help-13

[cedar kiln]

@junior merlin Has your question been resolved?

[junior merlin]

<@&286206848099549185>

simplify 9/4y^4 - 3/4y^2(y^2-y) to a(c+d) format
what i mean by a(c+d) is like, for example, if the final answer is smth like 4/2y^4 + 1/2y^3 put it as 1/2y^3 (4y+1)

[sage pasture]

Can you write it down on a paper if you can please

[junior merlin]

i got the asnwer

its ok

9/4y^4 - 3/4y^2 (y^2-7)
= 9/4y^4 - 3/4y^4 + 3/4 y^3
= 6/4y^4 +3/4y^3
= 3/4y^3(2y + 1)

[sage pasture]

Okay nice

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[jagged socket]

Doesn’t make sense. Author wrote that empty set and X are open sets in the Proposition 1.1.2 i and then in the first pic, he wrote that they’re closed

[tropic oxide]

yeah

they are in fact both

they are what are called clopen sets

[jagged socket]

Can i ask another question?

[tropic oxide]

don't ask to ask

just ask

[jagged socket]

Okay

I understood that (3,4) is open set, but i cant understand how {a} could be open and closed and {b,c} is neither

[tropic oxide]

(3,4) is an open set in the standard topology on R

i think when you're just starting with pointset topology it might help to let go of some of your intuitions from R when working with such explicitly-given finite topological spaces

{a} is open in (X, tau_1) by definition.

{b,c,d,e,f} is open in (X, tau_1) again by definition (of tau_1).

{a} is the complement of {b,c,d,e,f} in X, and since the complement of any open set is closed (by defn of closed set), we get that {a} is closed

really this is just definition-pushing

[jagged socket]

Is there a reason why all members of topology are open sets? Or should be it regarded as an axiom

[tropic oxide]

it's the definition of a topology!

for a topological space (X, tau), "open set" means nothing more than "member of tau"

[jagged socket]

That makes sense

Thank you

.close

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[olive gazelle]

Why is the 4 there

[tropic oxide]

have you attempted to solve the equation?

the 4 should pop out naturally

[olive gazelle]

yes

erm

no 4 haha

one sec

[tropic oxide]

what with your equation reading $-7 \cdot 3^{{\color{red}\frac{1}{4}}x} = -10$ and all...

[wraith dagger]

Ann

[olive gazelle]

perhaps there’s a different way to solve but I do it like a normal algebraic equation

[tropic oxide]

you have been doing alright so far

i would suggest simplifying -10/-7 into 10/7 though, unless you have a religious objection to doing so

you are one step away from the solution now

[olive gazelle]

erm sure

[olive gazelle]

what's the step though because where the hell does that 4 come

[tropic oxide]

if you had the equation 0.25z = 99

how would you solve it

[olive gazelle]

divide both sides by 0.25

which cancels out the coefficient on z

and leaves us with z = 99/0.25

[tropic oxide]

and 1/0.25 is what?

[olive gazelle]

erm

4 but i don't know how to draw that conclusion

[tropic oxide]

you don't know why 1/0.25 is 4?

[olive gazelle]

no

[tropic oxide]

0.25 * 4 = 1.

[olive gazelle]

i don't know where it belongs on my equation

[olive gazelle]

hahaha

[tropic oxide]

in your equation, the next step would be to divide both sides by 0.25 as you put it

i'm trying to get you to realize that dividing by 0.25 and multiplying by 4 are one and the same

[olive gazelle]

ohhh!!!!!!!!!!!!!!

[olive gazelle]

thanks appreciate

[olive gazelle]

(pink pen)

if I want to get x by itself, I multiply by 5 right?

[tropic oxide]

yes, multiply both sides by 5

[olive gazelle]

how did sal khan come to the conclusion that it's natural log 0.05?

where did 0.05 come from????

[tropic oxide]

1/20

he divided both sides by 20

1/20 is 0.05

it sounds as if you have some issues with converting between fractions and decimals, and arithmetic with the latter

[olive gazelle]

ehh kind of

i would say it's more conviction or intuition

not incomeptency

he just immediately put 0.05 he never elaborated he did /20

[tropic oxide]

this is probably because by the time you're working with logs you are expected to be more proficient with the stuff that comes before

like linear equations

[olive gazelle]

i try not to rush haha i'm really trying to be good at this stuff in my sleep

[olive gazelle]

idk so advice is nice if i'm trying to be great at algebra what would u say that i would practice ? specifically what rudimentary skills?

[tropic oxide]

idk what khan calls the things i have in mind

can you show a topic list for prealgebra

[olive gazelle]

https://www.khanacademy.org/math/pre-algebra

jesus! 18000 points 😭

what the hell is 74?

because i'm thinking 10 represents minutes :/

[tropic oxide]

no, the 10 in the formula does not stand for 10 minutes...

anyway, these might be of use.

and also the rest of the stuff in the prealg module

cause might as well

[tropic oxide]

74 is 74
it does kind of have a physical meaning but said meaning is irrelevant to the problem

[olive gazelle]

yeah but then what does 10 represent?

exponent represents minutes?

[olive gazelle]

i see. it's relevant to this formula, but it's true meaning it's out of scope for this problem

it's just something we accept as is

[olive gazelle]

and for sure i'm definetely going to incorporate this into my routine doing some prealgebra everyday

[tropic oxide]

10 is just 10, it does not represent anything in particular.

the number of minutes, as stated in the problem in clear language, is represented by the letter m

[olive gazelle]

lol

ok

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[hot widget]

H

[hot widget]

How do i prove the upper term with the binomial theorem?

Just a tip please

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[plush shore]

Hi.

[plush shore]

I'm struggling to solve this

I know how to apply L'Hopital, and multiplying by the conjugate, if that helps...

But honestly I don't know how to work with those factorial and the 9 raised to the n power

[proud barn]

what's sen(n)?

[plush shore]

I'm assuming that the limit when n approaches infinity will tend to 2 since sen (which is supposed to be sin) is limited

sen(n) is sin(n), it's just that in spanish is written like that

[plush shore]

But, most importantly, that 9 to the n power I assume will "grow" more rapidly than 7n! but idk

[proud barn]

is it (7n)! or 7 * (n!) ?

[plush shore]

Well... I'm not sure... it's written like that

[proud barn]

generally as n goes to infinity n! will grow faster than 9^n

because increasing n by one will multiply 9^n by 9

but it will multiply n! by n

so once n is bigger than 9, n! will grow faster

[plush shore]

A friend is telling me that a way of solving it is applying d'Alembert

I have no idea what that is

[proud barn]

googling it seems to be the ratio test

though that's generally applied to sums instead of limits

I don't know how rigorous you'd want to be but what I'd expect to happen is sin(n) and 9^n become insignificant as n tends to infinity so you're left with 7/4

if you actually want to prove it then you'd need to do a little bit of work to show that

[plush shore]

I'm on it right now. I've figured out that maybe dividing both quotient and divisors by n! leaves me with 7/4 + 2

Is that right?

Oh no. but also dividing 2 by n! leaves me with 0

so just 7/4

[proud barn]

the +2 isn't in the fraction so it should still be there

[plush shore]

So... +2 ?

7/4 + 2 ?

Thank you a lot Tom, my name is also Tom btw

[proud barn]

nice name

[plush shore]

Great choice by your parents

Have a good day

.close

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[chrome zinc]

can someone explain why this equations like this have a HA: y=0
when log graphs have a HA and when do it not

[hazy minnow]

HA?

[livid hound]

wdym by "like this"

[hazy minnow]

Ramonov do you know what they mean by "HA"?

[livid hound]

yes

based on context, horizontal asymptote

[hazy minnow]

oh am dumb thanks.

[livid hound]

it would be best to understand how such asymptotes are determined and lessen the focus on the logs themselves

[chrome zinc]

horizontal asymptote

[chrome zinc]

where x is in both numerator and denominator

with degrees greater than 1

[livid hound]

lets forget about logs for a sec,
if you were asked for the horizontal asymptotes of to a rational function would you be able to do it?

[cedar kiln]

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[chrome zinc]

Yes

Nvm I figured it out

.close

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[marsh pond]

Will I ever run into problems with dividing by a common factor first before using the quadratic formula?

Or should I always go with the original values as best practice?

[granite eagle]

Do what suits u best for example its a factor of 2 or 10 then u can always take ur time.

Otherwise if the factor is like 7 or 13

[marsh pond]

The instructor used a=6, b=-16, c=4 and we both got to the same answer in the end but I’m just wondering if my way can cause issue

[granite eagle]

AND ur allowed to use calculator i wouldnt bother

[cosmic steppe]

They have the same roots, so it doesn't matter

[granite eagle]

no issue at all do what u feel like

[marsh pond]

OK

[granite eagle]

doing

[marsh pond]

In that case I think I would prefer simplifying first if there is a common factor as it would be less work with the quadratic formula

Dividing and multiplying with addition and subtraction involved still feel like magic to me for some reason .. a+b=0 is the same thing as 2a+2b=0

But I just need to get used to that

[granite eagle]

think of it in terms of shopping

1 dollar gets u A and B

2 dollars get u 2A and 2B

[marsh pond]

Or with 0 as the answer I think that’s where it trips me up, I feel like it should be 2*0 but that’s still 0

[granite eagle]

hmm

tho thats whats u'll have to do the most later on

kay bye

[marsh pond]

Right with the quadratic formula

[granite eagle]

u still not clear?

[marsh pond]

Thanks 🙏

Makes sense

[granite eagle]

😘

[marsh pond]

https://tenor.com/view/jim-carrey-ace-ventura-you-got-it-good-thumbs-up-gif-14080310

[cedar kiln]

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[obsidian coral]

Do you know what f(-3) means?

[ashen palm]

no, idk what this entire question means

[obsidian coral]

Do you know what functions are?

[ashen palm]

yea kinda

[obsidian coral]

Here is my suggestion

https://www.youtube.com/watch?v=_e0EdFGpcvc&ab_channel=Mario'sMathTutoring

[ashen palm]

okay

[worthy bobcat]

yh

fg(x)
gf(x) are different btw many people mess up with these

[ashen palm]

okay thank you

[obsidian coral]

For that part, you can look up composite functions

[worthy bobcat]

^ yh

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[balmy apex]

Let $I = [0, 1]$ an interval and $\tau = {x_0,x_1,x_2}$ with $x_0 = 0, x_1=\frac{1}{2}, x_2 = 1$. Determine the basis of the spline "dimension" (not sure about the translation here) $\Bbb P_{3,\tau}(I, \Bbb R) = { s \in C^1(I, \Bbb R) : s|_{[x_i, x_i+1]} \in \Pi_2, i = 0, 1 }$ consisting of b splines. Sketch the base polynomials.

[wraith dagger]

illuminator3

[balmy apex]

not sure how to go about this

do I just

plug i=0 and i=1 into the equation for a b-spline where k=3 and then sketch those polynomials that I get?

[sage forge]

Hello, there

[balmy apex]

how would you translate "raum" as in "spline raum"?

[sage forge]

Maybe "spline space"?

https://www.henked.de/woerterbuch.htm#E

[balmy apex]

ah yes

good one

[sage forge]

That's what I'm using normally.

[balmy apex]

instead of dimension, space here

[sage forge]

But your question is obviously too advanced for me

[balmy apex]

just needed the translation

[balmy apex]

<@&286206848099549185>

[cedar kiln]

@balmy apex Has your question been resolved?

[balmy apex]

sure

my internet just went out lol

[cedar kiln]

@balmy apex Has your question been resolved?

[balmy apex]

.close

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[latent flame]

It's asking for the number of real roots of this equation

[quartz frost]

this might help

[latent flame]

aight

.close

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[amber cipher]

Can you use the rules of derivatives for ex: product rule, quotient rule for integration?

[zenith shadow]

Yes, but they won't be as powerful. Product rule becomes integration by parts and chain rule becomes u-substitution

[amber cipher]

so the formulas are a bit different?

[zenith shadow]

Yeah since they contain integrals, but they are derived from their derivative counterparts

[amber cipher]

Okay I get it

one more thing

if you have

2 / x^2

when you bring the x to the two is it 2 * x^-2 or 2 - x^-2?

[zenith shadow]

Oh yeah sorry

Oh but you get -3 in the exponent

[amber cipher]

yeah when you take the derivative

I was lost for a moment

[zenith shadow]

Nwm yeah that's just if you take the derivative

[amber cipher]

thanks for the help

[zenith shadow]

Np

[amber cipher]

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[amber cipher]

Another question

[amber cipher]

when you have 2x - 3x^-2

you can just do 2x /3x^2?

or does it need to be 2x * 3x^2 to apply that?

[long arrow]

wdym? you're asking can you change subtraction into a division?

[amber cipher]

No what I mean

if you have 2x - 3x^-2 can you change it into 2x / 3x^2

to remove the minus from the exponent

[long arrow]

you can change 3x^(-2) into 3/x^2

then it's 2x - 3/x^2

[amber cipher]

and the minus does it go away?

[long arrow]

yes

[amber cipher]

and if it was + would that become a minus

[long arrow]

$$a^{-n}=\frac{1}{a^{n}}$$

[wraith dagger]

Modus

[amber cipher]

No I meant

[long arrow]

minus from subtraction obv stays

[amber cipher]

really

[long arrow]

$$2x-3x^{-2}=2x-\frac{3}{x^{2}}=\frac{2x^{3}-3}{x^{2}}$$

[wraith dagger]

Modus

[long arrow]

you can rewrite it that way if you want to "subtract"

[amber cipher]

but you cant take the 3 with it?

so 2x / 3x^2?

[long arrow]

you definitely can't do that, it's not the same

[amber cipher]

Got it

[long arrow]

2x * 3x^(-2) then yes

but

it's (6x)/x^2

[amber cipher]

yeah so only the x goes

the real numbers stays above

[long arrow]

yes because it's 3x^(-2) not (3x)^(-2)

or smth like that

[amber cipher]

whats the difference between those two?

arent they the same

[long arrow]

$$3x^{-2}=\frac{3}{x^{2}}$$
$$(3x)^{-2}=3^{-2} \cdot x^{-2}=\frac{1}{9} \cdot \frac{1}{x^{2}}=\frac{1}{9x^{2}}$$

[wraith dagger]

Modus

[amber cipher]

Got it

thanks for the help

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[stoic bough]

I have a rather basic calculus question:
Suppose we have an arbitrary function f(x) and a function g(X) = c * f(x), where c is a real number other than 1 or 0.
Thus, g²(x) = c² * f²(x)
Taking a derivative of it:
dg²(x)/dx = 1/2 * g(x) = 1/2 * c * f(x)
Yet, also:
dg²(x)/dx = d( c² * f²(x))/dx = c² * 1/2 * f(x)

But it's obvious that 1/2 * c * f(x) is not equal to c² * 1/2 * f(x)
What am I doing wrong?

[stoic bough]

Oops, I sent it too early...

Just a minute 'till I edit it

[long arrow]

rather c^2 * f^2(x)

[stoic bough]

Alright

Alright, the question is fixed. Can anyone please see my mistake?

[wraith dagger]

Frogieder

[long arrow]

?

you have g^2(x) = c^2 * f^2(x) and now you want to differentiate both sides, right?

[stoic bough]

Yes, we can state it that way

The problem is that the results differ

c is squared only in the second case

[long arrow]

imo it should be:

$$2g(x)g'(x)=2c^{2}f(x)f'(x)$$

[wraith dagger]

Modus

[long arrow]

by chain rule

[stoic bough]

Ooooh, I see

So that's what I did wrong

And yeah, I messed up the 1/2 two

Rookie mistakes

Thank you

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[marsh pond]

How do you prefer reading / writing f(x) and why do you prefer using that cursive?

[violet flume]

anything consistent

[chrome zinc]

why are we posting writing questions in a math channel

[marsh pond]

It’s a math question

[chrome zinc]

not sure writing f(x) 3 times counts as math

[violet flume]

take it easy scarecrow

id say anything consistent

personally

players choice

sorta deal

[marsh pond]

https://tenor.com/view/you-see-me-trollin-trolling-weird-al-yankovic-weird-al-yankovic-gif-14439293

OK ty

[buoyant latch]

$f(x)$ looks the best

[wraith dagger]

Frosst

[buoyant latch]

With the little curl at the bottom of the f

[dire geode]

you guys done trolling yet?

[cedar kiln]

@marsh pond Has your question been resolved?

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[hot rivet]

How do I do the second part of this?

I specifically not sure how to convert to a directional vector

[bold hinge]

Line = (Position Vector) + (Direction Vector)(Free Variable)

Just separate out the constant terms

Keep only the terms that vary with t

[hot rivet]

Oh ok

so for R1 <2,-7,2>

[mental granite]

as a vector $[5+2t_{1},43 -7t_{1},2t_{1}]$

[wraith dagger]

duckduckdo

[hot rivet]

got it

thanks!

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[spare pelican]

the number of students visiting a school A in the xth year since its opening is A(x) = ka^(x), where k and a are positive constants. The number of students visiting the school in the 3rd year are 3110400 and in the 5th year: 4478976

(a) Find k and a

[spare pelican]

This is what I did but

When I try to solve the 2 simultaneous equations, I get an error

[sacred stone]

why you wrote $ka^{3110400}$?

[wraith dagger]

秋水

[sacred stone]

$$A(3) = ka^3 = 3110400$$

[wraith dagger]

秋水

[spare pelican]

oh

😭

thank you so much @sacred stone

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[spare pelican]

.reopen

[cedar kiln]

✅

[spare pelican]

i did that,
and after i solved them both i got logk = 1057536

and loga = 684288

but idk if thats right and idk how to go forward

[sacred stone]

$$A(3) = ka^3 = 3110400$$
$$A(5) = ka^5 = 4478976$$
then
$$\frac{ka^5}{ka^3} = a^2 =\frac{4478976}{3110400}$$

[wraith dagger]

秋水

[sacred stone]

,w 4478976/3110400

[wraith dagger]

Results provided by WolframAlpha

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

Requested by 秋水#5244

[sacred stone]

so $a^2 = \frac{35}{25}$, and you know $a>0$, so $a=\frac{6}{5}$

[wraith dagger]

秋水

[spare pelican]

Ohhhhh

[spare pelican]

thank you sooo much 😭

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[rigid valve]

How do I even start solving this?

It's supposed to be solved using the invariant principle, but I have failed multiple times in finding an invariant.

[sly iris]

This might be somewhat useful

If you can see what im going for here

[tropic oxide]

i have come up with an idea that does not serve as a solution in its own right but might be of use

if any of the edges of the square grid is clean (i.e. has no infected students), it'll always remain clean

[rigid valve]

Why is that?

[tropic oxide]

i'll use the front row as an example, but the same argument works for all four sides

if on some day the front row is clean, then for any student sitting in it there is at most one infected student adjacent to them

which is, by our rules, not enough to spread

[rigid valve]

Does that really hold?

Ah you mean the whole front row is clean

In that case, yeah I agree

[rigid valve]

Sorry, I don't see the purpose

[rigid valve]

I don't think the case for edges is necessarily true

[tropic oxide]

wdym

[rigid valve]

In the example in the text itself, the top right corner is initially clean, but it does eventually become infected.

[tropic oxide]

ok but that's a corner

in the example shown in the text, no edge starts out clean

[rigid valve]

What are you referring to by edges?

Like a whole outmost row or column?

[tropic oxide]

yes

[rigid valve]

Yeah right

Hmm still can't see what an invariant could be unfortunately

Other than the size of the classroom lol

[cedar kiln]

@rigid valve Has your question been resolved?

[rigid valve]

maybe writing down all the cases under which one cell can be infected would help?

that is, drawing all the combinations of 2, 3, and 4 cells that infect other cells

[cedar kiln]

@rigid valve Has your question been resolved?

[cedar kiln]

@rigid valve Has your question been resolved?

[rigid valve]

as a side note, how do I get better at invariants in general? as in, what point do I focus on improving?

may double each number in a row or subtract 1 from each number of a column. Prove that
you can reach a table of zeroes by a sequence of these permitted moves.```

Since this one is apparently another invariant problem, but I don't see where I could start.

[cedar kiln]

@rigid valve Has your question been resolved?

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[burnt sphinx]

help with 5?

[burnt sphinx]

these are things I tried but didn’t work

well, i didnt get the book answer

[ionic moon]

Don't you just need to express u and c?

[burnt sphinx]

express u in terms of other variables.

[ionic moon]

well, what seems to be the problem?

we can think of f' as f'/1

[burnt sphinx]

that I don’t know what to do to get the book answer

,close

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[quartz nebula]

Can i get help with this question

[pine saffron]

You need help for all of them?

[quartz nebula]

its all based on one question

but yeah

I do

[pine saffron]

Ok so first of all you should graph y = x^2

You know how to do that?

[quartz nebula]

yes

I do

[pine saffron]

You could graph it from x =-3,-2,…,3

After that you should create a table. In this table you write for every x coordinate the corresponding y value

So for example x=2 -> y = 4

Now for the transformation, instead of calling it y=x^2 call it g(x)=x^2

Just to make things clearer

Now the question is, what transformation to g(x) = x^2 has to be done to get f(x) = 2(x+1)^2 + 5

These transformations you graph separately

The first one would be g(x+1) = (x+1)^2

You then graph each transformation

[cedar kiln]

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[spiral dune]

may someone help me with 2 iii)

[spiral dune]

i’m not sure how to answer the question

[sick ruin]

@spiral dune which one is 2

[spiral dune]

the one in the middle sorry

Which states use the Intermediate Value Theorem

[sick ruin]

do you know what IVT says

[spiral dune]

Yes

Let f be a continous function on [a,b]. If k is any number between f(a) and f(b) , there exists a number c (a,b) such that f(c) =k

[sick ruin]

right

[spiral dune]

that’s how they define it in my curriculum

[sick ruin]

do you understand what that's saying though

[spiral dune]

but 2^x cannot be k right?

[sick ruin]

no

you want to show that there's a solution inside the interval

the fundamental idea of IVT is that if a function is positive on one end of an interval and negative on the other end, it must reach 0 somewhere in between

[sick ruin]

but the general definition expands this from positive/negative/zero to any value in between f(a) and f(b)

does that make sense?

[spiral dune]

please give me a second to try and understand it

okay i think i get it

[sick ruin]

ok lit

[sick ruin]

this is a hint. Try to use this idea to solve the problem

[spiral dune]

okay hold on

okay idk if this is right or wrong

i omitted the substitution to save time

[sick ruin]

almost, it should be 2^x + x = 4

[spiral dune]

ohh minor error💔

[sick ruin]

f(2) = 4 + 2 = 6

haha

but you've got the idea right

[spiral dune]

I keep rushing the calculations, it’s 11pm where im at, but i think i’m getting the hang of it

[sick ruin]

I did this:
4 - x - 2^x = 0
f(1) = 1
f(2) = -2
Hence it must reach 0 somewhere in between

[sick ruin]

dont worry about it lol

[spiral dune]

is that the way i should’ve done it or it’s another way to kill the cat?

[sick ruin]

another way to kill the cat, lol

[spiral dune]

okay okay

[sick ruin]

there's no "correct way" for anything, if it works it works lol

[spiral dune]

thank you 🫶🏿

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[steady plover]

Hi. Does conjugation only works for binomials? What about when there are more than two terms in the denominator of the expression?

[steady plover]

Like, $\frac{1}{x+2+\sqrt{2}}$?

[wraith dagger]

Shinutsi

[upper abyss]

Like, you want to rationalize the denominator? Then (x+2)-(√2) would work

@steady plover

[steady plover]

Oh I see

Wait, does multiplying it with the entire term (x+2+√2) also works?

[buoyant latch]

No

[steady plover]

Oh okay

[buoyant latch]

Why both +

If you have 2+√2 on the bottom and you multiply it by another 2+√2 you’d just get 6 + 2√2

There’s still a root

[steady plover]

Oh yeah

So it's just (x+2)-(√2) then

[buoyant latch]

If you multiply by x+2-√2 then it works

[upper abyss]

Yes, multiplying it by x+2-√2 would work, as that's the same as (x+2)-(√2)
I just put the parenthesis there to show off why this would work

[steady plover]

I see

[buoyant latch]

It’s the same as with the brackets they are just for show

[steady plover]

I thought at first they're the factored form of the trinomial lol

Alr, thanks guys

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[cedar kiln]

@tall finch Has your question been resolved?

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[dusty loom]

A proper solution is need
Please help

[muted bear]

the first thing i would do is separate the integral

[grizzled dome]

I can't stay to help, but I'd start by drawing a graph! Think about what happens between x=0 and x=1 (since [x] is constant in that range -- it's just zero. That'll make it easier to figure out what [[x]-sin x] is). Next think about what happens between x=1 and x=pi/2 (again, [x] is constant in that range -- it's equal to one). Do the same for the interval from x=-1 to x=0, and x=-pi/2 to x=-1.

[cedar kiln]

@dusty loom Has your question been resolved?

[dusty loom]

@grizzled dome
Okay lets say
Ceil x is always an integer which it is
So ceil (I + x)= I + ceil x
Is this correct?

[grizzled dome]

Is I an integer? Then that's a true statement... but actually in the question, [x] is the floor function, not the ceiling. (The largest integer less than or equal to x)

[cedar kiln]

@dusty loom Has your question been resolved?

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[cedar kiln]

@plain bridge Has your question been resolved?

[cedar kiln]

@plain bridge Has your question been resolved?

[cedar kiln]

@plain bridge Has your question been resolved?

[proud barn]

it may be easier to work with if you write the 2 new vectors as linear combinations of U

then try to figure out what x has to be to let you show the 3 original vectors are in the span of the new basis

[cedar kiln]

@plain bridge Has your question been resolved?

[quartz frost]

you know what a linear combination is?

[cedar kiln]

@plain bridge Has your question been resolved?

[limber rain]

Help me with this please

[dire geode]

read #❓how-to-get-help

[limber rain]

Read

[shell lance]

We can see that the subspace has dimension 3

So we know that a set of 3 linearly independent vectors of U will form a basis of U

[cedar kiln]

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[crimson sedge]

can someone explain how he got 20?

I dont understand the C4/3 part

[flint plinth]

well what do you think the value of $C_3^4$ is?

[wraith dagger]

OurBelovedBungo

[crimson sedge]

I dont know

[flint plinth]

$C_3^4 = {4 \choose 3} = \frac{4!}{3!1!} = \frac{4!}{3!} = \frac{4\cdot 3\cdot 2\cdot 1}{3\cdot 2\cdot 1} = 4$

[wraith dagger]

OurBelovedBungo

[crimson sedge]

ohh

[flint plinth]

you can also see it directly: how many ways are there to choose three numbers out of four if I don't care about order? if the four numbers are 1,2,3,4 then I can choose 1,2,3 or 1,2,4 or 1,3,4 or 2,3,4, that's 4 ways

[crimson sedge]

ok I understand this now

thank you

[flint plinth]

cool

pleasure

[crimson sedge]

.close

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[storm junco]

what do you do when you have something like 4^5 + 4^6 power? can you simply this further

[violet flume]

you can factor

[storm junco]

huh?

how

[violet flume]

factor out 4^5

idk if id call it simplification

[storm junco]

wdym factor out

oh u mean the outcome being 4^1

aka 4

[violet flume]

$4^5 + 4^6 = 4^5(5)$

[wraith dagger]

jan Niku

[violet flume]

yea

and i guess i mean

theyre numbers so u can just solve it

[storm junco]

that looks dif then what i said

[violet flume]

but idk what you mean simplify

[storm junco]

wait so what would that be in exponents next to the 4?

whats 4^5(5) whats that five doin

[violet flume]

$4^5 + 4^6 = 4^5(1+4^1) = 4^5(1+4) = 4^5 (5)$

[wraith dagger]

jan Niku

[violet flume]

its just multiplication

[storm junco]

but u couldnt simplfy or factor it anyfurther granted the 4s are x

[violet flume]

not in general, no

[storm junco]

what about 4^5+4^7

[violet flume]

obviously there are special cases

same deal

[storm junco]

can u show it solved

i want to see the differences

i dont quite understand yet

[violet flume]

,calc 4^5+4^7

[wraith dagger]

Result:

17408

[storm junco]

or no like the answer above

[storm junco]

t

[violet flume]

$4^5 + 4^7 = 4^5(1+4^2) = 4^5(1+16) = 4^5 (17)$

[wraith dagger]

jan Niku

[storm junco]

and the 4 in the first = on the right that 4 is the number of 4^7

aka if it was 4^5+5^7 it would = 4^5(1+5^2)

[violet flume]

no

you should review exponentiation

[storm junco]

where can i do that?

[violet flume]

you cannot factor this

are you in a math class?

[storm junco]

i looked at khan and they only showed multiplication

[violet flume]

do you have a book?

[storm junco]

no

[violet flume]

exponentiation is multiplication

[storm junco]

ye

4^4 = 444*4

oh italic

[violet flume]

ikwym

[storm junco]

but im purely confused on the addition and subtraction of exponents

idk where to learn it tho

thats why i came here

[violet flume]

addition and subtraction?

[storm junco]

of exponents

[violet flume]

i can link lectures or whatever but i think just doing problems

thats why i ask if you have a book

[storm junco]

x^2-x^4

uh

[violet flume]

this simplifies

[storm junco]

no i dont have a book

yeah but im a senior so its not gonna be in there anyways

could u link lectures?

[violet flume]

https://www.youtube.com/watch?v=LMmmRY-vvYg&list=PLX2gX-ftPVXV8Egh8GQFoB-4jjBjyn0jA&ab_channel=MichelvanBiezen

[storm junco]

ok dope ty

.close

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[violet flume]

you should obviously pause and try the problems by yourself

if you can

the practice will help more than the lectures IMHO

[storm junco]

ye i gotchu

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[crimson sedge]

i needed help with this

[fiery whale]

Can you answer any of them?

[crimson sedge]

yes

number 6 is f

[fiery whale]

Yea

What ones are you stuck on

[crimson sedge]

the rest

[fiery whale]

Ok consider d

What could that be

[crimson sedge]

a square since all of the sides of a aquare are congruent?

*square

[fiery whale]

Yea

So what would a be?

[crimson sedge]

a rectangle

?

[fiery whale]

Mhm

It could've been a square but that one is takenm

[crimson sedge]

yeah

[crimson sedge]

what about equilateral and equiangular and qudrilateral

[fiery whale]

Equiangular means identical angles on all vertices

[crimson sedge]

yes

[fiery whale]

So that would be rectangle or square

[crimson sedge]

yes

[fiery whale]

Equilateral means same lengths on each size

[crimson sedge]

yes

[fiery whale]

So can only be square

[crimson sedge]

but we already did square

[fiery whale]

Yeah equilateral quad = square
equiangular is rectangle

[crimson sedge]

so then what would it be

[fiery whale]

What would what be

[crimson sedge]

and isn't f isocles trapezoid?

[crimson sedge]

e

what would letter e be

[fiery whale]

Ohh

Ohh shit that would be the square

[crimson sedge]

yeah

[fiery whale]

Didnt see that one

Lol

Ig then a would be rectangle still

[crimson sedge]

and isn't f isoceles trapezoid

?

cause it says other sides congruent

and there is two sides left

and iscoles is two sides

[fiery whale]

Yeah

[crimson sedge]

ok

[crimson sedge]

so we have 1 3 and 5 left

i dont know what to do for kite @fiery whale

[fiery whale]

Pretty sure that would be c

[crimson sedge]

ah ok

[crimson sedge]

what would 1 be

b right?

and wouldn't number three be d

@fiery whale

.close

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[pseudo veldt]

Does anyone know how to solve these

[cedar kiln]

@pseudo veldt Has your question been resolved?

[cedar kiln]

@pseudo veldt Has your question been resolved?

[dire geode]

picture of a monitor and keyboard :|. can you just upload a screenshot?

[cedar kiln]

@pseudo veldt Has your question been resolved?

[ocean mural]

did you watch the video i sent

you cannot solve these if you have no idea how transformations affect the equation of a function

[cedar kiln]

@pseudo veldt Has your question been resolved?

[simple osprey]

hey i need help

[cedar kiln]

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[simple flare]

Hi May I know how to solve this ?

How to start?

May I know first octant is how and what’s the limit?

[vernal palm]

looks like we should convert to polar coordinates

do yk how to do that?

[simple flare]

I did like this

Is it correct?

[vernal palm]

lemme check

yeah looks good

[simple flare]

How about this?

This I have total no idea

Don’t know how to start also 😭

[vernal palm]

you should look at khan academy

that can give u an idea

[simple flare]

May I know how to start?

[vernal palm]

their multivariable calculus course

[simple flare]

I didn’t did any two spheres before

[vernal palm]

then that will teach you

[simple flare]

Erm, but can you tell me how to start?

[vernal palm]

I'm not confident enough in my abilities and also my phone is about to die

[simple flare]

Erm nvm, I tag helper again

[vernal palm]

no

please check khan academy first

[simple flare]

I learnt myself alrrady

I didn’t see both spheres

[vernal palm]

fine whatever then

[simple flare]

<@&286206848099549185>

May I know how to solve for this?

I need tips on how I start for two spheres

[simple flare]

I got this

But second one gave me 0

[gaunt hamlet]

How'd you get 0? @simple flare

[cedar kiln]

@simple flare Has your question been resolved?

[simple flare]

The second one

Second then I cannot solve

[gaunt hamlet]

Wdym second one

cos² is always positive, so I don't know how you're getting 0 from integrating

[simple flare]

This

I did 0

[gaunt hamlet]

I'm not quite sure what you're asking. Do you know how to integrate cos² θ?

[simple flare]

I use app

And the app give me 0 for that part

The limit correct?

[gaunt hamlet]

You must've put it into the app wrong

Did you make sure to put dθ dφ rather than dφ dθ?

[simple flare]

Oh, I make a mistake 🫠

Any way thanks

[simple flare]

.close

[cedar kiln]

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[warm cargo]

I'm pretty sure i need to use

[cedar kiln]

@warm cargo Has your question been resolved?

[warm cargo]

<@&286206848099549185>

meh I'll just ask my professor tmr

is ok its a weird one

baiiii

.close

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[zinc belfry]

This in exponential form is it

[buoyant latch]

That does work

[zinc belfry]

Okay sweet thank you

.close

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[odd seal]

is this right? I usually get longer numbers for answers so this time I'm concerned

[odd seal]

Ben why you still awake

what's your timezone man

[hazy minnow]

lol.

,ti

[wraith dagger]

The current time for BenJr is 04:27 AM (EDT) on Fri, 08/07/2022.

[odd seal]

holy shit man

I'm pst

,ti

[wraith dagger]

The current time for liluzibird is 01:27 AM (PDT) on Fri, 08/07/2022.

[odd seal]

I wonder how discord knows my location

must be ip address or something

[hazy minnow]

You set it.

Ok for the problem.

m = 18 is correct.

Your c = -sqrt(7) is correct.

[odd seal]

nice

I think this is the last one

pretty similar

[hazy minnow]

Both are correct.

[odd seal]

and I keep messing up on these so I've been practicing them

so if I understand f'>0 and f''>0 means positive

[hazy minnow]

Yeah

[odd seal]

and I draw them like that they seem to be going up

I usually have difficulty with f''

f' is pretty straightforward

[hazy minnow]

f’ > 0 means f is increasing.
f’’ > 0 means f’ is increasing.

At that point of interest.

[odd seal]

ohh

hmm that makes things slightly easier

so if f'>0 then f''>0

sometimes I see f'<0 and f''>0 though

[hazy minnow]

No not generally.

If f’ is increasing then f’’ > 0.

[hazy minnow]

That means f is decreasing but f’ is increasing.

[odd seal]

so am I doing this right?

The way I see it is we draw until the point where the graph changes

so it's starting to go back up

and that's negative

f''<0

f'>0

[hazy minnow]

Yeah.

[odd seal]

cool I think I got it then

[hazy minnow]

I am tired so I can’t think as fast right now.

[odd seal]

I'm sorry ben

maybe you should sleep bro

[hazy minnow]

It’s good, I am trying to reset my sleep schedule.

It’s all messed up.

[rotund vine]

like a way to think about this is that
f'(x) is the rate of change of f(x) (slope)
and f''(x) is the rate of change of f'(x)

[odd seal]

rate of change is the same thing as slope right

[rotund vine]

yeah

[odd seal]

so ben is saying when my f(x) goes down then f'(x) also goes down. Since f'(x) is going down then f''(x) is also going down?

[hazy minnow]

f’(x) is negative.

Try not to confuse things with the graph.

Also try being more precise for things like this.

If f(x) is decreasing then f’(x) < 0.

[odd seal]

yes

f'(x)<0 means that f(x) is decreasing got it

and if f''(x)<0 then that means f'(x) is decreasing?

eh I'll just try to keep drawing to the inflection point

hot damn it's late

.close

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[cedar kiln]

@dull thorn Has your question been resolved?

[cedar kiln]

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[rain temple]

I need help with radians

[tropic oxide]

what is this hat placed on top of the 0.275

[rain temple]

Negative numbers

[tropic oxide]

??

then why not just -0.275

when you say you "need help with radians" though, does that mean you would be able to do this if the question used degrees?

[rain temple]

Yea

[tropic oxide]

ok then the interval they give you for d is (180°, 270°)

[rain temple]

Yea

[tropic oxide]

does this enable you to solve the problem?

[rain temple]

Yes

I got ¯0.28603

Is that right

[tropic oxide]

definitely not

d is in the third quadrant, so tan(d) is positive.

[cedar kiln]

@rain temple Has your question been resolved?

[cedar kiln]

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[open dagger]

if sin theta = x then sin inverse of x should give you theta

arcsin, if you prefer that

it should look like $\sin^{-1}$ on your calculator

[wraith dagger]

Yash

[open dagger]

similarly for the tangent and cosine functions too

[spiral star]

Thanks

.close

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[wanton bison]

Can someone explain how to write the equations or they? For what value of k does the quadratic equation x2 + 14x + k = 0 have two distinct real roots?

[sand hazel]

so

[obsidian coral]

Use the discriminant

b^2 - 4ac

[sand hazel]

for a parabola to have 2 distinct roots

the discriminant must be >0

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@wanton bison Has your question been resolved?

[cedar kiln]

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[deft hatch]

So the question is of AP where
S4 is provided and it is said that
S4 = one - third of the next four terms

[deft hatch]

"next four terms" kinda thru me off

so im thinking

S4 = one third of T5 + T6+ T7 + T8

will this work?

first term is given = 1

[dusty hazel]

Send the question exactly.

If that is possible.

[deft hatch]

Yea Yea

One sec

Wait my phone is dead so ill just type it

T_T

Find the common difference of an A.P. whose first term is 1 and the sum of first four terms is one third of the sum of the next four terms

@dusty hazel

just tell if my method will work or not

i kinda wanna do it on my own

[velvet mortar]

Yeah makes more sense

"the sum of"

[deft hatch]

S4 = one third of T5 + T6+ T7 + T8

Yea so this is correct?

[dusty hazel]

Sure.

It is correct.

[velvet mortar]

Ye

[deft hatch]

Thanks guys

ill try it rn

ill tell if i face

any problem

[dusty hazel]

👍

[deft hatch]

d = 2

ty guys

.close

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[deft hatch]

Can someone tell what do to

[deft hatch]

if like an AP is given

and its asked

find the first term

thats negative

so i take Tn as?

[velvet mortar]

What if it's positive?

What do you do?

[deft hatch]

well generally its asked like

find which term is 85 or something

then u put Tn as 85

and so on

but like

first term negative

[velvet mortar]

So?

What is the original question?

[deft hatch]

Which term of the progression 27,24,21

is the first negative term

d = -3

a is given

so Tn formula

but what do i take Tn as??

[velvet mortar]

What is a given?

[deft hatch]

27 xD

[deft hatch]

see

[velvet mortar]

Oh

[deft hatch]

just like a hint

🙏