help-13

[keen merlin]

i dont blame you

for misreading it

0.001 is a typo yea?

[gaunt hamlet]

Either a typo there or there's a typo in the question

[keen merlin]

based on those values, it should be 0.01 tho?

[gaunt hamlet]

Yes

[keen merlin]

thanks bro i really appreciate that

i learnt a thing even though you misread the question 😅

do you have time for one more question?

if possible

.close

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[short blade]

need to compute $$\int_0^\infty xe^{-x^3},dx$$
got it into $\frac{1}{3}\Gamma(\frac{2}{3})$ but don't know where to go from here

[wraith dagger]

maximo

[short blade]

i tried expressing 1/3 in terms of gammas too but got to $$\frac{\Gamma(\frac{2}{3})\Gamma(\frac{4}{3})}{\Gamma(\frac{1}{3})}$$ which i couldn't do anything with

[wraith dagger]

maximo

[hollow portal]

Do you have to approach it a certain way? I may not be able to help but to solve the integral I'd probably set it as a limit and then do like integration by parts

[short blade]

i can do this any way i want, what did you have in mind?

[hollow portal]

So like this

Then use integration by parts to solve the integral, then evaluate the limit

[short blade]

how would you integrate this by parts

[hollow portal]

I just tried it and.. yeah I think it's beyond my current level lol

[short blade]

the integral calculator i used left it as gamma(2/3)/3 lol

i think thats as far as i have to go

[hollow portal]

X would be u, du would be 1, then dv is e^-x^3, and yeah it spits out gamma

[cedar kiln]

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[mint carbon]

https://cdn.discordapp.com/attachments/238956921581862913/1046670495069786132/image.png

[mint carbon]

How do I do this?

calc allowed

/close

.close

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[sterile sierra]

could someone help me with 8b

[grand raft]

sure

[sterile sierra]

um wait

[grand raft]

sry I meant the slope of the line at P

[sterile sierra]

yea

i did

[grand raft]

what is it

[sterile sierra]

y=4x+10

[grand raft]

ok thats right

[sterile sierra]

yea but im not sure how to relate that to part b in order to solve for the coordinates

[grand raft]

well, make the derivative equal 4 and solve for x

[sterile sierra]

why 4

sorry i dont follow

[grand raft]

because that is the slope

and since they are parallel

[sterile sierra]

oh like finding another coordinate with the same slope?

[grand raft]

yep

[sterile sierra]

thats interesting

never thought about it that way

thanks

i have another question if you dont mind

[sterile sierra]

wait i dont think thats it

the coordinate of q is (1,6)

[grand raft]

why not?

no, its (-1,6)

[sterile sierra]

according to the answer key

[sterile sierra]

im talking about Q

[grand raft]

oh

Q is not 1,6

Wait

[grand raft]

thats wrong

its 2x

[sterile sierra]

sorry

so 2x+10 = 2

then x=-4 which is the x coordinate of q?

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[simple hazel]

ignore the ans: -4.066 and 3.545

can someone explain what i did wrong for dy/dt?

[solar vector]

Your equation that you are differentiating at the start was z=(x/2)(y/2)?

But the problem says z=xy/2?

[simple hazel]

oh whoops

[solar vector]

Also the line after you messed up the product rule

[simple hazel]

there’s product rule?

[solar vector]

Yeah for derivatives if f and g are functions of t then (fg)'=fg'+gf'

Where f'=df/dt and g'=dg/dt ofc

[simple hazel]

oh i see

thank you :)

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[prisma gull]

I was trying to understand the geometrical interpretation of the definition of derivative of a vector valued function

the numerator r(t+h)-r(t) is a vector which actually makes sense

but when i treated 1/h as a scalar that scales r(t+h)-r(t) it throws off, because h is tending to zero, so the vector r(t+h)-r(t) is getting infinitely scaled up

can someone help me out with the correct reasoning ?

[sullen saffron]

Well, if r(t) is continuous then as h goes to zero then r(t + h) tends to r(t) so the limit might exist.

[crimson sedge]

Could be any point on a surface from what I know

[cedar kiln]

@prisma gull Has your question been resolved?

[sullen saffron]

Think of the derivative as the limit of the secant (the line segment joining two points on the curve as the two end points get arbitrarily close) then r(t + h) - r(t) = <r_1(t + h) - r(t),r_2(t + h) - r(t), r_3(t + h) - r(t)>.
By the law of the mean,
r(t + h) - r(t) = <r_1(t + θ_1h)h, r_2(t + θ_2 h)h, r_3(t + θ_3 h)h>, for 0 < θ_1, θ_2, θ_3 < 1*
*This representation basically means the input is between t and t + h.
Now divide by n and let h go to zero in
[r(t + h) - r(t)]/h = <r_1(t + θ_1h), r_2(t + θ_2 h), r_3(t + θ_3 h)> = <r_1(t), r_2(t), r_3(t)>.
This assume r_i ∈ C^1, i = 1, 2, 3 (continuously differentiable).

This shows the blowing up of 1/h as h goes to zero doesn't necessarily mean the limit won't exist as it cancels out.

[crimson sedge]

Simply put you take the derivative of the function for each vector component

[prisma gull]

let me comprehend

[sullen saffron]

x is a vector in the image, the parameter here is chosen so that it is also the arc length from a arbitrary starting point but doesn't change things for your purposes.

[crimson sedge]

$r^'(t)\ =\ <f'(t)i^\rightarrow,g'(t)j^\rightarrow,h'(t)k^\rightarrow>$

[wraith dagger]

[Master Chief [117]]
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[crimson sedge]

for a given function the prime or derivative at each point is the functions derivative times it's unit vector

[sullen saffron]

Think of the derivative, r'(t), as the vector with start point at r(t) and end point at r(t + h), then as long as you divide by any positive number, h > 0, it will point in the same direction.

[crimson sedge]

Which is the vector field tangent to a curve. Only with 3D vectors you've got a vector field.

[sullen saffron]

I have no idea where you're getting vector fields from.

This text delves into arc length s but can exclude that.

[cedar kiln]

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[crimson sedge]

https://www.youtube.com/watch?v=6OzkQYJiNQE

[cedar kiln]

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[crimson sedge]

If you take a point over the curve you get a 2D vector field

[prisma gull]

so essentially using our classical first principle inside each components of the vector ?

[crimson sedge]

There are some "rules" that are different

https://tutorial.math.lamar.edu/Classes/CalcIII/VectorFcnsCalculus.aspx

[prisma gull]

each components of a vector can be treated as a scalar so the first principle seems to work there

[crimson sedge]

And partial derivatives are just holding certain values constant and ignoring them.

[sullen saffron]

Yes. 🙂

[crimson sedge]

Very simple @prisma gull

[prisma gull]

so the nuances of going to infinity or going zero will be taken care classic first principle

i mean there will be factors which will cancel and the limit approaches to a solid value

[sullen saffron]

Of course, the components of vectors can be added.

[prisma gull]

it makes more sense now

[sage sail]

is it just me or im just very bad at maths

[prisma gull]

thinking it as an extension from first principle

[crimson sedge]

And you will have constraints on allowed values just like derivatives

e.g h != 0

[sage sail]

dude can you teach me some tips

[crimson sedge]

I'm self taught.

[sage sail]

oh

[sage sail]

i cant do grade 6 math when in grade8

[crimson sedge]

I honestly only started most of this year, before that I couldn't even add fractions together.

[sage sail]

dude me to

[sage sail]

then how did you over come that

[prisma gull]

i can relate

[sage sail]

you study harder

[crimson sedge]

I'm Autistic most of this just meshed with my head really easily..

[sage sail]

or

[crimson sedge]

Study harder isn't the right word.

You need to distil what you learn down into something that is universal mostly and condensed.

Combination of textbooks, videos, and resources.

Studying harder and doing questions again and again rote yeah ain't going to work @sage sail

Rote learning never works if you just mindlessly apply what you are told.

[copper crest]

What chapter is thus

[cedar kiln]

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[sterile sierra]

@grand raft

[sterile sierra]

?

[cedar kiln]

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[edgy hornet]

need help asap please?

[edgy hornet]

?

is that right

[tropic oxide]

,calc (1/2)/(3/4) - (3/4)/(1/2) - (-5/6)

[wraith dagger]

Result:

0

[tropic oxide]

yup

[edgy hornet]

oh it's you again

thanks

can i ask for another question

[cedar kiln]

@edgy hornet Has your question been resolved?

[tropic oxide]

@edgy hornet

also i see you opened a new channel so

.close

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[edgy hornet]

oh sorry for not closing

[cedar kiln]

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[crimson sedge]

How did they convert it?

[livid hound]

divide numerator and denom by cos(x/2)

[crimson sedge]

K now I got it thx

.close

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[crimson sedge]

.reopen

[cedar kiln]

✅

[crimson sedge]

One more I cant understand how they converted the marked part

[livid hound]

1 = tan(pi/4)

and then compound angle identity for tan

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

i can't get it by compound angle identity for tan...

[cedar kiln]

@crimson sedge Has your question been resolved?

[stark karma]

Use tan(A+B)= (tanA+tanB)/(1-tanA.tanB)
Keep A=pi/4 and B=x/2

[crimson sedge]

but iam getting something like this

@stark karma

[stark karma]

Tan(pi/4) = 1

Value of tan(pi/4) is 1
Then you will get the same expression as what they converted

[crimson sedge]

instead of 1 i added tan(pi/4) then i got this

[stark karma]

Denominator can be written in another way

1 - tan(pi/4)*tan(x/2)

Because tan(pi/4) is 1

[crimson sedge]

ok

thx buddy

[stark karma]

You’re welcome

[crimson sedge]

.close

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[halcyon orbit]

How to prove ?

[wraith dagger]

Arian

Arian

[halcyon orbit]

That's hints writen in the book, but I can't prove it

[cedar kiln]

@halcyon orbit Has your question been resolved?

[halcyon orbit]

<@&286206848099549185>

[dire geode]

what do you mean you can't prove it. did you calculate the two terms?

[cedar kiln]

@halcyon orbit Has your question been resolved?

[halcyon orbit]

I did, but I can't find any relation with them

[cedar kiln]

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[cedar kiln]

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[glad slate]

Hi, I'm kinda confused why this step is needed/how it works. Thanks in advance!

[south tundra]

5^2 + 5^4 = 5^2 + 5^(2 + 2) = 5^2 + 5^2 * 5^2 = 5^2(1 + 5^2)

It's helpful because some of the 5's cancel out after this step as you can see

[glad slate]

This is probably a dumb question, but I dont understand where the 1 comes from

[south tundra]

5^2/5^2 = 1

We factored the 5^2 out

[glad slate]

Ohhhhh, thank you!

.close

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[muted elk]

What am I missing

[dire geode]

probably just simplification

[muted elk]

okay

thanks

.close

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[raw kernel]

what do i write there?

[raw kernel]

honesty have never thought why it accelerates instead of going to the desired speed instantly when the energy input to the bicycle is the same

[granite wyvern]

Friction has an upper limit. \mu_s mg

So maximum acceleration is \mu_s g

[raw kernel]

whats \mu_s g??

[granite wyvern]

g is acceleration due to gravity

And \mu_s is coefficient of static friction

[granite wyvern]

What are forces A and B?
There should be context before this

[raw kernel]

i think air res and friction

not sure if im right

[violet night]

nice

[granite wyvern]

Aight

That should be correct

[raw kernel]

alr ty

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[celest otter]

Is there a way to do this problem without checking every possible matrix?

[celest otter]

I found the answer through brute forcing every possible matrix, but i want to know if there is a way to do it inductively.

Heres the answer:

3/512 is the probability

If possible.

[crimson sedge]

$\textup{det}\left(M\right)=a_{11}(a_{22}a_{33}-a_{23}a_{32})-a_{12}(a_{21}a_{33}-a_{23}a_{32})+a_{13}(a_{21}a_{32}-a_{22}a_{32})$.

[dire geode]

you just maximize each component in the expansion

[wraith dagger]

3317

[crimson sedge]

With that in mind, just find what will maximise the result.

[celest otter]

oh ok

lemme try that

[crimson sedge]

With 3 options, there's $3^9=19683$ different matrices to test.

[wraith dagger]

3317

[crimson sedge]

Quite heavy.

[celest otter]

yes

i already found the anser to that too

There are 240 possible matrices that have a determinant of 4, however I am not sure how to find them using your method from above.

I made a program to just test all the matrices given some parameters: size, and # of possible values. And then it gives me the determinants

[crimson sedge]

Think about them. They're all in the format $a(bc-de)$.

[wraith dagger]

3317

[crimson sedge]

Then, $a$ cannot be either $0$ or $-1$, else it would be null or negative.

[wraith dagger]

3317

[celest otter]

o

ok

[crimson sedge]

You're subtracting from $bc$, so neither $b$ nor $c$ can be either $0$ or $-1$.

[wraith dagger]

3317

[crimson sedge]

And if it's $1$, then either $d$ or $e$, or both must be $0$.

[wraith dagger]

3317

[crimson sedge]

But you can maximise even more if $d=1$ and $e=-1$ or the inverse. Then you'll have $1(1\cdot1-(-1\cdot1))$.

Then you'll have $2$ in the end.

Oh, wait, my bad.

I'm wrong.

But the line of thinking goes like that.

[celest otter]

yes thanks

i see what you are getting at

[cedar kiln]

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[valid bluff]

Can anyone tell me how I can quickly find exponential forms like in here?

[valid bluff]

How am I supposed to know that 810000 equals 30^4

[crystal raptor]

By knowing powers of 3

Or even just that 9²=81

[valid bluff]

How does that make sense

Could you elaborate a bit more

[crystal raptor]

Well what's 81 as a power of 3

[valid bluff]

What's a power of 3😭

Sorry I'm learning math in a different language

[crystal raptor]

Exponent

Index

3 to the what equals 81

[valid bluff]

So its what, 531441?

[crystal raptor]

What

[valid bluff]

☹️ 81^3

Man☹️

I just wanna know how to find big number in a form of exponents

[crystal raptor]

3^(what) = 81?

[valid bluff]

oo

4.32..

[crystal raptor]

??

Are you just guessing?

[crimson sedge]

,calc 81^(1/3)

[wraith dagger]

Result:

4.3267487109222

[valid bluff]

Yeah this

[crystal raptor]

Lol

Calculate some powers of 3

I'm not asking for the cube root of 81

[valid bluff]

Man

https://tenor.com/view/sad-depressed-depression-thor-chris-hemsworth-gif-22395141

[cedar kiln]

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[cedar kiln]

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[ember halo]

Among 58 people at least how many were born in the same month?

[ember halo]

I have no idea how to start to solve it

[gleaming umbra]

Not sure i understand correctly. But wouldnt it just be zero? Since no one HAS to be born in a specific month

[crystal raptor]

But there are not 58 months

[gleaming umbra]

True, i read it wrong

[ember halo]

I have no idea, I know it needs combination or permutation

<@&286206848099549185>

Seriously?

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[ember halo]

Thanks for nothing

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[keen merlin]

can anyone help me figure out this boolean for this system?

this is what i got but im not sure if its right

please if anyone can help it would clarify a lot for me in this assignment

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✅

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[dense frigate]

why is the bottom incorrect?

[dire geode]

your answer should include c=6

[dense frigate]

so I replace x with x-6?

[dire geode]

no. use the formula for interval of convergence

well maybe. write it out

[dense frigate]

oh, makes sense

thanks

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[bronze pivot]

Why did it become 2 only instead of 2sqrt(x)?

[dire geode]

definitely a typo

yea that's embarrassing

[royal hinge]

chad eminem enjoyer vs noob math

[bronze pivot]

I don't know what to do next after secu du

can I please ask for help on what to do next after getting integral of sec u du

here is what I have done so far

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[blissful moon]

if both amplitude and the "b" in period are negative, is their graph positive?

[blissful moon]

such as -2cos(-x/2)

[chrome zinc]

amplitude is always positive

the "b" being negative just means it's a reflection

[cedar kiln]

@blissful moon Has your question been resolved?

[blissful moon]

so is my graph wrong or right?

[chrome zinc]

looks good

though i will say that you should start trying label the x axis in terms of π

instead of degrees

if you have learned that yet

but that's nitpicking

the graph itself is right

[blissful moon]

oh oki, thx!

and our teacher said to write it in degrees so yeah

[chrome zinc]

yeah then it's good

[blissful moon]

Oh oki thx!

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[crimson sedge]

i need to solve for x

i got this for an answer but my teacher said its wrong

[sleek condor]

what is the log base i cant read

[crimson sedge]

8

[sleek condor]

ok

[rain drift]

just to make this more readable, is that $4x^{log_8(x)}$?

[wraith dagger]

MellowDramaLlama

[chrome zinc]

i want to say*

[rain drift]

ah okay

[chrome zinc]

this is right

[crimson sedge]

yes

[chrome zinc]

yeah that's def right

[crimson sedge]

is x^4

this is all my work

$4x^{log_8x}=x^4$

[wraith dagger]

Caleb.

[crimson sedge]

i needed to find the product of the positive roots

[chrome zinc]

$log_84$

[wraith dagger]

Scarecrow

[chrome zinc]

why did u get 3/2?

[crimson sedge]

oh

prob thought it was log_4(8)

or just wrote the wrong number

ty

[chrome zinc]

yeah that's the only thing

i found that's off

[crimson sedge]

just to confirm all the work is right?

aside from that

[chrome zinc]

everything else looks good

yeah

[crimson sedge]

i can just copy the work and write 2/3 instead?

[chrome zinc]

yeah, should be the exact same thing just replace it with 2/3

[crimson sedge]

my teacher wants me to correct the test question

alright thank you

[chrome zinc]

np

[crimson sedge]

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[merry tinsel]

could someone

[merry tinsel]

help

a=pir^2

idk what to d

nexy

[quartz frost]

we have a max error of 2%

we can write this as:
A=A0 * 1.02

lets call p=1.02

A=A0 * p

A=pi r^2

[merry tinsel]

1.02?

where did that come from

[quartz frost]

100%+2%=1.02

[merry tinsel]

ok

now what

[quartz frost]

A=A
pi r^2=A0 p

[merry tinsel]

ye

[quartz frost]

r=sqrt(A0 p/pi)

[merry tinsel]

ok

[quartz frost]

hmm, okay im not sure

i thought this would be straight forward but now im confused as well

[merry tinsel]

this is the solution

i just need help understanding it

@quartz frost

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[crimson sedge]

oops sorry

[golden raven]

.close

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[twin tinsel]

my brain is melting and i need to get this done as soon as possible. i know how. but im to fatigued to do anything

[dull oxide]

have you found the first and second derivatives?

[twin tinsel]

yes

sorry for the late responce

.clos

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[fair magnet]

i said profit = 30+x and quantity = 200 -5x so therefore revenue is -5x^2+185x+6000
which if you take the first derivative and solve you get x=18.5
but im unsure where i go from here

[twin tinsel]

mmmmm desmos graph it only look at whole numbers

:D

[fair magnet]

that helps me solve this

not learn how to actually do it

okay whatever i figured it out by myself.

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[manic mountain]

For this questions, what is the greatest product that can be made from two numbers that add up to ten, I saw the following way of solving it, but I can't seem to explain why For the greatest value, 10-2x=0, can someone explain it to me?

[vital creek]

yeah

[manic mountain]

yeah

[bright agate]

yeah

lol

[manic mountain]

no please I'm desperate

I have an assingment about this and it's due midnight today

help a homie out

[bright agate]

do we need to find maxima

[manic mountain]

yes

[bright agate]

its correct

at 5

[manic mountain]

yes I know

I know

but why does it have to equal 0

very funny

[dull oxide]

you set your derivate to 0, and that solution will give you a critical point.

[manic mountain]

OH THE critical point which is the vertex of the parabola

right?

[dull oxide]

If you want to prove that the critical point is a local min, max, or inflection point, you need to do the second derivative test.

[dull oxide]

Yes. That would be the "first derivative test"

[manic mountain]

what would the second be like?

[dull oxide]

take the derivate of the derivate, f''(x)

Then just evaluate the result.

[manic mountain]

if it's negative the parabola opens down?

[dull oxide]

If positive, then the function is increasing, so the inflection point is a minimum

If f''(x)<0, then the function is decreasing, so the inflection point is a max.

And if f''(x)=0, then the function is neither increasing or decreasing.

This critical point would be called an inflection point

[manic mountain]

wait so the derivative of 10-2n would be 0-2=-2?

so it would be the maxima

thanks

[dull oxide]

exactly right

100%

[cedar kiln]

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[manic mountain]

thanks

[cedar kiln]

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[dreamy tapir]

i dont really get how you're supposed to get an answer in radical form

[hushed spoke]

$\sqrt{72} = 36\sqrt{2}$

[flint plinth]

by leaving sqrt(72) as is, instead of replacing it with a decimal approximation?

[wraith dagger]

Deol

[hybrid glade]

This is wrong

[bright agate]

its $6\sqrt{2}$

[wraith dagger]

ayushch80

[dreamy tapir]

???

the answer is $4\sqrt{6}$

[wraith dagger]

sharter

[bright agate]

its the length of common side

$tan(\frac{\pi}{3})=\sqrt{3}$

[wraith dagger]

ayushch80

ayushch80

ayushch80

[bright agate]

(hypotenuse)^2 = (perpendicular)^2 + (base)^2

[wraith dagger]

ayushch80

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[crimson sedge]

Guys i dont exactly understand cross product and dot product

[crimson sedge]

What can i do

I watched videos i got idea but i still dont know why it works

[crystal raptor]

https://gregorygundersen.com/blog/2018/06/26/dot-product/#:~:text=The dot product as a projection&text=It is a transformation of,N (or vice versa).

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[crimson sedge]

Thanks

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[nova snow]

what am i suppose to sub in?

does 2f(-1) want me to replace all x's

if so then what does g want me to do?

[vast acorn]

that is tricky

dont take my advice but i think that means double the value of f(x) but negative minus the value of g(x) but negative?

[winged thicket]

it's equal to :
[2*f(-1)] - [g(-1)]

so u just need to do f(-1) and g(-1)

[nova snow]

but do i replace with x

[winged thicket]

yeah

[nova snow]

so i dont need to do f and g both because they both equate to the same values of -1?

[tropic oxide]

you are supposed to calculate f(-1), and you are supposed to calculate g(-1), and you are supposed to multiply one of these by 2 and subtract the other from it.

to calculate f(-1), you replace all x's in the formula for f with (-1) and do the arithmetic.

to calculate g(-1), you replace all x's in the formula for g with (-1) and do the arithmetic.

@nova snow

[nova snow]

So i should still write down both even though they have -1

Alright

[winged thicket]

yeah

u need an example ?

[tropic oxide]

you should

(a) not overthink things

(b) not try to do things at once

if you want to be instructed as to what to write down

for a first step, evaluate f(-1) and write down all of your steps and then show them here.

and ping me

[nova snow]

okay

3(-1)^2 - 8(-1) + 4 = -2(-1)^2 + 7(-1) + 1

@tropic oxide

[tropic oxide]

no. bad.

you did not do what i asked you.

[nova snow]

I replaced x's with -1

[tropic oxide]

you did not do what i asked you.

you did not

evaluate f(-1) and write down all of your steps

[nova snow]

is that not evaluating?

[tropic oxide]

no.

i am asking you to find the value of f(-1).

at this point, g isn't involved yet. it is at the moment incorrect to involve g. we will get to g later. we will not touch g right now.

you should write
f(-1) = 3(-1)^2 - 8(-1) + 4
f(-1) = ...

where the dot-dot-dot is the result of your arithmetic as you normally would

[nova snow]

Ok.

so that equals to -1

[tropic oxide]

does it?

[nova snow]

f(-1) = -1

yes

[tropic oxide]

show your steps!!

[nova snow]

I put it into the calculator

[tropic oxide]

take a photo of your exact input into the calculator.

because i do not think 3 * 1 - 8 * (-1) + 4 equals -1.

i think you screwed up when entering this into the calculator.

[nova snow]

you want the top equation right

[tropic oxide]

??

[nova snow]

Ok

i did mess up

i didnt put (-1) next to the 8

its 15

[tropic oxide]

ok, great, so we have f(-1) = 15.

write this down somewhere that you will remember. we will need this later.

ping me when you have done so, and tell me that you have written it down.

[nova snow]

I have written f(-1)=15 down on the paper

[tropic oxide]

ok, good.

now, find the value of g(-1).

in the exact same way as you did for f(-1).

show me all your steps.

[nova snow]

-2(-1)^2 + 7(-1) + 1 = -8

g(-1) = -8

[tropic oxide]

ok

good

now

you have the values of f(-1) and g(-1)

evaluate the expression 2 * f(-1) - g(-1)

again show all your steps.

[nova snow]

how would this look into the equation? im not quite sure where to add the 2x

just at the front?

[tropic oxide]

what 2x?

you are overthinking it.

[nova snow]

multiplied by 2

[tropic oxide]

you are overthinking it.

[nova snow]

2* -2(-1)^2 + 7(-1) + 1

?

[tropic oxide]

no, you're overthinking it.

[nova snow]

like that

[tropic oxide]

you have already calculated f(-1).

[nova snow]

ohhh

30?

for f(-1)

or rather

2f

[tropic oxide]

f(-1) is 15.

2f(-1), accordingly, is 2*15.

[nova snow]

and that becomes 30, and so 2g would be the same?

it becomes -16?

oh

30 - 8?

[tropic oxide]

g(-1) is not being multiplied by 2.

no.

g(-1) is -8 and it is being subtracted.

f(-1) = 15
g(-1) = -8
[this is something you SHOULD HAVE READY]

so 2 * f(-1) - g(-1) = 2 * 15 - (-8)

this is a matter of plugging things in without overthinking.

[nova snow]

38

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[ember plaza]

I have M ={1 , 2 , 3, 4}. What does this statement mean?

[ember plaza]

Every linear list where |a| is >= 3 and |a| is <= 14?

[elfin hemlock]

assuming you mean M* then yes

[cedar kiln]

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[vapid lotus]

Can you get to quaternions using only natural numbers?

[vapid lotus]

You can get to imaginary numbers

[red pumice]

yes

[vapid lotus]

How?

What’s the equation

[red pumice]

cayley dickson

[vapid lotus]

??????????

[red pumice]

the cayley dickson construction lets you construct the complex numbers, quaternions, octonions and sedenions from just the reals

and you can get the reals from just naturals

[vapid lotus]

How does it “use” the reals?

[red pumice]

https://en.wikipedia.org/wiki/Cayley–Dickson_construction

[vapid lotus]

That doesn’t explain how it “uses” the reals

There is no x+y=z

or x^y=z

Or anything

If anything it just changes definitions

[cedar kiln]

@vapid lotus Has your question been resolved?

[vapid lotus]

<@&286206848099549185>

[cedar kiln]

@vapid lotus Has your question been resolved?

[cedar kiln]

@vapid lotus Has your question been resolved?

[twin tinsel]

idk anything about this but they did give you a name, so try looking it up

[vapid lotus]

Bruh

[cedar kiln]

@vapid lotus Has your question been resolved?

[vapid lotus]

No it hasn’t

But since no one is helping

.close

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[tribal phoenix]

hello

[tribal phoenix]

i need help with something that google translate translated me to the principle of mathematical induction

sorry if this is some easy stuff but i cant really understand it

[tepid lodge]

You need to prove P(n) is true for every case of n

[tribal phoenix]

and how do i do that...?

[tepid lodge]

P(n): n+n+n=n(n+1)/2

Do you have a specific problem that you need help with, where you need to use induction?

[tribal phoenix]

so i just did this in school, my teacher sucks and i tried to understand it better

[tepid lodge]

It's not something I really ever use, but here goes, you use it to prove the statement P(n) is true

[tribal phoenix]

and there is something with p(k) and p(k+1 ) and then some things to show the equality and stuff

[tepid lodge]

So P(0)=0
0=0(0+1)/2

Then the statement is correct

Well P(k) is the same

If P(k)=true then P(k+1)=true

[tribal phoenix]

so there is a thing that uses this induction thing and it uses a symbol called sigma if i remember

that is the thing i acctualy wanted to understand how to use

[tepid lodge]

A sigma notation means the sum of everything

Sigma_n=1^4 would be the sum of n1 n2 n3 and n4

Written like this

example if you are doing P(n) 0+1+2+3+4+5+6+7+8+9

You can write it as such

[terse pine]

Do you know any programming?

[tribal phoenix]

not really

ty a lot NotZaj

[tepid lodge]

np I hope it helped

But I'm curious what grade are you at?

[tribal phoenix]

9

[tepid lodge]

Usually you don't get introduced to sigma notations and induction till highschool

[tribal phoenix]

i mean thats what number it is in my country

[tepid lodge]

Late highschool

You have gymnasiums then?

[tribal phoenix]

yes im into a math profile as its called here

like

[tepid lodge]

Usually you wouldn't see this till mat B or mat A in gymnasium

[tribal phoenix]

i finished 10 years of school

cause we start from grade 0

and go till 12

and im at 9

first goes from 0-4

then 5-8

and then 9-12

[tepid lodge]

I'm surprised you are being introduced to this already then

[tribal phoenix]

i dont really understand it but i try my best

[tepid lodge]

You gotta tell your teach this, and to go more in debts with it

It's his job XD

[tribal phoenix]

i acctuly go after school to his after classes and i pay for it

and i still dont understand

[tepid lodge]

Oh my

@terse pineWhat do you think of this?

Anyway I hoped my explanation of induction made some sense, but as I said it's not something I ever use

[tribal phoenix]

thank so so so much for even taking a look over my dumb question.

it acctualy helped me

tysm for your time i wasted

[tepid lodge]

dw

The thing about math is, trying to explain it to someone who doesn't understand, makes you learn it better aswell

[terse pine]

I am out of the loop, think of what, the grade?

[tepid lodge]

A teacher taking payment for extra lessons and still not explaining in an understandable way

[terse pine]

Well i think that Stock should try to find a new teacher if that problem remains..

[tribal phoenix]

that doesnt really work in my country

cause you have to stuck with that teacher for 4 years staright

and if you go to another teacher after school

you are gonna get targeted

[terse pine]

Math is pure understanding in my book. I did my degree in engineering with minimal memorization. Math, and all other logical subjects are nice as you can understand what the answer should be in a logical way, hence you don't really need to memorize everything. I know the memorizing thing works for many people, but not for me. So if you struggle with that yourself, i suggest you really sit down with each problem until you understand how each part works. This is why i asked about programming, as programming math problems is a great way to understand it, because you have to break it up in small parts when you write it as code. IF your teacher can't help you understand, you should check out lessons on the internet, there are many great resources for this, for free! Like khan achademy and 3blue1brown. No point wasting money on it if its no help.

[tribal phoenix]

whtwl, this actually is really helpful i will surely check out khan achademy and 3blue1brown. tysm, and hope you have a great day/night. and ima try to do programming problems too cause i want to do programming in the future.

[tepid lodge]

I agree with this, I have an understand of almost all subjects, but I don't have them memorized, but I have a general idea of where to find the information if I need to solve somthing I don't often work with

Memorizing how to do everything isn't really needed, more an understanding the basis they work upon

[tribal phoenix]

i usually try to do that more than memorizing

cause memorizing problems is gonna be for a short period of time

and you will forget that

the logical thinking part is the key

from what i can understand

[terse pine]

Yep ⭐ Also, math is really fun when you get into the understanding part of it. It is a joy to solve a problem.

[tribal phoenix]

i should try

[tepid lodge]

I'm a business engineer

[terse pine]

Yep!

[tepid lodge]

I'm the soft math path

Well not "soft" just not like traditional math

[tribal phoenix]

btw i want to warn you guys about other stock manns, there are 3-4 more which only 1 more of us acctualy cares about this server. we acctualy got here through a raid but some wish to stay here peacefully.

some other guys would maybe try to troll you but i want you guys to know im not contributing in that

[terse pine]

Cool! Computer Engineer myself. So you can say that is soft as well compared to mech and electrical. I only took calc1, calc2, calc3/multivariable calculus and analysis + physics, as the pure mathematical subjects in school. No fluid for me.

[tepid lodge]

I'm just doing applied mathematics atm, mostly stat and probability tho

[terse pine]

I see, i'm not a big fan of statistics and probability notation on paper but i love machine learning so i guess im stuck with that lol.

[tepid lodge]

Me neither, but I'm a supplychain/production optimization engineer

We kinda just do a little bit of everything XD

[terse pine]

hehe its good to have variations in the day to day life! g2g sleep, work in the morning, cya.

[cedar kiln]

@tribal phoenix Has your question been resolved?

[cedar kiln]

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• Show your work, and if possible, explain where you are stuck.
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[light pine]

for part b ive tried doing the epsilon - N proof

i started this but obv its wrong

since u cant use infinity like that

<@&286206848099549185>

[cedar kiln]

@light pine Has your question been resolved?

[inland fossil]

have you gone over bounded sequences yet

you can use the fact that -e^n is unbounded => not convergent

oh wait no sorry looks like u have to use epsilon proof

im assuming you cant use cauchy sequences either

[cedar kiln]

@light pine Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cedar kiln]

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.

[crimson sedge]

How would this be solved?

[crimson sedge]

Geometry ^^

[gusty vine]

If a line is perpendicular to another line

You can use m1m2=-1 and find the grad

Then use the (-3,10)

[crimson sedge]

So then would it be this equation?

Y-4 = 3(x-2)

[gusty vine]

Where did you get 4 and 2

And 3

okie wait

you are given an eqn in ur qn right

what’s the gradient there

[crimson sedge]

Wait that’s the wrong question

Lemme retype

I thought I sent a differ question

Y-10 = -3(x-3/4)

[gusty vine]

oh

what’s the question?

[crimson sedge]

Is that right?

That equation

[crimson sedge]

For this

Y-10 = -3(x-3/4)

Then I distribute the -3, then add 10 to both sides

[gusty vine]

for which qn?

you said you sent the wrong qn

[crimson sedge]

Yea but I realized that I still kinda need help on it

[gusty vine]

ohh okie

[crimson sedge]

This image

[gusty vine]

yeah it’s not right

why is m=-3?

okie so

u see the eqn of a line given in ur qn

what’s the gradient of that line

[crimson sedge]

What do you mean by gradient

[gusty vine]

Like m

The slope

[crimson sedge]

Isn’t 2x

The slope

[gusty vine]

Haha I learnt it as gradient

[gusty vine]

Slope shouldn’t have an x in it

And no it’s not 2

do u see the y=3/4 x -5/4 in your question

what’s the slope of this line

[crimson sedge]

I loooled at the wrong equation w

Again

Looked

Slope@is@3/4

[gusty vine]

yepp

so if a line is perpendicular to this

what would be its slope

using m1m2=-1

[crimson sedge]

Uh

Well if it’s perpendicular it wouldn’t have the same slope as If it were parallel.

But uh

[gusty vine]

yeah

goood

[crimson sedge]

Would it be 3-2

[gusty vine]

okie no but

here

so m1 •m2 =-1 is a formula u can use

to find the slope of a line that’s perpendicular to another line

but let me jst teach you a faster way

[crimson sedge]

Ok

[gusty vine]

so the slope for the line in ur qn is 3/4 right

[crimson sedge]

Yea

[gusty vine]

so for a line perpendicular

1. flip the fraction
2. add a negative to the front

[crimson sedge]

Reciprocal

[gusty vine]

and that’s the slope of the perpendicular line

yep

so what’s the slope of the perpendicular line

[crimson sedge]

-4/3

[gusty vine]

yep

[crimson sedge]

Then what do i do with the reciprocal and the rest of the equation?

[gusty vine]

so now use y-y1 = m(x-x1)

you know m is -4/3

and the line passes through (3,-10)

so y1= 10 and x1=-3

plug everything in and simplify

[crimson sedge]

So it would be

Y-10 = -4/3 (x - 3).

Then distribute

[gusty vine]

oop be careful tho

[crimson sedge]

Then you have -4/3 x 3/1 then you have to get to common demoniac or so it would be 9/3

[gusty vine]

remember x1 is -3

[crimson sedge]

Ohh

[gusty vine]

so it’s y-10= -4/3 (x-(-3))

but yeah afterwards you just distribute

[crimson sedge]

So then it becomes positive right

[gusty vine]

yep

[crimson sedge]

So then

4/3 x 3/1

Common demonitor right

And whatever you do to the bottom

You do to the top

So 3x 3x

9/3

Simplified into 3

So y-10 = -4/3 - 3

Then you add 10 on both sides

7

So

Y = -4/3 + 7

[gusty vine]

okay so

you had y-10= -4/3 (x+3) yesh

distribute

and you get

y-10 = -4/3 x + 3(-4/3)

what is 3• -4/3

[crimson sedge]

36/3

So 12?

[gusty vine]

no

why 36?

[crimson sedge]

You dont do common denominator?

[gusty vine]

it’s multiplication

[crimson sedge]

Oh

So then

[gusty vine]

yaya

[crimson sedge]

It would just be

-12/3

[gusty vine]

yepp

which is

[crimson sedge]

-4

[gusty vine]

yep

y-10= -4/3 x -4

+10 both sides

[crimson sedge]

Becomes 6

[gusty vine]

and that’s all yaya

[crimson sedge]

So y=-4/3 + 6

[gusty vine]

if no careless

then yepp

[gusty vine]

don’t forget the x

[crimson sedge]

OHHH

Right

I knew that

Im still a little confused on how you would set up the equation in the beginning.

[gusty vine]

oh okay so

[crimson sedge]

I know the y-y1 = _(x - x1)

Just how to know where y, and y1 and x and x1 are

[gusty vine]

thought process

1. qn said perpendicular so I can immediately find the slope of the perp line using the reciprocal and adding a negative sign

2. qn said the line passes through (-3,10) and since I also know the slope, I can use y-y1=m(x-x1)

[crimson sedge]

It says it’s wrong

Omg

I forgot to put X

LOL

Ok that makes sense

Can I post another one but then I do it and could you tell me if it’s right or not?

[gusty vine]

HAHAHA I KNEW IT

[gusty vine]

yayaya okie

[crimson sedge]

Ok imma solve it now

Y - 4 = -1/2 (x - 3)

Add 4 on both sides

[gusty vine]

okie let’s take it slow

let’s slowly read each and every word

[crimson sedge]

OH

ITS PARALLEL

[gusty vine]

yeah

HAHAHA

[crimson sedge]

So its same slope

[gusty vine]

yepp

[crimson sedge]

So then slope has to be 2

So then

It would just be

Y - 4 = 2 (x-3)?

Add 4 on both sides

4 + -3 = 1

Y = 2x + 1

Wait no that’s wrong

UGHH

[gusty vine]

this is good

distribute

[crimson sedge]

im

Dumb

[gusty vine]

issokiii HAHA

I’m dumb too

you have a habit of forgetting the x

[crimson sedge]

Shhhh

We dont talk abt that

Ok so 2 x x

Becomes