help-27

[uncut crow]

expected number of flips before string is seen has a numerical answer tho

[topaz axle]

that's not what they're asking

"number of flips to land at 3 heads in a row"

[ashen carbon]

on average

[topaz axle]

which is not flips overall

[ashen carbon]

if we can figure that out somehow

[ashen carbon]

shorty what is the numerical answer

[topaz axle]

wait i see

[ashen carbon]

let me know if im asking a broken question btw

i could try to clarify better

not a math guy so i come to the experts 😳

[topaz axle]

that is probably what you're asking, like if expected number is e.g. 12, then 1/12 of flips are "third in a rows"

assuming that follows

ok whatever i assume you just mean at least once

if you flip 3 times, there's 12.5% chance you have 3 in a row

if you flip 4 times, there's 18.75% chacne

┌──┬─────┬────────┐
│1 │2    │0       │
├──┼─────┼────────┤
│2 │4    │0       │
├──┼─────┼────────┤
│3 │7    │0.125   │
├──┼─────┼────────┤
│4 │13   │0.1875  │
├──┼─────┼────────┤
│5 │24   │0.25    │
├──┼─────┼────────┤
│6 │44   │0.3125  │
├──┼─────┼────────┤
│7 │81   │0.367188│
├──┼─────┼────────┤
│8 │149  │0.417969│
├──┼─────┼────────┤
│9 │274  │0.464844│
├──┼─────┼────────┤
│10│504  │0.507813│
├──┼─────┼────────┤
│11│927  │0.547363│
├──┼─────┼────────┤
│12│1705 │0.58374 │
├──┼─────┼────────┤
│13│3136 │0.617188│
├──┼─────┼────────┤
│14│5768 │0.647949│
├──┼─────┼────────┤
│15│10609│0.676239│
└──┴─────┴────────┘

[uncut crow]

based on all your other messages i'm not sure that's what you want

[topaz axle]

yeah it's not clear

14 is the expected number, so iguess it's "1/14 overall"

[ashen carbon]

wait yeah this is what i mean

if i flip x times theres a x % chance of winning 3 times in a row

on average

and i imagine the odds increase with every flip or something

[topaz axle]

not on average

[ashen carbon]

oh ok

if i flip a coin 50 times, im way more likely to hit tails 3 times in a row than if i was to flip 10 times

due to odds/numbers game right

[ashen carbon]

what is this

[topaz axle]

number of flips − how many ways to "lose" − odds of winning

if you make 3 flips, there's 8 ways it can go, and there's 7 ways you don't get 3 in a row

so 1/8 is the chance of winning

it's like percents

[ashen carbon]

i think i got it

[ashen carbon]

yes this is what i want

thats with 3 flips, and then that number goes higher the more i flip right

[topaz axle]

yeah, up to 100%

if you flip 8231982390 times surely you get 3 in a row somewhere

[ashen carbon]

haha

surely wont have to go that high, just looking for good odds

somewhere around 10 flips puts me at 50% odds

thats good enough

thank you @topaz axle youve been a great help friend

are you still there @topaz axle

id like to evolve the question if u dont mind

[topaz axle]

yeah i'm here

[ashen carbon]

if im right 60% of the time on a coin flip (dont ask how lol), how would the same question now work in terms of % just like you gave me

[ashen carbon]

basically this list which is perfect just how i want it, but instead of a 50% successrate on the coinflip, make it 60%

[topaz axle]

good question idk

[ashen carbon]

do i just leave the question here and it will get picked up ? or do i need to make another post

[topaz axle]

ok i know

brb 10 minutes

[ashen carbon]

ok no worries

[topaz axle]

┌──┬──────┐
│1 │0.0000│
├──┼──────┤
│2 │0.0000│
├──┼──────┤
│3 │0.2160│
├──┼──────┤
│4 │0.3024│
├──┼──────┤
│5 │0.3888│
├──┼──────┤
│6 │0.4752│
├──┼──────┤
│7 │0.5429│
├──┼──────┤
│8 │0.6032│
├──┼──────┤
│9 │0.6560│
├──┼──────┤
│10│0.7014│
├──┼──────┤
│11│0.7409│
├──┼──────┤
│12│0.7751│
├──┼──────┤
│13│0.8049│
├──┼──────┤
│14│0.8307│
├──┼──────┤
│15│0.8530│
└──┴──────┘
```like this i think

[ashen carbon]

this is awesome brother

ur sure its correct?

[topaz axle]

pretty sure

[ashen carbon]

ok i trust u and it seems about right

really appreciat your time man, thank u so mcuh

much*

[devout snow]

@ashen carbon Has your question been resolved?

Channel closed

Closed by @ashen carbon

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.

[halcyon yew]

help plz

[halcyon yew]

lemme get the photo

Im confused on tangent vs. secant line

<@&286206848099549185>

[ashen fossil]

Hm?

[maiden dew]

touching the curve = tangent
cutting through the curve = secant

[ashen fossil]

Yep

[maiden dew]

5 is a bit of an exception to the picture you might imagine though. touching = touching only at one point.

[ashen fossil]

If it touches it's tangent
If it cuts 2 times then secant

[halcyon yew]

wait what

is there an easier way to decipher which line it is @maiden dew @ashen fossil

like i want to write a formal definition for notes but have no clue what to write

[ashen fossil]

Just write what I sent ig

That's the easiest way to define it

Just write it in your own language

[halcyon yew]

@username can i go over each example with u?

[ashen fossil]

Yep

[halcyon yew]

@ashen fossil

thx

ok so

[ashen fossil]

Yep yep

[halcyon yew]

for 1

lemme look

[ashen fossil]

Mhm

[halcyon yew]

it is secant cause it touches at two points

[ashen fossil]

Yes

[halcyon yew]

thas only reason?

[ashen fossil]

Intersects rather than touches

[ashen fossil]

Yes

That's the definition

[halcyon yew]

then for 2 only reason is makes contact once?

then for 3 only reason it makes contact once?

[ashen fossil]

Yes

[halcyon yew]

then for 4 how can it be both????

@ashen fossil

[ashen fossil]

Ok so

Tangent means

Touching the curve

Which it does

Secant means intersecting

Also which it does

U see the bottom curve

Where it looks like tangent

That is where the line acts as tangent to the curve

[halcyon yew]

so tangent is touch and secent is intersect

[ashen fossil]

Yes

[halcyon yew]

wait then how is 5 tangent @ashen fossil

😭

[ashen fossil]

Ok ok

Lemme explain

Tangent line

[halcyon yew]

alr

[ashen fossil]

Is something that touches the line

Only touch

And then go away from it

Where as

Secant line is something which touches/intersects

The curve

U get it?

[halcyon yew]

no i feel stupid rn

😭

[ashen fossil]

Uhh

Ok so

Tell me what u understood about a tangent

[halcyon yew]

tangents dont intersect

[ashen fossil]

Mhm

And?

What do they do

[halcyon yew]

they touch

but then 5 does not agree with this definition

[ashen fossil]

Yep

Ok the bottom part

Does it look like it's touching and leaving the curve?

[halcyon yew]

for 5 or 4?

[ashen fossil]

Did u understand 4?

[halcyon yew]

i kinda wna focus on 5 first

it intersects

[ashen fossil]

Nop

It touches

[halcyon yew]

wait what 5?

[ashen fossil]

Look at the line and direction of the curve

[halcyon yew]

how does 5 touch]

[ashen fossil]

Same right?

[halcyon yew]

about the same

[ashen fossil]

Yes

So it's a tangent

Ull understand it better once u start to solve it mathematically

[halcyon yew]

but then 1 is also in same direction

wait does the definition in box make sense to u? maybe i should understand this

@ashen fossil my teacher said this

he said this before that tho

[ashen fossil]

Just a sec

[halcyon yew]

np

[ashen fossil]

How do u say

Line and curve look like they go in same direction

For 1 🙄

[halcyon yew]

like they are both generally traveling to top left or bottom right depending on how u look at it

[ashen fossil]

No no

Right at the point

Where they intersect/touch

[halcyon yew]

oooo

ur right

[ashen fossil]

Yepp

[halcyon yew]

i think it will help if i understand what these are trying to say too

@ashen fossil it would be appreciated if u could help me understand this

[ashen fossil]

Mhm

Which one

[halcyon yew]

the box at bottom right

of first piic

a better way...

@ashen fossil

[ashen fossil]

Yes

Yes

Ok so

[halcyon yew]

alr

[ashen fossil]

If u take 1st pic

The one which says secant

U see the line intersecting curve at 2 points

Right?

[halcyon yew]

yes

[ashen fossil]

So

Make the points closer

So that

They coincide

[halcyon yew]

into one point?

@ashen fossil

ur talking abt 1 on here right?

[ashen fossil]

Yes

Make the points come closer

And at the point where

They coincide

Ull see a tangent

Umm and I gotta go
My flight's starting

Be quick

[halcyon yew]

im just imagining a line with a dot in it

that is not touching the curve

[ashen fossil]

Mhm

Ok so making it simple

The line in 1st one

Move it slowly

To the left

The points of intersections keep coming closer and closer

Yes?

[halcyon yew]

so u move the curve too?

[ashen fossil]

Nop

Just the line

To the left

Without changing the slope

[halcyon yew]

u move the entire line or just one of the dots

@ashen fossil

[ashen fossil]

Like this

So what they mean is

If u make 2 points of intersections of secant come closer and closer, it becomes a tangent

[halcyon yew]

how the heck do u do that? u just drag the line down? where does the dots moving come into play?

[ashen fossil]

It's just explaining u

What that box means

If u make 2 points of secant come closer, u get a tangent

Which u can see here

In the image i sent

[halcyon yew]

so then how is the first one a secan and not a tangent with this box knowledge

@ashen fossil

[ashen fossil]

Look

I'm just explaining what the box says

U shouldn't move the line and curve

The equation of line will change

[halcyon yew]

so does this have no relevance to getting the answers to the other examples

[ashen fossil]

Just for the sake of explaining, I moved it to show how it will become a tangent if 2 points coincide

[ashen fossil]

Nop he is just explaining what a tangent is

In terms of secant

[halcyon yew]

oh man so im just not gna understand this then ig

cause i am confused

😭

[ashen fossil]

It's fine

Take a break

And read this again

Slowly

And yea I gotta go

Just dm me if u have doubts

[halcyon yew]

alr imma add u

[ashen fossil]

Mhm

[halcyon yew]

can i?

how else do i dm u

[ashen fossil]

Yes u can

Ok then

I'm going

[halcyon yew]

thx

<@&286206848099549185> is anyone able to take over and try to explain in a different way

[ashen fossil]

Anytime!

[halcyon yew]

<@&286206848099549185>

[devout snow]

@halcyon yew Has your question been resolved?

[devout snow]

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.

[inner ibex]

hi

[inner ibex]

do we differentiate first and then sub in h = 12-r or do we put in 12-r first and then differentiate

can soemone pls help me understand dis

[long pasture]

sub first, since it's better to do it with one variable

if you are doing with multiple variables, it'll be nasty

[inner ibex]

o oke

what ab for ids

dis q

what do i do wit hthe domain

[long pasture]

ah, 2nd question

i see

2 things to check

boundary conditions, and local extrema

since f'(x) always >0 in the domain, so we'll just have to check the boundaries, i.e. when x=-2 and x=1

[inner ibex]

so we only do 2

[long pasture]

yea

got it?

[inner ibex]

does that apply to everything

@long pasture how do i do it

pls

[long pasture]

heyyy

[inner ibex]

how i do

[long pasture]

check 2 things apply to everything

like with a function and a domain

[long pasture]

this

[inner ibex]

how

do i differentiate it

[long pasture]

1. boundary conditions:
   sub the min and max x into f(x)

2. local extrema, find f'(x) and set it to 0 to check

(and check for undefined cases too if have)

see if you can do it with this HW

[inner ibex]

o

[long pasture]

it's not that hard for this Question 10, it's good for starters

[devout snow]

@inner ibex Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[devout snow]

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.

[tough juniper]

Hi, i just did this arithmetico-geometric series problem, and I’m wondering if there a name for this “move” (in image below, lines 3-5), since I couldn’t really search it up

[tough juniper]

I multiplied by 1/3 to S to make a compact sum

[junior chasm]

uh

i think thats just multiplication

[tough juniper]

The place i labeled “is there a name for this move”

Oh ok

[junior chasm]

oh that complete thing

im not sure if there's a name for that

i just think its part of process to find the sum

[tough juniper]

It’s just clever manipulation ig?

[junior chasm]

manipulation yes

you can say that

[tough juniper]

Ok

[trail eagle]

It's sort of rearranging, manipulation probably does the trick. Regardless, note that this somewhat assumes that the series converges in the first place. In general, you could get wrong results if the series doesn't.

But I guess you can show that separately :p

Here it works though

[tough juniper]

Yes, because i showed that it can be rewritten as a converging series

[trail eagle]

Lots of diverging series can be rearranged into seemingly convergent series by such manipulations is what I mean.

[tough juniper]

Yeah

Thanks for the insight

Close

.Close

.close

[devout snow]

Channel closed

Closed by @tough juniper

Use .reopen if this was a mistake.

[devout snow]

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.

[lucid roost]

How to abuse on Desmos

[modest dune]

Wdym

[lucid roost]

Like solve this question in Desmos

[devout snow]

@lucid roost Has your question been resolved?

[junior chasm]

plot the equation in desmos

add a slider for p

and add a radius formula

then from where u can vary p using the slider and check the radius value and deduce the value of n

np = r
n(2) = 6
n=3

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[devout snow]

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.

[weary maple]

Question
Which statement is not true?
Precise measurements are always accurate.
Accurate measurements are always precise.
Precise measurements can be inaccurate.
Inaccurate measurements can be precise.

[topaz axle]

the first one

well the picture thinks 1st and 2nd

but if you have to pick one, 2nd is proly true

[weary maple]

alright thank you

.close

[devout snow]

Channel closed

Closed by @weary 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.

[visual jetty]

It says in the answer sheet the center of the circle I'm finding has diamater AB
How do you prove this?

[devout snow]

@visual jetty Has your question been resolved?

[upper schooner]

Non-formally: the greatest distance a line segment through two points on a circle can have is when it forms a diameter…

[visual jetty]

Think I got it roughly

The problem itself isn't too hard... just the reasoning was a bit confusing

Maybe ill come back to it later for now it's good, thanks!

.close

[devout snow]

Channel closed

Closed by @visual jetty

Use .reopen if this was a mistake.

[devout snow]

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.

[sturdy mango]

is there a formal definition of indefinite integral like for derivatives we have the limit definition for definite integrals we have riemann sum

[fiery marten]

The equivalence class of antiderivatives of f, where 2 antiderivatives are equivalent iif they differ by a constant

[sturdy mango]

know like

uk we can evaluate derivatives using this

[stone stump]

indefinite integration is basically just definite integration with some lower bound number and upper bound x

[fiery marten]

yes

up to a constant term

[sturdy mango]

but wouldnt that give us 0

[fiery marten]

no, you fix the lower bound and very upper bound

[sturdy mango]

if we put the same limit x

oh

[stone stump]

$\int_0^x f(x) dx = F(x)-F(0)$ which is basically the same as $F(x)+c$

[sturdy mango]

but we dont tho? is it -infinity

[woven radish]

Denascite

[stone stump]

not quite but more or less the same

[sturdy mango]

ohhh

but definite itnegras

dont have the constant of integ

[fiery marten]

Because they evaluate to a number

[sturdy mango]

yea

[fiery marten]

In definite integrals both bounds are fixed

[sturdy mango]

ohok

ik that

[fiery marten]

And here we fix only one, but since we could fix it as any number, we get an arbitrary constant term

[sturdy mango]

hmm

.close

[devout snow]

Channel closed

Closed by @sturdy mango

Use .reopen if this was a mistake.

[stone stump]

well not quite, nothing says that we could actually get any constant with F(a)

[fiery marten]

Yeah, true

[stone stump]

the constant basically comes afterwards because we know once we differentiate it wont matter again

[fiery marten]

That's why the definition with antiderivatives makes more sense

[sturdy mango]

yeah ik the definiton

but i thought maybe there is some more definiton like the limit one

we have for derivatives

[stone stump]

well that definition dodges the question whether an antiderivative exists in the first place

.reopen

[devout snow]

✅

[stone stump]

the existence of an antiderivative is the expression $\int_a^x f(x) dx$ in the first place

[woven radish]

Denascite

[fiery marten]

yes

But then we note that +c also produces an antiderivative

[stone stump]

yes once we have some antiderivative we can get all of them. but we need to get the first somehow

and thats still done via definite integrals

[sturdy mango]

oh

kinda went over my head ngl

kinda get it

we use definite integral to define the indefinite integral?

and we assume that +C helps with the non selected limit of the definite integral?

[stone stump]

ehhh

[fiery marten]

1. We prove that an antiderivative F0(x) exists using definite integrals
2. We show that there're automatically many more antiderivatives: F0(x) + c
   We define the indefinite integral as the class of all those antiderivatives (still not completely clean)

[stone stump]

the technical definition would be something like $$\int f(x) dx = \left{\int_a^x f(x) dx + C: C\in\bR\right}$$

[woven radish]

Denascite

[stone stump]

well, still missing technical details

[sturdy mango]

yea

[stone stump]

anyway, the point is definite integrals are the important bit

[sturdy mango]

got it

true

[stone stump]

indefinite integrals are more or less just convenient notation

[sturdy mango]

i use them a lot in physics

[stone stump]

and physics is well-known for caring a lot about the mathematical details

[fiery marten]

haha

[sturdy mango]

lol

[devout snow]

@sturdy mango Has your question been resolved?

Channel closed

Closed by @sturdy mango

Use .reopen if this was a mistake.

[devout snow]

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.

[primal abyss]

im confused 😦

did i set it up right?

[devout snow]

@primal abyss Has your question been resolved?

[primal abyss]

<@&286206848099549185>

[devout snow]

@primal abyss Has your question been resolved?

[devout snow]

@primal abyss Has your question been resolved?

[devout snow]

@primal abyss Has your question been resolved?

[primal abyss]

.close

[devout snow]

Channel closed

Closed by @primal abyss

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.

[fathom rune]

how i can deal wiyh it

[wicked turtle]

can you find a simple bound for sin(x^2)?

[fathom rune]

its next chapter in my textbook

[fathom rune]

what do you mean

1 and -1?

[flint spire]

yes, start with that and use it to squeeze the given function between two functions

$h(x) \le \frac{\sqrt[3]{x^2} \cdot \sin(x^2)}{x-1} \le g(x)$

[woven radish]

Emily

[fathom rune]

okkkk

[flint spire]

after that take the limit on the 3 sides

[fathom rune]

okkkk thanks

.close

[devout snow]

Channel closed

Closed by @fathom rune

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.

[prisma lodge]

how do i solve

estimate the rate of change of the function at the given point. f(x)=1/3x at x=4

[devout snow]

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

[prisma lodge]

1

.close

[devout snow]

Channel closed

Closed by @prisma lodge

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.

[scenic plume]

Would it be possible to define a system of mathematics with such a number j where the square root of j is equal to negative one? I think it might be a problem of definition as the square root function is broken up into the principal and negative square roots due to x^2 being irreversible. What do you guys think? Is it not possible or would it be possible to approach this like defining imaginary and complex numbers(which I was thinking about doing initially)?

[uncut crow]

yea?

[young plover]

Tbh you can define whatever you like

The results are what matter

[scenic plume]

That's what im trying to figure out

If it would actually work or not

[young plover]

So if you define j such that sqrt(j) = -1 then that’s allowed sure

But does it give you anything meaningful? Idk

You can derive that j=1

Or it could be -1 I suppose

So yeah there’s the branching issue you mentioned

[scenic plume]

Okay so what i'm getting is you're talking about somehow expanding or redefining the sqrt functon

[young plover]

No

[scenic plume]

Because last time i checked neither square root of 1 nor -1 was -1

[young plover]

It kinda is

-1 times -1 = 1

[dense lynx]

“Remember, you are not locked into a single axiom system. You may invent your own, whenever you wish—just use your intuition and imagination.” goes so hard right about now

[young plover]

Truly

[scenic plume]

I'm talking about the principal square root

In which case sqrt(j)=-1 is currently undefined

[young plover]

Okay well a number whose square root is -1

You could define it if it exists as j like you’ve done

Sqrt(j) = -1 is the property

So I suppose j must also satisfy |j| = 1

Its on the unit circle

[scenic plume]

So what i'm getting is it has a chance to work

[young plover]

If anything you may be able to express j in terms of i but I suspect that j must equal 1 tbh

I think that’s the only number whose square root is -1

[scenic plume]

Hmm okay

I'll do more research into this

Thanks for the help

[young plover]

The harder part is proving that lol

But it should be manageable

[scenic plume]

Ok

.close

[devout snow]

Channel closed

Closed by @scenic plume

Use .reopen if this was a mistake.

[devout snow]

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.

[timid peak]

where do you get the sqrt(2) from?

[upper schooner]

Magnitude of the complex number -1 + i

[devout snow]

@timid peak Has your question been resolved?

[timid peak]

ohh okok

got it

thanks

.close

[devout snow]

Channel closed

Closed by @timid 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.

[vale ether]

Suppose I have a group generated by the following permutations on 20 integers: A= (1,2,3,…,20) and B=(1,4)(2,3). Find the maximal group generated by these.

Obviously we have an even and odd permutation and I suspect it just goes to S_20, but haven’t the ideas on how to show that or explain why that must be the case. I know there is a solution beyond brute force computing an (i, j) so looking for a neat way

[devout snow]

@vale ether Has your question been resolved?

[vale ether]

<@&286206848099549185>

[spiral geyser]

what kind of group-theoretic tools have you covered so far?

[vale ether]

Uh the usual early bits up to conjugate classes, centralizers, isomorphism (inner outer, the lot)

I’m just unsure of anything to use

[spiral geyser]

well to start, you can get 20 different products of two 2-cycles by conjugating B by A

A B A^(-1) is (2 5) (3 4), A^2 B A^(-2) is (3 6) (4 5), and so on

[vale ether]

Yeah sure. And I get those will be distinct because A is cyclic.

So that gives us some terms, but is there a way to get like a (1 2) from that?

Or are we forming some sorta logic to get to 20!

[devout snow]

@vale ether Has your question been resolved?

[vale ether]

@spiral geyser Any thoughts?

[devout snow]

@vale ether Has your question been resolved?

[devout snow]

@vale ether Has your question been resolved?

[devout snow]

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.

[void knot]

Consider the curve ( y = y(x) ) in the upper half-plane with the condition (x > -\frac{1}{2} )
such that at any point ( M(x, y) ) on the curve, the tangent line intersects the x-axis at a point ( N ), and it satisfies
[ |OM| = |ON|, \quad y(0) = 1, \quad y'(x) > 0. ]
Find the function ( y = y(x) )

[woven radish]

ive

[devout snow]

@void knot Has your question been resolved?

[somber mortar]

I need help with a problem which is: prove that for any x ≤ 2, x + 1 + xe^(-x) ≤ 2x+1

[devout snow]

@void knot Has your question been resolved?

[devout snow]

@void knot Has your question been resolved?

[faint gorge]

This looks like it could be some root function

[void knot]

How so? I guess it could be some diff equation but I have no evidence

[faint gorge]

So that's interesting we have to make sure that the distance from point of tangent is equidistant the origin as the intersection point with the x-axis and tangent line

Say the tangent line had the form t(x) = mx + c

If t(x) = 0 then
mx + c = 0 implies x = -c/m
|-c/m| = |y(x)|

The root of the tangent line has the same distance as the point of y(x)

So we have to make sure that our curve is built in such way so that [x^2+y^2 = \frac{c}{m} \quad \forall x,y ]

[woven radish]

bacc

[faint gorge]

which actually resembles a circle equation but then we also need to make sure y'(x) > 0

circle makes actually sense

no it doesn't after further inspection

It has to be a an isosceles triangle actually

damn that problem is interesting but i gotta go 😢

|M(x,y(x))| = |T(x,0)|

[faint gorge]

(c/m)²

[void knot]

omg I just came back thank you Lemme take a look

[faint gorge]

Now that think about it

We have to derive a differential equation

Because it could be really any type of function

[void knot]

Half of my brain cells are dead after thinking about this

[void knot]

you mean these two line are the same?

[faint gorge]

,, y'x+y = \frac{y}{x}

[faint gorge]

Exactly

[void knot]

|y(x)| is not y0?

I understand the left line is |-c/m|

[faint gorge]

We know the tangent line looks like
[ t(x) = y'(a)(x-a)+y(a) ]

[woven radish]

bacc

bacc

[faint gorge]

So actually

[ x^2 + y^2 = \left ( \frac{y}{y'} \right )^2 ]

[woven radish]

bacc

[faint gorge]

Holy shit long ass solution 😭

I thought I was onto something

[void knot]

wdym

[faint gorge]

,w x^2+y^2=(y/y')^2

[void knot]

you have went so far, wait for me to follow up🥲

[woven radish]

Results provided by WolframAlpha

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

Requested by adoniszgks

[void knot]

you go from this to that ? from c/m to y/y'

[faint gorge]

Yes

[void knot]

from a circle to a diff equ

[faint gorge]

Yea kind of

Well x² + y² is pythagoras

[faint gorge]

Green triangle

[void knot]

what's the inspection here

[faint gorge]

But I think it's weong anyway as it's not a simple solution

[faint gorge]

Well I realized a circle equation does not satisfy |OM|=|ON|

[void knot]

you mean we need both equa hold simultaneously?

[faint gorge]

Yea

[void knot]

We still have a condition that havent use

[faint gorge]

Yea

[void knot]

y'=y-0/x-c/m >0

seems like wrong track

-c/m=x-y/y'

I need to gather all the current conditions

x^2+y^2=c/m=y/y'

uhh

nvm I think somewhere is wrong but idk

idk why we get different result

[faint gorge]

I am currently outside

I will see later

I wanna solve this

[void knot]

What did you sub in for this step, I feel this might be wrong, can you elaborate this step? (ofc later when you're available

[faint gorge]

Here

m = y' and c = y but you might be right thats its wrong

[void knot]

We can never deal with diff equ in this form

It's not a regular form covered in college

We have to think another way out

But I'm so headache rn, umm can't think of any

[devout snow]

@void knot Has your question been resolved?

[faint gorge]

@void knot

[crude wasp]

haven't read what u've done but i think this equation is wrong

if our original point M = (x_0, y_0)

i get that N = (x0 - y0/y'(x0) )

so our differential equation becomes

$x^2 + y^2 = \big (x-\frac{y}{y'} \big)^2$

[faint gorge]

I JUST GOT THIS

[woven radish]

LY

[faint gorge]

I SWEAR

I DID IT RN ON PAPER

[crude wasp]

i end up with ^

which wolfram alpha does give a nice solution to

[faint gorge]

https://www.desmos.com/calculator/wipzl0vlwx

[crude wasp]

so i'm tempted to think it's correct lol

[faint gorge]

I tried on desmos

😭 now everybody things i copied you

[crude wasp]

oh ok u've got the same equation as me

[faint gorge]

I have done mistakes previously

[crude wasp]

oh right ic lol nw

[faint gorge]

but now where I am at home I have this

[crude wasp]

aha it's fine

i'm sure no one's checking the history of a random help channel

[crude wasp]

anyway yeah lemme see how to actually solve the DE

[faint gorge]

Well I haven't solved it used a calculator

but what matters to me the most is the finding the right approach

now i can play minecraft 🥹

I think the suggestion was to do z = y'

[faint gorge]

I was just missing the x- 😭

[crude wasp]

yeah ok i think i know how to solve the DE too

[crude wasp]

@void knot lemme know if u manage to get this

also if u need help solving the DE

[faint gorge]

[ (y')^2 + y'(2xy) = y^2 ]

[woven radish]

bacc

[faint gorge]

[ (y'+xy)^2 = y^2+(xy)^2 = y^2(1+x^2) ]

[woven radish]

bacc

[faint gorge]

[ y' = y(\sqrt{1+x^2}-x) ]

[woven radish]

bacc

[faint gorge]

Looks separable

,, \int \frac{1}{y} : \dd y = \int \sqrt{1+x^2}-x : \dd x

[woven radish]

bacc

[faint gorge]

@crude wasp what do you think?

[faint gorge]

Did I do a mistake

[faint gorge]

From here I multiplied by (y')² and added (xy)²

[crude wasp]

yeah i got that too

[restive river]

You can use byparts here

[faint gorge]

Have you seen the desmos file I sent

[crude wasp]

yeah i saw

[faint gorge]

From here doesn't seem to be the same

ngl I am kinda proud of me it's been 1 year since i have had dge's

[devout snow]

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.

[ruby bridge]

Anyone able to help me with this question, i'm unsure where to start

[gusty nexus]

Let's say $sin(\alpha)$ is m, what is $arcsin(-m)$

[woven radish]

MetuMortis

[ruby bridge]

I have no idea what arcsin means

[gusty nexus]

Oh nvm then

sin(30) is 1/2 what is sin(-30)

[ruby bridge]

-1/2

[gusty nexus]

Yes so if sin(x) is -5/13 what is sin(-x)

[ruby bridge]

5/13

[gusty nexus]

Yes, create a right triangle, one of the angles should be -x

[ruby bridge]

Gotcha

And then?

[gusty nexus]

Find cos(-x) using the triangle

Then convert it to cos(x)

Not sure if "converting" is the true verb tho, maybe I should say "calculate"

[ruby bridge]

What does the misshapen E mean in this question

[brittle inlet]

That's not necessary though

[brittle inlet]

“belongs to“

It's saying that x lies within that interval

[ruby bridge]

What is the next step according to you?

[brittle inlet]

Do you know the fundamental equation of trigonometry?

The one that relates the squares of cos and sin?

[ruby bridge]

Which one are you referring to?

[brittle inlet]

The basic one

The one with sin and cos

[ruby bridge]

The sos cas toa ones?

[brittle inlet]

Uh, never heard of those abbreviations

Could you explain what you mean?

[ruby bridge]

Sin = opposite side/long side

Its a dutch abbreviaton

[brittle inlet]

No, not that one

Does sin^2(x)+cos^2(x)=1 ring any bells?

[ruby bridge]

Oh yeah

Pythogoras

Basically

[brittle inlet]

Yeah, the Pythagorean identity

[ruby bridge]

But thats only when the long side is 1 right?

[brittle inlet]

Well, from there, it follows that cos^2(x)=1-sin^2(x)

[brittle inlet]

Nope, it's universal, for any angle x, that is satisfied

Whatever angle that may be

[ruby bridge]

Alright

[brittle inlet]

And you should be able to go on from here

[ruby bridge]

It gives me a number but how would i make that number into a simplified fraction

[brittle inlet]

What have you done to get there?

[ruby bridge]

Cos² = 1- ( -5/13)²

[brittle inlet]

Yup

[ruby bridge]

I think i found one

I can Just do 5² and 13² and keep the fraction

Right?

[brittle inlet]

Those are fairly simple squares

And you need to subtract them to one

[ruby bridge]

Which makes 144/169

And then sqrt

[brittle inlet]

Yup, from there you get that cos(x) is the square root of that

[brittle inlet]

Yep

[ruby bridge]

And then i can divide cos and sin to get tan?

[brittle inlet]

Yeah, but there's one last thing you gotta keep in mind

Recall they mentioned that x was between pi and 3pi/2

That means it's an angle on the third quadrant(you can visualize the unit circle for this)

What's the sign of cos on the third quadrant?

[ruby bridge]

Negative

[brittle inlet]

Yup

So cos is (-1) times the value you got for cos

From there you can proceed normally

[ruby bridge]

So then (-5/13)/(-12/13)

And then we get 5/12

[brittle inlet]

Yup

[ruby bridge]

Thanks a lot

Have a good day

.close

[devout snow]

Channel closed

Closed by @ruby bridge

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.

[stark shale]

watching this video, it gives some perspective over the dot product.
https://youtu.be/LyGKycYT2v0?t=709
it talks about duality. Which i didnt came across in my studies.
just to understand a bit better, any vector of any dimension, i can interpret its components as the basis vectors of a transformation that maps the space into a line ?

[stark shale]

if you play it starts where i'm having my question

[graceful cosmos]

Watched the video. I think 3b1b is noting that a dot product with a given vector is itself a linear transformation

He's constructing
f: R² -> R
f(x) = x•(4,1)

f is linear

Using dot products, we can generate linear transformations. Or, we can write linear transformations using dot products

@stark shale

[stark shale]

i don't know how to read what you wrote there. maybe
f is a function that maps from R2 to R ?
and f is defined as a dot product between input vector x and some other vector.

? is this what you wrote there?

ok

[graceful cosmos]

Exactly. In 3b1b's version, the "other vector" is (4,1). You could use any other vector though

[stark shale]

ok yes i think i understand what is going on there

i was just reasoning on that specific part

of the dual

the dual argument is valid only when going from Rn to R ?

[graceful cosmos]

You can extend it further. See the Riesz representation theorem for more details

Basically, you can write any linear transformation as a list of vectors to dot with

[stark shale]

ok it's over my heaed

[stark shale]

a matrix baiscally

[graceful cosmos]

Meaning that "linear transformation" and "vectors to dot with" are essentially the same thing, and therefore those "vectors" are "dual" to linear transformations

[stark shale]

ok

i think i understand

so, to get back to my orig question at the top..

i have a vector in 3d space, with its components. i can see that vector as a .. vector, a point in space.
But i can create a 1*3 matrix with 3 basis vectors corresponding to the vector components.

[graceful cosmos]

(4,2) is just 4u + 2v, where u and v is an agreed-upon basis

[stark shale]

and that matrix, would map a 3d space to 1d space. so it's a dot product basically

does it makes sense what i wrote?

i need yes or no

[graceful cosmos]

Yes

[stark shale]

ok, if you want to expand you're welcome, it's just that my brain looks for that first, so i understand how to read the answer

if it's a "youre wrong , this is how it is instead" or "yes let me expand further"

[graceful cosmos]

Of course, I get it!

[stark shale]

cool thanks

[graceful cosmos]

Your explanation works

[stark shale]

ok thanks a lot for checking with me! really appreciate it

.close

[devout snow]

Channel closed

Closed by @stark shale

Use .reopen if this was a mistake.

[devout snow]

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.

[last egret]

any way to simplify this?

[devout snow]

@last egret Has your question been resolved?

[flint spire]

you could for example do this $\ \frac{y^3 \cdot \cos(xy^3)}{5-3xy^2 , \cos(xy^3)}=\frac{y^3 \cdot \cos(xy^3) ,,, / \cos(xy^3)}{[5-3xy^2 , \cos(xy^3)] , , , / \cos(xy^3)}$

[woven radish]

Emily

[flint spire]

$\frac{y^3}{5 , \sec(xy^3)-3xy^2}$

[woven radish]

Emily

[flint spire]

1 trig function instead of 2, ig expression is simpler in this sense

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[devout snow]

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.

[formal quarry]

Isn't C in the z=y plane?

[serene lance]

I think so yeah

z=x doesn't really make sense

[formal quarry]

Ok that’s what I thought too. I’ll email my professor and see what they say

I just wanted a second opinion to make sure I’m not going insane lol

[serene lance]

I was like wait a second but looked at it in desmos and seems it is z=y

And just algebraically speaking

Since $z\geq0, y\geq0$ you can get $z=\sqrt{9-x^2}$ and $y=\sqrt{9-x^2}$ so assuming $y=z$ we get an equality but for $z=x$ we just get $2z^2=9$ ig?

[woven radish]

Goran

[serene lance]

That has nothing to do with y

[formal quarry]

yeah, im definitely gonna ask them about this

[serene lance]

Took a bit of work but desmos proof (1st image is z=y)

[formal quarry]

and the second is z=x?

[serene lance]

Yeah

[formal quarry]

just emailed them. we shall see what they say

[serene lance]

Btw looked into this 2z^2=9 we get assuming that z=x which produces a singular solution and it's this corner here

[serene lance]

Good luck

[devout snow]

@formal quarry Has your question been resolved?

[devout snow]

@formal quarry Has your question been resolved?

[ornate prism]

Is this grade 12 math

[serene lance]

Well depends this kind of maths is in 1st year of uni mostly in my school system since it deals with multivariable curves

[ornate prism]

Yeah I expect it

[formal quarry]

this is calc 3

[devout snow]

@formal quarry Has your question been resolved?

[devout snow]

@formal quarry Has your question been resolved?

[devout snow]

@formal quarry Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[devout snow]

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.

[slate glen]

hii cld anyone explain how they got R=5 how i solve for r is using simul eqn and solving for alpha then replugging into the eqn and solving for r also cld anyone rlly explain what r formula does or rlly mean im preety curious

[woven radish]

ananas

[pastel pasture]

basically imagine a and b to be the legs of a right triangle

α is the angle such that tan(α) = b/a

and R = sqrt(a^2 + b^2) for you here

[slate glen]

so cld u say R reprsents the hypotenuse side of the right angled triangle?

[pastel pasture]

yeah exactly

[slate glen]

Is this how I would imagine the triangle to look like?

[devout snow]

@slate glen Has your question been resolved?

[slate glen]

Also this end eqn like the ans what does it represent

[brittle inlet]

This is an impossible triangle

[slate glen]

oh

could you explain why

[brittle inlet]

All the angles in a triangle sum to 180°

Cos and sin are bounded between 1 and -1, so they could, at most, be equal to 1

(leaving aside that there exists no angle such that both sin and cos are 1, we'll assume there is)

Assuming the maximum.value for both cos and sin, we'd get that one angle is 3°, another 4° and another one 90°

Which sum to 97°

[slate glen]

ohhh okayyy

[slate glen]

hmm then how wld i possibly represent 4sintheta +3costheta =5sin(theta+36.870)

[brittle inlet]

What are you trying to represent? That equation?

[slate glen]

yes in a traingle

[brittle inlet]

Hm, that's quite the strange exercise

I think it'd be better if someone else helped ya

[slate glen]

hmm sure tks!

[devout snow]

@slate glen Has your question been resolved?

[slate glen]

whjk

[devout snow]

@slate glen Has your question been resolved?

[devout snow]

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.

[mighty copper]

how do i show this

[mighty copper]

i am able to find the resultant motion

but how do i show that this resultant motion follows SHM?

[frozen aurora]

what have you found?

for the resultant motion

[mighty copper]

okay so the resultant motion will be in Acos(wt+delta) form

I am getting delta as

tan^-1(A2sin(phi)/(A1+A2sin(phi))

and then A as

(A1+A2sin(phi))cos(delta)

[frozen aurora]

great

[frozen aurora]

so, willthis motion be simple and harmonic?

it's just like x1 and x2: amplitude*cos(wt+phase)

[mighty copper]

yea i mean it should be as thats the pattern of a SHM motion

i thought there is a rigorous proof or something?

[frozen aurora]

i don't think so

they wrote "show that", not "prove"

[mighty copper]

oh

yea

[frozen aurora]

unless there's a very specific definition of SHM that this textbook uses

i think what you did is definitely enough

[mighty copper]

got it. thankyouuu

.close

[devout snow]

Channel closed

Closed by @mighty copper

Use .reopen if this was a mistake.

[devout snow]

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.

[split orbit]

hey, i was just wondering if i drew my boxplot correctly according to the right sets of data, the context of the question should be on the top beside “e.)”

[split orbit]

<@&286206848099549185>

[devout snow]

@split orbit Has your question been resolved?

[devout snow]

@split orbit Has your question been resolved?

[split orbit]

<@&286206848099549185>

<@&286206848099549185>

[devout snow]

@split orbit Has your question been resolved?

[drowsy pond]

yes

what is ur ques?

[split orbit]

I was just wondering whther my box plot was drawn correctly or not, i even provided the context of the question as well

The datasets regarding Q1, Q3 and IQR are all displayed in the photo too, just wanted to check if my boxplot is drawn accurately or illustrated presentably

This question is based off of a stats class btw

[bleak tinsel]

Unable to clearly understand the question in the image,
Please transcribe it

[devout snow]

@split orbit Has your question been resolved?

[split orbit]

.close

[devout snow]

Channel closed

Closed by @split orbit

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.

[ashen leaf]

So, I have an equation here for Xn which I know is for a hyperbola but I need to put it into a form that is recognizable as a hyperbola

[ashen leaf]

Intuition tells me this would be something like acosh(theta)+bsinh(theta) or maybe in this case i[acosh(x)+bsinh(x)] thus I would need to substitute my e^thetas back to cosh(theta)+sinh(theta) and so forth and then just separate the terms

but I feel like that is also very wrong

[devout snow]

@ashen leaf Has your question been resolved?

[devout snow]

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.

[weary parrot]

y = x^2 - 5 at P(2, -1)

[weary parrot]

find the slop and equation of the tangent line

[atomic dome]

What is your work so far?

[weary parrot]

(2 + h)^2 - 5 - ( 2^2 - 5 ) / h

4 + 2h + h^2 - 4 + 5 / h

2h + h^2 / h

h + 2

[atomic dome]

Alright, so the slope is?

[weary parrot]

-1

[atomic dome]

No…

Do you know the derivative?

[weary parrot]

I do, but we are not there yet

the derivative is 2x

[atomic dome]

With that knowledge, what is the slope

[weary parrot]

I already did Calculus 1 but I am struggling in Calculus 2

do I need to re do Calculus 1 and do limits all over again to be successful in Calculus 2?

[atomic dome]

No, you should focus on mastering the integral and derivative

[weary parrot]

my professor said I should re do Calculus 1 because at the end they use derivatives

I can't remember all the derivatives and integration formulas

there are so many

[atomic dome]

There are, but they all tie together

Focus on doing this problem first

[weary parrot]

should I just try to do Calculus 2 without going back to Calculus 1?

because whenever I see trig in Calc 2 I have troubles

I don't know the trig identities or anything

[atomic dome]

You can do what I did and memorise them all

Outside of the classroom

[weary parrot]

what country are you in?

[atomic dome]

US

[weary parrot]

ok so you think I should just keep going with Calculus 2?

[atomic dome]

What is the slope?

[weary parrot]

2

because h is going to 0 I guess

[atomic dome]

You told me the derivative is 2x

Plug in the x value of the coordinate into the derivative

[weary parrot]

they want us to do it with the old fashioned way

like derivative (f(x) + h) style

[atomic dome]

The definition of the derivative is what that is

[weary parrot]

ok so derivative is 2x

[atomic dome]

Yes

[weary parrot]

do I put 2(2) or 2(-1) ?

[atomic dome]

Plug in the x value

Into the x

[weary parrot]

oh right

4

[atomic dome]

Yes

Now find the equation for the tangent line

[weary parrot]

how do I do that

[atomic dome]

Use point slope form

[weary parrot]

its like y2 - y1 = m(x) + b?

[atomic dome]

Close

[weary parrot]

y2 - y1 = m(x2 - x1) + b

[atomic dome]

Yes

[weary parrot]

what is b in this?

[atomic dome]

There won’t be

You have everything you need to form the equation

[atomic dome]

There isn’t a b in the point slope form. The b would just subtract into the y1

b is only in slope intercept form

[weary parrot]

y - (-1) = 4(x2 - 2)

y + 1 = 4(x2 - 2)

y = 4(x2 - 2) - 1

[atomic dome]

Just keep it as y+1=4(x-2)

[weary parrot]

y + 1 = 4x - 8

is the only overlap in Calculus 1 derivatives for Calculus 2?

everything else is a waste of time?

[atomic dome]

Nothing is a waste of time

[weary parrot]

well Im pretty old and I've wasted a lot of years

I did Calculus 1 9 years ago

[atomic dome]

Wow

[weary parrot]

since it's been 9 years since I've done Calculus

should I redo Calculus 1

or can I just keep going forward

I remember the product rule and chain rule and derivatives or sin and cos and ln(x) but that's about it

when I get into tan and sec^2 and things like that I forget

the integrals are really hard

[atomic dome]

Why are you learning calculus again

[weary parrot]

because I need it for a computer science degree

once I did Calculus 1 the first time I took a break from university because I wasn't having fun

what do you think I should do?

[atomic dome]

Just take the next calculus course you can

[weary parrot]

yea that's Calculus 2

but I keep having to drop it

can you help me with this integral

or can you help me on another tangent line question?

[devout snow]

@weary parrot Has your question been resolved?

[weary parrot]

@atomic dome can you please help me

[atomic dome]

Sure, just give me a moment

[weary parrot]

k thanks

[devout snow]

@weary parrot Has your question been resolved?

[atomic dome]

Okay, what work have you done so far

[weary parrot]

e^ u u = -cot(x)

[atomic dome]

And what is du and dx

[weary parrot]

du = -sinx(sinx)^-1 + cosx -(sinx(cosx))^2

du / -sinx(sinx)^-1 + cosx-(sinx(cosx))^2 = dx

[atomic dome]

You don't have to do all of that

\begin{align}
\frac{dy}{dx}(\cot(x))=-\csc^2(x)\\
\frac{dy}{dx}(-\cot(x))=\csc^2(x)=\frac{1}{\sin^2x}
\end{align}

[woven radish]

mari

[weary parrot]

how do you get that?

memory?

[atomic dome]

Yes

[weary parrot]

I don't see it on the sheet

[atomic dome]

I memorised all of the trig identities and derivatives

[weary parrot]

so you think that would be better than re doing all of Calculus 1?

just remember all the indentities and derivatives and I can do Calc 2

[atomic dome]

If you can do that for all of the trig functions and their integrals

And you know how rates of change work, then yes

[weary parrot]

did you memorize them by just looking at a sheet or was it from Calculus 1 making you use derivatives

and then once you finished Calc 1 you had the deriviatives memorized so it made the integrals easier to memorize

[atomic dome]

I memorised them myself