help-0

[sudden hinge]

In your case it always evaluates to a constant between 0 and 1 so you have convergence for all values of x

[alpine sable]

hm ok

alright thanks guys

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[alpine sable]

Soh Cah Toa is used to find sinus, cosinus and tangent. is there a phrase for secant cosecant and cotangent?

[raven hill]

@alpine sable villiam there is not a phrase that I know of but you can just remember that csc is the reciprocal of sin sec is the reciprocal of cos and cot is the reciprocal of tan so all you have to do is flip the fraction to find the answer

for example if sin(theta) = 2/7 csc(theta) = 7/2

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[alpine sable]

I have absolutely no idea what to do

Dont these normally have an exponent?

[gray isle]

they're asking you to apply the relation between logs and exponents

watching the provided vid should help

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[blissful ether]

What is the correct answer to part C?

[blissful ether]

Is it just C'(42)-C'(40)?

[lone heart]

@blissful ether Has your question been resolved?

[blissful ether]

<@&286206848099549185>

[lone heart]

@blissful ether Has your question been resolved?

[icy crane]

no

[alpine sable]

I think so

[blissful ether]

Oh I forgot this was still open lol I figured it out

[alpine sable]

I think it wants you to just estimate though

[blissful ether]

nah it wasn't C'(42)-C'(40)

was something like C(40)+2C'(40)

.close

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[alpine sable]

Oh

[lone heart]

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[frosty flint]

given the function h(x):
determine a so h is continuous in x=2

[icy crane]

correct, congrats for figuring it on your own 😄

[marsh rapids]

so you need to find the limit of h(x) as x -> 2

[frosty flint]

i have

it is 1/4

wait, is that what a is?

[marsh rapids]

how is continuity defined ?

[frosty flint]

gz

[tacit arch]

#latex-testing FWIW

[frosty flint]

so uh, how would i go about solving it? i already solved the top part for x -> 2

[earnest mortar]

you need the limit of $h$ at $x = 2$ to match $\alpha $

[ocean seal]

Silfer

[frosty flint]

[earnest mortar]

that's how you satisfy continuity

draw the curve and see

[frosty flint]

this is confuse

[tacit arch]

what part

[frosty flint]

the stuff they're writing

not clicking in my brain

[tacit arch]

this should look familiar

[earnest mortar]

do you know how continuity is defined ?

[tacit arch]

what exactly

[frosty flint]

limit of h at X=2 to match a

[earnest mortar]

heresy, f(x) is not a function

[frosty flint]

not really?

[earnest mortar]

yeah so you just need alpha = (limit of f(x) when x goes to 2)

[tacit arch]

this is the definition. apply it to your $h(x)$

[ocean seal]

riemann

[earnest mortar]

f is a function, not f(x). f(x) is a value

[frosty flint]

so since i already solved this. its real simple?

[tacit arch]

yes

[earnest mortar]

yes. But do you understand why this condition on alpha satisfies continuity ?

[frosty flint]

so a is just that.?

[tacit arch]

read this

h(2) = ?

[frosty flint]

at that point it's not continuos

[tacit arch]

does your h satisfy this for $x_0 = 2$ ?

[ocean seal]

riemann

[earnest mortar]

isnt it 1/8 ?

[tacit arch]

for your choice of $\alpha$ ?

[ocean seal]

riemann

[frosty flint]

no 1/4

[tacit arch]

,w plot (sqrt(x+2) - 2) / (x-2) for 1.5 < x < 2.5

[ocean seal]

Results provided by WolframAlpha

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

Requested by riemann#2529

[earnest mortar]

nvm it's 1/4 indeed

midnight breaks my abilities

[frosty flint]

same

[marsh rapids]

Zote the mighty weakens as darkness appears ? Lame

[earnest mortar]

Zote hides his true powers you should know

[marsh rapids]

I have yet to see them in more than a distant dream

[tacit arch]

read this for more detail on continuity at a point

[frosty flint]

yse

i still don't really know what im supposed to find

or do

ah okay. so h(x) doesn't exist for x=2?

[tacit arch]

read this

h(2) = ?

[frosty flint]

1/4?

sorry

[tacit arch]

yes because you define alpha to be 1/4

[tacit arch]

as you were instructed to do so

[frosty flint]

so a = 1/4?

[tacit arch]

did you read this?

[frosty flint]

yes

[tacit arch]

do you understand the instructions here that you translated?

[frosty flint]

i feel my question was a simple yes, no answer.. apparently not

[frosty flint]

sorta

[tacit arch]

what don't you understand about it

[frosty flint]

its been a while since i have done continuaty stuff

[tacit arch]

if you don't want more help than necessary, then ignore it

[frosty flint]

[tacit arch]

what about continuity don't you understand

[tacit arch]

1, 2, or 3?

[frosty flint]

i understand that i guess

[tacit arch]

do you understand the question now?

[frosty flint]

yes

a=1/4

in x=2

ok then.

prob illegal, but when i put them equal one another and solved it i got a = 2?

[tacit arch]

put what equal to what

[frosty flint]

the top equal to a

[tacit arch]

you already found alpha. why are you trying to find a new value for it

[tacit arch]

top of what

[frosty flint]

the one thats over a...

saw yt vid and tried something out...

[tacit arch]

am i supposed to know what video you're talking about?

[main kraken]

ah yes, that video

we all know and love

[frosty flint]

no?

[main kraken]

[frosty flint]

so i've already solved the thing then?

[tacit arch]

what thing?

[frosty flint]

the task

[tacit arch]

here's a tip: communicate clearly

don't immediately make me ask you a question to clarify what you're saying

[frosty flint]

since you say i've already found alpha.. i have determined a so h is continous in x=2?

[tacit arch]

did you read this?

if your h satisfies all 1,2,3 then yes

[frosty flint]

okay

yes

.close

[lone heart]

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[oak temple]

Hi

[oak temple]

I currently stuck on

These two questions

I thought the bottom one was right

But doesn’t make correct

[dense sleet]

The thing can be factorable right

[oak temple]

It’s a quadratic formula

But you plot on a graph

It makes a U shape

[dense sleet]

$$(x-2)(x-3)$$

[ocean seal]

Pluton

[lime schooner]

(x-3)(x-2)<0

[dense sleet]

When is this negative

<0

[lime schooner]

oh typo

[lime schooner]

thanks!

x-3<0
and
x-2<0

[dense sleet]

Not really

[oak temple]

This got 1/4 marks

[dense sleet]

Take -1 for example

-3*-4

Positive

[oak temple]

I thought

You

Solve the fur la

Formula

And get the roots

And then

[dense sleet]

You can do that too

[oak temple]

Draw a sketch graph

[dense sleet]

Interval is -3 to -2

Typo

3 and 2

X should be less than 3 and bigger than 2

[alpine sable]

Couldnt you just find the solutions and look at the coefficient of x²?

[dense sleet]

You said its opposite

[oak temple]

You got it tight

Right

I don’t understand this one though

I tried rearranging

[dense sleet]

Solve first equation first

[frosty flint]

factorize it and solve

[oak temple]

X<-4,5?

[dense sleet]

Yep

[oak temple]

I don’t know how to write the answer is my main issue

[dense sleet]

Now look for integer solutions in
$$-12<x<-4.5$$

[ocean seal]

Pluton

[oak temple]

It says it’s wrong

[dense sleet]

What did you type

[oak temple]

That

That was my first answer from earlier

[dense sleet]

You arent supposed to type that

[oak temple]

H

But it worked for the other

[dense sleet]

You are supposed to type integer solutions

[oak temple]

😭

[dense sleet]

Well other one didnt ask you for integer solutions

[oak temple]

What are they

[dense sleet]

This one explicitly says "List the integers"

[oak temple]

So like -12,-11,-10

And so on

[dense sleet]

-12 isnt in that inequality

But yes

[oak temple]

Yay it was right thanks

Thank you for your help

Hope you both have a good day

[lone heart]

@oak temple Has your question been resolved?

[lone heart]

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[cosmic oasis]

How can I solve this for r?

[dense sleet]

Solve sum

1 - sum

[naive valley]

subtract the series from both sides to get $r = 1 - \sum_{i=1}^{N}-(s\cdot i)^2$ ?

[ocean seal]

OurBelovedBungo

[naive valley]

unless "+r" is meant to be included as a summand

[cosmic oasis]

Yeah sorry it's all inside the sum

[naive valley]

r does not depend on i, right? in that case the sum of N copies of r is just Nr

[cosmic oasis]

r is a constant yeah

So is s

[naive valley]

ok so $\sum_{i=1}^{N}(-(s \cdot i)^2 + r) = \left(\sum_{i=1}^{N}(-(s\cdot i)^2)\right) + Nr$

[ocean seal]

OurBelovedBungo

[naive valley]

and proceed as before

[cosmic oasis]

Oooh right

Thank you very much

[naive valley]

pleasure

[cosmic oasis]

So the answer would be:

$r = \frac{1}{N}(-\left(\sum{i=1}^{N}(-(s\cdot i)^2)\right)+1)$

[ocean seal]

Vertox

[cosmic oasis]

Did I make a mistake anywhere

[naive valley]

well you have some tex issues

but I think what you intended to type is correct

[cosmic oasis]

$1-Nr = \left(\sum{i=1}^{N}(-(s\cdot i)^2)\right)$

[ocean seal]

Vertox

[cosmic oasis]

Yeah still need to get used to it lol

[naive valley]

need to use _ before {i=1}

[cosmic oasis]

Ah oops didn't notice that it disappeared

Diacord does that

test

$r = \frac{1}{N}(-\left(\sum_{i=1}^{N}(-(s\cdot i)^2)\right)+1)$

[ocean seal]

Vertox

[naive valley]

that looks right now

can of course combine the two - into one +

[cosmic oasis]

$r = \frac{1}{N}((\sum_{i=1}^{N}((s\cdot i)^2))+1)$

[ocean seal]

Vertox

[cosmic oasis]

$r = \frac{1}{N}(\sum_{i=1}^{N}((s\cdot i)^2)+1)$

[ocean seal]

Vertox

[cosmic oasis]

$r = \frac{1}{N}(\sum_{i=1}^{N}[(s\cdot i)^2] +1)$

[ocean seal]

Vertox

[cosmic oasis]

Thank you very much 🙏

. close

.close

[lone heart]

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[grim pelican]

I need help which formula should I use?

[grim pelican]

should I use I=1/12(ML^2) or I=1/3(ML^2)

or is both my formulas wrong?

pic for reference*

<@&286206848099549185>

[forest harness]

it might be easiest to think of it as two parts and sum their inertias

since the meterstick isnt rotating about the center or the end

one rod will be 18.3cm and the other will be 100-18.3cm

and each will be rotating around their ends

(remember to divide the mass between them accordingly)

[lone heart]

@grim pelican Has your question been resolved?

[lone heart]

@grim pelican Has your question been resolved?

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[trim plinth]

how come $a^(\frac{m}{n})=\sqrt [n] {a^m}$?

[ocean seal]

sunflame

[trim plinth]

how come $a^{\frac{m}{n}}=\sqrt [n] {a^m}$?

[ocean seal]

sunflame

[trim plinth]

yes

can anyone prove

[regal acorn]

I think you know how $a^m$ is. So you're looking for proof of $a^\frac{1}{n} = \sqrt[n]{a}$

[ocean seal]

hiro

[regal acorn]

a simple goes like this

$a^\frac{1}{n}a^\frac{1}{n}$a^\frac{1}{n}a^\frac{1}{n}...\text{n times} = a^1$

[storm grotto]

isn't this only true when n=2?

[regal acorn]

Oh right, I forgot to multiply it n times

[ocean seal]

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

[lone heart]

@trim plinth Has your question been resolved?

[trim plinth]

hmm

[lone heart]

@trim plinth Has your question been resolved?

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[alpine sable]

i need help with my homework its linear functions on bigideasmath.com i have 3 questions already done

[alpine sable]

if possible i would like to call

heres the problem

[fierce prairie]

any ideas on going about it?

[alpine sable]

sort of

[split oriole]

Here whatever you put x you will get a fixed y, do you see which y value?

[alpine sable]

i can send a pic of the last one

[alpine sable]

i think its 3 right?

[split oriole]

Yup

So y=3

Boom

[alpine sable]

im confused cause theres multiple dots

ok

worked!

this is prob 5

i have 10 probs btw

[alpine sable]

thanks lol

[fierce prairie]

find the rate of change from the table

[alpine sable]

ok so i see it adds 4 to the x every tick thing

[split oriole]

If you know how to find equation of line the. You are done

[alpine sable]

i need help with most problems sorry the questions change also

[split oriole]

I am answering this question

[alpine sable]

and every tick for y is -1

[alpine sable]

ok

idk

[split oriole]

You are giving him/her answer

[alpine sable]

im a guy if u want u can call me nate

[spring glade]

ok

[alpine sable]

ok so y is +4 each time it goes so i tried 4 and it said it was wrong its y= answerhere

[fierce prairie]

@alpine sable do you know how rate of change works?

[alpine sable]

not really

i just started this unit yesterday

[fierce prairie]

alright so it's change of y / change of x

[alpine sable]

ok

[fierce prairie]

so let's just look at the first two points

[alpine sable]

ok

[fierce prairie]

the change in y is?

[alpine sable]

yeah

[fierce prairie]

-1

[alpine sable]

?

im sorry im really bad at learning

[fierce prairie]

sorry i explained it bad

basically

[alpine sable]

its ok

[fierce prairie]

just look at the y values first

2 and 1

[alpine sable]

ok

[fierce prairie]

the change between them

is the second one minus the first one

so 1 - 2

[alpine sable]

so x adds 4 and y subtracts 1 and it goes for each change

[fierce prairie]

yep

so if it's change in y / change in x

[alpine sable]

i kinda understand it im just bad at finding answers

ah ok

[fierce prairie]

then how can you use this info to find it?

[alpine sable]

i dont know

[fierce prairie]

as you just listed the change in y and change in x

[alpine sable]

is it 4-1?

or 4 over 1?

[fierce prairie]

no, it's dividing the change in y by the change in x

well

[alpine sable]

ohhh ok

[fierce prairie]

that's x over y

so other way around

[alpine sable]

so 1 over 4

got it ok

[fierce prairie]

close but

remember you said "subtracts 1"

so -1 over 4

[alpine sable]

ok

this didnt work and i tried putting a - in front of the 1 as well

[fierce prairie]

alright so there is something called slope intercept form

[spring glade]

you need to write your function in terms of x

[fierce prairie]

did you learn it in your class?

[alpine sable]

i think so but i have a hard time paying attention and remembering stuff

i remember my teacher mentioning it

is it y= mx + b

?

[fierce prairie]

it's alright

yup

[alpine sable]

ok

got it

[fierce prairie]

so m is the rate of change

[fierce prairie]

so simply put an x here

[alpine sable]

is it y = -1 + 4?

oh ok

[fierce prairie]

nah there's no b for this

b is y intercept

[alpine sable]

ohhh ok

[fierce prairie]

and the table says (0, 0) which makes it nothing

[alpine sable]

so its 1
_x ?
4

[fierce prairie]

with a negative yup

[alpine sable]

with a negeative yea i forgot to put it lol

worked

i always forget the x lol

[fierce prairie]

yea it comes with practice

[alpine sable]

ok ima try this one by myself and ill lyk how it goes

[fierce prairie]

alright

[alpine sable]

nah got it wrong i tried 2 over 3 x and 3 over 2 x

i have infinite checks btw so if i get it wrong i can keep checking

[fierce prairie]

yeah so the rate of change (or m) is 2/3 so you got that right

but here there is actually a b

[alpine sable]

i can tell the rot is +3 for x and +2 for y

ohhh ok

[fierce prairie]

hold on are you aware what a y intercept is?

[alpine sable]

yeah

its where on a graph the line crosses the y line

aka the origin sort of

[fierce prairie]

yep

so for this one it is?

[alpine sable]

2?

[fierce prairie]

nah

it's when x is 0

what is y

[alpine sable]

y is +2 each change

[fierce prairie]

because think of a graph, the x value would be 0 when the line hits the y axis

[alpine sable]

ohhh ok

[fierce prairie]

so what is y when x is 0?

[alpine sable]

3?

[fierce prairie]

alright man look at this table

[alpine sable]

ok

[fierce prairie]

what is just below the 0 in the x list

[alpine sable]

5

OHHHH I SEE

[fierce prairie]

ye

lmaoo

that's the y intercept

[alpine sable]

oh god lmao

[fierce prairie]

the line hits (0,5)

and that point is given in the table

so yeah just look at the y value right below, when x is 0 on the table

[alpine sable]

hmm ok

[fierce prairie]

so if it's y = mx + b

and b is the y intercept

whats the equation?

[alpine sable]

it would be y = 2x + 5?

[fierce prairie]

close but what was your rate of change?

[alpine sable]

for x or y?

thats dumb lol its 2

i asked a dumb question lol

[fierce prairie]

uh? rate of change is the change between x and y

just scroll up

you found it earlier remember

[alpine sable]

yea

1s ill find it

is it 0?

no that wouldnt work

hmmm

1s

lol

[fierce prairie]

it was 2/3 man

[alpine sable]

its 2/3

[fierce prairie]

how had you found it earlier

[alpine sable]

idk lmao

soon as u sent that i found it lol

[fierce prairie]

okay well you should know as it's a pretty important concept

gimme a sec

[alpine sable]

i looked at this

ok

[fierce prairie]

alright so here is the change of x and y

change in x = 3

change in y = 2

you see that?

[alpine sable]

yea

[fierce prairie]

so then just divide the change in y by x

and therefore you get 2/3

[alpine sable]

ah ok

[fierce prairie]

you're adding 2 each time in the y, and adding 3 each time in the x

[alpine sable]

yea

[fierce prairie]

so that's what i mean by change in them

[alpine sable]

ok

[fierce prairie]

so just change this with the correct rate of change?

[alpine sable]

so y = 2x + 3

nvm didnt work

[fierce prairie]

y = mx + b

its important to understand what each part is

m = rate of change, which we just found is 2/3

b = y intercept, which we found earlier was (0, 5) as listed by the table, but in the equation, you just put the y value

[alpine sable]

ohhhhh i see so its y = 2/3 x + 3?

[fierce prairie]

read this line please

[alpine sable]

ok

ok so for b i think u said to put the y value right?

[fierce prairie]

when x is 0, yup

so the y value directly below 0

in the table

[alpine sable]

ohhhh ok

5

[fierce prairie]

yepp

[alpine sable]

so 2/3 x + 5?

[fierce prairie]

yessir

well done

[spring glade]

im glad im watching this unfold

[alpine sable]

ah i see ok lol

thank u so much lol

[fierce prairie]

yeah np

[alpine sable]

lol u get to watch me be stupid

[spring glade]

@alpine sablehave u heard of rise over run before

[alpine sable]

yeah

[spring glade]

yeah thats what m is

[alpine sable]

ik how u do it

[fierce prairie]

its really important to know this concept, you'll see it all the time in math

[alpine sable]

ok

[fierce prairie]

thats why i really tried to make sure you understood what was happening :)

[alpine sable]

yea isnt this the foundation of something i forgot the name

[fierce prairie]

linear equations

[alpine sable]

yea lol thx i learned it like 3 months ago and we took a break and did something else and then came back to it

[alpine sable]

yea lol

[fierce prairie]

ohh i see

np

[alpine sable]

yea its hard to remember if i learn it and then do something else and then try to do it again 3 months later lol

ok this is the next 1

its y = mx + b again right?

[short cobalt]

yes

[alpine sable]

ok

ok i think the y int is 11 right?

[fierce prairie]

yup

[short cobalt]

yes!

[alpine sable]

ok

and the change is 1.5

[short cobalt]

yes

[alpine sable]

so y = 1.5x + 11?

[short cobalt]

yes

[fierce prairie]

what no

[alpine sable]

lol yea no

[fierce prairie]

alright so what is the change in y

[alpine sable]

1.5

[fierce prairie]

and change in x?

[short cobalt]

shoot, ur right

[alpine sable]

3?

[fierce prairie]

yep

[short cobalt]

i also forgot to account for change in x

[fierce prairie]

so divide the change in y by x

[alpine sable]

ohhh so its 3x + 1.5 or 3x + 11?

[fierce prairie]

its alr we all make mistakes

[fierce prairie]

y intercept (b) will stay the same, so 11

just divide 1.5 / 3

[alpine sable]

ok

[fierce prairie]

for the m part

[alpine sable]

0.5

or 1/2

[fierce prairie]

yep

so y = 1/2 x + 11

[alpine sable]

prolly gonna have to put in 1/2 bigideas hates decimans lol

ok

decimals*

does anyone see a pattern in the data set

[fierce prairie]

lmao

[alpine sable]

is it exponential?

[fierce prairie]

#❓how-to-get-help

[alpine sable]

got it 😄

[fierce prairie]

nicee

[alpine sable]

and now it says

wait im dumb lol i can do this

[fierce prairie]

lmao yea u got this

[alpine sable]

yea it was 1/2 and 11 inches

got it lol

ok same thing i think i can do it

[fierce prairie]

nicee

[alpine sable]

change in x is +2 and change in y is -0.2

[short cobalt]

y is -.4

[alpine sable]

so -0.2 / 2 for this right?

[fierce prairie]

close but change in y is -0.4

[alpine sable]

oh ye lol

i messed it up with the + 2

i meant 0.4 lol

its like 12:07 lol

[fierce prairie]

lol so yeah -0.4 / 2

[alpine sable]

ye

-0.2

[fierce prairie]

yea

and y intercept?

[alpine sable]

i think its 0.4?

if i messed it up its cuz i did it fast lol

[short cobalt]

where is x zero?

[fierce prairie]

well just look at the y value when x is 0

[alpine sable]

ye its 0.4

[alpine sable]

ohhhhhhhhhh

[fierce prairie]

0.4 is the rate of change you had to calculate (also called slope if it helps)

[alpine sable]

ok

[fierce prairie]

but y intercept is simply

the y value when x is 0

[alpine sable]

this is what i need help with im kinda confused about this

[short cobalt]

if you think about the term y intercept. its saying when the line crosses the y axis.

[alpine sable]

yea

[short cobalt]

when it crossing the y axis, x must be zero. This can be seen visually on a graph.

[alpine sable]

so it crosses the origin aka at 0 and goes up one because y is 1?

is it 0.2?

[fierce prairie]

no, right there

y is 1

when x crosses 0

[alpine sable]

ok so its 1?

[fierce prairie]

yup

[alpine sable]

got it oki

[alpine sable]

and its 1 divided by -0.2?

[fierce prairie]

heres a graph of it which could help understand it

[alpine sable]

that desmos lol?

[fierce prairie]

?

[alpine sable]

for y divided by x?

or is it the other way

shit i forgot

[fierce prairie]

-0.2 is your slope (m) which you already solved with y over x, and 1 is your y intercept (b)

[alpine sable]

ohhh ok

[fierce prairie]

so now all u gotta do is put them in the equation

[alpine sable]

yea

got it lol

oki

ill do the bottom shit now

[fierce prairie]

yeah tell me if u have questions with that

its a bit different than what we just did

[alpine sable]

yea i tried 2 and it didnt work

for the first one

[fierce prairie]

yeah so look at the question with logic

we're talking about battery power

so it would be 0-100%

and your values go from 0 - 1

so essentially

if you're rate of change is -0.2, you're losing 20%

essentially converting to a percentage by *100

[alpine sable]

is it 10? cause its 1 per hour? or is it 20

no its 2 per hr lol

ok wait so is it 20?

[fierce prairie]

20 because your rate of change was 0.2 yea

[alpine sable]

ok

yea it worked

the battery lasts 2 hours then right?

[alpine sable]

nvm that didnt work

[fierce prairie]

yeah so that's asking what the x intercept is

one second

[alpine sable]

ok

[fierce prairie]

so what is x intercept?

[alpine sable]

1

oops

-0.2

thought u said y lol

[fierce prairie]

no like from a conceptual point

like what does it mean

to say x intercept

[alpine sable]

ohh its the hours

[fierce prairie]

nah

its simply

when the line intercepts the x axis

[alpine sable]

ohhhh ok

[fierce prairie]

heres a good example

[alpine sable]

ok

[fierce prairie]

x intercept is when the line is colliding with the x axis

therefore

when the y value at that point

is 0

so, -4 is the x intercept

x is -4, y is 0

[alpine sable]

ok

[fierce prairie]

and its colliding with the x axis

so, let's look at your problem

we have y = -0.2x + 1

now to find the x intercept, we need to set the y value to 0

so 0 = -0.2x + 1

[fierce prairie]

and solve that for x

[alpine sable]

ohh ok

its -1 = 0.2x

[fierce prairie]

ye

[alpine sable]

thats a lin equ right?

[fierce prairie]

sorry i made a mistake

see my edits then solve

[alpine sable]

ur good lol

ok

[fierce prairie]

yea

[alpine sable]

oh its just 1 = -0.2x

[fierce prairie]

no?

[alpine sable]

wait huhhhh?

[fierce prairie]

0 = -0.2x + 1
-1 = -0.2x
5 = x divide by -0.2

[alpine sable]

oh shit i forgot abt that step

ok

yea

[fierce prairie]

yea

so yea you have x = 5 which is therefore the x intercept

[alpine sable]

ok

so then it lasts 5 hours

[fierce prairie]

yup!

[alpine sable]

got it oki

[fierce prairie]

in context

that battery is at 0%

after 5 hours

[alpine sable]

ye

[fierce prairie]

and then just put the y intercept you found earlier

for the last one

[alpine sable]

ok

uhh i forgot what that was lol

which is it

sorry my brain is just shit right now lol im tired

[fierce prairie]

its alright

when x is 0

whats y

simply look at the table

the y that corresponds to the x

[alpine sable]

1?

[fierce prairie]

yup

[fierce prairie]

ah shit its 1am my brain

yeah so remember the context here again

[alpine sable]

lol

[fierce prairie]

for some reason they gave the battery

from 0 - 1

so just make it percent

1 is 100%

so 100%

[alpine sable]

ohhh ok

alr i think i got this

[fierce prairie]

yeye

substitute 0.75 into your equation you found

[alpine sable]

so y= 0.75x + 1?

[fierce prairie]

sorry, i mean into x

[alpine sable]

o lol

[fierce prairie]

so you have y = -0.2x + 1

replace x with 0.75

and solve

[alpine sable]

so y = -0.2x + 0.75

[fierce prairie]

read this carefully homie

[alpine sable]

ok

[alpine sable]

i thought thats what i did up here?

[fierce prairie]

no, okay ill just tell you

[alpine sable]

ok thank u

[fierce prairie]

so you got this equation, y = -0.2x + 1
replace x with 0.75 --> y = -0.2(0.75) + 1

[alpine sable]

got it ok

[short cobalt]

Remember the equation y= mx + b!

[alpine sable]

ok

wait so is it y = -0.15 + 1 cause i multiplied -0.2 x 0.75?

[fierce prairie]

yep

[alpine sable]

ok

[fierce prairie]

add the 1 lol

[alpine sable]

1.15?

[fierce prairie]

well it's -0.15 + 1

so 0.85

[alpine sable]

no im dumb lol

ok

it said 0.85 is wrong

[fierce prairie]

hm

try 17/20

[alpine sable]

i do have math help in the morning lol

[fierce prairie]

if they really hate decimals so much

[alpine sable]

yea it does

didnt work

o shit its 12:32 i gotta get to bed

i have math help in the morning before math class so i can do the last 3 in there

[short cobalt]

Good luck!

[alpine sable]

ty

[fierce prairie]

alright sorry abt that last part i have no idea what I messed up on

[alpine sable]

alr gn thanks for helping me tonight @fierce prairie and @short cobalt

[alpine sable]

all good lol

thank u so much lol

[fierce prairie]

prob bc its 1:30am lmao

yeye np

gn

[alpine sable]

lol

gn

nice meeting u guys

[short cobalt]

I know how to do the last part

If u need to know

But no worries cause it’s also late!

[alpine sable]

yea prolly

i might stay home tmrw im pretty sick

[fierce prairie]

btw maybe leave this open and someone may figure it out overnight

[alpine sable]

ok

if anyone knows how to do this please @ me with a response

[short cobalt]

Can I DM you how to do it?

[alpine sable]

sure

[fierce prairie]

why not say it here lol?

I want to know too!

[alpine sable]

lol

[fierce prairie]

i have no idea what i did wrong

weird

i even checked with desmos, y is 0.85 at x 0.75

[alpine sable]

lmao im shiverin rn its cold ima go to sleep and stay warm gn dm me it and ill check in the morning put it here too tho

alr gn guys

[fierce prairie]

yikes yeah get rest

gn

[alpine sable]

my heat goes off at 12:30 so i have to go to sleep or freeze lmao

[alpine sable]

gn 🙂

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[alpine sable]

@fierce prairie u like sleepy hallow lmao i like his music

[fierce prairie]

lmao yeah but sleep my guy

[alpine sable]

alr

add me if u wanna lol gn\

[lone heart]

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[alpine sable]

i can help u in val lmao

[alpine sable]

anyways gn guys

[fierce prairie]

oh shit u opened a channel

probably .close

[alpine sable]

.close

[lone heart]

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[fickle dock]

Hey, would anyone mind explaining to me how I can arrive at this answer? (it's correct, I checked already)

[lone heart]

@fickle dock Has your question been resolved?

[lone heart]

@fickle dock Has your question been resolved?

[oak perch]

It means T(e_1,e_2,e_3)=(e_1,e_2,e_3)A where e_1,e_2,e_3 is the standard basis of R^3

[lone heart]

@fickle dock Has your question been resolved?

[noble sinew]

<@&268886789983436800>

[sly mantle]

b&

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[lone heart]

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[little berry]

Why is $2-\pi$ negative?

[ocean seal]

Shinutsi

[little berry]

I don't get the, "Because pi = 3.14" part

OH WAIT

[dreamy wyvern]

π ≈ 3
2 < 3
a - (a + 1) = -1

[little berry]

2-3.14 yeah

thank you im so dumb wth

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[alpine sable]

Hello! I have a problem getting a sample of circles rotated by an angle theta.. here you can see the sampled circles..

I want to rotate them like this:

but after applying 2D-Rotation-Matrix I get something like this:

I also created a question at Stack-Exchange where more Informations are given: https://math.stackexchange.com/questions/4405604/rotate-samples-of-circles-around-an-angle-theta maybe someone can help me finding my mistake?

[lone heart]

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[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[granite sluice]

how can I solve this?

[hoary socket]

First

And thenand then

[granite sluice]

ok

still

[hoary socket]

Ask someone else

Do i look like god

[weak field]

Use cosine rule

[granite sluice]

u mean I have to use like beta=arccos(blabla)?

like this?

[weak field]

Yes

[placid zinc]

Wtf 1/cos

[granite sluice]

i divide cos for cos and on the other side i get arccos

because arccos is 1/cos

am i right?

arcsin*

[placid zinc]

Arccos is the function that undoes cos.
arccos is the inverse function to cos

[granite sluice]

yes

[granite sluice]

so it's right enough to use it?

[weak field]

U have calculator ig...

[placid zinc]

cos(x) = y
arccos(cos(x)) = arccos(y)
x = arccos(y)

[granite sluice]

yep imma do it rn

[granite sluice]

isn't it what I'm saying?

[placid zinc]

No you said 1/cos which is a wtf

[weak field]

Like this

@granite sluice

[forest jacinth]

No, you said that $f^{-1}$ is $\frac{1}{f}$

[ocean seal]

JarrGarde

[forest jacinth]

Which isn't true, because if f is a function, f^(-1) is used to label its inverse, not reciprocal

The inverse of arccos is cos, not 1/cos

[granite sluice]

so what is it?

[forest jacinth]

Kaynex actually wrote everything well a few messages up

[granite sluice]

why 44?

[weak field]

144-(36+64)

[granite sluice]

right right

[granite sluice]

is the second line right?

[weak field]

What is X here ??

[granite sluice]

now what?

[granite sluice]

x is beta

[granite sluice]

.

[weak field]

U get cos B =(-44)/96 which implies B=cos inverse (-44/96) ... Now u can use the cos inverse function of calculator

[granite sluice]

it says math error

do i have to use radiants or degrees?

I'm using deg rn

[granite sluice]

idk why it's not working on the calculator but in my head it makes sense

[weak field]

Breh... It's -44/96

[weak field]

U r evaluating something out of range..

[granite sluice]

u mean I have to work on the left side? so dividing 44 by 96 is the right thing

am i right?

[weak field]

Yes...

[weak field]

U r dividing (-96) from both sides

[granite sluice]

yes

works fine thank you so much

[weak field]

Wlc

[granite sluice]

how do I stop the bot?

[weak field]

Idk.. I joined the serv today

[granite sluice]

same

uhm

one last thing

[granite sluice]

is a=b/cosBeta?

and if i have c and b how do I calculate a?

in a 90° triangle

[weak field]

Umm what is a, b, c?? @granite sluice

[granite sluice]

ab ac and cb

[granite sluice]

.

[weak field]

@granite sluice can u draw a diagram..

??

I'm confused

[lone heart]

@granite sluice Has your question been resolved?

[lone heart]

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[brittle sun]

Hey fellas,
I have encountered the question below*, and while trying to prove it I naturally assumed that the line lined with blue is correct. But when I thought about it, I wasn't really sure how to go about proving it. Can somebody nudge me in the right direction?

[lone heart]

@brittle sun Has your question been resolved?

[brittle sun]

<@&286206848099549185>

[granite sluice]

btw i just did the test and it went well thank you for the info earlier

[lone heart]

@brittle sun Has your question been resolved?

[lone heart]

@brittle sun Has your question been resolved?

[lone heart]

@brittle sun Has your question been resolved?

[glass lichen]

Apply definition of being a subset (and not a subset) in terms of power sets

[brittle sun]

Wait, is this an solution to the main question, or to the smaller proof I was asking about?(the one in the blue lines)*

[glass lichen]

Blue lines

[brittle sun]

Cheers

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[leaden aspen]

Do I have this right?

[leaden aspen]

4pi(5^2)*.009

<@&286206848099549185>

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[bright osprey]

hey i have to prove that this

[bright osprey]

can be devided

by 5

for n > 0

i proved that it is divisible by 5 for n = 1

and managed to get to this

[hot spear]

@everyone 1+1

😔

[bright osprey]

dunno what to do next

[summer kite]

mathematical induction?

[bright osprey]

yes

[olive oar]

I mean, if you can show that 6^n always ends in 6, you're done yea

[bright osprey]

but it never ends in 6?

[olive oar]

6^1 = 6
6^2 = 36
6^3 = 216
...

[bright osprey]

ou

damn

hmm how do i show that

tho

[olive oar]

6^1 has remainder 6 when divided by 10

Let's say 6^k has remainder 6 when divided by 10

What can we say about 6 * 6^k when divided by 10?

Remember 6^k has remainder 6

If I have:

• • • • • -... 6
          x 6

where the -'s represent digits

whats the last digit gonna be?

[bright osprey]

well 6

[olive oar]

yea

so if it holds for 1, k, and k+1 it'll hold for an $$n \in Z^*_{+}$$

[ocean seal]

ohNoiAmHere

[olive oar]

So we've shown that for all natural n > 0, 6^n ends in 6, so 6^n - 1 ends in 5. And thus is divisible by 5.

[bright osprey]

yea but i cant calculate 6^k

right?

[olive oar]

if i tell you k is 10 you can, but in general you leave it like 6^k

cause its any positive integer

[bright osprey]

hmm that is fair

tnx

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[chilly tangle]

Be 𝑉 = 𝑀2×2. Given two vectors 𝑢 = [1 2
−1 1] e 𝑣 = [0 2
1 1]. Determine |𝑢 + 𝑣|.

[earnest mortar]

$$u = \begin{bmatrix} 1 & 2 \ -1 & 1 \end{bmatrix}$$
$$v = \begin{bmatrix} 0 & 2 \ 1 & 1 \end{bmatrix}$$

[ocean seal]

Silfer

[chilly tangle]

Thanks, man.

[earnest mortar]

is |𝑢 + 𝑣| a norm ? if so, which one ?

[solemn grove]

yeah,

so you know how to add matrices

and then find the det of the sum

[chilly tangle]

The problem doesn't say to me.

[fluid basin]

likely the determinant

[earnest mortar]

you might be right

[solemn grove]

yeah, that’s the determinant

that’s why i said det

[chilly tangle]

I tried sum both matrix first, but I don't know what to do later.

[earnest mortar]

tho i prefer the |M| for the norm and replacing [] by || around a matrix for the determinant, but that's just me

[solemn grove]

find the det of that matrix

[fluid basin]

sum the matrix, then find the determinant of the sum

[chilly tangle]

Is the det of a matrix its modulus?

[fluid basin]

most people use double vertical bars for the norm

[solemn grove]

yes

[solemn grove]

yee

[earnest mortar]

true

[solemn grove]

modulus

I think you meant that

but yeah

det is what they want you to find

I just say det for determinant