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[empty mason]

it would be less clean i think

from here, because idk all my summation formulas by heart, let us call z^1+z^3+...+z^13=S which we want to find a closed form for S. Notice that when multiplying S by z^2, it is the same as S but taking away the z^1 and adding the z^15. We can rewrite this into an equation as z^2(S)=S-z^1+z^15, S(z^2-1)=z^15-z^1 in which S=(z^15-z^1)/(z^2-1) in which we have found the closed form for S

[rapid gate]

ok lemme expand it term by term

[empty mason]

ok

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[alpine sable]

Im trying to figure out a formula to calculate the time needed between each letter in a 4 letter word to satisfy an inputted int wpm

[alpine sable]

so say I input the number 60

it should know that i should need 0.25 seconds between each letter to type 1 word every second

that 0.25 input is the number I need as output

i input wpm, output is time between letters needed in 4 letter word

the time between each letter should be bigger the lower the wpm and vice versa

[exotic canopy]

60 wpm is 1 wps

so just do wps/4

[alpine sable]

true true I thought og that

but how do I figure out the wps?

[exotic canopy]

divide by 60

[alpine sable]

but then the time between each letter would be bigger the higher the wpm

[exotic canopy]

complete formula is wpm/(60*4)

[alpine sable]

Ohhh times 4

not /4

wow

[exotic canopy]

oh wait that's true

[alpine sable]

hmmm

[exotic canopy]

my bad

[alpine sable]

nono its fine

[exotic canopy]

1/(wps*4) like this yeah

[alpine sable]

how do I figure out the wps??

[exotic canopy]

divide wpm by 60

[alpine sable]

I see I see!

wow this is complicated xD

ill test it one sec

THIS IS AMAZING

it works!!!

[exotic canopy]

nah not really

[alpine sable]

it was for me xD

[exotic canopy]

completely simplified it is $\frac{15}{wpm}$ if you need to implement it as code or something

[ocean seal]

artemetra

[alpine sable]

Im so happy

[exotic canopy]

where 15 is because of 60/4

always welcome!

[alpine sable]

thank you so much

[alpine sable]

woah

[exotic canopy]

generalized is $\frac{\frac{60}{n}}{wpm}$

[ocean seal]

artemetra

[exotic canopy]

where n is the length of a word

[alpine sable]

its better less simplified cause I can edit the avg letter per word

depending on the sentence inputted

[exotic canopy]

okay okay

[alpine sable]

yesyes

stay safe

byebye

.close

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[alpine sable]

I appreciate it

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[cyan sable]

I dont understand the math used in the solution of an electrical engineering assignment

[median oar]

can you show us?

[cyan sable]

Yes one moment, let me pull it up

Here it is

I dont understand why its ((1,5)^2)/(1^2)

[edgy ingot]

!original

[lone heart]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[cyan sable]

One second

So its about a diode with the capacity of 47pF

And a forward voltage of 0.8V

The goal is to to choose the capacitance and inductance, so that it resonates on two frequencies

10MHz and 15MHz

If no voltage is applied on the diode, its own (default) capacitance is 47pF, but when 10V is applied it, it changes to 12.8pF according to the calculation

So we have two different total capacitances depending on whether direct current is on the diode or not

I understand whats going on, but i just dont see why the prof has calculated it that way in the circle

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[trim summit]

Can anyone please explain to me what does the dash symbol ' mean?

[trim summit]

right after 47

[coral flower]

Minutes i think

1/60 degree

[trim summit]

huh

[coral flower]

Like 1 hr 47 min
That's another unit

[trim summit]

how is that trigonometry tho

[coral flower]

It's a further divided unit of degree

1/60 degree = 1minute

[trim summit]

how would i put it into the calculator

[coral flower]

47 minute is 47/60 degrees

So angle A is
101 * 47/60 degrees

[trim summit]

is it always going to be /60?

[coral flower]

Yes

Btw if there are 2 dashes

Like ''

That's 1second

Further division of minute

1 second = 1/60 minute
1 minute = 1/60 degree

[trim summit]

so it would be /360?

[coral flower]

3600, yes

[trim summit]

ohhh okayy

tysm

[coral flower]

Np

[trim summit]

damn thats weird

[coral flower]

Ik

[trim summit]

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[misty nebula]

ok so

[misty nebula]

to know if the matrix is regular or not

it shld have all slots non zero number

and if not i shld check for like

i have matrix T

if it has zero in it

i shld check for T^2

if it still got zero

i shld check for T^3

and so on

until i find a T that has all numbers non zero

if i didnt find that then its not regular

thats what i found on yt

but my teacher said otherwise

if for example

A belongs to M7_R

i shld have B belongs to M7_R

so like it becomes like this

AB=BA=I

how

how shld this happen

i dont understand it

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@misty nebula Has your question been resolved?

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@misty nebula Has your question been resolved?

[slate barn]

can you condense the question down to like one paragraph

[misty nebula]

A belongs to Mn_R

B belongs to Mn_R

how does AB=BA=I proves that A is a regular matrix

[slate barn]

oh because regular just means it's invertible right

depends on your original definition but if you have AB = I then B is the inverse to A and you've proved that A is invertible

[misty nebula]

oh ok tysm

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[thick latch]

Is my answer for a and b correct

cause idk what to do with the ln(2)

cause i need the value to count the error bound

?

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[thick latch]

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[cloud elk]

help

[meager rivet]

help

[cloud elk]

chill

alr so

yo hello?

imma js wait

simplify

i just need a reminder on how to do this

[fleet pawn]

Simplify like make it in simplest form?

[cloud elk]

yeah

the one in the middle

[cloud elk]

wow thank you

for taking your time to help me

wait which one is that for

[fleet pawn]

U said middle one

I did
i)

[cloud elk]

oh ok

where did Y go

.close

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[rapid sentinel]

@here for people who need help with math that is SPECIFIC to economics...
The Edunomix Institute is a not-for-profit organization devoted to expanding access to practical economic education.

This message is being sent to inform you of our upcoming summer camp, which will be centered around entrepreneurship. Our camp will be held virtually and free of charge from July 8-12, 12-2pm EST.

Additionally, there will be two guest speakers this time. One is a CEO of a successful startup and the other is a Forbes Next 1000 finalist!!

Website: edunomixinstitute.com
Instagram: @edunomix.official
Link to Sign Up: https://docs.google.com/forms/d/1tmSbArlRr0JRMjAr8DXxDB2T8XCM-GZoic-E4KOmDQo/viewform?edit_requested=true

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[young sundial]

My notes say this has something to do with natural log but I don't have the slightest clue what to do...

[median oar]

What’s the fundamental theorem of calculus?

[young sundial]

that much I know. It's the antiderivative part that's tripping me up.

[median oar]

What’s the anti derivative of 5/t?

[young sundial]

Don't know what to do from here...

[hushed locust]

do you know what ln(1) is?

[young sundial]

I got the answer right but I still don't understand what it means...

[subtle light]

like what the definite integral represents?

[young sundial]

Logarithms, especially natural logs have always been a mystery to me... 5Ln8 might as well be an imaginary number to me.

[subtle light]

logarithms are inverse of exponentials

like lets say we had 10^x

the inverse function would be log(x)

natural logs are just with base e

or the inverse of e^x

[young sundial]

Had to flip through old notes to get this...

[subtle light]

yep thats showing how they are inverses

basically the same idea as the square root and the square

they cancel out each other

[ocean seal]

y0shi

y0shi

[young sundial]

That's easy enough to understand. What happens if the b in the argument is c instead?

[subtle light]

then it wouldn’t cancel out

it depends on what c is

[young sundial]

Alright then... I'll stumble forward from here... Thank you for the help.

.close

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[fleet pawn]

How do I find antilog of -4.05

[fleet pawn]

I mean how do I find antilog of -ve numbers? Why was +1 and -1 added?

[fleet crown]

What is written there

?

[fleet pawn]

How to find antilog of -4.05

[past saddle]

https://tenor.com/view/hachikuji-monogatari-minecraft-mayoi-hachikuji-enchantment-table-gif-27334415

[fleet pawn]

🤨

[fleet crown]

I think I'm starting to decipher it

log base 10 of ???? = -4.05 - 1 + 1

is that it?

[fleet pawn]

Yes

But why +1 and -1

Log(x)to base10=(-4.05)

How do I find antilog of this

[fleet crown]

x = 10 to the power of -4.05

[fleet pawn]

But I think I don't get answer by solving like that

[fleet pawn]

I want to know the method that is shown here

The +1 -1 thing and 5 bar

[fleet crown]

I can barely read what's written there

I'd help you but I need some context for this

[ocean whale]

More context would be useful

Hard to tell what is going on exactly

[fleet pawn]

Well it is a chemistry question

I just need help in solving antilog -4.05

[ocean whale]

More context is still needed if you want to understand why + 1 - 1 was done

[fleet pawn]

Does this work

[ocean whale]

Oh that's pH related

[fleet pawn]

Yes

So...
How do I solve antilog of -4.05

[ocean whale]

By raising both sides to the power of 10

[fleet pawn]

But the guy did +1 -1 and solved

I want to know that method

[ocean whale]

Because log(10) = 1

[fleet pawn]

Calculator are not allowed i need to get the answer in the option

And if I did 10 to power -4.05 I wouldn't get the answer

.close

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[granite iron]

how do Iconvert weekly spending to monthy

[granite iron]

I keep thinking its just weekly cash amoutx 30 days

[vapid drift]

if a month has 30 days you can do 30 x (weekly spending)/7

if thats what you mean

[granite iron]

sort off

its $200 a week being spent and neeed to convertit to montly

[alpine sable]

yeah do what he said

[granite iron]

ill try it

is it 857.142

would it be yearly to monthly spedning be 1,000.00/52 weeks?

[fleet pawn]

U mean u want to convert weakly spending to yearly?

[granite iron]

yearly spending to monthly

i thik its 1,000.00 divided by 12

[fleet pawn]

Divide yearly spending by 12

[granite iron]

thabk you

close

close.

[soft pawn]

.close

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[crude grove]

how can i find the volume of these two hemi-ellipsoids who share the same flat surface, but are different heights?

[livid sage]

you apply volume formula (and you may derive it if necessary)

[crude grove]

ok thanks

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[crude grove]

.reopen

hold on

[lone heart]

✅

[crude grove]

wait

what about surface area?

[livid sage]

surface area of an ellipsoid

hahahahahahhaaah......

[crude grove]

why is it using the approximately sign

[livid sage]

have you heard those jokes about finding the perimeter of an ellipse

[crude grove]

no im not advanced enough to be laughing at those jokes

[livid sage]

well basically there does not exist a result in elementary functions that you can make use of

hence why any simple formula you see will have an approximately equal to sign

[crude grove]

oh

so how would i approximate it

[livid sage]

?

[livid sage]

apparently, u have the formula

[crude grove]

at the end

[livid sage]

so u use the formula

[crude grove]

when my final answer is the approximately something something

how would i convert it to equal sign

cause ive seen people approximatingf

[livid sage]

well u can try to set up the integral and numerically approximate an answer like that

[crude grove]

ok i dont want to hear the i-word before i get into gr12

[livid sage]

well u don't

[crude grove]

i think ill be fine with approximately 😂

i'll be rounding it anyway

rounding is approximation itself

[livid sage]

the formula will be a bit imprecise compared to setting up an integral but

for ur purposes i assume u don't need a precise answer

[crude grove]

yeah

itll be in 10ths

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[crude schooner]

by factorising $e^x(x+2)^2$

[ocean seal]

e=mc^2

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[young roost]

What inequality is this? And is it correct?

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[crude schooner]

the answer should depend on the values of a,b ,c

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[noble sinew]

Not without any conditions on a,b,c. For example a=b=c=1 makes it false

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[meager rivet]

for part A
(x+7)(x raise to power 2 - 7x + 49)

[unreal meteor]

cubed root of 343

[limpid turret]

!nosols

[lone heart]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[noble ruin]

erm what the sigma

[meager rivet]

shouldn't i help?

[meager rivet]

what sigma?

[verbal galleon]

7

[verbal galleon]

I need to understand how not just the answer

[meager rivet]

what?

[fallen verge]

are you familiar with sum of cubes void?

[meager rivet]

it's a cube+ b cube formula

[verbal galleon]

Don't think so

[meager rivet]

a^3 + b^3

[meager rivet]

bro can you look into help 21

?

[fallen verge]

theres a formula that states
a³+b³ = (a+b)(a²-ab+b²)

[verbal galleon]

Identities right

[fallen verge]

yeah

[verbal galleon]

Damn I gotta memorize them again ;-;

Ok so one sec imma try solving

(x+7)(x^2-7x+49)

Am I correct?

[fallen verge]

yup

[verbal galleon]

Ayy

Now for the 2nd

Is the formula (a-b)(a²+ab-b²)

[limpid turret]

+b²

[verbal galleon]

Oh thanks

There's no cubic root for 432 tho?

<@&286206848099549185>

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@verbal galleon Has your question been resolved?

[verbal galleon]

<@&286206848099549185>

[alpine sable]

Yes?

@verbal galleon what do you need help with?

[verbal galleon]

B and c

[alpine sable]

Send me a pic of the questions

[alpine sable]

Call the gaps A, B and C respectively.

We get:

$-2n^3-432=A(n+B)(n^2-6n+C)$

[ocean seal]

Jadεn

[alpine sable]

Factoring:

[verbal galleon]

Wdym call the gaps?

[alpine sable]

$-2n^3-432=An^3-6An^2+ACn+ABn^2-6ABn+ABC$

[alpine sable]

The empty slots

that we have to find

[ocean seal]

Jadεn

[alpine sable]

And then you solve using a simple system

$-2=A,$
$0=-6A+AB,$
$0=AC-6AB,$
$-432=ABC$

We get the equations from the coeffiecients

[ocean seal]

Jadεn

[verbal galleon]

I don't get this part What are the An and ACn etc?

[alpine sable]

An = A*n and ACn = A*C*n

@verbal galleon

[verbal galleon]

Oh alr it's just I've never seen this method before as usually we use some sort of identities

[alpine sable]

it's alright

@verbal galleon did you get it?

It's just substitution

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[mellow iris]

without diff of cubes how

[vestal flume]

Try rewriting sec^2(x) as 1+tan^2(x) on both sides (so it's that cubed on the left)

And then see what happens

Or if you prefer, you can let u = tan^2(x) so that 1+u = sec^2(x) and do it like that, if it makes moving stuff around easier for you.

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[topaz sedge]

Why is this false? (It is, right?)

[vestal flume]

You can't divide in fractions like that

You'd need to have x(1+1)/x(x-1)

[topaz sedge]

Can't you just "cancel out" the Xs?

Or does that only work when dividing monomes?

[pale kestrel]

try and see with actual numbers

[topaz sedge]

monomials*

[jagged cobalt]

you can only cancel things that are common factors of the numerator and denominator

x isnt a factor of '1', or just (x+1) i should say

so you cant cancel

[pale kestrel]

,,\frac{2+1}{4-1}=\frac{1+1}{2-1} ???

[pale kestrel]

there is also no such thing as 'cancellation' in math

to simplify a fraction, youre usually either adding 0 to it or multiplying it by 1

[topaz sedge]

When you "cancel" you are actually diving both the numerator and denominator by the same value, no?

[pale kestrel]

youre multiplying the fraction by k/k for some k that isnt 0

(k/k = 1)

[pale kestrel]

thats not what youre doing here though

[topaz sedge]

Hm ok i got it i think

So this would be correct?

[pale kestrel]

unusual way to write 46 multiplied by xyz

usually the number literal goes first

thats correct as long none of x, y, z are 0

[topaz sedge]

Oh yeah, my bad

So this is possible because you're dividing monomials?

Since they are only one term, anything multiplying it is multiplying the whole whing

[pale kestrel]

your dividing the fraction by 1

if you like

your dividing by (xyz)/(xyz)

or youre multiplying by (1/(xyz))/(1/(xyz))

i mean yeah what you said i guess...

[topaz sedge]

Ok

So, how would you simplify this without using notable products or derivatives?

[pale kestrel]

factorisation

no idea why derivatives are relevant at all

[topaz sedge]

For some reason i have a very hard time remembering the notable products, and i haven't learned derivatives just yet

[pale kestrel]

the numerator is linear

the denominator is quadratic

this highly suggests for you to attempt factorising the quadratic

(x + 1)(???) = x^2 - 1

[topaz sedge]

And how do you do that? (Sorry for sounding braindead, it's just that this specific part my math teacher never taught well 😦 )

Without having the notable products in your memory

This is the kind of thing i mean

[pale kestrel]

well, i suppose one of these is useful

but more generally you should be remembering how to expand (a + b)(c + d)

[topaz sedge]

Are you supposed to just remember it, or is there an easier way? I'm terrible at remembering'em

[pale kestrel]

you shouldnt need to remember anything

all you need to know is how to expand (a + b)(c + d)

using some algebra

[pale kestrel]

and then use this suggestion

[pale kestrel]

this is merely a shortcut

[topaz sedge]

c(a + b) + d(a + b)

[pale kestrel]

yes, but thats not the full expansion

[topaz sedge]

(c.a + c.b) + (d.a + d.b)

[pale kestrel]

yes, and then the brackets are redundant

[pale kestrel]

now for this idea, you will have to think about what the general form of the ??? must take

for a quadratic

[topaz sedge]

It needs at least an x

So it can result in the x squared

[pale kestrel]

whats the general form of a linear term

[topaz sedge]

angular coefficient . independent variable + linear coefficient

ax + b, in other words

[pale kestrel]

yes ax + b

[pale kestrel]

(x + 1)(ax + b) = x^2 - 1

so now all you need to do is expand the left side

[pale kestrel]

you can either use what youve just worked out

and substitute in, or do from scratch.

it doesnt matter

But now theres not as much to memorize right? even if its more work

The more you practice (do more work), the more automatically these things will come to memory.

[topaz sedge]

Yes

[pale kestrel]

all 3 of these forms are specific versions of (a + b)(c + d)

[topaz sedge]

(x + 1)(x - 1) = x^2 -x +x -1 = x^2 - 1

I had trouble figuring out how it would not result in having some x^1

Didn't think on the possibility of x - x

So the main idea is that you can always express a quadratic by a multiplication of two linears right?

So you just need to figure out the coefficients of the specific linear needed

[pale kestrel]

yeah this is right

[pale kestrel]

yes and no

depends what you mean really

you definitely cant factorize all quadratics into two 'nice' linear terms (integer coefficients)

you cant even factorize all quadratics into two linear terms with real coefficients, but im not sure if youve come across this

[pale kestrel]

x^2 + 1 is one such quadratic.

The ones you will be asked about, like in this question, you can factorize nicely though. usually.

[topaz sedge]

That is exaclty the one i'm trying right now lol

[pale kestrel]

yeah, so it doesnt have a factorization in the reals

only with complex coefficients

[topaz sedge]

So in this case you can just replace x with -1, since x=-1 is not a point of discontinuity, right?

Gonna eat dinner, might take a while for me to read whatever you answer next

[lone heart]

@topaz sedge Has your question been resolved?

[lone heart]

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[crimson island]

Having trouble evaluating/integrating the following:

ʃcos(ln(x)) dx

My approach right now is let u = ln(x), du = 1/x dx

[zinc haven]

on the right track

[bright star]

can someone help me with this

need it done asap

[zinc haven]

!occupied

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[crimson island]

idk the next step. I mean I know like it becomes cos(x) xdu

[zinc haven]

thats wrong

[crimson island]

oh

[zinc haven]

you subbed u=lnx

so du=1/x dx

[zinc haven]

but from this you can also deduce x = e^u

[crimson island]

and dx = xlnu

i mean dx = xdu sorry

oh ok

[zinc haven]

yes

so dx = e^u du

now just sub back in

that should give you a hint

[crimson island]

ok one second

cos(u) e^u du?

or no

[zinc haven]

yes

$\int e^u\cos u\dd u$

[ocean seal]

your local hot fungus

[zinc haven]

alright

what do you think the next step will be?

[crimson island]

i guess du

[zinc haven]

?

[crimson island]

sin u du

[zinc haven]

blud i dont know what youre talking about

[crimson island]

im tryina do integrateion by parts here so i think thats why im confused

so i had int u dv = uv - int v du

[zinc haven]

just say ibp

ok

[crimson island]

what is ibp

[zinc haven]

integration by part

[crimson island]

oh ok

yea so thats where i was stuck so the next step i thought was gona be like v du so sin u du

but thats apparently wrong

so im stuck

[zinc haven]

i should also say, the u-dv method will be tiring for this

[crimson island]

ok

im down for better route

im terrible at this

[zinc haven]

https://youtu.be/2I-_SV8cwsw?si=Crw9RXLd_gRu69Lq i suggest you watch this

[crimson island]

my lowest exam grade was this topic and this is exam review

now im worried

ok checkin tha now

[lone heart]

@crimson island Has your question been resolved?

[crimson island]

im still stuck

[lone heart]

@crimson island Has your question been resolved?

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[sharp gust]

not a specific problem but im wondering when writing out sin/cosine graph equations, knowing which of these two equations to use:

[unkempt mica]

second one is better

because then 2pi/|B| is your period

and c is the horizontal shift

[sharp gust]

so for a problem like this i would just say

oh but its horizontal so make it cos

[unkempt mica]

almost

you should write it as

but then you can factor out 2pi/40

[sharp gust]

so i should do that even though my phase shift is -pi, does factoring out 2pi/40 not distort that?

[unkempt mica]

it depends on how you view phase shift tbh

your actual phase shift is half a turn

[sharp gust]

yeah my actual phase shift is half, so thats the confusing part for me, why you have to factor out the 2pi/40 as that messes with the half turn phase shift

a lot of like videos i see of creating an equation from looking at a graph dont factor anything but just put B outside the parenthesis right away

[unkempt mica]

it depends on the type of problem you are trying to solve

in this case you look at the circle graph

so you gave the phase shift in terms of the unit circle

[sharp gust]

so as a rule of thumb, when looking at a sine/cose graph i can just create the equation how i did, but looking at the circle graph/going around a circle, doing it the other way is better?

[unkempt mica]

you can do it however you like

if you know what you are doing both will work

for me the phase shift in the problem is 20 seconds (because a whole turn is 40secs) so the equation would be

and you can see it clearly on the xy graph :

but if you want to think of the phase shift in terms of the unit circle, then write it as

both are exactly the same function

[sharp gust]

ahhh okok wait that makes a lot of sense, it really just depends on the problem and what units your graph is in

[unkempt mica]

exactly because in your case you were looking at the circle

but sometimes you will be looking at the actual graph of the function

[sharp gust]

yeah, like the picture you showed

and in that case it is easy to just see the phase shift is 20 units

[unkempt mica]

thats it

[sharp gust]

that makes sense, tysm

[unkempt mica]

youre welcome

also you can check that your answer makes sense by plugging in 0

[unkempt mica]

for example in the answer you gave plugging in zero gives you something weird

but you should logically expect -15

[sharp gust]

and if its sine you should get 0 + D and is its cos you should just get D

i think

thats if you start at the 2pi position of course

[unkempt mica]

im not sure what those letters are

[sharp gust]

for the Asin(Bx-c)+D

[unkempt mica]

oh sure

well it depends on the phase shift again

but without looking at the equation, think about the fact that you are trying to model the horizontal distance from the center

so at t=0 you should get -15, because the carrousel starts at the leftmost point in the circle

[sharp gust]

yeah that makes sense, thank you

i think the way im going to do it is when giving a circle use this equation

and when your given an actual grpah where you can visibly see the phase shift, this one

[lone heart]

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[vestal stag]

How dod they went from the first highlighted integral to the second one

[lone heart]

@vestal stag Has your question been resolved?

[vestal stag]

I tried to solve the integral separately

[lone heart]

@vestal stag Has your question been resolved?

[lone heart]

@vestal stag Has your question been resolved?

[lone heart]

@vestal stag Has your question been resolved?

[vestal stag]

.close

[lone heart]

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[vague gazelle]

can someone help me illustrate and solve

[pale glen]

have you tried drawing the problem

[vague gazelle]

not yet

[pale glen]

try it first

you can represent the building with a tall, thin rectangle

and maybe the sun on the left

meaning, the shadow will form on the right

[vague gazelle]

wait ive tried

isnt this will form angle of elevation instead of depression?

[pale glen]

yea youre in the right track

[pale glen]

just form a triangle like that

and you can now apply the trigonometry

since it wants the angle of depression

we essentially want to find this angle

[pale glen]

since thats the angle of depression

[vague gazelle]

what about the measurements

[pale glen]

what did the problem say

about the height of the building

and the length of the shadow casted

[pale glen]

yea thats right

also draw the things ive drawn as well

[vague gazelle]

what will be used? sin or tan

[pale glen]

what will be the measurements

if you are gonna use this triangle

[vague gazelle]

whats next

wait hold on

right?

[pale glen]

yea correct

now since that green angle is our reference angle

which sides do we have

opp?? adj?? hyp??

[vague gazelle]

opp and adj

so tan ?

[pale glen]

and what function is that

yea

tangent

alright now write the equation

we dont know what the measure of the angle is

[vague gazelle]

tan = 100/300 right

[pale glen]

so lets say its theta

[vague gazelle]

tan x = 100/300

[pale glen]

ye but tan must have an input

thats right

now how do you solve for x

[vague gazelle]

i forgot what to press 🙏 😭

[pale glen]

well in the left side

we are taking the tangent of x

to "undo" that function

we can take the inverse tangent of both sides

like this

,,arctan(tan(x))=arctan(\frac{100}{300})

[ocean seal]

Renz

[pale glen]

,,tan^{-1}(tan(x))=tan^{-1}(\frac{100}{300})

[ocean seal]

Renz

[pale glen]

or that

they are the same

[vague gazelle]

oh yes i know now

hold on

soooo 18.43?

[pale glen]

yep

[vague gazelle]

ok thx what about this one

[pale glen]

try to draw it again

[lone heart]

@vague gazelle Has your question been resolved?

[lone heart]

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[vast pecan]

Vertex on the line 2x - 3y +8=0 focus on the line 4x + y-1=0 y= -1

[vast pecan]

y=-1 is its directrix

well witht hat i know it has a vertical axis

i just dont know how

[north perch]

the axis is perpendicular to directrix

so axis is along y axis

[vast pecan]

yes

i already have an answer btw

i just dont know how to come up w a solution for it

i solved it by graphing

[north perch]

assume the vertex to be (t,(2t+8)/3) and focus as (u,1-4u)

[vast pecan]

where is that coming from

[north perch]

if in first line, x is t then y will be 2t+8/3

similarly in second line..

did you get it?

[vast pecan]

I dont get

[vast pecan]

Where u got this one

[north perch]

ok suppose that x coordinate of vertex is t

then 2t -3y +8=0

3y=2t+8

y=2t+8/3

now?

[vast pecan]

yes

but why did u make it t

[north perch]

it looked good

[vast pecan]

Oh

ok

well the second line

u made y u right

or still x

[north perch]

x

[vast pecan]

y-1/4

oh nvm

u just made x u right

[north perch]

yeah

[vast pecan]

4u+y-1=0
y=1-4u

[north perch]

now since axis is vertical, the x cordinate of focus and vertex will be same.

so t=u

[vast pecan]

u, 1-4u
t, 2t+8/3

[vast pecan]

ohh yea

[north perch]

also the vertex is in the middle of directrix and focus

[vast pecan]

so midpoint

[north perch]

yeah

1-4u is mid of 2t+8/3 and -1

[vast pecan]

what do i do with the fact that t=u

do i just change the variables

i pick one then just roll w it

[north perch]

yep

[vast pecan]

so

2u+8/3?

[north perch]

yeah

[vast pecan]

why am i getting

1/26 as u

[north perch]

u did smth wrong

(8+2u)/3=(-1+1-4u)/2

u=-1

[vast pecan]

wait

[vast pecan]

yea thats about right

[north perch]

so u got the focus and the vertex

now u can plot axis

[vast pecan]

if u just got the focus and the vertex

just get the distance ?

of the y

[north perch]

no

[vast pecan]

youll get that as a

focal length

[north perch]

wait . what do u want to find out

[vast pecan]

uhhhh just the equation

haha

[north perch]

what does the question ask

[vast pecan]

u needa get the equation of the parabola

ig

[north perch]

ok

then u were doing right

[vast pecan]

whatdu think

i was tryna get

[north perch]

the eqn of axis

[vast pecan]

that exists????

of

oh

isnt it just x=-1

thats a cool solution

i think im done now

can i ask an algebra related question

y=-4a+1

u cant just make it 4a-1 right

itd be wrong

[north perch]

yeah it is

[north perch]

u can make it 1-4a

not the other way around

[vast pecan]

yea

thx

r u like

in college

[north perch]

no

i am in yr12

[vast pecan]

have u encountered this problem alread

[north perch]

what problem?

[vast pecan]

this problem that we just solved

[north perch]

no

[vast pecan]

but u just knew

can we be friends? i really would like to communicate w some person good at maths

i like maths too

[north perch]

i am not really online on discord

[vast pecan]

oh alr

[north perch]

today is the first time i opened it in weeks

[vast pecan]

well damn

[north perch]

also entrance exams prep needs time

[vast pecan]

u have entrance exams?

where r u from

[north perch]

india

[vast pecan]

well damn

good luck bro

i heard its hard

[north perch]

thanx

[vast pecan]

r u gonna take

JEE

[north perch]

yeah

[vast pecan]

goodluck bro

[north perch]

how did u know

[vast pecan]

idk

u said entrance exams

and jee is like the test in india so

[north perch]

ohk bye

[vast pecan]

🤷‍♂️

.close

[lone heart]

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[jade prawn]

https://cdn.discordapp.com/attachments/903481109420048385/1234824912422567946/image.png?ex=663223d1&is=6630d251&hm=a95b2fc961baf7be394d36872b54e9198502eba471c5983800a735d3e92e8fa3&

[jade prawn]

How to do this question?

@craggy dagger

[zinc haven]

!15min

[lone heart]

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

@jade prawn Has your question been resolved?

[weary birch]

!status

[lone heart]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

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[strange fractal]

how would id o part b

[past musk]

do -(a+b) then normalize it

[strange fractal]

what does normalise mean

[past musk]

fancy way of saying make it a unit vector

[strange fractal]

oh

strange

ok thx

.close

[lone heart]

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[strange fractal]

.reopen

[lone heart]

✅

[strange fractal]

how come they also have = root 5

do u need that

[past musk]

because the length of -(a+b) is root 5

you want to make the length 1 so you divide by root 5

[strange fractal]

but its asking for da vector

[past musk]

in general you can get a unit vector by dividing any vector by its magnitude

[strange fractal]

ohh is trhere a formula

oh

[past musk]

yeah

[strange fractal]

lol

[past musk]

although i think it's intuitive

[strange fractal]

dam i cant wait for this to get even harder

[strange fractal]

whats that mean

[past musk]

fancy way of saying "i can mostly see why it is true"

[strange fractal]

oh why?

oh so unit vector is just one

[past musk]

well if you multiply a vector by a number it just scales the vector

yeah it has length 1

[strange fractal]

so to get one we can divide the vector thingies by

the magnitude we get

[past musk]

so for example lets say the vector v has magnitude x, then the vector kv has magnitude kx

so if k is 1/x then the magnitude is just 1

[strange fractal]

wait im confused

so it'd be -1i + 2j

so (-1/sqrt(5), 2/sqrt(5))

[past musk]

-1/sqrt(5) but yes

ye

[strange fractal]

oh how come the answer doesnt say it like that

[past musk]

probably because they lazy and they dont like ugly looking fractions inside a vector

but mathematically the same

[strange fractal]

is this also the same

thats how i'd put it in a test lol

wait no

GRRRRRRRRRRRR

ok ill just do it the ugly way

[past musk]

lol

[strange fractal]

who cares

[echo portal]

ello

[strange fractal]

hi friend

[past musk]

if theyre super duper strict for no reason they migjt also want you to rationalize

[echo portal]

do u want help with smthin?

[strange fractal]

naur im fine

RYANCANTPVP IS TO GOOD AT MAFAMATICS

[past musk]

so -sqrt(5)/5, 2sqrt(5)/5

no im not

[strange fractal]

if they do im gonna cry

[echo portal]

lol

[strange fractal]

hey..

yes u are..

im struggling with this topic sm..

my teacher said next year theyre teaching it to us

but in 3d

pray for me

[past musk]

Ryan, good, and math do not belong in the same sentence

[echo portal]

isnt rationalizing supposed to be given in the question

[past musk]

idk

[echo portal]

any ways rationalizin is ez

[past musk]

most of the time i see it not rationalized but yeah

3D vectors arent that different

[echo portal]

just 1/ sqrt of 5 * -sqrt of 5/-sqrt of 5

[echo portal]

u mean 1 cap j cap k cap?

[past musk]

interesting

[strange fractal]

have i drawn this diagram right

for the parallelogram

[past musk]

ive never seen anyone say i cap j cap k cap

ive only heard i hat j hat k hat

[echo portal]

bruh which grade r u in?

[strange fractal]

grade 10

[past musk]

i think you need to join the lines

[echo portal]

ur struglin with this

[echo portal]

well they do

[strange fractal]

yes this is HARD MAN

I STARTED 2 DAYS AGO OK

[echo portal]

chill

i started 1 day ago

[strange fractal]

😠

[past musk]

to be fair grade 10 is very slightly early for vectors

[echo portal]

bro

[strange fractal]

omg shush ur lips no one cares

[echo portal]

i do vectors at 9th

im 9th

[past musk]

good for you

[echo portal]

well they didnt go to adv vectors

they taught a lil abt vector algebra

[past musk]

tbh the best way to test if you fully understand vectors is to use it on a bunch of physics

[strange fractal]

lesgo im taking physics

but they said no vectors until later

[past musk]

igcse physics does not use vectors

[strange fractal]

whats igcse

[past musk]

forget i said anythkng im dumb

[strange fractal]

WHAT

NO U ARENT WDYM

[echo portal]

we r doin physics only rite??

[past musk]

anyways high school physics usually does not involve vectors

unless its some super difficult curriculum

[strange fractal]

watt my teacher said we're using vectors later in the year

[past musk]

depends

[strange fractal]

like the f=ma stuff

[past musk]

thats easy

[strange fractal]

yeah

i think they introducing it to us and it gets hard in uni idk

icl

I AM A TINY LITTLE BIT STUCK

[past musk]

i meant stuff like very simple path integrals

[past musk]

go from A to B to Q

[strange fractal]

yeah i checked my syallabus it says vectors in kinematics

wait

[strange fractal]

i tried 😢

[past musk]

i dont think thats using vectors at all

i meant using vectors to do actual calculations

[strange fractal]

idk.. im not the brightest student

LOL

wait

ohh i think im getting it

bc i dont have BC i can find it using BA+AC

and then i can just do

1/2(BA+AC)

:d

[strange fractal]

Oh but does it matter where i like put the points

Like the PQRS

[past musk]

probably not

[lavish cave]

It does actually

[past musk]

as long as its close to the midpoint

[lavish cave]

P is the midpoint of AB

[strange fractal]

OHHHHHHHHH

[lavish cave]

So P has to go on AB and so on

[strange fractal]

thx if they gave me that in a test i wouldnt have known

[lavish cave]

But yes what you've drawn is correct

[strange fractal]

and probs wouldve stuffed the question up

[strange fractal]

I GUESSED IT CORRECT?

the points

[lavish cave]

Yeah, somehow lol

[strange fractal]

yess THX ISAAC NEWTON

ok thx guys

.close

[lone heart]

Channel closed

Closed by @strange fractal

Use .reopen if this was a mistake.

[lavish cave]

nwnw

[lone heart]

Available help channel!

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[tawny python]

Hi

[tawny python]

.close

[lone heart]

Channel closed

Closed by @tawny python

Use .reopen if this was a mistake.

[lone heart]

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.

[sleek timber]

I’m stuck