help-10

[next lantern]

could somebody explain the end bit of the induction

i understand up to the substitution of the inductive hypothesis

and the lone after

however im not sure why the k^2-2 is dropped

[tardy epoch]

you're just proving something is bigger than something else

[next lantern]

right

[tardy epoch]

since k^2 - 2 > 0, the inequality is also true when you drop that term

[next lantern]

ohhh

im thinking about it backwards

you made the right side smaller

i dont know why i was thinking that removing it makes it bigger

lol

ok thank you

.close

[obtuse pebble]

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[hard citrus]

Can someone help with 2a?

[brisk grove]

Try tan(x) = sin(x)/cos(x)

[hard citrus]

ok

[brisk grove]

and simplify the right hand side

should give you cos(2x)

[hard citrus]

@brisk grove is that correct so far

oops its meant to be a + at the bottom

[brisk grove]

yes

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

[warm shale]

RedstonePlayz09

[brisk grove]

what do you think you should do now?

[hard citrus]

somehow simplify it

[brisk grove]

yes

either ||common denominator||, or ||multiplying both numerator and denominator by cos^2(x)|| will work

you can look at the spoiler if you are stuck

[hard citrus]

okay

[hard citrus]

I multiplied by cos^2(x)

[brisk grove]

good

what do you notice

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

[warm shale]

RedstonePlayz09

[hard citrus]

the denom is 1

[brisk grove]

good

and the numerator?

[hard citrus]

its uh

i have no clue

oh my god

double angle

:OOOO

[brisk grove]

yes

[hard citrus]

holy shit i gotta revise trig

thank you

🙏🙏🙏🙏🙏🙏

[brisk grove]

no problem!

[hard citrus]

.close

[obtuse pebble]

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[timid silo]

Okay this time I think I got he graph right. But how do you find the minimum value??? It’s literally alr if y’all can’t explain the graph to me or whatever- just.. How do you find the minimum value T-T

[timid silo]

Cause I do not know in the slightest

I think it’s x = 0 , 3
and y = 0, -5
???

[thick gyro]

@timid silo have you learnt differentiation

[timid silo]

I have

though like when a number like 6x comes in with no power, you just have to write uh.. 6 back right? Or is it sumn else

My friend then told me to use differentiation and then equal it with 0

[thick gyro]

yh

your friend is right

[timid silo]

Idk how to equal with 0

[thick gyro]

yh 6x becomes 6

[timid silo]

it’s also not really a method my school teaches so I’m a little weary on this actaully

[thick gyro]

you just literally find dy/dx

then make dy/dx = 0

[timid silo]

But I suppose it’s alr

[thick gyro]

its literally the way youre supposed to find the minimums of functions

[balmy mortar]

thats not what the question wants u to do

it says using the graph

[timid silo]

So like this and then you change dy/dx to 0?

[balmy mortar]

ie. literally find where the function is at its lowest point

[timid silo]

Yeahh.. 🥲 But I don’t know where to look in the graph. I look at the lowest points and then what

[thick gyro]

yh

[balmy mortar]

the coordinates of the lowest point

[thick gyro]

well the other guy is right too

[timid silo]

1, -5?

[balmy mortar]

no, dont differentiate if u havent been taught how

yes correct

[final carbon]

help me i didnt listen in class all my life

[thick gyro]

how does he know that the 1,-5 is the lowest point

[timid silo]

the graph I think

cause this thing

[obtuse pebble]

Please read #❓how-to-get-help

[thick gyro]

how do you know its not 1.05, - 5.1 or something

[balmy mortar]

its just a plot question

dont think too much

[timid silo]

Oh

I need 4 numbers to make a line though

Does this question need me to draw a line?

[thick gyro]

i think it wants you do draw a smooth curve

[timid silo]

I did that with the graph

[thick gyro]

it does also ask you to draw the line y = 4x - 7

on that graph

[timid silo]

i should’ve listened more th, but sometimes the teacher is too quick

[timid silo]

Yep

And I have to find that too

Tuition starts again in an hour, and I’m.. Weeeee I don’t get this

I know the steps, but not hot to get there

[thick gyro]

well start at (0,-7)

then draw a line with gradient of 4

so 1 right 4 up

[timid silo]

I’m a little confused

[thick gyro]

on the 1 right 4 up?

[timid silo]

i don’t know what you mean by that 🥲

[thick gyro]

for every 1 you go to the right

go 4 up

well how about this

just draw a line from

(0,-7) to (3, 5)

[timid silo]

Ah okie

Also I think I found the minimum value

1.2

If I counted correctly ofc

This took me a day

I’m ashamed

I drew the line also

How did the answer happen though

The method

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

Uh yes

But

[timid silo]

For d I don’t know how that got to that

I need to show my teacher working too

So it’s better for me to know the method as wel

Okay so I found out for y

But why is x (3, 5)

I can’t seem to get that answer for now

I think I’m doing it a bit wonky

[obtuse pebble]

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[gray pulsar]

help

[nocturne minnow]

• Show your work, and if possible, explain where you are stuck.```

[gray pulsar]

5xy+49xy = 459xy + 4z * 5y + 56x

[nocturne minnow]

What's the goal?

All I see is an equation

[gray pulsar]

to find the Diagonal

Z

Or equation

xyz

I need to solve that equation above

to find the answer to

x y and z

[gray pulsar]

yk what forget kit

it*

i can just do it on Chat GPT

Since it does all type of math

for me

.close

[obtuse pebble]

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[nocturne minnow]

Having fun getting it wrong

[gray pulsar]

and also did you realized

[nocturne minnow]

You shouldn't be using that to do math

[gray pulsar]

that the equation

was impossible

bc you can't find xyz

by just little numbers

so you should work on being a good helper

no offense

btw

[nocturne minnow]

Nobody asked for your opinion

[steep scaffold]

this simplifies to 405xy+20zy+56x=0

[teal turret]

Wdym impossible?

[nocturne minnow]

They asked chatgpt, I bet

[teal turret]

Lol hopefully not

[steep scaffold]

405xy+56x=-20zy

[gray pulsar]

I said

whats the values

of X y z

[steep scaffold]

bro im solving it

[gray pulsar]

and i said it was impossible

well i calucated

it comes down to

54xy = 54xy

which you can solve for xy but you can't solve for z

[wise talon]

if you asked chatgpt why keep this channel open

close

[gray pulsar]

bc

i closed it?

.close

see?

[nocturne minnow]

You can solve for z, in terms of x and y

[steep scaffold]

where did you even get this question

[nocturne minnow]

Probably chatgpt lmao

[gray pulsar]

imao i made it up

[obtuse pebble]

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[tacit quest]

very simple question, log 2 1

[tacit quest]

like base 2 and the subscript 1

But theres no x

so I don't know what i'm solving for

[tardy epoch]

Neither do we

[tacit quest]

What

that's what the textbooks asking for

find the exact value of each log without using a calculator and idk how to do that

[tardy epoch]

I see

[tacit quest]

is it just

2^1

[tardy epoch]

No

[tacit quest]

ok

[tardy epoch]

$\log_2(1) =x$

[warm shale]

riemann

[tacit quest]

so it's still

[tardy epoch]

Raise 2 to both sides

[tacit quest]

2^x = 1

i'm confused

[timid silo]

welp 2 to the power of what would be 1?

[tacit quest]

0

Oh

I see

alright ty

.close

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[dreamy sorrel]

can I get some help with this

I was having with undersetting the equation and relating it to the graph

[obtuse pebble]

@dreamy sorrel Has your question been resolved?

[obtuse pebble]

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[sinful seal]

im doing geometric sequences but i dont know how to do this question using the formula?

[sinful seal]

<@&286206848099549185>

Bruh

[obtuse pebble]

@sinful seal Has your question been resolved?

[sinful seal]

.close

[obtuse pebble]

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[digital wasp]

Is tabular method possible, or a waste of 15 minutes

[high lily]

,rcw

[quaint sequoia]

looks like an integration by parts problem tbh

[high lily]

looks doable with tabular

it shouldn't take 15 minutes with tabular

[digital wasp]

I'm assuming the x^2+2x is the derivative one

[quaint sequoia]

hmm i never learned that method, just integration by parts

which is always annoying kekw

[high lily]

tabula is a structured layout for multiple iterations of ibp

[digital wasp]

Does it matter what way I do the tabular method

,w integrate negativesinx

[warm shale]

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[digital wasp]

Ahhhh

,integrate -sinxdx

[high lily]

Does it matter what way I do the tabular method
wdym

[digital wasp]

,w integrate -sinxdx

[warm shale]

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[digital wasp]

Like using cosx for the integration or derivative and same with x^2+2x

,w integrate cosx

[warm shale]

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[digital wasp]

,w integrate -cosxdx

[warm shale]

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[high lily]

choosing which part to integrate and which part to differentiate matters

[digital wasp]

Yes, I'm saying for this equation specifically does it matter

Bc ik it's easier to do it some ways rather than other for most but some it doesn't matter

[quaint sequoia]

https://tryitands.ee/

[digital wasp]

I feel like the way on the left is better than the way on the right but idk if it actually works

,w sin(x)(x^2+2x)+cos(x)(2x+2)-2sin(x)

,w integrate (x^2+2x)(cos(x))dx

[warm shale]

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[digital wasp]

Well I did it wrong

I did it right but I just can't add

.close

[obtuse pebble]

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[fickle tapir]

I have no idea how to set this up

[obtuse pebble]

@fickle tapir Has your question been resolved?

[fickle tapir]

<@&286206848099549185>

[ruby path]

How much angular displacement would the wheel cover in one rotation?

Note that $\bar{\omega} = \frac{\Delta \theta}{\Delta t}$

[warm shale]

NEONPerseus

[fickle tapir]

I am still lost

[ruby path]

How much angular displacement in one rotation?

If a wheel rotates once, through how many degrees would it have rotated?

[fickle tapir]

360?

[ruby path]

Correct

And what's that in radians?

[fickle tapir]

2pi

[ruby path]

Good

So 1 revolution = 2π radians

Now how many would 15 revolutions be?

[fickle tapir]

30pi

[ruby path]

Good

[fickle tapir]

wait... that's it?

[ruby path]

And what is an rpm?

[ruby path]

Close we're not done yet

[fickle tapir]

rotations per minute

[ruby path]

Yup so we have 30π radians rotated through in one minute

Can you put that through in radians per second?

Oh nvm

[fickle tapir]

yeah that already gave us the answer lol

[ruby path]

They ask for it in rads per min

Yeah so 30pi is your answer

[fickle tapir]

part 2 asks for ft/min

[ruby path]

The speed of the wheel?

$v = R\omega$

[warm shale]

NEONPerseus

[fickle tapir]

Find the speed of the current in
ft/min Round to one decimal place.

[ruby path]

So multiply 30pi with the radius

[fickle tapir]

so 188.5?

[ruby path]

,calc 30 * pi * 2

[warm shale]

Result:

188.49555921539

[ruby path]

Looks right

[fickle tapir]

aight, so lemme see here, last part is in mph

so I just convert?

[ruby path]

Idk how many feet in a mile 😂

Sure

[fickle tapir]

looks like I got it right, 2.1

Thank you very much btw!

.close

[obtuse pebble]

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[supple quest]

x^2 +y^2 +z^2 = r^2

I had a little note for my juniors about this coordinate transformation

@native mirage wanna have a look?

pdf or google docs link?

https://docs.google.com/document/d/1cNrdnLX-5CCWwF8frS_ds03wUG7KosavhsmP2ByenrY/edit?usp=sharing

as you have seen the docs file, it would be 'r'

'r' will change if it is in cylindrical

because in cylindrical, we have a 'h' component

for the height of the cylinder

which actually accounts for the z component of caartesian

whereas in spherical, all of them can be diffusivity transferred into 'r

close the channel if you are done

[obtuse pebble]

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[nocturne bloom]

<@&286206848099549185>

<@&286206848099549185>

[gloomy pine]

You got any useful rule on your mind ?

[nocturne bloom]

https://www.integral-calculator.com/

[gloomy pine]

One that relates the derivative of a fonction with the derivative of the inverse function ?

[nocturne bloom]

https://www.derivative-calculator.net/

https://www.symbolab.com

[nocturne bloom]

how do I build the equation

[nocturne bloom]

not the patronizing answer I was looking for...

[gloomy pine]

I didnt mean it to be like that

[nocturne bloom]

so how do i build the equation that is to be solved

[gloomy pine]

Well the f'(x)=1/[f-1(y)]' considering f(x)=y

[ruby path]

$\dv{x}f^{-1} = \frac{1}{f'(f^{-1}(x))}$

[warm shale]

NEONPerseus

[nocturne bloom]

$1/((2-x^2)/(1+x))$ doesn't seem to work - I'll try finding the derivative and putting that into the equation

[warm shale]

PeculiarProductions

[ruby path]

I think this is what crank meant to say

[nocturne bloom]

this doesn't work either way

[nocturne bloom]

so I get the derivative of the inverse of f(x)?

[ruby path]

Well that's the formula to get the derivative of an inverse function if you know it's counterpart

[nocturne bloom]

this question is 10x more complex than any of the others - could one of you just provide the actual formula, with variables filled in, you get to solve it as well as what you do with this equation to obtain the answer(simply, as in 'find the derivative' or 'find the integral')

[gloomy pine]

First step: find the derivative of f

Second step: find (f-1)(2) (given)

Third step plug (f-1)(2) in 1/f'(x)

Then you should get the answer

[nocturne bloom]

derivative of f, with f being $[(2−x^2)/(1+x)]$, is $−(x^2+2x+2)/(x+1)^2$

[warm shale]

PeculiarProductions

[nocturne bloom]

is this correct first step

[gloomy pine]

Yes

[nocturne bloom]

then I find $−(x^2+2x+2)/(x+1)^2$ minus one, replacing each x with a two before solving?

[warm shale]

PeculiarProductions

[nocturne bloom]

now this is what i meant

[gloomy pine]

Oo im sorry

When i wrote minus one in the formulas i meant it as the inverse function

[nocturne bloom]

so then I get $\frac{-x-1+\sqrt{-x-1}}{x+1}$ as its inverse

[warm shale]

PeculiarProductions

[nocturne bloom]

<@&286206848099549185>

am trying to follow these steps and want to know if I'm doing them correctly - #help-10 message

[gloomy pine]

$\dv{x}f^{-1}(x) = \frac{1}{f'(f^{-1}(x))}$

[warm shale]

crank

[gloomy pine]

Plug in 2

[nocturne bloom]

plug 2 into #help-10 message ?

[gloomy pine]

No in this

[nocturne bloom]

for what reason did I find the derivative of the other one? (answering this reply - $1/f'(f^-1(2))$

[warm shale]

PeculiarProductions

[wary bronze]

$(tan2x)/(tanx)$

[nocturne bloom]

what is this

[warm shale]

EmmetBrown

[nocturne bloom]

is this supposed to be related to my problem?

[ruby path]

Did you put -2 in here

[nocturne bloom]

no?

.close

[obtuse pebble]

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[hollow granite]

When are you allowed to square both sides of a modulus inequality and when can't you?

[hollow granite]

Is it when it's impossible for both sides to be negative

for example here

but not here

[obtuse pebble]

@hollow granite Has your question been resolved?

[main rose]

So usually the way you solve these type of questions by writing it out as
-4 >= 2x - 1 >= 4
then you add 1 everywhere
-3 >= 2x >= 5
and finally you divide by 2
-3/2 >= x >= 5/2

but when you can 12 - 2 | 2x - 3 | >= 7 you need to first free the modulo. Squaring the modulo is gets the first results as the method I showed, but again the modulo doesnt get eliminated if you square 12 - 2 | 2x - 3 | due to the cross-terms.
@hollow granite
If anything remains unclear just let me know.

[hollow granite]

So yea for the first one you’ve an square both sides cause it’s never negative

But the second one you have the way you wrote out

[main rose]

You can also do the other way for the second one;
12 - 2 | 2x - 3 | >= 7
| 2x - 3 | >= 5/2
1/2 >= 2x >= 11/2
1/4 >= x >= 11/4
(I did it very quickly so not entirely sure if its 100% correct but thats the idea)

[obtuse pebble]

@hollow granite Has your question been resolved?

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[hollow granite]

Thanks

[obtuse pebble]

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[vestal trout]

i have a problem in understanding how to find derivation of composite function for f(g(x))
where i have learn a rule in school's book says (fog)' = g'(x).(f'og)

[vestal trout]

i know how to calculate a derivation but what's the difference between (fog)' and (f'og)?

[warm shale]

MathIsAlwaysRight

[trim portal]

In f'(g(x)) you calculate just f', and then plug g inside

not making derivative of g

[vestal trout]

ow is that it?

can i find the same result for f(x) = ln(x)

i want to understand why its derivation is 1/x

[obtuse pebble]

@vestal trout Has your question been resolved?

[obtuse pebble]

@vestal trout Has your question been resolved?

[obtuse pebble]

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[sleek nest]

how do you prove the second cosin law

[fierce lagoon]

Wdym second cosine law

[sleek nest]

that above your head

[ancient jacinth]

this one?

[sleek nest]

mhm

[ancient jacinth]

a^2 = b^2 + c^2 -2bccosA

[sleek nest]

yeah

both are the same

[ancient jacinth]

switch the places of a^2 and 2bccosA

2bccosA= b^2 + c^2 -a^2

divide by 2bc

cosA=(b^2+c^2-a^2)/2bc

it's not really a second law

its just the first one rewritten

algebraic manipulation

[fierce lagoon]

Yeah no that's legit the same law

[ancient jacinth]

@sleek nest papi do you understand?

[sleek nest]

so i mean the fist one

how to prove i

t

[ancient jacinth]

you want to prove this a^2 = b^2 + c^2 -2bccosA

?

[sleek nest]

mhm

[ancient jacinth]

hmmm

ok

one sec

[fierce lagoon]

Drop an altitude from angle A

[sleek nest]

mhm

[ancient jacinth]

consider this triangle

[fierce lagoon]

Well gee this is gonna require visualizations I think

[ancient jacinth]

i will gladly give my visualizations

uhh

[fierce lagoon]

So if you drop an altitude from the top angle, split side a into two parts: a-x and x

[ancient jacinth]

i meant to put the letters differently

[ancient jacinth]

A is the blue side, c is the green side and b is the red side ok

[fierce lagoon]

And I guess I'll prove c^2 = ... but really the process is the same for all variations

[sleek nest]

yeah i know

[ancient jacinth]

so far so clear?

[sleek nest]

mhm

[ancient jacinth]

consider drawing this line

[sleek nest]

the altitude

[ancient jacinth]

perpendicular to the base of the triangle

yup

[sleek nest]

and call that dot something like H

[fierce lagoon]

Actually Blighter can you label those points

[ancient jacinth]

how do you do that

[fierce lagoon]

Uh you're using desmos right

[ancient jacinth]

when i do it just shows number

[fierce lagoon]

There should be a "Label" option

[ancient jacinth]

s

i did that

[fierce lagoon]

And then you can type a letter

[ancient jacinth]

OHHH nvm

ok one sec

@sleek nest dw papi chulo me and umbra will explain

[sleek nest]

kk

[sleek nest]

i think using the pitagorath could do something

[ancient jacinth]

Consider the angle A

[sleek nest]

mhm

[fierce lagoon]

Mmhm you'll have to use pythag

[ancient jacinth]

the cos A =AD/AC

[sleek nest]

isnt its AC/AD

[ancient jacinth]

or AC * cos A = AD

[fierce lagoon]

So you can say that DA = cos(A) CA

[sleek nest]

wait

OH

yeah

[ancient jacinth]

ad sounds better

[sleek nest]

ad/ac is a name of a rock band

[ancient jacinth]

hey imma label the sides

[fierce lagoon]

This means that:

DB = AB - DA

= AB - CA cos(A)

[sleek nest]

ok

[fierce lagoon]

And then finding CD is easy. It's just CD = AC sin(A)

[sleek nest]

yeah

what app ya using

[fierce lagoon]

Gimmie a sec imma latex this

It's desmos

[ancient jacinth]

cos A = AD/a
a cos A = AD
BD = b- a cos A (1)
sin(A) = CD/a
a sin(A) = CD
c^2 = CD^2 + BD^2
c^2 = (a sin A)^2 + (b-acosA)^2

c^2 = a^2 sin^2 A + b^2 - 2abcosA - a^2 cos^2A

c^2 = a^2 sin^2 A + b^2 + a^2 cos^2A - 2abcosA

[sleek nest]

mhm

[fierce lagoon]

Using Pythagorean theorem. Note that $AB = b$, $AC = a$, and $CB = c$

$$\begin{align*}
CB^2 &= DB^2 + CD^2 \
c^2 &= (b - a\cos(A))^2 + (a\sin(A))^2 \
&= (b^2 - 2ab\cos(A) + a^2\cos^2(A)) + a^2\sin^2(a) \
&= a^2(cos^2(A) + \sin^2(A)) + b^2 - 2ab\cos(A) \
&= a^2 + b^2 - 2ab\cos(A)
\end{align*}$$

[ancient jacinth]

c^2 = a^2(sin^2 A+cos^A) + b^2 - 2abcosA

[sleek nest]

yeah i understand

[warm shale]

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

[ancient jacinth]

sin^2 A + cos^2 A =1

c^2 = a^2 + b^2 - 2abcosA

[sleek nest]

OH

[ancient jacinth]

mmhm

[sleek nest]

I FORGOT THE FIRST THING

[fierce lagoon]

I have it right here in one image

[ancient jacinth]

simp

jk

[fierce lagoon]

Same thing Blighter's doing

[sleek nest]

thank you kids

.lose

.close

[obtuse pebble]

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[ancient jacinth]

np cutiepie

💋

@fierce lagoon we should beat him up irl

he called us kids

[obtuse pebble]

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[wise hedge]

Why did they hide some of the help channels?

[fierce lagoon]

Probably something to do with rate limit

Discord has rate lomits

[wise hedge]

Ok

I have a question. Even though we use a unit circle to express angles, we are always talking about triangles in the context of trigonometry, yes?

[sleek nest]

yes

[wise hedge]

When I see a unit circle and angles, I'm always thinking we're talking about an 'X' percentage of the pie because it's a circle and size of the pie slices are always determined by degrees or radians.

So, a $\Pi$ radians circle would be half the pie the way I see it.

[warm shale]

j4w4

[wise hedge]

Or a $\Pi$ radians 'angle' I should have said would be a half-rotation.

[warm shale]

j4w4

[fierce lagoon]

You could say that yeah

For visual's sake

[cosmic berry]

hi

[wise hedge]

Hi

But when we talk about an angle that always begins on the x-axis and rotates or travels to, lets say 270 degrees, are we considering the whole area of that rotation or just a portion closest to the actual (x,y) coordinate where the terminal ray intersects the unit circle?

Is it better for me to visualize rotating a right-angle triangle around the origin or to consider the entire angle at 3/4 of the full unit circle?

[long plinth]

As a drive-by comment: letter case matters in mathematics. The number of radians in a semicircle is called $\pi$, not $\Pi$.

[warm shale]

Troposphere

[wise hedge]

Okay, thank you. I didn't realize....

[long plinth]

I would recommend thinking of the unit circle as the main definition. For angles less than 90° you can draw a right triangle inside the unit circle and it will make nice geometric sense because all the lengths are positive. But it just piles on conceptual trouble to insist we need to tweak that definition into something that also works for larger angles, when the unit-circle definition is right there, smooth and straightforward.

[wise hedge]

But that's my problem right now. I am confused at what we are talking about past 90 degrees if it's triangles when it looks more like a percentage of an apple (or pumpkin, whichever you prefer) pie.

[long plinth]

My point is that your "apple pie" picture is easier and better, and you shouldn't feel you have to torture your mind to make it about triangles.

[wise hedge]

Yes, but the fact is I can only get right answers by visualizing a right-triangle starting out from the x-axis and rotating towards the final angle measure like a car would travel a circle on a map. Because then I say to myself, "Okay, I drove my right-angled car to the angle on the map. Now I can figure this out".

So, in one sense, by my method, I'm disregarding most of the distance traveled and only focusing on the final area of the angle on the circle.

[long plinth]

Hmm, why does there have to be a triangle? Can't you just think of the coordinates of the point on the circle periphery? It seems to be a lot easier to wrap one's head about how coordinates can be negative numbers, than to try to imagine a way a triangle can have sides with negative length.

[wise hedge]

Agreed

So the unit circle doesn't have to be about triangles, wow, that's amazing.

Because that's where I started with cosine, sine and tangent.

But I have to disconnect those now.

[long plinth]

Yes, there's a tradition in education that right-angled triangles is the first application of trigonometry one sees. That makes a certain sense -- young students might find it more concrete just to measure lengths on a diagram than to understand coordinate systems first. But the cost is that later you'll have to make the conceptual jump to the unit circle instead of triangles, and education often gives you precious little help in making that jump.

[wise hedge]

So, you see me as one of many, who has this issue with the transition...that's good to know...I'm sure I will get over it eventually.

[long plinth]

Yeah, this is very common.

[wise hedge]

Okay good. I'll just keep at it. I keep wanting to understand it but I just need patience.

.close

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

How did he come up with the left endpoint formula??

I understand that f(mi) means the sum of each rectangle's height

however I dont know how to come up with a formula

that can effectively include every rectangle height by simply inputting a value n

<@&286206848099549185>

<@&286206848099549185>

[hidden garnet]

it's not taking n as an input, but i instead

imagine that [0,2] is being broken into subintervals

Let's assume you just make 3 subintervals

So, you need to make two partitions right?

if those are equidistant

then what would you do

[timid silo]

I understand that, but the question doesnt provide me with a number of intervals

[timid silo]

What is this?

mi is the height of the rectangles

each*

m1 m2 m3 m4

How do I make a formula for the sum of every rectangle

[random depot]

S(n) = ∑_{i=1}^{n} (2/n) * f(x_i)

f(x) is the function ur approximating
2/n is the width of each sub interval
x_i is the right endpoint of the i-th subinterval, given by x_i = i * 2/n

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[steep snow]

Help 🙏

[steep snow]

is it A? right

<@&286206848099549185>

[lost tree]

well this isnt really a math question, so if u dont get a response here u can try asking it on a physics server in #old-network

but isnt the magnetic field perpendicular to both compasses?

im not sure how a compass needle behaves in such a situation

[steep snow]

ooo I see but let me try waiting to get response

[topaz hornet]

has to be either a or b

hmm

[kindred oasis]

I think the direction of the arrows is the same as the direction of the magnetic field the wire creates. You have a situation similar to the picture, although you have a wire instead of a magnet. So it should be C, with both arrows pointing down, as the magnetic field is pointing down on both sides as well

[steep snow]

alright thanks

[kindred oasis]

You're welcome

[steep snow]

.close

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[steep snow]

How to solve this, I use s=ut+1/2 at^2 to calculate but answer D is not matched

[teal turret]

Show ur work

Also, for the English translation, it should be a “16th”

@steep snow

[steep snow]

1/16(9.81) ?

[teal turret]

Yes

[kindred oasis]

I think they mean 1/6

Moon's gravity is about a sixth of Earth's gravity

[teal turret]

Sorry yes 1/6

[steep snow]

yep question has technical problem

[teal turret]

Thank you Andrea276

[steep snow]

I think now I can solve

[teal turret]

Ok so can u send ur work erujin?

[steep snow]

30=0(t) +1/2(1/6*9.81) t^2
t=6.06s

k ty guys

[teal turret]

Yea that looks right

[steep snow]

.close

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[onyx ravine]

How do i go about finding these missing measurements only given 10 and 12?

[onyx ravine]

im not sure if W is = 10 because itd be congruent to the other side?

[royal basin]

it is questionable what "the other side" could refer to, but the diagonals of a rectangle do cut each other in half.

[sage geode]

Diagonals of a rectangle cut themselves in half, so w = y = 10

It felt weird when I typed "cut themselves", now I see

[royal basin]

each other, not themselves.

[onyx ravine]

i see many many thanks. for finding X where would i start?

[royal basin]

you already (almost) know the length of the rectangle's diagonal.

might also first find z, for clarity's sake.

[sage geode]

Consider applying Pythagorean theorem in any of the right triangles

[onyx ravine]

alright.

.close

[obtuse pebble]

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[exotic creek]

how do i get to the second line?

is there a rule somewhere i didn't know?

[tardy epoch]

That's the definition of arcsin

https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-solve-for-an-angle/a/inverse-trig-functions-intro

[exotic creek]

oh right

ok

thanks

.close

[obtuse pebble]

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[exotic creek]

where does $pi/6$ come from>

[warm shale]

yomiko

[trim portal]

sin(pi/6)=1/2

[agile mesa]

i really need help with math :(((

[trim portal]

That statement is equivalent to the statement sin(30°)=1/2

[exotic creek]

bruh

[obtuse pebble]

Please read #❓how-to-get-help

[trim portal]

And this can be proved by 90-60-30 triangle

[exotic creek]

but i wont know that its pi/6 initially

[tardy epoch]

You should

[trim portal]

Doesnt need

he can draw a triangle :]

[tardy epoch]

,tex .unit circle

[warm shale]

riemann

[timid silo]

lol snow's factoids coming in clutch eh

[exotic creek]

1 min lemme take a pic

is it somewhat right?

[trim portal]

At this point you should recognise the kind of triangle

[exotic creek]

what do you mean

[trim portal]

You should recognise 90-60-30 triangle

[tardy epoch]

I'm gonna need more factoid triangles

[exotic creek]

and then?

oh

[trim portal]

Then you get that alpha=30

[exotic creek]

yeah yeah

right ok

[trim portal]

I mean there is no magic way to just compute arcsin(1/2) without thinking about it or having unit circle memorized

[exotic creek]

.close

[obtuse pebble]

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[mental cipher]

Hi guys i just have a small problem, I cant seem to understand how the 3 on the bottom rewrites itself above to 3t any help would be appreciated

[hybrid gull]

Create a common denominator

[hollow portal]

Multiply top and bottom by 3 of first frc

[mental cipher]

ahhh okay i see now cause 1/3 is the same as 3/9

.close

[obtuse pebble]

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[cerulean heart]

I got the right answer for the last part, but why is that the answer? Why can’t I plug in r= 0 to make it the limit approaching 2cos(theta)/cos(theta) = 2?

[dark stirrup]

The left side of the equation is the initial expression

Plugging in r=0 doesn't work there

[obtuse pebble]

@cerulean heart Has your question been resolved?

[obtuse pebble]

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[timid silo]

How can i find the perimeter of a lune

[timid silo]

I cant find any information online

[twin sapphire]

you can derive it by calculating the ength of arc-circles

length*

[timid silo]

I was recommended this method by my math teacher when i asked and that works, but isnt there an alternative method?

[wooden cipher]

Perhaps you forgot to link something

[timid silo]

?

[wooden cipher]

What method?

[timid silo]

I am asking if there is another method

[wooden cipher]

The arcs are the only way i know of

[timid silo]

Thanks for the info

.close

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[teal turret]

Where have I gone wrong with this problem?

It was a sign error in the equation ;-;

.close

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[open meteor]

How do you maximize the value of $\sin(2(\theta + \phi)) - 2\tan(\theta)\cos^2(\theta + \phi)$, where $\phi$ is in terms of $\theta$ (ie. need to find $\phi$ in terms of $\theta$ so that the expression is maximized)

[warm shale]

NotOrz

[open meteor]

help pls

<@&286206848099549185>

[fierce lagoon]

!15m bruh

[obtuse pebble]

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.

[open meteor]

i already asked it before but no one replied

[fierce lagoon]

You still wait 15 minutes when you open a new help channel

[open meteor]

ok

.close

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[frank comet]

When we say disk in complex numbers do we assume the radius is non-zero?

[obtuse pebble]

Please don't occupy multiple help channels.

[frank comet]

closed other one

.close

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[rough shard]

can someone please help me translate this to English? i understand most of what is being said, but confused. the actual homework problem is the next problem, i figure if i can figure out what is being asked with this problem, then i can figure out what the next problem is asking.

[frank comet]

it's asking you to determine if that function is injective and if it is surjective

[rough shard]

i know what injective, surjective, and bijective means, ya

[frank comet]

Is it injective?

You have to answer yes or no

[rough shard]

i don't know

[frank comet]

What's the def of injective?

[rough shard]

trying to figure out why i don't know, i figure it's because i can't understand what exactly is being defined

injective is when each element of a set is mapped to one element of another set

[frank comet]

given a function f: A -> B, it's injective if for any two points x != y in A, f(x) != f(y)

So for that function f(1, 0) = 1 and f(1, 1) = 1

So two different things map to the same thing

what does that mean

[rough shard]

i can't remember if, for something to be injective, it each element has to map to a unique element in the 2nd set, or if it's just all elements in the first set are mapped to something. verifying now

ah, so, has to be uniquely mapped

so that means it isn't injective

[frank comet]

good

surjective means everything in A has to have an element from A x B which maps to it

So if 3 was in A

give an example point which will map to it

[rough shard]

this part confuses me

are we considering A x B to be another set?

[frank comet]

Look at your question

origiainl

[rough shard]

i don't think it can be surjective, because it can map back to different combinations of ordered pairs

i'm not sure if i'm looking at it correctly, though

i figure i'm not, because then if something were injective, it would imply that it must also be surjective. so i figure i must be looking at it wrong

unless there's the possibility that something in the second set is unassigned

[rigid agate]

You need to show that every element of A gets mapped to by some element of A x B

So given any element a of A, construct some element (x,y) from A x B, such that f(x,y) = a.

[rough shard]

in that case, it seems that any element (a, n) from A x B maps, via f(a, n), to a, with n being any arbitrary element

i feel like that's either too easy an explanation, or not concise enough, or just a poor explanation

[rigid agate]

Yep that's about right.
Given a€A, we find that f(a,0) = a, so f is surjective.
(Aassuming 0 is an element from B. That way we have a concrete element from A x B).

[rough shard]

we can have multiple elements of (a, n) that all map to a, and still have it be considered surjective?

[rigid agate]

Yes

In that case, it may not be injective

[rough shard]

maybe my understanding of the definitions of injective and surjective are incomplete

it seems, then, that injective implies a unique quality of mappings, while surjective implies a complete quality of mappings

unique meaning that each element maps to no more than 1 (but at least 1), and surjective means everything maps at least to 1

[rigid agate]

It's a propery of every function that each element gets mapped to no more than 1. (Also not less than 1).

If the function is injective, no two different elements map to the same element.

If it is surjective, every element of the range gets mapped to at least once.

[rough shard]

but each element must map to at least one, ya? at least one, but only 1 (for injective)

ah, using range and domain may be better to be clear. injective meaning that each (and every) element of the domain maps to exactly one element in the range, whereas surjective means that each element of the range maps to at least one element (can be more) of the domain?

if that's correct, then in the original question, it would not be injective, but could be surjective

[rigid agate]

No that's a property of every function (also non-injective functions). f(1) is always some value, not 2 different values.

And no, elements of the range are not mapped to anything. They are being mapped to.

[rough shard]

crap. then i'm still not quite understanding the concise definition of injective and surjective. i think it's the language that's messing me up

when i think of elements of a range being mapped, i'm thinking "reverse mapped". i should be more concise i guess, sorry

[rigid agate]

Ah no problem. I know it's confusing

[rough shard]

i'm reading the definition out of the book, and trying to reword it in my own words to make sure i understand it

the book states that "a function....is called injective if each element of B is the image of no more than one element of A."

[rigid agate]

Yep that's correct

So it can't be that f(x)=f(y) if x and y are different

[rough shard]

that seems to imply to me that it means that all elements of the domain are
1 - mapped to an element in the range and
2 - mapped to an element in the range that no other element in the domain maps to

[rigid agate]

1 is actually not a conclusion from that definition, because it is also true for non-injective functions.

2 sounds good

[rough shard]

so then surjective, by strict definition, is when all elements of the range are images (reverse-mapped) of at least one element in the domain?

[rigid agate]

Correct

[rough shard]

in that case, the answer to the original question should be that it is not injective, but is surjective

ya?

[rigid agate]

Yes

[rough shard]

would you mind checking my work on the next problem? i want to try to do the work, but could use the eyes, if you don't mind

[rigid agate]

Sure

[rough shard]

i want to say that this is bijective, as the x in (y, x) is unique for the x in (x, y), and likewise for the y. i'm not sure if there's some fancy proof way to say this

[rigid agate]

Yeah I think you got the idea. For a formal proof we need to show it's both injective and surjective.

And use the definitions in the process.

[rough shard]

basically, both elements, x and y, that are in the resulting pair are uniquely and concisely defined by the given pair (x, y)

[rigid agate]

Ok let's start with injective. What is the definition from your book?

[rough shard]

A function...is called injective if each element of B is the image of no more than one element of A.

i think we know that to be true because the image (y, x) cannot be the image of anything other than (x, y), x in A, y in B, and (x, y) in A x B

[rigid agate]

Ok, yeah that's kind of ok. Depends on how rigorous we want the proof to be.
I like this definition of injectivity: If f(x) = f(y) then x=y.

So in words "If two elements map to the same element, then they had to be equal".

So for this function, if we assume (y1,x1) = (y2,x2) then we know that y1=y2 and x1=x2, so (x1,y1) = (x2,y2).

[rough shard]

hmm. i'm going to try to write that out real quick, the rigorous way

i think the most difficult part for me is the language seems foreign and much of it feels kind of "hand-wavy". almost like trying to explain something that seems extremely simple in an unnecessary complicated manner. i'm sure there's a good reason for it, to be concise and not leave anything to semantics, but that's how it feels

[rigid agate]

Yep feels super "over the top". Altough if things get less trivial, you will be glad, that you are familiar with the mechanics🙂

[rough shard]

like, in the example above, if you hadn't provided the more concise and rigorous definition, i wouldn't have known to guess to write it like that, though i feel like i said the same thing in the earlier comment, just using english and logic

so the screenshot of the work above looks correct? i feel like half of it is your work 😛

[rigid agate]

Yeah so we know that f(x1,y1) = (y1,x1) and f(x2,y2) = (y2,x2). To complete the argument, you have to arrive at (x1,y1)=(x2,y2)

[rough shard]

i guess i can be more concise by stating the equality of the pairs (x_1, y_1) and (x_2, y_2)

thanks! going to try the surjective proof and more problems. thank you so much for your patience!

[rigid agate]

Alright, good luck to you

[rough shard]

.close

[obtuse pebble]

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[left forge]

QUESTION 8 please

[obtuse pebble]

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[delicate pawn]

i’m stuck

<@&286206848099549185>

[obtuse pebble]

@delicate pawn Has your question been resolved?

[obtuse pebble]

@delicate pawn Has your question been resolved?

[bold bane]

Your notation is a little unusual and some of your mathing is incorrect.

[obtuse pebble]

@delicate pawn Has your question been resolved?

[paper forge]

well, since there are 3 equations and 4 variables, the system doesn't have a definite solution, or it is unsolveable

of course, you see that the variables x, y, and v are in all the equations

z can be any value really, and it would be solveable because you have the required amount of equations for 3 variables

[obtuse pebble]

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[tight pewter]

help

[tight pewter]

math and code problem

how to do

variable1 - (variable2 * 10 ) / 5

in C#

what i really mean is

you see the brackets on the "variable2 * 10"

a human knows that you multiply those numbers before everything else

but C# doesnt

what do i do

without creating another variable

[high lily]

doesn't it?

[random depot]

double result = variable1 - (variable2 * 10) / 5;

[tight pewter]

i dont think so cause i tried

result?

is that

ok

ill try that

oh im also trying to floor it

if that changes anything

plsss some one help cause codecademy made it hard terms

they didnt show me this

they just made another variable

i dont want to make another variable

ok nvm

.close

[obtuse pebble]

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[high lily]

what's with the division by 5

[tight pewter]

so you know how

you go to get money out of eftpos machine

so you want to get 185 bucks out

you will be given a 100 note

[obtuse pebble]

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[obtuse pebble]

@rotund vector Has your question been resolved?

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[smoky kayak]

someone help me I’m stuck

[trail musk]

what is secx

[brisk matrix]

do you know of any other ways to write sec(x)?

[trail musk]

lol.

[green epoch]

Sus edit

[runic void]

@smoky kayak

Now write, $\sec(x)= \frac{1}{\cos(x)}$

[warm shale]

.doc

[smoky kayak]

I think I got it someone helped me in #precalculus

[runic void]

Great

[obtuse pebble]

@smoky kayak Has your question been resolved?

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[timid silo]

wat

[tacit briar]

thats the question

[deep elk]

📉 📈

[obtuse pebble]

@tacit briar Has your question been resolved?

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[tacit briar]

oh snap

@tardy epoch want me to repost the q?

[tardy epoch]

no it wasn't clear enough

[tacit briar]

ok

you guys cant solve market making qs here?

[obtuse pebble]

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[timid silo]

How do I have to think about this transformation?

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

<@&286206848099549185>

[crimson oyster]

2(x^3n -1) + 6x^n(1-x^n) taking 2 and 6 common

use a^3 - b^3 formula

a^3 - b^3 = (a-b)(a^2+ab+b^2)

x^3n - 1^3 = (x^n-1)(x^2n + x^n+1)

[timid silo]

Okay, I get it, thanks

.close

[obtuse pebble]

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[misty gate]

#1074210038895353876 message

[fathom flicker]

?

[misty gate]

sir i need your help

[fathom flicker]

paste your question in this channel then

[misty gate]

the link above is the questio

[tardy epoch]

if it wasn't clear, copy, then paste

[hidden garnet]

I think it's an help forum question.

[misty gate]

oh yeah sorry how do i close this

[fathom flicker]

( .close )

[misty gate]

.close

[obtuse pebble]

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[daring rock]

What have you tried so far?

[stuck finch]

a-b=3

101a-101b=303

[daring rock]

Okay, and since you want four digit numbers, a, b >= 10

since 9*101 is only three digits

[stuck finch]

we need 2 digit

[daring rock]

If n is divisible by 101, then n+303 is also divisible by 101

[stuck finch]

number

like 17 14

[daring rock]

sure

but seems like you could just start with the smallest possible case and check if the HCF is 101

and move up until you find it

[stuck finch]

13 and 10?

bcz if we multiply 13 10 smallest

but

idk

if 13 10

[daring rock]

Well 10 and 13 share no factors

and 101 is prime

[stuck finch]

no am saying 101 x 13

and 101 x 10

[daring rock]

yes I understand

That's 1010 and 1313

So they differ by 303

and is their HCF 101?

[stuck finch]

yes

becuase we multiply by 101 both

so hcf must be 101

[daring rock]

Yes, since 10 and 13 are coprime

So yeah, that's it 👍

[stuck finch]

but is it smallest?

[daring rock]

Well 1010 is the smallest four-digit multiple of 101

[stuck finch]

oh

[daring rock]

so it must be

[stuck finch]

.close

[obtuse pebble]

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[warm shale]

hibyehibye

[timid silo]

and is there a way to check this w/ wolfram or something?

[neon eagle]

that doesn't look right to me

[timid silo]

oops

Where did I go wrong?

oh