

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[safe radish]

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[paper laurel]

I need help with this question. It says it is a linear combination but v3 is a free variable

[quick iron]

In simple words it's asking if we can write vector w in the form of the combination of 3 vectors that is v1 v2 and v3 ?

[paper laurel]

So I write it in an 2x4 augmented matrix

[quick iron]

Never learnt matrix and determinant in depth...

😞

[paper laurel]

No worries. Is there someone who has?

[quick iron]

I guess so

There are many people

[paper laurel]

How can I reach one?

[quick iron]

Just do "<@&286206848099549185>"

Uh oh

After 15 minutes

[paper laurel]

Okok

[safe radish]

@paper laurel Has your question been resolved?

[paper laurel]

<@&286206848099549185>

[lean otter]

Hello

You need help?

[paper laurel]

Yea

[lean otter]

What's the problem/question?

[paper laurel]

I need help with this question. It says it is a linear combination but v3 is a free variable

[lean otter]

Isn't v3 a vector?

It's not a free variable

[paper laurel]

It’s a 2x4 augmented matrix. Wont v3 be a free variable?

[lean otter]

There is no 2*4 matrix

[paper laurel]

How would u set it up?

[lean otter]

Assuming w is a linear combination of v1, v2, and v3, we get: w = a*v1 + b*v2 + c*v3

And then solve for the values

Well, I will be right back

My doordash is here

Hey, I'm back

[paper laurel]

I don’t quite understand

How do I solve for a,b,c

[safe radish]

@paper laurel Has your question been resolved?

[safe radish]

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[safe radish]

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[lean otter]

Hey, can someone please help me with this problem?

[lean otter]

BRU

IS THE WHOLE THING ONE QUESTION???

[lean otter]

Yes

It's a single proof

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

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[arctic stone]

Is this the right answer?

[twilit spindle]

why do you think it's wrong?

[arctic stone]

I am just double checking because I am not sure what to do and mathaway can be wrong sometimes

.close

[safe radish]

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[safe radish]

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[pale grotto]

wouldnt the answer be 3?

or am I wrong

[indigo wave]

At 3 it is zero

[wild mountain]

negative is when the slope goes downward

[pale grotto]

oh so -1

[wild mountain]

it goes upwards at -1

[indigo wave]

After what X value does the graph begin to slope down

[pale grotto]

oh ok at 5 it begins to go down

[indigo wave]

Not 5

The turning point is at x=3

[pale grotto]

yeah..

[indigo wave]

At all x values strictly greater than 3, the instantaneous rate of change is negative

[pale grotto]

ok I kind of get it

ok i got it

thankss again

.close

[safe radish]

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[safe radish]

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[feral finch]

im just asking if i can do dydx or dxdy, and it wont matter in the end?

like how they did dydx, if i did dxdy instead, would it matter, other than length of work?

(i dont feel like doing the work)