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[wet lark]

$$\sin80^{\circ}=\cos(90-x)^{\circ}$$
$$\sin80^{\circ}=\sin x^{\circ}$$

[ocean seal]

gekka

[wet lark]

do you see what i've done?

[wheat isle]

Hm

[wet lark]

also i sent the wrong identity lol

it's suppose to be cos to sin

not sin to cos

mb

[wheat isle]

This identity stuff is really confusing to me

[wet lark]

it's annoying at first, but you'll get used to it

just think of the identity are true statements

so you can just modify the identity (if needed) and it would still be true

[wheat isle]

I still don’t know what to do with this I think

[wet lark]

You just replace $\cos(90^{\circ}-\theta)$ to $\sin\theta$.

[ocean seal]

gekka

[wet lark]

that's what it's trying to explain

[wheat isle]

sin80 = cos(90-theta)

?

[wet lark]

what about that?

[wheat isle]

Is that the identity or something

[wet lark]

the statement you posted isnt an identity

but you can use one of the existing identity to replace one of them

[wheat isle]

Hm

Like sub it in?

[wet lark]

correct

https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-complementary-angles/v/showing-relationship-between-cosine-and-sine-of-complements

this should explain about those identity

[wheat isle]

sin(80) = sin(90-theta)?

[wet lark]

that is not an identity

the identity are already defined

so you can just use those

[wheat isle]

This is what I get after subbing the identity in

[wet lark]

from this?

[wheat isle]

From here

[wet lark]

that is an identity

so you dont really have to modify it

[wheat isle]

I subbed in sin(90-theta) for cos

[wet lark]

so that would be cos theta = cos theta

which is true

[wheat isle]

But I don’t think it gets me anywhere

[wet lark]

because you are looking at the identity itself

you are not focusing on the problem

,align \tan22^{\circ}&=\cot(90-y)^{\circ}\&=\tan y^{\circ}\y&=22^{\circ}

[wheat isle]

So original problem is sin80=cos(90-x)

[wet lark]

mhm

[wheat isle]

i don’t see anything to sub in

[ocean seal]

gekka

[wet lark]

you can sub in cos(90-x) with sin(x)

[wheat isle]

where’s the sin(x)

is it sin80

[wet lark]

no you need to look at the identity to replace that

$\cos(90-x)=\sin x$

[ocean seal]

gekka

[wet lark]

^^identity

[wheat isle]

So I’m supposed to get rid of the sin80

[wet lark]

well not really

you should leave that be

[wheat isle]

What am I supposed to be getting rid of

Or doing first

[wet lark]

okay lemme explain what are identities

imagine you have a $20 bill

because $20 is also 4 $5 bill

you can replace that $20 bill with 4 $5 bill

and it still is $20 bill

you are just simply replacing stuff with the identity

[wheat isle]

Yeah

[wet lark]

so let's go back in terms of math

$\sin80=\cos(90-x)$

[ocean seal]

gekka

[wet lark]

so

sin80

we cant really do anything with that

so we can just simply ignore that

[wheat isle]

Yeah

[wet lark]

but we know that $\cos(90-x)$ is technically $\sin(x)$

[ocean seal]

gekka

[wet lark]

because of the identity

so we can just simply replace $\cos(90-x)$ with $\sin(x)$ in that equation

[ocean seal]

gekka

[wet lark]

so this would become $\sin80=\sin x$

[ocean seal]

gekka

[wheat isle]

Ah

[wet lark]

and by logic

x is 80

so our x value must be 80

[wheat isle]

that makes sense

[wet lark]

cool

do you now get how to use identities?

[wheat isle]

Yeah I think so

so tan22=cot(90-y)

tan(y) = cot(90-y) is the identity?

[wet lark]

correct

[wheat isle]

so tan22=tan(y)

y is 22?

[wet lark]

bingo!

[wheat isle]

Ah cool

Thank you so much for the help

[wet lark]

yw :)

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[weary abyss]

im lost at finding the value of the left endpoint

[weary abyss]

so far i have (6-0)/8 = 0.75

[fathom grove]

it’s (6-2)/8

but ur x-values reflect that already

[fathom grove]

when you say left endpoint do you mean an endpoint value or the whole Riemann sum

[weary abyss]

left endpoint riemann sum

is it 0.5 * all the rectange heights?

[fathom grove]

0.5 is the width

the heights are determined by the value of f(x)

You don’t need the value for f(6) here but for every other value just add together and multiply by 0.5

[weary abyss]

why dont i need f(6)

nvm i see

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[sweet flame]

I wanna understand what this MVP really means in graphically.

[sweet flame]

Is there any article or video to understand it?

[lone heart]

@sweet flame Has your question been resolved?

[sweet flame]

<@&286206848099549185>

[naive valley]

the integral is just taking the average value of f on a circle of radius r centered at a

the MVP property holds if that average actually equals f(a), for every a and r such that the circle is contained in the domain

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@sweet flame Has your question been resolved?

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[dense plover]

I have a geometry EOC tomorrow but my teacher is not being helpful enough, could anyone please go over the questions I got wrong with me?

[craggy hill]

me too! sadly cannot help tho lol i don't understand it

[dense plover]

It is a weird question because usually, I can do these stuff pretty well, but I don't get how they got -5/7

[lone heart]

@dense plover Has your question been resolved?

[ocean seal]

Result:

149

Result:

9.1549167118003

[dense plover]

nvm I did all of them by myself

.close

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[lost flax]

i need help finding if this converges or diverges please!

[lost flax]

i was able to solve a similar problem where the numerator was (-1)^(n+1) by converting that to (-1)^n(-1) and then applying the alternating series test, but i dont know how to turn (-1)^(n-1) to a similar format

[woeful pulsar]

what do you remember about the alternating series test

it is an alternating series right

[lost flax]

yes

[woeful pulsar]

so what do you need to check

[lost flax]

i need to check if the limit of absolute value of an goes to 0

this was another problem

but i dont get how to separate the (-1)^n for this problem

[woeful pulsar]

$(-1)^{n-1}=(-1)^n\times(-1)^{-1}$

[ocean seal]

Element118

[lost flax]

ohh okay

so then it would also just be (-1)^n times (-1), right?

[woeful pulsar]

similar idea yeah

[lost flax]

is

?

oops

lol im bad with the bot

[woeful pulsar]

it turns out to be the case

[lost flax]

alright interesting

i can handle it from there, thank you!

[woeful pulsar]

since $(-1)^2=1$, so $(-1)^{n+1}=(-1)^{n-1}\times(-1)^2$

[ocean seal]

Element118

[lost flax]

yess

cool cool

.close

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[acoustic mirage]

How do I proceed with the question if the intervals given for both the functions are different ?

[acoustic mirage]

I proved that f(x) and g(x) are discontinuous in their interval

[woeful pulsar]

which one is the question

illustration 4.18?

[acoustic mirage]

Yep

[woeful pulsar]

firstly you can write f(x)+g(x) as a piecewise defined function

[acoustic mirage]

But how ? Aren't the intervals different in both the functions?

[woeful pulsar]

i'm gonna write it

[acoustic mirage]

Oook

[woeful pulsar]

$f(x)+g(x)=\begin{cases}
|x+1|+|x|+1&x\leq0\text{ and }x\leq1\
|x+1|-|x-2|&x\leq0\text{ and }x>1\
x+|x|+1&x>0\text{ and }x\leq1\
x-|x-2|&x>0\text{ and }x>1
\end{cases}$

[ocean seal]

Element118

[woeful pulsar]

so in each case, we combine one case from the f function, and one case from the g function

now one of these 4 cases is silly

can you tell which one

[acoustic mirage]

Ok yes i see it
So now i check the continuity at all the 4 cases ?

[woeful pulsar]

before that, one of these 4 cases cannot happen

[acoustic mirage]

The second one ig ?

[woeful pulsar]

yeah

and you can simplify the other 3 cases

$f(x)+g(x)=\begin{cases}
|x+1|+|x|+1&x\leq0\
x+|x|+1&x>0\text{ and }x\leq1\
x-|x-2|&x>1
\end{cases}$

[ocean seal]

Element118

[acoustic mirage]

So i simply remove the second case from existence?

[woeful pulsar]

yeah you can just yeet the second case

[acoustic mirage]

I c its become real simple now thanks

But can u explain what did the book do ?

[woeful pulsar]

the book realises that the only interesting points are x=0 and x=1

since x=0 is interesting for f and x=1 is interesting for g

[acoustic mirage]

Ig i will stick to what u said thanks

@woeful pulsar can u help me with another ques :) ?

[woeful pulsar]

[acoustic mirage]

Omk

What does this illustration mean ?

I didn't understand the ques

[woeful pulsar]

There are certain (a, b) such that it makes f continuous at x=1 and discontinuous at x=2

plotting all those (a, b) creates a straight line excluding where b=3

[acoustic mirage]

But what does "locus of (a,b)" mean ? What are the constraints ?

[woeful pulsar]

"locus of (a, b)" = "what you get when you plot all the (a, b) that satisfy the given conditions"

[acoustic mirage]

And the given condition is f(x) right ?

[woeful pulsar]

the condition is "f(x) continuous at x=1 and discontinuous at x=2"

"locus of all points a certain fixed distance from X" = "circle centered at X"

[acoustic mirage]

Where it cuts y = 3 means it is discontinuous at a point when f(x) = 3 ?

[woeful pulsar]

no

let's focus on "the set of all (a, b) such that the condition is fulfilled"

focus on that first

then we can draw it out to see what shape it has

[acoustic mirage]

Ok lemme just solve it real quick

I should start by doing lim x-> 1 f(x) = f(x), right ?

[woeful pulsar]

yeah you should look at the left hand and right hand limits

[acoustic mirage]

Yep

I got an equation

a-b= 3

Now what ??

[woeful pulsar]

have you included the condition where f is discontinuous at x=2?

[acoustic mirage]

No, i don't which kind of discontinuity it is...so how I proceed? Should I assume it to be removable discontinuity?

[woeful pulsar]

no

because it is defined at x=2

it cannot be removable discontinuity

[acoustic mirage]

Ok i c
So RHL = LHL

Ok i got another equation

Im solving it to get a, b

[woeful pulsar]

yeah

[acoustic mirage]

Ok so i got the values, now what ??

[woeful pulsar]

what did you do

if both are continuous, then you found a, b?

[acoustic mirage]

At 1 it is continuous and at 2 it has a removable discontinuity...and yes then i found out a and b.....a = 6 and b=6

[woeful pulsar]

wait what

but a-b is not 3

[woeful pulsar]

also note

[acoustic mirage]

How ? It is continuous at 1

[woeful pulsar]

6 - 6 is not 3

somewhere something went wrong

[acoustic mirage]

Oh sorry mb

B = 3 and a = 6

I typed out the wrong thing

[woeful pulsar]

so this is when f is continuous at both 1 and 2

but we want the points where f is continuous at 1, but not at 2

so we take all a-b=3, and remove the point (6, 3)

[acoustic mirage]

What does that mean exactly? What should I do next ?

[woeful pulsar]

f continuous at 1 => a-b=3

[acoustic mirage]

Yep got this

[woeful pulsar]

f continuous at 1 and 2 => a=6, b=3

[acoustic mirage]

Ok yes

[woeful pulsar]

so f continuous at 1 and f not continuous at 2 implies $a-b=3$ but $(a,b)\neq(6,3)$

[ocean seal]

Element118

[acoustic mirage]

Ok so the locus is a-b= 3 excluding b=3 ?

[woeful pulsar]

the locus is a line

excluding a point where b=3

so that solves the question

[acoustic mirage]

Ah yes

Gotcha

Thanks

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[long void]

How would I solve this

[lone heart]

@long void Has your question been resolved?

[copper delta]

looks like brute force trial and error

make a tree

see if you can eliminate some options

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@long void Has your question been resolved?

[long void]

.close

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[cunning trout]

how should I approach this question?

[coarse peak]

Start with the framework of probability:
(Chance of the event happening)/(All possible events)

What is the chance that all three double yolked eggs are picked? How many ways are there to pick three eggs?

[cunning trout]

so there are 6 ways to pick 3 eggs

[prime badge]

how come

there's 2 ways to get 4

there's no way to get 6

[cunning trout]

how did you get 4?

[prime badge]

either you say "i get 0,1,2 or 3 double yolks" or you divide 12 by 3

both are wrong, just it's some kind of reasoning

[steel olive]

P(1st egg double yolk) = 3/12 = 1/4
P(2nd egg double yolk) = 2/11
P(3rd egg double yolk) = 1/10

P(all 3 eggs have double yolks) = 1/4 x 2/11 x 1/10 = 1/220

is this right

[prime badge]

how did you get 6

[cunning trout]

wait did i type 6?

…

so what do you mean by ‘2 ways’

[cunning trout]

in here

[prime badge]

like i came up with 2 methods that will tell you there's 4 ways

to illustrate the surprise, that i couldn;t find a way that gives you 6 ways

[cunning trout]

oh

[steel olive]

isnt the number of ways to pick 3 eggs from a dozen just 12 C 3...?

[cunning trout]

so does that mean 3/12?

[prime badge]

what means what

[cunning trout]

the chance of the event / the total outcomes

[steel olive]

@prime badge can you please elaborate about what are you saying there are 4 ways to do?

[prime badge]

why

[steel olive]

i dont get what you are trying to say

there are 12 C 3 ways to pick 3 eggs from 1 dozen

[prime badge]

it's not interesting, it's interesting that they got 6, now they are saying they didn;t mean 6

so there's nothing left to discuss

only boring stuff

[cunning trout]

what

i meant that i thought i typed something else

and not 6

that’s phrased soo poorly but yeah

mm got it

.close

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[alpine sable]

Apply arctan to both sides and go from there

Alternatively you can sub y=4x

Find the solution set for tan(y)=1

And then sub x back in

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[safe tartan]

I gotquestion a which was (a-x)u(x) but couldn’t do question b. I’m not sure what to do for that questions. Thank you!

[safe tartan]

<@&286206848099549185>

Hmmm do I @ again or wait

I wait

<@&286206848099549185>

[alpine sable]

What have you tried?

Also which one are you on

[safe tartan]

i tried question a which i got the answer to

and i am currently stuck on question b

(a-x)u(x) was what V'(x) was but im not too sure how to do b

it says hence so i assume its using the previous answer but i have no idea...

[alpine sable]

I think this is incomplete

[safe tartan]

uhh

could you elaborate

[alpine sable]

What did you get for the derivative of the integral

[safe tartan]

U(t)

[alpine sable]

U(x) I believe

[safe tartan]

yeah t and x are the same thing i believe

[alpine sable]

They definitely aren't

[safe tartan]

oh

[alpine sable]

But I guess for the purposes of this problem it doesn't really matter

[safe tartan]

sorry im quite bad at this topic as i just started but from my knowledge i thought f(x) and f(t) were the same thing

[alpine sable]

That's fine, your answer checks out

I got messed up too

Anyways

[safe tartan]

yep

[alpine sable]

Ah this was trickier than I thought

I thought I had a solution but it didn't work

Sorry

You'll have to wait for someone else 🙏

[safe tartan]

no worries

[alpine sable]

I might give it another shot later

[safe tartan]

thanks for your time!

<@&286206848099549185>

PM]ㅠㅠ: I gotquestion a which was (a-x)u(x) but couldn’t do question b. I’m not sure what to do for that questions. Thank you!
Image

what the heck

.close

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[tired flame]

Hi, a question about notations and answers. I have this question:

[tired flame]

Is correct to use the following notations to answer the question in the final answer?

(the equation is already solved, this just a question about the answer and how to formulate it using notations)

[vague coral]

no

[tired flame]

Ok, how should one do it then?

[vague coral]

you can write it as a set

for example : $S = {y = x^k \lvert x²y'' - 2y = 0, k \in {-1, 2}}$

[tired flame]

?

[ocean seal]

Herels

[rocky atlas]

Why there a need to write S seperately, can't y be the set itself?

[vague coral]

its good, but it should be better to say which equations they are solutions to

[vague coral]

wdym ?

[rocky atlas]

$$y={x^{k}|k \in {{-1,-2}}}$$

[vague coral]

y is a function, not a set

[rocky atlas]

Ohh

[tired flame]

Is this what you mean?

[ocean seal]

Calamity

[vague coral]

kinda, but without using english words lol

[tired flame]

2 sec, let me try again

Is that correct?

[vague coral]

write the equation before the conditions on k

[tired flame]

?

[rocky atlas]

Cant you write (x,y), $S = {(x,y) | y = x^k, x²y'' - 2y = 0, k \in {-1, 2}}$

[vague coral]

no

the solution to a differential equation is a function, not a couple

no

[ocean seal]

Calamity

[tired flame]

Did it look like you wanted it now?

[vague coral]

yea that looks ok now

[tired flame]

Alright cool, thanks!

[rocky atlas]

Because function is a set of relation with some conditions

So (x,y) can also be written

[vague coral]

if you want to translate it you can say : S is the set of all y = x^k such that x²y'' -2 y = 0, with k = -1 or k =2

[vague coral]

if you want, but we dont really care about x, unless they want to add the domain of y

[rocky atlas]

That's also one way of writting a function as set I guess

[tired flame]

Alright thanks guys!

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[alpine sable]

nvm

.close

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[alpine sable]

How do I come up with a solution like this?

[alpine sable]

How do I gather the intuition required?

[subtle birch]

That comes with practice

Do not mug up the formulas, instead try to understand and visualise what they mean

Especially ones that you can derive

[alpine sable]

yea i've been trying to work on that recently

but i get confused sometimes

thank you so much

.close

[lone heart]

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[strange fractal]

can help me

[strange fractal]

is it a trick questiont

too hard

[subtle birch]

All these lengths are equal to 60

@strange fractal

[strange fractal]

yeah

the answer is 23.4 metres but i keep getting

20.4

u try it ITS IMOPOSSIBLE

[subtle birch]

The answer is 23.4 only

[strange fractal]

what

can u explain to me how u got it

[subtle birch]

Hint- Try to break the shape into rectangle and few lines

Separate all lengths

[strange fractal]

wdym

now i got

[strange fractal]

33.0 m

[subtle birch]

No

[strange fractal]

so for the ones in the middle

i got 3m

[subtle birch]

Better send your work

[strange fractal]

and then for the whole rectangle i got 10.8 m

oh im not doing it on paper im doing animal farm essay

so now all i need is the lines

and then for the long lines i got 9.6m

[subtle birch]

Break the figure as I've shown (or any way that seems easy to you)

[strange fractal]

oh

[subtle birch]

Wait that is correct

3+9.6+10.8=23.4

[strange fractal]

ok thx

.close

[lone heart]

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[strange fractal]

.reopen

[lone heart]

✅

[strange fractal]

why cant i do like

240 x 6 + (60 x 5 ) + (60 x 5 x 2)

?

oh..

its right

.close

[lone heart]

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[static stirrup]

Confused

[lone heart]

@static stirrup Has your question been resolved?

[frozen tiger]

get the vector components of the 3 miles 20 degrees north of west

[static stirrup]

Vector components?

[frozen tiger]

vectors can be three dimensional but this is 2 dimensional so there's only x and y

[static stirrup]

So how would I approach it?

[bitter marten]

vectors can be represented as a combination of vectors in multiple directions. For example, when you walk 3 mile 20 degrees north of west, you travel some distance x west and some distance y north

Vector 'components' are usually referring to the horizontal and vertical directions, usually denoted by x and y

[lone heart]

@static stirrup Has your question been resolved?

[static stirrup]

So how would i find say x amount of miles west?

[bitter marten]

draw a triangle of the 3 mile part of the journey

the hypotenuse will be the 3 miles

[static stirrup]

But i already have the bottom side which is 2, and by the pyth theorem i get sqrt 5 for the last side

[bitter marten]

the 3 mile line goes past the 2 mile line

so the bottom side is not 2

all you have at this stage is the length of the hypotenuse and one angle, what else can you get from this information?

[lone heart]

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[quaint pine]

Hey, I am trying to calculate how much I need to get in the final exam to get my desired grade.

Midterm is worth 10% and I got 72/100

Coursework is worth 20% of the final grade and I got 68.8/100

Final exam is worth 70%, how much do I have to get in order to achieve 80% overall grade?

[tender gale]

85%

[quaint pine]

How much do I need to get out of the final exam which is 70%?

To achieve an overall grade of 80%

[tender gale]

if it is out of 100 then you need 85 marks

[quaint pine]

Can you show how you got to this number

[tender gale]

(0.1 * 72)+(0.2 * 68.8)+(0.7 * x)=80
x=85

well, 85 is the lowest mark which gives you an overall of 80+

[acoustic beacon]

If you wanna calculate it using a calculator, this also works.

[tender gale]

👍

[quaint pine]

Thanks a lot guys

.close

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[tender gale]

no worries, best of luck

[lone heart]

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[vapid steppe]

in interval notation shouldn’t you say x>0 as $(0,\lim_{n\to \infty}{n})$

[ocean seal]

Jash

[vale wigeon]

define "should"

[vapid steppe]

since you can’t actually get to the number ∞

[vale wigeon]

do you think that the notation $(0, +\infty)$ is illegal as a notation

[ocean seal]

Ann

[vapid steppe]

yea

[vale wigeon]

it is not

you can simply have (a, +∞) and (-∞, a) be special cases in the definition of interval notation

from a formal standpoint

you can also construct an object known as the extended real number line, which is the real number line with the two infinities (-∞ and +∞) added in, and with their relationships to other points explicitly defined (and some explicitly left undefined like 0 * (+∞) )

so in fact there is no illegality to speak of

[vapid steppe]

oh

[vale wigeon]

despite the presence of the scary infinity symbol

[vapid steppe]

ok ty

.close

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[ocean seal]

Ganymede

[lone heart]

@grizzled garden Has your question been resolved?

[lone heart]

@grizzled garden Has your question been resolved?

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@grizzled garden Has your question been resolved?

[lone heart]

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[coral cosmos]

you'll have to find all the values of theta for which sin theta = -1/2

you can use graphs, or general equation of sin function

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[surreal meteor]

How would you determine a vector (that cannot be the zero vector) that belongs to both the kernel of T and range of T?

[lone heart]

Please don't occupy multiple help channels.

[surreal meteor]

"Let's denote the linear transformation T as a matrix A. The kernel of T, denoted ker(T) or nullspace of A, consists of all vectors x such that Ax = 0. The range of T, denoted ran(T) or image of A, consists of all vectors y such that there exists x satisfying Ax = y.

To find a vector x that belongs to both ker(T) and ran(T), we can choose a non-zero vector from the nullspace of A. Since the nullspace contains all vectors x satisfying Ax = 0, we can pick any non-zero vector from the nullspace to satisfy the conditions."
Can't I just pick any vector?
(1, 1, 1) and then do gauss elimination using the (k_1, k_2, v) (so a matrix of the base vectors in ´ker T and then after show for in ran T as well using (r_1, r_2, v)
to show that the vector does indeed span out

[lone heart]

@surreal meteor Has your question been resolved?

[surreal meteor]

Nope 😢

[gusty gorge]

Maybe finding where A^2x = 0, but Ax is not 0

To find a vector x that belongs to both ker(T) and ran(T), we can choose a non-zero vector from the nullspace of A. Since the nullspace contains all vectors x satisfying Ax = 0, we can pick any non-zero vector from the nullspace to satisfy the conditions
this doesn't seem true

[lone heart]

@surreal meteor Has your question been resolved?

[lone heart]

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[rain trench]

Hey, can someone help me with the ones that are highlighted 💀💀

[rain trench]

Last did this in grade 8 and I don’t remember much I struggled with these things 💀💀💀

Hey can you help me?

[west pasture]

Take a look at this and see how many you can do

[rain trench]

Grade 10 and ma’am gave this too us to do but I don’t remember anything

I hated this in grade 8

Nah it’s geometry idk what E math is lol

I’m South African 😭😭

[west pasture]

To receive help please find an available help channel and post your question there

Do you see the section in discord that says Math Help (Available)?

Great. So send your question in one of the channels that is named "help-<number>" and that channel will be yours

[rain trench]

.close

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[proven robin]

can I put two different integrals both with respect to x in one equation or do i have to integrate with respect to x, and then with respect to y?

[proven robin]

like this for example

[limpid turret]

show the original problem please

[proven robin]

what?

this is not a problem its for me

i want to create a scary looking problem with an answer of pi

and I have 2 integrals in there

so I am asking

[alpine nacelle]

with respect to x, then y

you can't just take the product

[proven robin]

so this is not correct?

[alpine nacelle]

it is correct, you just renamed y as x, it doesn't change anything, what you can't do is assuming it's the same x and mashing it together

[proven robin]

is it ok to write it like in the picture?

[alpine nacelle]

if what your notation means is calculate both integral and then take the product, yes

[proven robin]

alright thx!

.close

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[hardy lodge]

I got this problem in a past exam and I don’t know how to solve it, it has been bugging me. I’m asking here since I am worried I may make this mistake in the future.

The problem is to prove that 4x^2 - 10.(something)x^3 is the volume for the four conjoined square based rectangular prisms of base x^2, height y, and has some relation to 10 units^(something else).

[hardy lodge]

Here I tried to prove what structure the volume might take if I had a volume I then removed a cube from or remove something from a cube.

.
The other solution I tried was the obvious one, 4X^2 x Y, but that didn’t mesh with the result, and plugging in an algebraic twisting of a formula back into itself should lead to nothing new.

On the left in this image I show why I’m confused about the line being volume, scaffolding, or surface area.

.
I didn’t perfectly remember the question, which is why there are the two areas of uncertainty.

[lone heart]

@hardy lodge Has your question been resolved?

[lone heart]

@hardy lodge Has your question been resolved?

[lone heart]

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[lone heart]

@alpine sable Has your question been resolved?

[remote heron]

one way to try it might be like

okay consider proposal 10

it has a sum of 236 and a median of 4.0

so the average rating is 236/50 = 4.72

it has a median of 4.0, so half are at most 4.0, and half are at least 4.0

say that all the ratings are 4.0

then the average rating would be 4.0 and you couldnt reach 4.72

so some have to be higher

if you do proposal 1, lets see

the average is 164/50 = 3.28

median rating is 3

so some must be 4

but we cant be certain any are higher than 4

i dont think thats accurate

half of the scores will be at least the median

and half will be at most the median

using the deduction i talked about like with proposal 10 or 1

lets say

i write these in order:

from least to greatest

1 2 2 3 ?

whats the median

okay

say i tell you the mean is 2.6

can ? be 4?

could it be 3?

dont directly calculate it, just think about it

the question mark number

[real wadi]

yes

[remote heron]

lets give you some numbers that arent in order

1 ? 4 2 3

the median is 3 and the mean is 2.8

can ? be 5

dont directly calculate it

@real wadi why are you answering

no offense

[real wadi]

we can use the graduated axis?

[remote heron]

the point is how much values can drag around the mean

its no because a 5 would leave the distribution balanced

the mean is below the median

so lower numbers have to dominate

idk im just trying to give some sense of what is happening in the problem

you can just follow the example of 1 and 10 though

so some of these distributions are gonna be skewed enough to make a statement

lemme see if i can make pictures

yea im not sure off the top of my head how to do this, sorry

the pictures i mean

but follow the example of 10 and 1

because its possible that 4s could drag it up that much

but if the median is 4 and the mean is 4.6

there is no way for 4's to drag the mean up that high

so in case 8

median is 2, sum is 95

so mean is 1.9

i mean the numbers could be 7

all you can say is that its not necessary for some of the ratings to be 5, 6 , or 7

consider 1,1,1,1,....,7

has sum 56

median 1

but still has a 7

all you are looking for is proposals that must have a 5 6 7

they all could possibly have those numbers

but only some of the must

it is not

okay

in what?

honestly, you could just look at the mean for these, i think

although the median gives some away

like if the median is 4.5 then ...

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[surreal meteor]

For any $a \in \mathbb{R}$, consider the vector $\mathbf{u}_a=(1, 1, a, -a)^T \in \mathbb{R}^4$.

[ocean seal]

SimonWin

SimonWin

[surreal meteor]

So, lemme explain what my initial thought was

[alpine sable]

what is U

[surreal meteor]

subspace

I thought I could use the basis shift matrix to calculate the coordinate

[alpine sable]

any subspace?

[surreal meteor]

And then I would get something like v=x1b1+x2b2 and then be like, and we can see this is inside the span

hence it must also belong to the subspace u since it's calculated using the basisshift matrix

[surreal meteor]

What?

[worn fox]

you have to tell us what U is

[surreal meteor]

Isn't it just a subspace of R^4?

[surreal meteor]

From here?

[worn fox]

we dont know any more than you. if you havent been told explicitly what U is then the question "show that u_a belongs to the subspace U" doesnt make any sense

[ocean seal]

SimonWin

[alpine sable]

what is b1, b2, b3?

[worn fox]

...

[alpine sable]

give us all context

[surreal meteor]

Well it's not in your language, hence why I am literally translating everything hahaha

I am not trying to cheese yall for information I promise xD

[worn fox]

always just send a picture of the question no matter the language, then translate as needed

[surreal meteor]

Okay got it, well that's all^^

So, u is the subspace that spans across the basis B, but isn't it a subspace of the vector room R^4

[alpine sable]

u_a = b1 + a b_2 - a b_3

[surreal meteor]

Ye, that's the determine the vector coordinates $[\mathbf{u}_a]_B$ and $[\mathbf{u}_a]_C$, right?

[ocean seal]

SimonWin

[surreal meteor]

Just do the linear combination

[alpine sable]

since u_a is a linear combination of B, it is inside U

what is the basis C?

[surreal meteor]

Ah, makes sense, so it actually answers two questions in one

That one I had to determine myself

So I have that one

But it's just the same as for b1 right

[alpine sable]

prolly

[surreal meteor]

u_a = c1 + a c_2 - a c_3

What's the transpose part all about?

Is that just to show it's actually a column vector and not (1, 1, a, -a) like a point

[alpine sable]

to show that its a column vector not a row vector

[lone heart]

@surreal meteor Has your question been resolved?

[surreal meteor]

Ye, makes sense

But, how would I do this, since it's a 4x1 matrix it can't be multipled with it's basis shift matrix

which is 3x3

$-2$

I was thinking something like this

[ocean seal]

SimonWin

[surreal meteor]

But that won't work since its 3x3 and 4x1

Aah, I need to find coordinates of course too

lemme try that

Perhaps, something like this

I don't know why I wrote o*() at the end I think i got confused so nvm that, but the rest could be fine right (since basis only consists of b1 b2 and b3 but subset of R^4)

[surreal meteor]

I get this on echelon form

Which is the coordinates

perhaps that is enough to say Show that $\mathbf{u}_a$ belongs to the subspace $U$, and determine the coordinate vectors $[\mathbf{u}_a]_B$ and $[\mathbf{u}_a]_C$.

[ocean seal]

SimonWin

[lone heart]

@surreal meteor Has your question been resolved?

[true sinew]

guys can you give me some tips because i have my algebra 2 final test tmr

😔

[surreal meteor]

I solved it!

great success

💪

[lone heart]

@surreal meteor Has your question been resolved?

[lone heart]

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[lone heart]

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[wet lark]

you opened two channels

💀

close one channel

@alpine sable

[alpine sable]

sorry bro

[placid zinc]

[sour dove]

lol good luck getting help talking to ppl like that

[alpine sable]

mb

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[bitter pond]

pls solve this

I

question i

[vale wigeon]

we don't do your homework for you.

[bitter pond]

QUESTION I

i dont know if my answer correct

[vale wigeon]

show your work and answer

[bitter pond]

ok

wait up

so what i did

wait

i took x = -2

0

and 2

[vale wigeon]

weh???

do you have your work on paper? this isn't making any sense to me

[bitter pond]

x -2 0 2
y -3 -2 -1 For x-2y=4

[bitter pond]

i do but i dont have a phone

im on mac

[vale wigeon]

so you made a table of values? why?

what even is your answer?

[bitter pond]

its graph answer

i am getting y -3 -2 -1

for both the equations

keeing x -2 0 2

keepin*

so

?

[vale wigeon]

i'm having trouble understanding you

[bitter pond]

. . . .

for x-2y=4 i did

x -2 0 2
y-3-2-1

for 2x-4y=8 i did

x-2 0 2
y-3-2-1

for both i got same

so i thought its wrong?

?

@vale wigeon u there?

[vale wigeon]

i'm still having trouble understanding you

[bitter pond]

bruh

i will ask someone else

[wary stream]

The way you have it typed makes it hard to understand you, so if you get someone, they're going to have a hard time too

y-3-2-1

What does that mean?

[bitter pond]

i replace em

[wary stream]

Still doesn't answer my question

[burnt thistle]

watch a yt tutorial or something

[wary stream]

What does y-3-2-1 mean?

[bitter pond]

when u solve with replacing x to -2 or. 0 or. 2 y comes that

[wary stream]

No it doesn't

[bitter pond]

?!?!?!?!

[burnt thistle]

https://www.youtube.com/watch?v=rgvysb9emcQ

[wary stream]

Why did you input 3 negative signs?

[burnt thistle]

bruhh 8th grade? :yikes:

[wary stream]

What is y-3-2-1 suppose to mean

[bitter pond]

8th grade?

look

i swap -2 = x

so

[wary stream]

Can you write it out on paper and send a picture of what you mean?

[bitter pond]

-2-2y=4

[burnt thistle]

@bitter pond just watch the tutorial dude

[bitter pond]

then -2y = 6

y=6/-2

y=-3

nothing close it

i was correct

the sir finnaly came

[burnt thistle]

...

[bitter pond]

nothing i was correct

i felt i was wrong

[burnt thistle]

nice

[bitter pond]

because answer was infinity

thats why i felt a bit

[burnt thistle]

i feel like ill forget math

[wary stream]

-2-2y=4
then -2y = 6
y=6/-2
y=-3
That made more sense than whatever this was
for x-2y=4 i did

x -2 0 2
y-3-2-1

for 2x-4y=8 i did

x-2 0 2
y-3-2-1

[burnt thistle]

adios

[bitter pond]

adios

.close

[lone heart]

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[burnt thistle]

how the fuck can that even be infinte

[bitter pond]

it can

[burnt thistle]

arent you supposed to substitute values on the RHS?

[bitter pond]

because both equation in 1 line

i asked sir

he said its infintu

so yeah

[burnt thistle]

okay

[bitter pond]

both equation in same line

cya

[burnt thistle]

ciao

[lone heart]

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[proven robin]

is there a way to solve this?

[remote heron]

what do you mean solve

[proven robin]

get to pi

[slender blaze]

we need to prove?

[proven robin]

well yes

get to pi from the right hand side

do you have any idea

[slender blaze]

it looks like a infinite series for me , because the n ranges form (1 - infinity)

Sorry man this is pretty complex for me

[proven robin]

alright

do you know anyone here who is good at this?>

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<@&286206848099549185> ....

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!15m

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[proven robin]

<@&286206848099549185>

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@proven robin Has your question been resolved?

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[full cairn]

can someone explain how it goes from the 2nd equation to the 3rd?

[full cairn]

like step by step

like how does it all become just n^2/(n+1)^2

[noble notch]

they change -2^n+1

into (-2)(-2)^n

then they just simplify

[full cairn]

oh ic, so i can just move the constant like that, then factor it out of the limit?

and for the next step they multiplied the denom and numer by 1/n^2?

[noble notch]

yes

[full cairn]

thank you

[noble notch]

they moved the n^2 down

[full cairn]

moved it down?

[noble notch]

so it became 1/(n+1)^2 *n^-2

[full cairn]

ohh

[noble notch]

like this

[full cairn]

thank you so much!

i really appreciate the visual!

[noble notch]

👍

[full cairn]

sorry to bother again but whats that 2nd to last step?

1/(1+11n)^2?

[noble notch]

just evaluate the limit

sub n=infinity

i’m just gonna type the bottom bit of the fraction

(1-1/infinity)^2

1/infinity is 0

so 1^2

[full cairn]

oh so basically its just 2 lim n infinity, 1

[noble notch]

and u get 2(1)

[noble notch]

yes

[full cairn]

thank you sm

[noble notch]

but not lim

once you’ve evaluated it

it’s not there anymore

[full cairn]

uh

so just to be clear, that 2nd to last step is just 1 + lim ^2?

in the denom

or should i just completely ignore that and focus on the constant

[noble notch]

i’m not sure what this means

but i’ll show u what i mean

[full cairn]

thank you

[full cairn]

oh i see now

thank you so much!

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[fresh bolt]

Does anyone know how to solve this:
This is a record of ECDH Key Exchange protocol Alice and Bob had using a elliptic Curve E : y^2 = x^3 +ax +b that is defined on a finite field that has p number of elements.

Round 1
A->B : (92,1101)
A<-B : (1,891)

Round 2
A->B : (1010,191)
A<-B : (76,1324)

Using this, fthe Coefficient a, b of the elliptic Curve and the p number of elements to find the value of a+b+p.

[lone heart]

@fresh bolt Has your question been resolved?

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@fresh bolt Has your question been resolved?

[woeful pulsar]

can you provide the definition of what the numbers refer to, from your notes

under round 1, round 2

[fresh bolt]

I have no other information, this was the exact question

[woeful pulsar]

do you have notes where you learn about ECDH Key Exchange

[fresh bolt]

nope, this is not a homework or something I learn in school

ok wait maybe I have some notes

but its complicated

[woeful pulsar]

does it come from a textbook where it describes what the pair (92, 1101) means

[fresh bolt]

nope, this is all the notes I have

[woeful pulsar]

hmm

okay it seems the pair (92, 1101) are (x, y) coordinates

finally understood the question

so round 1 and round 2 are different exchanges that use the same elliptic curve

is there a method simpler than complete search? that I'm not sure

though from the 4 points I would know that
p divides $92^3+92a+b-1101^2,1^3+a+b-891^2...$

[ocean seal]

Element118

[woeful pulsar]

and then we can use some euclidean algorithm stuff to try to find p from there

so p shouldn't be too hard @fresh bolt

from there probably we can solve for a and b too

[fresh bolt]

🤔

[formal snow]

how do u ask for help in this server?

do u have to tell ur question to the bot

[lone heart]

@fresh bolt Has your question been resolved?

[fresh bolt]

just ask in the available channels

[lone heart]

@fresh bolt Has your question been resolved?

[woeful pulsar]

#❓how-to-get-help

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@fresh bolt Has your question been resolved?

[lone heart]

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[winter dirge]

help not sure if im doing this right or nit

[shy dove]

you can make sure by plugging a number in the original equation, and plugging the same number in your answer, and if it gives you the same result, you'll know you did it right

to be honest, your work gets kinda cluttered, it's hard to see

[winter dirge]

can you help me out after the second step?

im confused what to do

[bold venture]

Hi

[winter dirge]

i cross out one bottom and too cos(theta)

is that the right direction

<@&286206848099549185>

[shy dove]

Sorry I went and helped someone else meanwhile. In the screenshot you sent, I don't see what's on the denominator, but if it really is cos(theta), then you'd get something like:

$\frac{cos\theta \cdot tan\theta + sin\theta}{cos\theta} \newline \frac{cos\theta (tan\theta + tan\theta)}{cos\theta}$

ah no oops

[ocean seal]

imTyp0

[shy dove]

and yes 2tan(theta) is right

(@winter dirge)

[winter dirge]

thank you

wait

i broke down tantheta

for sin over cos

if i do that

$frac{cos\theta (tan\theta + tan\theta)}{cos\theta}$

[ocean seal]

steph1235

[winter dirge]

no idea how to use that

[shy dove]

it's \frac

[winter dirge]

ah

$frac{cos\theta (sin\theta\cos\theta + sin\theta)}{cos\theta}$

[ocean seal]

steph1235

[winter dirge]

fuck

i sub the middle tan for sinovercos theta

and then im not sure what to do

i cancel out

to elimate denomitao

[shy dove]

$\frac{cos\theta (\frac{sin\theta}{cos\theta} + sin\theta)}{cos\theta}$

[ocean seal]

imTyp0

[shy dove]

you did this?

even if you did, you should be able to find the solution, just put everything on same denominator and reduce. But you don't need to

[lone heart]

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[lone heart]

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[lapis parcel]

does anyone know how to do this

I assume its sin(pi/2 - 4/9)

but idk how to simplify it

[alpine sable]

No it's not

[
\map \cos \theta = \f 49 \textss{not} \theta = \f 49
]

[lapis parcel]

oh

[alpine sable]

Anyways I can just dump the identity in your face, but that wouldn't make you understand why

So how about you whip out a paper and draw a graph

And draw an acute angle in the first quadrant

[lapis parcel]

aghhh my pencil wont sharpen

one sec

[alpine sable]

Okay sure

Draw the unit circle too

[alpine sable]

yep now highlight theta for the angle

And also to write the adjacent and opposite in terms of theta

[lapis parcel]

this is cos right?

[alpine sable]

Which one

[lapis parcel]

what were drawign now

the triangle

the adjacent would be 4

hyp 9

theta is 63.6

.close

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