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[thorn fjord]

😭

we're learning about finite fields

this is a part of it

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[somber remnant]

The given adjoining solid object is formed with the combination of a pyramid and a square-based prism where the slant height of the pyramid is 13 cm and the length of the side of the prism is 10 cm. If the volume of the solid object is 900 cubic cm, find the height of the prism.

[somber remnant]

<@&286206848099549185> pls help

bruh .close

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[ocean linden]

From point A to plane a, an oblique line AB is drawn. Find the projection of this oblique line onto plane a, if AB = 26 cm, and point A is located 10 cm away from this plane

[ocean linden]

I drew this, but I don't know how to continue(

[misty lodge]

How do you get the distance from a point to a plane?

You draw a perpendicular line from the point to the plane, right?

[ocean linden]

i dont know 😭

[ocean linden]

yes

[misty lodge]

So you do know)

If its a perpendicular line then what is the angle formed by it and any line IN the plane?

You can imagine a stick that is held perpendicular to the floor

[misty lodge]

What would be that angle then?

[ocean linden]

90 degrees

[misty lodge]

What is the angle ACB then?

[ocean linden]

90?

[misty lodge]

Exactly

So AC is the given distance of A from the plane

AB is given too

Do you know what is the projection of AB to the plane?

[ocean linden]

no

[misty lodge]

You draw perpendicular lines to the plane from the endpoints of AB to get the projection

So whats the projection of AB?

[misty lodge]

The projection is the line that connects the points where these perpendicular lines meet the plane

If you dont see it just draw perlendicular lines from the endpoints of AB to the plane and show it here

[torn jolt]

@ocean linden

look as we have a sqaure base

which means the base of pyramid is the same as the width of the square base

which is 10

we get this

and now can you find the height of this triangle?

[ocean linden]

hmm

[ocean linden]

like this?

[torn jolt]

quite not

[ocean linden]

oh

[torn jolt]

like imagine in your mind a tright angle traingle

[misty lodge]

Nope. Didnt we say that AC is perpendicular to the plane?

[torn jolt]

with slant height given

[misty lodge]

And B is on the plane

[torn jolt]

and the base same as of sqaure

[misty lodge]

Idk what is this it doesnt seem right

[torn jolt]

this is just basic math

like sqaure base

means 10 cm acroos

[misty lodge]

I dont know how is it related to the problem

He doesnt even know what is a projection

[torn jolt]

to find the height of pyramid

this question is of simple maths

not higher grade

like pyhtagroes theorem

[misty lodge]

Its exactly pythagorean theorem here

[cyan walrus]

let's uh, try to help instead of being condescending?

[torn jolt]

@ocean linden do u have the answer

[misty lodge]

I am literally explaining what a projection is

Waqar is telling something else

[torn jolt]

i apologise if i was not in same boat as you

[misty lodge]

There is no need to apologize. If you know a better way to explain, go on

[torn jolt]

i jsut used pythagoroes theorem

as the question has given that the height of pyramid is 90 degree to the plane of sqaure

which means it divides it in two equal halves in 5 and 5

[cyan walrus]

why is a pyramid being mentioned here...

[ocean linden]

like this? 😭

[cyan walrus]

use a shadow to explain projection?

[misty lodge]

I have no idea

[ocean linden]

nope

[misty lodge]

Okay look AC is you

[torn jolt]

we need to find AB reyl

[cyan walrus]

the answer is 24, we all can agree on that at least I think

[misty lodge]

Your head is A and C is your feet on the ground

[torn jolt]

yeah 24 is what i got

[misty lodge]

You are perpendicular to the ground

So if I say draw a perpendicular line from your head to the ground you just draw your body

[torn jolt]

like this

[misty lodge]

Your body is AC

[torn jolt]

and u can find AB by pythagoroes theorem

[misty lodge]

Yep. We can also agree that pythagorean theorem wont help since we need to explain what is a projection first

[cyan walrus]

let fen explain what projection is

making the chat messy won't help

[cyan walrus]

yes

[misty lodge]

So again. Which one is a perpendicular line from A to the plane? @ocean linden

Plane is the foor

A is your head

And you are standing on the floor

[ocean linden]

this? 😭

[misty lodge]

Which one is your head?

The letter

Your head is?

[ocean linden]

A

[torn jolt]

yo unrelated note but

This correct?

[misty lodge]

And your feet?

[misty lodge]

Make a new chat

[ocean linden]

C

[misty lodge]

And your body?

[ocean linden]

AC

[misty lodge]

Which is perpendicular to the floor right?

[ocean linden]

AC?

[misty lodge]

Yes!

[torn jolt]

AC aint perpendicular

[ocean linden]

like this?

[cyan walrus]

wrong

[torn jolt]

ohh

[misty lodge]

No

[ocean linden]

ohh

[misty lodge]

Can you connect A to C?

[ocean linden]

yes

[misty lodge]

Show me

[misty lodge]

And AC is your body right?

[ocean linden]

yes

[misty lodge]

So doesnt it mean that the perpendicular line is AC?

Cause your body is perpendicular to the ground

[ocean linden]

yes

[misty lodge]

So again

Show me the perpendicular line that connects A to the plane

[cyan walrus]

if they understand it's perpendicular, proceed,
the figure doesn't have to be pixel perfect...

[misty lodge]

Im sure he didnt get it

[misty lodge]

We agreed that AC is perpendicular and he showed me this

[cyan walrus]

@ocean linden what does perpendicular mean?

[cyan walrus]

could be just bad drawing?

[misty lodge]

Nope

@ocean linden we got this! Which one is the perpendicular line connecting A to the plane?

[misty lodge]

Its a different problem

[torn jolt]

this is the same question

[misty lodge]

Not at all but lets not argue

[ocean linden]

this?

[ocean linden]

lines that intersect

[misty lodge]

Told ya @cyan walrus

[misty lodge]

No no

Perpendicular lines are the ones that form 90° angle after intersection

reyl you should really check again what all these terms mean

In a nutshell. AC is the perpendicular line that I am asking you about

And the projection of AB is BC

We get ABC triangle where ACB angle is 90°

And use pythagorean theorem to calculate BC

But you need to find out what perpendicular lines are and what projection means

[torn jolt]

btw Fen

[ocean linden]

oh, thanks

[torn jolt]

the diagram provided in the book is this

for the questio and ABC is 90 degree

so how can ABC and ACB be 90

[misty lodge]

It has nothing to do with this problem

[torn jolt]

that would mean these two add up to 180

[cyan walrus]

where did you even get that...

it wasn't sent by anyone other than you

[torn jolt]

yeah

from gauthmath as a question with pricture

[misty lodge]

Waqar, again, these are two different problems

[misty lodge]

This was the given task

[cyan walrus]

Suppose you have a random stick AB obliquely on a plane,
to find the projection of the stick,
you shine a light source directly above the point A of the stick.
the shadow will be it's projection.

shining a light source straight above means the shadow will start from a point on the plane straight down from point A, which is C.

since C is straight down from A, they form a 90 degree angle with the plane.

in the figure, the red line is the shadrow or, projection

once you get that much, it's just applying the pythagorean theorem

[ocean linden]

thank you very much

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[torn jolt]

@misty lodge

[torn jolt]

i sincerely apologise

[torn jolt]

i was looking at this the whole time

[misty lodge]

Nah all good

[torn jolt]

still pyhtagroes theorem

[misty lodge]

Yea we use it in the end

[torn jolt]

middle school paid off

[misty lodge]

Heh. All the best mate

[torn jolt]

Goodbye

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[sweet patio]

ask the question

[strange basalt]

a part and b part both?

!status

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5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[strange basalt]

hm , ok so , do you know this is called a quadratic equation

[brave crater]

do you know the quadratic formula?

[brave crater]

and this?

[sweet patio]

since it's a polynomial of power 2 you can reliably factorize it as two terms, thus (x+a)(x+b)

[torn jolt]

middle term breaking

[sweet patio]

think what values of a and b would lead to (x+a)(x+b)=x^2+9x+14

that's x^2+(a+b)x+ab

so a+b=9 and ab=14

[strange basalt]

think what a and b can be

yeah pretty much

[sweet patio]

type .close

[strange basalt]

for b part can you tell the type of graph it will form ,
like this is also a quadratic equation

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[compact cipher]

hello

[compact cipher]

I am trying to find if this function is differentiable

using alternative derivatife form

my question is when the piecewise function has a function for x = 0, where do I use that?

[compact cipher]

for example here when finding the limit from the right, instead of f(0) do I input x + 1?

[buoyant pewter]

the function is not differentiable at x = 0, because f is not contnues at x = 0,

lack of continuity of a function at a point, it is enough to state the lack of differentiability, because if a function is differentiable, it is continuous,

[rare dock]

why did they choose to define the function as x + 1 when x = 0

why not just 1

[buoyant pewter]

exactly, should be written 1

[compact cipher]

Thanks @buoyant pewter @rare dock, btw this is not real exercise its just something i came up with to check if such thing is even possible lol

Also if it was 1 it wouldnt change anything right?

Still not differentiable

[buoyant pewter]

if you put, 1, still lack of continutiy

since the left and rgith sided limits are diferent

you need to change form of yoru function

[compact cipher]

Thanks

[buoyant pewter]

yw)

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[abstract crescent]

For which X does the following makes even sense:

[ x \in X \ , \ k \in \mathbb{Z} \hspace{1cm} x \leq k ]

[glossy valve]

Tobi

[abstract crescent]

Clearly for

[ X = \mathbb{N \ Z \ Q \ R } ]

But are there others

[glossy valve]

Tobi

[fast peak]

well you can for example set X=some function space and then partially order that

and then f<=k means that f(x) <= k for all x

or you can have something like hyperreals or whatever

[abstract crescent]

True okey , then I have to define myself somthing to make sense, are there like already existing definitions I can use

[fast peak]

I mean if you want to use the <= as you are using it right now, then by definition that only works for real numbers

so X some subset of R

so that kinda makes the question pointless

[abstract crescent]

yeah

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[misty lodge]

https://tenor.com/view/meow-sad-gif-3806846082438439943

[misty lodge]

I know the answer is A

I dont know why

I also know that f is concave up and $f^{'}$ is strictly increasing

[glossy valve]

Fen

[misty lodge]

And I know that f(x) decreases from -2 to 0 and increases after that

<@&286206848099549185>

Well guess we aint sleeping this night

Its not even about math anymore. I have a personal beef with this problem

Yes

The derivative is negative

[rough bolt]

Actually you know that f' is <0 for all x<0, f'>0 for all x>0 and f'=0 in x=0

So you can say that f is strictly decreasing from negative infinity to 0, then in 0 there is a minimun and then it is strictly increasing from 0 to positive infinity

[misty lodge]

Yeah I think I got that part

<@&286206848099549185>

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[harsh elk]

help?

[ember shadow]

you can call the total number of new at-bats "n"

so you add "n" to the denominator, and a multiple of "n" to the numerator. then solve for "n"

[harsh elk]

well ik the thing is that its 24+.35x/110+x=.3

right?

[ember shadow]

yes, so just solve it

[harsh elk]

why why is .35 on the numerator

[ember shadow]

? you just showed it yourself

[harsh elk]

ik the answer but i dont get how

why is .35 on the numerator?

[ember shadow]

re-read the problem carefully

[harsh elk]

i am tho

[ember shadow]

read it again then

it's all in the problem

[harsh elk]

it says at bats

and at bats is denominator

[ember shadow]

you responded too quickly to have read it carefully

[harsh elk]

so future at bats will be average of .35

and at bats is denominator

[ember shadow]

yes

[harsh elk]

so the denominator is. 35x?

[ember shadow]

no. the denominator is what you wrote above

denominator is at-bats. numerator is hits

[harsh elk]

and the problem says for all of her futurare at bats she will have a batting avg of .350

[ember shadow]

yes

[harsh elk]

so denominator?

bro im not getting this

[ember shadow]

there will be N additional at-bats. 35% of those (0.35N) will be hits. so you add 0.35N to the numerator, and just add N to the denominator

[harsh elk]

wait how do u know 35% will be hits?

wait thats what batting avg means?

[ember shadow]

you are given that

[harsh elk]

which is 35%?

[ember shadow]

re-read the problem

[harsh elk]

can u just clarify this one thing? why do we add 24+.35x?

[ember shadow]

I clarified that already

hits are in the numerator

[harsh elk]

here?

@ember shadow do u have any tips for these types of world problems?

[ember shadow]

just read them carefully and use what is given to you

[harsh elk]

bro please

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[barren badge]

yo

[barren badge]

I have a calculus problem under the packet “6.5 Behavior of Accumulation Functions”

I am stuck on #’s 3 & 4. If someone could give me detailed instructions for #3 I could try the same combination for #4. Thank you.

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[clever zodiac]

Hi there, I am trying to solve a second order differential equation (non homogeneous and also its an amended particular integral) to find the general solution

[clever zodiac]

I have found so far, GS = Ae5x + Bxe5x + Ce5x, where *C * is a constant.

However after solving the equation, I have found C to be 0. Is this possible?

Where this was the original equation;

So therefore, GS = Ae5x + Bxe5x

?

[kindred grove]

yeah

Ce^5x is already one of your homogeneous solutions when you think about it

you'd expect it to end up being 0 after plugging it in your DE

so you have to use the same old "multiply by x trick"

https://math.jhu.edu/~brown/courses/f18/ExampleProblems/UndetCoeffBadGuesses.pdf here's a pdf which explains that in more detail

@clever zodiac

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[clever zodiac]

Ohh, I see where I went wrong!

I forgot to include the x in the working out, meaning I came to 0.

Therefore, I couldn't find the constant for C.

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[pastel walrus]

Help

[quaint prawn]

!status

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2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[pastel walrus]

I know where to begin but i just don't know if im solving it right

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[rugged plank]

Where did I go wrong? Apparently there is a simplification where (N / (20-N)) = Ce^(1/4)

[vernal ice]

You're not wrong but when you e both sides you get $$e^{t} = e^{4 \ln \lvert \frac{N}{20-N} \rvert + C}$$ which using the index laws becomes $$e^t = e^{4 \ln \lvert \frac{N}{20-N} \rvert} \cdot e^C$$ and $e^C$ is itself a constant (another number) which you could probably rename to $A$ so you end up with $$e^t = Ae^{4 \ln \lvert \frac{N}{20-N} \rvert}$$

[glossy valve]

I can't believe you've done this

[vernal ice]

if you used your value of C you got you would still end up with the correct answer albeit a bit different because ln(6561) = 4ln(9) (= 8ln3 but 4ln9 is more useful) and when you combine the ln using the logarithm rules you get t = 4 ln (9N/20-N)

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[rugged plank]

I see. So how would you get (N / (20-N)) = Ce^(1/4) ? Like if you move A to the other side I could see (e^4)(N/(20-N)) = Ae^(1/4) but not (N/(20-N)) by itself

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[vernal ice]

e^(4ln(N/20-N)) doesn't equal e^4 * e^ln(N/20-N) since theyre multiplied by each other in the power

it's also probably better that before solving for c you make N the subject since imo it makes calculating the final answer a lot easier

[rugged plank]

Yeah ok, Ty!!

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[calm trail]

I have gotten 8pi/3 is this right?

[gritty rose]

Show your work

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[calm trail]

<@&286206848099549185>

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[tranquil fiber]

hi no one answered last time hoe to do part b

[tranquil fiber]

<@&286206848099549185> i know it hasnt been 15 mins but my previous attempt to ask was timed out so

[inner grove]

It's not easy to read that

[tranquil fiber]

@inner grove

great no one's gonna help me huh

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[torn jolt]

not sure what to do with this

[glacial pasture]

Plug in the solutions

[torn jolt]

for b and c?

or plug in for x

and solve for b and c

solutions are pi/6 and pi/4

but how would you solve with two unknowns

[buoyant pewter]

system of two linear equations you receive, ...

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[cedar monolith]

hello, what is the inverse of the isomorphism of the chinese remainder theorem between Z/aZ et Z/bZ?

[cedar monolith]

$\phi : \mathbb{Z}/ab\mathbb{Z} \longrightarrow \mathbb{Z}/a\mathbb{Z} \times \mathbb{Z}/b\mathbb{Z} \
\quad x \mod ab \longmapsto (x \mod a, x \mod b)$

[glossy valve]

lilisworld

[cedar monolith]

<@&286206848099549185>

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[sick karma]

what part of this are you struggling with

[high blaze]

all of it

or well

i did it

and got 824.25

but when i enter it its wrong

[sick karma]

did you directly plug in 13

[high blaze]

13?

nvm i got it

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[crystal gate]

how would i approach this?

[crystal gate]

ive gotten to

sin(x)ln(5x+2) * cos(x)

but im not sure if thats right

[sick karma]

are you trying to differentiate it

[crystal gate]

derivative

which is making me believe what i put is wrong

[sick karma]

you use implicit differentiation

take the ln of both sides

[crystal gate]

lny=cos(x)ln(5x+2)?

then derive to

[sick karma]

no

you take dowjn the sin(x)

[crystal gate]

ohh

not derive yet

lny= sin(x) * ln(5x+2)

then may i derive?

[sick karma]

yes

[crystal gate]

i assume product rule

[sick karma]

yeds

[crystal gate]

1/y= sin(x) * 5/5x+2 + cos(x) * ln(5x+2)?

[sick karma]

you forgot one term

[crystal gate]

then multiply the orignal function over to the other side

[sick karma]

well yeah

[crystal gate]

which?

[sick karma]

I usually write 1/y * dy/dx

cause youre technically using chain rule but yeah

[crystal gate]

you right

[sick karma]

you multiply y, the original function, to isolate dy/dx which is your derivative

[crystal gate]

so what i wrote plus the orginial function?

is final?

what was i missing

[sick karma]

not plus

[crystal gate]

multiplied

yeah

[sick karma]

would be yeah

[crystal gate]

thank you

[sick karma]

so (5x+2)^(..) * (chain term 1 + chain term 2)

[crystal gate]

ya

preciate it gang

have a good one

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[red pivot]

for part C do I have to consider whether or not the set spans H (I don't think I do) or can I just say whether or not the set of matrices is linearly independent? Additionally, for part D, if the answer just false because the set only has two matrices, but the minimum required to span is 3 since the dim(B) = 3?

[north sparrow]

For c) you only have to see if the given matrices are in H and linearly independent of each other

For d) I think you are having the right thinking

alternative phrasing: can 2 2x2 matrices form a basis for all upper triangular matrices?

[red pivot]

So since the matrices given in the set for part C are upper triangular matrices and since they are linearly independent, can we say that the set is a linearly independent subset of H?

[north sparrow]

there's two aspects to this, are they in H? clearly

are they linearly independent? if you say so ( i dont care to check)

If both are fulfilled they are a linearly independent subset

the definitions are just legos added to each other

[red pivot]

alright that makes sense

thanks a lot. I appreciate it

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[marsh tusk]

I think i found a mistake in a problem

[marsh tusk]

Each afternoon Enrico rides the 20km from work to home but one day he got a flat tyre and had to walk the rest of the distance. He rides at an average speed of 30km/h but walks at 6km/h. If the entire journey took one hour, how far did he have to walk

wait brb

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[marsh tusk]

ok

so basically

i did this:

x/30 + y/6 = 1

x+y=20

and through substitution, i got y=2.5

and since 2.5 is the time

and the question is asking how far

so distance = speed * time

so 6 * 2.5 = 15 as my answer

but in the solutions they just had 2.5 as the answer

am i corret

<@&286206848099549185>

[proper hawk]

yo

[wild sleet]

i get 2.5 as answer

30x +6(1−x) = 20
24x + 6 = 20
x = 14/24

6(10/24) = 2.5

x/30 + y/6 = 1 clearly uses y to mean how far

[marsh tusk]

oh

ok

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[rough temple]

Z-test with an alpha level of .05

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[rough temple]

<@&286206848099549185>

[rough temple]

?

<@&286206848099549185>

[rough temple]

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[slow dirge]

<@&286206848099549185>

[slow dirge]

how do you do this quesiton?

this is based on poisson's distribution

<@&286206848099549185>

[cursive dock]

!noping

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[cursive dock]

!15m

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[cursive dock]

wrong one.

[slow dirge]

what?

bro I need help plz

can anyone do this question?

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[fair flower]

Combination probably

1-nCr

not sure tho

nvm

[slow dirge]

bruh

thanks

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[odd bloom]

f

[odd bloom]

not sure how to start

its linear programming

reviewing

<@&286206848099549185>

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[odd bloom]

alr

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[odd bloom]

no

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[ionic path]

we can start by substituting cosx = (e^ix + e^-ix)/2

right

but then when you sub t = ix (i - iota)

is it possible

because then what is the new upper limit

inifinty times iota 🤔

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[subtle thorn]

why are you doing this substitution?

[torn jolt]

feynman technique

can that be applied here?

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.reopen

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[torn jolt]

I don’t understand this at all, he kept doing so much and I just couldn’t understand it

[torn jolt]

And I thought that X would be half of 49 but it was 10 so idk what to do

[tawdry whale]

wouldn't the angle be the same?

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[ocean urchin]

could someone show me why C isnt the answer? whats an example of a function defined on [0,3] that doesnt have an extreme value??

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[wild sleet]

bunch of horizontal lines

like, the last line is "all maxima" but no point is special, they can't all be extremal at the same time

i think it's like that

hm maybe not

yeah i agree with you now

@ocean urchinthis one

not on [0,3], just generally

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[sturdy mango]

when you bring the constant out of a integral do you have to multiply the bounds by the constant?

[sturdy mango]

like if i have
pi/4
| 1/2(cos^2(2x))
-pi/4
I dont multiply the pi/4 by 1/2?

[fast peak]

no

[sturdy mango]

idk what im doing wrong in this problem but i keep getting the wrong answer 1 sec

[minor crater]

you are still integrating from the same bound

[sturdy mango]

okay thats what i thought

why am i getting pi/16 w instead of pi/8 which is the right answer?

ive done it like 5 times i dont understand where im going wrong ???

oh i forgot ab -pi/4 so when u minus the neg pi/16 + pi/16 = pi/8 ok

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[silk nexus]

Please someone explain to me

what happened after Ln (x/r)

[gritty rose]

,tex .log rules

[glossy valve]

riemann

[gritty rose]

Second row

[silk nexus]

So we did not need to replace Ln(r) at first

since it cancelled out

or change it to square root form

[gritty rose]

There are a lot of different ways to simplify

[gritty rose]

An arguably simpler way is to use the first row in the first line

[silk nexus]

ln (rcos O)

??

[gritty rose]

Correct

If by O you meant theta

[silk nexus]

Yes haha

Thank you

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[brittle parcel]

If n, m ∈ N\{0}, the number of functions f : {1, 2, ..., n} -> {1, 2, ..., m} that are monotonically increasing is C(m-1, n-1)

is that true? Answer given by Bing AI

[brittle parcel]

or

[harsh pilot]

Nah, doesn't look true to me.

Can you take an example like n = 2, m = 2. Then Bing AI claims that there are C(1,1) = 1 such functions.

[brittle parcel]

chatgpt said using the principle of inclusion/exclusion which sounds ok until I try to use it

and idk how

[harsh pilot]

It's a so-called stars-and-bars problem.

[brittle parcel]

alright, I'll look it up

[harsh pilot]

These chat bots are still horrible at math, I haven't been able to get a right answer out of any of them for any non-trivial problem.

[plush ginkgo]

indeed there's only one mapping of 1..2 to 1..2 that's increasing

the question can be reframed as: how many ways are there to map the range 1..n to 1..m

[tidal pivot]

can anyone help

[harsh pilot]

Agreed, but according to the picture below, the term meant is "non-decreasing".

[tidal pivot]

Find the smallest value of N for which we can say: among any N number of numbers, there are 18 numbers such that their sum is divisible by 18

[plush ginkgo]

this channel is occupied

read #❓how-to-get-help

[plush ginkgo]

i see, that is peculiar

but it wouldn't make as much sense anymore, no?

[harsh pilot]

For strictly increasing, it would be C(m,n).

[harsh pilot]

How so?

[brittle parcel]

right, but for >/= what is the answer?

I saw the stars and bars problem and understood it

but how do I apply it to find the number of functions here

[harsh pilot]

It's C(n+m-1, m-1)

[plush ginkgo]

if they're nondecreasing, i could just map everything to 1, i don't think any degree of surjectivity is specified

[brittle parcel]

you're right, but could you explain it, please? where does -1 come from?

ik C(stars+bars, bars)

oh wait

bars is m-1

right

but why?

[harsh pilot]

Indeed that is a possible map.

[harsh pilot]

It's like, let there be a star for each number in {1, 2, ..., n}. Perhaps ¤¤¤¤¤¤¤

If I put the first bar somewhere, it means that everything to the left of the first bar is mapped to 1 in {1, 2, ..., m}. The next bar I put, it is everything between the first and second bar that is mapped to 2.

So ¤|¤¤||¤¤¤|¤ corresponds to the map 1 -> 1, {2,3}->2, {4,5,6}->4, 7->5

[brittle parcel]

right, ok

if you guys don't continue your topic

I'll close this

[harsh pilot]

We won't continue.

[brittle parcel]

ty guys

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[carmine badge]

I know this is true but I forgot why you put ln there again?

[carmine badge]

my question is just basically why the answer to the 2nd one is ln3 * 3x

[clear folio]

because of the formula. x is an exponent here.

[carmine badge]

what formula

[carmine badge]

but why the ln then?

I forgot the function of ln

what it means

[fathom saddle]

Have you seen the limit definition of the derivative?

[analog pendant]

because d/dx = a^x follows the rule ln(a) * a^x

[carmine badge]

oh I just remembered

thanks

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[torn jolt]

just to make sure, the answer is c?

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[torn jolt]

ρ = {(1, 2),(2, 3),(3, 4),(1, 3),(2, 4),(4, 4),(1, 4)}.
this relation is only transitive right?

[trail barn]

which properties are you checking?

[torn jolt]

symmetrucal, anti, reflexive and transitive

it's only transitive right

[trail barn]

it's also antisymmetric

[torn jolt]

oh because there's 1,3 and 1,4 but nothing to compare them to?

or am i misunderstanding?

[trail barn]

what do you mean by 'nothing to compare them to'? there's nothing special about those

[torn jolt]

(∀x, y ∈ A) (x, y) ∈ ρ ∧ (y, x) ∈ ρ) ⇒ x = y

this is the def of antisxm right?

[trail barn]

yes

[torn jolt]

now i might be blind but there's (x,y) but there's no (y,x) so it's automatically antisym?

[trail barn]

ah

yes

sorry you bringing in specific examples confused me

actually

yes with the one exception of (4,4)

[torn jolt]

now i'm confused

oh i see your point

nvm me

may i ask you another question? another exercise is unclear to me

[trail barn]

go ahead

[torn jolt]

The relation ρ is defined on the set of N natural numbers
m ρ n ⇔ 3m and 5n give the same remainder when dividing by 7.
Examine whether the relation ρ is reflexive, symmetric, antisymmetric, transitive

so am i to find what m and n is here

[trail barn]

you're meant to either find m,n naturals that are counterexamples to the properties

so e.g. if it is irreflexive, find specific n s.t. 3n and 5n have different remainder so not n ρ n

OR show that whatever you're picking, the property holds

i.e. work with completely general m and n

[torn jolt]

and am i just supposed to bruteforce it?

or is there a method

[trail barn]

if you can see how to use properties of natural numbers and remainders, you can use those

or you can brute force

(in this example the counterexamples to the properties seem to be small)

[torn jolt]

what do you mean by this?

[trail barn]

just that using things you already know about how remainders work might help you guess which properties hold, or how to find counterexamples

[torn jolt]

ah so it's basically bruteforcing

okay tyvm

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[wraith river]

Does anyone know

[wraith river]

Why does this circle mean

The underground part

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[sharp fable]

It means the graph is lower than 0 at that point.

[sharp fable]

The underground part.

[wraith river]

Oh ok

Ohh

Thats why they set the equation to 0?

H(t)

OK thx

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[sleek quest]

i have to graph the antiderivative of this function

[left bone]

doesnt seem right? it appears to me that it should always be negative

[sleek quest]

wait wdym?

im honestly pretty confused on how to graph this

[left bone]

antiderivative is signed area under the curve

alternatively, you can consider what the derivative of your function should look like

if your answer was right, the slope should be positive from 1 to 2.5, and the original graph definitely isnt positive from 1 to 2.5

[sleek quest]

like this?

[left bone]

no

it should be decreasing from 0 to 2, increasing from 2 to 3, and decreasing again from 3+

but it definitely never goes positive

you are graphing how much area is under the curve from 0 to that point (not really but its close enough for this)

[sleek quest]

how come its never positive

[left bone]

theres never a positive amount of area under the curve!

theres always more negative area than positive area

[sleek quest]

how do you know this?

[left bone]

because theres only negative area from 0 to 2

so the area is going down

[sleek quest]

ohhh

[left bone]

the antiderivative is graphing area under the curve of the original function

[sleek quest]

but isnt the area from 2-3 positive?

[left bone]

yes

so its increasing during that section

[sleek quest]

so why did you say the whole thing is negative

[left bone]

do you think theres more positive area between 2 and 3 than negative area between 0 and 2?

I dont think so, so the total area will stay negative

[sleek quest]

oh

[left bone]

remember total area from 0 to the point

[sleek quest]

right

[left bone]

in reality its actually total area from some previous point to that point, which means the "starting area" by the time you get to 0 can actually by any amount

im rooting this at 0 for intuition purposes, but the integral graph is allowed to shift up and down freely

[sleek quest]

so something like this?

[left bone]

yeah thats much closer

[sleek quest]

what am i missing?

[left bone]

well you drew it by hand so its gonna be a bit off by default, but you can try thinking about how fast area is changing to play around with the slope

i think thats probably in like good enough territory though

[sleek quest]

cool! thank you so much

and for part b, i have to sketch f'

any tips for that?

[left bone]

derivative is the slope at each point

f' is positive when the slope is positive and negative when the slope is negative

the more positive the slope, the more positive f' is

[sleek quest]

i see

btw, did we have to take the critical points of f in account for the graph of F?

@left bone

[kindred burrow]

@left bone

[sleek quest]

?

[left bone]

what

[kindred burrow]

Are u good at trig good sir

[left bone]

critical points are just the zeroes of the derivative

so yeah i guess those would help

but it should like end up coming naturally if you do what i said

[sleek quest]

so my sketch is innacurate?

[left bone]

im good at everything, but this isnt your channel and im not going to help you here

idk i havent seen your sketch for f'(x)

[kindred burrow]

Wow

That hurt my feelings

Ngl

[sleek quest]

i was talking about F

[left bone]

oh no critical points dont really matter for F

in fact i think they matter like not at all

[sleek quest]

ah got it

here is my sketch for f'

wait i messed up

here @left bone

wait no i messed up again

you there?

[left bone]

something like this

yeah looks about right

my lines are straighter, but i suppose its plausable it oculd be a function such that they could be curved

[sleek quest]

ah yeah

thanks!

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[glad umbra]

can any1 help me solve this

[glad umbra]

quadratics r involved 😦

[kindred burrow]

(11+n) *400-20n=4760

[glad umbra]

what does n represent here?

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@glad umbra Has your question been resolved?

[kindred burrow]

N represents the tickets price going up by 1

Its 14$

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[strong apex]

how do i find the average daily balance?

[undone vector]

Why is balance increasing

[strong apex]

my teacher said something about it increasing because on a credit card it charges

something like that

[undone vector]

Oh I see

The +55 is correct because of what u said, but the +20 should be -20 because you are paying it back

[strong apex]

ohhh i see so that was my only mistake

[undone vector]

And the # of days thing

[strong apex]

why do i have to add 1?

and for the balance for the july 3-14 the balance stays the same as the july 1-3 right?

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@strong apex Has your question been resolved?

[strong apex]

how can i tell the difference between simple and compound interest in these word problems

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@strong apex Has your question been resolved?

[strong apex]

not yet

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[glossy isle]

Can someone help pls? I’m not sure on how to find x

[tulip oriole]

pythagorean theorem

[glossy isle]

It’s special right triangles how I do that

[tulip oriole]

do you know trigonometry?

[glossy isle]

No

[tulip oriole]

it's alright

are you allowed to use the ratios of special triangles

[glossy isle]

Idk it just says to find x

[tulip oriole]

alright let's use this then

so it's just a^2 + b^2 = c^2 with added steps

[glossy isle]

I already have all the stuff for the first triangle I js don’t know what to do for the second

[tulip oriole]

it's the same thing u did for triangle 1

just 4sqrt(2)/2

[glossy isle]

Wait why did u do this

[tulip oriole]

.

for 60-90-30 triangles the hypothenuse is always 2 times the base

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[pliant heron]

Can anyone verify that a few relation proofs are correct/

[gritty rose]

Just send one at a time

And wait until someone checks one question before asking another

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@pliant heron Has your question been resolved?

[pliant heron]

Okie will do!

[pliant heron]

Yup for sure got it! wouldn't want to overwhelm anyone : )

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[wide sundial]

Where did the 2pi come from on the last step

[fast peak]

length of interval

[wide sundial]

How does that appear

It doesn’t look like ML inequality since that has the absolute values on the outside

[fast peak]

they are bounding the integral by $\int_0^{2\pi} number dt$ which is equal to length of interval times number

[glossy valve]

Denascite

[fast peak]

where number=the supremum

[wide sundial]

So the sup is not dependent on t

And when you integrate yoy get t * sup

[fast peak]

yes

[wide sundial]

Then you evaluate the bounds and get the 2pi

[fast peak]

yes

[wide sundial]

Ah

[fast peak]

or just geometrically, its a rectangle

[wide sundial]

A bit wack with the sup stuff

Yeah right

Makes sense ty!

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[twin wolf]

Find the volume of the solid generated under the region when $y=\frac{1}{x^{4}+1}\left{0\le x\le1\right}$ is rotated about the y-axis.

[glossy valve]

water beam

[twin wolf]

(do I have to integrate $\frac{1}{x^{4}+1}$ is there no way around this?)

because like

it doesnt look fun

[glossy valve]

water beam

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[buoyant pewter]

$\left| V_{OY} \right|=2\pi\int_{0}^{1}xf\left( x \right)dx=2\pi\int_{0}^{1}\frac{xdx}{x^{4}+1}=\\=2\pi\int_{0}^{1}\frac{\frac{1}{2}dt}{t^{2}+1}=_{\cdots }$

[glossy valve]

Joanna Angel

[twin wolf]

whats going on there

with the t substitution stuff

[buoyant pewter]

i gave you a hint

i tis self explanatory i hope

[twin wolf]

so I don't have to integrate 1/x^4 + 1?

[buoyant pewter]

write it in your exercise book and continue solvign ti, it is alsmot done

[twin wolf]

oh wait

$V=2\pi\int_{0}^{1}x\left(\frac{1}{x^{4}+1}\right)dx$

[glossy valve]

water beam

[twin wolf]

I forgot the shell method saves this whole thing with the x

[buoyant pewter]

it's ok

[twin wolf]

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[sacred sparrow]

continuity question:

[sacred sparrow]

let f(x) be some function that is defined this way:

for any x e R \ {-1, 2}:

for x=-1: f(-1) = A

for x=2: f(2) = B

how can I show that continuity holds at the point x=-1 for certain A using epsilon-delta?

I know that I can show lim[x->-1]f(x) = -2 and therefore A must be -2, but I want to show it using epsilon-delta

what I have so far:

[dusky locust]

$0 < |b- a| < \delta$

[glossy valve]

tales

[dusky locust]

For $b\neq a$, we have $f(x) = $ something defined at x = -1

[glossy valve]

tales

[sacred sparrow]

ys

[sacred sparrow]

how would you continue from there

[dusky locust]

,w (x^4 -5x^2+4)/(x^2-x-2)

[glossy valve]

Results provided by WolframAlpha

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Requested by talestitan

[dusky locust]

$f(x) = \dfrac{x^4-5x^2+4}{x^2-x-2} = x^2+x-2$ for $x\neq 1$ and $x\neq 2$

[glossy valve]

tales

[sacred sparrow]

ys

[dusky locust]

Call $g(x) = x^2+x-2$

[glossy valve]

tales

[dusky locust]

g is continuous

[sacred sparrow]

yup

[dusky locust]

Then apply definition of continuity at x = -1

Nah, wait

I am complicating

[sacred sparrow]

I tried applying it here, but from then onwards I don't know how to fetch a delta

[dusky locust]

f(b) = 1

ok

[sacred sparrow]

what I essentially need to show is that there only exists a delta for A=-2, but I can't yet presume that I know it only exists for A=-2

[dusky locust]

From continuity of g, applied on x = -1, you have

$\forall \varepsilon \exists \delta ( |x +1| < \delta \implies |g(x) - g(-1)| < \varepsilon )$

[glossy valve]

tales

[sacred sparrow]

ys

[dusky locust]

I dont wanna do the math, but you should get the same inequality

[sacred sparrow]

but how does that prove that A must be -2

[dusky locust]

A

'-'

[sacred sparrow]

or generalised, how does that limit the possible values of A

I'll repaste the question, but thx for the attempt @dusky locust :)

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[tough marsh]

!status

[full forum]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[rapid mulch]

1

[tough marsh]

What is "amplitude", "period", and "angular frequency"?

[rapid mulch]

How do I find amplitude, period, and angular frequency? Is there a formula?

[tough marsh]

What does your math textbook say about that?

[rapid mulch]

amplitude is easy it, is apparently the absolute value of a or the number in from of cos or sin
period is 2π/absolute value of b (which b is the number being multiplied by x or in the case of this problem t)

I think I am fine for the rest of this problem now, thank you!

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[foggy shore]

STATISTICS

When I am harvesting 2,000 silkworms, I am expected to get 11,000 threads of silk

How do I get the standard deviation for +/- threads from harvesting all the 2,000 silkworms?

info:
Silkworm drops between 1-10 (ONLY INTEGERS) threads and you can assume each value (1, 2, 3..., 10) are equally likely

STATISTICS

[foggy shore]

Please guys, im trying to find if I have a reasonable suspicion for my worker to have stolen some of the silk threads

Its for hit game Growtopia

[torpid stag]

Calculating the precise standard deviation most likely would require the use of the multinomial theorem, which would be pretty tedious to have to use

Your best bet would probably be to run a simulation

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@foggy shore Has your question been resolved?

[foggy shore]

Wait, actually? So thats why they always give you the standard deviation in high school statistics problems

I was also surprised how no one else commented anything on this

[torpid stag]

Well, for some distributions the standard deviation is pretty straightforward to calculate

What you're describing is the sum of 2000 discrete uniformly distributed random variables