help-19

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[cedar cargo]

I need help

[cedar cargo]

So the deminsions are 28:20

And the scale is 1:2

So how would I know when to multiply or divide

Do I divide when the first number is greater

.close

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[wet spoke]

I know that question 37 has something to do with inscribed angles but am not sure on how to solve it, can you go over it step by step?

[odd edge]

@wet spoke Has your question been resolved?

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@wet spoke Has your question been resolved?

[wet spoke]

.close

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[nimble silo]

can someone explain me this solution pls

[nimble silo]

How are both maxima?

[broken kite]

maxima is a relative term which is a local maxima

If just after it and just before it, the qtity is less than itself its an local maxima

if a qtity just before it and after it is greater than itself its local minima

[nimble silo]

oh

[nimble silo]

I got it

thanku so much

[broken kite]

Sure

[odd edge]

@nimble silo Has your question been resolved?

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[mystic saffron]

Hi there, I need some quick help with means and scalar multiplication.
I have a set of 3D vectors that I evenly cut into 4 non-overlapping subsets of equal size n, A, B, C, D.
I then calculate the mean of each of these subsets, a, b, c, d.
Now I would like to get the mean of a union of these subsets by only using the values of a, b, c, d and n. As an example, let's take the union A ∪ B ∪ C.
Following the train of thought from the attached image, I should be able to get the combined mean by doing (na+nb+nc)/3n = n(a+b+c)/3n = (a+b+c)/3.
Is my assumption correct or have I made a mistake somewhere? Thanks in advance.

[mystic saffron]

Also please ping if you respond, thank you :D

[odd edge]

@mystic saffron Has your question been resolved?

[lavish knot]

you are correct

the math works out nicely since they all have the same cardinality

and are disjoint

so the average of the union of any m sets would be the average of the m individual means

[mystic saffron]

Awesome, thanks a lot

.close

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[little osprey]

Not sure how to solve this

I was initally thinking it would be zero, but zero is at the equilirium point

Thanks in advance

[faint knot]

is that a graph of displacement or velocity

[little osprey]

Id assume displacement?

?

[faint knot]

as a graph of displacement, you can look at the "y=-2" part of it

[little osprey]

someone posted and removed immediately lol

[faint knot]

yea because it really is 0 and theres no catch

[round bone]

Think about the slope of the tangent line

[little osprey]

ohhhh

[round bone]

Maybe recall Rolles theorem from your analysis class

[faint knot]

this is wrong
the graph has zero velocity at the ends
the graph is its maximum velocity at the equilibrium points

[round bone]

If f(a) = f(b) with a < b, then there exists c with a < c < b such that f'(c) = 0

[little osprey]

Im not in college yet lmao, its a long story, but im taking an AP physics class for fun (i am graduated on a gap year and all)

[little osprey]

OHHH

[round bone]

Let me know if this makes sense

[little osprey]

Can you tell i havent slept in a while lol

[faint knot]

you sound as slow as everyone else here

[little osprey]

A little over my head, but i get ya

[faint knot]

I think we're all tired

after your question I gotta post one of my own

[little osprey]

Well, I think this really helped! Thanks guys

[faint knot]

np

remember to .close

[little osprey]

.close

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[silver thicket]

can someone explain this to me, i thought it was logn

[lavish jackal]

try a programming server

but I think it explains to you why it's o(n)

"geometric sequence"

[odd edge]

@silver thicket Has your question been resolved?

[odd edge]

@silver thicket Has your question been resolved?

[hasty dome]

The outer loop might be log(n), but that's not the only thing that runs.

• j <- 1 runs once.
• z <- 5 runs log(n) times.
• j <- 2j runs log(n) times.
• z <- z^2 runs 1 + 2 + 4 + 8 + 16 + ... + n times.

Does that make sense so far?

Then, you can notice that:

• 1 + 2 = 3
• 1 + 2 + 4 = 7
• 1 + 2 + 4 + 8 = 15
• 1 + 2 + 4 + 8 + 16 = 31

Which is:

• 1 + 2 = 4 - 1
• 1 + 2 + 4 = 8 - 1
• 1 + 2 + 4 + 8 = 16 - 1
• 1 + 2 + 4 + 8 + 16 = 32 - 1

[odd edge]

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[cinder kelp]

i need help

[cinder kelp]

with a trig sum

can anybody help me

help

pls

somebody

anybody

[faint knot]

you need to post the question

[cinder kelp]

sorry

it is

taking time

[faint knot]

that thing on the left looks like the half-angle formula

[cinder kelp]

what is that

[faint knot]

oh then you dont know the half-angle formula thats not good

you wont need it

[cinder kelp]

no im a tenth grader

so like

[faint knot]

yea you learn the half-angle formula in trig

in other words right now, maybe yesterday

[cinder kelp]

?

[faint knot]

what you can do instead is

[cinder kelp]

yeah?

[faint knot]

,,\frac{\sqrt{1+\sin\theta}}{\sqrt{1-\sin\theta}}\color{yellow}\cdot\frac{\sqrt{1+\sin\theta}}{\sqrt{1+\sin\theta}}

[clever fjord]

matt07734

[cinder kelp]

OHHHH

RATIONALIZE ITT

[faint knot]

yea

[cinder kelp]

I GOT ITTT

THANK YOU SM

[faint knot]

nice

np

oh also

[cinder kelp]

yeah?

[faint knot]

,,\pm\sqrt{\frac{1+\cos\theta}{2}}=\cos\frac\theta2\
\pm\sqrt{\frac{1-\cos\theta}{2}}=\sin\frac\theta2

[clever fjord]

matt07734

[faint knot]

these are the half-angle formulas

[cinder kelp]

ohhh

[faint knot]

you have to manually write down in the ± whether the number is positive or negative though

thats a responsibility

[cinder kelp]

okay sir

🫡

thank you sm for the help

[faint knot]

np

[odd edge]

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[quasi pumice]

Can anyone help me with this logic question?

[quasi pumice]

I cant answer it genuinely

[late dust]

Only single-digit numbers?

[quasi pumice]

Yeah

[quasi pumice]

Natural numbers ranging from 1-9

and can u tell me how do you do it, because i really cant. Ive done this a lot of times and it always ends up with 1 single box being false

[late dust]

Ok first let's label the boxes

[quasi pumice]

Alright

Oh and btw

I forgot to tell you that 8+4:2=6, not 10

[late dust]

?

[quasi pumice]

It says that the operation doesnt follow normal mathematics

for example A+E:I

[faint knot]

the puzzle has to work left-to-right and ignores PEMDAS to be easier to calculate

[late dust]

Oh it goes from left to right and top to bottom?

[faint knot]

yea

[late dust]

That's stupid

[faint knot]

no its not

[quasi pumice]

Yeah ik, its weird

[quasi pumice]

Maybe for a genius like you it isnt, I am not and I dont know how these works LOL

[faint knot]

??? only a "genius" would think its stupid tf are you on about

its just a puzzle

[quasi pumice]

but i havent got the answers for a long time man

ive tried it, and it always leaves me with 1 single box being false

LOL

[faint knot]

I have a feeling there isnt one at all

[quasi pumice]

oh, damn

[faint knot]

Ill go test values

[quasi pumice]

alright man take your time

[faint knot]

hopefully Nel sees a way to solve this before I stumble across a solution

[quasi pumice]

Haha, alright the two of you

[late dust]

Lol fair enough

Let's look at C first, considering the first row

Only possible values are 1, 2, 3, 6

But if you consider the third column, it can't be 6, because you'd get 24 - K = O, and that can't fit

[quasi pumice]

How about A B C being 9:3x2

thats also possible isnt it?

[late dust]

Yes, C can be 1, 2, or 3

[quasi pumice]

Alright

[late dust]

No divisor can be greater than 4 (can't divide a single digit by 5 or more)

So B, I, L, N can be 1, 2, 3, 4

Oh never mind since the order of operation isn't standard, it only applies to B and N

No 0 allowed, right?

[faint knot]

always have the option of widening whats allowed and whats not if thats whats causing one box to be false

[quasi pumice]

I was thinking that what matters is the end value

So for example, I can say that A+E:I=M as 9+7:2=8

[late dust]

I guess it doesn't say whether an intermediate value can be negative?

[quasi pumice]

Nope, it only says that the missing value must be filled with natural numbers ranging from 1 - 9

[late dust]

Alright I don't know how to solve without trying each value for C

This should work:

I just picked 1 for C and tried to pick low values everywhere

[faint knot]

looks like H is a bit off

heres a question

you said that you could never get one square right

was H that square?
did you keep track of which squares were like H?

oh wait nvm I misread that + as a x

wait thats it

how did you get stuck on this

[late dust]

I wonder if there are multiple solutions tbh

[faint knot]

then Ill continue finding these solutions

[odd edge]

@quasi pumice Has your question been resolved?

[faint knot]

man you didnt even use any other numbers than 1 2 3 6 for this solution

[late dust]

Like I said, I tried to pick low values everywhere, easier to keep track of

If you pick 1 for C, then H can't be 2 (there are complex contraints on E, F, and L)

Can't be 1 either since 7 is prime

Not sure about 4 or greater

It's such a large search space and I don't know how to reduce it unfortunately

[odd edge]

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[quasi pumice]

.reopen

[odd edge]

✅

[quasi pumice]

Hey, I just want to say thanks to @late dust and @faint knot for your time and help

you both are helpful, have a blessed day guys

This is now resolved

[late dust]

[faint knot]

np

[odd edge]

@quasi pumice Has your question been resolved?

[faint knot]

remember to .close

[odd edge]

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[buoyant narwhal]

Hello everyone!
Can someone help me out with the exercise c) from this example?
I dont really understand how we can get such a Solution set if x3 = free variable.
How can I determine the solution set accordingly?

[odd edge]

@buoyant narwhal Has your question been resolved?

[odd edge]

@buoyant narwhal Has your question been resolved?

[vapid zinc]

Hey sorry, I have a pretty good understanding of vectors and planes but im not sure what a solution set is?

probably not the best person is to help you with this, but if you could explain that to me, I might be able to help?

[buoyant narwhal]

So the solution sets are given in the exercise. Basically if you have an SLE and you transform it with Gaus-Elimination or whatever and get a solution for x1, x2, x3 you can write it as a solution set.

[vapid zinc]

oh ok

[buoyant narwhal]

So the exercise is basically instead of finding the solution for the SLE we want to find the SLE from the solution.

[odd edge]

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[unborn flicker]

How is 1+2+3+4+5+6... called? It is not factorial, for factorial is multiplication.

[crisp wadi]

The sum $1 +2 + 3 + \dots + n$ is called the sum of first $n$ positive integers, but, if you are referring to the infinite sum, then you can call it the sum of all natural numbers

[clever fjord]

孤独な豆

[unborn flicker]

Okay, thank you.

.close

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[odd edge]

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[mystic saffron]

g(x) is 1/x + 1

confused how I would incorporate that into g(1/x)

would it be g(1/((1/x)+1)

[wise idol]

g(x) = 1/x + 1
g(1/x) = 1/(1/x) + 1

[mystic saffron]

$\frac{1}{\frac{1}{x}+1}$

[clever fjord]

mj

[mystic saffron]

is what im getting

$\frac {1}{\frac{1}{x}} + 1$

is what the answer is

[clever fjord]

mj

[mystic saffron]

^ i don't understand why

[cold plover]

Order of operations you have to do division first

So you plug 1/x into where x is

Divide first, then finally add 1

[mystic saffron]

but why wouldn't 1 be added in the numerator

is what I'm asking

1/x + 1 is the corresponding x value of g(x)

[odd edge]

@mystic saffron Has your question been resolved?

[cold plover]

Why would 1 be added to the numerator?

Even in what you thought was the answer you didn't add 1 to the numerator

[odd edge]

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[acoustic owl]

Linear Algebra questions (dimensions proof):

Let $\mathbb{F}$ be a subspace to $\mathbb{F}^2$. Let $x,y \in \mathbb{F}^2$ be two non-zero elements so that $x \in W$ and $y \notin W$. Determine dim(W).

I am unsure of how to approach this question and need some guidance.

[low locust]

there are some symbols missing

could you post a picture?

[acoustic owl]

oh, thanks! will fix!

what s Latex for ∉? lol

[low locust]

\notin

the first sentence doesnt make sense. I assume you mean that W is a subspace of F^2?

[clever fjord]

binnet

[acoustic owl]

Let's see if that did it... sorry, not used to wringing stuff like this on here...

Looks correct now 🙂

[low locust]

well, what are the possible dimensions of W

[acoustic owl]

1?

0,1 or 2?

[low locust]

yes

what would those mean geometrically?

[acoustic owl]

A vector space with a base that has 0, 1 or 2 vectors?

[low locust]

yes I mean imagine that we were in R^2. what kind of shape would W be if it had dimension 0,1 or 2

[acoustic owl]

The origin(nothing), a line, a plane?

[low locust]

well a point, not nothing

but yes

[acoustic owl]

Ah!

[low locust]

and if W is a plane, then its all of R^2

and then in general, if it has dimension 2, then its all of F^2

[acoustic owl]

Okay

[low locust]

so, now you have those two vectors x and y

both not the origin

x is in W. what does that mean with regard to those three options

[acoustic owl]

That W has at least 1 dimension?

[low locust]

yes

y is not in W

what does that mean

[acoustic owl]

Does that mean that it can't have more than one dimension?

[low locust]

why?

[acoustic owl]

I don't get this part. Nowhere does it say that x and y are linearly independent, so could there not be other vectors in W?

[low locust]

there could, yes

there are

0 is in W. 17x is in W

the point here is, if W had dimension 2, then it would have to be all of F^2

[acoustic owl]

Does this have anything to do with the definition that the dimension is the sub of the dimension of the bulls pace and so subspace?... (or something like that) =S

[acoustic owl]

Oh....!

I see!

Now it makes sense...

I guess that is enough of a proof to say that W has dimension 1 then!?

[low locust]

yes

[acoustic owl]

Thank you!

This looked so confusing, but was actually pretty straight forward.

!close

[low locust]

with a .

[acoustic owl]

!close.

like that? lol

.close

[odd edge]

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[acoustic owl]

oh, i get it... derp! Thanks a lot 🙂

[odd edge]

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[elfin warren]

Given the point A=(8,-1,3) the plane pi: 7x -2y +2z=7 and the line L: (-6,3,-1) + t(4,9,-5). Show that the line L and the plane pi are parallel. Determine the distance between them.

[elfin warren]

I don’t know how to do a pi sign but anyways

Does anyone know how to solve this?

[torpid harbor]

$\pi$ is how you do it

[clever fjord]

mophra

[elfin warren]

Oh okay

I know that n = (7,-2,2)

But how do I check if they are parallel to each other?

Do I do (7,-2,2) • (4,9,-5) and if that equals 0 then they are parallel?

[odd edge]

@elfin warren Has your question been resolved?

[elfin warren]

.close

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[supple shuttle]

would kindly need help

[storm granite]

Volume of Can / Box

[supple shuttle]

but how do i find the volume of both those things all i know is that for the cube its V = x^3

[storm granite]

area also can work but nvm

the volume of tin is
πx³/4
(r=x/2 and h=x)
and the volume of box is x³

[supple shuttle]

wait where does pi x cubed come from

isnt the volume formula for a cylinder = π x r^2 x h so π times x^2 x X ohhhh so its simplifies to πx^3

why do we divide by 4?

[storm granite]

r=x/2

[supple shuttle]

can you explain it further and how do i find the percentage

[storm granite]

there is nothing further to explain tho

just volume of tin divide by box
where tin = πr²h = π(x/2)²x = πx³/4
the final answer would be π/4 ≈ 78.5%

[supple shuttle]

V(prism) = a^2 h = (2r)^2 h = 4r^2 h
V(cylinder) = πr^2 h. πr^2 h/4r^2 h = π/4

cant i do that also?

[storm granite]

can

[supple shuttle]

thanks

[odd edge]

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[odd edge]

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[lime harbor]

question 11 is hard help

[lime harbor]

A theatre contains a central block of seats with n seats per row. Blocks on either side contain 4 seats per row. The number of rows is 5 less than the total number of seats per row. In total there are 126 seats in the theatre. Find the value of n.

[ember oak]

,rotate

[lime harbor]

i tried everything

it ijust aint working

this lesson is about quadratic formula and just quadratic equations in generak

maybe that information will help

[wheat flame]

the main thing to understand here is that 126 is a result of some "area" function

where the "length" is the total number of seats in a row

[lime harbor]

the key answers say the answer is 6 buy i have no idea how to get to it

[wheat flame]

and the "width" is the number of rows

[lime harbor]

soi what do i do

[wheat flame]

well you could represent the number of rows using the total number of seats per row

which will give you an equation with a single variable, which is then solvable

[lime harbor]

so what do i write

[wheat flame]

well, how do you represent the TOTAL number of seats per row?

[lime harbor]

🤷‍♂️

[wheat flame]

the central block has n seats per row

and the two side blocks are given

[lime harbor]

wow

andd now what

[wheat flame]

what's the total number of seats per row?

[lime harbor]

4…?

wair nkwas

no

126

its 2 am sorry

[wheat flame]

per row, not the entire theater

[lime harbor]

oh

4

i think

(its the only other number)

[wheat flame]

4 is the number of seats per row in one of the side blocks

[lime harbor]

n - 5

i rhink

[wheat flame]

no

[lime harbor]

just

just tell me the answer

and how to solve it

[wheat flame]

i am asking you to complete a very, very basic operation

[lime harbor]

uh

[wheat flame]

just ... try to understand what you're trying to solve

[lime harbor]

i promise im not that stupid its just 2 am

but i genuinely dont understand the question

[wheat flame]

ok there's 4 seats in a row on each of the two sides right

[lime harbor]

yes

[wheat flame]

and the central block has n seats in a row

[lime harbor]

yes

[wheat flame]

so now how many seats per row are there in total

[lime harbor]

31.5

no

wait

i dont know

[wheat flame]

theres 4 on one side

and another 4 on the other side

and theres n in the middle

[lime harbor]

8 + n

[wheat flame]

finally

that's your total number of seats per row

[lime harbor]

yes

[wheat flame]

but what's the total number of rows

[lime harbor]

n - 5?

[wheat flame]

well no, it says 5 less than the TOTAL number of rows

[lime harbor]

ohh

n * 4?

no what

[wheat flame]

this one is close

well... somewhat

[lime harbor]

126 - n

n - 126

[wheat flame]

sorry i mean

5 less than total number of seats per row

[lime harbor]

n - 5(8)

wait no

8(n-5)

[wheat flame]

ok wait

what's the total number of seats per row

[lime harbor]

8

[wheat flame]

... ?

[lime harbor]

dude trust me im a visual learner

i understand better if you just write the equations

[wheat flame]

yeah but you already gave me the answer awhile ago

[lime harbor]

i did?

[wheat flame]

i'm just asking you to repeat it

[lime harbor]

n - 5

maybev

OHH

per row

im so silly

4

[wheat flame]

oh my god

[lime harbor]

holy shit

im reatarded

im convinced

[wheat flame]

read through this again

[lime harbor]

8 + n

[wheat flame]

what's 5 LESS than that

[lime harbor]

5-n

[wheat flame]

ok i'll change it a little

what happens if you subtract 5 from 8+n

[lime harbor]

3-n

[wheat flame]

try it again

[lime harbor]

n-3

[wheat flame]

again

[lime harbor]

3+n

[wheat flame]

right

[lime harbor]

oh my god im reatarded

[wheat flame]

so you have your hypothetical "rectangle" right

[lime harbor]

yes

[wheat flame]

you have the area (total no. of seats)

[lime harbor]

yes

[wheat flame]

and to get that area you have "length" (total no. of seats per row) and "width" (total no. of rows)

[lime harbor]

OHHHHH

I GET IT

[wheat flame]

and both length and width are expressed in terms of n

[lime harbor]

I GET IT

(8+n)(3+n) = 126

[wheat flame]

YES

solve that

i know how it feels to do math past 11 or 12

DO NOT do this ever again

[lime harbor]

sir yes sir

[wheat flame]

you are likely to get two different n's solving this

since this is a physical quantity you should only take the positive solution

[lime harbor]

Oh mt GOD

-17 AND 6

I GOT IT RIGHT

im

smart

no im not

but still

hooray

thank you so much

i get it

im going to sleep now

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[quartz agate]

I have confusion with this question.

[quartz agate]

So first of all, these are the prior question

Ive solved a-c. And here are my answers.
1a.

0 0 4 x_1 0
[ 0 -2 6 ] [ x_2 ] = [ 0 ]
3 6 -3 x_3 0

b. rank 3

c.
L = [[1,0,0],[0,1,0],[0,-1,1]]
U = [[3,6,-3],[0,-2,6],[0,0,10]]
P = [[0,0,1],[0,1,0],[1,0,0]]

When I tried question d, i tried to follow this video.
https://www.youtube.com/watch?v=NLHbe_DTrP4

and these are the answers ive got.

x1 = 1/3 , x2 = 1/10 , x3 = 1/5

I tried to get ChatGPT's opinion but it gave a different answers. and now im unsure if I did it right because P matrix wasnt used.

is ChatGPT method or mine is correct?

[odd edge]

@quartz agate Has your question been resolved?

[quartz agate]

I think at chatGPT's step 2 is wrong.

it should be
z1 = 1
z2 = 1
-z2 + z3 = 1
replace 1 at z2.

• (1) + z3 = 1
  z3 = 1 +1
  z3 = 2

Am i right?

ah, im sorry, i dont know how to use that,

ok

Like this?

[quartz agate]

I think I solved it. ChatGPT was wrong. thanks for helping me.

.done

@odd edge

how do I press done?

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[clever fjord]

Riku

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[light osprey]

Man.

.close

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[round bone]

Help me derive Bezouts Lemma

[round bone]

If gcd(a,b) = 1 then ax + by = 1

First let's start with gcd(a,b) = gcd(b,r) where r = a mod b

So we have:
a = bq + r

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[odd edge]

@tall iris Has your question been resolved?

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[waxen owl]

I'm confused on c

I can represent the left side of this equation as a series but unsure where to go from there

unsure how the binomial theorm helps with this

this is the binomial theorm

[quasi sparrow]

Use the other parts of the hint

a=1 and the identity with binomial coefficient

[waxen owl]

I don't really get what "after expanding n(1 + b)^(n-1) by the binomial theorem" is trying to tell me. Is this a process I do from my series?

[quasi sparrow]

You use the identity in the right side of the sum here

[quasi sparrow]

Yes

[odd edge]

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[waxen owl]

!close

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[mystic saffron]

not sure how to do this question, I got a=b=0 gives a consistent matrix with infinite solutions, but not sure what to do after

[mystic saffron]

<@&286206848099549185>

someone help 😢

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@mystic saffron Has your question been resolved?

[simple condor]

I'm a bit dumb here, what was the lecture about?

linear algebra?

[mystic saffron]

yeah its a q from my linear algebra class

[simple condor]

Okay, we have here basically as system of 2 equations but 5 unknowns, which somehow depend on a and b.
But I mean, whatever value you plug in for a and b, you will always have at most 2 equations and so this is just underdefined with infinitely many solutions, because if you have 5 variables, you need 5 independent equations to solve this system. That's what I'd say. Don't know if it's correct though, because that task is a bit weird if that was the answer.

consider the vector x=(1, 0, 1, 0, 0) or any vector of the form x=(1, z, 1, 0, 0), where z can be any number
Then it satisfies the system as long as a=b.

I pretty much saw that from first adding the two equations on top of each other, thus having $(a\ 0\ b\ a^2+1\ b^2+1\ |\ a+b)$,
and then getting rid of the squared terms by only allowing vectors of the form $(x_1, x_2, x_3, 0, 0)$.
With this our vectors satisfy $ax_1 + bx_3=a+b$ if $x_1=x_3=1$.
$x_2$ still can be anything because it's not part of the equations anyway.
The individual equations are also fulfilled by these vectors.

[clever fjord]

TRAMPELTIER

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[warm gate]

help

[late dust]

What do you not understand?

[wide jackal]

well there is a perfect example to follow above

!showwork

[odd edge]

Show your work, and if possible, explain where you are stuck.

[warm gate]

this is what I did

I cant isolate any variable

[mystic saffron]

what did u write for f(1)?

[warm gate]

ohhh wait I have to include that too

wait

[mystic saffron]

yes so lets list everything out

what is f(1) firstly

[mystic saffron]

the last one should be equal to 7, not 3

[late dust]

Why did you change f'(3) to 3? You had it equal 7 in the previous picture...

[warm gate]

OH my bad

[mystic saffron]

anyways this is now solveable

you have as many equations as there are variables

so just solve the system of equations

[warm gate]

.close

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[wispy granite]

can someone help me using the limit for a derivative for: 11+54t-5t^2

[wispy granite]

so far I have: $\lim_{{h \to 0}} \frac{11 + 54(x + h) - 5(x + h)^2 - (11 + 54x - 5x^2)}{h}$

[zenith jasper]

ill try to do it

[clever fjord]

Maggi

[manic sleet]

expand everything out

you may notice some things cancel nicely 👀

[wispy granite]

$\lim_{{h \to 0}} \frac{11 + 54x + 54h - 5(x^2 + 2xh + h^2) - (11 + 54x - 5x^2)}{h}$

[clever fjord]

Maggi

[wispy granite]

ok I see that the 11 and 54x cancel out nicely

[manic sleet]

you would be right about that

but so does another term

[wispy granite]

$\lim_{{h \to 0}} \frac{ 54h- 10xh -5h^2)}{h}$

[clever fjord]

Maggi

[wispy granite]

gosh writing everything in latex is so exhausting

[zenith jasper]

factorize out the h

[odd edge]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[manic sleet]

that would be right :) then the h's go away very nicely

applying the limit then is easy

[wispy granite]

yay, idk why I didn't see that when I did it on paper

[manic sleet]

writing it all out neatly takes extra time but when you have algebraic monsters like these, it's really good to write it out neat

[wispy granite]

thanks thanks :D

.close

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[manic sleet]

also

may I just quickly ask

[wispy granite]

yes

[manic sleet]

your pfp, who is that a portrait of?

[wispy granite]

it's called the jewish girl or the girl in the picture frame - it's by rembrandt

[manic sleet]

tysm! looked like a cool painting haha, have a good day

[wispy granite]

it is! you too

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[warm gate]

help

[warm gate]

not sure what to list here

[mystic saffron]

okay so do you know what the derivative denotes?

[warm gate]

uhh not sure wym by that

[mystic saffron]

The derivative denotes the slope of the tangent line

[warm gate]

ohhh

[mystic saffron]

what is the slope for the line equation y = mx + b?

[warm gate]

m

[mystic saffron]

right

so you know the tangent equation is y = -4x + 9, what is the slope of the tangent line

[warm gate]

-4

[mystic saffron]

right

and what did we say the slope of the tangent line is meant to denote?

[warm gate]

that the derivative denotes the slope of the tangent line or sum

[mystic saffron]

yes

so the derivative is equal to -4 at x = 2

you know the derivative equation is f'(x) = 2ax + b

so sub in -4 and x = 2 as we mentioned

[warm gate]

oh

WAIT

my bad

[mystic saffron]

ye

now uh

make a third equation

[warm gate]

okay okay let me try it from here

[mystic saffron]

ok

[odd edge]

@warm gate Has your question been resolved?

[obsidian yarrow]

@warm gate the parabola also passes through the point (2,1)

[warm gate]

i got it alr

i tried solving it with the equations I listed

and gotten nothing

am I missing an equation

that I forgot to list idk

[mystic saffron]

like

[warm gate]

BRU

IM

i just realized

[mystic saffron]

yes?

[warm gate]

I wrote bx^3

instead of squared

WAIT

my bad man

I need new pair of glasses

[mystic saffron]

okay

[mystic saffron]

also like

in the second equation

you already know d = 1

so just like

put 1 instead of d lol

[warm gate]

alr alr

thanks btw

i got alr

.close

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[onyx tapir]

Which of the following statements is an example of a contingency?
c. "If it is daytime, then it is nighttime."
d. "If it is daytime, then it is sunny."
e. "If it is nighttime, then it is dark."
f. "If it is nighttime, then it is daytime." I thought it'd be d because if it's daytime it's not always sunny, but e and f can be true or false at the same time just depends where on earth of you are. I think I'm overthinking it?

[late dust]

In "if A then B", ask yourself:

• can B be true if A is true?
• can B be false if A is true?
  If you answer yes to both, then it's a contingency

[odd edge]

@onyx tapir Has your question been resolved?

[onyx tapir]

i don't think any one of them are a yes to both

[late dust]

You said "if it's daytime it's not always sunny", did you change your mind?

[onyx tapir]

hmm okay i think it's d now, thank you

[late dust]

What about e?

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[storm wharf]

How do I solve for n? 278^3n-7 = 21^2n+5

[clever fjord]

! What the hell am I doing here?

[viral frost]

@storm wharf

[storm wharf]

Neither lol

3n-7 and 2n+5 is all part of the exponent

[viral frost]

Do you know logarithm?

[storm wharf]

Yes sir

[viral frost]

That's all you need.

Use any base.

[clever fjord]

! What the hell am I doing here?

[storm wharf]

Oh crap power rule

So do I log and power rule both sides of the equal sign?

[viral frost]

yes.

Pretty much.

[storm wharf]

ok thanks

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[onyx tapir]

e doesn't make sense to me because it can be dark if it is night time, but it can't not be dark if it is night time, and it can only be one answer choice i think

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[mystic saffron]

Can some one help me I only understand German 🙂

[gilded vector]

i can

was ist das problem

[lavish jackal]

translate it for us as you can

I might help too

[gilded vector]

ich bin deutsch, frag deine frage

[mystic saffron]

Hallo, ich bräuchte Nachhilfe bezüglich, Exponenfunktionen, Logarithmusgleichungen, Wachstum, Zerfallsprozess.

[gilded vector]

meinst du polynome?

da kann ich dir helfen, beim rest bin ich mir nicht sicher

[mystic saffron]

Kann ich dir Beispiele schicken?

[gilded vector]

klar

übrigens der link zu deiner website in deinem profil ist leer

[mystic saffron]

Mir fallen Textbeispiele schwer.

[gilded vector]

sorry so weit bin ich noch nicht ich glaub da müsstest du wen anders suchen

[mystic saffron]

Ok danke trotzdem falls du jemanden kennst der mit weiter helfen kann leite mich gern weiter

[gilded vector]

wenn du’s auf englisch formulieren kannst, kann dir sicher jemand helfen

sind ja eig nur die begriffe die anders sind

[gilded vector]

die schrift ist echt clean

[mystic saffron]

Hello, I need help with exponential functions, logarithm equations, growth, decay process.

[lavish jackal]

which question?

hard to understand what it saying on the paper

[gilded vector]

nice

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@mystic saffron Has your question been resolved?

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[fallow gyro]

I need help on question c

You want to make a deposit of $600 in a savings account. Account A gives you 3.5% simple interest per year. Account B gives you 3.3% compound interest per year.
a. Which account should you choose if you want to invest your money for 3 years?

b. Which account should you choose if you want to invest your money for 6 years?

c. After how many years is the balance of account B greater than the balance of account A?

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[fallow gyro]

.clos

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[zinc chasm]

i am so stuck lol

[zinc chasm]

i’ve had my friend try and she’s also stuck

nevermind we got it! sorry haha!

.close

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[eager verge]

Hello! I wanted to start learning some linear algebra, however it seems I need some review first. I received a copy of the book "linear algebra done right" however I encountered this notation: 𝑎, 𝑏 ∈ 𝐑. To my understanding this means "where the ordered pair a,b is any real number" but I'm not sure. What resources / topics should I look into to learn more? Thanks!

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[hollow carbon]

how do i get the second derivative of f inverse

[odd edge]

@hollow carbon Has your question been resolved?

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@hollow carbon Has your question been resolved?

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@hollow carbon Has your question been resolved?

[hollow carbon]

<@&286206848099549185>

[winter pecan]

Yo

@hollow carbon you here

[hollow carbon]

ye

[winter pecan]

Is this your problem?

[hollow carbon]

this

[hollow carbon]

f2/f3?

[winter pecan]

What

[winter pecan]

Just derivate the result of the first derivative

Thats how you get the second derivative

[hollow carbon]

.close

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Channel closed

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[acoustic coral]

what is the answer?

@hollow carbon

[hollow carbon]

66/6859

[acoustic coral]

okay thanks

you got it right?

[hollow carbon]

yes

[tropic ermine]

can someone help finding this limit

without using

L'Hopital's rule

[odd edge]

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[lofty wyvern]

for this question:

we have 5 beers, 4 ciders, and 3 sodas

you want to get 8 drinks to go. What this means is that the order of the drinks no
longer matters - we only care about how many of each drink you have.

question. How many ways total can you order 8 drinks? Remember, order doesn’t matter.

does 19choose8 work?

i used the combinations formula with repetition

[hushed island]

uhhhh

isn't it 12 choose 8

[severe needle]

Hiii i have a question

[round bone]

no

[hushed island]

!help

[odd edge]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[lofty wyvern]

bruh

.close

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[severe needle]

!help

[odd edge]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[hushed island]

what

[round bone]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[odd edge]

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[scenic mesa]

can someone help

[scenic mesa]

i just need an explanation on this problem

hello

<@&286206848099549185>

<@&286206848099549185>

[desert marlin]

!15mins

[odd edge]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[scenic mesa]

it hasnt been asnwered for almost 20 mins now

[desert marlin]

Your first ping was before 15 minutes, but the reason I warned you is because it says, only once

[scenic mesa]

alr can i get help now

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@scenic mesa Has your question been resolved?

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[frozen sail]

hello

[frozen sail]

.close

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[pine pasture]

I really have no idea what to do here

[green elm]

should be the other way around

f(a+h) - f(a)

[pine pasture]

would that be causing my issue though

[green elm]

yea, your answer is the negative of what it should be

you have f(a) - f(a+h)

[pine pasture]

okay so i fixed the net change

but average rate of change still seems to be false

wait

yeah no

net change i have right now but i have no clue whats wrong with avg roc

[green elm]

where did ah come from

you square sqrt(a+h)
the result is a+h, not ah

[pine pasture]

true

but still wrong

25a/5sqrtA + 5sqrtA+H

still false

[rancid yew]

heyy, can someone help me with this question

[pine pasture]

i was commandeered

help...

<@&286206848099549185>

[leaden quiver]

hi @pine pasture I think you just have them backwards

i think the net change would be f(a+h) - f(a)

then the average change is (f(a+h) - f(a))/h

[broken kite]

25a+25h-25a=25h which is not equal to 25a

[pine pasture]

yes i have the net change part right but my avg change is still incorrect

[pine pasture]

tried that, still wrong 😦

[broken kite]

How about cancelling 5 and 25?

[pine pasture]

nope 😦

[broken kite]

And cancelling h too?

[pine pasture]

not sure where i would?

i have turned my answer into a monstrosity and lost the math i did for this problem

while i was progressing in the assignment

[broken kite]

We got 5h/h(√a+√(a+h)

So like 5/√a+√a+h

[pine pasture]

holy crap

it worked

i see where the mistake was

thank you so much lol

[broken kite]

Sure

[pine pasture]

.close

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[zenith zephyr]

How do I solve further ?

[river lily]

split it up

wait

my bad my eye balls lied to me

[zenith zephyr]

😅

[river lily]

you could do another u sub but that would just make it more ugly

have you tried using trig sub?

[zenith zephyr]

I tried substituting u^2 , and I couldnt solve

No, I didn't try tri sub

[river lily]

yea no here you want to u sub u+1

but you get a super long problem if you do

which makes me think thats not the optimal route here

[zenith zephyr]

Was the initial approach to the question wrong in any way ?

[river lily]

no seems right to me

i thought it was smart to multiply top and bottom by x+5

i would never have thought of that lol

[zenith zephyr]

😁

What if I add and subtract 1 in numerator
(u^2+1-1)/(u+1 ) ???

[river lily]

yea im doing that math right now

then u sub the x+5 in the denom

[zenith zephyr]

Trying

[river lily]

then another u sub

ok got it

a bit of morphing to get it into trig sub format

[river lily]

I did this

then brought the demoninator into the sqrt

to get 1 - 1/ sqrt

then from here it becomes sin i think

one of the trig subs

yea you can sin sub from here

[zenith zephyr]

Does it match any of the options

[river lily]

would be one of the cos

cosec

since its sin sub

wait

lemme check

no it would become sec

[river lily]

i think running from here

we would sec sub the denomiator

sec theta = x+5

then dtheta = sec tan

then it would be

lemme write it

something like this

[zenith zephyr]

Ok

[river lily]

then from here 1/sec becomes sin because 1/(1/sin)

[zenith zephyr]

Yes

[river lily]

then you wuold apply sin^2 definition

simiplify the cos with tan

and integrate

[zenith zephyr]

The correct answer given is option D

[river lily]

yes that makes sense

we gotta plug and solve for theta, and plug u back in

[zenith zephyr]

Thanks @river lily

[zenith zephyr]

👍

.close

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[acoustic relic]

TEDDY?!?!?

MY DOG??

[placid kindle]

☠️

[acoustic relic]

there can only be one

watch out

[placid kindle]

https://tenor.com/view/tonoysumariachi-mexico-mariachi-pena-lol-gif-20783904

[quasi sparrow]

! redir

[odd edge]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[quasi sparrow]

Stop spamming other people's channels and focus on your own

[acoustic relic]

dont tell me what to do

[placid kindle]

bro nobody is helping me im bored as hell

[quasi sparrow]

Just did. Stop spamming

[acoustic relic]

im telling daddy on u

[quasi sparrow]

Doesn't mean you interrupt other people's channels

[placid kindle]

is he bothering you?

[odd edge]

Channel closed

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[feral igloo]

I dont understand how it gets 2

[feral igloo]

Is it because the m+5 cancels out?

Welp. Hopefully I remember enough to pass the test today...

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[bold topaz]

i have to calculate the value of sin a, if cos a = 0,7 and a is a 4th quarter corner

[bold topaz]

apologies if the translation is inaccurate

by quarter i mean this thing

could anyone walk me through on how to solve this? im not even sure where to start

[little grove]

cos(a) is given as a coordinate?

hmm thats strange 💀

[bold topaz]

i guess so, i roughly translated it but the coordinate part should be 100% correct

that is also what im weirded out about

[little grove]

if the coordinate is (0,7) then it shouldn't be in the fourth quadrant anyway

[latent scaffold]

Could it not be cos(a) = 0.7? That would make the most sense in the context.

[little grove]

yeah

[bold topaz]

it just says

cos a = 0,7

but

[latent scaffold]

Depending on language, sometimes comma is used instead of the decimal point.

[little grove]

interesting

[bold topaz]

we use commas for seperating coordinates

[latent scaffold]

I know in french it's comma

[bold topaz]

e.g x = (4, 3)

but if its 0.7 it is a value

[latent scaffold]

Yeah I know that but in this context there is no reason for it being a coordinate and cos(a) = 0.7 would just make sense.

In any case, you would use trig ratios or Pythagoras to find sin(a) making sure you take the right sign since it's in the 4th quadrant.

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[lime moat]

PROBLEM:

You enter a casino:

They have a game "Heads or Tails"

The casino flips a FAIR coin with TWO SIDES.

If it lands on heads, you get $2.
If it lands on tails, you lose $1

What is the expected return with which coin flip?

What are the odds you turn a profit after
1 flip
10 flips
100 flips
1,000 flips
10,000 flips
100,000 coin flips?

[lime moat]

I know the expected return is 50 cents.

But I don't know how the solve part of the problem

[open onyx]

1 flip is easy: there's only 2 possibilities, how many of them result in a profit?
extending it to 10 flips: think about the minimum number of heads to guarantee a profit
same thing aftewards

[lime moat]

So I just need 33.33333% of the flips to be heads to make a profit?

[open onyx]

technically 1 more than that (exactly 1/3 would only break even) but the idea is right

[lime moat]

So the odds I turn a profit regardless of how many times the coin is flipped will be 1/3 + 1?

[open onyx]

that's not the correct odds

[odd edge]

@lime moat Has your question been resolved?

[lime moat]

How would I calculate the odds?

(1/3)^(Number of flips) = odds I don't turn a profit?

[odd edge]

@lime moat Has your question been resolved?

[odd edge]

@lime moat Has your question been resolved?

[odd edge]

@lime moat Has your question been resolved?

[bleak shard]

So you're always expecting to get half your number of flips as heads, and half as tails.