help-0

[analog locust]

like, some number?

and I thought some derivative of y is a constant?

[vale wigeon]

what do you mean by "some number"

the derivative of a constant is 0

[analog locust]

then why does it goes to dy/dt? and not 0?

since y is a constant(I assume?)

[next pulsar]

dy/dt = 0

[vale wigeon]

no

no it isnt

nobody said y had to be constant

you're doing ODE right

[next pulsar]

if y = const.

[analog locust]

@alpine sable can I have the link? 🙂

[vale wigeon]

y is a function of t

[analog locust]

yup

[vale wigeon]

y is a function of t

[analog locust]

ooooooh

[vale wigeon]

in an ODE the unknown is a function

often denoted with y

[analog locust]

I feel dumber and dumber ._.

[vale wigeon]

you're trying to bite off way more than you can chew

i'm doing the equivalent of explaining quadratic equations to a preschooler who hasnt learned to multiply

[next pulsar]

if i want to divide two polynomials modulo n, do i have to work inside Z_n the whole time or will the answer be the same if i work in Z then convert at the end?

[analog locust]

umm

im guessing, I need to finish my ODE first before taking discrete optimization?

OHHHH

this is like a skill tree in a game

I need calculus first before doing Linear Algebra/Discrete Math/ODE?

[vale wigeon]

discrete optimization?

you don't need ODE for discrete optimization

linalg does not have calculus as a strict prerequisite

neither does discrete math

[analog locust]

is there like an overview or a diagram or some sort to see how math connects with each other?

I want to learn math as if I am unlocking skills in a video game

[vale wigeon]

if there is, i don't know of one that would be comprehensive

[queen wing]

You can try websites like Brilliant, or...

The International Baccalaureate's math syllabuses, that are shaped like diagrams.

[analog locust]

oooh sounds interesting

thanks guys!

[quartz cedar]

Is this correct

Or teacher made mistake

[charred flint]

seems like they reversed n and k, mistake

[pale terrace]

I'd appreciate if someone can help me get started with this question. It's been bothering me for some time

[rough spear]

uh

try drawing out a triangle

but why's there a negative length

[analog locust]

@quartz cedar what is V?

[quartz cedar]

Although it was a mistake, the solution turned out to be nice

[charred flint]

yea just the notation or definition is mistaken

the numbers after are right

[quartz cedar]

Permutation for combinatorics

[vagrant rover]

Am I doing this correctly?

[gray isle]

your expansions look ok,
your conclusion is wrong

[vagrant rover]

hm

[gray isle]

especially since you had:

which indicates that option d) does indeed represent the volume of a cube

[vagrant rover]

@gray isle

[gray isle]

yes

[vagrant rover]

❤️

[spring forum]

Confused on how I can use the given integral values for this?

[strong dome]

A: F(-4.5) - F(-9) = 10,
B: F(-7.5) - F(-9) = 8,
C: F(-4.5) - F(-6) = 10

You need to find F(-6)-F(-7.5) to solve it (equation system)

[spring forum]

How would I solve it is my question. I did think that -7.5 to -6 should be a negative value since all others show positive?

[strong dome]

Do A-C and you get:
-F(-9) - (-F(-6)) = 0
F(-6)-F(-9) = 0

Then substract B from what we got

F(-7.5)-F(-6) = 8
And this is what we need but the opposite sides, so the answer is -8

[manic quail]

You could even just draw that out on the number line, if you wanted.

[spring forum]

hmmm let me try to draw the numberline like you suggested since im not really following the calculations. I dont understand how -F(-9) - (-F(-6)) = 0

[strong dome]

Maybe you see this now? Doing the first equation minus the second equation

[spring forum]

would -4.5 to -9 be -10?

[strong dome]

This is given it's 10

[spring forum]

Oh okay hold on so i thought that we would start with the base number and travel to the -4.5 if that makes sense. Sorry I am not that good with integrals as we just started this unit.

So we would go from -9 to -4.5 and the area of that would be 10 as you listed

i guess in function form the -4.5 is represented first but it's still the same thing as listed

[strong dome]

it's okay you just started no worries 🙂 Did you learn this ? this is what I used to interpret each integral to equation

[spring forum]

Oh I just remembered that from an earlier section in the chapter. I didnt think of it much but now it makes more sense as I though we were reversing the order initially lol

[strong dome]

Good. I only reversed the order once it in the last step when I got F(-7.5)-F(-6) = 8
Because we wanted to find F(-6)-F(-7.5). So after reversing it's -8

This is based on this

[spring forum]

Yes that's when we reverse as you described

[modest crow]

shouldn't it be as easy as getting 3 equations from the given 3 integrals containg F(-6) and F(-7.5) and then getting what they ask?

[agile plover]

Is anyone know how to do this question :
A pregnancy test has a sensitivity of 0.97, and a specificity of 0.92. Suppose only 29% of people who take a pregnancy test are really pregnant. If a person takes the test and it says they are pregnant, what is the probability they are really pregnant?

[limpid spade]

What's sensitivity and specificity?

[gritty aspen]

This is really the proof behind the hypergeometric distribution formula

But im unsure as to how, the number of ways to select the red chips, regardless of the order in which they are chosen is rPk - since they say regardless of the order, wouldn't it be rCk?

[in the third line in the Proof paragraph]

[snow tundra]

Determine the excise tax to be paid on a house that sells for $268,210 if the buyer makes a $25,000 down payment and the seller takes back a second mortgage for $50,000?
[7:56 PM]
A)$536 .42 B)$537 C)$533 D)$538
[7:57 PM]
so the answer is B but can anyone explain how you get the answer please?

amp12128 — Today at 8:34 PM
$268,500/500 = $537
this is all it says soo idk where they got 500 from

posted this yesterday anyone got any ideas?

[gritty aspen]

Mate uh channel is busy tho - even tho u posted it yday

[snow tundra]

should I just post it in another chat?

[gritty aspen]

Yeah

[misty moat]

any1 know Geometric Probability

[gritty aspen]

um

again

channel is busy

[misty moat]

again?

[gritty aspen]

well not @ u

but generally, not the first time ive said that it's busy for this q ahahah

#help-0 message <@&286206848099549185>

[lunar relic]

What exactly is the | > notation around Ψ(t)? Does that just mean it's an imaginary quantity?

[charred flint]

@lunar relic a complex vector

[lunar relic]

ah okay

what branch of mathematics does it come from? I know up to diff eq and multivariate calculus so I'm assuming this is linear algebra?

[charred flint]

yea linear algebra for the basics

[lunar relic]

ah okay

[charred flint]

hilbert space is the keyword

[modest crow]

yes

multiply top and down with sinx+cosx

you get (sinx+cosx)^2 on top

which equals to 1+sin2x

and (sinx)^2-(cosx)^2 on bottom

which is -cos2x

=sinx^2+cosx^2+2sinxcosx

=1+2sinxcosx

=1+sin2x

nah

we get (1+sin2x)/(-cos2x)

because cosx^2-sinx^2=cos2x

but we had sinx^2-cosx^2

hence -cos2x not cos2x

hence the minus

okay, then tell me the final form you get and the differentiate

we have the same differentiate and we use the transformations i mentioned above to simplify

[safe island]

how do i split the variance of a matrix?

[terse vale]

can someone show the steps to this?

please ping me

[carmine ermine]

Like just simplifying that?

do you know about polynomial division?

[swift igloo]

how does

$ln(\frac{2y+1}{2y-1})$

turn into

$ln(1+\frac{1}{2y}) - ln(1-\frac{1}{2y})$

[ocean seal]

reaps

reaps

[rough spear]

rewrites

what's log a - log b?

[swift igloo]

log a/b

[rough spear]

good

[swift igloo]

but that would make ln(2y+1) - ln(2y-1) right?

[rough spear]

whats 1+(1/2y)

yes

[swift igloo]

2y+1 / 2y

[rough spear]

so that's ((2y+1))/2y)/((2y-1)/2y)

then you apply fraction rules

$\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a}{b} × \frac{d}{c}$

[swift igloo]

= ad/bc

[ocean seal]

Vaara

[rough spear]

so $\frac{2y+1}{2y} × \frac{2y}{2y-1}$

[ocean seal]

Vaara

[swift igloo]

right

[rough spear]

right

[swift igloo]

i guess you can split them up into two logs with a +, then on the second log raise it to the power of -1 and change the symbol to - to make it do nothing

which, i guess, gets it into that form

but why would anyone think to do this? it doesn't seem like a normal rewrite of a log

[rough spear]

looks simplified

[swift igloo]

well, i mean, putting it into that form seems to be the only way to move on with this question

[rough spear]

what's the question

[swift igloo]

but i mean, i don't know why i'd be expected to realise it can be simplified like that

my initial attempt was using

$ln(1+\frac{2}{2y-1})$

[rough spear]

you could just get to ln((1+1/2y)/(1-1/2y)) and leave it that way

[ocean seal]

reaps

[swift igloo]

but that leads nowhere

[rough spear]

but adding it to become a single fraction is usually better

what the

[swift igloo]

i think the idea is to use the log expansion of ln(1+x) on the two terms once you split it into two logs

which is fine, but i don't really see why i'd identify that it can be split up like that

[stiff locust]

How was it simplified!!! please help

[noble sinew]

log(|2x-2|)=log(|x-1|)+log(2)

and then log(2)/2 is just a part of C

[celest gorge]

help quick

<@&286206848099549185>

[stiff locust]

@noble sinew isn't c separate though? why is ln of 2 part of it

say i was asked to simplify just -(ln(2x-2))/2

[noble sinew]

C is just some arbitrary constant, say we had C from line 2 there then we could just redefine the constant as D=C+log(2)/2

[noble sinew]

That is how you simplify it

[slender stump]

Someone knows how to do this one

[noble sinew]

Write it as 2x/(6x-1)-3/(6x-1)<0

then move 3/(6x-1) to the other side and isolate x

[barren palm]

erm wtf does this evne mean

what is a and b supposed tobe

are they assuming its x and y

[ocean seal]

Chai T. Rex

Chai T. Rex

[oak chasm]

Other than that, I don't know what it means.

[sly mantle]

@barren palm the definition of a limit has a lot going on, so it's hard to answer 'what does it mean'

but individual parts can be explained fast

a & b are any real numbers where a<b presumably. (a,b) is the open interval with a & b as its endpoints

f is an arbitrary function with (a,b) as its domain and R as its codomain

also one of the lines has a typo

it should be: if $0<|x-c|<\delta$ then $|f(x)-l|<\ep$

[ocean seal]

RokabeJintaro

[barren palm]

oh switch delta/eps ight

oh yeah i added two o

open interval ay need to check what that means again

heard it

[sly mantle]

also $f(x)\overset{x\to c}\to l$

[ocean seal]

RokabeJintaro

[sly mantle]

for any $a,b\in\bR$, the open interval with $a$ and $b$ as its endpoints is $(a,b):=\brc{x\in\bR:a<x<b}$

[ocean seal]

RokabeJintaro

[barren palm]

oh yeah

[muted raft]

I like to think of epsilon-delta definition of limit as some sort of game. Each time, someone gives us some epsilon to work with, and we are tasked with finding the appropriate delta such that if 0 < |x-a| < delta_i then |f(x) - L| < epsilon_i. And we will continue this on and on and on until we reach very very very small value of epsilon.

[sly mantle]

why the i index?

[muted raft]

Someone gives us the first tolerance. Call this epsilon_1. We found appropriate delta for this, called delta_1. Now the next time someone gives us another epsilon, that same distance may not work, which would mean I would have to find a new delta. Call this delta_2. And repeat the process so on.

Which was why I used i

[barren palm]

right yeah the text makes sense alongside khan acam vid which talks bout the game thing u on bout of satisfying it

[muted raft]

But yea in a formal proof, just single value of delta works fine.

[surreal meteor]

I have the level curve f(x,y)=k <=> -0,1·x^2-0,1·y^2+5=2,5 where k=2,5 how do I proof that this is of the type circular equation ( (x-a)^2+(y-b)^2=r^2 ) with a radius of 5?

[shell widget]

@surreal meteor divide both sides by 0.1

[alpine sable]

hi do you guys know what 9+10 is im very confused i think its 21

[shell widget]

its 10.9

[alpine sable]

im pretty sure its 21

[shell widget]

then why are u asking

[alpine sable]

just to make sure 😩

[shell widget]

well its 10.9

[alpine sable]

no

its 21

[surreal meteor]

@shell widget like this right?

[shell widget]

yep

and x^2 = (x-0)^2

same for y^2

[ionic jewel]

lmao i love the language

Swedish?

so close to English i can read it

[alpine sable]

yo 9+10 IS 21 RIGHT

[ionic jewel]

wow you really are so funny

doesn't it feel good to troll people who go out of their way to help others

peak comedy

haha

[surreal meteor]

Yep I wrote that too

[surreal meteor]

Haha it's danish! 😄

[surreal meteor]

Exactly, why would you go on here to troll, legit people are on here to help people with their studying and this guy doesn't have better things to do 😂

[surreal meteor]

Anyway, thank you my guy 😗

[shell widget]

np

[spring forum]

I think they would be the same but not sure of the reasoning

[ionic jewel]

they are not the same

the one with the integral actually cares about all the values in the middle

the top one essentially draws a line from the start to endpoint and finds the slope

bottom one is actually average velocity

[spring forum]

wait isnt the top one average velocity as well

[subtle mantle]

it's poopy approximate average velocity

[spring forum]

lol okay so the integral is specified to values in the middle? not sure i understand that fully

[ionic jewel]

think about y = x^2

do the points -5, 5 for both equations

to see the difference

[subtle mantle]

the integral adds up the velocity for every single infinitesimal duration of time (by definition of the integral)

[viscid yacht]

Hey is this open

<@&286206848099549185>

[ionic jewel]

dude

[glass lichen]

read the rules

[spring forum]

Thank you bunny and wew lads

took me a sec to process lol

[snow folio]

Someone help with abstract algebra maybe? Why is g•a independent of choice of g bar?

[ocean seal]

danmarino900

[stuck berry]

Can someone quickly explain why the signs are wrong?

I thought since the equation for a circle is (x-h)^2+(y-k)^2=r^2, I was supposed to pick the answer with positives?

because then when we rewrite it, we'd take the negative?

[gray isle]

wdym by pick the answer with the positives

and take the negative when rewritimg

[smoky zenith]

Is the set { 2·q | q is rational } equal to the set of rationals or a strict subset?

[umbral folio]

how to solve this?

its from -2pi to 2pi

[sly plank]

well u know that the thing inside the cos can be either pi/2, -pi/2 , 3pi/2, or -3pi/2
solve it for each of those

[umbral folio]

I sorta get what to do but my math book has like 2k + 1 as part of the equation

which idk where that comes from

[ionic jewel]

solve by find every pair of x,y that makes it true?

[umbral folio]

but how does that represent 2k + 1

im confused

[slender stump]

Someone knows spanish? needing help

[alpine sable]

Is 2,8 a solution to this?

Can someone please help with that one

[ionic jewel]

a point is a solution if it inside all the shaded areas

in this case if its inside both shaded areas

[alpine sable]

Its on a dor

Dot

So idk

Its like right on a sot

Dot

But its a dashed line

So im confused

[ionic jewel]

its not then

your equations use greater than, not greater than or equal to

which makes the lines not part of the shaded area

you can show that it doesnt work with your equations above

y > 10 - x

plug in (2,8)

8 > 10-2

8 > 8

doesnt work

[alpine sable]

On the calculator it shows that point on the table tho

So im confused

Cause if it shows the point in the table does that mean it is a solution

[ionic jewel]

i have no idea what the table is

[umbral folio]

can someone explain?

[alpine sable]

On the calculator

[ionic jewel]

i havent used a calculator in like 10 years my dude

[alpine sable]

That’s great lol

[ionic jewel]

not sure what kind of table yours makes

[alpine sable]

Your prolly right then

So

Whats a good way to explain why mikey is not correct

[ionic jewel]

(1) it doesnt satisfy the equations
or
(2) its not in both shaded areas on the graph

[alpine sable]

Ok

[glass lichen]

$\cos(x)=0$ when x is an odd multiple of $\frac{\pi}{2}$

[amber iron]

How do I do dilations for a polar equation?

[ocean seal]

moshill1

[umbral folio]

but where does 2k + 1 come from

[glass lichen]

so 2k+1 is odd for all $k\in\mathbb{Z}$

[ocean seal]

moshill1

[ionic jewel]

scalar multiples of r? @amber iron or do you mean x, y dilations

[umbral folio]

is it just some memorization thing or whats the logic behind it

[glass lichen]

$\cos(x)=0\implies x=\frac{(2k+1)\pi}{2}, k\in\mathbb{Z}$

[ocean seal]

moshill1

[glass lichen]

it's an odd number.

odd numbers are 1 more than even numbers

by parity logic of the integers

[umbral folio]

alright

[ionic jewel]

as a note you can do anything for that that works to represent an odd number

2k-1, 4k+7

[umbral folio]

why does it have to be an odd number

[glass lichen]

cause those are the roots of cos(x)

like how sin has roots at multiples of pi

$\sin(x)=0\implies x=k\pi , k\in\mathbb{Z}$

[ocean seal]

moshill1

[amber iron]

@glass lichen red is graph of r=1+costheta. when I did r=2(1+costheta) i got the light blue graph, but i want to create the dark blue graph

like a shifted dilation

[glass lichen]

why did you ping me?

[amber iron]

oh sorry

wrong person

[ionic jewel]

dont do it

also i have no idea how to do that

[glass lichen]

Yeah polar co-ords arent taught until 2nd year at my uni

[alpine sable]

is <5 congruent to <6

lol

[ionic jewel]

wait looks like you just want to add 1 at every point

[grim delta]

where do I start here

none of the ones in the table even resemble it

[alpine sable]

does any1 know if <5 is congruent to <6

[glass lichen]

if you're less than 5, you're less than 6

but if you're less than 6 you're not necessarily less than 5

since 5.5 exists

[alpine sable]

so

no its not congruent

[amber iron]

ok

[alpine sable]

or it is

[glass lichen]

it is not

[alpine sable]

okay thanks

c:

[umbral folio]

if inverse cos of 1 = 0 why would it be 2k*pi

[glass lichen]

since 5!=6

[umbral folio]

for the equation above but 1 instead of 0

[amber iron]

so i just converted it to rectangular coordinates and expanded it, thx

[glass lichen]

cause cos has a max at even multiples of pi

[umbral folio]

max at even multiples?

where does the pi come from

[glass lichen]

yes, the maximum of cos(x) is 1

[umbral folio]

because inverse of 1 is 0

[glass lichen]

cause cos is 2pi periodic

so everything repeats every 2pi

A function f has period a if $f(x+ka)=f(x),k\in\mathbb{Z}$

[ocean seal]

moshill1

[grim delta]

does anyone know about my question

[glass lichen]

can you put the table you have?

[amber iron]

ok so i have 2 functions in which y is not isolated. how do i shade in between them on desmos?

[viscid yacht]

The solving part

[glass lichen]

$\sum_{n=0}^\infty x^{4n+5}=x^5\sum_{n=0}^\infty (x^4)^n$

[ocean seal]

moshill1

[glass lichen]

@grim delta

and that sum is on your sheet

[grim delta]

jeez that was so easy
how did I not see that

[glass lichen]

$\sum_{n=0}^\infty x^{4n+5}=\frac{x^5}{1-x^4}$

[ocean seal]

moshill1

[grim delta]

ye i got it after that

thx

[ionic jewel]

always look at difference between terms

[delicate lake]

ik it says quiz but it's a review assignment of calc 1 and i totally forgot how to do this

can someone help?

[ionic jewel]

do the limits from both directions equal the same value?

if they do then its the value they equal, if they don't, the limit does not exist

[delicate lake]

so it this case the limit does not exits then

since they can't be equal

[ionic jewel]

yes

[delicate lake]

wow i put that at first but thought it was wrong

that means

is this one wrong then

i thought that after you take each derivative the number gets bigger meaning the x intercept gets bigger

but that sounds very wrong

[ionic jewel]

this one is unrelated to the last one

f(2) = 0
f'(2) = negative (the slope is negative)
f''(2) = positive (the slope is increasing)

[delicate lake]

gosh i should've paid attention in calc 1

thanks so much

can u explain?

like why is it negative and positive

[ionic jewel]

the first derivative is the slope of the graph

the graph is going down at x=2, so the slope is clearly negative

the second derivative is the change in slope. Since the slope is getting closer to 0 (flatter) and we know its negative now, that means the slope is increasing from some negative number to 0

so the second derivative is positive

[dull bay]

help

I don't know if I should start at a/(1-r)

or what to do even

[wispy urchin]

What the heck is a limit and what does it have to do with asymptotes? Are they hard?

[ionic jewel]

a limit is when you approach a number but dont actually get to it

[celest tinsel]

Here is an easy one you want to buy a pc and you already have 7.31$ and the pc cost 802$ how much money do you need?

[ionic jewel]

you have any work so far?

[celest tinsel]

No I just made it up lol

[ionic jewel]

wait do you need help or is it an example for someone else

[celest tinsel]

For ppl who like math

[ionic jewel]

ah

[celest tinsel]

And wanna do some ig

[cinder cloud]

Hi For any defined hypothesis test at level alpha=0.05, as n decreases, does the beta(probability of of accepting the null hypothesis when it's false) increase?

[clear wolf]

@celest tinsel it is $794.69 right?

[dull bay]

when n is lower all false positve and false negative probability rise

[celest tinsel]

I got 794.67 so now I'm kinda concerned I didnt fo the math right

@clear wolf

[ionic jewel]

,calc 802-7.31

[ocean seal]

Result:

794.69

[celest tinsel]

Ya I suck at math lol

Wait it would be 68 cause I thought I had 31¢ but I actually had 32

[clear wolf]

yes

[cinder cloud]

@dull bay thank you! may I ask what would happen to variance, if I'm testing mu for hypothesis and n decreases?

variance would remain constant right?

[dull bay]

depending on how much data you lost

[celest tinsel]

O I was actually 1¢ off nice

[dull bay]

@cinder cloud

[cinder cloud]

from 200 to 100 for example?

H0: u=u0 vs Ha:u=ua

the data follows normal distribution

[dull bay]

probably constant then

[cinder cloud]

Right, thank you!

[dull bay]

np

[woven shuttle]

𝕳𝖊𝖑𝖑𝖔

[glass lintel]

yo just a quick question about sig figs

ive got a value at 88,967 and they want it to 3sf

i want to say that's 89,000

but thats 2sf in itself

isnt it impossible to have that value as 3sf?

wait

[ionic jewel]

yeah it probably is

you would write 89,000 and write that the third 0 is sigificant

[glass lintel]

should i just say its 89,000?

ahh ok

[ionic jewel]

the only "trick" i know is 100. has 3 sig figs

[glass lintel]

i mean it was a question to do with hydrostatics

so i dont know if they are too fussed with it

then again online syntax can be a pain

but when will you ever see 100. XD

[modest wadi]

Im supposed to write an exponential equation using these numbers how do I begiN?

[woeful pulsar]

Firstly, figure out the general form of such an exponential function

y = ... expression involving x

figure out what your unknown coefficients are

[modest wadi]

Wait like

do I do this for all of them

or just one

[woeful pulsar]

yeah, it's a nice reliable way

you just need one equation for one curve

[modest wadi]

oog ok

so how do I do that I can just plug in the point given alrdy right

[woeful pulsar]

yeah

because you know the point is on the curve

[modest wadi]

nice

[woeful pulsar]

you can try it out here and I can see how you are doing

[modest wadi]

Do I chose two points to do it right

[woeful pulsar]

you can check all 3 points to make sure

[modest wadi]

So kinda like this right

b^-1 btw

@woeful pulsar

[woeful pulsar]

Okay so there's like some steps you glossed over

but the idea is there

[modest wadi]

uh oh

[woeful pulsar]

firstly we know $y=Ab^x$, then we can substitute.

[ocean seal]

Element118

[modest wadi]

yep

[woeful pulsar]

the main idea is there, so it should be fine, but it would be better presentation to write $y=Ab^x$ first

[ocean seal]

Element118

[modest wadi]

oh ok

[woeful pulsar]

then it should be easy to solve for A and b, and you should be done

[modest wadi]

wait ik this might be dumb

since 6=b^-1

how do I find b lol

is it -6

[alpine sable]

guys how do i do this how is it not pi/2 and 3pi/2

[woeful pulsar]

okay, what you want to do here is to do the same thing to both sides of the equation

[modest wadi]

yep

so divide both sides by -6>

[woeful pulsar]

yeah it's not, plug it in, it's cos not sin

[alpine sable]

it's 0 and cos is x axis, so it's pi/2 and 3pi/2

[woeful pulsar]

cos is x axis for unit circle

[modest wadi]

uihhh Sushi

[woeful pulsar]

hmm, let's see what happens when we divide both sides by -6

[modest wadi]

can u go to a diff chat ssushi

pl0x

[woeful pulsar]

$\frac{6}{-6}=\frac{b^{-1}}{-6}$

[alpine sable]

so x axis 0 means pi/2 for y and 3pi/2 for other y

[ocean seal]

Element118

[modest wadi]

Swag

[woeful pulsar]

hmm, doesn't look any simpler

[modest wadi]

no not at all lol

[woeful pulsar]

how else do you know how to write negative exponents?

[modest wadi]

uhhhh

I just use my calculator not even gonna lie

bro my math has deteriorated

[woeful pulsar]

like $x^{-2}$ is $\frac{1}{??}$

[ocean seal]

Element118

[modest wadi]

huh

uh

what is the question mark supposed to be

[woeful pulsar]

the expression you need to know

basically $b^{-1}=\frac{1}{b}$

[ocean seal]

Element118

[modest wadi]

ohhhh shoot

[woeful pulsar]

negative exponents are obtained through dividing

positive exponents is repeated multiplication

[modest wadi]

oh dang

[woeful pulsar]

negative exponent is repeated dividing

[modest wadi]

hmmm so anything negative is associated with division

and subtraction

[woeful pulsar]

negative exponents

[modest wadi]

oh

damn I guess that does make sense

[woeful pulsar]

can you solve it now given that?

[modest wadi]

I think I can

lemme solve it

and send it again

@woeful pulsar

[woeful pulsar]

yeah?

[modest wadi]

I think I did it

@woeful pulsar

[woeful pulsar]

how did you get b=-6?

[modest wadi]

uhhhhhhh I thought that to make it a positive we had to divide

[woeful pulsar]

you remember $b^{-1}=\frac{1}{b}$, right?

[modest wadi]

yes

[ocean seal]

Element118

[woeful pulsar]

so $6=b^{-1}=\frac{1}{b}$

[ocean seal]

Element118

[modest wadi]

bruh

so wait

if its b^-1

its just six

but why

[woeful pulsar]

b^{-1} is 6. Now I'm using 1/b to rewrite b^{-1} because fractions are easier than exponents

[modest wadi]

ok

[keen sluice]

angie

[main flame]

idk how to do this

[modest wadi]

@woeful pulsar hmmm

I think Im beginning to understand a little more

[woeful pulsar]

do you get it yet?

[modest wadi]

I think so

the next part is kinda confusing though

now that I found a and B

for this

what do I do with this info

[woeful pulsar]

there are many ways to solve this, but I think the cleanest way is to use the right angle triangle

[woeful pulsar]

you write $y=Ab^{x}$ substituting in $A$ and $b$.

[ocean seal]

Element118

[woeful pulsar]

that's the equation of the curve

[modest wadi]

y=3(6)^x

right

@woeful pulsar

Oh shoot

bro

this actually makes sense lmao I did this last week

and isn't it supposed to be -x

[woeful pulsar]

yeah, you need to solve for b carefully

yeah, -x can work

but another way is to solve for b too

[modest wadi]

ooh

ok

I have another one I have a Question on

I think this one I have to use fractions

So I chose to do 1,9 and -1,4

so far I got 2 ^1/4 = b^2

[copper charm]

Can someone help me with this question I don’t get it

[vale wigeon]

you are asked to find the length of an arc

a circular arc

do you know how to find the length of a circular arc using its radius and angle?

[copper charm]

No

[jade spade]

I don't know the formula off the top of my head

[vale wigeon]

@copper charm okay, then do you know how to find the length of the full circle?

[copper charm]

Ugh no I don’t remember

[vale wigeon]

you don't remember C = 2πr?

[copper charm]

Oh yeah o do

[vale wigeon]

literally the definition of pi, no less

okay so your arc is not the full circle but only 66 degrees

how many degrees are there in a full circle?

[copper charm]

What would the r be in this question

?

[vale wigeon]

you didn't answer my question

but r is the radius of your circle

and the problem gives it to you

[copper charm]

Ik that r is radius but what would it be 10?

[vale wigeon]

of course it'd be 10

what else could it possibly be lol

anyway,

how many degrees are there in a full circle?

[copper charm]

I get 62.8

[vale wigeon]

how many degrees are there in a full circle?

are you saying a full circle measures 62.8 degrees?

[copper charm]

360

[vale wigeon]

great, there are 360 degrees in a full circle.

but your arc covers only 66 degrees.

therefore its length is 66/360 of the circumference.

does that make sense to you? Y/N

[copper charm]

Yea

[vale wigeon]

great

are you able to find the length of your arc now?

[copper charm]

5.4?

[vale wigeon]

how did you get that?

did you just guess at random or what

[copper charm]

When I divide 360/66

[vale wigeon]

why are you calculating 360/66 and then claiming that to be the answer?

[copper charm]

I’m not sure how to do it that’s why I’m asking you for help...

[vale wigeon]

i was under the impression that we just walked through how to do this problem, but it now appears that you have ignored it all

we have established that you know how to get the circumference

and i told you how the arc length relates to the circumference

and it should have been abundantly clear that finding the arc length is your goal here

i'd greatly prefer to be like, listened to when i attempt to provide help

[copper charm]

I was listening but I didn’t understand

[vale wigeon]

if there's something i said you don't understand then quote the thing and ask me about it.

which part did you not understand?

[copper charm]

So I do 2 * 3.14 * the 5.4

?

[vale wigeon]

why 5.4 ???

[copper charm]

360/66

[keen sluice]

where u get that from

[vale wigeon]

no, this won't give you the answer.

the value of 360/66 is almost irrelevant to the problem

you might want to find the circumference first.

[keen sluice]

no almost.. it is

[vale wigeon]

before finding the arc length.

find the circumference first.

@copper charm

[copper charm]

62.8

Is the circumference

[vale wigeon]

no

you are rounding too crudely

notice how it says to round to the nearest hundredth

you are rounding to the nearest tenth

[copper charm]

That’s what it showed in my Calc only 62.8

[vale wigeon]

and ideally, for intermediate calculations you should round to more decimal places than for the answer

are you using 3.14 for pi?

[copper charm]

Yes

[vale wigeon]

get more decimal places

[copper charm]

What?

Wdym

[vale wigeon]

replace 3.14 with something like 3.14159

[copper charm]

I get 62.8

[keen sluice]

whats the full circumference without rounding

[vale wigeon]

something that has more decimal places of pi

not just two

does your calculator not have a dedicated pi button anyway?

a lot of them do

[keen sluice]

dont calculators hav pi button

yeah

[vale wigeon]

and if yours does then really you should use that instead

[keen sluice]

you can find circumference calc online

[copper charm]

It’s 62.8318

[vale wigeon]

okay great

[keen sluice]

what is it to nearest 100th then

[vale wigeon]

so that's your circumference

[keen sluice]

ez dubz

[copper charm]

62.83

[keen sluice]

good job

[vale wigeon]

ethan the circumference is an intermediate result not the answer, let's not

[keen sluice]

l

[vale wigeon]

so 62.8318 is your circumference

great, there are 360 degrees in a full circle.
but your arc covers only 66 degrees.
therefore its length is 66/360 of the circumference.

now look at this again

[copper charm]

That’s gives me .183...

[vale wigeon]

really? you are calculating (66/360)*62.8318 and getting some number less than 0.2?

[copper charm]

Do you not understand what I’m calculating?

When I do 66/360 I get .183...

I get 11.5 as my answer

[vale wigeon]

the arc is 66/360 of the circumference

and there you go again, rounding too crudely.

no, your answer is not 11.5

[copper charm]

Then?

[vale wigeon]

go through the calculations again, this time rounding appropriately

they tell you to round to the nearest hundredth.

when they tell you to round to the nearest hundredth, you round to the nearest hundredth. you do not round to the nearest tenth as you did.

[copper charm]

11.50

[vale wigeon]

no, now it's just wrong.

,calc 66/360 * 2 * pi * 10

[ocean seal]

Result:

11.519173063163

[copper charm]

Idk

11.52?

[vale wigeon]

i cannot see what you're doing so i cannot tell you how you're fucking up your calculator input

yes 11.52

[copper charm]

My Calc showed 11.50

Whatever

Ty

[vale wigeon]

again

i don't know what you put in your calculator that resulted in 11.50

and not 11.52

[winter gulch]

Hi guys, I came across this problem and I felt that the question had a typo

Because I think the arc CRI is independent from wherever point R is so doesn’t that mean R could be anywhere

Idk it never mentioned I

lmao

I checked online and it seems to be a typo, it should be major arc CR (then the solution is obvious)

neither would I know lol

[upbeat gorge]

It’s definitely a typo as I isn’t defined

[winter gulch]

Yeah that feels about right

Actually that’s definitely right lol

[idle brook]

Can someone explain to me what i got wrong? thank you

[alpine sable]

since the function is differentiable the limit as h approaches 0 from the positive direction and the negative direction would be the same, so choice A would give you the value of f'(3)

so A should not have been circled

[idle brook]

So would C and E be the answers?

[alpine sable]

E is the only one that needs to be circled for question 13

[idle brook]

Thanks, are you able to explain question 14 too?

[alpine sable]

B is just the definition of the derivative and to get from B to C we can substitute x=3+h

E would need to be circled here as wel

consider the absolute value function, |x|

its continuous at x=0 but not differentiable at x=0

f'(0) does not exist, but it is continuous at x=a

the two-sided limit f(x) as x approaches 0 does exist

and there is no hole or vertical tangent at x=0

so none of A B C or D are necessarily true

[idle brook]

Thank you!

[alpine sable]

i had a question

is that - in the equation a mistake

cuz idk why its there

[gray isle]

the sign affects the concavity

the -sign is there as it should be since you have a concave down parabola

[alpine sable]

ohhh

Hello ,may I ask a question here?

[vale wigeon]

this channel is free at the moment so yes

[alpine sable]

I was wondering why sin(x) is in O(x) but not in O(x^2) since the taylor expansion of sin is of much higher order than x^2

[ionic jewel]

i hate how often that rule is relevent

really sad

[sour spindle]

Me and my friends got a maths puzzle

we been working on it for a day and can't figure it out

[alpine sable]

google is your best friend

[ionic jewel]

rip king Johan's question

[sour spindle]

they gotta all add up to the same number. best we got was this

bruh

[alpine sable]

by not studying for your test?

[ionic jewel]

nicholas please spare us and stop talking, we aren't going to help you cheat

[ionic jewel]

each row and column adds up to the same number?

[sour spindle]

Yeah, diagonal included

[ionic jewel]

what number is that?

[sour spindle]

we can't get it best we got was that

dunno it didn't say

[ionic jewel]

sum/3

[sour spindle]

just gotta figure it out

[ionic jewel]

I'm too lazy to add them up

[sour spindle]

lowest you can get is 4

and that will fail

I feel like it's 4 2/3 or 5

maybe 5 1/3

[ionic jewel]

15 total, each row, column, and diagonal adds to 5

[sour spindle]

It doesn't tho, cause diagonal from top right to bottom left equals 4. the rest are 5.

[ionic jewel]

that just means you set it up wrong

it's supposed to be 5 each

[sour spindle]

is it tho

[ionic jewel]

assuming diagonals have to be the same

[sour spindle]

what if it's 4 2/3 idk

[ionic jewel]

it's not

it's 5

[sour spindle]

everything gotta be the same number

[ionic jewel]

there's 15 total points, and 3 rows

[sour spindle]

ahh I see

[ionic jewel]

that means 5 per row since evenly distributed

which means 5 for everything

[sour spindle]

Well I know 1 1/3 is center peice

I'll just keep rearranging them

[ionic jewel]

how do you know that?

[north jungle]

help anyone

[sour spindle]

That was like the only hint

[ionic jewel]

actually i see

yes it does have to be in the middle

let's see what else we can get

[limpid spade]

Stop mutlipsoting

[ionic jewel]

yeah idk it would be easier if i had them irl, but there's probably a clean math solution to this

[north jungle]

@limpid spade channels are busy

[sour spindle]

id take another picture but I don't even have it with me atm

my friend took it

[ionic jewel]

this one is busy and you posted in it anywayd

try a better excuse

[sour spindle]

Hmm wait lemme check smth

[north jungle]

didnt notice it

[vocal zealot]

How do i solve sin(3x)=a. a is a given number that is in interval 0<a<1. x is in radians

[ionic jewel]

i think 1 and 2/3 has to be in the center

yeah changing the center nice

good puzzle

[versed isle]

Is this correct?

[alpine sable]

,rotate

[sour spindle]

can't change the numbers tho

so um

[versed isle]

Here @alpine sable

[sour spindle]

yep

[alpine sable]

ask in an unoccupied channel, also i'm a little suspicious that this is your work for one of the questions on your test

[sour spindle]

looks like a test

I thought test stuff was forbidded

[sour spindle]

[versed isle]

hmm its practice paper

[alpine sable]

<@&268886789983436800>

[sour spindle]

just ask your math teacher for help

[sly mantle]

what's up

[sour spindle]

rules state no test/exam stuff

[alpine sable]

suspected case of test help

[ionic jewel]

^

[sour spindle]

I legit just joined this server and the rules said no cheating on tests. I came to ask help for a math game lol

which still hasnt be solved 😔

[alpine sable]

scratch that. it's a confirmed case

[ionic jewel]

someone posted the answer for you

[sly mantle]

ok banned

[ionic jewel]

oh shoot

ur right my bad

lemme keep working then

[sour spindle]

lol

[ionic jewel]

i didn't read your soln just saw you posted lmaoo

[sour spindle]

It confuses me, cause what I had is the best possible solution, or atleast I thought so

[ionic jewel]

middle one is 1 2/3

[sour spindle]

really

actually it might be

[ionic jewel]

can you repost the squares i can't find it

[ionic jewel]

wait why does your solution not work?

it seems right

divide each by 3 to get the puzzle

[sour spindle]

It is right, but it's a different question.

[ionic jewel]

it's the same question times 3?

[sour spindle]

Yeah but...

wait

[ionic jewel]

they all add up to 15 as far as I can tell

[sour spindle]

I'll just divide em all by 3

boom, answer

[ionic jewel]

nah it's pure skill

yes there you go

Edwin is too smart

[sour spindle]

k thanks

should be able to solve it now

Yep, solved.

Thanks.

[ionic jewel]

I'll say yw even tho i didn't actually help

so yw

[unreal valve]

Can somoene please help me, i dont know how to do this question

[agile plover]

It's in statistic

[gray isle]

subtract 2 from both sides and combine the stuff on the left into a single fraction

[unreal valve]

wait so (x/x-2 )-2

?/

also im sorry im really stupid, but if it is wouldnt the -2 cancel out

?

[unreal valve]

oh ok thanks guys

[brave aurora]

how do I do part B?

[alpine sable]

integrate v(t) to get x(t), the position function

(2,0) is a point on x(t), use this to figure out the value of the +C

the particle moves to the left when the velocity is negative

find the values of t for which v(t) is negative

[median osprey]

hey

i have chemistry problem i need some help with

i did this

but in their solution they converted 0.6 g to 6g... i dont understand why

[vale wigeon]

they didn't "convert 0.6 g to 6 g"

they converted 0.6 g / 100ml into 6 g/L

100ml of solution contains 0.6 grams of glucose

therefore a liter will contain ten times as much

[median osprey]

but in other examples they didnt do that which confused me

[vale wigeon]

arent you finding the number of moles per liter

can you show an example where this conversion didnt happen

[median osprey]

trying to find it

like here

they didnt convert 1.2 g

@vale wigeon

[vale wigeon]

they did.

= 1.2 g/0.1 L = 12 g/L

[median osprey]

OK so we always convert?

like we make sure its g/L

@vale wigeon also for the first picture i think they have it wrong

do we say 1L or 0.1 L?

so we convering 100ml to L = 0.1

[brave aurora]

how do i do part B

[vale wigeon]

@brave aurora channel busy please move

[vale wigeon]

yes because molarity is measured in moles per L

[median osprey]

so it should be 0.1L not 1L

correct?

[vale wigeon]

?

sorry, had to go for a moment

idk what "it" is

[vocal zealot]

Give a thirdgradepolynom p(x) that has zero points -3,3 and 1 also p(0)=18

I need help please

[slender marten]

If x = -3, x = 3 and x = 1 are roots then (x+3), (x-3) and (x - 1) are factors of p(x).

p(x) = a(x + 3)(x - 3)(x - 1) is what you effectively need to look at.

[vocal zealot]

THANK YOUY

[alpine sable]

forthis semi circle, if i were to integrate it, first with x then y, will the bounds for both limits of
x = √(-y^2+1) and y will be both 0?

[woeful pulsar]

the semicircle?

[alpine sable]

yes

[woeful pulsar]

do you have the integral?

[alpine sable]

the integral is

[woeful pulsar]

are you integrating by slices perpendicular to the x axis or by slices perpendicular to the y axis

[alpine sable]

3y dx dy

by x axis

[woeful pulsar]

where did you get 3y from?

is it the function you need to integrate inside the semicircle?

[alpine sable]

yes sorry thats the function given

[woeful pulsar]

idk there's missing information that is not given

[alpine sable]

3y dy dx

[woeful pulsar]

I think you might want to give the original question so it's not that confusing

so you want to write it somewhat like $\int\int3ydydx$?

[ocean seal]

Element118

[woeful pulsar]

or are you trying to write it like $\int\int 3ydxdy$?

[ocean seal]

Element118

[alpine sable]

this one

[woeful pulsar]

okay so the y is outside

[alpine sable]

fhe one with dxdy

yws

yes

[woeful pulsar]

so the range of y is from 0 to 1

[alpine sable]

yup

[woeful pulsar]

deal with the outside first

[alpine sable]

oh wait

how does it bcome 0 to 1 for y

[woeful pulsar]

$\int_0^1\int 3ydxdy$

[ocean seal]

Element118

[woeful pulsar]

because the minimum y in the semicircle is 0, and the maximum y is 1

[alpine sable]

bcos the Q gives y as 0 to √1-x^2

[woeful pulsar]

what is x

[alpine sable]

x is from -1 to 1

[woeful pulsar]

where is x?

it's not outside y

y is the variable that is outside

[alpine sable]

sorry can u explain this part again

[woeful pulsar]

we haven't parameterised x yet

when writing $\int\int 3ydxdy$, it should be effectively $\int f(y)dy$

[ocean seal]

Element118

[woeful pulsar]

the inside an expression that depends on y

x is inside, so x depends on y

y cannot depend on x

[alpine sable]

ok i think i get that part but then im still confused abt choosing the limit bounds

[woeful pulsar]

y is between 0 and 1

[alpine sable]

does this mean y isnt from 0 to √(1-x^2) ?

[woeful pulsar]

because of our order of writing the variables we need to write x in terms of y

not y in terms of x

[alpine sable]

ok sorry last Q. but the Q didnt state the max val of y is 1 but how did u derive the max val of y as 1?

[woeful pulsar]

from the semicircle

[alpine sable]

im still confused man :( cos i still see it as the max val of y from the semi circle is y=√(1-x^2) how does that turn to 1? @woeful pulsar

[woeful pulsar]

okay the function is given

[vocal zealot]

How to solve sin(3x)=a if a is given number in the interval 0<=a<=1

[woeful pulsar]

1 is the maximum value of that function

[alpine sable]

oh wait is it u sub the val of x given which is 0 to 1 into the y function to get the val of y?

[woeful pulsar]

it's just finding the maximum of the function

[woeful pulsar]

How to solve sin(x)=a? Then just replace x with 3x

[alpine sable]

yeah so i jus sub the value of x given to the function of y to find the max val right? is my understanding right tho

[woeful pulsar]

erm... if you can figure out which value of x would give the maximum then yeah

but if you can't figure out you might need to differentiate and find critical points and stuff

[vocal zealot]

I did it dw

[jovial mica]

Can someone help with this question.

[vale wigeon]

there's no question here

this is a function

[jovial mica]

Sorry.

[vale wigeon]

what are you asked to do with it?

find f(19)?

[jovial mica]

Determine the derivative by first principal.

[vale wigeon]

okay

and have you made any progress?

[jovial mica]

not really.

[vale wigeon]

do you know how to take derivatives of functions using first principles?

[jovial mica]

sort of.

Nevermind, i think i might ask my tutor tomorrow. Thanks anyways.