help-42

[strong mulch]

hat do i do if the asymptote isnt -1...

[gleaming kelp]

u graphed f right?

f should have an asymptote at y = -1

maybe zoom in a bit

[strong mulch]

look at the picture

it goesto -1

it touches it

[gleaming kelp]

oh thats just cuz desmos has to round

it gets VERY VERY close to -1 at that point

[strong mulch]

i had to zoom in a s#it ton lolll

[gleaming kelp]

b^x in general will have an asymptote at y = 0 because b^x -> 0 as x -> -infinity (or +infinity if 0 < |b| < 1) and here we are subtracting 1 so yeah

[strong mulch]

so this is good?

[gleaming kelp]

yea

looks good

[strong mulch]

okay
thank you so much

[gleaming kelp]

np

[strong mulch]

okay so for this
itsasking for me to get 5^3?

hat doi do ith the 2?

[gleaming kelp]

err

it should be just x = 5

[strong mulch]

i kina anna ork it out though

and use my brain 😭

[gleaming kelp]

okay then use ur nog!

[strong mulch]

hat do i do ith the 2

[gleaming kelp]

whats the first step

just bring it over

[strong mulch]

oh yeah

[gleaming kelp]

to the RHS

[strong mulch]

😭

[gleaming kelp]

lol

[strong mulch]

I FEEL SO DUMB LMFAOAOAOAO

[gleaming kelp]

its okay

[strong mulch]

do you think this suffices for "shoq your ork"? lol

ait no bc i have to

finish it out

[gleaming kelp]

u put 5 = 5

[strong mulch]

yeah
because 1 (right hand side) to the poer of 5 (the base) is 5or

5

to the poer of 1

i said it backards

[gleaming kelp]

u should keep the x tho

[strong mulch]

i dont kno hat to do from there to simplify it tbh

OH AIT

the

log trick!

right?

[gleaming kelp]

yea

[strong mulch]

di i do that part right?

[gleaming kelp]

lol the 5 is on the wrong side but yea good job

its technically true though

[strong mulch]

Oopsies lol

hich one?

is on the rong sie?

[gleaming kelp]

the notation on the left is typically used for tetration (one level higher than exponentiation) but it just so happens that this is also true

[gleaming kelp]

on the right

should be 5^1

[strong mulch]

oh fr?

[gleaming kelp]

yea the base should always be on the left

like dat

[strong mulch]

oooooooo i see

okay so this?

should i make the 1 smaller

lolll

[gleaming kelp]

yeaa but its fine

[strong mulch]

okay i fixed it

purty

[gleaming kelp]

looks good

[strong mulch]

ooooo thank you im saving this

hat is ln again?

[gleaming kelp]

ln(x) = log_e(x)

e is that cool transcendental number 2.71828...

[strong mulch]

Oh right

eulers

[gleaming kelp]

yurp

[strong mulch]

so for this

uh

can i foil this?

or

no

[gleaming kelp]

nope

[strong mulch]

dang

[gleaming kelp]

x-5 is the argument for ln its not like ur multiplying by ln

[strong mulch]

o

[gleaming kelp]

that would be like saying f(x-5) = fx-f5 (well, it might be true, depending on the function, but thats besides the point)

[strong mulch]

oh okay

[gleaming kelp]

anyway so what should u do first here

[strong mulch]

divide by 2?

[gleaming kelp]

yueh

[strong mulch]

from there i get x to one side?

hoq do i get rideof the ln?

[gleaming kelp]

remember, ln is just a log

so you do the same trick

[strong mulch]

it is?

[gleaming kelp]

yea

ln stands for natural log

well ok the l and n are backwards i think its that because of french

[strong mulch]

oh so its just log but a natural number

[swift laurel]

log with base e

[gleaming kelp]

yea

[strong mulch]

oh gotcha

[gleaming kelp]

no

natural has a different meaning here

[strong mulch]

i got it noq

[swift laurel]

actually i think it's latin

[gleaming kelp]

okok

[gleaming kelp]

oh, really?

[strong mulch]

the key beteen q and e is broken bte

if you couldnt tell LOL

[gleaming kelp]

yeah i noticed

[strong mulch]

okay so this?

sorry for the messiness

and i add 5 to the other side?

doi have to find a specific value bc it just says "solve the equattion for x"

[gleaming kelp]

nope u just put the ln on the other side

you need the inverse of ln

[strong mulch]

oh lol

okay so this?

[gleaming kelp]

colder

[strong mulch]

huh?

oh

i just get ridof it?

i havent really orked ith ln stuff

so sorry if im being too much

[gleaming kelp]

this is the crucial step

remember ln is just log_e

so they cancel out on the LHS

[strong mulch]

i dont get it

hy is only e on the right side?

oh

nvm

okay

[gleaming kelp]

its alright, learning takes time

[strong mulch]

that gives me x-5=e^12.5?

[gleaming kelp]

yep

[strong mulch]

this looks so chopped lol

[gleaming kelp]

looks great

[strong mulch]

im putting lines in beteen the steps just to my teacher knoqs for sure

eh?

[gleaming kelp]

sure

either way i think its understandable

[strong mulch]

thank you or helping me out i ouldve never figured out the e or ln thing

that tripped me up bad

this is asking me basically to find "hat exponent value illmake 5 be 1/125" right?

OMG I UNDERSTAND THE LOG THINGY NOQ

OMGGG THE LIGHTBULB

[gleaming kelp]

uhh

yea

[strong mulch]

YAYYY

[gleaming kelp]

try it out just to make sure i know what u meant

[strong mulch]

uhhh so if i had log5 1/125=-3

5^-3=1/125

[gleaming kelp]

yea

[strong mulch]

thats hat i meant

i think

😭

[gleaming kelp]

thats good

so u can see its both a left and right inverse

[strong mulch]

a qut O_O

[gleaming kelp]

does that make sense

its like the order doesnt matter

they both give x

[strong mulch]

ill have to come back to this once im done

illdm myself the message link

i have to rite the inverse of a function noq

sorry im just on a
"get things done" kick rn

[gleaming kelp]

btw this is just to show that exponentiation has two kinds of inverses, depending on whether you want to cancel the base or the exponent (you should be familiar with the second one)

idk if that helps or not

[strong mulch]

you shoed me the 2nd one hich is hy its familiar i think

[gleaming kelp]

i meant g(x) and its inverse

[strong mulch]

it should but i really dont kno if ill be able to

i feel like im gonna pass out
d im fine its normal bt if i dont respond soon just kno i passed out 😭

[gleaming kelp]

okay lol

[strong mulch]

okay so inverse function

do i divide by 6 first?

no no no

[gleaming kelp]

no yea ur right

divide by 6

i mean if u want u should like rename the variables

[strong mulch]

but theres nothing on the left yet to divide

[strong mulch]

no id like to keep them so less confusion

[gleaming kelp]

thats fine just do f(x) / 6

[strong mulch]

oh okay

doi divide the 2x and 6 by 6 too or no?

[gleaming kelp]

no thats inside the log

[strong mulch]

yeah thats hat i as thinking and hy i hesitated to

[gleaming kelp]

well even if it was just multiplication u wouldnt do that because its in parentheses anyway (that means the 6 is already acting on the entire expression)

like for example y = a(b+c) => y/a = b+c

[strong mulch]

i dont understand that either

😭

itd take me like

5 minutes of piecing it together

[gleaming kelp]

its okay lets just move to the next part

so now we have to get rid of log_5

we do the same thing as always

[strong mulch]

yeah i as looking at my ork and just about to ask if i do that LOL

[grizzled flame]

Imverse function is integral?

Cuz if so I can help

Its easy

[gleaming kelp]

we arent doing integrals

[grizzled flame]

Idk what inverse function is in my language and I thought it is integral

My bad

[gleaming kelp]

its ok

[gleaming kelp]

this an inverse function (the notation at least)

[strong mulch]

okay i got this noq

[gleaming kelp]

yea looks good

i think u can do the rest

the LHS is gonna look really ugly lol

[strong mulch]

oh nooooo okay ill do it though

eh?

[gleaming kelp]

close

but you cant divide the base by 2

because well it has an exponent

so unfortunately you just have to make the whole thing a fraction

thats why i said it was gonna look ugly

[strong mulch]

oh no...

[strong mulch]

oh thats not as bad as i thought

i got the fraction messed up but

[gleaming kelp]

u should have the inverse function now

replacing x with f^-1(x) and f(x) with x

boom ur done

[strong mulch]

ait fr?

[gleaming kelp]

yea

what was once the input variable is now the output variable and vice versa

well, by "output variable" i just mean the function itself

[strong mulch]

eh?

[gleaming kelp]

yea

for a second i thought the -1 was a -2

my eyesight sucks

[strong mulch]

LOL no orries i get it

if i didnt have my glasses rn i oulnt be able to see anything on my screen rn

meaning like

nothing at all identifiable LOL

[gleaming kelp]

yikes!

my eyes are good enough that i dont bother wearing my glasses

though if i ever got a drivers license id probably have to use them

[strong mulch]

yeah it has to be 20/40 or better

here i live at least

this ismy next problem
basically i fill in s ith 320 and the solve?

[gleaming kelp]

sorry my reading comprehension sucks

gimme a sec

[gleaming kelp]

ok yea

[strong mulch]

have i done it right so far?

[gleaming kelp]

yea

sorry i was doign somethign

[strong mulch]

no orries!! you have alife :3

ivethought on it an idk hat to do next

[gleaming kelp]

divide by 95

and then do the log trick

btw you dont have to simplify 245/95 u can do it later

[strong mulch]

oh okay
once again i second guessed myself

😭

[strong mulch]

is it different this time bc d isnt in subscript

[gleaming kelp]

d is just the uh

whats inside of it

log(d)

the base is 10 because thats the default

[strong mulch]

Oh
OH YEAH

[gleaming kelp]

log_10(d)

[strong mulch]

I forgot the base 10 ruleeeee

so id just end up ith d?

(eez nu-)
SORRY I HAD TO

and

sorry its messy but the parenthesis are supposedto be exponent

[gleaming kelp]

yea thats good

[strong mulch]

Do i simplify it?

I kinda have to actually

[gleaming kelp]

i think they might want an approximation

[strong mulch]

yeah

😭

[gleaming kelp]

245/95 can be simplified to 49/19 but you dont have to show that
nvm!

thats how they wanted it i guess

[strong mulch]

im just gonna put both an approximation and uh

the simplified

[gleaming kelp]

oh wait i thought this was

nvm

[strong mulch]

hatd you think it as?

[gleaming kelp]

yea

do dat

[strong mulch]

is that the approximate sign

here i fixed it

i hope this is okay

i think ill just submit it and hope its good, it cant be orse than a 40 %

[gleaming kelp]

looks good

[strong mulch]

Thank you so much

[gleaming kelp]

np

[strong mulch]

thnk you for your patience, understanding, and genuinely helping me learn. i really appreciate it. im gonna do some other ork no and tak a break from math bc i did 3 hole math assignments LOL

thank you!!!

.close

[calm coral]

Channel closed

Closed by @strong mulch

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[ruby kraken]

Hello! I’m taking topology and i’m not completely sure about this question.

[ruby kraken]

It’s the showing it I have issues with, here is my work

Kind of just restating

[calm coral]

@ruby kraken Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[quartz adder]

need to test convergence by ratio or root test, super lost on this

[leaden thunder]

ratio test looks promising

[quartz adder]

hmmm

i just dont know how to notate the top

oh wait would it just cancel to 2n + 1

or 2n

[leaden thunder]

just try on paper and show it

[calm coral]

@quartz adder Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[runic snow]

could someone explain these concepts to me? like why do we do: (x-6)^2 = (2i)^2 or like why does x=2-5i turn into (x-2)^2=(-5i)^2?

like just how to approach such problems, because i couldn't really find any youtube videos that constructed a polynomial function in standard form from a worded description

[edgy leaf]

a polynomial can be expressed as a(x-p)(x-q)(x-k)... where p,q,k are the roots of the equation

[runic snow]

so sorry if this is dumb to ask, but roots of the equation are the zeroes in this case, right?

[edgy leaf]

so we would have (x+3)(x-(2-5i))(x-(2+5i))

now try expanding the latter half

[edgy leaf]

yes

a complex root is such that if a+bi is a root then a-bi is also a root

this is called the conjugate root theorem

[runic snow]

i guess im just confused as to why like we have to split 2-5i into (x-2)^2=(-5i)^2, but thats a part of the conjugate root theorem, right?

[edgy leaf]

i guess

[edgy leaf]

it makes more sense imo to approach it like this

[runic snow]

because we still end up with the final product of x^3-x^2+17x+87 right

[edgy leaf]

yup

[runic snow]

ohh okay ive never done it that way before but it honestly makes more sense, i think i was js tryna do it the given way since my teacher deducts points for alternative solving methods

thank you !!

.close

[calm coral]

Channel closed

Closed by @runic snow

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[dull tangle]

I got the bounds for z but how do you know how to graph the shape on the xy plane

[dull tangle]

How do you know its a triangle or whatever

[swift laurel]

well you have that the plane intersects the xy plane through the line 2x + 2y = 4 just by setting z = 0

and x = 0, y = 0 were given as bounds

[dull tangle]

Oh

Yeah set z=0 because xy plane

Done

Thanks

.close

[calm coral]

Channel closed

Closed by @dull tangle

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hollow frigate]

R u allowed to take moments from any point here?

I set Rn equal to 80g

and I took moments about A and got it wrong

ping me

[unreal isle]

to take moments about A wouldnt you need the force applied by the pivot?

the anticlockwise moment

@hollow frigate

[hollow frigate]

see that was what i wasnt sure about

oh wait

[unreal isle]

yep

[hollow frigate]

u r talking about this right?

[unreal isle]

what

qq what's Rn

[hollow frigate]

sry Rc

should be

the force coming from up from here

ahhh wait

[unreal isle]

whered you get that value tho

[hollow frigate]

erm

cause its in equilibrium

can u not just set

upwards force = to downward force

[unreal isle]

oh wait yeah

i mean

that gives the same answer

[unreal isle]

you're right i just got confused cos you wrote 80g instead of 80kg 😭

[unreal isle]

realise that you're changing the frame of reference when taking A as the pivot, so the distance youd find would be from Roshan to A, not the distance x shown

any particular reason for not taking moments about C directly?

[hollow frigate]

No i j didnt think of it when i was doing the q lol

ok thanks

I guess i j made a silly mistake then

[unreal isle]

you got it?

[unreal isle]

perchance

[hollow frigate]

yeah when i took it about c

.close

[calm coral]

Channel closed

Closed by @hollow frigate

Use .reopen if this was a mistake.

[unreal isle]

try doing it with the other one too

||80kg * 5 = 50kg * y||
||y = 8m||
||x = y-5||
||x = 3||

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[surreal peak]

Need verification for the answer of this question

[unkempt drift]

,w (2x + 1) y'' - 4(x + 1)y' + 4y = 0

[potent lotus]

Results provided by WolframAlpha

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

Requested by sooouth.

[unkempt drift]

great, that's equivalent

you can combine the multiplication of the constants $-c_2 e$, and that's a new constant

[potent lotus]

south

[surreal peak]

Okayy

So its all correct right?

[unkempt drift]

yep all correct

I'm trusting that you did the variation of parameters steps correctly

[surreal peak]

Yeah alright

.close

[calm coral]

Channel closed

Closed by @surreal peak

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[torpid widget]

Can anyone tell me how to approach these kinds of problems?

[velvet osprey]

kind of depends, but here it makes sense to square both sides and try to match term by term

[torpid widget]

oh, i'll try that

one sec

i got it

thanks

i got the answer as 15

its correct

thanks

.close

[calm coral]

Channel closed

Closed by @torpid widget

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[outer sedge]

when dealing with surfaces like a cylinder for example, what would be the difference between -3<=z<=3 and: z = -3, z = 3

[calm coral]

@outer sedge Has your question been resolved?

[spark stratus]

there shouldnt be a difference, those both represent the same way of restricting to z between -3 and 3

[outer sedge]

isn't -3<=z<=3 uncapped?

or does it include the planes

how would i describe a closed cylinder

[spark stratus]

neither way ever describes it to begin with

youre better off stating the cylinder is closed outright

[outer sedge]

would I say: bounded by surface z = 3 and z = -3

[spark stratus]

a closed cylinder bounded by z=3 and z=-3

also: a closed cylinder with -3 ≤ z ≤ 3

[outer sedge]

btw, does -3<=z<=3 include the planes?

[spark stratus]

-3 ≤ z ≤ 3 is not a plane

[outer sedge]

I know, but its edge is a plane no?

[spark stratus]

wdym by include the planes

[outer sedge]

if you have -5<=y<=5, its edge is a horizontal line

right?

[spark stratus]

you need to state what you are including the planes for

are you attaching the planes to the cylinder?

[outer sedge]

Nope. I'm just seeing if the edge of -3<=z<=3 is made up of two planes.

[spark stratus]

then yea it does

[outer sedge]

.close

[calm coral]

Channel closed

Closed by @outer sedge

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[snow maple]

(a) expand (2-x^2)^2 in ascending power of x up to and including the term in x^4 simplifying the coefficient
(b) state the set of value of x for which the expansion is valid

am i doing this right?

[calm coral]

@snow maple Has your question been resolved?

[calm coral]

@snow maple Has your question been resolved?

[snow maple]

<@&286206848099549185>

[calm coral]

@snow maple Has your question been resolved?

Channel closed

Closed by @snow maple

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[outer sedge]

how to find if a point is inside a closed surface?

[outer sedge]

do we need to find the limits for z, limits for y, limits for x?

or is there an easier way

[eternal shard]

generally, a closed surface is described by equations or inequalities for example, so you would test the point by plugging it in and see if the constraints are satisfied

[outer sedge]

let's say we have the following surface
I wanna test if (0.6, 0.5, 0.4) is inside the surface. What do I do with the inequalities?

it satisfies both inequalities

[eternal shard]

That point is either inside the region which means x^2+z^2 < y and 0 < y < 1 but it cannot be on the blue disc because y=1 is violated

[outer sedge]

I want to test if it's inside the closed surface

[eternal shard]

the strict inequalities imply that its inside

else it would be on the surface or outside

[outer sedge]

I see you wrote x^2+z^2 < 1, but isn't that for y only?

[eternal shard]

y is x^2+z^2

[outer sedge]

how do i test the x and z coordinates

[outer sedge]

I know, so that only tests the y value

whether it's valid

x^2+z^2 < y < 1

right?

[eternal shard]

x=0.6,y=0.5,z=0.4 ok, you see 0 < y=0.5 < 1 is satisfied but y=x^2+z^2=0.6^2+0.4^2 is not

,calc 0.6^2+0.4^2

[potent lotus]

Result:

0.52

[outer sedge]

that's because it's not on the surface

[eternal shard]

yes

[outer sedge]

I wanna see if it's inside the closed surface

so after doing x^2+z^2 < y < 1

what's the next step

[eternal shard]

but it's not

your point is just not inside, find another

[outer sedge]

do you know why am i doing this btw? I am checking if the normal vector is outwards.

[eternal shard]

no i didnt know why you were doing this

[outer sedge]

i have point (0.5, 0.5, 0.5) on the surface and normal vector (1, -1, 1)

someone told me in another server to find a point inside the surface, create a vector with the point on the surface, and dot product that vector with the normal

is this correct

for example, let's say that (0.4,0.4,0.4) is inside the surface...

My vector would be (0.5, 0.5, 0.5) - (0.4, 0.4, 0.4) = (0.1, 0.1, 0.1)

Dot product with the normal gives: 0.1 -0.1+0.1 = 0.1, since it's greater than 0, the normal is outwards

[eternal shard]

that cant be

the dot product being positive implies that the angle between the normal and the vector from (0.5,0.5,0.5) to (0.4,0.4,0.4) is between 0 and pi/2

if you want to get from (0.5,0.5,0.5) to (0.4,0.4,0.4) you need to do (0.4, 0.4, 0.4) - (0.5, 0.5, 0.5) = -(0.1, 0.1, 0.1) then the dot product is -(0.1, 0.1, 0.1).(1,-1,1) = -0.1 which implies an angle between pi/2 and pi which implies the normal facing outwards

so yea it seems that methods works

havent encountered that yet

[calm coral]

@outer sedge Has your question been resolved?

[eternal shard]

here for example

[outer sedge]

if the origin is inside, i can just use the origin, right?, what if the origin is located directly at the surface (like in our example)

then i can't use it?

[eternal shard]

yes any point interior works

[eternal shard]

it still seems to work here as an exception because the vector is still going inside the surface

i want you to think of the idea like this

the normal would be orthogonal to the tangent vectors at (0.5,0.5,0.5)

the moment you take a vector that faces inside the surface, the angle becomes greater than 90°

it will vary between 90° and 180° which causes the dot product to be negative because cosine is negative

actually i cant tell yet if thats always a good idea and rule to go by

[calm coral]

@outer sedge Has your question been resolved?

[calm coral]

@outer sedge Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[spice venture]

can someone help me with part C,D

im not getting how to find the direction it is moving

[fickle hearth]

Well for the first image in the plane mirror, the velocity of the image would be in the opposite direction with the same magnitude as of the object velocity.

[spice venture]

yep got that

[fickle hearth]

Do you know this formula then?

[spice venture]

which one

[fickle hearth]

Image velocity for curve mirrors

[spice venture]

oh yes

oh so it would be -(1/5^2 + v)

which means its moving in negative direction

towards convex mirror

[spice venture]

could u just check this part?

[fickle hearth]

Yh wait a sec

[velvet osprey]

,rccw

[fickle hearth]

Considering that you took positive sign for the direction left-right, then it's right.

[spice venture]

yeah

okay thank you

.close

[calm coral]

Channel closed

Closed by @spice venture

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[brittle sail]

How do we solve such questions?

[ancient grotto]

I guess visualize it?

[upbeat venture]

1. find the obtuse angle between the planes using their normal vectors
2. find the plane whose normal vector is at half the angle as the normal vectors in (1)

[calm coral]

@brittle sail Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[blazing coyote]

This is the formula I have to use

for one point, we'd just have $f(-0.75) + \Delta f(x_0)$ right

[potent lotus]

What a wonderful world !

[blazing coyote]

I mean for first degree interpolation

[old falcon]

wont it just end up being point point

or am i missing your confusion

[blazing coyote]

I meant first degree polynomial interplolation

[old falcon]

but i mean, with x_0 and some other point, its just a line through two points

[blazing coyote]

yea

[old falcon]

the only special thing is the range

[blazing coyote]

so $f(-0.75) + \frac{x- x_1}{2!(x_0-x_1)}f(x_0)$

[potent lotus]

What a wonderful world !

[blazing coyote]

Is this right?

[old falcon]

i thought it was just taylor but you made me nervous im trying to be sure

[blazing coyote]

oops

yeah, this is a lagrange interpolation

[old falcon]

https://mathworld.wolfram.com/NewtonsForwardDifferenceFormula.html

[blazing coyote]

That's better

so $f(-0.75) + \frac{x- x_1}{2!(x_0-x_1)}f(x_0)$

[potent lotus]

What a wonderful world !

[old falcon]

1! not 2

im a little worried that they give everything for a in [0,1]

[blazing coyote]

Hmm, yea

same

[old falcon]

but i feel weird about (-a)_n

maybe you can just do $f(x-a) = \sum _{n=0} ^\infty \frac{ (-1)^n (a)_n \Delta ^n f(x) }{ n! }$ then

[potent lotus]

jan Niku

[blazing coyote]

hmm, yea

wait

no

I haven't done taylor series yet

[old falcon]

we can use this i just am worried about the binomial its actually a polynomial right

[blazing coyote]

Yea

It should output a polynomial

$\delta$ is the forward difference

[potent lotus]

What a wonderful world !

[blazing coyote]

$\Delta$

[potent lotus]

What a wonderful world !

[old falcon]

so $P_1 (x) = f(x_0) + \binom s 1 \Delta f(x_0)$

[potent lotus]

jan Niku

[old falcon]

but s

[blazing coyote]

Unless I'm mistaken s is the number of iterations

wait, no

[old falcon]

isnt it one of those rational factors

[blazing coyote]

I'm trying to find out what my book has to say

ah

[old falcon]

$\binom s k = \frac{ s(s-1) \cdots (s - (k-1)) }{ k! }$

[blazing coyote]

step size

[potent lotus]

jan Niku

[blazing coyote]

looks like s is the step size

[old falcon]

so its just $\binom s k = \frac{ (s) _k }{ k! }$

[potent lotus]

jan Niku

[old falcon]

guess we should have figured

[blazing coyote]

which looks like it's 1/4

this is confusing the hell out of me

so we have $\binom{\frac{1}{4}}{1}$

[potent lotus]

What a wonderful world !

[blazing coyote]

which is just 1/4

am I doing something wrong

[old falcon]

google says $s = \frac{x-x_0}{\Delta}$

[potent lotus]

jan Niku

[blazing coyote]

yes

which is 0.25 here, right

[old falcon]

wouldnt it be $s = \frac{-\frac 13 - (-0.75)}{ 0.25 }$

[potent lotus]

jan Niku

[blazing coyote]

hmm

I suppose

[old falcon]

,calc 4 * (-1/3 +3/4)

[potent lotus]

Result:

1.6666666666667

[old falcon]

5/3

[blazing coyote]

I also just realised it's the forward difference and not divided difference

oops

[old falcon]

so $P_1\qty(\frac 13) = f(-0.75) + \frac{ \qty( \frac 53 )_1 \Delta f(-0.75) }{ 1! }$

[potent lotus]

jan Niku

[blazing coyote]

hmm

Makes sense I suppose

[old falcon]

and (5/3)_1 is just 5/3

[blazing coyote]

Yup

thanks

[old falcon]

[blazing coyote]

I'll continue this tomorrow

tq again

.close

[calm coral]

Channel closed

Closed by @blazing coyote

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[calm coral]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[calm coral]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[pseudo lake]

Hey

[pseudo lake]

Can some pls check my work

I know I made a mistake but I am not sure where

Number 30

The integration

[calm coral]

@pseudo lake Has your question been resolved?

[pseudo lake]

<@&286206848099549185>

[calm coral]

@pseudo lake Has your question been resolved?

[wise moss]

what is the answer then?

[pseudo lake]

this

[wise moss]

oh right

second implication is wrong

[pseudo lake]

what do u mean by second implication?

[wise moss]

$ \int_{r^2}^{8-r^2} zr^2 ,, dz = r^2 \cdot \frac{8-r^2 -(-r^2)}{2} = \frac{8r^2}{2}$

bot ?

$$ \int_{r^2}^{8-r^2} zr^2 dz = r^2 \cdot \frac{8-r^2 -(-r^2)}{2} = \frac{8r^2}{2}$$

[potent lotus]

Syrenate

[wise moss]

what

hang on

nvm mixed my notes with yours

but still wrong

$$ \int_{r^2}^{8-r^2} zr^2 dz = r^2 \cdot \frac{(8-r^2)^2 -(r^2)^2}{2}$$

[potent lotus]

Syrenate

[wise moss]

that

[pseudo lake]

oh i see

now

thx

[wise moss]

👍

[pseudo lake]

.close

[calm coral]

Channel closed

Closed by @pseudo lake

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[gusty lance]

Stuck pls help

Idk what to do next

I can use a calculator for this btw

[tranquil wasp]

hmm

[hot pecan]

r can be +- 1/2 then u can sub r into ar^2 = 40 or the other one to find a

[manic sandal]

why are you infinitely summing the term you already infinitely summed?

[gusty lance]

idk......

[gusty lance]

oh tru

[gusty lance]

i thought id js use the calculator for the infite sum - partial sum but the n variable made it hard

[hot pecan]

based off finding a u can find S_infinity

[sweet stag]

r = -1/2

S_infty = a/(1-r)

[gusty lance]

a = 160 either way i dont see why r has to be -1/2

[sweet stag]

they said that the sequence can be negative

if r = 1/2 u cant get negative elements

[gusty lance]

oh

true

[hot pecan]

isnt it liek squared anyways to find a

ar^2 = 40

[gusty lance]

no but if we had used r = 1/2 then we can't get g5 = 10

[hot pecan]

oh lol nvm i get it

[gusty lance]

wait no

im stupid

but it can't be negative

[sweet stag]

squared on odd terms

[gusty lance]

infinite sum = 320/3?

[sweet stag]

yes

[gusty lance]

kk

can i set infinte sum - finite sum = 0.01and see what Sn is

wait no

[hot pecan]

yes

or n yea

[gusty lance]

but then id have to subtract 0.01 from what Sn is

right?

nvm i think

im on the right track

[calm coral]

@gusty lance Has your question been resolved?

[gusty lance]

i am not

What am I doing wrong cuz when I type this into my calculator it can’t solve it

[hot pecan]

well it doesn’t = 0.001

sub a and r into the S_n formula

then from that u can | s_infinitg - s_n | <0.001

then it’ll be (1/2)^n < ‘that number’

then plug in number that’s are closest but doesn’t go over ‘that number’

[gusty lance]

o

i js typed in the whole expression and went to table and found that it was less than 0.01 at x = 14

[hot pecan]

then there ur answer

it should be right

[gusty lance]

oh kk nice

ty

.close

[calm coral]

Channel closed

Closed by @gusty lance

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[summer bane]

How would I approach this to solve for x? I have found that angle CBP is 40, and ACB is 50. Line BP is perpendicular to AC. aswell that angle CPB + x = 210

[odd moon]

cpb is 40?

[summer bane]

oh mb

cbp

not cpb

[calm coral]

@summer bane Has your question been resolved?

[calm coral]

@summer bane Has your question been resolved?

Channel closed

Closed by @summer bane

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[ruby jackal]

i need hlep understanding transformations and dilations of graphs

[ruby jackal]

notation for transformations + accurate order for it

[dapper sable]

I don't know what you mean by notation, but first you get the transformations for x. Then you work outward from that.

Like 2x changes to -4x.

[ruby jackal]

like u have dilation by a factor of 3 from the x axis maybe

where (x,y) -> (x,3y)

thats notation

[ruby jackal]

yea awesome sauce mate

.close

[calm coral]

Channel closed

Closed by @ruby jackal

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[vivid arrow]

does anyone know why this is false?

[swift laurel]

well it could have two separate oblique asymptotes i suppose (one in each direction)

[vivid arrow]

wdym by one in each direction?

[swift laurel]

like it could have one approaching positive infinity and one approaching negative infinity

[vivid arrow]

sorry I’m having trouble visualizing this 😭

[leaden thunder]

have you ever plotted hyperbolas

[vivid arrow]

yeah but I assumed they weren’t functions since they fail the vertical line test

[vivid arrow]

ohh

gotcha thank u !

.close

[calm coral]

Channel closed

Closed by @vivid arrow

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[gusty lance]

may i get help with C

i dont get what the first given is saying

<@&286206848099549185>

[calm coral]

@gusty lance Has your question been resolved?

[calm coral]

@gusty lance Has your question been resolved?

[calm coral]

@gusty lance Has your question been resolved?

[rustic osprey]

These two areas are equal

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[twilit delta]

I need to calculate the limit of this function as it approaches 0

[twilit delta]

I tried simplifying but I don't know what do next

[velvet osprey]

write sin^2(x) as 1 - cos^2(x)

[velvet osprey]

also this first image is very bad tex

$\frac{\sin(x) \cdot \tan(x)}{1-\cos(x)}$

[potent lotus]

Ann

[velvet osprey]

this is how to write it better

[twilit delta]

ah thanks my latex sucks

thanks I managed to do it

.close

[calm coral]

Channel closed

Closed by @twilit delta

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[gusty lance]

...

what does it mean when it says the graph is symmetrical to x - a if f(x) = f(2a-x)

[unkempt sphinx]

it means that if you graph it, it will be symmetric with respect to the line x=a

[calm coral]

@gusty lance Has your question been resolved?

[gusty lance]

ya but how can a curve be symmetric to a line

like how can i visualize that

[rustic osprey]

The result when you reflect the curve over the line is the curve itself

,w graph y=(x-1)^2, x=1

[potent lotus]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon

[calm coral]

@gusty lance Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[pale cedar]

isnt this just $\int_{-1}^1\int_{-1}^1e^{x+y}\dd x\dd y$

[potent lotus]

pirateking0723

[supple mural]

no, as the area is not a rectangle from -1 to 1

[pale cedar]

it is a rotated rectangle

ah i see what you mean

it doesnt have the same area

this rotated rectangle has a side of length sqrt(2) whereas to the one that you are talking about which has a side of length 1

hmmmm

what about this : $\int_{-1}^1\int_{x-1}^{1-x}e^{x+y}\dd y\dd x$

[potent lotus]

pirateking0723

[supple mural]

i think you need to split the integral into parts

[pale cedar]

how

for example split it into 2 double integrals, one for the triangle to the right of the y-axis and another to the left of it ?

[supple mural]

have you learned change of variables?

[pale cedar]

yes

this is an exercise to change of variables

i did it

but i thought that change of variables isnt needed here because the integral seemed easy to integrate without it

it turns out that this is not the case

[supple mural]

bit tricky as e^{x+y} is not symmetric

[pale cedar]

ah i see

[supple mural]

variable change is def the way to go

[pale cedar]

yea now i see this

[supple mural]

you could split it up into 4 parts

but its a waste of time tbh

[pale cedar]

yea it is

[supple mural]

and jacobians are fun so thats a plus

[pale cedar]

nvm now i understand why change of variables is the way to go

[pale cedar]

hahahahaha

i have a question

[supple mural]

shoot

[pale cedar]

when i want to do change of variables

how to determine the bounds

so sometimes one of the variables will be written in terms of the other

and other times all of the variables will have their bounds purely numbers

well technically the latter is when the transformation maps to a rectangle oriented in the normal way , ie with its sides parallel to the axes right ?

and otherwise it will be the first case ?

or am i missing something

[supple mural]

been a long time since ive done this, but pretty sure you can solve the inequality for u and v

[pale cedar]

yea this question is on the easier side (probably) but i am talking in general

[supple mural]

i think thats how i usually solved those types of problems

[pale cedar]

you can just check the boundary here , ie |x|+|y|=1 then you get 4 equations of straight lines and after you change variables you can find the boundaries from there

[pale cedar]

i see

yea it is reasonable

you only need the boundary

because the transformation will map the boundary to the boundary of the new region in the new plane

alright tysm

[supple mural]

np

[pale cedar]

have a great day/night

.close

[calm coral]

Channel closed

Closed by @pale cedar

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[trail lark]

what is the answer is it 3e^4 + 2 / 2e^3

[calm coral]

@trail lark Has your question been resolved?

[tulip spear]

$\int_{-1}^1\int_{x-1}^{1-x}e^{x+y}dydx=\int_{-1}^1e^x(e^{1-x}-e^{x-1})dx$ try to use this

[potent lotus]

ooaa

[trail lark]

thanks

[calm coral]

@trail lark Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tulip folio]

hello

[tulip folio]

i need help

complex numbers in polar form

[marsh valley]

What's the question you're working on?

[tulip folio]

here u go

i am lost

[marsh valley]

Polar form has 2 parts : the modulus and the argument.
Think of it as a triangle with side lengths sqrt(3) and sqrt(2).
The modulus is the length of the hypotenuse, and the argument is the angle between the two legs.

[tulip folio]

ok

[marsh valley]

Do you think you can figure out the modulus?

[tulip folio]

no

i have no idea what im doing

or where to start

[marsh valley]

Well you have a right triangle with legs sqrt(3) and sqrt(2). What's the length of its hypotenuse?

[tulip folio]

sqrt(5)

[marsh valley]

Yep, so that's the modulus

[tulip folio]

oh ok

[marsh valley]

For the angle you'll have to use trig ratios

[tulip folio]

ok

and what are trig ratios

[marsh valley]

You found r.

[tulip folio]

so im using sin and cos to find theta

[marsh valley]

Yes

You know two legs and you want the angle

Any trig function you know uses opposite and adjacent?

[tulip folio]

tan

[marsh valley]

Good

[tulip folio]

sqrt(2) / sqrt(3) is theta

[marsh valley]

Not quite

You know that $\tan(\theta) = \frac{\sqrt{2}}{\sqrt{3}}$

[potent lotus]

Azyrashacorki

[tulip folio]

ok

[marsh valley]

You must solve for theta in there

Using, say, the arctan function

[tulip folio]

inverse of tan?

[marsh valley]

Yes that's the same

[tulip folio]

so sqrt(3)/sqrt(2)

[marsh valley]

No not inverse in that sense

The inverse function

[tulip folio]

oh

[marsh valley]

$\tan^{-1}(x) \ne \frac{1}{\tan(x)}$

[potent lotus]

Azyrashacorki

[tulip folio]

oh shit

my past 3 months have been a lie

[marsh valley]

inverse tan is a separate function

tbf the notation is confusing, I prefer arctan because it avoids this

[tulip folio]

so i whip out a calc for this part then

[marsh valley]

Yep

Unless the trig ratio is obvious and you can figure it out from known identities

But I don't think it's the case here

[stoic pagoda]

arctan(mag(b)/mag(a)) will give you the reference angle, you then need to find the quadrant of the point. eg. Q4, then you need to manipulate arctan(mag(b)/mag(a)) to lie within Q4. Also recall that Arg(z) is defined from (-pi, pi], so make sure to manipulate it with these contraints in mind

[tulip folio]

ok gimme a sec

i got a number

like a degree number

shouild i change mode

[stoic pagoda]

it should be radians

nvm your question wants degrees

[tulip folio]

i got .6847

oh ok

degrees thgen

i got 39.23

[marsh valley]

That looks good.

[tulip folio]

ok so far so easy then

[marsh valley]

Then the polar form of your complex number is $r(\cos(\theta) + i\sin(\theta))$

[potent lotus]

Azyrashacorki

[tulip folio]

ok so cos(theta) is sqrt(3)/ sqrt(5) right

[marsh valley]

Yes, but look at the answer form

You need only put in the angle, not the actual cos

[tulip folio]

oh ok

so theta is just like the angle

which is 39.23?

[marsh valley]

Yep

As sonder pointed out in a general case, you do need to check which quadrant your triangle falls into, because arctan only gives you an angle in [-90, 90], which means you might need to add multiples of pi

In this case it isn't necessary

[tulip folio]

so whats like an example of a number it might give me and how i correct it

[marsh valley]

But, for instance, if you had started out with $-\sqrt{3} - i\sqrt{2}$, then you still would have had $\tan(\theta) = \frac{\sqrt{2}}{\sqrt{3}}$, so you would've gotten the same angle.
However, the point is in quadrant 3, so you need to add pi to it

[potent lotus]

Azyrashacorki

[tulip folio]

oh ok

seems easy enough ig

[marsh valley]

In general, just draw it out in a plane

[tulip folio]

alr

so my final answer should be sqrt(5)(cos39.23 + isin39.23)

[marsh valley]

That should work, yes

[tulip folio]

what now

[marsh valley]

They say nearest tenth for the angle

Maybe that?

[tulip folio]

ok that was my fault

thanks

seems pretty easy but i will be back for 2 reason

either a harder question that im lost in

or when i get a demoivres theorem question

.close

[calm coral]

Channel closed

Closed by @tulip folio

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[karmic willow]

how do i find the period of cos((t/2)+(pi/2))

[torpid canopy]

Period of $\cos(at)$ is $2\pi/a$ I believe

[potent lotus]

Ari

[karmic willow]

oh ok

how do i make an equation for a cos graph with just a visual and one point?

[stoic pagoda]

AMPLITUDE IS 5

PERIOD IS 6

[karmic willow]

ah i see

randome question

why is 1/3pi and pi/3 the same?

[stoic pagoda]

its not wht

[karmic willow]

huh?

i got the same in desmos

[stoic pagoda]

wdym

[torpid canopy]

do you mean 1/(3pi) or 1/3*pi

[karmic willow]

probably (1/3)pi?

i just inputted 1/3pi and pi/3

[viral isle]

y=5cos2pi/6(x)

[karmic willow]

how do i find the period

wait i got it

finally kinda understanding these

[viral isle]

Nice

[viral isle]

Use the formula 2pi/|b|

[karmic willow]

for this is the period (2pi/2pi/5)?

or is it just 5

[viral isle]

2pi/5

[viral isle]

Wait

Try 2pi/5?

[karmic willow]

its 5

cause years

this is really confusing

[viral isle]

Oh nvm😂😂😂

You need help with that?

[karmic willow]

im assuming itd be a -cos cause its starting at the low point right?

yeah

[viral isle]

Okay

[viral isle]

Don’t assume

Do maths