help-28

[exotic mason]

0.9^3 = the oak's volume

807 is the 807k per cubic meter, so times that will get around 588

[flat phoenix]

ok so the exponent is 3

cuz its a cube

and thats the equation for the cube

the length cubed

right?

[exotic mason]

yes

[flat phoenix]

ok

thank you Jon

[exotic mason]

no problem:)

[flat phoenix]

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[snow nymph]

How do I find the maximum distance of a polar graph drawn from a polar equation from the pole?

[granite torrent]

depends on situation

one approach is try to maximize r

[snow nymph]

could you explain how to do that

[granite torrent]

uh

.. heavily depends on situation

though in most cases it is fairly obvious

[snow nymph]

so lets say I had this, how would I maximize that?

[granite torrent]

u find when 3 - cos(6t) is at a maximum absolute value

[snow nymph]

so how do I do that without derivatives

do I just use the graph of cos(x)

I'm assuming so

[granite torrent]

pretty much

[snow nymph]

ok it all makes sense with trig functions thanks 💀

[granite torrent]

cos(ax) ranges from -1 to 1 so that's all u need to know

[granite torrent]

welcome

[snow nymph]

🙏

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[clever bridge]

How to solve this?

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[fierce moon]

find the linear function with the properties f(-4)=0 and the slope is -3

[fierce moon]

i dont know what to do

[red blade]

you have a point and the slope

.... point-slope form

[fierce moon]

sorry i fucked my numbers up

f(-4)=2

and slope is 3

[vapid barn]

y - y0 = m(x-x0)

[fierce moon]

is the 2 the y ?

[vapid barn]

2 is y0

[fierce moon]

what would the x be

since im not given that

[vapid barn]

Huh

[fierce moon]

i have the slope and the y

but not the x

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[fierce moon]

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[gleaming quartz]

702 / 3

[gleaming quartz]

702/ 3 = 23?

I dont understand the last digit

i think its 234 MBB

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[stiff musk]

obviously false

[gleaming quartz]

Mf

Mb

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[sly solstice]

why to find when x is +ve for the dy/dx

u find the stationery point aka grad = 0?

and also what does this mean

[shell temple]

they took the domain for y for which x is positive (3/2,infinity) and the domain for dy/dx (-1,4) for which x is positive and took the intersection of the two domains and got (3/2,inf)

[shell temple]

i dont understand what u meant by this but any other values of x outside the range of -1<x<4 will give -ve values for dy/dx

They solved the inequalities for dy/dx and y seperately and took the intersection

[sly solstice]

so by finding the statianry points you can find all +ve values?

[shell temple]

yes

[sly solstice]

see what if theres like a turning point in the negative region though

it works for this one but other ones?

[shell temple]

turning point as in?

like it starts becoming positive?

[sly solstice]

hmmm

im mixing myself up

[shell temple]

theres only one turning point since its a quadratic

[sly solstice]

i did indeed mean turning point as gradient = 0, but i figured if u do set dy/dx = 0, then its not negative

but im just thinking if yoiu choose the set values between two staitoney points, how come they should be +ve, as in ik they are here, but if it was different

without looking at te graph/graphing it they kinda assumed it did they not

[shell temple]

well if im guessing ur solving the inequality wrong then

theres certain ways to solve the inequalities

[sly solstice]

or is it just because you know its parabola, and the top part of it should be all +ve

hence all vlaues in between

[shell temple]

yeah u can assume that too

since the parabola is downward

and critical points are -1,4

the values in between that should be positive

this what the graph should look like

the blue line is 2x+3 but i think u already understood that part

[sly solstice]

got it ty

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[vivid berry]

can this also be workers is inversely proportionate to time

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[sacred yarrow]

yep, the more workers you get, the less time you need

[vivid berry]

oh! So the order dont matter

[sacred yarrow]

wdym order?

when you get a worker, you need 2 hours
once you have two, you just need an hour

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[scenic palm]

how do i even start this

[scenic palm]

i know the equation A = P(1+r/n)^nt

but im not sure how to compare the two equations

i did 50001.07 = 5350
and 5000(1.07/12)^12

but the number for the latter equation doesn't seem to make sense

<@&286206848099549185>

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[solemn gate]

you cant simplify while there is an addition like that on top

you cant simplify (a+b)/a=b

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[desert cypress]

,rotate 270

[desert cypress]

help i dont get 12

what do i do

how do i start

[static bramble]

do you know what horizontal tangent means?

[desert cypress]

yes

[desert cypress]

=0

[static bramble]

=0?

[desert cypress]

yew

yea

[static bramble]

that doesn't mean anything

[desert cypress]

like its at 0

[static bramble]

try again

what's "its"?

[desert cypress]

equal to zero

tangent

it’s horizontal at 0

[static bramble]

that's better but also not correct

what does "at 0" mean?

[desert cypress]

on axis?

[static bramble]

what axis?

[desert cypress]

x

axis

[static bramble]

so a horizontal tangent means it's horizontal at x=0?

[desert cypress]

yea

[static bramble]

ok no, that's incorrect

[desert cypress]

ogh gosh

[static bramble]

perhaps you need to review what "tangent" means

[desert cypress]

😭

horizonatal tangent occurs when the derivative is 0

[static bramble]

the tangent in question occurs at x=-1, so if you're talking about x=0 then you've lost the plot i'm afraid

ok that's better

it's redundant but better

a tangent is horizontal when its slope is 0

[desert cypress]

yes

[static bramble]

ok so with that in mind, what information do you have?

[desert cypress]

the function itself

the point it passes through

and a point on the horizontal tangent

[static bramble]

your goal is to find the coefficients a, b, c

[desert cypress]

yes

[static bramble]

you should construct some equations that will help with your finding

[desert cypress]

yea

[desert cypress]

,rotate 270

[desert cypress]

i did this

i duno wat to do

[static bramble]

well you've used this info about the two points the quadratic passes through

you've not yet made use of the horizontal tangent info

[desert cypress]

nvm i got it smhmhhmhmmhmhmhmhmhmhmhmh

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[wintry panther]

how to show there is no real number a such that for arbitrary constants c_1 and c_2, c_1 cos(ax) + c_2 sin(ax) = cos(2x) + sinx

[nova basin]

Look at the behavior over a given period for the only a that could work

[wintry panther]

are you saying to restrict cos(2x) and sinx

[nova basin]

Periodic functions are much easier to study
You'd be a fool not making use of that

[wintry panther]

alr

So I was thinking

Two periodic functions are equal iff they have equal periods

But I don't know where to go from there with the linear combination side

[nova basin]

that iff is very bold

[wintry panther]

is it false?

[nova basin]

sin and cos have equal periods

[wintry panther]

ah you're right

shoot

so they're not equal if they don't have equal periods I think

[nova basin]

Yeah, so they must have equal periods

[wintry panther]

ok

So the fundamental period of sinx + cos(2x) is 2pi

I graphed it

I'd have to show that

but I'd worry about it later

How would I know the period of the linear combination side

[nova basin]

If you know some theory on periodic functions it's fine
Otherwise what's required here is frankly on the simple side of things

[nova basin]

Well, one more general question you can ask is
"If f is p-periodic and g is p-periodic, what can we say about the periodicity of f+g ?"

This is a very interesting question, which is not too complicated to think about. In your case here, again, it's on the simpler side and I hope you don't need any actual hints from me

[wintry panther]

It feels like you'd need more information about f and g to say what the periodicity of f+g is definitively

[nova basin]

Yeah you might have cancellations and a faster period than expected
That's part of why I kept it vague with my phrasing

[wintry panther]

so it doesn't seem like this could apply nicely to the problem

because the arguments of cos and sin are varying

they are always the same

[nova basin]

It is a harder problem for sure
Whose answer is much more general than this exercise

[wintry panther]

ig I just don't know how to force c_1 sin(ax) + c_2 cos(ax) to force a contradiction

I don't think I can really know much about the period of this

Even if sin(ax) and cos(ax) always have the same period regardless of the choice of constants

[nova basin]

Then please think harder

[nova basin]

This is the much simpler case where p=q

[wintry panther]

it seems to always be 2pi periodic but idk how to show that

my intuition is that the amplitudes are all that's varying

[nova basin]

Try to

[nova basin]

And you'll see it's roughly a one liner

[wintry panther]

oh yea

ok

constants don't matter, so sin(2pi + x) + cos(2pi + x) = sin(x) + cos(x)

so both sides are 2pi periodic

this doesn't force any contradiction

alr whatever

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[glass adder]

The Product Matrix is AB, A matrix times B Matrix but i forgot how to find what that equals can someone help explain

[livid scarab]

I think it's just asking you to multiply the matrices A and B

[glass adder]

yeah i get that but im having trouble mutipying them togehter

[livid scarab]

the 3rd row, 2nd column of the product matrix is going to be the result of multiplying the 3rd row of A with the 2nd column of B

[fathom saddle]

I like to think of this when I multiply matricies

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[maiden knot]

how is it that they both pass through (2,1). i dont get it. at x=2, its clearly near 0 and not 1 on the y side

[maiden knot]

oh wow nevermind lmao

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[nova ice]

google says -2 -3 and 0 are right

but

why do i have to factor?

[spare ingot]

Because it asks for all the solutions

[nova ice]

why does pllugging the suggested x value into the equation not work

[spare ingot]

oh

[nova ice]

like i tried plugging in -2 and i got -80

[spare ingot]

well

[nova ice]

0 was easy plugging worked there

[spare ingot]

2(-3)^3 = -54
10(-3)^2 = 90
12(-3)=-36

-54 + 90 = 36

36-36 = 0

@nova ice

double check your math, be careful with negatives!

[nova ice]

i even checked with symbolab

damn

how did i screw up so bad

[spare ingot]

well

how did you get -80?

[nova ice]

ok so

lets say x is -2

[spare ingot]

ok

[nova ice]

-2^3 is -8

[spare ingot]

yes

[nova ice]

2*-8= -16

[spare ingot]

yes

[nova ice]

-2^2 is -4

[spare ingot]

uh no

[nova ice]

-4*10=40

wait

ih shit

pos 4

[spare ingot]

negative * negative = positive

yes

[nova ice]

yeah whoops

oh lemme keep going and see if that was it

[spare ingot]

yea, that's what i mean, be careful with the negatives

[nova ice]

so far i have -16+40

[spare ingot]

yes

[nova ice]

then 12*-2 which is -24

[spare ingot]

yes

[nova ice]

-16+40-24

[spare ingot]

yes

[nova ice]

oh

whoops

ok phew

i was about to lose my mind

all i know is plug in and hope for the best so

[spare ingot]

Yeahh, remember even exponents will yield a positive number regardless

Odd exponents can yield negative numbers

[nova ice]

yipee!

thank you very munch

[spare ingot]

yep

[nova ice]

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[wide sundial]

does this sentence sound right?

[minor needle]

naw it doesnt

[wide sundial]

$\mathbb E[g(X)]$ exists if and only if $g$ is a $X_*P$-integrable function

[glossy valve]

Frosst

[sharp fable]

taylor swift

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[wide sundial]

or perhaps it should be that $|g|$ is $\mu_F$-integrable where $F$ is the CDF of $X$

[glossy valve]

Frosst

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[hard veldt]

Which part?

All of them?

[bleak wolf]

c and d

[hard veldt]

So there are 5 ways to choose the exit that the 3 people leave out of

and then there are 4 ways to choose the exit that the final person goes out in

Giving us 20 ways to choose the exits

And each of the adults has a 1/5 choice to choose the exit we have specified

so it is 20/5^4

or 4/125

[bleak wolf]

but isnt that the same as part b

[hard veldt]

!occupied

[bleak wolf]

use a different channel please

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[hard veldt]

o wait

mb

[bleak wolf]

oh sorry i forgot to say

[hard veldt]

You would multiply this by 4choose3

[bleak wolf]

answers r 16/125 and 108/125

[hard veldt]

Because you have to choose 3 of the adults

Giving you 16/125

[bleak wolf]

oh

[hard veldt]

makes sense?

[bleak wolf]

hmm

yep got it

[hard veldt]

ight

For d, I think its important to have a proper mental model

Instead of having a room with 5 exits, it would be easier to think of it as five distinguishable boxes, and 4 distinguishable balls

[hard veldt]

So the question is asking in how many ways can we put the balls into the boxes, such that each box has no more than two balls

If we find the number of ways, we can just divide by 625

[bleak wolf]

right

[bleak wolf]

wait why divide by 625

[hard veldt]

5^4

Each of the balls can be in one of five boxes

[bleak wolf]

mhm

[hard veldt]

So the first ball has 5 options

The second ball has 5 options

and so on

[bleak wolf]

ohhhhhh

okok

[hard veldt]

So how can we break up 4?

[bleak wolf]

wdym by break up 4?

4 what? balls?

[hard veldt]

We have to separate four balls, so writing out the different possible distribution amounts will help us

So 4 can be written as 1+1+1+1, 1+1+2, or 2+2

Anything else will require a three

[bleak wolf]

rightt

i see

[hard veldt]

So we will take cases

For the first case, 1+1+1+1

We have 5 options for the first ball

[bleak wolf]

mhm

[hard veldt]

4 options for the second ball

3 options for the third ball

and 2 options for the last ball

Giving you a total of 120 cases

Next

For the second case

1+1+2

There are 5 ways to choose a box to have 2

And there are 4choose2 = 6 ways to choose 2 balls to go into that box

Then there are 4 ways for the third ball

and three ways for the last ball

Giving you a total of 360 ways

Understand so far?

[bleak wolf]

yes

[hard veldt]

Now, for the last case

2+2

[bleak wolf]

?

[hard veldt]

I dont like that method

[bleak wolf]

oh

[hard veldt]

Lets try a diff aproach

[bleak wolf]

is this just for that last case all for that entire part

[hard veldt]

Last case

[bleak wolf]

alr

[hard veldt]

nvm i think the first aproach will be the easiest

Oki

So we have 5choose2 = 10 ways to choose 2 boxes

And then you have 4choose2 =6 ways to choose 2 of the balls to go in the first box

Then you have 2choose2 = 1 way to put the rest of them in the other box

Giving you a total of 60 ways

So summing up all of the cases

we get

120 + 360 + 60 = 540

And 540/625 = 108/125, the answer that you provided

[bleak wolf]

:OOOOO

ohhh okok i get it

thanks for helping 🙂

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[bleak wolf]

i dont get the logic behind this

[azure sky]

do you have an attempt?

[bleak wolf]

ik the denominator is 5^5 =3125

i dont get the numerator like i thought it was just 5x4x3x2x4

but that was wrong so

[azure sky]

okay, you have a really good start

the last person (person w/ 4 options) can order anything that the others ordered

[bleak wolf]

mhm

[azure sky]

so we can multiply that by 5,

but since when 2 people have the same meal,

they're are indistinct, meaning it's combinations

and when u have repeated objects, you divide by how many

so 2, in this case

[bleak wolf]

wait a min but isnt the 4 options already like considering the orders of the others

[bleak wolf]

and im also confused by this

is that turning a combination into a permutation?

or the other way round?

[azure sky]

it's more like a permutation question that has a combination inside it

like when you have a question like

[bleak wolf]

;-; that is just amazing

[azure sky]

"how many ways can you rearrange the words in 'mathematics' with the t's together"

[bleak wolf]

oh

10! * 2!/2!2!2!

[azure sky]

hmm, could you explain your thinking

[bleak wolf]

soo u take the two t's as a unit

so altogether theres 10 'units'

and then u can rearrange the T's

so its x2!

and with the 2!2!2! i just learnt that if u hv duplicate items, u divide by the number of it factorial, i dont rly know the reason behind it

[azure sky]

ohh okok, yeah i see

[azure sky]

yeah, so the reason is because

[bleak wolf]

[azure sky]

lets say you have the word aaab

[bleak wolf]

mhm

[azure sky]

actually,

lets have it as

a1 a2 a3 b

[bleak wolf]

alr

[azure sky]

but ignore the numbers, im just showing u that there are different a's

"different" a's

would a1 a2 a3 b be the same as a2 a1 a3 b?

[bleak wolf]

yep

oh wait

[azure sky]

oh wait

[bleak wolf]

yes

[azure sky]

mbmb

are you sure?

disregarding the numbers

so, is aaab the same as aaab

[bleak wolf]

yes??

[azure sky]

right

but i rearranged the a's

but u cant tell, right?

[bleak wolf]

nope

[azure sky]

exactly, so we have to divide the amount of repetitions because no matter how we rearrange the a's,

it will always be the same

[bleak wolf]

ohhh got it

[azure sky]

sorry, the numbering a's was a bit confusing

[bleak wolf]

algalg

soo

how does that apply to the

diners question

wait firstly, can u explain the multiplying by 5?

im still confused by that

[azure sky]

the last person (the only one who needs to really be considered with ordering): he can be put any where amongst the other 4, so multiply the answer by 5. Then, divide by 2 since 2 people have the same meal

[bleak wolf]

but doesnt the x4 options mean that hes already stacking up on top of the other 4 ppl

[azure sky]

wdym "stacking"

[bleak wolf]

like the other 4 ppl have taken all the options except the last one that isn't chosen

and so the last person has 4 options which are the options that the 4 ppl hv already taken

wait 4 ppl? i forgot the number of ppl

[azure sky]

theres 5 people in total

[bleak wolf]

oh right

[azure sky]

yep

we want to multiply by 5 because the "repeated order" can be anywhere

lets think of 5 * 4 * 3 * 2 * 4 as a list,

[bleak wolf]

mhm

[azure sky]

the last 4 can be anywhere in this list

since there are 5 places in this list,

we multiply it by 5

[bleak wolf]

gimme a minute i need to process this

[azure sky]

okok

here's a more mathematical way to approach

let x be any person ordering, where x1 is the first person

and x5 is the last person

[bleak wolf]

okk

[azure sky]

x1 has 5 options, x2 has 4 options, x3 has 3, x4 has 2, x5 has any of the previous options, so 4

this leads us to 5 * 4 * 3 * 2 * 4

however, we can also say

x1 has 4 options, x2 has 5 options, x3 has 4 options, x4 has 3 options, x5 has 2 options

notice how x3 is the person that repeats the order instead of x5?

we account for this by multiplying all of it by 5

[bleak wolf]

OHHH so like any of the 5 ppl can be the theortical 'last person'

[azure sky]

yes

nice

[bleak wolf]

OHH i get it now ty

[azure sky]

👍

mb, janky explanation ngl

[bleak wolf]

algalg

[azure sky]

but im glad u understand

[bleak wolf]

so then why do u divide by 2?

[azure sky]

because remember, it becomes a combination since there's repetition

like how ABCDA

if we swap the A's together,

it's still the same thing

[bleak wolf]

oh yea

[azure sky]

its essentially 2!

but 2! = 2

[bleak wolf]

oh so thats like the identical element thingy

[azure sky]

mhm

so your general formula would be something like

acc

i'll let u figure that one out urself

[bleak wolf]

😦

[azure sky]

:D

[bleak wolf]

lmao ok i'll try

ok is it

wait

n^2(n-1)^2(n-2)!/2n^n

[azure sky]

okay so your denominator looks good

[bleak wolf]

uh oh

[azure sky]

could you explain the (n-2)!

[bleak wolf]

so if theres n people, the number of options will just keep decreasing by (n-2)(n-3)(n-4) etcetc until it reaches the 'last person' which is (n-1) again

[azure sky]

ahhhh

okok i see

yeah that's right

[bleak wolf]

[bleak wolf]

[azure sky]

i just didnt think of the answer like that

nice nice

[bleak wolf]

ayy

thanks for your help

[azure sky]

yeah no worries

are u american or canadian?

[bleak wolf]

nope im australian

[azure sky]

ohhhhh

wow

[bleak wolf]

wbu?

[azure sky]

okok thats awesome

canadian

[bleak wolf]

oo cool

[azure sky]

i took data management last year when i was in my final year of hs

which is like this stuff

permutations, combinations, stats

[bleak wolf]

whoa sounds prestigious

[azure sky]

etc.

nahh

its not at all

[bleak wolf]

ye that is definitely not my type of thing

[bleak wolf]

sure..

[azure sky]

lol yeah, it's definitely tricky trying to understand what the question is asking for sometimes

but it's awesome that you're getting help for it

[bleak wolf]

its so idk theortical sometimes

[bleak wolf]

yes thanks to u i actaully get it now

[azure sky]

👍

okay, good luck in ur future math class

[bleak wolf]

tyty i'll need it

cheers

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[full forum]

@inner finch Has your question been resolved?

[inner finch]

Help

I don’t know how to continue from here

[minor crater]

huh?

[torn jolt]

our little comedian 🥰🥰

embarrassing icl

[granite torrent]

wrong img?

they have couple thousand msgs here so i assume not regular troll

[torn jolt]

nah js read the message underneath

they trolling

[granite torrent]

just feels rly out of place given what they’ve sent in this server before

has happened to me i leave my acc open and someone types some random stuff so perhaps

<@&268886789983436800> though that msg should prob get deleted

[spice orchid]

@inner finch can you explain?

[inner finch]

Bruh… was not me…

I have 10k messages in here I have never written anything like that

[wise kelp]

Why you write that kinda of stuff in here?

[inner finch]

I just have a very dumb little brother who thinks it’s fun to prank me

[inner finch]

This is what I have to essentially show and this is what I’ve done using induction

[inner finch]

That’s exactly what happened….

Delete and find a new channel please

[inner finch]

Go look at my 10,000 messages. It should be pretty clear that I don’t type that way and I don’t troll in this server…

[turbid saffron]

Ahh wher shld i go

Sry I'm new here

Well I'll lookup

[full forum]

@inner finch Has your question been resolved?

[inner finch]

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[junior tendon]

i need help

<@&286206848099549185>

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[junior tendon]

…

[torn jolt]

hi idk how to help BUT NICE USERNAME

[junior tendon]

which the bubbles or hayapapaya

[torn jolt]

hayapaayyaa O:

[torn jolt]

bubbles

[minor crater]

what's the formula for torque?

[junior tendon]

ah thankyouu

[torn jolt]

mhm so unique omg

[junior tendon]

what is a torque..

[torn jolt]

OP's problem

[minor crater]

the question is asking you about the magnitude and direction of torque

[junior tendon]

yes

[minor crater]

have you not heard of that term before doing that test?

[junior tendon]

its not really a test but okay..

also yea

never

[minor crater]

oof

[junior tendon]

oh

wait

isnt that

the

dFsintheta

[minor crater]

the thingy majingy that makes stuff spin

yes

[junior tendon]

yes

[minor crater]

precisely that

[junior tendon]

that

so

go on

why did my math turn into physics all of a sudden

kill me

[minor crater]

what's your d

[junior tendon]

0.08m

oh

OH??

0.08(12)sin(44)???

[minor crater]

yep

[junior tendon]

but its not in one of these options..

[minor crater]

you sure?

[junior tendon]

yea

[minor crater]

what do you get when you calculate that

[junior tendon]

double check

oh

0.66687203

[minor crater]

uh

hm

[junior tendon]

hmm

[minor crater]

0.72 is the closest one ig

[junior tendon]

oh

okays

ok so

direction is parallel to the

negative or positive y acis

axis

positive

am i right

no wait

[minor crater]

well you got a positive value

[junior tendon]

oh

so positive?

[minor crater]

yes

right hand rule

[junior tendon]

okayys

thats all

thanks for ur help

[minor crater]

no problem

if you are done type ".close"

[junior tendon]

okayy

.close

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[waxen flicker]

why is the answer 36? :((

my reasoning: we gotta use the a,b,c anyway, so let's count their permutations – 6
now, we have four places to insert something – _abc, a_bc, ab_c, abc_
and in each of those configurations we choose one symbol from a,b,c. Hence 4•3 and times their permutations x6 = 6•4•3 = 72

[hallow walrus]

you can have duplicates the way you're doing it here

[waxen flicker]

oh yeah

oh

I see

[hallow walrus]

for example, abbc and abbc

[waxen flicker]

_abc and inserting a is the same as a_bc and then inserting a

[hallow walrus]

yeah

[waxen flicker]

but we will have a repitition 100%, so we can simply divide by 2:
72/2=36

[hallow walrus]

a better way to count is to count all possible ways you can form a function with 2 a's

[waxen flicker]

thank you!

[hallow walrus]

and then multiply that with 3

[waxen flicker]

hmm

[hallow walrus]

what makes you say 100% repitition rate?

oh yeah well

true

that works

[waxen flicker]

1. how do you do it? 🫠
2. why will x3 give the answer?

(sorry if that's a dumb question – only starting to learn comb)

[hallow walrus]

just find all the possible ways of placing two a's

which would be 4c2

and then the b and c need to be permuted

which gives 2 cases

and you multiply by 3 since there can either be 2 a's, 2 b's or 2 c's

and each case is symmetric

so 3x2x4c2=36

[waxen flicker]

by don't we also need to /2, since two aa is the same symbol?
or we don't, because we only counted once? 🤔

I think the latter

thanks!

closing

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[lean radish]

no matter what I do my final answer is different than the one I get in symbolab.

[hallow walrus]

i can't read anything

it's too small

[lean radish]

oof hold on

damn its not working :(

[sweet bison]

bro whats this

[lean radish]

i give up

the image is like 2 pixels

i will just post it in parts

[sweet bison]

i had a derivative exam today

[lean radish]

ooh how did that go

[sweet bison]

well not bad

[lean radish]

I'm taking calc 2 and regretting it currently.

[sweet bison]

i think ill get 19

[lean radish]

out of? lol

[sweet bison]

20

you wanna see it?

[lean radish]

thats awesome

[sweet bison]

sorry man icnt help u with this iam too dumb

[lean radish]

oh sure but I want to wait for someone to see this problem first :)

[sweet bison]

ok

[lean radish]

don't worry about it I'm sure someone will one this server lol

on*

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@lean radish Has your question been resolved?

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[lethal oxide]

Trying to figure out why this change is possible:

[lethal oxide]

Why does -y turn positive y

[exotic idol]

a - b - c -> a - (b+c)

Try distributing the negative sign to the terms in the parentheses

[lethal oxide]

Hmm but aren’t I distributing 1* (x -y)

Which is -y and x

[exotic idol]

A helpful way to think about it is to replace all of the terms with real numbers

[lethal oxide]

Ok. (3-2) + (5-4) seems like it would equal (3+5)+(-2-4)

I mean I know I’m wrong I just don’t get what process I’m not seeing

[exotic idol]

Ok so

(3-2) + (5-4)

And then the 2nd phrase becomes

(3 + 5) - (2 + 4)

[lethal oxide]

Why does the 4 turn positive

[exotic idol]

Distribute the negative and this becomes 3+5-2-4

[lethal oxide]

I see.

So it’s not a simplification I guess, it’s jsut one way to factor it ?

[exotic idol]

Yes

[lethal oxide]

Thank you very much that was helpful

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[shrewd hamlet]

ive tried a couple things but, im not seeing them go anywhere lol

im trying to do part b atm

this is what ive done

i think im missing the equation that sums to 1, but im not too sure how to get it

<@&286206848099549185>

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[pseudo ether]

Need help with graphing trigonometric functions (sec)

[pseudo ether]

The equation is: y=5sec(x/3)-2

What would the b value be

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[marble fable]

In a certain right circular cylinder, the height is twice the radius. Express the volume as a function of the

radius.

16. Using the information given in Exercise 15, express the radius as a function of the volume.

[marble fable]

Alrighty so ik how h = 2r

But im kinda confused how like

For volume, we had a formula of PIr², but radius doesn't really have a formula unless you count D/2 but that doesn't help

So how would I express radius as a function of volume

I already did 15

[glad hound]

Am I overlooking something simple, or is it just asking for the formula for the volume of a cylinder

yes, with h in terms of r, but.. same thing

Do you know the formula for the volume of a cylinder, @marble fable

[marble fable]

V = PIr²h

Wait hold on I may be a little dumb

Can't I just plug in 2r for h, then isolate for r

Then wouldnt I have radius in terms of volume?

🙏🙏

Tysm

[glad hound]

I din do nuffin

[marble fable]

Your moral support was great enough

Cya

[glad hound]

😉

[marble fable]

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[lusty cargo]

How should I do this?

[sick olive]

for the second one it should be 100%

because there are no red marbles labeled 10

[lusty cargo]

so like 1/1?

since it will be a whole number

[sick olive]

ig

and the first one is 3/11

[pliant stump]

1/11 since only one marble is blue

where do you get the three?

[sick olive]

oh right sorry

idk it was a careless mistake

[pliant stump]

ya lol i was thinking something was off but your completely right about b

[lusty cargo]

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[silk rock]

what does this R stand for?

[quaint prawn]

the set of real numbers

[silk rock]

it is not the typical symbol

so it got me confused

[quaint prawn]

you're right

I assume it is still $\mathbb{R}$ but I don't know about Gaililean transformations so I can't be sure

[glossy valve]

Austin

[nimble crane]

it's definitely still the real numbers

physicists love to use boldface for stuff instead of blackboard boldface

it's one of the things i dislike about physics notation

[silk rock]

ohh

it wouldn't make sense if it wasn't the real numbers

[nimble crane]

indeed

[silk rock]

thx

[nimble crane]

imagine living in a world described by complex number coordinates

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[torn jolt]

i have some chem questions

[torn jolt]

I have this data

I have the fact that the order is 1

and that the k value is 0.032 s^-1

How much time is needed until only 0.2M remains?

[eager glacier]

might be wrong cause its been a while since i've done chem but shouldn't you use the integrated rate law?

[torn jolt]

yes

so

ln[A] = -kt + ln[Ao]

so I know k

i have to solve for t

but what am i solving for

[eager glacier]

youre solving for t

[torn jolt]

oh sorry

i knew that

what i meant was

what are A and Ao

presumably 1 is 0.2 mol/L

[eager glacier]

[A]o = [Zy]o im assuming

[torn jolt]

but which?

[eager glacier]

[A] = 0.2

you can use any of them i believe

[torn jolt]

doesn't that change my answer tho

[eager glacier]

oh okay i think i understand

so we know from the first order reaction that the rate law is rate = k[A]

[torn jolt]

yuh

[eager glacier]

so we were given the initial rate and the [A]o to find the value of k

which you solved for 0.032

[torn jolt]

yuh'

[eager glacier]

ln [A] = -kt + ln[A]o
t = ln[Ao/A]/k

[torn jolt]

yuh

wait

[eager glacier]

so lemme plug in the values in a calculator real quick

[torn jolt]

did u forget a negative

or do we ignore that

[eager glacier]

i dont think so. if you add kt to the LHS then subtract ln[A] from the RHS we can use the logarithimic rules to combine ln[Ao] - ln[A] to ln[Ao/A]

[torn jolt]

oh i did it the other way round

i subtracted Ao and moved it to the LHS

shouldn't matter tho

i think

so can i just pick any num from my table

should i pick the highest?

[eager glacier]

i think you are missing a part of the question?

"How much time is needed until only 0.2M remains?"

[torn jolt]

i have the order, rate law, rate constant, and the table

should i have another part of the question?

[eager glacier]

so when we plug in the values (Ao = 0.2, A = 0.2, k = 0.032) from the first row we get t = 0 because ln(0.2/0.2) = 0

[torn jolt]

wait

i think i know what's up

in the next q it asks

what is the half life for the reaction if 0.255M Zy is initally present

[eager glacier]

oh haha

that would make more sense

[torn jolt]

that doesn't help us in the half life eq tho lmao

[eager glacier]

yeah idk why they would ask that initial part haha

maybe im wrong tho. could be the blind leading the blind 😂

oh dang

i realized where i messed up

okay so if the question is asking "How much time is needed until only 0.2M remains?" and i took the value where [Ao] = 0.2 then obviously the time would equal = 0

so i'm assuming the question is implying that [Ao] = 0.6 as we are trying to find out how long it takes for [Zyo] to go from 0.6M to 0.2M

[torn jolt]

then what is the point of the 0.255

[eager glacier]

uh lemme figure that out after i finish this one

so im getting t = 58.43682387 seconds for [Ao] = 0.6M to [A] = 0.2M

are you getting something similar?

okay so for the question "what is the half life for the reaction if 0.255M Zy is initially present"
we know that this is a half life question and that the reaction is first order.
t 1/2 = ln(2)/k

so we would need to find the rate constant

hmm it seems like we are missing some information though

[torn jolt]

the rate constant we found

0.0320

[torn jolt]

no

i got 34.3

<@&286206848099549185>

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[torn jolt]

how do i do this

[sacred sparrow]

what's this in eng

[torn jolt]

which afirmation is true

im thinking c will be in the middle

and it will be a> c >b

but i dont know how to prove

oh sorry not c

b

a > b > c

i tried also eliminating the square root

and got

a = 2016^1070

b = 2015^1071....

c = 2014^1008

[sacred sparrow]

will help in a sec (if nobody comes along), currently in other channels :)

[full forum]

@torn jolt Has your question been resolved?

[sacred sparrow]

k, I think they'll become greater left to right

hm I'd attempt it analytically

maybe there is a faster approach by taking logarithms and using comparisons that way

but I'd construct a function: f(x) = x^sqrt(4030-x)

and show that its derivative is negative for these values

which implies that c is largest

b is 2nd

a is smallest

a < b < c

@torn jolt

are thee there 🐛

[torn jolt]

yea

where does that function comes from

maybe logs is the way

[sacred sparrow]

look at the terms

they have a linear progression

2016 -> 2015 -> 2014

and the exponents

[torn jolt]

i know

[sacred sparrow]

yea

so we can construct this function

[torn jolt]

why 4030

[sacred sparrow]

because of this linear relationship

if the base increases, the exponent gets reduced by 1 right

so if the base is 4030

then the exponent is 0

and if the exponent is 4030

the base is 0

because the middle is at 2015^sqrt(2015)

[torn jolt]

i think logs is way easier than this

[sacred sparrow]

hm k

[torn jolt]

thank you tho

[sacred sparrow]

I'll briefly try it with the function

[sacred sparrow]

we can rewrite it as: