help-38

[full fossil]

and why negative x and y values aren't ok here, since you end up with x = y anyway

so what problems will you run into with a negative base here?

[ionic pendant]

the equation is the same as x = y, for the domain where log_x makes sense to talk about in the first place

[full fossil]

the only thing i can think of is it would work for change of base formula but that also doesn't seem like much of an issue in this context?

[full fossil]

right so why didn't they make a point of discontinuity at x = 1?

[ionic pendant]

i agree with you that it should have such a discontinuity marked

[full fossil]

my math teacher said that x = 1 would work for x = y which was why the answer was the way that it was so I was really confused about why it couldn't be negative numbers lol

since either way you would end up with issues if you were to use the change of base formula based on what you told me

[ionic pendant]

i suppose that if you were to define log base 1, the most sensible way would be for it to only input 1 and output 1

since log_b (b) = 1 in general

still a bit dicey

[full fossil]

right lol

thank you so much for the help (:

[ionic pendant]

no problem

[full fossil]

how do I mark this as solved?

[ionic pendant]

you use .close or .solved

[full fossil]

tyty

.solved

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[onyx dove]

already have the solution to this but it's not quite clicking,

Recursive Definitions:

For each of the following descriptions of sets, write a recursive defini-
tion of those sets. Your recursive step MUST build on existing elements
of the set. You may need more than 1 base case in the basis step. You
may raise your hand for clarification as to whether or not specific elements
are in the sets.

[onyx dove]

more elaboration on the then part is what im asking for to sum my question up

[edgy willow]

for recursion you're trying to create a whole set with some starting points and simple rules to get everywhere else

in normal recursion you have n=1,2,3... which can be explored by starting at 1 and getting a way to go to the next one

here it's on this weird 2d tilted grid so you'll need more rules on where to go if you want to get everywhere

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@onyx dove Has your question been resolved?

[onyx dove]

just saw this oops

[onyx dove]

so why exactly is it (x+ 1, y- 1) and what does this have to do with being divisble by 3?

[edgy willow]

you can tell it works because the sum won't change, x+1 + y-1=x+y so it'll still be divisible by 3

basically just take a point at look at the nearby ones, like (0,3) works and (1,2) does too, which is a change of (x+1,y-1)

the way the image explains it is the grid is a bunch of lines x+y=3k, to traverse the line x+y=3k you can add 1 or subtract 1 from x and y, which is (x+1,y-1) and (x-1,y+1). Also, you need a way to get to the higher and lower lines, which is (x,y+3) and (x,y-3)

[onyx dove]

ohhhhhhhhhhh

wetplmkwtwt

s

yes

Yess

ok i understand now ty

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[sly sky]

Hi

[sly sky]

I need

Help

[velvet bolt]

just post your question perhaps someone will help you

[sly sky]

I know

.close

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[neat herald]

Guys help me

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[wraith hinge]

HI PLEASE HELP ME

[wraith hinge]

Please

Help 🥺🥺

<@&286206848099549185> Pleaseeeew I acc need help

With my homework

😭😭

Why is everyone receiving help except me

🥺

💔

💔

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[wraith hinge]

.close

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[potent smelt]

help

[potent smelt]

<@&286206848099549185>

idk what to do

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[potent smelt]

.reopen

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✅

[potent smelt]

<@&286206848099549185>

[hallow cliff]

There should be a cos^2(x) over there, you only have cos(x)

[potent smelt]

ohhh

thank you

ill try again

.close

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[lethal ivy]

O no

[lethal ivy]

Plz help

I need this answered within 5 mins plz help me out <@&286206848099549185>

[tight obsidian]

have u calculated the friction force?

[lethal ivy]

Yes

[tight obsidian]

make the difference between the force YOU are putting and the friction force

what would the result be?

[lethal ivy]

Im actually on the second part with kinematics

But i keep getting a negative value for displacement

(Left)

[tight obsidian]

what will the speed of the block be after 2 secs

[lethal ivy]

Idk

[tight obsidian]

ok so first of all you have to calculate the total force on the box when u are pushing

making the difference and dividing for the mass

[lethal ivy]

I get acceleration

Already

[tight obsidian]

which is what u did in the photo

ok sorry

[lethal ivy]

Acceleration positive right?

I get. -d

[tight obsidian]

i believe so otherwise the block would not move

can u give me the value of acceleration u have?

[lethal ivy]

18.2

[tight obsidian]

ok that’s great

since it’s telling u that the block is moving for 2 second

u are able to calculate its velocity

[lethal ivy]

Its gives velocity

2.0m/s

And then final would be 0

[tight obsidian]

ok

[lethal ivy]

Im jus wondeeing how i get -d

[tight obsidian]

so calculate the acceleration of the friction force

[lethal ivy]

Acceleration of friction force?

[tight obsidian]

d=0.5 x acceleration x time

time square

[lethal ivy]

Whats the time

Why doesnt mine wrk?

[tight obsidian]

just know that the time u have to determine thoroug velocity block + velocity u loose = 0

[lethal ivy]

???

[tight obsidian]

velocity u lose = acceleration of the friction x time

the difference of both velocities equals 0

acceleration of friction = f / m

[lethal ivy]

Wait js acceleration

Different now?

[tight obsidian]

its the acceleration of the friction force

u know the force of friction

[lethal ivy]

1.7?

[tight obsidian]

u know the mass

[lethal ivy]

Is it 1.7 for a?

[tight obsidian]

yes

[lethal ivy]

Ok ok

And thas negative

Im not getting right answer for d

[tight obsidian]

and that’s correct

the friction force gives a negative acceleration on the block

[lethal ivy]

Im not getting answer

[tight obsidian]

since its trying to slow it down

[lethal ivy]

Answer is .11m

0.11m

[tight obsidian]

first u have to calculate in how much time it is stopping

[lethal ivy]

Wait y

We have vi vf and a

[tight obsidian]

u say 0 = velocity - acceleration of friction X time

[lethal ivy]

???

[tight obsidian]

at the end of the table the block will have 0 velocity

[lethal ivy]

Yes

[tight obsidian]

0 = velocity (2 m/s) - velocity of the friction force

[lethal ivy]

Cant we do what i did

Idk that way

Enough

[tight obsidian]

velocity of friction = time X acceleration

total space = acceleration of friction x time x time x 0,5

[lethal ivy]

Bro i havent done it that way ever

Why dont my last pic work?

[tight obsidian]

i don’t know what u did in the last picture

[round mango]

The acceleration is not 1.7

[lethal ivy]

What

Im gna fail 😭

[round mango]

After you leave the block, only friction is acting on it

[tight obsidian]

that the acceleration of the force of friction

[lethal ivy]

Yes

[round mango]

0.18 x .1 x 10 is the force, divide that by your mass .1

Giving you 1.8 as your acceleration

Then go ahead an apply v²-u²=2as

[lethal ivy]

Okay plz dont leave let me try

I have some@hope

Doing it rn

@round mango

[round mango]

You should get 4/3.6 or 1.11 as your answer

[lethal ivy]

I dont know what im doin

Why is this not right?

:

I def did smth wrong

[round mango]

This is right, I approximated g =10, yours is more accurate

Look at the decimals tho

You're messing them up

It should be .1764

[lethal ivy]

O

[round mango]

Then you divide by .1 again to get 1.764

[lethal ivy]

I get 17.64

Wait

1.764/.1

[round mango]

0.1764/0.1

Is 1.764

[lethal ivy]

O ic ic

Ok

Tru

Whas answer?

[round mango]

1.11metres

Roughly

[lethal ivy]

Wait i not getting that

[round mango]

0²-2² is -4

[lethal ivy]

Ooo

I got it

Finally thx so much

Trying to pull an all nighter

.close

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• Show your work, and if possible, explain where you are stuck.
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[halcyon schooner]

We store randomly 5 shirts in 6 drawers (independantly, with the same probability for
each drawer).
(1) What is the probability that one drawer contains exactly 5 shirts ?

[halcyon schooner]

hi, can someone help with this? I tried mapping out the possible outcomes

but it gets really long

my teacher said the total list of possible outcomes is 6^5 but im having trouble seeing why that is the case

[swift ledge]

basically

wait

have you learned about combinations?

[halcyon schooner]

yeah

[swift ledge]

ok

it will be 1 divided by the total number of possible outcomes

understand?

[halcyon schooner]

the answer is 6 divided by 6^5 tho

wheree 6^5 is total possible outcomes

[swift ledge]

wait

[gusty raptor]

$6/6^5$

[swift ledge]

im dumb

[solid kiln]

Aqua.

[halcyon schooner]

why do both these numbers appear in the first place tho

[wraith hinge]

iif this is the right answer i can explain @halcyon schooner

[halcyon schooner]

yeah it is

[wraith hinge]

ok so

[swift ledge]

yeah i was doing something totally different mb

[wraith hinge]

the formula of probability is

favoured outcomes/total outcomes

[halcyon schooner]

yeah

[wraith hinge]

we have to arrange 5 shirts in 6 drawers

every shirt has 6 possible cases

[halcyon schooner]

yes

[wraith hinge]

so thats 6^5

[halcyon schooner]

ohhhh

[wraith hinge]

thats total outcome

[halcyon schooner]

ok i got it

[wraith hinge]

favoured outcome is one of the drawers having all the shirts

thats possible 6 times

[halcyon schooner]

yup. i see it now

[wraith hinge]

ye nice

[halcyon schooner]

thanks

.close

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[potent smelt]

help

[potent smelt]

ignore the bounds, is this correct?

n = 2020

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@potent smelt Has your question been resolved?

[potent smelt]

<@&286206848099549185>

[toxic jewel]

If you're just referring to the integration, then yes

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@potent smelt Has your question been resolved?

[potent smelt]

thank

i got the q wrong tho

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[stoic junco]

under the corona epidemi there were 40 people with the virus and the (idk the word in english) says there will be an exponential growth of people with the virus in 3% every week from now make a function s(x) that shows how many people that will get the virus in x weeks

[stoic junco]

so i came to the conclusion that its s(x)=40*1.03^x

but idk how it works

ping me if u are here to help

<@&286206848099549185>

.close

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[potent smelt]

yo

[potent smelt]

question

im doing part c

i know theres an easier way to do this

but why is mine wrong

also here 1st ss, 4th line from the bottom, first cosx should be cos^2(x) which i fixed and did on next page

ah

ive sent the wrong workings

answer somehow simplified to the last page underlined thing

sorry for how bad they are

but u get how i just represented the ()^2020 as a summation

but wolfram alpha gives me a 200 digit number

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[sly sky]

Hi

[sly sky]

@vernal warren

I need help

@lilac cloud

@wraith hinge

[wraith hinge]

dont ping

immediately explain your problem/where you stuck

[sly sky]

Kk

I am confused what should I do at number 4

@julia

[vernal warren]

just post ur problems in the new channel instead of pinging everyone

[sly sky]

Ohh hi

[vernal warren]

its faster and there maybe someone who has a better understanding of the problem

[vernal warren]

hello

[sly sky]

It's the 3rd time

Can u help

Tho

[vernal warren]

its would be way faster if u posted that image instead of "hi" and pinging 3 ppl

[sly sky]

💀

[vernal warren]

m = a
passes through (0,a)

u know the formula , plug in the values

[sly sky]

I already did

But I think it's wrong

[vernal warren]

its correct

[sly sky]

What?

It is?

[vernal warren]

y - ax - a = 0

[sly sky]

I didn't

Wrote like that

How to bring this in this form

[vernal warren]

all forms are ok , that is better tbh

[sly sky]

No I still wanna understand

[sly sky]

How this comes

[vernal warren]

$$y-a = ax$$
$$ y -a -ax = ax -ax$$
$$ y - a - ax = 0$$

[solid kiln]

JustToPro

[sly sky]

Ohh

I did a mistake

I wrote two a's

[sly sky]

What if u brought ax to the left side

How did u bring two ax in the right

@vernal warren

$$y-a=ax$$

[solid kiln]

Zuhayr

[vernal warren]

$$y-a = ax$$
subtracting ax from both sides
$$ y -a -ax = ax -ax$$
$$ y -a -ax =\cancel{ ax} -\cancel{ax}$$
$$ y - a - ax = 0$$

[solid kiln]

JustToPro

[sly sky]

Like I got that

But

Y-a=ax

[vernal warren]

hm

[sly sky]

That ax to go left.If that ax got to left how another ax came in the right with along anothrr

[wraith hinge]

its great u got a helper lol i didnt know how to do it

[wraith hinge]

i think he subtracted both sides

[sly sky]

Ye

[vernal warren]

i subtracted from both sides u can write it like this if u want
$$y-a = ax$$
$$ y -a -ax =0 $$

just understanding

[sly sky]

Ohh

[solid kiln]

JustToPro

[sly sky]

I didn't understood the both sides part

Lol

[vernal warren]

its explanation for how we got -ax , but it ok

[vernal warren]

if u get how i did this , then thats good

[sly sky]

Kk

I need help with number 2

Now

I can't do that at all

@vernal warren

[vernal warren]

2 points given , u need to find equation

there is a formula for that (which i forgot) let me try find it online

[sly sky]

Kk

And like what is my main objective here

[vernal warren]

to find the equation of the straight line

[sly sky]

Y=mx+c

It's the formula right

[vernal warren]

thats for when 1 point is given

ik there is 1 for when 2 points are given

[sly sky]

Oh

What should I do then

@vernal warren

[vernal warren]

https://www.youtube.com/watch?v=lzqTD0JWwhY

[sly sky]

I should watch this?

This guy is sometimes rlly complicated😭

[vernal warren]

its simple

[sly sky]

Wait then lemme watch it

[wraith hinge]

i dont know how to explain but i got something like this 😭

[vernal warren]

u used y = mx+c to find the equation of line for both the points and then solved them simultaneously for m and c

both ways are correct (im pretty sure)

[wraith hinge]

hope so, now wait for him

[vernal warren]

i gotta go , if u have mroe problems u can open a new channel and send the problem straight

instead of pinging and looking for ppl to come and then to send the problem

[sly sky]

I am back

@wraith hinge

[wraith hinge]

ya

[sly sky]

Can u check

If this is right

[wraith hinge]

show me ur work

sure

[sly sky]

I am not

Done yey

Yet

And got stuck

[wraith hinge]

thats correct but not fully done

[sly sky]

Y-3=2x-2
What should I do

[wraith hinge]

u need to isolate for y

[sly sky]

That I don't know how to do

So wait I remove

3

[wraith hinge]

yes

add 3 to both sides

[sly sky]

This both part is confusing

Why we add to both sides

[wraith hinge]

wait

let me find a vid for that

https://www.youtube.com/watch?v=wShnYemIr28

this vid is only 2 minutes long

[sly sky]

Wait

Lemme watch

[wraith hinge]

you can check this video anytime u want later or right now. its 25 minutes long and i think this is enough for your basic algebra https://www.youtube.com/watch?v=Z-ZkmpQBIFo

[sly sky]

Thnxx

[sly sky]

She said

To take the smallest

[wraith hinge]

do you understand this or is that video not enough?

[sly sky]

Number

[wraith hinge]

that is not necessary

[sly sky]

And do stuff in both sides

[wraith hinge]

what necessary is the both side thing

the opposite

like

[sly sky]

Ohh

Like I can take any number?

[wraith hinge]

the opposite of addition is subtraction
the opposite of multiplication is division

[wraith hinge]

noo

wait

i made example

myself

[sly sky]

?

[wraith hinge]

(2x+1=0)

[solid kiln]

!

[wraith hinge]

do you have any idea how to find the value of x?

[sly sky]

Yea

I do

[wraith hinge]

how

how would u solve it?

[sly sky]

Wait

[wraith hinge]

its basically the same thing

look

[sly sky]

Ye

[wraith hinge]

this is my work

at first i subtracted both side by 1

leaving 2x=-1

and the i divide both side by 2

[sly sky]

No like what is the side part

[wraith hinge]

leaving x=-1/2

[sly sky]

I didn't use the both side

Part

When solving

[wraith hinge]

did your teacher say something like "move it"

[sly sky]

Yea maybe

[wraith hinge]

hm

ill try my best to explain

[sly sky]

Kk

[wraith hinge]

(2x+1=0)

[solid kiln]

!

[wraith hinge]

what is our goal?

our goal is to isolate x righht

[sly sky]

To make x the subject

[wraith hinge]

yes

[sly sky]

Ye

[wraith hinge]

so the first thing i will do here is

i will look at "+1"

now the symbol there is a positive

[sly sky]

Why +1

[wraith hinge]

because we want to get rid of the numbers

we want x alone

to make x the subject

[sly sky]

U mean we'II look at the number which doesn't has a variable

@wraith hinge

[wraith hinge]

to solve an equation like (2x+1=0) you cant do (2x) first. you first need to get rid of (+1)

[solid kiln]

!

[sly sky]

Ohh

[wraith hinge]

(2x+1=0)

[solid kiln]

!

[sly sky]

.

[wraith hinge]

if you do 2x first u will just get 0/2

[wraith hinge]

yea sure that

[sly sky]

Ohh

[wraith hinge]

so

[sly sky]

Make me understand the both sides part

[wraith hinge]

chill man u are learning it

so we take the opposite of (+1)

[solid kiln]

!

[wraith hinge]

which is???

[wraith hinge]

-?

[sly sky]

-1

[wraith hinge]

yes

so i will subtract -1 to both side, and what i mean "both side" is the left side before equality sign, and the right side which is the side after the equality sign

(2x+1=0)

[solid kiln]

!

[sly sky]

Ohh

[wraith hinge]

it will look something like this

[sly sky]

So basically we always take the opposite of sign of whatever - or + and make sure the number is not with a variable

[wraith hinge]

yes

now we have

(2x=-1)

[solid kiln]

!

[wraith hinge]

are u ok so far/

[sly sky]

Ye

[wraith hinge]

now we look at (2x)

[solid kiln]

!

[sly sky]

Yea I am getting it

[wraith hinge]

now what makes (2x) ?

[solid kiln]

!

[wraith hinge]

(2x) is (2\times x)

[solid kiln]

!

[sly sky]

Yea that I know

[wraith hinge]

so, again we are taking the opposite

which means we have to divide both side by 2

[sly sky]

Can I do it and show it to u

[wraith hinge]

sure

[sly sky]

Is it okay

[wraith hinge]

sorry but that is incorrect 😅

[sly sky]

Np

[wraith hinge]

where did you get 2x+1=1?

[sly sky]

U said the signs become opposite

[wraith hinge]

dont worry i will explain your mistake so you wont repeat it again

[sly sky]

I maked the sign

[wraith hinge]

hm

not like that

[sly sky]

Opposite and added with both sides

[wraith hinge]

this is what actually we do

[wraith hinge]

we already take the opposite which i use the colored one

[sly sky]

I can do this

In my way

But not like

Yours

[wraith hinge]

yes i understand

but this way is widely used too

[sly sky]

Yea

[wraith hinge]

its when u subtract to one side, u have to subtract it to the other side too

okay but i still want to show you though. can you explain to me your way soving 2x+1=0?

solving*

[sly sky]

U mean that's the basic but I do it without showing steps

[sly sky]

My way?

[wraith hinge]

can you explain it to me

yes

ur way

[sly sky]

Kk

[wraith hinge]

(2x+1=0)

[solid kiln]

!

[wraith hinge]

https://www.youtube.com/watch?v=wArrEhGbmq0

u can also watch this vid later. it uses the "both side" way

[sly sky]

Basically what do we is remove (1) to the right side to make it negative
And then to make x the subject we that number always down to the (other side)

Is that okay

[wraith hinge]

do you know why that number is negative?

[sly sky]

Yea I know

[wraith hinge]

oh

but trust me it pretty much the same thing

[sly sky]

Cuz it's moved to the other side and when it's moved to the other side the sign changes

Cuz there is an = sign

(Right)?

[wraith hinge]

2x+1=0

subtract both side by 1
2x=-1

divide both side by 2

x=-1/2

[wraith hinge]

yeah

[sly sky]

??

[wraith hinge]

lets look at step by step

2x+1=0

subtract both side by 1

okay so lets look at the left side

2x+1, now we subtract this by 1
2x+1-1
what is 2x+1-1?
well 1-1 is just zero, so it leaves us with
2x

and now lets look at the right side

at the right side, we have 0
what were we substracting again earlier?
we subtract by one,
0-1 is just -1

so we're left with the left side being 2x and the right side being -1

2x=-1

[sly sky]

Yea?

[chilly bobcat]

what's the damn question lol

[wraith hinge]

lol im just teaching some basic algebra

[chilly bobcat]

huh?

no like what is the OPs main concern here

[sly sky]

Yea

I have equation problem

[wraith hinge]

straight line equation

[sly sky]

Like I was doing my homework

And got stuck

[chilly bobcat]

oh

[sly sky]

Yea it's kinda making sense to me

[chilly bobcat]

in like a specific question?

[sly sky]

No in a normal

Equation

[chilly bobcat]

yeah so what is that equation

2x + 1 = 0?

[wraith hinge]

you just move "-3" to the other side so it will be "+3" @sly sky

[sly sky]

No like now I am fine

[wraith hinge]

nope

2x+1=0 was just some basic algebra i was teaching him

[wraith hinge]

yea u got it

[sly sky]

I might have more problem

And then I would call u

[wraith hinge]

what

?

mk

i highly suggest u watch the link videos i sent. it will be helpful for ur algebra understanding

[sly sky]

Yee

I would

[wraith hinge]

though u already have ur own way. its always better to know how to solve it in multiple ways!

[sly sky]

And u should probably teach me math basics 😅

[sly sky]

Yea

[wraith hinge]

sure

[sly sky]

Like quadratic equation

Simultaneous equation

Tho I mastered simultaneous equation

[wraith hinge]

that is nice

[sly sky]

But not sure if remember it

[wraith hinge]

theres a couple of way to solve simul eqn

u can either use calculator and directly get the answer without showing work, use substitution method, elimination method or using matrices

anyway is there anything else

[sly sky]

Ye

[sly sky]

I would tell when I am facing problems

[wraith hinge]

u should close this channel.. Btw i highly suggest before u go on discord and asking people, u should watch some tutorial on youtube too

so we know where's ur problem and not rely too much on people teaching

[sly sky]

Yea I do watch tutorials

And when like I have personal problems

That time I come here

[wraith hinge]

that is good

[sly sky]

For the basics it's better for me to watch

Tutorials

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[potent smelt]

can i reopen this

[potent smelt]

someone please help

<@&286206848099549185>

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[wild stump]

I tried to find the height of the monster using sine rule in the bigger triangle and then using sin(40)

[wild stump]

but it didn't work

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[clever ferry]

is this correct

just wondering

[round mango]

Check B's y coordinate

[clever ferry]

hm

oh

6?

[round mango]

Yes

[clever ferry]

yo

onesec

could you go through equations of parallel lines w me?

[woven locust]

send it over

[clever ferry]

one sec

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[slim shore]

In the figure, a right parallelepiped is represented in the reference frame 𝑂𝑥𝑦𝑧.
It is known that:

The origin of the reference frame is one of the vertices;
The vertices 𝑃, 𝑅, and 𝑆 belong to the axes 𝑂𝑥, 𝑂𝑦, and 𝑂𝑧, respectively;
The vertex 𝑈 has coordinates (2, 4, 2).
Consider the line 𝑟 defined by the equation (𝑥, 𝑦, 𝑧) = (2, 0, 2) + 𝑘(0, 0, 1), 𝑘 ∈ ℝ.
What is the point of intersection of the line 𝑟 with the plane 𝑂𝑈𝑉?
(A) Point 𝑃 (B) Point 𝑇 (C) Point 𝑈 (D) Point 𝑉

I keep getting point T but the correct answer is point P

[edgy willow]

I'd try drawing the line and also seeing if you can find another point on OUV

[slim shore]

wdym?

[edgy willow]

like check if there's another corner of the box that's on the plane

[slim shore]

figured it out, ty tho

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[coarse turtle]

Can someone tell me where I messed up

I am so confused

It is differential equation using substitution

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[quasi dagger]

Could someone help explain how they get Ae^(-kt) from exponentiation? It feels like there's a leap in logic here.

[buoyant sluice]

To get rid of the log base e on the lhs we exponential both sides

[quasi dagger]

right, that gets us this but how do we get Ae^(-kt)

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[edgy willow]

I think there's a typo in the image, and A is just saying that e^-Dk is a constant

like to get here from the equation above you multiply by k so there needs to be a kt and kD

[quasi dagger]

ahhhh, i see

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[jagged wharf]

Does the series $$\sum _{k=1}^{\infty }k\tan \left(\frac{1}{k^3}\right)$$ converge? Intuitively, if I write the $\tan$ as $\sin$ over $\cos$ and use the small angle approximation, and use that $\cos(1/k^3)$ tends to $1$ as $k\to\infty$, we should get convergence. But how can I make this more rigorous, i.e. is there some test or comparison I can use?

[solid kiln]

Philip

[wraith hinge]

look at the tail of the series

the series converges if and only if its tail does

so eventually the small angle approximations will hold... and then...

[jagged wharf]

ok, I'm trying to make that explicit by writing it down, but I'm unsure what inequalities are floating around in the argument you presented

[wraith hinge]

you can start with sinx < x

and find a similar inequality for cos

[jagged wharf]

ok, thanks, what is the inequality for cos x that can be used here?

it's in the denominator, and the smallest cos gets is 0

[hollow dove]

you can use limit comparison test with 1/k^2

since tan x / x -> 1 as x -> 0

[jagged wharf]

ok 👍

[blissful bison]

you can use such an inequality:

[jagged wharf]

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[woven sinew]

Number 3

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[woven sinew]

?

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[lament pine]

On wikipedia it is saying addition maps two natural numbers to another one. I have an issue with this definition. What about 1 + 1? Only one natural number is being used here

[rigid portal]

let a = 1 and b = 0
then S(b) = 1
therefore
a + S(b) = 1 + 1 = S(a + b) = S(1 + 0)
1 + 0 = 1 as defined by (1)
so S(1 + 0) = S(1)
which is 2

[tepid prism]

its not specified that it cant be the same number

1 is a natural number and 1 is still a natural number

[lament pine]

Would you agree that only one natural number is being used?

[brazen forge]

it completely can be only one number but used twice

wikipedias def is right

tho didnt specified that addition is a map NxN->N

[lament pine]

Maybe this is more philosophical, but how can the exact same thing exist twice? There would need to be a distinguishing property between them?

[brazen forge]

it can take 1 from the first N set and 1 from the 2nd N set

[brazen forge]

as im saying here it takes 1 from the one N set and 1 from the second N set

it gives you a ordered pair (1,1)

[lament pine]

So that would be the distinguishing property?

[brazen forge]

i think so

[lament pine]

Then I feel like it break equality though

[brazen forge]

you know what cartesian product is?

for example NxN as here

[lament pine]

Because doesnt equality mean all properties for both objects must be the same for equality, as in they are indistinguishable

[lament pine]

It would be all possible pairings of each element in both sets

[brazen forge]

yeah, but most important is that cartesian product gives you a set of ordered pairs

you know what ordered pair is?

[lament pine]

Yeah 2 elements from 1 or more sets right

[brazen forge]

kinda

(1,1) is an ordered pair

[lament pine]

Yeah

[brazen forge]

which is in a set NxN

so

its not that 1 and "the 2nd other, diffrent" 1 is maped here

but the ordered pair (1,1) is mapped to the number 2

and an ordered pair (1,1) is not equal to 1

[lament pine]

Is there infinite amount of set N?

[brazen forge]

set N is infinite if that what youre asking

[lament pine]

I mean it seems like we have 2 instances of set N to make (1,1)

Or is it just 1

[brazen forge]

dont really get what are you trying to say here

wdym by N making (1,1)

[lament pine]

Does NxN mean 2 sets that are N?

[brazen forge]

NxN mean cartesian product of N with itself

there are not 2 diffrent N sets

[lament pine]

One sec

Trying to think lol

[brazen forge]

i get you lol

maybe start with an easier set?

like {1,2}?

{1,2}x{1,2} = {(1,1),(1,2),(2,1),(2,2)}

[lament pine]

(1,1) mean two 1s existing or no?

[brazen forge]

no

[lament pine]

What about 1+1?

[brazen forge]

what about it lol

aaaaaaaaaaaaaa

[lament pine]

Does it mean two 1s are here or just one?

[brazen forge]

there are no 1s here

its an ordered pair

(1,1)

aaaaa

learn about ordered pairs first

[lament pine]

I see two symbols of 1 at least

[brazen forge]

im too tired sorry

im going bye

[lament pine]

Lol its okay. I understood what you are getting at though

Thank you

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[brazen forge]

@lament pine you're really asking "why (1,1) exists since there are not two different 1s i can use"

and thats the question im not going to answer

[lament pine]

Its because its a mapping to itself I guess?

I assume its not saying 2 distinct objects are existing, rather the object is pointing back to itself

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[dense viper]

hi, can anyone explain to me what she wants me to do for the part about using rileys definition to prove ABCD isnt an isosceles trapezoid 😭😭 im so confused (i fixed the slope for CD btw i know its 1/7..)

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[dense viper]

<@&286206848099549185>

[glacial plover]

1/-5 is not equal to 1/5

[dense viper]

dont u have to change the negatives to positives when simplifying fractions?

[glacial plover]

thats only when the numerator and denominator is negative

rise over run

[dense viper]

ooohh

[glacial plover]

if you go up 1 and left 5 its 1/-5

when you go right 5 its positive but you aren't going right 5

[dense viper]

oh my god im so tired my brains not working LMAO idk why i thought 1/5 then 1/7

[dense viper]

oooh

so mCD would just be 1/-5?

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[barren crescent]

can someone check my work?

[golden garden]

Question 5, I would do the last option. After factoring the gcf quadratic formula is best for the 2r^2 + 6x + 1

[barren crescent]

ohhhhh

the rest lookin good?

[golden garden]

10 and 9 look good.

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[golden garden]

On question 11, nonreal / complex conjugates come in pairs so there can't be a odd number of them. Since there's a maximum of 4 rational roots because of the degree, there could be either 4 rational and 0 irrational or 2 rational and 2 irrational or 0 rational and 4 irrational. In this case, there would be
Two rational roots and two irrational roots to answer the question.

[barren crescent]

ohhhhh

thank you! that was a very succint answer

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[finite tusk]

where did the cosx come from

im tryna solve the same question but on X-axis

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[trail ingot]

https://math.stackexchange.com/questions/735182/a-question-for-epigraph-and-affine-function the comment here says the backwards direction looks good, but is it? the t worries me. what exactly is the halfspace that epi(f) is equal to here?

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[dawn dune]

Help XD

[dawn dune]

I need help expanding this stuff

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[supple bluff]

I need help to explain why $x_0 + P'(x_0)dx$ is closer to $x_0$ than $x_0 + dx$ when $|P'(x_0)|<1$

[solid kiln]

schrödinger

[supple bluff]

<@&286206848099549185>

[olive canyon]

That's not true, it's true if it's less than 0.5

[supple bluff]

i think it is true for all |P'(x0)|< 1

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[marble wharf]

the distance of x_0+something to x_0 is just |something|

and |P'(x0)dx| < |dx| if |P'(x0)|<1, just by properties of the absolute value

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[fervent wraith]

if I want to calculate the pressure P1, I have to use the formula in red

[fervent wraith]

but does the height have to go as deep as the point or as deep as the container

for example if the container is 5 meters long and we want to calculate the pressure point P1 which is 4 meters deep

do I have to use h = 4 or h = 5?

or do I have to use the formula for hydrostatic pressure?

[sacred sapphire]

h = 4

[woeful bramble]

z2 is from the bottom to the top and z1 is from the bottom to p1 and h=z2-z1 so that means its from the top to p1

yeah 4

[fervent wraith]

ok well for what do we use the formula for hydrostatic pressure then?

[fervent wraith]

that makes sense

[sacred sapphire]

first one

[fervent wraith]

???

[sacred sapphire]

P₀ + ρgh

[fervent wraith]

Hmm I think I understand

well what about this

Px is the same on the two levels right

because its the same liquid and they're on the same height

following that logic, would P2 and Py also be the same?

[sacred sapphire]

yeah

[fervent wraith]

poggers

thanks

.close

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[sacred sapphire]

well they are at the same height but Py has that extra liquid on top

so the height is technically not the same

[fervent wraith]

what

[sacred sapphire]

actually nvm im talking shit

ignore

[fervent wraith]

ok epic

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[tepid hamlet]

when thinking about polar equations, how do you determine symmetry over axes analytically? looking at this graph, it's pretty obvious this is symmetric over the polar/x axis. I guess because cos(theta) = cos(-theta) this makes some sense, becuase the lower part of the graph will behave the same as the upper one...so if i had to guess it would be that whenever theta is locked behind a cos it'll be symmetric, but i can't imagine this is only case, like if you replaced cos with any other even function it would still be the case?

[tepid hamlet]

i guess r(theta) = r(-theta) would mean symmetry over polar axis?

what about graphing 1 - cos(theta) alongside 1 + cos(theta), how would we know without looking at the graph, just the equations these are reflections over the y axis?

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[wraith hinge]

Any wants to ask questions

because I am free

Plus I have a degree in Harvard - Calculus and Geo statistics

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[brisk tapir]

I'm trying to run a significance test on a game that I play. It tells me that probability that I get a specific card is 2.91%. I believe they're lying and that it's either below or above that percentage. I'm having trouble making the significance test though.

You get cards by spending gems. One card costs, let's say, 150 gems. Let's say my friend spends 5 million gems and gets that card X amount of times. How do I run a significance test to see if my friend's sample is extreme and didn't happen by chance? I'm not getting how I continue this

[trail ingot]

i dunno anything about statistical tests really and there’s some subjectiveness in them anyway but i can tell you the numbers of cards received follows a binomial distribution

[brisk tapir]

That is true, but I feel like it's rigged

Based on how long I've played the game and the amount of cards I get, 2.91% just isn't true imo. It's much lower (afai see it, so I'd like to test it out with data)

[hallow crane]

[brisk tapir]

What does mean

[trail ingot]

with just that knowledge you can say things like “there is a 99.99% chance of getting at least K cards after spending this many gems”

no statistical tests needed

and enough evidence for it not really being how it is claimed

[brisk tapir]

What do you mean? I'm trying to get samples to see if this has happened by chance. If they haven't happened by chance, then I have enough evidence to prove that the percentage is rigged

[trail ingot]

wdym get samples

[brisk tapir]

As I mentioned, you spend gems and see how many cards you get.

That's the sample. Spend 5 mil gems and get the card X times

[trail ingot]

yea, so i’m saying

[trail ingot]

you’ll be able to say something like this (it’s under the assumption the game works like how it is claimed)

if you do it and don’t get K cards

then that’s evidence it doesn’t work how it is claimed

[brisk tapir]

I'm trying to prove it's rigged. Me doing a random claim based on that doesn't sound creditable

I'm sorry I don't quite follow what you mean. Maybe I'm misunderstanding what you meant

[trail ingot]

you aren’t going to be able to prove it without the game code lol

[wintry stag]

This is in every first year statistics textbook you can find off the shelf. This is a pretty straight forward explanation of the process: https://www.cs.cmu.edu/~bhiksha/courses/10-601/hypothesistesting/hyptesting_onesample_Bernoulli.html

[brisk tapir]

Why not?

[brisk tapir]

Yeah, I wanted to make a sampling distribution. I know the probability, but the thing is ... I have a population that's in proportions. And the data we get returned is in means

So I'm having issue on converting it back

[trail ingot]

at the end of the day you just have the data you collected. no matter what it is, it was possible for it to happen when you just have a 2.91% chance for a card on each purchase

you can’t “prove” it’s rigged

[brisk tapir]

Tell me if this makes sense JessicaK.

I make a sampling distribution of 2.91.
I use an alpha level of 0.01.
I check the probability at z = 0.01
I calculate the number of cards we get at z = 0.01 and compare it to the mean

[brisk tapir]

I don't think you're getting my point

I can make a sampling distrubtion with the probabilty given. I can prove it's rigged by literally showing data that doesn't follow the probabilty

You can prove the chances are rigged by actual data and a distribution like this. I can show that there's a VERY low chance to get this X amount of cards based on what they're claiming

[wintry stag]

I don't know what you are asking that the link I gave you does not address

[brisk tapir]

I'm only explaining my process actually. I know how to run a significance test

[trail ingot]

VERY low chance is the most you’ll be able to say but ok

[brisk tapir]

The problem is converting that data

[brisk tapir]

... ?

If the chance of something happening extreme is 0.001%, and that extreme happens, we have some nice evidence to prove that their claim might be wrong

I'd just need to confirm it with more samples

[trail ingot]

yes

that is not proof

[brisk tapir]

Are you saying I'd never TRULY know if it's rigged?

[trail ingot]

yep

[brisk tapir]

I think that depends. If I were to show that something extreme keeps happening again and again

It's pretty good proof

[trail ingot]

agreed

[brisk tapir]

On the topic of objectivity, I'd need to know the game code to know for sure (yeah, I get that). But if it keeps happening again and again, we have pretty good evidence to show that an extreme shouldn't keep happening again and again.

That there's definitely something wrong

[brisk tapir]

So this should make sense

since I'm trying to convert different data types for a test

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[noble mesa]

.close

[fierce marsh]

I’m so lost on 12 (ignore the writing above red) and I think I’ve made a mistake somewhere

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[fierce marsh]

Ok I watched a video and it said to plug the values in but now I’m stuck again

.close

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[proven current]

hey could someone help me with this please?

[umbral ginkgo]

The problem declares a relationship between the weight and the amount of blood

You're also given an example which demonstrates this relationship

[proven current]

so how do i graph an equation out of this information?

[umbral ginkgo]

Is the linear equation familiar to you?

[proven current]

y=mx+b yes

[quasi dragon]

you are also given a point that would lie on the line in the question

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[wraith hinge]

what is I do to solve here problem what

[wraith hinge]

I got

0=((4x)(1/3(y^(-2/3))(dy/dx)+(4)(y^(1/3)))+4y(dy/dx)

issue is that dy/dx is in there twice, and one of them is within a chain rule within a product rule

ill ask again later, gtg

.solved

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[wooden path]

is this valid

[woeful bramble]

yes you found a counterexample

thats the easier part as proving its true for all a and b xD

[wooden path]

right

what wouldve been the better approach

[woeful bramble]

no yours is the right because there is a counter example
if you have to prove something isnt true counterexample is often an easy way if you find it

[wooden path]

makes sense yeah

same method but as long as I prove it right?

@woeful bramble

[woeful bramble]

yea

[wooden path]

ok thank you

ever since trig identities, im having a hard time identifying if my answers are valid

!close

.close

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[azure wagon]

write the trigonometric ratio cos(-175) as the ratio of an acute angle with the correct sign attached

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[rain wharf]

this isnt a school related thing at all, just a personal endevour. i was talking with someone and they said that this was not true and i didnt know how to peove it. how is 1/cosx+1= sec^2(x/2)/2

[burnt mulch]

$\cos 2x =2\cos^2 x-1$

[solid kiln]

Civil Service Pigeon