help-0

[ocean seal]

TrueBoxGuy

[gleaming warren]

i know

wait

[quartz stone]

so the answer is both are correct

they're the same

[gleaming warren]

what should i do know

[quartz stone]

simplify it

sqrt(2) - 0 is sqrt(2)

0 - 1 is -1

square both of them then

[gleaming warren]

how

[quartz stone]

if you subtract 0 from something it doesn't change

[gleaming warren]

2-0?

oh

[quartz stone]

what is sqrt(x)^2 ?

[gleaming warren]

$x$

[ocean seal]

TheGameBot

[quartz stone]

yes

and 1^2 is 1

So $\sqrt{2 + 1}$

[ocean seal]

TrueBoxGuy

[gleaming warren]

so i have to cancel $/sqrt{2^2}with /sqrt{}$

[ocean seal]

TheGameBot

[quartz stone]

ye kinda

[gleaming warren]

ok

Like this

[quartz stone]

yes

[gleaming warren]

what about this square

[quartz stone]

sqrt(2)^2 is 2

[gleaming warren]

so the$^2$ is for the \sqrt

[ocean seal]

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

[quartz stone]

yes

[gleaming warren]

op thx

[winged sphinx]

can anyone help me with compounding interest and fixed amounts added on regular basis

[sacred vigil]

Hmm, gimme the questions

I can try

[winged sphinx]

well i have one source generating weekly payout of interest but with a ceiling and one with no ceiling for interest but at lower rate and with monthly interest payout

im trying to figure out the perfect ratio

[sacred vigil]

Actually is it commercials mathematics?

I mean is it accountancy?

[winged sphinx]

economical yes i would say so

[sacred vigil]

I ain't familiar with the terms or I would've helped you

[winged sphinx]

well if you break it down its still just percentages 😄

[sacred vigil]

But the ceiling interest and other things

I don't know the terms

[winged sphinx]

ceiling just means you can only gain interest on a maximum amount not unlimited

like its limited to 1000 or 10000 or whatever

after that you dont gain any interest

[sacred vigil]

Does this mean
A limit on amount on which you can get interest

[winged sphinx]

yes

[sacred vigil]

Then I can help u if I'll be getting the calculation

[winged sphinx]

im figuring out if its best to always max out this limit and move funds every time

well i want to do the calculation lol

i can give you the numbers

or setup

[sacred vigil]

Anything but not so technical

[winged sphinx]

lets say account 1 is interest rate 12% and has a limit of 100000 with weekly interest payout (so compounding every week) - the other account has 11% interest rate and no limit on interest with monthly interest payout

now there is a little limitation to it as there are withdrawl and deposit fees

[sacred vigil]

So you want to get the ratio of interest?

[winged sphinx]

im not entirely sure if the ratio of interest would help here?

can you explain

my thought is rather should i always keep the limit maxed out and move funds after payout

[sacred vigil]

@urban summit can you help?

[winged sphinx]

or should i have it a bit below and collect to minimize transaction fees

[urban summit]

Someone decipher this Puzzle for me

👁👄👁

[sacred vigil]

[urban summit]

It’s Uuh very important 🙏🏾😙

[sacred vigil]

@winged sphinx I'm sorry sir but I don't think that I'll be able to help, you can wait and tag helpers after sometime

[scarlet thunder]

Da hell is that… alien quiz?..

[urban summit]

It’s basically a puzzle

I’m tryna decipher the words

[sacred vigil]

The dot in shapes and empty squares are pigpen cipher

[scarlet thunder]

[winged sphinx]

wasnt there a rule about not using channel twice when someone asked a question 🤣

[sacred vigil]

The numbers are numbers-for-letters cipher @urban summit

[winged sphinx]

who are the helpers

[sacred vigil]

They're the one who primarily help the server members, they're dedicated to this

[scarlet thunder]

Oh, The channel is already of occupied, then ya need to ask your question / ask of help in another channel, @urban summit

[sacred vigil]

I play games so I identified these ciphers, easy

@winged sphinx just wait for 10-15 min and then you can tag helpers, till then wait for someone who can help

[winged sphinx]

kk

[sacred vigil]

And i am very sorry for wasting your time

[winged sphinx]

is that english

[gleaming warren]

Q.1

[winged sphinx]

<@&286206848099549185> can anyone help me with my more complex compouding issue here? 😅

hey who changed my name 🤣

[rose imp]

use distance between 2 points formula

and verify

[sly mantle]

@winged sphinx i gave you a pingable name. do you want smth else?

[gleaming warren]

but there are three points

[winged sphinx]

yes help with my actual question would be great 😄

[sly mantle]

i meant another name

[winged sphinx]

my name back 🤣

[sly mantle]

a pingable name

[winged sphinx]

NukNuk

[cinder wedge]

can someone tell me you have to put everything in brackets and then square on both sides or square each term?

[rose imp]

the first one

[gleaming warren]

So both sides are same I think?

[cinder wedge]

z+4 ≥ xy + yz + zx

is it right so write (xy)²+(y+z)²+(zx)²

without +

[final crest]

I'm solved all except part B.
How should I go about it?

[crisp condor]

Hi. I am new here.

What are you guys approaches to studying maths?

Any answer will do

[heady crest]

the most important thing is to practise doing calculations and drawing stuff and figuring it out in your head

[crisp condor]

Drawing stuff?

You mean graphs?

For me, I mainly just try to understand why the numbers move the way they do

Which takes a lot of time

[vague coral]

understanding how formula works before absorbing them like sponge

[rose imp]

i look at the formulas and try to derive them from the base ones

[crisp condor]

I see

[vague coral]

I'm pretty sure a lot of people can't prove why product rule or chain rule works, and that's really bad

[winged sphinx]

how do i integrate weekly contributions in a compounding formula

[crisp condor]

😂

😂

[winged sphinx]

whats so funny

even online calculators dont get it right

[vague coral]

he/she is not laughing at you

[winged sphinx]

i tested 3 online calculators with random but same numbers

all of them give me different results

maybe one of the helpers can help me to figure out the right formula

because im stuck

[winged sphinx]

i found this but it doesnt seem to reflect on the contribution thats weekly compared to the monthly compouding

[quartz stone]

@winged sphinx aren't the results close enough though 😉

They're like within 100

[winged sphinx]

well i wouldnt say a range of 200 is close

[quartz stone]

Like you could easily get that variation within technicalities like whether you put in a contribution at the very start / end (like how the contributions line up)

[winged sphinx]

but how would you explain the third it should be either or

[quartz stone]

?

[winged sphinx]

3 different results end or beginning should give max 2 different results

[quartz stone]

I mean there's also whether the contribution happens after you've applied the interest at the end of the last month / whether that last month has interest at all

Maybe the report will give u more info

there's like also the fact that months and weeks don't align exactly

So I'm saying I could easily see where all the variance comes from and you need to know exactly those conditions

[dull shuttle]

(a+b)(m+n) how do i to do this?

[winged sphinx]

there is another factor that interest compounds daily but payout is monthly

the weekly contribution counts from day of contribution

[quartz stone]

m

[winged sphinx]

but again also plays into the daily interest that compounds and is paid out monthly

[plucky crow]

what do u need to do

whats the q

[dull shuttle]

Foil?

[plucky crow]

just expand each term individually

ill start you off

am+an

now do the same with b

[dull shuttle]

Did a am and am come from a × m and a × n

[crisp condor]

@winged sphinx oof yeah i wasn't laughing at you

[winged sphinx]

so lets say you start with 1000 and then pay 100 into the account on beginning of week 2 you earned 11% on the 1000 and from week 2 11% on the 1100

[crisp condor]

Pretty sure what you are doing is more advanced than me

[winged sphinx]

but inbetween is also the compounding interest

[crisp condor]

Just wifi being slow

[dull shuttle]

Did am and an come from a × m and a × n

[plucky crow]

now do the same with b

[plucky crow]

yes

[dull shuttle]

ma + an + bm + bn

[plucky crow]

yes

[dull shuttle]

Is it ok when i write am + na + mb + nb

[plucky crow]

yes

[dull shuttle]

Thank @plucky crow

[alpine sable]

How can I determine the amount of force needed to pull a 200lb wakeboarder through the water?

[plucky crow]

well theres drag in water

do you know what that value is

[alpine sable]

No unfortunately

[plucky crow]

are they on the water bed

or are they moving down or r u keeping them up and dragging them

so essentially carrying them

[alpine sable]

Keeping them up (from sinking) and dragging them forward across the surface of the water

[plucky crow]

is this a school q

[alpine sable]

Nope, personal

[plucky crow]

ah well

i cant answer that its quite arbitrary

[alpine sable]

could you point me in the right direction at least?

What variables I need and how to figure them out

[plucky crow]

nah i honestly dk

weight,

upthrust

drag in water

prolly some other stuff too

[alpine sable]

maybe it’s best I go trial and error

[jade sail]

wakeboards float

[alpine sable]

well, not really

not when you’re standing on them

[jade sail]

https://www.waterskiworld.com/wakeboards/Wakeboard_Sizing_Chart/wakeboard_sizing_chart.html

[plucky crow]

so are you standing on it

?

whats keeping it from going down

oh a 200lb person

well

yeah

[jade sail]

just try it out theres too many variables plus wakeboarding isnt a simple physics thing

also speed shouldnt vary that much

[plucky crow]

you need to know the dimensions of the wakeboard

and U = axpg

to find the upthrust

and the weight using mg

[alpine sable]

no no I’ve been wake boarding a long time lol. I’m wanting to know how much force the boat is applying

[plucky crow]

wait what is wakevoardingh

[alpine sable]

snowboarding on the water behind a boat basically

[plucky crow]

is the boat connected

[alpine sable]

yea you hold on to a rope connected to the boat

[plucky crow]

oh

[jade sail]

wait when you get on the wakeboard do u start to sink immediately

[alpine sable]

yep

[plucky crow]

you need to find the speed of the boat

[alpine sable]

until the boat pulls you out of the water

[plucky crow]

like if the boats accelerating

youre gonna be held by a tension

in the string

[alpine sable]

15 - 25 mph

average range

[plucky crow]

in a vertical component keeping you from sinking

and a horizontal component pulling you across

[jade sail]

just start at 15 and if they sink increase

[plucky crow]

theres air resistance

[dull shuttle]

What do FOIL stand for?

[plucky crow]

its quite compliocated

Drag depends on the properties of the fluid and on the size, shape, and speed of the object. One way to express this is by means of the drag equation:

{\displaystyle F_{D},=,{\tfrac {1}{2}},\rho ,v^{2},C_{D},A}F_{D},=,{\tfrac {1}{2}},\rho ,v^{2},C_{D},A
where

{\displaystyle F_{D}}F_{D} is the drag force,
{\displaystyle \rho }\rho is the density of the fluid,[11]
{\displaystyle v}v is the speed of the object relative to the fluid,
{\displaystyle A}A is the cross sectional area, and
{\displaystyle C_{D}}C_{D} is the drag coefficient – a dimensionless number.

oh

yeah its just from wikipedia

[alpine sable]

sheesh

well I’ll look into it thanks

[ocean seal]

ceeces

[dull shuttle]

Wait do x^1 × x^3 = x^4 or x^3

[glacial hedge]

@dull shuttle do you know exponent rules

x^1*x^3 = x^(1+3) = x^4

[dull shuttle]

Ok

2x^1 and 2x is the same right?

[glacial hedge]

yes

anyone know what the heck this question is asking and what n is?

[winged sphinx]

its asking for min and max in the question 😄

[dull shuttle]

Omg what is that

[strong furnace]

question is asking for absolute maximum and absolute minimum values of function defined at a point in n-space (n is the dimension of the space indicated by the index of final element in the tuple which is the input of given function ) which satisfy the given inequality

[burnt mica]

Lucas played 4 games against Chris.
Lucas played 4 games against Nico.
Chris Played 3 games against Nico.

Nico’s record is 6wins 1loss.
Chris record is 3wins 4loss.
Lucas record is 2wins 6loss.

How has Lucas played 8 games while Nico and Chris only played 7?

[glacial hedge]

@strong furnace how am i supposed to do it??

[uneven raptor]

because they only played 3 times betweent theirselves

[strong furnace]

idk , consider the neighborhood of that point and treat this as a one variable problem around it , the answers look trivial but idk the formal/consistent way of solving this

[winged sphinx]

in what context did you get that question? school?

[glacial hedge]

school

(online school)

[winged sphinx]

shouldnt you know best then 😄

[glacial hedge]

its in the lagrange multiplier section

[winged sphinx]

didnt they explain you min max before?

[glacial hedge]

so i have no idea how to do this with multipliers

they have its just really confusing with the n?

[winged sphinx]

n is just amount

undefined

[glacial hedge]

[woven pollen]

Can you show me how to integrate this please?

[glacial hedge]

@woven pollen hint split up the sqrt

and move the constant outside

then it will become easier to see what to do

dude

its

b= $(2+2h)/5c$

[ocean seal]

Elonmosqito96

[woven pollen]

Is this what you would get too?

[worldly pagoda]

🙋Hi! I have a mathematical question. Here I have a "cloud" of points on the chart and I am building a curve that should describe it as accurately as possible (see Photo). What accuracy criteria do you know (some mat. Terms so that I don't google blindly)? In general, I need to iteratively select the coefficients for the functions until it describes the distribution of the cloud as accurately as possible

[woven pollen]

Least Squares curve fitting ?

[glacial hedge]

@woven pollen i was thinking you could use a trig substitution

[woven pollen]

oh. Which one??

the 2 is killing me

[glacial hedge]

move the sqrt(2) outside because its a constnat

[winged sphinx]

still no idea how to implement compounding with compouding with monthly payout for itnerest but daily compouding for of interest

[woven pollen]

I thought I did?

[glacial hedge]

@woven pollen

[woven pollen]

thank you.

[glacial hedge]

yw

[woven pollen]

Do you have a sample problem to solve?

[winged sphinx]

thats the problem 😄

i need a formula

the picture is the closest to a the problem i could get

[woven pollen]

What is the question?

[winged sphinx]

well

i think its better to dissect the whole situation

im trying to figure out optimal interest generation

i have one account that pays out monthly interest but compounds the interest itself daily

the other one compounds weekly

but is limited to 100k as interest base

or any other limit (im just amking numbers up for practicality)

[woven pollen]

You can't "pay out" interest. Do you mean you take a withdrawal against the current balance (aka principle)?

[winged sphinx]

the interest can be paid out 😄

it can be "stored" in a pool then later on paid out

yes basically paid out to the account

from the pool

[woven pollen]

the "Balance"

[winged sphinx]

well the balance is untouched before the interest is paid out

yes

[woven pollen]

ok. ok.

[winged sphinx]

but the principal is the balance 😄 if i withdraw it i lose all interest

even prior gained one

so its not realized before its "paid out"

balance will say "principal" until interest is added especially in the first period

[woven pollen]

there you go. inject 30 days of intereset into your balance each month (at a daily rate), then subtract your desired amout at the end of the month - you have a new balance now - and run it again for the next 30 days.

[winged sphinx]

there are several factors to it

firstly the interest compounds daily

i dunno how to integrate this in the formula with the addition that you add more interest to the pool aswell

[woven pollen]

Ending Monthly Balance = Beginning Monthly Balace * (1 + dailyRate)^30

Then, there is an adjustment. Beginning Montly Balance = Beginning Monthly Balance - X

X is your payment

run it again.

[winged sphinx]

youre not reflecting the compounding of the interest itself if i see it correctly

this is just very basic monthly compounding

[woven pollen]

(1 + dailyRate)^30 <- this is compound interest over 30 days

dailyRate = monthlyRate/30

[winged sphinx]

daily of the principal but the interest rate compounds aswell

🤔

am i overthinking it

sorry the interest itself

i meant that with interest rate

the initial investment compounds monthly

the interest on the other hand compounds daily

within the interest pool

its a very specific case i think reading a whole book for it would be quite overkill 😄

and the case would probably not even been answered in there

thats also just the peak of the iceberg as there are weekly contributions aswell

which obviously influence generated interest

i believe that

its still a very specific case 😄

i know how it works i just dont know really how to reflect it in maths

[lost notch]

I have almost 0 clue on how to do this

[ancient creek]

well the first step is to find out "how much of a circle does 120 degrees take"

so 120 / 360

= 1 / 3 of a circle

[lost notch]

yes

Oh I think I know what to do

Do I find the area of the circle and divide it by 3?

[ancient creek]

yea basically

[lost notch]

ok ty

[ancient creek]

np

[lost notch]

This one I also have little clue how to do

[rose imp]

take it as 2 isosceles triangles

and then add the areas

[next sequoia]

help

how do i calculate the angles beneath?

[glacial hedge]

do you know area of kite = diag * diag/2

[lost notch]

no I did not know that

[alpine sable]

Subtract 67° from both sides

[normal zenith]

k

[alpine sable]

And solve for cupcake

[normal zenith]

bet

[alpine sable]

What

Looked like a cupcake

[normal zenith]

done

[lost notch]

not sure how to do this one

[ancient creek]

I'm not sure either, but maybe start by breaking this shape into smaller simpler shapes. For example draw a line from Q to a point on SR to form a right triangle. Use trigonometry to figure out the triangle's side lengths and get it's area. Then do the same for point S, you will now get three shapes whose areas are easy to calculate, and then of course sum them all up.... Idk if this will work but do try it

[lost notch]

so it will create 2 traingles and one rectangle?

[ancient creek]

I believe so

[worldly gulch]

I can't solve this problem

[ancient creek]

[worldly gulch]

Ty

[sly mantle]

@worldly gulch don't troll

[worldly gulch]

Alright.

Sorry

[timid wind]

is there a number os positive integers calcaultor

?

<@&286206848099549185> ????

[vague coral]

??

[timid wind]

like for example

this

is there a calcaultor to solve this

[vague coral]

no

[timid wind]

is there a number of positive divisors calculator

[vague coral]

no

[timid wind]

ok.

[vague coral]

you can do it without a calculator dude

[timid wind]

how

[vague coral]

if you don't know how, why are you doing this exercise ?

[timid wind]

because my teacher speaks ass language

and her handwriting is even worse than my 3 year old brothers

[vague coral]

then ask your teacher how to do it, if you didn't follow the lesson, that's not my job to do it

[timid wind]

alright jesus fuck

u rlly think my teacher gonna help me xd

[vague coral]

I don't know, it's his job to do it right ?

if he doesn't do it, he shouldn't be a teacher

[timid wind]

i like how u assume the gender

ik

wait nvm

shes a fucking ass

cant eeven understand

never reponds to me

[vague coral]

[timid wind]

LOL

[gray isle]

<@&268886789983436800>

[alpine sable]

<@&268886789983436800>

[sly mantle]

b&

[alpine sable]

Sorry

For double

[ashen wave]

what determines what side is shaded?

[glacial hedge]

@ashen wave well a nice test

is to test the origin

or test it for (0,0)

if its true you shade the side that contains the origin, if its false you shade the other side

(this works with any point) but (0,0) is the easiest to plug in

[ashen wave]

ohhhhhh

omg thank you so much I was so confused

[glacial hedge]

yw

[gray isle]

if y already isolated, you could identify whether you should shade above or below the line based on the direction of the inequality

[tardy robin]

Hey, I have a question about something a mathematician said which I put into a paper I had to hand in - I don't really understand what was meant by the statement however, and I'm a little anxious that they might ask me about it when I'll have to defend the paper orally.
Could someone help me understand perhaps? The statement is the following:

Some mathematicians are talking about why math might be good at explaining the universe and a mathematician named Kontsevich says something along the lines of:
"I think it incredible that the laws of nature are quantum mechanics. We live in vector spaces [...] Why would nature choose vector spaces? It should be manifold."
Something along those lines: here's the clip: https://youtu.be/eNgUQlpc1m0?t=1126

[alpine sable]

Nature isnt sentient and cannot choose

[tardy robin]

Ok, but could anyone perhaps help me understand what is meant by the distinction between vector spaces and something being manifold.
Sorry for the inconvenience.

[glacial hedge]

not a clue

[tardy robin]

Is there perhaps anyone I could ask about manifolds?

[strong furnace]

you can try the discussion channel

or math-general maybe

[tardy robin]

Ok, thank you.

[quartz stone]

Humans seek to understand.

I believe we can only see / explain what we understand, and humans only understand the simplest of things, so naturally everything we understand / can see will be composed of simple ideas and be neatly modeled by some abstraction

[lost notch]

anyone know if this is referring to larger or smaller portion?

[gray isle]

smaller

[lost notch]

oh ok

thank you very much

[alpine sable]

@quartz stone I would argue we can see more than we can understand

[quartz stone]

We only see understanding in what we understand

As in all the explanations we see, we understand

[alpine sable]

And we often try to explain what we see with as much as we understand

[minor dagger]

For number 2, is a 4 and b 83?

[manic quail]

,w maximum -3x^2+24x+35

[ocean seal]

Results provided by WolframAlpha

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

Requested by veryhappyperson#1152

[manic quail]

,w -3x^2+24x+35, x=4

[ocean seal]

Results provided by WolframAlpha

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

Requested by veryhappyperson#1152

[manic quail]

Yes.

[minor dagger]

thank you

Can someone help me with #3?

[lost notch]

I found 1/3 of the area of the circle but how do I find the area of the triangle to subtract from it?

[alpine sable]

why is 51 double the angle A?

is it because they meet at the same minor arc

my teacher said something about inscribed angles can someone give me a definite answer?

[gray isle]

its not

it's the other way around

look up inscribed angle theorem

there is plenty big stuff telling you how it's derived

[minor dagger]

<@&286206848099549185>

[minor dagger]

this one

[gray isle]

where are you stuck for 3?

[minor dagger]

what doiuset o solve it

i have to graph it so i need points

do i just plug in whatever number i choose?

[gray isle]

identify the roots, how the curve behaves around those roots from multiplicty

[minor dagger]

is it okay if you provide me with an example so i can do 4-7?

[gray isle]

consider the degree and where the curvevstarts

on phone atm

[minor dagger]

okay

[gray isle]

from the factor of x^3, you should expect cubic behaviour around x=0

from the factor of (x+2)^2 you should expectthe curvevto bounce of the x-axis at x=-2

and pass through naturally at x=1 from (x-1)

consider what happens for very large positive and negative values of x

and you can consider subbing a few values of x of your choice to determine how high/low certain parts go and get a more accurate representation of the graph

[marsh linden]

could someone help me solve these two questions? i keep getting ln(x/4)1/2 for the second one

and 80-12h-6h^2 for the first, and they’re both not in the answer choices

not sure what im doing wrong

[tall kayak]

I am getting ln(4-x)/2

of 2nd one

[marsh linden]

can u tell me how u solved it? im having trouble when it comes to ln inverses

can u also tell me where the x >4 comes from?

[tall kayak]

y = 4+e^-2x
e^-2x = y-4
1/y-4 = e^2x
take log both the side
2x = ln(1/y-4)
now ln(a/b) = ln(a)-ln(b) formula in ln(1/y-4)
ln1 - ln(y-4)
value of ln 1 is 0

also ln(e) = 1

now x = ln(y-4)/2

interchange x and y

[marsh linden]

thank u so much

do u know a good resource i could practice more of this?

[tall kayak]

clear your basic concept of this from ur book

after clearing the basic concept u can practice many questions from internet

i dont know any perticular resource coz i genreally prefer books for problem practice

[somber oak]

Would 10 to the power of -12 be -1200000000000 or 0.00000000012

nvm

[tall kayak]

2nd one

[somber oak]

Ignore the 2

[tall kayak]

even power cant give u -ve

[cunning crow]

x^t = 1/x^-t

[ashen wave]

Can someone explain to me the difference between these? Im so confused

[tall kayak]

what is lined up means parallel?

[ashen wave]

what?

[cunning crow]

top right is arguably lined up

implicitly at least

[ashen wave]

Wait what does lined up even mean-

[patent badger]

hey guys

how can I get the x values from sinx = 1/root(2)

[tall kayak]

yep thats what i am asking

[ashen wave]

lol thats what im asking as well xD

[tall kayak]

in and interval of genral solution?

[patent badger]

yes as in general

[cunning crow]

thatd be my guess, suppose you want to subtract polynomials from each other, you'd want the terms that can combine to be organized by column

[patent badger]

I want to know the x values from this equation

[ashen wave]

ohhh ok thank you

[tall kayak]

n(pi)+(-1)^n(pi/4)
where n is an integer

[flat reef]

I NEED HELLPPPPPP PLEASE

[hybrid owl]

Got no clue for 4a, anyone got any ideas?

[hybrid owl]

<@&286206848099549185>

[hybrid owl]

I understand that C1 is the perpendicular bisector of the points O and 4d^2 - 36 and that C2 is a line starting from 12d - 3i with an angle of 1/4pi anti clockwise from the horizontal

But I have no idea how to find the intersection point in terms of d

[glass lichen]

can you find their cartesian equations?

[hybrid owl]

How would I do that? Use z = x + iy?

Even then, no idea what to do

[glass lichen]

that, or just treat the complex plane as a cartesian one

[hybrid owl]

I can try using d = x + iy but I’m still kinda clueless what to do from there

[glass lichen]

$\abs{z-0}=\abs{z-(4d^2+36)}$ so you have the perpendicular bisector between $(0,0)$ and $(0,4d^2+36)$

[ocean seal]

Mosh

[glass lichen]

d is real

[hybrid owl]

Yep, got this

[hybrid owl]

Oh yeah

[glass lichen]

so clearly it'll be a horizontal line at the midpoint of those points

[hybrid owl]

Ahh

Okay, makes a lot more sense if it is a horizontal line

[glass lichen]

wait pause, getting mixed up

points (0,0) and (4d^2+36,0)

[hybrid owl]

Wait, but that’s just a point tho

[glass lichen]

perp. bisector is a line

[hybrid owl]

Nvm, it’s horizontal

Yeah

[glass lichen]

vertical, since you're other reference complex number is strictly real

you have 2 points on the Re axis

[hybrid owl]

Oh yeah

[glass lichen]

so x=2d^2+18

[hybrid owl]

Wait so, how do they intersect then?

[glass lichen]

this is just the cartesian of C1

you still need the equation for C2

[hybrid owl]

Gradient for that is 1

[glass lichen]

yep

cause tan(pi/4)=1

[hybrid owl]

Ye

[glass lichen]

$arg(z-(12d+3i))$

[ocean seal]

Mosh

[glass lichen]

so also needs to go through the point (12d,3)

[hybrid owl]

Yep, I see

[glass lichen]

and of course, restricted cause you cant go backwards from the reference point, as that's a different arg

[hybrid owl]

Yeah

Wait so, what do I now do with those 2 points?

[glass lichen]

you dont have 2 points

[hybrid owl]

Oh, just find the x intercept

[glass lichen]

you have 2 equations of functions, solve however you wish

[hybrid owl]

Aight

[glass lichen]

very fun integral

[hybrid owl]

this looks wrong, idk

[glass lichen]

yeah cause it is

[hybrid owl]

oof

[glass lichen]

line with slope 1 and point (12d,3) is $y-3=1(x-12d)$

[ocean seal]

Mosh

[hybrid owl]

Ah, forgot the d

[glass lichen]

in use

the channel is in use. . .

unless xRyann is done

[hybrid owl]

Ye sry

[alpine sable]

lol

[hybrid owl]

I think this is good right?

[glass lichen]

$y-3=2d^2+18-12d\implies y=2d^2-12d+21$

[ocean seal]

Mosh

[hybrid owl]

Huh, where did the 18 come from

My brain is melting lmao

[glass lichen]

the perp bisector eqn

$x=2d^2+18 \ y-3=x-12d$

[ocean seal]

Mosh

[hybrid owl]

Ohhhh

Got it

[glass lichen]

that's the system

assuming I havent royally fucked it up

[hybrid owl]

So this?

[glass lichen]

yes, should be right

[hybrid owl]

Ayyy

But then…

This leads to the next question, why isn’t this valid when d = 3?

Sorry, there are other channels btw

#help-1

[glass lichen]

then use a different channel.. . .

[hybrid owl]

There are 10 total different channels

[glass lichen]

it's not, they crossposted

use common sense.

[hybrid owl]

I’m assuming that what I got is wrong because this applies nowhere

[glass lichen]

well plug in d=3, what does the point (complex number) become

[hybrid owl]

(36, 3)

[glass lichen]

$d=3\implies z=36+3i$

[ocean seal]

Mosh

[hybrid owl]

Similar numbers to before

[glass lichen]

now plug both z and d into C2

[hybrid owl]

Ahhhhh

Damn.

Arg(0)

I see.

[glass lichen]

which isnt defined, so it certainly cant be = pi/4

[hybrid owl]

Yep.

[glass lichen]

so the complex number we would get as the intersection, isnt even on one of the curves

[hybrid owl]

Thank you so much btw

Really appreciate it.

[rocky dock]

for B

why didnt he add [4,∞)?

[glass lichen]

cause you wont get a real number from sqrt(4-x) if x>4

[rocky dock]

oh ok, that makes sense

so if it was just sqrt(x)....

then infinity would be included

is that correct?

@glass lichen

[glass lichen]

you cant plug in infinity, but yes, domain of sqrt(x) is [0,inf)

[rocky dock]

ok, ty

[meager zodiac]

I can’t seem to get b

as when I do the dot product it gives me a result in a and a result with no a

[glass lichen]

how did you get b (the vector)?

[meager zodiac]

Cross product

[glass lichen]

of what vectors?

[meager zodiac]

The direction vectors

which gives (-3, -1, 8)

(As a vector)

[glass lichen]

right, the vectors that act as the slope

[meager zodiac]

Yeah

[glass lichen]

so consider the 2nd line (just to avoid a)

is (2,0,5) on that line?

[meager zodiac]

Yes

It’s the origin vector

[glass lichen]

right, so if I changed the position vector to another point on the line, I could write a vector from the new position vector to (2,0,5) which is just a scalar multiple of the direction vector

[meager zodiac]

I think so

[glass lichen]

ie (2,0,5)=k(-3,1,-1) for some k

and the dot of b and (-3,1,-1) has to be 0 since they're obviously orthogonal

so the dot of (2,0,5) and b must also be

[meager zodiac]

I don’t quite see

[glass lichen]

Ok so: Ik b and the direction vector are perpendicular, so if I can show that (2,0,5) is just a scalar multiple of the direction vector, im done

[meager zodiac]

Right but there is no such k

[glass lichen]

there is

[meager zodiac]

-ie 3k = 2 and -k = 5 aren’t both true for any k

[glass lichen]

if I pick mu=1, then I get the point (-1,1,4) so the vector from (-1,1,4) to (2,0,5) is (3,-1,1) which is -(-3,1,-1)

which is a scalar multiple of the direction vector

basically, cause the position vectors are on the lines spanned by the direction vector, they have to be perpendicular too

[meager zodiac]

ok

so an origin vector isn’t fixed

[glass lichen]

no

the direction vector is fixed

[meager zodiac]

ie it just has to be a point on the line

[glass lichen]

yes

it's just the point where the parameter is 0

[meager zodiac]

Ohhh ok

So when μ = 1 then the point on the line becomes (-1, 1, 2)

[glass lichen]

(-1,1,4)

[meager zodiac]

Yeah sorry

Because 5-1

[glass lichen]

so the 2nd line is equivalently (-1,1,4)+t(whatever)

since the parameter just runs on R

[meager zodiac]

How would I use that to show the dot products are equal tho

[glass lichen]

you can write the original position vectors as scalar multiples of the direction vector

since the direction vector is constant in the equation

and b was constructed to be ortho to the lines and thus the direction vectors

[meager zodiac]

Ok so (-12, a, -1) and (2, 0, 5) are scalar multiples of some direction vector

[glass lichen]

of their respective direction vectors, yes

[meager zodiac]

So I just need to find those direction vectors which satisfy that equation

Should I just do trial and error?

[lost notch]

Im not sure how to find this answer in radical form, I know what it is but in decimal, how do I get it in radical form?

[gray isle]

don't use a calculator

or at least don't use the pi or sqrt key on it

[lost notch]

should I use the volume formula but just put in h?

[gray isle]

you mean solve for / isolate h?

[lost notch]

yes

[gray isle]

yes

[gray isle]

also why would radical form be relevant here,
the height for this question will be an integer

[lost notch]

wait

so when I do it should I just keep the pi?

and not multiply it?

[gray isle]

isolate h and simplify first

before resorting to touching a calculator

[lost notch]

Isolating the h right away would be h = v/pi r^2

[gray isle]

not quite

missing parentheses

[cinder vessel]

Question: what does this Z+ mean?

[gray isle]

and capitlisation

h = V / (pi * r^2)

V and r are given

[lost notch]

so that would be: h = 243pi / (pi * 3^2)

[gray isle]

yes, keep simplifying

[lost notch]

for pi, should I just attach it to the number like a variable or actually multiply

?

Im left with h = 243pi / 9pi

[gray isle]

()

[heady crest]

https://en.wikipedia.org/wiki/List_of_mathematical_symbols#Blackboard_bold

[gray isle]

pi is just a number

[cinder vessel]

god bless @heady crest

[gray isle]

simplify your fraction like any other

[lost notch]

like, you want me to multiply it?

[gray isle]

simplify by identifying and cancelling common factors in both the numerator and denominator

[lost notch]

ok I got 27

[quiet crown]

So i have this worded question right, i'm confused on how what it's exactly asking me to find. Jessica is flying a kite attached to a string 12m long. She is holding the string at a height of 0.9m from the ground. How high is the kite if it makes an angle of 48°30’24” with the horizontal?

Like does it want me to find the hypotenuse or

[lost notch]

use one of the other channels

[quiet crown]

What other channel should i use?

[lost notch]

the other ones

this is question-0

[quiet crown]

Why?

[lost notch]

use questions-1

because I am still asking in this one

Its literally in the rules

[gray isle]

looks good

[lost notch]

when I plug it into the formula i dont get the right volume tho

[gray isle]

what exactly are you plugging in

[quiet crown]

Ah thanks

[zinc vigil]

how come when I sub -100 into this equation I get something different for the y value then the graph on desmos

that's my equation

[jagged imp]

are both those exponents 2/3 its kinda hard to read

[zinc vigil]

yeah

[gray isle]

what exactly is the difference you're seeing?

[zinc vigil]

I get like 0.85 when I put it in myself but on desmos it's like 1. something

[gray isle]

g(-100) should give you 1.something

you're probs doing something wrong when doing it by hand

[glass lichen]

-(-100)^(2/3)

likely missing brackets

+(100)^(2/3) gives .85 whatever

[woven pollen]

integers 1 or greater

[zinc vigil]

yeah that was it

[alpine sable]

Is there a name for the derivative of a derivative?

Like

oh wait

[mild cargo]

Hey guys I will be taking cal 2 next semester but I forgot bunch of shit from cal 1

Any tips for getting an A in cal 2 with minimal effort?

[polar whale]

If you can understand what's taught then it won't take much effort at all

But if u can't then u have to study

[alpine sable]

So the derivative of
Square root of ln(x) = 1/2x(sqrt(ln(x))

[polar whale]

I'll suggest look up some videos on calc 1 so that u can brush up ur concepts

[alpine sable]

Is there a name for the derivative of the derivative?

[mild cargo]

True I’ll start tomorrow

[alpine sable]

or is it an actual thing to begin with

[polar whale]

Double derivative

[mild cargo]

I hate studying in summer but I must get an A

For this cal 2

[alpine sable]

Oh so a double derivative

Could be there n derivatives of a function?

That shit would be interesting

[polar whale]

Well in some cases it starts repeating itself, in some cases it becomes undefined at some point

[alpine sable]

When something gets to a certain value, its converging right?

And

[polar whale]

Idk haven't learnt calc 1 that well

[alpine sable]

I see then

Could there be a fórmula or something that gives the exact amount of derivatives a function can have without repeating itself / becoming undefinied?

x is 110 degrees but how do u find y?

oh nvm

its 180 - 110 divided by 2

cause its an isoceles

wow im large brain :D

HAHA LETS GO

[glass lichen]

Yes... the nth derivative

As long as the function is differetiable you can get a deeivative

[alpine sable]

can someone help me out on this

the answer said 13.b is 1.7cm...

idk how bro

[woeful pulsar]

can you calculate the distances between the chords and the centre?

[alpine sable]

uh yea

well its 16 and 12

cause it said opposite side of the center of the circle right

[vocal kelp]

whats 9+10?

[woeful pulsar]

doesn't matter, that's just the length of the chord

[woeful pulsar]

try out the ,calc command

[vocal kelp]

,calc 9+10

[ocean seal]

Result:

19

[vocal kelp]

ong

[alpine sable]

god given power

[vocal kelp]

,calc 696969+9999999999999

[ocean seal]

Result:

1.0000000696968e+13

[rocky dock]

is this channel free?

i need a bit of help

[vocal kelp]

idk man im bumb

[woeful pulsar]

hi bumb I'm element

[rocky dock]

can anyone help me figure out the domain

sqrt(x^2-20+20)

[woeful pulsar]

I don't see any issue with plugging in 0 for x.

[rocky dock]

sqrt(x^2) = 0

like that?

@woeful pulsar

[woeful pulsar]

well yeah so 0 must be part of the domain

[rocky dock]

what do you mean?

how would i solve sqrt(x^2)=20?

[gray isle]

where's sqrt(x^2) = 20 coming from?

[rocky dock]

if you put g of x

into f of x

you end up with sqrt(x^2 - 20 + 20

-20 + 20 = 0

so just x^2

no?

[woeful pulsar]

you forgot the square root

[gray isle]

(fog)(x) = sqrt(x^2)

[rocky dock]

sqrt(x^2)

yes, im stuck there

[woeful pulsar]

so is it possible that x would cause a negative value in the square root?

[rocky dock]

no because anything squared is always positive

[gray isle]

and you should also consider if there are any values of x that would make g(x) undefined

[rocky dock]

none

theres no denominator

[gray isle]

overall g(x) is defined for all reals
(fog)(x) is defined for all reals
hence the domain of (fog)(x) would be all reals

[rocky dock]

i was looking at this example and it confused me

why does it say [-4,∞)

when the problems are very similar

[gray isle]

that's for (gof)(x)

which is different to (fog)(x)

[rocky dock]

oh

im still a bit confused

[gray isle]

f(a) needs to be defined for
g(f(a)) to be defined

[rocky dock]

ok so here

g(x) is all real numbers

and f(x) is all real numbers except anything less than or equal to -20

[gray isle]

the question isn't asking about the domain of f(x) though

but the domain of (fog)(x) = f(g(x))

[rocky dock]

so we combine the two

and intersect them?

[gray isle]

uh yeh.

consider the domains of f(g(x)) and g(x)

[rocky dock]

i guess i get confused because

we are putting g(x) into f(x)

and f(x) has a square root

which i know cannot have anything less than 0 in this case

do you see why im getting confused? if that makes any sense...

idk...

[alpine sable]

what are all the trig identities?

[gray isle]

it seems it was because you were considering the domain of f(x) instead of f(g(x)) as mentioned earlier

[rocky dock]

hmm..

am i making the same mistake?

[gray isle]

there are more things to consider here

g(x) has the domain you entered

$f(g(x)) = \sqrt{\frac{x-4}{x+5}}$

[ocean seal]

ℝamonov

[rocky dock]

yep, this is the part i mess up on

when i get here i dont know what to do

[gray isle]

as for when that sqrt is defined, you should consider where both the numerator and denominators are positive, or both negative, or numerator is 0

[rocky dock]

so how do i do that

set x+5 = 0?

[gray isle]

no

whoops typo

edited

[rocky dock]

ok what do i do?

😭 ..

[gray isle]

determine when both the numerator and denominator are positive

that will result in the fraction inside being positive

similarly, determine when they're both negative which will also have positive result

and when the numerator is 0

[glacial hedge]

Anyone know what the difference between abstract mathmatics and abstract algebra is?

I have seen abstract algebra on different college catalogs

and heres abstract mathematics course description

[remote heron]

this almost looks like a proofs class

[glacial hedge]

yeah

[remote heron]

abstract algebra is a totally separate thing

[hard sage]

I'm told to simplify this, than factor. I've already simplified now how do I factor it?

[glacial hedge]

@hard sage there are common factors

look very closely

[hard sage]

yea nvm i got it lol

exam review and im tired i havent done any of this stuff since september

[glacial hedge]

yep i know that feeling

xD

@alpine sable i remember something like this

yeah that guy

yeah that guy

xD

[vital dagger]

can someone help me with factorials

[glacial hedge]

well right off the bat you know the semi and quater circle area's

@vital dagger sure

area?

its pi*r^2/4 = pi * 100/4 = 25pi for the big quarter circle

@kindred nebula yo this area is being used use #help-1

dafuq

@kindred nebula thats called cheating

...

read the rules

dont bro him, read the fricking rules

also it seems like your the one taking the exam xDDD

yeah

[vital dagger]

can i dm u?

[glacial hedge]

yeah that works

lmao

1 sec

[alpine sable]

rip

[sly mantle]

they're banned

[alpine sable]

谢谢我的英雄rojo

yeah that's illegal

that's why banning speedrunner worked with me

bc you helped someone doing exam

whoever they're

save it

yes lol

jk

speedrunning is fun tho

so go back to speedrunning your challenge problem

[glacial hedge]

ummmm 1 sec i gotta a family thing

[sacred flax]

My b

[glacial hedge]

yeah man sorry i gotta talk to my mom

[sacred flax]

10 is default

The problem is 3^log(m-n)

I really have no idea how to start

Lol let me try something

Simplified

I tried converting to exponential but that didn’t work

...I think this was a trick question

It’s already simplest form

This is rigged

I’m sueing

:( thanks for the help :)

[gloomy hazel]

can someone help me with this question

in details pls

[jagged imp]

try to apply pythag identity

you'll have to factor something out first

[modest dragon]

$sin(x)^2+cos(x)^2=1$

[ocean seal]

Hero328

[modest dragon]

sec(x) is 1/cos(x)

so you can put

$\frac{cos(x)}{cos(x)}+\frac{sin(x)^2}{cos(x)}$

[ocean seal]

Hero328

[modest dragon]

i guess if you change sin^2(x) to 1-cos^2(x) you can get something

$1+\frac{1-cos(x)^2}{cos(x)}$

[ocean seal]

Hero328

[modest dragon]

$1+sec(x)-cos(x)$

[ocean seal]

Hero328

[modest dragon]

i get to no where 😦 sorry

[gloomy hazel]

the answer should be sec theta

[modest dragon]

i got it

$cos(x)+sin(x)^2 sec(x)$

[ocean seal]

Hero328

[modest dragon]

$cos(x)+(1-cos(x)^2) sec(x)$

[ocean seal]

Hero328

[modest dragon]

$cos(x)+(1-cos(x)^2)/cos(x)$

[ocean seal]

Hero328

[rotund quartz]

@ocean seal help

[ocean seal]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[rotund quartz]

,help

[ocean seal]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[modest dragon]

$cos(x)+\frac{1}{cos(x)}-\frac{cos(x)^2}{cos(x)}$

[rotund quartz]

oh

[ocean seal]

Hero328

[rotund quartz]

,list

[ocean seal]

My commands!

Use ,ls to obtain a briefer listing, and use ,help <cmd>to view detailed help for a particular command, or ,help to view general help.

If you still have questions, talk to our friendly support team here.

Meta

View or set meta-information about me.
​ ​ ​ ​ ping: Check heartbeat and API latency.
​ ​ ​ ​ help: Bot and command usage information.
​ ​ ​ ​ list: Lists all my commands!
​ ​ ​ about: Shard status and bot statistics.
​ ​ invite: Sends the bot's invite link
​ ​ prefix: View bot prefixes and set a personal prefix.
​ support: Sends the link to the bot guild
feedback: Send feedback to my creators

Page 4/4

[rotund quartz]

i-

[modest dragon]

$cos(x)+sec(x)-cos(x)$

[ocean seal]

Hero328

[modest dragon]

$sec(x)$

[ocean seal]

Hero328

[modest dragon]

there you go

[harsh sigil]

i dont understand the second part because i verified the soloution, and he wasn't correct so how can i graph that

[alpine sable]

guys can someone help me?

i have a question about integral

feel free to attach the question and what progress you've made! 💕

,w x-2y=12, 3x-2y=4

[ocean seal]

Results provided by WolframAlpha

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

Requested by Tasmav#3708

[alpine sable]

ok maybe graph your linear function and Guy's graph

[cinder wedge]

I have this inequality For x, y, z ∈ R+, xy + yz + zx ≥ x√yz + y√zx + z√xy.

I squared both sides

[alpine sable]

holy fuck

[cinder wedge]

and simplified

[cinder wedge]

?

then I receive x²y²+x²z²+y²z²+ (2x+1)≥ 2√xy +4√yz

Is that right up to here?

[alpine sable]

wait whats teh question

[cinder wedge]

look up

x, y, z ∈ R+, xy + yz + zx ≥ x√yz + y√zx + z√xy.

[alpine sable]

$xy+yz+zx\geq x\sqrt{yz}+z\sqrt{xy}\mid x,y,x\in\bR^+$

[ocean seal]

Πολλά άτομα είναι

[alpine sable]

ok yeah so whats the objective

[cinder wedge]

okey

I understand

I realize thank you

[alpine sable]

what

[cinder wedge]

divide by x y z

[alpine sable]

ok dude but you're not answering my question

[cinder wedge]

firstly

[alpine sable]

what do you want to do with that inequality

[cinder wedge]

prove

[alpine sable]

prove what