help-33

[still temple]

so far i have

$$5g^2(x) + 4g(x) = frac{5x^4 / 9} + frac{17x^2 / 3} + 21$$

oop

$$5g^2(x) + 4g(x) = 5x^4 / 9 + 17x^2 / 3 + 21$$

[elfin berry]

Caleb.

[still temple]

how do I solve this

i got to the point

$$5x^4 + 51x^2 + 189 = 9g(x) (5g(x) +4$$

$$5x^4 + 51x^2 + 189 = 9g(x) (5g(x) +4)$$

[elfin berry]

Caleb.

[dry prawn]

Fwiw the syntax is $\frac{5x^4}{9}$

[elfin berry]

Steakanator

[still temple]

Thank you, do you have any tips?

[dry prawn]

They're asking about the coefficients of g, which you know to be quadratic

So maybe it'd be worthwhile to write g(x) = ax^2 + bx + c

Sub that in, do some algebra, see if there are some things you can compare

[still temple]

@dry prawn How do I know what to plug in

[dry prawn]

f(g(x)) = 5g^2(x) - 3g(x) + 7

Expand g(x), compare with what they tell you f(g(x)) is

[still temple]

what do you mean expand g(x)

[dry prawn]

.

g is quadratic so it looks like that

For some values of a,b,c

And since it's asking about values of a+b+c, it seems like a good idea to look at them

[still temple]

do you mean like f(g(x))=5(ax^2 + bx+c)^2-3(ax^2 + bx+c) + 7

@dry prawn

[dry prawn]

Yes

[still temple]

$$5a^2x^4+5b^2x^2+10ax^3b+10ax^2c+10bcx+5c^2-3ax^2-3bx-3c+7$$

[elfin berry]

Caleb.

[still temple]

@dry prawn This is the expansion i dont see how this will help me tho

[dry prawn]

If you collect terms, you'll have a more manageable looking quartic

Which you can compare with what they tell you f(g(x)) is

[still temple]

how

[dry prawn]

Wym how

[still temple]

what do you mean collect terms

[dry prawn]

Combine like terms

[still temple]

I did

[dry prawn]

You didn't

[still temple]

what like terms are here

[dry prawn]

There are multiple x^2 terms

Multiple x terms

Multiple constant terms

[still temple]

I dont know what you mean

the only constant I see is 7

[dry prawn]

a, b, c are all constants

Your only variable is x

[still temple]

oh

[dry prawn]

Better

[still temple]

@dry prawn

[dry prawn]

Looks about right

[still temple]

I'm not sure how this compares

there is a cube

[dry prawn]

You have something of the form (number)x^4 + (number)x^3 + ... + number

They have something of the exact same form

Compare the numbers

[still temple]

a^2 = 1/9

but i dont know how to solve the others

i guess 5c^2 - 3c +7 = 21

[dry prawn]

What's the coefficient in front of their x^3 term?

[still temple]

10ab

[dry prawn]

Theirs, not yours

[still temple]

there is no x^3 in theirs

[dry prawn]

They haven't written one

But one implicitly exists, with a specific coefficient

[still temple]

0?

[dry prawn]

0

[still temple]

so 10ab = 0

and 10bc - 3b = 0

10ab = 10bc -3b

[dry prawn]

Don't overcomplicate it

[still temple]

will I really have to solve this with a 3 way system of equations

[dry prawn]

You found a already, so what must b be?

[still temple]

oh

[still temple]

10/3

wait no

[dry prawn]

No

[still temple]

what am i talking about

would it not just be 0?

[dry prawn]

It would

That should make sense when you also look at the coefficient in front of x

[still temple]

how can I make a relation with x^2

i cant solve for c with 10bc - 4b = 0

[dry prawn]

No you can't

You can with your constant term though

[still temple]

c = real in that equation

oooooh

i can

[dry prawn]

And with your x^2 term

Since you know a and b, c is the only unknown

[still temple]

i dont know how to make the relation

[dry prawn]

Wym?

Sub in your values of a and b

[still temple]

nono

[dry prawn]

Your coefficient will be an expression involving only c

[still temple]

its 17x^2/3

[dry prawn]

Ok

[still temple]

i dont know how to seperate the x^2 from the denominator without making it really annoying to solve

with multiplying it all by 3

[dry prawn]

$\frac {17}{3} x^2$

[still temple]

just a pain

[elfin berry]

Steakanator

[still temple]

oh mb

for some reason was applying the rule where its addition not mult

@dry prawn

my only concern is that the question is asking for all possible sums of the coeff

I only found one

[dry prawn]

Then there's only 1

[still temple]

damn that was a long question

Thank you so much for your help

I really appreciate it

[dry prawn]

Np

[still temple]

.close

[marsh citrus]

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[marsh citrus]

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[still temple]

Hi does anyone know what I should do?
The question is to find the slope of the tangents to x^2 - x + 4 that passes through an exterior point at (3,2)
I already tried setting up two formulas for slope to get the slope, but when I put my slope in y=mx+b my line does not pass through 3,2

[upper briar]

whats ur working

[still temple]

I did y - (k^2 - k + 4) = 2k-1(x-k), simplified it and subbed in 3 for x and 2 for y to get a k value

then i subbed it back in to the above equation but my line didnt touch 3,2

nm thanks

.close

[marsh citrus]

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[cedar saffron]

was absent one day of school and i’m lost now

function notation

[main frigate]

f(3) just means that x=3

so 3*3-1

[cedar saffron]

i got 5

thank you

[main frigate]

should be 8

[cedar saffron]

oh

6-1?

[main frigate]

3*3 is 9 not 6 lol

[cedar saffron]

OHH

my b

i’m real tired

appreciate it

ight so what do i put for R?

[paper fiber]

if R is range

its just the set of output values

of each of the domain value

[cedar saffron]

ah

[paper fiber]

domain is possible input values

range is possible output

since domain is provided

the only possible output is with the numbers in domain

as input

[cedar saffron]

thanks

[marsh citrus]

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[marsh citrus]

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[frozen ridge]

I tried to derive it but it became weird. Any help

[marsh citrus]

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[frozen ridge]

Found answer online

.close

[marsh citrus]

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[tropic marten]

hello so im currently studying projectile motioin

[tropic marten]

motion)) is there a way to know where the given velocity is the horizontal one or vertical?

[cobalt sentinel]

i think its both

like the resultant vector

so u would make a right triangle, label theta, and find horizontal and vertical velocities w/ trig

[tropic marten]

i see...how do you do that tho without knowing the dimensions of the triangle?

[cobalt sentinel]

ill show u, 1 sec

[tropic marten]

ok

[cobalt sentinel]

@tropic marten

[tropic marten]

oh so its slanted then

so just to recall if youre gonna solve for x

is it gonna be (x/15)sin37? i think im getting this wrong

oh wait x sinangle thing is for the angle right

then the trigo is for the sides?

[hollow quest]

you have $$\sin\theta=\frac{x}{15}\hspace{5mm}\rightarrow\hspace{5mm}x=15\sin\theta$$ as your initial condition, then you know that the acceleration in the x-axis in this case (i dont agree with the choice of x and y here but whatever), then using an equation of motion for constant acceleration you can just find out when your x-component of your velocity becomes the same as but opposite of the initial speed. when this is the case the ball will hit the ground again so you can solve for $t$

[elfin berry]

Duh Hello

[hollow quest]

but i would recommend renaming the x and y to be the opposite so that you have y for the vertical component and x for the horizontal one

[marsh citrus]

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[tropic marten]

derivatives, shouldnt the 2 be 2n then the exponent is n-1?

[marsh peak]

Yes, instead of 2x^(n - 1) it should be 2nx^(n - 1)

[tropic marten]

ok isee

how about the invert e at the right side, whats that for?

[marsh peak]

Are you sure that this is the entire image?

[tropic marten]

yeah

[marsh peak]

The symbol means "is in" and is followed by some set, for example the set of all integers

But it's missing here for some reason

[tropic marten]

hmm i see

thankss

how about this one, isnt this supposed to be 4x^3/4?

or thats the answer but simplified

ok last question sorry how did this become like this?

[thin bison]

Ye

So

You can write

2/x as $2x^{-1}$

[elfin berry]

Basudev

[thin bison]

Then use power rule

So, $-1×2x^{-1-1}$

[elfin berry]

Basudev

[thin bison]

$-2x^{-2}$

[elfin berry]

Basudev

[thin bison]

$-\frac{2}{x^2}$

[elfin berry]

Basudev

[marsh citrus]

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[pine wren]

I'm using the product-sum pattern in this equation but my answers are double what they should be (x¹ is supposed to be 1 and x² is supposed to be 2.5). This is the second time this has happened. What am i doing wrong?

[late geode]

you tried to skip steps
and didn't factor the 2x^2-7x+5 properly

[pine wren]

how should it be?

[late geode]

that factor of 2 at the start could be cancelled earlier,
considering the pair of values you found, that could be used to split the middle term

$2x^2 - 2x - 5x + 5 = 0$

[elfin berry]

ℝamonov

[late geode]

and then continue with factorisation by grouping

[pine wren]

at which line should this be?

[late geode]

after this

[pine wren]

i got the answers but i cant understand why u removed the 2

is it cause i can just divide the 0 by 2 and still get zero?

[late geode]

yes

its what you attempted to do at the end, but done a lot earlier

[pine wren]

alright thank you

.close

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[nocturne cosmos]

Putting this here for my friend, he's trying to find what x is equal to, i'm lost as well, if anyone can help that'd be great

[late geode]

usually you'd try approaching with rat root theorem
in combo with synthetic division and/or
factor theorem / poly long division

[nocturne cosmos]

We still don't have a clue

[late geode]

neither of you have heard any of the terms
rat(ional) root theorem, synthetic division, factor theorem / poly(nomial) long division
i mentioned?

[nocturne cosmos]

I personally haven't, haven't really had "advanced" maths like this just yet

And considering he's still equally lost, I think he hasn't heard of them either

[late geode]

then short of CAS, it doesn't look like you've been given the required tools to solve this

[nocturne cosmos]

Does that mean it's essentially not solvable?

[late geode]

just double checking

,w solve 3x^4+1x^3+11x^2-4x-4 =0

[elfin berry]

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[late geode]

its already bad if you don't know the terms relating to how you'd usually approach these types of questions

[sage fable]

2 complex roots damn

[late geode]

and its worse that this doesn't have nice roots

what class is this coming from?

[nocturne cosmos]

1 second let me ask him

[marsh citrus]

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[hollow wolf]

Could someone help me identify whether these are open, closed, adherent points, accumulation points or isolated points?
\begin{align}
S &= (a,b)\
S &= [a,b]\
S &= {a_1, \cdots, a_n}\
S &= \mathbb{Z}\
S &= {1/n|n\in\mathbb{Z}^{+}}
\end{align}

[elfin berry]

𝙹o

[marsh citrus]

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[still temple]

Could you not do u = sec(x) at this point?

I just got a very different answer. so i was wondering

[marsh citrus]

@still temple Has your question been resolved?

[marsh citrus]

@still temple Has your question been resolved?

[still temple]

Anyone? Or can you not u-sub there?

[marsh citrus]

@still temple Has your question been resolved?

[hazy lion]

wow howd an integration problem hang out for so long

are you required to use trig sub?

https://www.youtube.com/watch?v=qaRLaDfsvJM

shoot sorry

https://www.integral-calculator.com/#expr=(5x-2)%2F(x^2%2B25)

if youre curious

[still temple]

Yes.

[hazy lion]

can you track the link i sent

[marsh citrus]

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[true yarrow]

I am always really bad at these and get caught up on the words, can someone help walk me through this question? The function f(t)=345(1.03)^t/4 represents the total amount, in dollars, in an investment account that earns 12% annual interest, compounded quarterly, where t is the number of years since the initial deposit was made. If no additional deposits or withdrawals are made, which statement is true about the function when graphed on a coordinate plane?
Possible answers:

The function has a y -intercept at ( 345 , 0 ) .

The function has a y-intercept at (0,345).

As t increases, f ( t ) decreases without bound.

As t increases, f(t) decreases, eventually approaching 0.

[marsh citrus]

Please don't occupy multiple help channels.

[nova totem]

Man I love trig sub

[nova totem]

Start with finding the function's y-intercept

Plug 0 in for x

[true yarrow]

what? isn't t = y so where would I find x?

.close

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[true yarrow]

The graph models the function f(x), which represents the value of a television, in dollars, x years after the television is purchased.

[true yarrow]

Which statement is true about the function on the interval from x=1 to x=3

The average rate of change on the interval is −369, representing an average decrease of $369 per year.

The average rate of change on the interval is −369, representing an average increase of $369 per year.

The average rate of change on the interval is −184.50, representing an average decrease of $184.50 per year.

The average rate of change on the interval is −184.50, representing an average increase of $184.50 per year.

Alright, so what confused me on this one is I was using the average rate of change formula which ill show in a moment but it didn't match any of the answers.

thats what im doing and its coming out as 815

[fossil osprey]

Did you plug in the values correctly? it seems you plugged in (f(a) - f(b))/(a-b)

[true yarrow]

is that not how im supposed to do it?

alright i think i figure it out. can you tell me if I got it? the average rate of change on the interval is −184.50, representing an average decrease of $184.50 per year.

[marsh citrus]

@true yarrow Has your question been resolved?

[tight furnace]

✅

[true yarrow]

alright thank you!

.close

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[frozen cloud]

The question is
If cos theta - sin theta = m and sec theta - cos theta = n . Prove that (m²n)⅔ = 1

I am stuck after doing this after expanding the m² and can't do anything to cancel the power after the bracket

[frozen cloud]

I am struck here

<@&286206848099549185>

Help me please

[glacial hedge]

That's why parentheses matter. You forgot them in (sec theta - cos theta) so you just did ((...)*sec theta) - cos theta instead of having cos be part of the product

[frozen cloud]

I couldn't get what you mean. Could you plz tell me clearly

Did you mean the power 2/3?

[glacial hedge]

I'll write x = theta for conciseness
(cos x - sin x)^2 * (sec x - cos x)

You forgot the 2nd set of parentheses

[frozen cloud]

It will get the same result right?

[glacial hedge]

No

(a+b)c + d != (a+b)(c+d)

That's clear with a = b = c = 0 and d = 1

[frozen cloud]

So I just wanna elaborate (cosx-sinx ) ² and multiple it by secx - cos x?

[glacial hedge]

Yes

You shouldn't be confused by how multiplication works if you're trying to prove such identities

[frozen cloud]

Plz wait let me check what I get

I got upto this

I think I did wrong let me check again

[glacial hedge]

It's wrong on line 1

You copied it wrong

[frozen cloud]

Yeah sorry

Cos²x + sin²x =1 right?

[glacial hedge]

Yes

[frozen cloud]

What could be written after minus?

Or is something wrong?

[glacial hedge]

Just keep going

• 2 sin x + 2cos^2 x sin x

[frozen cloud]

I got it as
secx-cosx-2sinx cosx secx + 2sinx cos²x

[glacial hedge]

Looking at it it would be lucky for it to equal 1 lmao, but we'll see

[frozen cloud]

Can the -2sinx and +2sinx be canceled?

[glacial hedge]

No, they don't have the same coefficients

[frozen cloud]

Oh

[glacial hedge]

Brb 15 min

[frozen cloud]

I can't get it!

Could you help me?

[loud hinge]

Anyone know how to simplify 4x(3+-2y)-5(2x-3y)

[frozen cloud]

Themateo
a quick doubt, is this question wrong? I wrote the question correctly as it was written in board but I think somethings fishy.
Or maybe just a passing thought

[glacial hedge]

Actually, a quick look at the functions does make it clear this can't work at all

The product goes to infinity as theta nears π/2

,w plot (cos x - sin x)^2 * (sec x - cos x)

[elfin berry]

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[glacial hedge]

By all means not constant equal to 1

[frozen cloud]

So does the answer get 1?

[glacial hedge]

It's wrong on one way or another

[frozen cloud]

I can't get it so, is my steps wrong?

[glacial hedge]

The question is wrong. It asks to prove something wrong

[frozen cloud]

Oh thnx for confirming my thoughts

And also sorry for wasting your time

I think I wanna see my 'friend' who wrote this question of board tmrw . Hehe

Sorry

I am closing the channel.

Thnx for helping me

.close

[marsh citrus]

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[long cape]

Is it OK to talk about end behaviour this way? Q being that quadrant

I’m wondering if it matters Q1 / Q2, vs Q2 / Q1, etc. and if there should be a specific order to the quadrants when talking about end behaviour?

Like should end behaviour always be talked about from left side of the graph to right side or really doesn’t matter?

[devout mauve]

what do you even mean with "end behaviour" in relation to quadrants

[long cape]

End behaviour of polynomials

In regards to multiplicity

Touch/bounce with even multiplicity or cross with odd multiplicity

(Professor Leonard pre Calc video 29) @ 24 minutes

[still temple]

you mean the limits?

[long cape]

I don’t think he’s talking about limits quite yet, just multiplicity

Limits will come in Calc 1

So how a factored polynomial with multiplicity would shape a graph

With even and odd multiplicity combined

[still temple]

well theres even and odd

[long cape]

Yes

[still temple]

the first and forth is even

[long cape]

I’m just wondering if my way of writing it is OK with quadrants in order from Q1,Q2,Q3,Q4 or if I should always talk about this left side of the graph (Q2 and Q3 first) to right side of the graph (Q1 and Q4 second)

[long cape]

Do you mean the first and fourth on my examples above?

Because I do see that and understand that, in the order as per above it goes: even, odd, odd, even.. but I am more curious about the proper syntax to describe odd or even multiplicity using quadrants

For the first example it can be talked about either way? Q2-Q1 OR Q2-Q1?

Or should it follow a pattern such as lowest quadrant to highest quadrant. Or left side of graph to right side of graph?

[marsh citrus]

@long cape Has your question been resolved?

[twilit arrow]

i’m still confused by what you mean by quadrant

[twilit arrow]

yeah but i don’t understand why you’re dividing the quadrants with each other

ohhhh ok i think i understand now

i’ve rarely seen function behavior be discussed through ending quadrants. what you have makes sense , but it’s not common as far as i’m aware.
in general we’d say “the function tends to negative infinity as x tends to positive infinity” or something of the sort

but to answer your question, it shouldn’t matter which quadrant goes first. i can’t speak to the common convention, but saying Q2 and Q3 are the end behaviors of a function is the same as Q3 and Q2

@long cape

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[feral solstice]

So on the second step can someone explain why xy prime isn’t positive

[feral solstice]

If you need more clarification I can explain

[worn nimbus]

they factored out a -1

[sour relic]

Yes

[spark otter]

-(a+b) = -a - b

[still temple]

Delta math unreal

[feral solstice]

Wait what

Once you use product rule shouldn’t it look like this

[hushed egret]

which is -y - xy'

whats the difference?

[feral solstice]

Shouldn’t x be positive?

[hushed egret]

x isnt "positive"

there is no stipulation on the values of x

there is a negative sign in front of x

do not refer to variables that have plus signs in front of them as "positive"

[feral solstice]

So -1 times -x is what then

[hushed egret]

-1 (-x) is x

but

there is no -1

https://cdn.discordapp.com/attachments/907022703230345237/1025485685353885717/unknown.png

you have -1(y) + -x dy/dx

thats the same as -y - x dy/dx

[feral solstice]

Than why does it say distribute

Then

[hushed egret]

where does it say distribute

if you mean this line

then -(y + xy') = -y - xy'

[feral solstice]

It’s on my screen is says distribute negative

[hushed egret]

by distributing the - sign into the brackets

[feral solstice]

So they factored out a negative and then distributed it back?

[hushed egret]

yes

its kinda dumb

[feral solstice]

Bruh I hate delta math

Okay I get it now thanks

[marsh citrus]

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[flat sierra]

I've a few questions for Matrices that I cant understand

1. What is a determined compatible system/matrix
2. Incompatible system/matrix
3. Undetermined compatible system/matrix

Thanks in advance 🙂

[marsh citrus]

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[dreamy spindle]

Hello, does anyone know how to deal with such equation? Im looking for the lowest value in (0 ; sqrt2] range

[marsh peak]

Is this a calc question?

[dreamy spindle]

I don't know

[marsh peak]

(calc is calculus)

So are you familiar with calculus or not?

[dreamy spindle]

i learned about derivatives this week

[marsh peak]

Nice, so you need to find values of x for which f'(x) = 0 where f(x) = x^3/4 + x + 1/x

(you also need to make sure that f''(x) > 0, as it'll determine that the point is indeed the minimum)

[dreamy spindle]

Ok, I will get the f'(x) first, Im just worried that 1/x will cause problems with finding 0

[marsh peak]

Eh it shouldn't

In fact without that 1/x there are no extremas

[dreamy spindle]

is that right? how do I calculate 0 now?

[marsh peak]

Derivative of 1/x isn't 1/x^2

[dreamy spindle]

is it -1/x^2 ?

[marsh peak]

Yes

[dreamy spindle]

ok

[marsh peak]

Now set that equal to 0 and solve for x

[dreamy spindle]

So i got x = sqrt(6)/3

now f''(x)

[marsh peak]

Yeah, also note that x = -sqrt(6)/3 is also a solution but it's not in (0, sqrt2], so we can ignore it

[dreamy spindle]

ye i took that into consideration

is it right?

[marsh peak]

As long as c = 0

And it should be 2/x^3

[dreamy spindle]

ok

f''(x) > 0 for x greater than 0

so the minimum exists

[marsh peak]

Yup

So x = sqrt(6)/3

[dreamy spindle]

Ok, that should be my answer

thanks for the help!

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[burnt lava]

Hello, im having trouble understanding what exactly makes the S row all Truths (This is Discrete Mathematics) https://gyazo.com/a03bf73975c6b3506449df63d4448f4b

[burnt lava]

Its not as simple as "oh its a tautology so its just all true!" there has to be something that makes it that way from the way the table is presented, right?

[marsh citrus]

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[burnt lava]

<@&286206848099549185>

[burnt lava]

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[dim wasp]

Hi! I was wondering if someone could help me with this question

[hidden plaza]

,rotate

[hidden plaza]

Hint: Difference of two squares

[dim wasp]

Ahhh I see

So do you just end up with 2+1?

Actually lemme try again

😅

[hidden plaza]

Okay

[dim wasp]

Do I rationalise it?

Like this?

[dim wasp]

? 🙂

[hidden plaza]

No like 4^n -1 is (2^n+1)(2^n-1)

[dim wasp]

i see

so it just cancels out

2^n + 1

[hidden plaza]

Ye

[dim wasp]

legend

[dim wasp]

thank you so much

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[still temple]

how can i solve this question

[upper briar]

wow

ur diagrams look scary

[lucid hinge]

nice handwriting

neater than mine

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[eternal pike]

If i have a general formula convert it to standard formula and put those in a graphing calculator should the same graph appear?

[eternal pike]

(ellipse)

so the question was to convert the general form into the standard form. i convert and put the standard form and gen form in desmos graphing calculator

[marsh citrus]

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[eternal pike]

<@&286206848099549185>

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@eternal pike Has your question been resolved?

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@eternal pike Has your question been resolved?

[eternal pike]

damn

.close

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[cinder wharf]

in this example, are there any further steps needed if I am only asked to rationalize the denominator?

[craggy needle]

id say ur good

with this

[cinder wharf]

ok, thank you :D

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[cobalt anchor]

can someone walk me through the steps

becaus i did it but i d=believe i have the wrong answer because my y primes cancel

here is my work

[marsh citrus]

@cobalt anchor Has your question been resolved?

[still temple]

||2x2/3x5||

[marsh citrus]

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[turbid mirage]

Hi, does anyone know how one would evaluate this limit?

[late geode]

partial fraction decomposition

[turbid mirage]

I still get lim(1/inf) + lim(1/inf) though, which is basically 0+0 so it evaluates to zero, right?

at least that's my best guess, but it's not an option 😂

[late geode]

no

what do you have after decomposition

[marsh citrus]

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[sinful hazel]

how to do?

[marsh citrus]

@sinful hazel Has your question been resolved?

[sharp vessel]

What are you stuck on?

[sinful hazel]

i figured it out

nvm

[sharp vessel]

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[ripe sluice]

How do I evaluate the following 2-forms on (vp, wp) given v = (2, 1, −1), w = (2, 0, −1), and p = (0, 3, 2 ) for this-> φ ∧ ψ where φ = (x − y)dy + z^2dz, and ψ = 2y^2dy − dx.

[chrome sparrow]

anyone knows why i get two different answers to the same equation?

btw the one at the top is the correct one, but i need to know the steps

[ripe sluice]

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[short wadi]

I have attached two exercises, 2.6 and 2.5. In both, one is asked to formulate the equilibrium moment equation about a point, however in Exercise 2.6, there is an extra Moment in the equation AND in the free body diagram. On the other hand, in Exercise 2.5, there is no Extra Moment. Not in the equation, nor in the FBD. Can Someone explain to me how I am supposed to distinguish this from the question?

[quasi osprey]

Holy cow that’s a lot

[short wadi]

Its a simple exercise if I just understood why they add extra Moments sometimes. Thats the ontly thing I get wrong

[quasi osprey]

Ok I think I get it

M_a is a hypothetical moment that the hinge of the beam exerts

[short wadi]

It is that little 'wiggle rom' of a beam right?

[quasi osprey]

I think so yeah!

[short wadi]

okay but

so when its wall mounted, the wiggle room has to be accounted for an extra Moment

It seems so, because in this exercise theres also an extra moment at the wall

here though, the Moment should be negative right? Because, if you were to let everything go, the tool would rotate to the right. But I guess when you add the extra Moment, its always positive?

[quasi osprey]

Wait which problem u referring to?

[short wadi]

the last screenshot i sent

[quasi osprey]

The M_C should be positive

[short wadi]

why?

[quasi osprey]

Positive moment is counterclockwise and negative is clockwise

[boreal vault]

^helo

[short wadi]

But why is M_C not negative?

Intuition tells me it should be

[boreal vault]

because mcdonals

[short wadi]

bad intuition..

[quasi osprey]

Without M_C, the entire crane will rotate clockwise, or positive moment

In order to make it equilibrium, we need to counter positive moment with negative moment

So M_C is negative

[short wadi]

isnt this force countering the other forces?

oh no

forget this

[quasi osprey]

Not the crane?

[short wadi]

okay I get it now

thanks a lot

much apreciated

[quasi osprey]

Np!

[short wadi]

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[marsh citrus]

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[solid peak]

im not sure what to do here. it gives us t and x. but also gives dx/dt at t = 2 = -5. it doesnt give directly what dx/dt is in general...

[sacred stump]

try using the chain rule

[solid peak]

what?

where

[sacred stump]

$$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}$$

[elfin berry]

ibzi

[solid peak]

but i dont need dy / dx

i need dy/dt at t = 2

[sacred stump]

use this formula to find dy/dt

you can find dy/dx

and u have dx/dt

[solid peak]

im lost bro

idk what u mean

[sacred stump]

first find dy/dx

$$\frac{dy}{dx}}*{\frac{dx}{dt}=\frac{dy}{dt}$$

[elfin berry]

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

[sacred stump]

@solid peak

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[last flare]

I hope this question fits this channel, but its a bit of a coding/simulation question. I am trying to find an accurate but efficient numerical integration technique for a system of 2nd order coupled differential equations. I am currently using RK2, but I could definitely use more precision as angular momentum doesn't seem to be conserved

[last flare]

this is my current numerical integration

geodesicKerr is a function that returns an acceleration vector that is dependent on the position and velocity vector

not that it makes much difference, but I initiate the position and velocity as follows

its important to note that I also use a dynamic timestep

[marsh citrus]

@last flare Has your question been resolved?

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@last flare Has your question been resolved?

[marsh citrus]

@last flare Has your question been resolved?

[marsh citrus]

@last flare Has your question been resolved?

[marsh citrus]

@last flare Has your question been resolved?

[plucky void]

maybe have a look at scipy.integrate.odeint for dynamic timestep

[marsh citrus]

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[worn nimbus]

how can a subspace be part of a basis?

[worn nimbus]

isnt a basis formed by vectors

im confused

my book says the equivalence class of a vector can form a basis

[devout mauve]

can form a basis in what space

[worn nimbus]

this was an answer to an exercise

i had personally written the standard bases of polynomials and of polynomials divisible by (t-1)^2 and concluded that one basis had 2 elements fewer than the other

therefore V/W was 2 dimensional with dimension with standard basis 1 and t

[devout mauve]

remember that the equivalence classes are now single elements

aka in V/W the equivalence class [1] is now a vector, not a set anymore

[worn nimbus]

i am so confused

[devout mauve]

[1] is a set that consists of vectors in V

but now we consider it as a single element of V/W

[worn nimbus]

oh because the vectors of V/W are affine* subspaces?

[devout mauve]

well they are cosets

affine subspaces if you want

[worn nimbus]

so that>?

[devout mauve]

the elements of V/W are affine subspaces of V

yes

which we now again treat as vectors

[worn nimbus]

alright

could you check a solution of mne

submission has passed btw

so there's no academic integrity issues

besides it wasnt for any grade

i wrote [x] - x = W

and [x] - x = {y - x in V | x ~ y}

and we could that U formed by [y - x]

[devout mauve]

so you want to set U=[y-x] ? I don't really see where you want to go with this

[worn nimbus]

i figured that would show it W is just U shifted by a vector

[devout mauve]

what is y tho

is it fixed now?

[worn nimbus]

oh wait no

its not fixed at all

w is just a normal subspace then right

[devout mauve]

you have two sets

[x]-x and W

how do you show that two sets are equal

[worn nimbus]

double set inclusion

two way

[devout mauve]

yes. then do that

[worn nimbus]

alright

wait so would i write the set [x] + x = {y in V | x - y in [x]} + x

like i cant really use W

as a subspace

[devout mauve]

this was correct

now take an element from that set and show it is in W

then take an element from W and show it is in that set

[worn nimbus]

the + x at the end is important too though right

[devout mauve]

why do you want to add x now

[worn nimbus]

because [x] + x

wait isnt it totally wrong to write [x] = {y in V | x - y in [x]} as that is circular reasoning?

[devout mauve]

what

[x] = {y in V: x~y}

how is x~y defined

[worn nimbus]

x - y in some subspace

[devout mauve]

not in some subspace

specifically in W

[worn nimbus]

even here?

[devout mauve]

well yes

otherwise the question wouldnt make sense

[worn nimbus]

ohh

okay cool that seems to make it easier

[devout mauve]

easier
possible

[worn nimbus]

hahah

but the [x] -x thing

is that a bad step

[devout mauve]

no

it doesn't really help in the sense that it just changes which sets you have to show are equal which essentially follows the same argument either way

but it's not bad

[worn nimbus]

oh alright

like it is not wrong to add a vector to a set?

[devout mauve]

no you can do that

just like you did

pointwise addition

that's what the RHS x+W also means

[worn nimbus]

okay good

i cant just pick some specific element such that it is obvious that it is in x + W right

because every element has to be

or am i already allowed to use that the intersection of two affine subspaces is either the empty set or the subspaces are equal

[devout mauve]

pick an element y in [x]

what do we know about y

[worn nimbus]

x-y is in W

and y-x too by symmetry

so can we say therefore y is in w + x?

[devout mauve]

x-y is in W

so x-y=w for some w in W

then y-x = -w

so what is y?

[worn nimbus]

x-w

working with elements on both sides makes a lot more sense hahah

[devout mauve]

or x+(-w)

which is an element of x+W

yes, break it down to elements

[worn nimbus]

oh lord alright tysm

[devout mauve]

and now the other direction

pick an element y in x+W

what does that mean about y?

[worn nimbus]

y = x + w for some w in W therefore y - x = w

x - y = -w such that -w is obviously in W

and x - y is in [x] therefore [x] = x + W

[devout mauve]

x-y in W, so x~y and y in [x]

[worn nimbus]

oh lord yeah my bad

i forgot that i was supposed to prove y in [x]

[devout mauve]

yeah that's never good to forget what you want to prove

[worn nimbus]

how come x - y is in W?

is it

[devout mauve]

well x-y=-w

and because w is in W and W is a subspace, also -w in W

[worn nimbus]

oh like that

thank you so much

this really clears it up

[marsh citrus]

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[sterile gazelle]

An arch in an amusement park has a parabolic shape. It has a height of 74 feet and a base width of 38 feet. What is the height of the arch 8 feet from it's vertex?

is the question

how do i graph it?

i got it solved

but i forgot how i graphed it

[marsh citrus]

@sterile gazelle Has your question been resolved?

[marsh citrus]

@sterile gazelle Has your question been resolved?

[median raven]

Did you choose (0,0) in the middle of the arch or on the side?

Oh I see

You just have to fill in x=8 in your equation

[marsh citrus]

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[wide summit]

for any n>N how do i prove (or do i need to) that sqrt n^4+16n^2+4/7n^2+2n > sqrt N

[hardy slate]

$ \sqrt{\frac{n^4 + 16n^2 + 4}{7n^2 + 2n}}$

$\sqrt{\frac{n^4 + 16n^2 + 4}{7n^2 + 2n}}$

[elfin berry]

Kaisheng21

[wide summit]

yeh

is it just a given by some power rules

[marsh citrus]

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[marsh citrus]

@wide summit Has your question been resolved?

[marsh citrus]

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[brittle totem]

How do I make a function that tells me what deviation the input is from the mean? My niave method is a guess and check that takes the mean + (i•dev) and checks to see if that is equal to the input. This method sucks for a lot of reasons. I was hoping that there would be a way to instead make a formula that that just tells you what deviation the input is from the mean.

stdev(src, len, mul) => ta.sma(src, len) + ((float(mul) * 0.001) * ta.stdev(src, len))

std_val(float src = close, int len = 200) => //{
    float result  = na
    var dev = 0.0
    for i = -6000 to 6000 by 1
        dev := stdev(src, len, i)
        if src - dev >= -0.1 and src - dev <= 0.1
            result := i/1000
    result //}

My niave attempt in pine script.

[marsh citrus]

@brittle totem Has your question been resolved?

[main idol]

write the math formulas out if you want help

[brittle totem]

turns out I was looking for the z score

z=(src-avg)/dev

.close

.close

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[marsh citrus]

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[hard stratus]

How do I do this?

[slow barn]

you need to put in 2 numbers that multiply to 50

1x50 is already given

[hard stratus]

5x10 where do I put it?

[slow barn]

well for the second row

it wants you to use 2

as one of the numbers

[hard stratus]

2x25

[slow barn]

exactly

so you can put that in

and then you only need one more so im guessing you can use the 5x10 you mentioned

[hard stratus]

Thanks this?

[slow barn]

do you know how to find factors?

you could probably use a factor tree to show how you got it

[hard stratus]

No

K

169 is divisible by 3?

It gave me a decimal tho

[slow barn]

that means it isnt

[hard stratus]

But it’s an odd number and 3 is odd

How do I find out if it’s divisible?

[slow barn]

odd numbers arent neccesarily divisible by three

[slow barn]

can you use a calculator?

[hard stratus]

Yes

[slow barn]

just plug it in to that and see if you get a whole number

[hard stratus]

Then what

[hard stratus]

😔

They’re all decimals?

Nvm 13

[slow barn]

remember it asks you to support your answer with a diagram or table of some sort

[hard stratus]

But it’s 13

[hard stratus]

I’m doing it rn

Oh alr

I can’t find what to divide by

[slow barn]

well 169 only has three factors

[hard stratus]

How do you know that tho

?

[slow barn]

you have to divide by prime numbers

to find the factors

[hard stratus]

?

K

But every single one?

[slow barn]

no

so once you get to one that gives you an answer = or greater than the number you divided by

then you will have them all

[hard stratus]

169 divided by 12 will work?

It has 14 as a whole number

[slow barn]

12 is not prime

but also

169/12 = 14.083333...

[hard stratus]

7 then

It has 24 as a whole number tho?

Idk what to do 😔

[slow barn]

169/7 = 24.143

im not sure about those maybe your calculator is messed up or not very precise

[hard stratus]

Lol

[slow barn]

one moment

[hard stratus]

Ok

I have a quiz tomorrow 😔

[slow barn]

169/1 = 169
169/2 = 84.5
169/3 = 56.333...
169/5 = 33.8
169/7 = 24.143
169/11 = 15.3636...
169/13 = 13 (I stop here as the result is equal to or greater than the number I divided by)

this is how the prime factorization would work

[hard stratus]

What’s half of 13?

Or does it just end

Because I can’t multiply anything to get it

Plss

I don’t have time

[slow barn]

im sorry

[hard stratus]

Nooo it’s okkk

[slow barn]

I think im explaining this poorly so you might have to find someone elses help

sorry again

[hard stratus]

Aw alr

Thanks for trying to help me tho

[slow barn]

best of luck with your quiz

[hard stratus]

.close

[marsh citrus]

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[still temple]

help

fast please I dont understand the t-1

what do they mean minimum at t=1

please help quickly thx

[main idol]

why quickly?

[still temple]

i have gtg somehwere in 5 min i understand all of it

but dont know know that part

[marsh citrus]

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[marsh citrus]

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[still temple]

<@&286206848099549185>

[brazen siren]

hi wassup?

[marsh citrus]

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[still temple]

.close

[marsh citrus]

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[marsh citrus]

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[still temple]

how would I solve this?

[proven timber]

What have you tried

[still temple]

plugging in 2

[proven timber]

-2, you mean?

[still temple]

yea

[echo bough]

so what do you get in the numerator and denominator?

[still temple]

numerator is a-21

denom is 8

right?

[proven timber]

How'd you get that

[still temple]

I plugged in -2 for all x

[proven timber]

Remember x² when x = -2 is not -4

[still temple]

right

its 4

[proven timber]

I would double check your arithmetic after plugging in

[still temple]

a-8

over 8

numerator is a-8

denominator is 8

[proven timber]

It's not

It shouldn't be anyway

Show all your work for how you got that

[still temple]

21-a is numerator

denominator is 0

[proven timber]

Yes

Now, for the limit to exist, what must the numerator be since the denominator is 0?

[still temple]

21

[echo bough]

what should be equal to 21?

[still temple]

a

[echo bough]

yeah not the numerator

so actually what you know is that

if a=/=21

the limit doesnt exist

but that doesnt prove that its now converging

if a=21

for it you have to show that indeeds it works with a=21

what you just did only proves that if a=/=21 it doesnt work

but it might not work for 21 either

[still temple]

ok

how would I get the second part

[proven timber]

What does the limit become with a = 21?

[still temple]

including x?

-20/0

[livid fulcrum]

ok, so you don't understand what limit means. can you explain it in your own words what it means?

[proven timber]

Don't evaluate the limit

Just plug in a = 21 to the original question

[still temple]

ok

3x+15/x-1

[proven timber]

Where'd the x² go

And how did x² + x - 2 become x - 1

Did you already factor it?

[still temple]

yes

[proven timber]

I haven't done the working yet for the factoring, gimme a sec

[still temple]

ok

[proven timber]

Okay yeah that works

So what happens if you plug in -2 now?

[still temple]

-3

[proven timber]

Yep

That's the limit

[still temple]

thanks

.close

[marsh citrus]

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[swift beacon]

both 47 and 53 go together. i am dyslexic and having trouble understanding what is being asked so if someone could just help me try to understand this better that would be great :,)

[still temple]

dont you have to read discord messages too

[swift beacon]

yes of course but sometimes can be very hard to understand what things are being said lol, fortunately i am literate. most times i have my dyslexic teacher helping me out with my accomidations but cannot contact her atm. im sorry

[still temple]

uhh

well

47 is a dot plot

you know what those are right

each dot represents a situational entity, which in this case is a soccer game played

so basically each dot represents a soccer game played by the US team

and each dot has a value associated with it which is determined by where each dot is placed