help-0

[oak chasm]

@wispy olive Sorry, this channel is busy.

[wispy olive]

I do not have any question, and sorry for interrupting.

[oak chasm]

@unkempt umbra Well, you can write that if the metric space is ℝ, then .... If the metric space is ℚ, then .... If the metric space is ℤ, then ....

Or something like that.

[odd drift]

How do you divide fraction?

[oak chasm]

@odd drift Sorry, this channel is busy.

[odd drift]

: (

[oak chasm]

Try #help-8.

[gentle prism]

can someone help with question 20 and 21

[oak chasm]

@gentle prism Sorry, this channel is busy.

[gentle prism]

ok

[unkempt umbra]

ok, so let's say that i take the metric space as R
how do I formulate this?
would it be correct if I said this?

no not that

this

but there exists is crossed

forgot to cross it

because it does not exist

[pastel wyvern]

Pls help me

[oak chasm]

@pastel wyvern Sorry, this channel is busy.

[quaint rock]

Find the next number in the series?
2, A, 9, B, 6, C, B, D, ?
(A) 9 (B) 10
(C) 12 (D) 19

[oak chasm]

@quaint rock Sorry, this channel is busy.

@unkempt umbra Are you proving it?

[unkempt umbra]

i'm not proving, but i have to illustrate how I came to the conclusion that a certain set is/is not a neighbourhood

i don't think it has to be as rigurous as proof

[oak chasm]

@austere elk Sorry, this channel is busy.

[austere elk]

aight

[oak chasm]

Oh, then you can say that if r is rational, then -1 + r/π is in B(-1, r). Since π is irrational, then -1 + r/π is irrational and is not a member of ℚ. If r is irrational, then -1 + r/2 is in B(-1, r). Since r is irrational, -1 + r/2 is irrational and is not a member of ℚ. In all cases, a member of B(-1, r) is not in ℚ.

Since ℤ ⊆ ℚ, that applies to ℤ as well.

[vague coral]

how do you write in maths without latex ?

[unkempt umbra]

this is pretty much what i was looking for

it think it could count as actual proof as well, right?

[oak chasm]

Yes, I think so.

[oak chasm]

Get the Unicode symbols from Wikipedia or something and get a program that will replace you typing \\in (doubled \\ so that you can still type LaTeX without it replacing) with ∈ or something.

[crisp grove]

simplex is just one method

obviously it can be solved

[vagrant rover]

is 1/5 km/liter equal to 5/1 liter/km?

it is right?

[oak chasm]

@vagrant rover No, one's a reciprocal of the other. They're only equal if 1 km = 5 liters in your problem.

[crisp grove]

for all b?

like for all b in R^m?

[silk terrace]

so the question is written really weirdly imo. It states that;

[crisp grove]

holds for all b means F(b) must be constant

btw

[silk terrace]

for all b_1,b_2 in R^m, lambda in [0,1]. Show the general result

[silk terrace]

But what is it that I have to show as the hint doesn't resonate with me.

[crisp grove]

it that the whole question btw?

[silk terrace]

Assume that F(b) is optimal for all b. Then it holds that f(b) is convex in b

Show the general result

[crisp grove]

still don't get your question :/

what's b? Ax=b?

this b?

[silk terrace]

yes

[crisp grove]

then there's only one b :/

[silk terrace]

f(b) denotes the optimal value of a linear program

[crisp grove]

or no matter what b we choose

[silk terrace]

P(b) is F(b).

[crisp grove]

confusing as hell... which b is which? which b is the variable and which one is the constant??

can you please post the whole question? like from the book/paper

[silk terrace]

its in swedish so give me a second. The question is weirdly written that is why I am currently stuck haha. Hold on

[pastel wyvern]

Pls help me

[crisp grove]

just got back

and also I don't think I understand the question correctly, so, no

[twilit relic]

Hi, I'm just going over already submitted test questions that I bombed yesterday. This was my 2nd attempt at it. Still doesn't feel right. Can anyone help me identify where my thinking went wrong?

[alpine sable]

any math tutors can help me? Can pay money I have a test tomorrow I really need help please dm me if you can. :)

[turbid anchor]

top: arrange teachers and students; bottom: students in a group are not ordered so divide by number of arrangements. this is multichoose (do google that) if i'm not mistaken.

[twilit relic]

Alright thanks! Gonna do investigating in multi choose right now!

[turbid anchor]

the basic idea is: decouple teach assignment with student assignment, then imagine lining up students in a row, take first 3 in first group (one is teacher), next 4 in second group, last 5 in last group and shuffle them (the denominator)

[twilit relic]

Your formula is (or looks like) permutations with identical elements. Is this the same idea as what you've said? (Sorry, my mind is a little slow today)

As in treat it like permutations with identical elements

This was also what I submitted

I had no clue what I was really doing as I was really burned out 😅

[turbid anchor]

i could be wrong, that's what i believe currently. i haven't heard the term 'permutation with identical elements' but my calculation is also 166320.

hey maybe you're right on that test all along!

[twilit relic]

Ahaha I do hope so

[alpine sable]

hi can someone help with this question, i forgot how to do it

A function is given by:

f(x) = x^3 + 1

Determine an equation for the tangent at the point with the first coordinate

[devout sigil]

what is first coordinate?

[fresh sluice]

Maybe at x=1.

[alpine sable]

yes 1

[fresh sluice]

So f(1)=1^3+1=2.

[devout sigil]

anyways tangent gradient is f’(x)

[fresh sluice]

So the first coordinate is (1,2).

[alpine sable]

first coordinate 1.

[sick ledge]

3P3x12P4x8P5x3P3

[alpine sable]

where did u get 2 from

[fresh sluice]

Wait, nevermind.

Scrap that.

jy is right, the gradient is f'(x).

[alpine sable]

yh

[fresh sluice]

So you take the derivative of the equation x^3+1.

First of all, we can apply the power rule, so nx^n-1.

[devout sigil]

parenthesis

[fresh sluice]

We subsite 3 as n, since the power is n.

Yes.

Sorry.

I like to type the process :).

[sick ledge]

Change them all into c rather than p,forgot there is no arrangement difference

[alpine sable]

so it gives us 3x

and 1 disappears

[fresh sluice]

Anyways, we get 3x^2, and since the derivative of a constant is zero.

We get 3x^2, so f'(x)=3x^2.

Just remember to use the power rule.

nx^n-1, where n is the exponent.

[alpine sable]

yes

[fresh sluice]

In this case n=3, since in the equation x^3, 3 is the exponent.

[devout sigil]

parenthesis for the second time

[fresh sluice]

Now, we input 1 for f'(x), and get f'(1)=3(1)^2.

Sorry, I forget to use them a lot, normally when typing.

We get 3.

So that's the answer.

[alpine sable]

3

ye

[devout sigil]

that’s not the equation

[fresh sluice]

Sorry, thanks for reminding me, though.

[fresh sluice]

Wasn't the question for x^3+1?

So the derivative of that is 3x^2+0, or 3x^2.

[alpine sable]

yh

[devout sigil]

the equation of the tangent

[fresh sluice]

Oh.

[devout sigil]

3x² is just the gradient

[fresh sluice]

I forgot that.

True.

[alpine sable]

i have to find

[devout sigil]

so when x=1, 3 is only the gradient

[alpine sable]

these

[fresh sluice]

Yes.

True.

[alpine sable]

once i find them i plug them in the tangent equation

but idk how to find those

[fresh sluice]

Now, equation for tangent line is y-y_1=m(x-x_1).

M is the gradient, or slope, or how steep it is.

I'm pretty sure, correct me if I'm wrong.

[devout sigil]

f’(x)=3x²=3 if x=1

[fresh sluice]

Yes.

I said that, already, but still, thanks.

[alpine sable]

ok so f'(x) is 3

[fresh sluice]

Yes.

[alpine sable]

what is f'(x_0) and x_0

[devout sigil]

apparently she couldn’t plug that into the table so i just said it

[alpine sable]

x_0 = 1

[fresh sluice]

Oh.

[alpine sable]

right

[fresh sluice]

Okay.

Well, if x_0 means 0, then f'(0)=3(0)^2, so zero.

If x_0 means zero.

[alpine sable]

yh so

[fresh sluice]

I'm pretty sure it is, since x_1=1.

And for the tangent line, just use the equation.

You get the coordinates first, so f'(1)=(1,3).

I think it's like that.

Or at the coordinate of f(1)=(1)^3+1.

Correct me if I'm wrong.

[devout sigil]

1^3+1=3(1)+c

[fresh sluice]

Yes.

[devout sigil]

using y=mx+c

[alpine sable]

x_0 = f'(0)=3(0)^2 = 0
f’(x)=3x²= 3

what about f'(x_0)

how do i find that

[devout sigil]

f’(x)=3x²

[fresh sluice]

f'(x_0)=3(x_0)^2

[devout sigil]

f’(1)=3

[fresh sluice]

You input x_0 as the x coordinate.

[alpine sable]

that gives zero as well

[fresh sluice]

Yep, so for x=1.

You take for the non derivative graph, where it's (1,2), and the gradient for the tangent line equation.

[alpine sable]

ok so
x_0 = 0
f'(x) = 3
f'(x_0) = 0

then plug that in the tangent equation

[fresh sluice]

Mostly, tangent line equations are used for two points.

[devout sigil]

f’(x) ≠ 3

[fresh sluice]

Yep.

It can't, unless x=1.

You put f'(x)=3x^2, since you're taking the derivative of f(x).

[alpine sable]

yh

what was the equation for the tangent

[fresh sluice]

Say the question one more time.

[devout sigil]

3x²

[fresh sluice]

That's the equation of the tangent line, so I guess so.

[devout sigil]

is gradient

[fresh sluice]

True.

Derivatives are meant for tangent lines though, right?

[devout sigil]

so use y=mx+c

[fresh sluice]

Yep.

[devout sigil]

i alr mentioned that above

[fresh sluice]

And put the gradient as m, since gradient=slope, I think.

Gradient means steepness of slope, so the same thing.

[alpine sable]

ok so y = f'(x_0) * (x - x_0) + f(x_0)

[devout sigil]

m=f’(x)

[fresh sluice]

Yes.

Or 3x^2, since d/dx (x^3+1)=3x^2.

[devout sigil]

y=[f’(x)]x+c

[fresh sluice]

Oh yeah.

[alpine sable]

y = 0 * (1 - 0) + 3

y = 3x^2

or is it just y = 3x

[fresh sluice]

Well, you use 3x^2 as m in the y=mx+b.

No.

Do y=(f'(x))x+c.

Like that.

[alpine sable]

what is c tho

[fresh sluice]

C represents the y intercept.

In the equation.

Like y=3x+7, 7 is the y-intercept.

I like to use y=mx+b more often though.

[alpine sable]

idk how to use y= mx + b

lol

so the tangent gives 3

how do i write the equation

[fresh sluice]

@devout sigil come back.

y=mx+b is mostly used for writing a linear equation.

Or a straight line.

[alpine sable]

yh

y = 3x + 1

or smth

[fresh sluice]

No.

[alpine sable]

😦

confused..

[fresh sluice]

Remember, you sue the derived equation as m.

[alpine sable]

ye

[fresh sluice]

Like you literally put it in.

Like y=(f'(x))x+c.

That's what @devout sigil mentioned.

[alpine sable]

yh f'(x) = 3

but idk what to put in c place

[fresh sluice]

Melena.

I have to go, sorry.

[alpine sable]

ok np

[fresh sluice]

Please wait, I'll be back.

[alpine sable]

kk

ill just write this down on my paper for now

@ me when u r back

[wanton beacon]

I get discount but not markup and finding the original price

<@&286206848099549185>

[tiny crown]

@wanton beacon what was ur answer?

[wanton beacon]

$75.60

But I don’t get markup and the other one

Like how to solve these type of problems

[tiny crown]

Ahh, one sec

Markup first

$general=$15$\
$box=$20$\
$tax=8%$

[ocean seal]

Ricky

[tiny crown]

@wanton beacon this is what you're working with right?

[wanton beacon]

Yeah

[tiny crown]

$P_{final}=P_{initial}+P_{tax}$

[ocean seal]

Ricky

[tiny crown]

does this make sense?

[wanton beacon]

Yeah

[tiny crown]

try to calculate each price using this formula then

[alpine sable]

ok

is this clear?

can some1 help me with this

https://cdn.discordapp.com/attachments/879132863117791273/893905052736049252/unknown.png

my brain

is fucked

[tiny crown]

try #help-8

I'll help u there

[alpine sable]

oh ok

[wanton beacon]

Actually i dont get it

[tiny crown]

which part?

If a book is priced at $100, and a tax of 10%, what would be its final price?

[wanton beacon]

So would it be x = 20 + 0.08

Or something

For one of them

[tiny crown]

This first, ez example

What would be the final price?

[wanton beacon]

10 dollars

@tiny crown

[tiny crown]

Should the final price be more expensive or cheaper than the original price?

[wanton beacon]

Cheaper

[tiny crown]

Why

[wanton beacon]

Bc discount

Oh wait

[tiny crown]

Tax is a discount?

[wanton beacon]

Lmao

I mean

More

So

[tiny crown]

Yes

See it from a POV of a seller. If u sell a book at $100 bucks, and the govt taxes u 10% of it, what would u sell it for, to ensure you get the same profit?

[wanton beacon]

Idk

How to dot hese problems

[tiny crown]

$100 + (10%*$100)

$110

Do u know why?

[wanton beacon]

No

Ok so pls tell me how to solve markup problems

@tiny crown

[tiny crown]

If you add tax to a price of a product, the final price of the product is the price itself + tax equivalent of price

if a product is priced at $100

and a tax of 10%

the tax price (ONLY TAX) is $10

and final price is $100 + $10 = $110

markup is basically increasing one's price due to external factors, in this case, tax.

[wanton beacon]

Ok

So for my problem

Would it be $16.20

@tiny crown

[tiny crown]

For general ticket?

Yes.

How about box ticket?

[wanton beacon]

21.60 dollars

@tiny crown

So now I need help on the original price one

Is the original price 2250/7

@tiny crown

For the last problem

[tiny crown]

Yeah

Or $321.43 (2d.p.)

[wanton beacon]

Thanks!!

[fresh sluice]

@alpine sable , post it here.

[gloomy aurora]

I have a question

[fresh sluice]

Yes?

[alpine sable]

im also alive

[gloomy aurora]

Suppose I have an equation of the form
1/x + 1/y = 2

I use implicit differentiation to obtain dy/dx
Can I instead rearrange the equation to x+y = 2xy and then use implicit

[alpine sable]

idk calc

[loud blade]

Hi could someone explain 1) a? I got -8,6 but in the textbook my answer was wrong

Do I not just add the first pair for each of the f and g functions?

[astral dagger]

maybe it is required to work like sets

f and g are the set with those pairs

[tidal trellis]

??

[loud blade]

Wdym by that

[alpine sable]

wat

[tidal trellis]

whats the answer

[astral dagger]

consider (5=(\sqrt{5})^2)

[ocean seal]

SubGui

[astral dagger]

then apply difference of squares

[tidal trellis]

what ?

[astral dagger]

for example, if f and g shares a pair, the difference between them only get rids of this pair

same for adding, but it only appears one time and every other term of each

well, I'm not certain

[loud blade]

Right above the question it says that

[loud blade]

If you don’t mind could you explain what this question is trying to ask for? Is it saying that I can only add functions. That have the same corresponding domains

[wispy olive]

Can someone explain the reason and intuition behind the graphs(parabolas) of quadratics equations? Like I know we arrange it in the form $y = a(x-h)^2 + k$ and (h,k) is a point where the parabola touches and the axis of symmetry is x = h. But why is it so?

[astral dagger]

aren't these parabolas?

[alpine sable]

Vertex form, and it's written like that to show obvious transformation of functions. Adding k will change the up and down, and h will change left and right

[wispy olive]

Yes.

[alpine sable]

I'm curious what you're asking. Why what?

[ocean seal]

Senku Ishigami

[alpine sable]

It's explained in transformation of functions. Its written in this form (vertex form) so the vertex and transformations are easily visible and understandable

a will change how "fat" the function is, and it changes how wide it is. H changes the x intercept, and k changes the y intercept

[astral dagger]

yeah, the canonical form of a parabola equation is given by (y-y_0=\dfrac{1}{2p}\cdot(x-x_0)^2), in which ((x_0,~y_0)) are the vertex coordinates and (p) , called parameter, is half the distance between the foci and the directrix

[ocean seal]

SubGui

[small bear]

y = a(x-h)^2 + k    (a > 0)
 >= 0 + k           (we used a(x-h)^2 >= 0)
  = k

Minimum when a(x-h)^2 = 0   =>  x=h, thus the axis of symmetry


y = a(x-h)^2 + k    (a < 0)
 <= 0 + k           (we used a(x-h)^2 <= 0)
  = k

Maximum when a(x-h)^2 = 0   =>  x=h, thus the axis of symmetry```

[small bear]

Algebraic explanation of maximum/minimum part, implying the axis of symmetry due to the symmetry of (x+h)^2

[meager nimbus]

"(x-1)(x-2)(x-3)....(x-10). Calculate dy/dx when X = 6".

I tried expanding it, but I think it takes too long and the numbers get too big. I don't think it's the ideal solution. Any ideas on how to solve this? Thank you in advance

[wispy olive]

Elaborate please.

[small bear]

When a parabola is written in the form a(x-h)^2 + k we know the vertex must be at (h, k) due to the above argument.

We use standard inequalities like t^2 >= 0 for all t

And equality is achievable when t = 0

Let me change the variable name

[wispy olive]

Yes.

But.

I asked why.

[small bear]

That is an algebraic explanation of the why, I think you are probably looking for something else however

And to answer that, you probably need to start from the very definition

[alpine sable]

Not honestly sure WHAT he is asking

[small bear]

How the parabola is formed, using the foci and the directrix

[crystal narwhal]

why cant this be -7rs

?

[high crest]

Since when is -3+4=-7?

[crystal narwhal]

In my head I did 2 - 9 = -7

[oak chasm]

-5 + 4 isn't -9.

[crystal narwhal]

I was wondering why one way and not the other

Ah shit

I see

Thanks

[oak chasm]

No problem.

[crystal narwhal]

Im tired af

[tawny fox]

Lol

[vast cypress]

hey, i'm trying to study for my midterm and this is one of the practice problems

i have no idea where to start

cos(pi*t) will be cos of pi which is 1

the other one will approach 0

wait no i mean 2

ah bruh

it was that easy

[high crest]

cos of pi is -1...

[vast cypress]

yeah

oh

yeah its -1

[prime badge]

is it?

[silk terrace]

yes

I am told it is ^^

[prime badge]

cuz like if it was x - y = 2

[silk terrace]

But it is no where obvious to me

[prime badge]

oh Q is rational

[silk terrace]

ye

[prime badge]

ok ok

[silk terrace]

Would you know how to proceed (or how to in general)?

[prime badge]

no

[alpine sable]

how to calculate distance PT

[turbid anchor]

OC=10,move PT up until T hits C, notice now PO=6-4=2, use pythagorean theorem to calculate PT.

[pseudo surge]

what shouild i learn before integrals_

[zealous ice]

i need help voice

[turbid anchor]

ah i'm tired please think a little yourself, google stuff like high school geometry problems or prism formulas and the like. these don't look like hard problems.

[zealous ice]

<@&286206848099549185> voice help

[wispy olive]

In $x^2 + 6x + 7$, is the answer x = $+ or - sqrt(2) - 3$?

[ocean seal]

Senku Ishigami

[verbal ermine]

no

its $\sqrt2-3$ or $-3-\sqrt2$

[ocean seal]

Aerials

[verbal ermine]

u have one of them

ur other one is -sqrt2+3

u cant write it in a +- form, you'll need more signs

[wispy olive]

Yeah.

[wispy olive]

Why?!!?

[silver current]

.

[verbal ermine]

wdym why

use the quadratic formula

[wispy olive]

It should be +sqrt(2) - 3 and -sqrt(2)-3.

[wispy olive]

I am using completing the square xD.

[verbal ermine]

yes

[wispy olive]

Yeah.

[verbal ermine]

but u said the answer is +- (sqrt2 - 3)

if u expand that you get sqrt 2 is 3

and -sqrt2 + 3

[wispy olive]

Oh no.

[verbal ermine]

which isnt the same

[wispy olive]

I meant that symbol.

Representing.

• and -.

[verbal ermine]

wdym?

[wispy olive]

±.

[verbal ermine]

yes

thats what i meant

same thing

[wispy olive]

Yeah.

[verbal ermine]

$\pm(\sqrt2-3)$

[ocean seal]

Aerials

[verbal ermine]

thats what u think it is right?

[ocean seal]

MikeRoma

[grand oak]

how can I simplify that to get the value of c?

[hushed pasture]

so f'(c) = -1/2

[grand oak]

yes

[hushed pasture]

this is the derivative

so find the derivative of f

[grand oak]

(oh and we cant use the power rule cause we havent learned that)

the original function was f(x) = 1/sqrtx

[hushed pasture]

so use fraction rule first and then sqrt rule

[grand oak]

we havent done those either .-.

which is why im tryna directly solve for f'(c)

and not f'(x) first

[hushed pasture]

use this one is much better: $\lim_{h \to 0} \frac{f(c+h) - f(c)}{h}$ this also the formula of derivative at c

[ocean seal]

Salah

MikeRoma

[grand oak]

conjugate pair?

[hushed pasture]

nah it will give you $\lim_{h \to 0} \frac{\sqrt{c+h}-\sqrt{c}}{h}$ and multiply up and bottom with $\sqrt{c+h}+\sqrt{c}$

[ocean seal]

Salah

[hushed pasture]

also in this limit you can multply up and bottom with $\sqrt{x} + \sqrt{c}$

[ocean seal]

Salah

[grand oak]

ight give me a sec

[sand geode]

sorry for that

[grand oak]

ohmygod https://i.imgur.com/IKmrDbV.png

that was so painful

thanks a lot @hushed pasture !!!

[hushed pasture]

$\lim_{x \to c} \frac{\sqrt{x}-\sqrt{c}}{x-c} = \lim_{x \to c} \frac{x-c}{(x-c)(\sqrt{x}+\sqrt{c})} = \lim_{x \to c} \frac{1}{\sqrt{x}+\sqrt{c}} = \frac{1}{2\sqrt{c}} = -\frac{1}{2}$

[ocean seal]

Salah

[hushed pasture]

@grand oak it's simpler than you think🤣

[grand oak]

wait-

[hushed pasture]

I think there an error

is that sqrt{c} = -1???

[grand oak]

no?

[grand oak]

its $\lim_{x \to c} \frac{\frac{1}{\sqrt{x}}-\frac{1}{\sqrt{c}}}{x-c}$ not $\lim_{x \to c} \frac{\sqrt{x}-\sqrt{c}}{x-c}$

[ocean seal]

MikeRoma

[hushed pasture]

ah ok so it's this is such a massive derivative hhhhhhhhhhhhh

[trim oracle]

This is physics but I just want to make sure I’ve rearranged correctly?

[glass lichen]

check 3rd to 4th line

did you multiply by c^2 correctly?

[alpine sable]

How do I find out e, f, and g?

[upper spruce]

Is this room free?

Someone pls help

I understood that the expression inside log is Tan(x+45)

[golden nymph]

e solve for time when s=0 again
f sub this time in v
g double the maximum height

[upper spruce]

How to solve further?

[golden nymph]

Differentiate cosx-sinx

You’ll get -sinx-cosx

Wait no oof

That’s sth else

[upper spruce]

I would get –( cos+sin )

[golden nymph]

Yeah idk how to do that

My bad

[upper spruce]

Can u atleast suggest what to do of cos2x

?

[orchid kayak]

ay, I just wanna to confirm if I did the math correct
Is this channel open or being used?

[upper spruce]

Yeah it's open

[orchid kayak]

ayt

So, it's my math correct?

remember that '','' = ''.'' for you guys

[golden nymph]

,calc tan(34*pi/180)

[ocean seal]

Result:

0.67450851684243

[golden nymph]

,calc 2.12*0.675

[ocean seal]

Result:

1.431

[golden nymph]

Yup seems correct

[orchid kayak]

o wait I forgot to put 3m instead of 2

[golden nymph]

Oh lol

[orchid kayak]

also thanks for checking it for me

[golden nymph]

,calc 1.431+1.64

[ocean seal]

Result:

3.071

[golden nymph]

I have no idea 🙁

[upper spruce]

Ohk np

I got the soln but the method book is using is way complicated

[golden nymph]

Oh

Differentiate the log ofc 🤦‍♂️

[toxic delta]

Using this channel?

[golden nymph]

So do you need help understanding that or what?

I think that’s the best method

[upper spruce]

I understood the soln but I'm preparing for competitive exam and I don't have much time to take longer steps

I guess that there is some shortcut via which the soln will become shorter

[golden nymph]

I am not sure there is

[upper spruce]

@toxic delta u may use the channel

[toxic delta]

Thanks!

Can someone help me figure out what I did wrong please! I know the last part I added but it’s still wrong

[golden nymph]

Yeah I don’t expect baby pluto to ask a calculus question but what do I know

[toxic delta]

LMAO

[alpine sable]

sub this time in v? wdym? sub what in for v? v = 0?

[undone garnet]

Question: How can I prove that Ax = b has a solution for every b when T: R^m --> R^n? Ik that b should be a linear combination of all vectors in Matrix A, but idk how to prove that either? so any ideas?

[golden nymph]

Sub the time in e inside the v function

[golden nymph]

Occupied

[golden nymph]

You want from y=0 and not from x=0

You have to solve for the x where y=0

[undone garnet]

oops sorry!

[toxic delta]

Ohhh

[upper spruce]

What are the limits of the function?

[toxic delta]

Uhhhhh 9 and 1

Right? That’s where I goofed up?

[golden nymph]

Yup

[toxic delta]

Ah man haha simple mistakes. Thanks!

[golden nymph]

Wlc!

[toxic delta]

Good to go if you need

[undone garnet]

Perfect!

[undone garnet]

so lol again:How can I prove that Ax = b has a solution for every b when T: R^m --> R^n? Ik that b should be a linear combination of all vectors in Matrix A, but idk how to prove that either? so any ideas?

[quartz osprey]

shouldnt the horizontal asymtope be 1?

since its the power of 1/1

[golden nymph]

Occupied

[quartz osprey]

after 🤪

[golden nymph]

No

[golden nymph]

.

[quartz osprey]

😒

after

[golden nymph]

.

[alpine sable]

so that solves the velocity upon impact, but what about finding its speed? second part of f

[thick shard]

how can I solve this? I can't seem to factor it by grouping

[golden nymph]

GUYS CHECK WHETHER THE CHANNEL IS OCCUPIED OR NOT!!!

[quartz osprey]

ok

[golden nymph]

Just remove the negative lol

[alpine sable]

lol

[upper spruce]

You can prove it graphically.... here I have taken example of 2x=10

[undone garnet]

oh by Ax = B, I mean for a matrix

Sorry I shud have specified that before

[glass lichen]

You can have a system w/o solutions...

so you cant prove this

[upper spruce]

A and B are constants ?

[undone garnet]

No, A is a matrix

[glass lichen]

$\begin{bmatrix}0&0&0\0&0&0\1&1&1\end{bmatrix}x=[0,0,0]^T$

[ocean seal]

Mosh

[glass lichen]

you haven't specified what n and m are either

[undone garnet]

Let me send the question, 1 sec

[glass lichen]

Good idea... send the question when you ask it.

[undone garnet]

My answers are:
A - Onto
B - One to One
C - Both

my issue is that idk how to prove my answers

[glass lichen]

nowhere does it say prove

[undone garnet]

well they want a short explanation

they are looking for that

doesn't have to necessarily be a proof, but instead something like an explanation that explains my answer

[upper spruce]

Onto: T:Rn→RmT:Rn→Rm is said to be onto RmRm if each b in RmRm is the image of at least one x in RnRn

One-to-one: T:Rn→RmT:Rn→Rm is said to be one-to-one RmRm if each b in RmRm is the image of at most one x in RnRn

And then, there is another theorem that states that a linear transformation is one-to-one iff the equation T(x) = 0 has only the trivial solution.

That doesn't say anything about onto.

Then there is this bit that confused be about onto: Let T:Rn→RmT:Rn→Rm be a linear transformation and let A be the standard matrix for T. Then: T maps T:RnT:Rn onto RmRm iff the columns of A span RmRm.

[glass lichen]

ok well when m>n, you have more columns than rows

so if you take the set containing the columns of A ${A_1,...,A_m}$ this is a spanning set by extremal properties. So the set spans and is thus onto

[ocean seal]

Mosh

[glass lichen]

That's my guess, linear algebra in this sense was my weak side

[undone garnet]

What is a spanning set? Sry we havent learned that yet

[glass lichen]

a set that spans the space

$\mathbb{R}^2$ has a spanning set ${[1,0]^T, [0,1]^T}$ for example

[ocean seal]

Mosh

[distant talon]

if a whole year fits into a month how many minutes is a day?

[vague coral]

?

[distant talon]

how many minutes does a in game day need to be to fit a 365 game days in a normal month on earth (trying to make a game)

[fringe comet]

Question, what is the second question asking exactly and did I do the first question right?

[alpine sable]

HI i need help

A function is given by

Determine f '(x).

[harsh nimbus]

did you try using power rule

[fresh sluice]

Real zero's are when the function equals zero.

And the numbers are real.

[fringe comet]

i figured that problem out

[fresh sluice]

Oh.

Oops.

[fresh sluice]

First of all, we can simplify all the terms.

First of all, 1/3*x^3=x^3/3. Now, -1/2 times x^2, since they're next to each other, gets you -x^2/2. Now, we get x^3/3-x^2/2-6x.

We can simply find the derivative of any number with a constant combined with x, it is that constant.

Now, for x^3/3, and -x^2/2.

Now, we can do x^3/3 by the following.

First we take out the constant, and if we look back, we multiplied x^3 by 1/3.

Now, we have to find the derivative of x^3, since d/dx(1/3)=0.

The derivative of x^3=3x^2.

Now, we multiply both numbers again, and we get x^2.

Since a third of three=1, and we have x^2 leftover.

Now, we can apply the same for -x^2/2.

We can take out the constant which we concluded to be -1/2, before.

Now, we have to take the derivative of x^2, which is 2x.

Now, we multiply each terms together, again.

We get -x.

Now, we can conclude this as x^2-x-6.

There.

@alpine sable , there.

[alpine sable]

ohh

[velvet cobalt]

Find and sketch the domain of the function:

My answer: x >= 0, y >= 2

correct answer:

Basically, I'm really confused with the x^2 + 1/4y^2 <= 1 part of the correct answer.

[alpine nacelle]

4-4x²-y² >= 0 iff 4 >= 4x²+y² iff 1 >= x²+1/4 * y²

[velvet cobalt]

Alright, I understand the problem. However, can't you just leave it at 4 >= 4x^2 + y^2?

[hushed pasture]

yeah you can

[wintry sail]

any word of advice in being able to do math problems faster as I feel lie

[velvet cobalt]

👍

[wintry sail]

I am getting slower with doing integration with calculus 2

[hushed pasture]

practice and always try to learn the concept not just learning ways to solve problems

[wintry sail]

Okay as for me did not do math is 5 years and my parents never enocurage in doing hard math but feel like passion in doing it and getting back into it

#calculus message

[hushed pasture]

go for logic, sets and applications, those courses will improve your thinking

[wintry sail]

Okay as am using UDEMY krista king calculus 2 course

[hushed pasture]

is he\she doing highschool or college programme?

[wintry sail]

Just for fun but do think college

This is a course online and all

https://www.udemy.com/user/kristaking/

[alpine sable]

Are u guys in a middle of convo?

can i ask a question here?

I'm guessing im good

If I were to find the limit of this function at x = -5

would it be -2 or -3? I was thinking it's probably -3 because limits don't actually approach x = -5...

[buoyant edge]

The function approaches -3 the closer you get to x = -5 from either side, so the limit as x --> -5 is -3

This is a case where the value of the function is different from the limit, since the function is discontinuous at x = -5

[misty mortar]

What test should I use for this?

[hard ether]

Is there a quick formula for this

[fringe comet]

is there a way to figure out the equation of the graph from the pic?

[gusty fog]

Which grade question is this

@fringe comet

[wary stream]

You don't need the equation, all the info you need to answer that question is in the graph

[fringe comet]

11

[fringe comet]

wait really how

[gusty fog]

Is this pre calc

[fringe comet]

yes sir.

[gusty fog]

Ah

[wary stream]

Do you know what domain and range is?

And intercepts

And asymptotes?

[fringe comet]

domain is the x-ints, no? and the range being the y-ints, the ints are where it hits a certain axis, and the asymptotes are places where the graph never reaches but infinitely approaches

[wary stream]

Domain and x intercepts are two different concepts

[fringe comet]

huh? do i have it confused?

a set of all possible ints?

[gusty fog]

Domain is possible set of input values

[wary stream]

The domain of a function is the set of values that we are allowed to plug into our function

[gusty fog]

Exactly

[wary stream]

So looking at the graph, what is the allowable domain?

[fringe comet]

that's what confuses me but ill try: 1 and -1?

[wary stream]

No

[gusty fog]

What is it

[fringe comet]

wait

-1 < x < 1 ?

[wary stream]

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:introduction-to-the-domain-and-range-of-a-function/v/domain-and-range-from-graphs

Perhaps that will help

[gusty fog]

DM me answer plz @wary stream

just curious

[fringe comet]

is it -infitity < x < infinity ?

[wary stream]

Nope

[alpine sable]

I did that but got the question wrong

[wary stream]

Closer though

[fringe comet]

im confused bc of the way the graph is

could u run me through it in vc?

[wary stream]

No

[gusty fog]

Rip

[fringe comet]

well...

ok.

[wary stream]

It's because of the dotted lines too

[fringe comet]

i agree

but those just referance the asymptotes

[gusty fog]

All real numbers?

[wary stream]

They are there for the domain and range too

[fringe comet]

they are?

wait

nope

im still confuded

confused

[gusty fog]

Huh?

[buoyant edge]

@alpine sable Are you being asked for the limit or the function value at that point?

[wary stream]

Yes they are

,w plot 1/x

[ocean seal]

Results provided by WolframAlpha

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

Requested by dldh06#2659

[gusty fog]

So what's the domain

[fringe comet]

is it 1 / x^2

[gusty fog]

@wary stream

[alpine sable]

yes

[wary stream]

Like for that graph, f(x) = 1/x, the domain is (-inf, 0) U (0, inf)

[buoyant edge]

what

[wary stream]

Because there in an asymptote at x = 0

[wary stream]

No, I was showing an example

[fringe comet]

oh

but how would that work for my example

theres a parabola in the middle

[wary stream]

Use the asymptotes

[fringe comet]

so (infite, 0) U (0, -infite)

[wary stream]

Closer but not correct

You do use union in there

[fringe comet]

im so so confused

im gonna fail 😢

[alpine sable]

I have to find what y value i get when lim x -> -5

[buoyant edge]

Oh, the y value is -2

The little white circle is a hole, which means the function is discontinuous at that point. The black dot is the actual function value.

[wary stream]

The asymptotes are values you can't use. So for the left side, it would be (-inf, -4) U (-4, ___). That blank is some other value that I won't say so you can figure it out yourself

It goes up to that asymptote but does not include it

[fringe comet]

-inf, -4) U (-4, inf) ?

[wary stream]

No

There's more to it

There are two asymptotes

[misty mortar]

How do I solve this problem?

@ me with the response

[queen mural]

can someone help me plz?

[fringe comet]

-13<x<0 , how do i convert this to a notation that uses {x | x ... }

i think its called set builder notation?

[warm brook]

{x : -13<x<0}

[alpine sable]

what trig identity is this talking about

I was able to simplify to $4cos(8t) - 3cos(\frac{\pi}{2} - 8t)$ but idk what to do after that

[ocean seal]

bee_ryan

[alpine sable]

what do you need to do after that, assuming that's correct?

since it's using only cosine

they likely want you to use

one of the two terms will have a square root

oh i see, ill try that

[astral stump]

im not sure if this is the right place to ask but anyways
how does a person find the aspect ratio of a screen size

eg.
1920×1080 = 16:9
3440x1440 = 21:9

i don't know how given the input of 1920 and 1080 how do i come up with the 16:9 number

[alpine sable]

1920 / 1080 = 16 / 9

or 1920:1080 = 16:9. It's just reducing it to lowest terms

[astral stump]

is there formuial?

[alpine sable]

It's just fractions

[astral stump]

im trying to make a script so i need to some how program it

[alpine sable]

Do you know how to reduce 15/3 to 5/1?

[astral stump]

i can do it ez pen and paper yeah but i'm not sure scripting wise i guess

[alpine sable]

You could write a GCD algorithm

I'm sure there are packages that will reduce fractions for you though

[turbid anchor]

search for something called euclid's algorithm for gcd, copy stackoverflow code, etc.

[warm brook]

the O(N) way to do it is to divide width/height and just multiply by every integer until you get something close enough to another integer and that’s your aspect ratio 😉 (don’t do this, euclid’s algorithm is way better)

[astral stump]

kk lol thanks guys

[fringe comet]

how do i do this? do i need to figure the equation?

[warm brook]

no, just find the intervals that f(x)>0 and f(x)<=0

[fringe comet]

im not sure how to do that tbh

[low topaz]

how many digits are there in TREE(3)

[placid zinc]

Too many to be expressible

[warm brook]

huh, where is the graph > 0 and <= 0

[alpine sable]

wat am i doing wrong in the last one

[fringe comet]

IDK

im sturggling

[low topaz]

is pi equal to the circumference over the diameter of any circle

[warm brook]

no

wait

over they diameter yes

i thought you just said circumference

C = 2pi * r

[warm brook]

start by just finding where the graph is 0

[glass lichen]

yes... it doesnt magically break for some random circle

[visual ermine]

dunno how to do this question I need some help w

I stuck

[low topaz]

if it can be shown as a fraction wouldn't pi be rational

[glass lichen]

no

cause either C or d will have some irrationality

thus it isnt rational since it fails the definition

You cant have a circle with integer circumference and diameter

[low topaz]

ok

[woeful pulsar]

R formula?
https://brilliant.org/wiki/trigonometric-r-method/

[alpine sable]

#multivariable-calculus

[stiff holly]

Kinda lost on how to get the equation of the perpendicular line?

[ancient saddle]

Hello, do you know how to get the equation of a plane given its normal vector?

[stiff holly]

Not that I know of

I assume its something to do with taking a cross product

[tight locust]

i don't think you even have to do any math for this specific problem

just use a bit of common sense

if a point is on the yz-plane then what can you say about it?

[ancient saddle]

No, in the yz plane, y and z can take any value, but x is fixed

[stiff holly]

rip i thought it was xy

[ancient saddle]

Hello, I'm really curious about this, could you elaborate please?

[ancient saddle]

I asked this because with this concept we could get the answer much faster, but there's still another method I know. Anyway, maybe EndTimes' method is much better

[stiff holly]

i feel like you have to put it into a parametric form and use the point for t right?

wait no that wouldnt work

[ancient saddle]

Take any pair of vectors contained in the plane, how is their cross product related to the plane?

[stiff holly]

orthognal

[ancient saddle]

great, so if you want the line to be perpendicular to the plane, how can you use that?

[stiff holly]

My problem is im only giving one equation, how do i take the cross product of one vector

[ancient saddle]

You can find 2 vectors contained in the plane

just plug in random values to x and y so you can find z at least 3 times so you get 3 different points, with those 3 points you can get 2 vectors contained in the plane

[stiff holly]

Ohhhhh

then take cross product

thx

[analog arrow]

[elder glacier]

can someone help me with b)

i seem to get 14

[tight locust]

what are you trying to find out lmao

[tight locust]

draw a venn diagram

[elder glacier]

@tight locust i have drawn a ven diagram

and i get it to people not studying art, not studying english but people studying german

i get |E^c intersection A^c intersection C|

[jaunty root]

Why is there no symbol for irrational numbers?

[placid zinc]

There kind of is: R\Q

[jaunty root]

Yeah that's right but I'm kind of wondering that there is still no notation for irrationals

[elder glacier]

@tight locust god i hate venn diagrams, appreciate your help, but is there a way to use set law algebra in this case so you don't have to use a venn diagram?

[tight locust]

de morgan's law and distributive law

[elder glacier]

right so you get |E^c intersection A^c intersection C|

[tight locust]

yeah

[woven horizon]

Expand The following Cubes

(2a+3b)^3

(1+2z)^3

[tight locust]

$(a+b)^n = \sum_{k=0}^n \binom{n}{k} a^kb^{n-k}$

[ocean seal]

EndTimes

[tight locust]

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

[woven horizon]

Can u type it again?

[tight locust]

?

[woven horizon]

its confusing what u wrote :/

[tight locust]

i literally gave you the formula lmao

how could i make it any clearer

[woven horizon]

o i needed the process f

[tight locust]

this is the process

[pseudo ocean]

$\forall a>b\geqslant 3; a,b \in \mathbb{N}, prove~that~b^a>a^b$

[ocean seal]

bo may lai so may vcl

[pseudo ocean]

is it possible to let a=b+k for some k

and then let g(b)=(b+k)lnb-bln(b+k)

then we have g'(b)=lnb-b/(b+k)

since b>=3, g'(b)>0.... qed

im just wondering whether

you can consider the k variable as a constant

im confused

bc a and b changes right.......

[rigid smelt]

i think you might be overthinking this

[pseudo ocean]

wdym

[rigid smelt]

using the inequality they gave, a>b, you can obtain the information that a^a>a^b

by raising a to the power of both sides

and since a and b are affirmatively positive and a>b, the sign is not changed

[pseudo ocean]

but b^a<a^a

[rigid smelt]

and then you also have that a^a>b^a

oh wait

nvm i miscalculated my sign

[pseudo ocean]

so

is my method correct....

[rigid smelt]

im not sure if you can consider k as a constant

[velvet condor]

actually

i think you can try

[rigid smelt]

hmmm wait but does it matter tho

[velvet condor]

induction...?

[pseudo ocean]

idk

[pseudo ocean]

yes

[pseudo ocean]

to differentiate this

if k is not a constant then boom

[rigid smelt]

i mean technically we only need the partial derivative wrt b anyway if it werent, since we only cared about the change wrt b

[velvet condor]

it makes more sense when you let k=1, and then 2,....

right....

correct me if im wrong

[rigid smelt]

well technically k is any natural numbers here

[pseudo ocean]

hmm

[rigid smelt]

so yeah, thats why i was thinking it also does play a role in g

[pseudo ocean]

i think i understand what u are trying to say

[rigid smelt]

but then it looks like you were only caring about the change wrt b

[pseudo ocean]

(for any natural number k)

[rigid smelt]

so it wouldnt matter either way

[light kestrel]

are yall done

?

[pseudo ocean]

yes

[rigid smelt]

no

oh

nvm then

[light kestrel]

ok

i got a long af ans

[rigid smelt]

what is your answer

[rigid smelt]

,rotate

[light kestrel]

oop i forgot to multiply the first 2 terms

[rigid smelt]

uhh im not sure what you are doing

[velvet condor]

can try using wolfram alpha to double check

[light kestrel]

ye lol

[velvet condor]

,w d/dx (5tanx +2cscx)

[light kestrel]

im using product rule

[ocean seal]

Results provided by WolframAlpha

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

Requested by Minh Baka#9435

[rigid smelt]

theres no product here

[light kestrel]

what

[rigid smelt]

there is no product (of two functions in x) in 5tan(x) + 2csc(x)

why would you use product rule

[light kestrel]

bro

f is the 5 tanx

[velvet condor]

u mean tanx= sinx(1/cosx)?

[light kestrel]

and g is the 2cscx

[velvet condor]

5 is a constant.......

[light kestrel]

5 is attached to tanx tho

[rigid smelt]

yes, f and g can be respectively that

but you are looking at f+g

not f*g

[remote parcel]

alr so call me dumb

[rigid smelt]

channel is occupied, please move

[remote parcel]

but how would you conver this into slope formula

ok mb

[light kestrel]

o

so the product rule only works when the 2 terms are multiplied?

[rigid smelt]

there is a reason its called product rule

[light kestrel]

bro i aint the brightest

anyway so i would i solve that without product rule

[rigid smelt]

and there is a reason its written as $(uv)'=uv' +u'v$

[ocean seal]

waler

[rigid smelt]

how do you differentiate f+g wrtx where f and g are two functions in x

i think you have done this quite a lot already

having seen you done it in the other channels

[light kestrel]

well

umm

sorry bro im clueless

[tight locust]

what is the derivative of 2x?

[high palm]

rip

[light kestrel]

2

[tight locust]

and what is the derivative of x

[light kestrel]

1

[tight locust]

so what is the derivative of (x+x) ?

[light kestrel]

1

:/

[tight locust]

what is x + x?

[light kestrel]

x^2

oh lol

2

its 2x

no its 2

[velvet condor]

2

$\frac{d}{dx}{(x)}=\frac{dx}{dx}=\frac{1}{1}=1$

[ocean seal]

Minh Baka

[velvet condor]

big brain

[tight locust]

good job. but i was asking uwu

[light kestrel]

ok so

lets see

it would be

5sec^2x

2-cscxcotx

[tight locust]

(f+g)' = f' + g'

[light kestrel]

yes

derivative of 5tanx = 5sec2^x

isnt it?

[tight locust]

yes

[light kestrel]

right

[tight locust]

and what's the derivative of 2csc(x)

[light kestrel]

so that would be 2-cscxcotx

[tight locust]

not quite

there is no subtraction

[light kestrel]

the rule says theres - infront of cscx tho

[tight locust]

d/dx 2csc(x) = -2csc(x)cot(x)

[light kestrel]

the - would go infrotn of 2?

[tight locust]

yes but there is an order in which symbols have to go. you wrote it as subtraction instead of multiplication

[light kestrel]

oh ok

[devout hornet]

any clue on part d

[warm brook]

@devout hornet lagrange interpolation is fine for any x_j, even if they're not uniform. The textbook you're using (bc I'm 99% sure that is a screenshot from a textbook) will describe the lagrange interpolation better than I could on discord message

[devout hornet]

this is jsut an assignment i have not from a textbook as far as im aware

I have part a and b now i think but not sure how to go one from that

[warm brook]

Here you just need to do the 3rd degree polynomial centered about j-1,j,j+1

Ah okay

Okay, it's a little better now, so error is taken by the taylor expansion of f about x_j

It looks like you have a theorem for it, let me look through my numerical analysis notes to see if I have something similar

[devout hornet]

thanks so much

[warm brook]

Okay so for Lagrange interpolation on the interpolation $P(x)$, $f(x)$ has the form
[f(x) = P(x) + \frac{f^{(n+1)}(\xi_x)}{(n+1)!} \prod_{k=0}^n(x-x_k).]
The proof of this I can provide, but I'll leave it to you/your notes, as I presume it's already been shown

[ocean seal]

kirby

[warm brook]

So the error at a given point $x$ would be
[|f(x)-P(x)| = \left|\frac{f^{(n+1)}(\xi_x)}{(n+1)!}\prod_{k=0}^n(x-x_k)\right|]

[ocean seal]

kirby

[glossy briar]

that looks like a pain

the sum of all power fractions

hey kirby

[warm brook]

Not particularly, it's just a lot of variables, and in reality, you're already given that $|f^{(3)}| \le M$ and $n=2$ in this case

[ocean seal]

kirby

[glossy briar]

do you know what that symbols called

[warm brook]

$\xi$?

[ocean seal]

kirby

[glossy briar]

yes

[warm brook]

xi

[glossy briar]

how do you pronounce it I mean

[warm brook]

It's hard to write it, but it's pronounced zye

[glossy briar]

thanks

i only know $\xi$ 2=pi^2/6

[ocean seal]

Mrmangoman1123
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[warm brook]

No, that's $\zeta(2)=\pi^2/6$

[ocean seal]

kirby

[glossy briar]

ohhhh