help-23

[lusty pendant]

because there's a right angle marking there

[pale lily]

that is in 2 different triangles

[lusty pendant]

correct

so it's not 90

[pale lily]

correct

so if a triangle adds up

to 180

and u already have

2 of the 3 angles

what is 2

equal to

[lusty pendant]

110

[pale lily]

what are

the 2 angles

we already know

[lusty pendant]

60 and 30

[pale lily]

no

bruh

[lusty pendant]

for RWS?

[pale lily]

for triangle RWS

[lusty pendant]

oh

[pale lily]

yea

[lusty pendant]

30 and 90

ohhhhh

so angle 2 is 90 also

90 and 30 is 110

wait no

[pale lily]

what is 90 plus 30

[lusty pendant]

120

mb i made a lil mistake

[pale lily]

ok so

what do the angles of a triangle

add up to

[lusty pendant]

bro that's 230????

this isn't making sense

[pale lily]

brio

[pale lily]

listen

are u here

rn

[lusty pendant]

yea

[pale lily]

i want u to watch me type

ok

im about

to

blow your mind

[lusty pendant]

okay

lets hear it

[pale lily]

RWS interior angles add up to 180 cause ALL triangles add up to 180 on the inside

right

[lusty pendant]

right

[pale lily]

and we already know 2 out of the 3 angles

in the inside

are 90 and 30

which is 120 together

right

[lusty pendant]

right

[pale lily]

so whats 180-120

[lusty pendant]

60

OHH SHII

[pale lily]

so whats 2 equal

[lusty pendant]

60

[pale lily]

good

and

what does the

little red thign mean

in the corner

of triangles

[lusty pendant]

right angle

which is 90 deg

[pale lily]

so if you know right angle means 90 and you know that 2 equals 60

what does 1 equal

[lusty pendant]

30

[pale lily]

🤯

u did it

[lusty pendant]

ty ty

don't close this channel yet i'm still writing stuff

[pale lily]

did u do the other t riangle problems

there

[lusty pendant]

no..

i fear those are gonna be like hell

[pale lily]

solve 2 rn

if u dont solve 2 rn

im done helping u

u can do it

i gurantee it

[lusty pendant]

alright

i'll lyk

question rq

do linear pairs play a part in question 2?

[pale lily]

idk what that exactly means

i know geometry

but

i dont know the proper things the things u do are called

[lusty pendant]

okay

so

i got

angle 1 is 66, angle 2 is 50? (not so sure fr) and angle 3 is 122

bro this is not riight

[pale lily]

why do u think

1 is 66

[lusty pendant]

because following the linear pair ruke

rule

[pale lily]

bro

did you forgety

what i just taught u

what does the inside of a triangle add up to

[pale lily]

u have 2 of 3 angles

[lusty pendant]

so 66 plus 58

is 124

180 - 124?

is 56

[pale lily]

you tell me

[lusty pendant]

so is 1 56?

it has to be

because orignally that all added up to 190 at first

ty

[pale lily]

yes

[lusty pendant]

okay so

do i use those orrr

to find angle 2

@pale lily

<@&286206848099549185>

[pale lily]

theres a rule

u can do

to uh

[lusty pendant]

abt time

[pale lily]

if u have 1

u know what 3 is already

[lusty pendant]

yea

[pale lily]

atleast im p sure

so did u get it

[lusty pendant]

that's the linear rule i was telling you abt

[pale lily]

i know

[lusty pendant]

but i'm struggling w angle 2

not 1 or 3

1 is 139

wait no

[pale lily]

they are the same

both sides

[lusty pendant]

what?

[pale lily]

isnt thatl ike the first rule u learn

in geometry

opposite angles like that are equal

[lusty pendant]

oh

1 and 80

hy

[pale lily]

what

1 and 80

no

[lusty pendant]

yes

you're right

[pale lily]

do u see

where i put

[lusty pendant]

1 is 80?

[pale lily]

the number 3

[lusty pendant]

yeah

[pale lily]

that angle

where the red 3 is

[lusty pendant]

oh that's called the vertical rule

yeahh

[pale lily]

equals

the blakc 3

and u can solve 2 from there

[lusty pendant]

thanks again

[lusty pendant]

okay so i got 109 for angle 1

where do i go frrom here, there's no way to tell angle 3

oh nvm 3 is 35

is it?

it's been 10 mins.

@pale lily

i need u.

back.

now.

[pale lily]

im not gonna

repeat

what ive already told u twice

figure ito ut

[safe radish]

@lusty pendant Has your question been resolved?

[safe radish]

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[onyx narwhal]

Could one of you lovely individuals tell me where I went wrong with this guy

[onyx narwhal]

I’m not sure where I should be getting the 19/4 from instead of 3/4

[prisma wren]

first step, you shift but forget to adjust the s in the numerator

[onyx narwhal]

Could you remind me how I do that

[prisma wren]

how did you go from the first line to the second

[onyx narwhal]

Replace with s-2?

[prisma wren]

close

you substitute in s' = s-2, (where s' is your new s). Therefore s = s'+2

[onyx narwhal]

I just remembered something about pulling out a number and replacing it with e^at, tbh I was freestyling on that line

Oh that’s cool I like that lemme give that a shot and make sure I’m doing it right

[prisma wren]

the translation thrm just states that you can apply the substitution s' = (s-a) if you multiply by e^(at). Just like a u sub in an integral, you have to turn all previous s terms into terms of s'.

[onyx narwhal]

Thank you very much 🙏🙏

I’ll touch up on translation theorem

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[echo cloak]

Need help please

[vagrant ice]

the inner product is just the dot product

ah but for part a you don't need the dot product at all

I mean you could dot B with the vector C = (1, 0)

and use $B \cdot C = |B| | C| \cos \theta$

[flat frigate]

south

[echo cloak]

where is vector c?

[vagrant ice]

it's the vector (1, 0)

so the unit vector on the x-axis

[echo cloak]

i did thetaB = tan-1(y/x) then subtracted that from 180 degrees and got 116.6 degrees, is that right?

i found the magnitude already just having trouble with the direction

[vagrant ice]

yeah that's correct

,w arctan 2 in degrees

[flat frigate]

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[vagrant ice]

,calc 180 - 63.43

[flat frigate]

Result:

116.57

[echo cloak]

oh great, took me a minute to figure it out, thanks for help!

[vagrant ice]

no worries!

[echo cloak]

.close

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[granite igloo]

I know the process and how to do the problem, I just made a mistake along the way somewhere and can't find it

[granite igloo]

???????

Woops nevermind

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[lean otter]

?

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[limber atlas]

would 0.690 not be the only answer?

[distant monolith]

It said 3 decimal place you did 4

[limber atlas]

oh well

[distant monolith]

Nah there will be 2 values

[limber atlas]

how tho 😭

cause like

[empty gyro]

There would be another

[distant monolith]

One in 1st quard and 2nd in 2nd quad

[empty gyro]

,w plot sin x

[flat frigate]

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[limber atlas]

it cant be negative right

[distant monolith]

Math

[limber atlas]

oh 😭

[distant monolith]

Hehe

[distant monolith]

Btw

The 2nd answe will be just

Pi-1st answer

No need to calculate the 2nd any other complex way

[limber atlas]

hmm

2.168?/

im confused why tho

ohh

[distant monolith]

See the graph

[distant monolith]

Draw a horizontal line in your domain

It will cut at 2 different x value

If you asking how I got the 2nd answe is pi-1st answer

[limber atlas]

huhh

[distant monolith]

2.451

[limber atlas]

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[distant monolith]

Solved?

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[remote lintel]

i need help understanding Which of the following is an equation of the line that
passes through the point (0, 0) and is perpendicular to
the line shown above? this question, i have a pic of the graph

[willow frigate]

A

[remote lintel]

ah ok, its review for a placement test and i dont really understand whats going on so what is the question actually asking and how do i find it

[distant monolith]

Ok so

First find the slope of the line given

And then it will be just y=mx

C = 0 because it passes through 0

[remote lintel]

how do i find the slope and what is c?

[willow frigate]

first. the answer is A or C.

line is throw 1.4and 3.4 part.

so m > 0

[remote lintel]

how am i supposed to calculate for m?

[willow frigate]

if u wanna calculate m, u 'll know the first line's equation.

[remote lintel]

you cant calculate it off the 2 cords?

[willow frigate]

first line's equation y = mx + b

the answer is y = -1/mx + c

[remote lintel]

huh? if i wanna find out the line on the graphs slope

i dont really understand how im supposted to find the first lines slope

[vapid folio]

You wanna start this problem by finding the black line's slope. Use the 2 black dots to help you. From the first one, count how many units it goes down and how many it goes right. It should be 4 down and 5 right.

The slope is rise/run, meaning the change in y over the change in x. Therefore, the slope is 4/5. BUT WAIT, the slope is negative, since the line is going downwards and it goes down 4 units. So the slope is actually -4/5

We want to find the equation of a line that is perpendicular to this line but passes through (0,0). If it passes through (0,0), then it's in a simple form y=mx since there is no vertical translation. The slope of this line, or m, will be perpendicular to the black line

To find a perpendicular slope, you have to take the negative reciprocal, so the slope would be 5/4 (-4/5 's reciprocal is -5/4, and then negate it so 5/4).

Therefore, the answer is y=(5/4)x, so A

[remote lintel]

dang ok i gotta figure how to remember all that TT

[vapid folio]

Just remember the general steps

1. Find slope of line
2. Determine if there's a y-intercept for the new line
3. Determine the slope of the new line (negative reciprocal)

Finding slope is ez, just count the units moved between 2 dots

You determine y-intercept based on what point the line passes through

and the slope of the perpendicular line is the negative reciprocal of the OG line's slope

[remote lintel]

i wish i was allowed notes on the test

[vapid folio]

that wouldve been nice

[remote lintel]

cause i gotta test into precalc

this is the next question on the practice exam

[vapid folio]

this is for precalc????

dang very different cirriculums

[remote lintel]

no its to skip from algebra to precalc

[vapid folio]

oh

[vapid folio]

Ok on a rectangular prism, there's 6 sides

However, there are 3 sides that have an equivalent side

So we wanna find the sum of the area of those 3 faces

[vapid folio]

In the diagram, the 3 faces are the one that's pretty much shown to you

[topaz tree]

see this diagram

[vapid folio]

So you do 3x9 for the area of the front one, 4x9 for the area of the top one, and 4x3 for the area of the right one

[vapid folio]

or this sure

[vapid folio]

Then add them up, so 27+36+12=75

And since there's another 3 sides that's equivalent, just multiply by 2 so the surface area of the rect prism is 150

[remote lintel]

i dont do 3x9x4?

[vapid folio]

Nope that's the volume

[remote lintel]

how am i supposed to remember that equation TT

[vapid folio]

Well

Just remember this

um

if you label the sides a b and c

then its ab + ac + bc

then times 2

[vapid folio]

All you're doing is multiply each side by each side once

[remote lintel]

oh ok

i kinda get it

for this one dont i make the weird square for polynomials?

[safe radish]

@remote lintel Has your question been resolved?

[safe radish]

@remote lintel Has your question been resolved?

[willow frigate]

B

[safe radish]

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[obsidian briar]

should i /2 then -4

[vast sluice]

No

-4 and then divide by 2

Then take inverse sin

[peak estuary]

you can divide by 2 first

but then the 4 also gets divided

dont forget that

[vast sluice]

So you can do both but its easier to do the simpler operations first

[distant monolith]

Do what's easy for you

Dividing first will yeild a fraction here

Its always better to avoid fractions

Till you reach the last step

But if this was 2sinx+4 = 4

Dividing 2 is better because it yeilds into a simpler equation

For this the diff isn't that big

[peak estuary]

always often

[distant monolith]

But for a equation like

7x+ 49= 144

[distant monolith]

Nah it's always

Better

Fractions just increase the complexity+ the time

[distant monolith]

Show me where you prefer fractions instead of intgers

[peak estuary]

I dont have a specific example in mind but I know that there are some

[distant monolith]

Hm never encountered them

[peak estuary]

fractions arent evil. they make numbers smaller which is also a benefit

say x+1/3=2 vs the same thing multiplied by 192

[distant monolith]

Eh ?? Just simplify it as 3x+1= 6

[distant monolith]

• you aren't gonna spot that simplification easily

[obsidian briar]

is x = 7pi/6 and 11pi/6 in radians

[distant monolith]

Eh

Why 2 answers ?

Only one or a general answer

[distant monolith]

Both are wrong tbh

Particular solution of sinx

Lies between -pi/2 to pi/2

You should get that particular solution if it isn't specified

[junior smelt]

(Worth checking whether there’s a restriction first, and what OP’s conventions are)

[distant monolith]

Hm maybe but he didn't send any

The conventions are the same everywhere no?

Then why we got convention 💀

[junior smelt]

If only everyone ever agreed on stuff and kept it consistent

[obsidian briar]

huh? doesn't sin(7pi/6) = -1/2

[distant monolith]

Ngl those who don't follow gerenal conventions have some issues

Cough cough America cough cough

[distant monolith]

Yeah buts its out of the particular solution range for sinx

[distant monolith]

There is inf solution for sinx here

Get general solution or particular solution as specified by your teacher or question

If nothing specified

Just get both fr

[obsidian briar]

nothing is specified

[distant monolith]

Time to get both

And hit the teacher with the answer

[obsidian briar]

??? how do you get the solution range

[distant monolith]

Its given usually

Or its -pi/2 to pi/2

For sinx

[obsidian briar]

so is my answer right if nothing is specified

[distant monolith]

No its wrong

[distant monolith]

Get the answer in the range -pi/2 to pi/2

4th quad for negative

1 quad for positive

[obsidian briar]

then it's 11pi/6

[distant monolith]

.

[distant monolith]

How

11pil6

11/6

Is like (1+5/6)*pi

We need it to be less than 1/2

5/6 is greater than 1/2

[obsidian briar]

alright -pi/6

[distant monolith]

Yep

[obsidian briar]

Thanks.

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[opaque fern]

How does one "define" addition as a map between rationals? Does the below definition suffice?

\medskip
Fractions are equivalence classes of ordered pairs of integers $(a,b)$, where $b\neq 0$ . Addition of fractions is thus defined by [
\frac ab + \frac cd = \frac{ad + bd}{bd}
]

[flat frigate]

Aero

[peak estuary]

thats fine

you would need to prove well-definedness

[opaque fern]

So prove the following: [
\text{if }\frac ab = \frac{a'}{b'}, , \frac cd = \frac{c'}{d'},\quad \frac ab + \frac cd = \frac{a'}{b'} + \frac{c'}{d'}
]
Is that correct?

[peak estuary]

yes

[flat frigate]

Aero

[opaque fern]

okay I see

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[charred hare]

Is there an answer to item 12 of the rectangle and item 11 of the kite?

[valid bobcat]

it left out the angle for q12

probably adb

[marsh gust]

item12' s answer is 7x-58=2x+22.

[safe radish]

@charred hare Has your question been resolved?

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[jaunty finch]

hello. i have to find its limit using the criterion of the pincers. i want now to rewrite a_n

[jaunty finch]

no sorry

i want sto write b_n

b_n<=a_n<=c_n

so i change 1,2 .... n to n,n...n

and then i get b_n

=1/rad(n+n) + 1/rad(n+n) + ... +1/rad(n+n)

and that is n/rad(2n)

i wanted to change the power of 2n by doing this:

rad(2n)= 2n^1/2= 2n(2n^(1/2) /2n)

2n^(1/2) /2n i would say this limit goes to 0

i want to know if thats correct

rad is square root sorry

i figured it out guys

.close

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[fathom adder]

Meh

[brave wolf]

?

[wild copper]

And what is the question?

[broken isle]

Do you know how to solve it?

[fathom adder]

Its binary

[rigid inlet]

Solve what

[wild copper]

That's not an equation to be solved.

[brave wolf]

its already solved

[fathom adder]

Go from base 2 to base 10 and add it

Nothig to be confused

[brave wolf]

❓

whyy

[broken isle]

[fathom adder]

Top is 7

[brave wolf]

adding in binary is much simpler

[fathom adder]

Bot is 10

[fathom adder]

Sure

Anyway

[kind tinsel]

it’s already a solved question. you would have to ask something else about the image in order for there to be anything to solve

[safe radish]

@broken isle Has your question been resolved?

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[frank lodge]

Hi I'm in pre calculus and have a simple question that I'm having a hard time with an can't find any information on?

I need to find the Slant Asymptote of the attached problem. I can find the Horizontal and Vertical asymptotes just fine but I can't figure out Slant?

I am aware that it involves long division but I wasn't sure how you would perform that long division for this problem (I'm not very smart sorry haha)

[frank lodge]

With the variables I wasn't sure how you'd go about simplifying before dividing- or if you simplify at first at all?

I'm very visual if I was shown I could figure it out from there but everything online has the denominator as something simple like x^1 or 2 ;w;

My friends please save me from this hell

[deep lily]

not sure what the difficulty in just forcing long division is

Now is it obvious that the slant asymptote is just y=x+1

[frank lodge]

I SEE THANK YOU I DIDNT know if you did break up the top first in simplify? But it seems that you do not thank you thank you

The whole denominator only fits in the numerator once... I understand

[pure bolt]

For long division , you do not simplify first before dividing

You can immediately do long division for that problem 🫶🏼

[frank lodge]

OKAY i was confused about the x^3 -x^2 how that would all fit into x^-16
But it seems you're going to have an x remainder whatever you do? The x^2 just scared me lolol

.close

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[hazy pollen]

Does anyone have a python code to solve the continuous-time algebraic Riccati equation given a state space representation of a system

[austere cypress]

scipy probably has

[hazy pollen]

It has the general Riccatti equation solver but I need one for a Kalman filter problem. It's a slightly different equation

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@hazy pollen Has your question been resolved?

[hazy pollen]

.close

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[coral dagger]

I can't understand this for da life of me. How and why are we doing x^2 + x^2 = 1??

[open junco]

Line y=x and circle equation is x^2+y^2=1

[open junco]

Look

[coral dagger]

I understand this so far

[open junco]

The substitute x=y in the circle equation

[coral dagger]

Okay

Okay

So

Why does that

Specifically help us find t = pi/4

[open junco]

Draw a straight line vertically from the point of intersection to the x axis

The distance from origin to that point will be 1/ root2

[coral dagger]

With any point?

[open junco]

The point where line and circle meets

There a simpler way to understand the angle tho

[coral dagger]

Like dis ?

Blue being a point

[coral dagger]

Lmk please

[open junco]

Drawhat

[open junco]

What

Ok the entire circle has angle 2pi
Then you cut it into 4 equal quarters making each pi/2
Then you cut it by half making it pi/4

[coral dagger]

I understand this

[open junco]

Ok

[coral dagger]

Now what lol

I'm just confused on how we got the point coordinates from the terminal point

I understand we substitue x^2 into y^2 because x=y due to symmetry, but what this tells me is that every point on the unit circle is equal to this

[open junco]

Becausevyhe line and circle are intersecting

[coral dagger]

But I guess we differ it in different quadrants

Am I right?

[open junco]

X=y is a unique line making angle pi/4 with x axis

[coral dagger]

Sorry I don't understand man

Like why are these different then?

Like how would I find pi/6 for example

[open junco]

The first point is on the x axis

Last on the y axis

[coral dagger]

I understand this

[open junco]

Pi/4 on x=y

[coral dagger]

Oh okay, so it's unique to pi/4?

I see

[open junco]

Yes

[coral dagger]

Pi/6 and pi/3 how

[open junco]

Do you know trignometry

[coral dagger]

This is the first chapter

[open junco]

Ok imagine cutting the quarter In to three pieces

Pi/6 includes only the first piece

[coral dagger]

So can I find pi/4 then divide in half?

[open junco]

No
I'm sorry I can't really explain it don't get more confused

[coral dagger]

I see

You helped me though, ty bro ❤️

.solved

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[coral dagger]

Do we only subtract from 2pi if the terminal angle is in the 4th quadrant or greater?

[open junco]

We love to minimize thr no

[coral dagger]

I don't understand wym

[primal parcel]

Wdym by the terminal angle?

[coral dagger]

Terminal point**

[primal parcel]

?

You mean

0 degrees?

[open junco]

Shortest angle from the point to the x axis

[coral dagger]

Nah like dis

[primal parcel]

Ahh

K

Got it

[coral dagger]

Was my terminology incorrect?

[primal parcel]

No

New terminology for me

[primal parcel]

That is correct

But only for the 4 the quad

[coral dagger]

Only for 4th quadrant yeah?

[primal parcel]

1 sec

[coral dagger]

N trynna minimize if the terminal point is greater than 2pi

[primal parcel]

Lemme draw a diagram for u

[coral dagger]

ty

[primal parcel]

,rotate

[primal parcel]

This is one way

And the other

[coral dagger]

Yeah true, I'm not on actual angles yet though I'm building my way up but that still helps I see what you did there

tyty

.solved

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[primal parcel]

@coral dagger

,rotate

[primal parcel]

Hope I didn’t confuse you

[coral dagger]

It makes sense, it actually helps ty

[primal parcel]

Np

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[tropic charm]

How do I do part C for this question? I’m kinda confused about it

[tropic charm]

(Ignore the bad parabolas)

[primal parcel]

I’d suggest you to find the cores images for where the width is 4 mm

Coordinate

Then find the turning point of the graph

And then, compare the y values for get part .c

@tropic charm

[tropic charm]

im just confused about what the x and y represent here

like which one is the width

[primal parcel]

Width is on the x axis

The y axis is the length

[tropic charm]

wait how do u get that?

[primal parcel]

??

[tropic charm]

like how do u know

[primal parcel]

It’s it obvious?

U know shapes?

As in 3d ones

[tropic charm]

yeah

[primal parcel]

Let’s use a cuboid

We have the length from front to back

Width from left to right

And height from top to botttom

Right?

[tropic charm]

yeah

[primal parcel]

Isn’t that how you would name it?

[tropic charm]

wait so is my part c correct?

[primal parcel]

Would you name the top to bottom as width?

[primal parcel]

No

It won’t be 0

[tropic charm]

if you were to flip the cuboid it would be names width

[primal parcel]

But would you really?

[primal parcel]

Think again

Or to be precise,

[tropic charm]

if x axis is width wouldnt x=4 then y=0

[primal parcel]

Look at the graph

“How long is the tip of the pen?” Asking for the length of the pen from the 4mm width point to the tip of the pen

What’s the answer? @tropic charm

[tropic charm]

would it be 4

[primal parcel]

Correct

And you’ve done .c

Assuming you have the correct turning point

Do you know how to find the tp?

[tropic charm]

wait so x is width of cross section and y is length of cross section

[primal parcel]

Yea

Idk if the graph, tp is correct as I haven’t looked at it properly

[tropic charm]

the vertex are correct

[primal parcel]

So complete the square to get the tp

[tropic charm]

i checked them

[primal parcel]

Ok

Then your answer should be correct

[tropic charm]

wait but why is the vertex the tip of the pen?

[primal parcel]

Are you telling me that the tip of your pen is flat?

[tropic charm]

wdym by that?

[primal parcel]

Is your pen like this or this?

[tropic charm]

what is this:?

[primal parcel]

This

Left or right?

[tropic charm]

right

[primal parcel]

There you go

The pointy bit is the vertex

[tropic charm]

but its at 2,-4 and if y is length how is it -4 in distance?

[primal parcel]

It’s not

It’s 4

You can’t have negative distance

Or length

Or mass

It is only our perspective that makes it negative

So it is 4

@tropic charm getting confused?

[tropic charm]

a bit yeah

[primal parcel]

Ok

So In laymen terms

We cannot have negative; mass or length

That also applies to this question you’ve asked

So

We have to make it positive as -4 mm is not possible

By making -4 positive we get 4 or +4

Is it easier to understand?

[primal parcel]

From where the 4 mm is (the width) we measure downwards and ignore the sign. Which makes the length +4

@tropic charm

[tropic charm]

wait im thinking abt it rq

i think i get it now

thx @primal parcel

[primal parcel]

Your not confused anymore?

[primal parcel]

Np

[tropic charm]

ye

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[bitter tangle]

just question 2, how do I find the other points? I know there’s one at the origin, and at (0, -2). But how do I use 1/2a = -1 for the points on the side?

[bitter tangle]

,rccw

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@bitter tangle Has your question been resolved?

[bitter tangle]

<@&286206848099549185>

.close

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[north raven]

https://media.discordapp.net/attachments/540211747613704221/1314377853172711454/image0.jpg?ex=67538d44&is=67523bc4&hm=da5755ec74e33d56d09784c3943ba849945770287d1bfecdd50dfc69eda5020c&

[north raven]

I’m trying to mirror my prof’s steps I just don’t understand why they’re following this method

I understand how to get the coordinate matrix

they’re seeing how the transformation transforms each basis matrix and putting that together

I see how they get the image of the coordinate matrix

but idk how to use that to get the image/kernel of the transformation

I just tried getting the coordinates in the image of the basis with what I wrote beyond that

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@north raven Has your question been resolved?

[north raven]

<@&286206848099549185>

[white umbra]

Is this the solution to something? What's the question?

[safe radish]

@north raven Has your question been resolved?

[north raven]

here’s the question, my bad

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@north raven Has your question been resolved?

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[north raven]

.reopen

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✅

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@north raven Has your question been resolved?

[distant gull]

Um bro

What does non standard basis mean

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[elder cypress]

What is the easiest proof of the rms-am inequality?

[elder cypress]

I thought about using the power mean inequality but do we need the rms-am inequality itself to prove it?

[obsidian oracle]

I would have said cauchy schwarz

[desert pasture]

Cauchy Schwarz

You can prove it using LA

[obsidian oracle]

cauchy schwarz says:

if $\langle\cdot,\cdot\rangle$ is an inner product on $V$, with its associated norm $|\cdot|$, then:

$$\forall x,y\in V, |\langle x,y\rangle|\leq |x|\cdot|y|$$

[flat frigate]

rafilou is not not born in 2003

[elder cypress]

You don't need rms-am to prove that?

[obsidian oracle]

nope

[obsidian oracle]

proof of cauchy schwarz:

[elder cypress]

And what about power mean

Power mean seems more direct5

[obsidian oracle]

power mean is proved by jensen inequality on log

cauchy schwarz can be proved using the discriminant of a quadratic

[elder cypress]

Lmao
Every inequality is a special case of another inequality

[desert pasture]

For more than 2 variables?

[obsidian oracle]

wdym?

[obsidian oracle]

this is cauchy schwarz

proof is:

[elder cypress]

If there are more variables we can use Holder to prove cs

[obsidian oracle]

?

I've never heard of holder used for c-s proof

anyway proof for cauchy schwarz

if $x = 0$ then proof is trivial. Suppose $x\neq 0$, then consider the polynomial:
$$P(t) = |tx+y|^2 = t^2|x|^2+2t\langle x,y\rangle + |y|^2$$

[flat frigate]

rafilou is not not born in 2003

[obsidian oracle]

It's a quadratic, and it's always non negative. Thus the discriminant is non positive

[elder cypress]

For p, q = 2 it becomes the cs inequality

[obsidian oracle]

$(2\langle x,y\rangle)^2 - 4|x|^2|y|^2 \leq 0$

[flat frigate]

rafilou is not not born in 2003

[obsidian oracle]

it becomes cauchy schwarz FOR the natural inner product on R^n

there are many other vector spaces

[elder cypress]

I don't know what that means

Is it related to vectors

[obsidian oracle]

yes

[elder cypress]

I haven't done vectors in maths

Only in physics

[obsidian oracle]

ok xd

[elder cypress]

Thank you

.close

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[lean otter]

.reopen

[whole forge]

For example, consider the standard topology in $\mathbb{R}$. let $A_i={\frac{1}{i}+\frac{1}{k}: k \in \mathbb{N}^+}$ for $i \in \mathbb{Z}^+$. Notice that $\overline{\cup {i \in \mathbb{N^+}} A_i}$ contains $0$ but $\cup{i\in \mathbb{N}^+} \overline{A_i}$ does not.

[flat frigate]

somethingwrong

[whole forge]

I think this example works to show that statement is false

But im having some trouble showing that $0$ is indeed a limit point of of the union of $A_i$

[flat frigate]

somethingwrong

[peak estuary]

consider 1/i+1/i

[whole forge]

ah okay

thank you

.close

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[vestal summit]

A cube of side lenght 8cm is immersed completely in a rectangular vessel containing water. If the base is 16 cm long and 10 cm wide, then, find the rise in water level in vessel

[safe radish]

Please don't occupy multiple help channels.

[vestal summit]

A cube of side lenght 8cm is immersed completely in a rectangular vessel containing water. If the base is 16 cm long and 10 cm wide, then, find the rise in water level in vessel

Dang my discord kept crashing

Bymistake sent twice

Hmmmmm

<@&286206848099549185>

Dang did my discord crashed again or is there nobody to help me

<@&286206848099549185>

[obsidian oracle]

how much volume change does putting the cube inside contribute to?

[vestal summit]

I dont know

I have sent the whole question

[obsidian oracle]

... what's the volume of the cube?

this is something that you can deduce from the question

[vestal summit]

Volume of cube is 512 and cuboid is 1280

So
1280 - 512 = 768

[obsidian oracle]

uh

where does 1280 come from

[vestal summit]

768

(Answer is 3.2 cm in answer sheet)

[obsidian oracle]

well yeah I don't know what you're computing right now

[vestal summit]

What do you mean?

[obsidian oracle]

like I don't know what 1280 references to

[vestal summit]

Cubiod attributes
Height = 8
Breadth = 10
Long = 16

Cubiod Volume = 8 x 10 x 16 = 1280

[obsidian oracle]

yes but there is no such cuboid we're considering

if you're talking about the vessel

we don't know its height

[vestal summit]

Well yeah

I just assumed its as long as cube

[obsidian oracle]

Yeah... I wouldn't assume anything

in any case

[vestal summit]

Well how else i can find the answer

[glass coral]

if the water volume is the same as the cube volume, then the ratio between the water volume and the cube surface equals the height

[obsidian oracle]

if you let h be the height rise in water level

then

the change in water level

is a cuboid

of height h

and other dimensions... given by the vessel

[vestal summit]

Eeeee

There is no way to find height

I cant figure it out

Hmmmm

[obsidian oracle]

we're literally doing this

even if you don't know the height of water rise

call it h

and express the volume change in terms of h

[vestal summit]

Ok let it he h

Be*

How can i find volume change if i dont know volume of cube and cubiod

[obsidian oracle]

?

I told you the water change

is a cuboid

of height h

[vestal summit]

Water change is cubiod of height h ok

[obsidian oracle]

breadth... (the water is in the vessel)

and length... (the water is in the vessel)

[vestal summit]

Uhhh

[obsidian oracle]

Like if you look at the water from above, it's literally the shape of the base of the vessel

[lean otter]

,calc 512/160

[flat frigate]

Result:

3.2

[obsidian oracle]

that's kinda spoiling

[vestal summit]

Well i amnt very good with english

So i didnt understood what he just sent

Well i still cant figure it out

Cube volume is 512 and i dont cubiod volume

[vestal summit]

If i dont know how much water the cubiod have, how can i find how much water level will rise if i place a cube in it

[obsidian oracle]

I'm sending pics xdd

[vestal summit]

Ok

Area of rectangular vessel is 16 x 10

160

Area x height is volume

[obsidian oracle]

yes

[vestal summit]

Cube volume/Area of rectangle = height of rectangular vessel

[obsidian oracle]

sorry for low quality

if this is your vessel before adding the cube

so dimensions: 16cm, 10cm, height we don't care

[vestal summit]

Alright

[obsidian oracle]

now we added a cube inside

and it corresponded to the purple volume of "added water level"

[vestal summit]

Which is 512 volume

[obsidian oracle]

yep

[vestal summit]

Alright

[obsidian oracle]

512(cm^3)

but there's another way to compute this volume

if we had the height of the purple cuboid

call it h

what's the volume of the purple cuboid in terms of h

[vestal summit]

Volume of cube/area of base?

I still dont get one thing

[obsidian oracle]

well that's the height h you've directly given me

[vestal summit]

How much water does the cubiod have

[obsidian oracle]

in total?

like the total amount of water in the vessel?

[vestal summit]

No like as much water the cubiod have the more the height it will reach right?

[obsidian oracle]

we don't know if the cuboid is all water also

[vestal summit]

Yeah

[obsidian oracle]

since part of the submerged cube could be in there

[vestal summit]

Hmmmm

[obsidian oracle]

if you add more water into the vessel

then it amounts to some volume V

so it correspond to a change in total height of

V/(16 * 10)

similar to what we did in the exercise

"adding a cube"

except the cube is made of water

[vestal summit]

Cube is basically just adding 512 volume water to vessel

Now then to find the height which is water level
We do 512/lenght x breadth of rectangular vase

Hmmm i got the answer but i still dont get it

Cubiod area is 16 x 10 x 3.2 = 512

Which is apparently same as Cube too

[vestal summit]

If cubiod had even 100 volume of water already in it, then i guess we can say its leaked due to adding cube in it which volume is same as cubiod

[vestal summit]

@obsidian oracle

[obsidian oracle]

yes

you mean volume

the volume you add with the cube

is the same volume of water rising

there is no loss in volume

[vestal summit]

Yes

[obsidian oracle]

like

you place the cube at the bottom of the vessel

so

all the water you shooed away by placing the cube

has to go somewhere

[vestal summit]

It went somewhere

[obsidian oracle]

yep

it went on top

[vestal summit]

I guess it went out of cubipd

[obsidian oracle]

and formed the cuboid

10 * 16 * 3.2

there is nothing lost

if you put a cube in the vessel

the volume that the cube occupies, that the water used to occupy

[vestal summit]

Cube is 512
Cubiod is 512
Well, then the water in cubiod went outside when you put cube in vessel

[obsidian oracle]

the water went outside?

[vestal summit]

Yep

[obsidian oracle]

uh

no

the vessel in total is not 512

the "512" cuboid refers to the water change level

[obsidian oracle]

the purple dashed cuboid

that's where the water went

when you placed the cube at the bottom of the vessel

[vestal summit]

Cube height is 3.2cm and water level also reach 3.2cm, did the vessel even had any water?

[obsidian oracle]

?

cube height is 8cm first of all

then

h represents the CHANGE in total height of water

it's the height of the surplus, given by the purple dashed cuboid

it's

(new total height) - (total height before)

[vestal summit]

Then what the water level before cube was immersed in it

[obsidian oracle]

your question is 'what was the water level before the cube was immersed'?

[vestal summit]

Yes

[obsidian oracle]

we don't know, we don't care

[vestal summit]

We cant know whats the water level before,but we somehow know whats the water level after adding cube in it

[obsidian oracle]

no, we don't know the total water level afterwards either

we only know the change in height

which is the height of the little purple dashed cuboid

[vestal summit]

Hmmm

[obsidian oracle]

Like

if it were an experiment

put a mark at where the height of the water initially is before adding the cube

put a mark at where the height of the water is after adding the cube

we know h = the distance between the marks

but we don't know the initial height

nor the final height

[vestal summit]

We dont know what is the height of water(before we add cube)

[obsidian oracle]

nope

nor do we need to know

right now we only know and need to know h, the answer we wanted

if you know the initial height of water, you can compute the final height of water

just add h to the initial height

vice versa, if you know the final height

subtract h

you get the initial height

but we don't need to know either

to find h

all we needed was the dimensions of the base of the vessel

and the volume added in between (the volume of the cube)

[vestal summit]

Dang

Ok i guess.

.close

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[lean otter]

Hi

[lean otter]

<@&286206848099549185>

[plucky elk]

!15m

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@lean otter Has your question been resolved?

[lean otter]

<@&286206848099549185>

[glass coral]

Can you give more information?

[shy beacon]

I mean.. you can try averaging with weight maybe?

[lean otter]

Which weight?

[shy beacon]

Life span

Put the average of each life span as weight?!

[lean otter]

What formula should i apply

[shy beacon]

((life span)(printers with that life span) + (another life span)(printers with that life span) + .... )/(sum of the life spans)

[lean otter]

Ok

Thank you

[lean otter]

Can i use standard deviation formula for this?

[shy beacon]

Yep you can
It would be more accurate

[safe radish]

@lean otter Has your question been resolved?

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[peak meteor]

wouldn't the Ts cancel each other and leave you with 0 making the final answer 0?

[plucky elk]

no

is k an integer?

[peak meteor]

ye

[plucky elk]

do you know how to simplify sin(2 k pi)?

[peak meteor]

no

[plucky elk]

try evaluating it for a few small k

[peak meteor]

oh I see

it's always 0

my bad

.close

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[proud zealot]

how do i solve this?

[plucky elk]

find a common difference

[dapper nacelle]

cos(2+4n) if n starts from 0

[proud zealot]

ok. CD is 4