help-39

[white walrus]

Why is one root 1

Sure ser

[rigid mist]

i dont really know but u can just clearly see that x=1 is its root

[white walrus]

Oh yea

[rigid mist]

i think this is the only way u can say that

[white walrus]

But other root huh?

[rigid mist]

not sure maybe they used quadratic formula

[quartz citrus]

you can see the sum of coefficients is 0, what is the polynomial evaluated at x = 1? it's exactly the sum of coefficients

[mint flax]

The product of roots of an eqn is equal to c/a (the constant and coefficient of x)

[white walrus]

Nevermind got it

[rigid mist]

oh yea @mint flax thanks for helping, u got one of its root is 1, u can just use what he said to get other root

[quartz citrus]

this, it comes from vieta formulas

[white walrus]

If root is alpha then alpha*alpha = b-c/a-b

[quartz citrus]

c/a is the simplification for a 2nd degree polynomial

[white walrus]

And since root is 1 and both roots are equal hence alpha^2=1

Then alpha= sqrt(b-c/a-b)

And alpha is 1 so b-c/a-b=1

Makes sense

They write it directly with no context

.close

[pearl pond]

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[pearl pond]

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[glossy vector]

this is what i have SO FAR

i don't know if my CD is right tho

[lean saddle]

do you know what sine rule is?

[glossy vector]

yes

i used it

to get BD

[lean saddle]

ok yeah thats good

you cant do it driectly from there

but a prettier way (imo) would be to find the other angles

so you can find the last angle in A B D right?

,w 180-45-30

[jolly parrot]

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[lean saddle]

and you know for any quadleratial the angles inside must add up to 360

and for any triagle 180

so you know that angle CDB + CBD = 90

and that 90 + CDB + CBD +45 + 30 + 105 = 360

nvm thats stupid

yeah you get the side BD

then you use pythagoras to just get the leg

and 1/2 BC x CD

[glossy vector]

by leg do u mean CD?

[lean saddle]

yeah

[glossy vector]

okay , but im not sure if my CD is correct

[lean saddle]

ok so BD is 8 times sin(30)/sin(45)

we know what sin(30) and sin(45) are

so can you find an exact number for BD?

[glossy vector]

Bd is 5.65

i'm sure of that

i used sine rule to calculate it

[lean saddle]

but that wont help you find it in the fomr of a sqrt(b)/c

if you have a non exact result for BD you wont be able to extract the exact result for the area

[glossy vector]

wdym by non exact result, and how do i get an exact result

[lean saddle]

what is sin(30)

[glossy vector]

1/2

[lean saddle]

and sin(45)

[glossy vector]

sqr2/2

[lean saddle]

ok so then BD is?

[glossy vector]

i'm

not sure

[lean saddle]

BD is 8 times sin(30)/sin(45)

so solve for BD

[glossy vector]

so x= 8 x sin 30/sin 45

[lean saddle]

yes

dont use x for multipliaction and your variable

what is sin(30)/sin(45)

[lean saddle]

use this

[lean saddle]

and this

[glossy vector]

5.65

the same thing

[lean saddle]

dont put it in a calculator

what is (1/2)/(sqrt(2)/2)

[glossy vector]

idk 😭

[lean saddle]

try to solve this

ill write it out in an easier to see way $$ \frac{\frac{1}{2}}{\frac{\sqrt{2}}{2}} $$

[jolly parrot]

_MAN_OF_FIRE_

[lean saddle]

simplify this

[glossy vector]

nvm i just found out tis isnt on the exam

sorry to waste ur timesir

.close

[pearl pond]

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[lean saddle]

you shouldnt really only study to knwo whats on the exam

itll make you life infinitely harder when you get older and stuff gets harder

[pearl pond]

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[inland ivy]

$f(x)=\lim_{n\to\infty}\frac{x^2+2(x+1)^{2n}}{x^2+1+(x+1)^{2n+1}}, n\in\mathbb{N}$

[jolly parrot]

kheerii

[inland ivy]

$f(x)=\begin{cases}
\frac{2}{x+1}; &x\in (-\infty, -2)\cup (0, \infty)\
\frac{x^2}{x^2+1}; &x\in (-2,0)\
1; &x=0\
\frac{3}{2}; &x=-2\
\end{cases}$

just wanna confirm if I've done this correctly

[jolly parrot]

kheerii

[inland ivy]

.close

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[pearl pond]

@chrome flame Has your question been resolved?

[pearl pond]

@chrome flame Has your question been resolved?

[pearl pond]

@chrome flame Has your question been resolved?

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[hidden epoch]

help

[shell nymph]

your going to have to be more specific than "help", if you have a math problem, feel free to post it here

[hidden epoch]

Oh i thought that’s how you made the channel, sorry. new to this server

[shell nymph]

its alright

[hidden epoch]

Can you help me with this trig work? angles of elevation and depression etc

[hybrid basin]

!status

[pearl pond]

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

[hidden epoch]

my hand writing is sloppy i do apologize so lmk if you need help understanding what i wrote

[hybrid basin]

Are you locked in a basement

[hidden epoch]

me)

?

[hybrid basin]

Yes

[hidden epoch]

what makes you think that?

[hybrid basin]

Your picture

Either your camera has blood

[shell nymph]

just confirming that the angle is 31.5° and the bottom leg is 60

[hidden epoch]

no, it’s led lights .

[hybrid basin]

Or you're in one of those picture making rooms

[hidden epoch]

led lights.

[hidden epoch]

Yes , and the height of my (building) is 650

[shell nymph]

which value are you trying to find, the question dosen't make that too clear?

[hidden epoch]

My height is 60 inches , so the angle of elevation in degrees is 31.5 and i’m trying to find how far i am from my building basically using trig

[shell nymph]

ah

so you know the angle between the horizontal and the top of the building (31.5), the height of the building above the horizontal (650) and are trying to find the total hight, am i reading that right?

[hidden epoch]

yeah

[shell nymph]

can you send photos of all the steps you have done so far please?

[hidden epoch]

ofcourse, one sec

for the depression - basement

like of sight looking down

line *

[timber flare]

好看的照片

[pearl pond]

@hidden epoch Has your question been resolved?

[hidden epoch]

no

<@&286206848099549185>

[pearl pond]

@hidden epoch Has your question been resolved?

[hidden epoch]

<@&286206848099549185>

[granite summit]

yo ok i see a lot of scs

what exactly you want help with

[hidden epoch]

My height is 60 inches , so the angle of elevation in degrees is 31.5 and i’m trying to find how far i am from my building basically using trig

[pearl pond]

@hidden epoch Has your question been resolved?

[pearl pond]

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[visual canyon]

Old Faithful is a geyser in Yellowstone National Park that erupts according to an arithmetic sequence. The eruptions generally happen in 46 minute intervals with a constant difference of 12 minutes. Suppose that you are in the park and you know the last eruption was at 12:22 p.m. That eruption was the 4th eruption of the day. About when can you expect the geyser to erupt again? Explain.

[visual canyon]

i dont understand,
what does a constant difference mean
?
does it erupt every 46 minutes or every 12 minutes?

[vital estuary]

it means the time between the first and second eruption is 46mins
then between the second and third is 46+12=58mins
then between the third and fourth is 58+12=70mins and so on

[visual canyon]

ohhhhhh

[pearl pond]

@visual canyon Has your question been resolved?

[pearl pond]

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[acoustic pollen]

Question: The 7 digit numbers 74A52B1 and 3261B4C are each multiples of 3. Which following could be the value of C?

[wicked mortar]

Ooh that looks fun

[acoustic pollen]

I'm thinking of 7+4+5+2+1+A+B= a multiple of 3

3+2+6+4+A+B+C=multiple of 3 also

(19+A+B)-(15+A+B)= multiple of 3 - multiple of 3

c-4=Multiple of 3- multiple of 3

C=3(n-m)+4

I don't know next step

[unborn abyss]

the step that i marked with doesn't make sense to me

[acoustic pollen]

hmmmm

where do you think i did wrong

[wicked mortar]

Actually, looking closer, something's weird

This might be a trick question
Can I see the question in its original context?
E.g. a screenshot or photo?

[acoustic pollen]

I don't think i have the original screenshot sorry

i found it in my notebook

[wicked mortar]

Could you possibly have mistaken an A for a 4?

[wicked mortar]

In particular in the second number

[unborn abyss]

A isn't in that second number

[wicked mortar]

Cause things would make much more sense that way

[acoustic pollen]

hmm

i don't think so

[wicked mortar]

Was this a multiple choice question?

[acoustic pollen]

yes

[wicked mortar]

Was it choose which answer is correct
Or choose all applicable answers?

[acoustic pollen]

there were 5 options

1,2,3,5 and 8

i'm kind of wondering though what if there was a way to solve it without trial and error

[wicked mortar]

I think you either wrote it down wrong or there's a typo

[wicked mortar]

There is

But your question kind of just doesn't work right now?

[acoustic pollen]

I don't know if I made a typo

Let's say i made a typo

how would u solve it

[wicked mortar]

Let's say the 4 in the second number is an A

[acoustic pollen]

okay

[wicked mortar]

74A52B1 and 3261BAC

[acoustic pollen]

okay

[wicked mortar]

This part is true

[acoustic pollen]

okay got it

[wicked mortar]

That would be that 19+A+B is divisible by three

Yeah?

[acoustic pollen]

okay

[wicked mortar]

18 is divisible by 3
So if we subtract it out
It'd still be divisible by 3, right?

Side note, have you done modular arithmetic

[wicked mortar]

You don't need it, but it makes writing this out prettier

[acoustic pollen]

i don't think i know

but it sounds familiar

[wicked mortar]

You might see it soon

But still

[acoustic pollen]

okay

[wicked mortar]

You follow?

[acoustic pollen]

yep

[wicked mortar]

So 1 +A+B is divisible by 3

[acoustic pollen]

okay

[wicked mortar]

Try doing that with 3261BAC

[acoustic pollen]

okay

4+B+A+C right?

[wicked mortar]

No?

3+2+6+1 is 12
Which is divisible by 3

[acoustic pollen]

okay

wait sorry i need to go

can i pause this channel or something?

[pearl pond]

@acoustic pollen Has your question been resolved?

[pearl pond]

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[pearl pond]

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[serene kelp]

GUYS WHEN I HAVE A VECTOR MULTIPLIED BY SCALAR IT BASICALLY MEAN THAT IM MOVING AT THAT SPEED (SCALAR) AND IN THIS DIRECTION (VECTOR)

[pearl pond]

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@serene kelp Has your question been resolved?

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[midnight haven]

is it ok to swap differential operators as they did in 6-52?

[midnight haven]

as in, [
\pdv t\8{\curl \vv A} \overset?= \curl\8{\pdv[\vv A]t}
]
always

[midnight haven]

good to mention that A is a four dimensional vector field

,, \vv A\8{\vv r, t}

[pearl pond]

@midnight haven Has your question been resolved?

[pearl pond]

@midnight haven Has your question been resolved?

[pearl pond]

@midnight haven Has your question been resolved?

[midnight haven]

.close

[pearl pond]

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[pearl pond]

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[midnight haven]

i need help finding out whether f(x) = |x| is continuous or not, and i dont really know where to start outside of redifining the absolute value. this is what i did, and honestly, i dont even know what i did in step 2, i just copied it to show the direction im supposed to be going

[midnight haven]

i know how to do basic limits, but i cant really figure out how to do this

[autumn topaz]

are you trying to find the derivative?

[midnight haven]

the question says:
find out if f(x) = |x| can be differentiated when x=0

should've included question mb

also its translated from a different language so im not sure if i worded it properly

[autumn topaz]

then you need to use the correct formula for the derivative

it's not just lim f(x)

[midnight haven]

as in (f(x+h)-f(x))/h?

that one?

[autumn topaz]

yes

[midnight haven]

do i plug this into f`(x) then just replace x with 0

[autumn topaz]

plug what into f'(x)? you don't know what f'(x) is yet

[midnight haven]

doesnt this formula give f`(x)

i will write this down actually hold on

[midnight haven]

@autumn topaz something like this and i can use my redefinition of |x| here but i dont know what to do after

[autumn topaz]

so now you have 2 cases, when h -> 0 from above, and from below

[midnight haven]

yes

and i need to find what each of those values is

and i dont really get it

[autumn topaz]

yes

what don't you get?

[midnight haven]

i dont really know how to find those values

i know it involves f`(0)

and i plug that in from the top and bottom

hold on

[autumn topaz]

when h -> 0 from above, what is |h|

[midnight haven]

positive

and the other one is negative

do i use the entirety of |h|/h or something

giving me 1 and -1

because from the top its h/h

and from the bottom its -h/h

[autumn topaz]

yes

[midnight haven]

but why do i use the entirety of h/h

thats what i dont really get

[autumn topaz]

what do you mean "the entirety of"

[midnight haven]

why doesnt the limit approach 0 with only h

why isnt it lim h-> 0 h = 0

instead its lim h -> 0 h/h = 1

[autumn topaz]

because it's as h approaches 0

[midnight haven]

oh

i think i understand now

[autumn topaz]

for the limit to exist, it has to be the same whether h approaches 0 from above or below

[midnight haven]

so this limit is discontinuous because it doesnt approach the same number

they both stop at 1 and -1 respectively

is that right?

[autumn topaz]

it is not discontinuous

[midnight haven]

my bad i do not know the word

[autumn topaz]

it is showing that f'(0) doesn't exist because the left-hand and right-hand limits are not equal

[midnight haven]

yes

that should be it thank you

.close

[pearl pond]

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[pearl pond]

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[hidden epoch]

My height is 60 inches , so the angle of elevation in degrees is 31.5 and i’m trying to find how far i am from my building basically using trig

[compact veldt]

you have a height

the height is opposite to the angle you have

you're looking for an adjacent side to that angle

(use tan)

Or

cotangent

Would be better

[pearl pond]

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[thin sigil]

Masses in mathematics? Blasphemy

[olive otter]

[thin sigil]

How would you approach this?

[errant fable]

are they spherical

[errant fable]

well that doesn't matter i think

[atomic oracle]

I think its some random 3 dimensional shape

[timber heron]

Do you know about scaling factors/enlargement?

[errant fable]

||S²/V³ is constant?||

[atomic oracle]

Mass depends on volume

[timber heron]

I think so cause they're similar

[pearl pond]

@midnight haven Has your question been resolved?

[pearl pond]

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[thin patio]

Suppose a population, p(t) satisfies, dP/dt = 0.4P - 0.001P^2. If P(0)=50, what is the equation that governs the population's growth over time?

[pearl pond]

Please don't occupy multiple help channels.

[sterile tusk]

do you know what the general solution is to a logistic differential equation? or do you have to do the partial fractions and all that

[pearl pond]

@thin patio Has your question been resolved?

[thin patio]

No

I was just given the question like that

Lemme snap a picture

Forgive the penmanship

I tried integrating but it's hard making one variable the subject when you have logarithmic, exponential and linear forms of the same variable in the same equation

[sterile tusk]

well so you would use separation of variable here

and then partial fractions to split them up

can you show your work?

[pearl pond]

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[drowsy flare]

what i get is with comparison method: (2+(1/sqrtn))/n

[acoustic path]

this works yes

(though if your only goal is to test for convergence then it's not fully necessary)

[drowsy flare]

but this gets me a wrong result

it converges

this method says

but the result says otherwise

[acoustic path]

how?

[drowsy flare]

i mean the written result

[acoustic path]

using your method you have the summation of 2/n + 1/nsqrtn

using p-series, 1/nsqrtn converges but 2/n diverges; therefore, by direct comparison test, the original sum diverges

[drowsy flare]

oh shit

ur right i missed this detaiò

i just ignored the 2

[acoustic path]

oh

[drowsy flare]

since im used to calculating the limits

numbers like that get ignored and written out

so i just went and did that u see?

[acoustic path]

sounds valid

[drowsy flare]

do u mind if i ask u confirmation for some other exercise results i got of this kind

some dont have a written solution and i cant tell if i did right

[acoustic path]

yeah that's fine you can use this channel however long you want

[acoustic path]

btw what i meant here was that at the start you could directly compare with 1/n without having to rewrite the e^(sqrt(1/n)) term

[drowsy flare]

i didnt write e?

just sqrt(1/n)

[drowsy flare]

u mean here?

[acoustic path]

ye i meant you rewrote e^(sqrt(1/n)) as 1 + 1/sqrtn

u didn't need to do that since the presence of the (1 + something)/n in the original summation already lets you conclude it diverges

[drowsy flare]

okok

thx

lemme show u 1s

this exercise i got this

tell me if u agree

[acoustic path]

it's close

the first term is -1/2n^2

actually idk what your goal was there so maybe -2/n^2 was right for your purposes

[drowsy flare]

i used this

[acoustic path]

i see

using that, the 2 would be on the denominator

[drowsy flare]

ur right i corrected it

[acoustic path]

but yeah regardless, you should come to the correct conclusion about the behavior of that summation

[drowsy flare]

that it doesnt converge yes ?

[acoustic path]

ye

[drowsy flare]

ok, but heres my doubt

[acoustic path]

without the 1/2n term, it converges

with it, it diverges

[drowsy flare]

this almost same i got this

sry for bad quality

[acoustic path]

it looks like you have another 2 in the numerator

[drowsy flare]

oh sry i forgot to remove it

OH

that makes 0 lol

[acoustic path]

yep

[drowsy flare]

so thats uhm

...what does it mean when its 0?

uhmmmmm

oh taylor

[acoustic path]

yeah you can just add in another term from the taylor expansion

then by limit comparison, you have the correct conlusion

[drowsy flare]

i have 1/(4!n^2)

so it converges

nice thx bro

do u know in this case what happens when alpha is 0?

[pearl pond]

@drowsy flare Has your question been resolved?

[pearl pond]

@drowsy flare Has your question been resolved?

[drowsy flare]

<@&286206848099549185>

[drowsy flare]

<@&286206848099549185>

[strange egret]

If alpha is equal to zero then n to the power of alpha is equal to one

[drowsy flare]

but what when n is infinite

[strange egret]

i guess its an inderterminate form

[drowsy flare]

.close

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[willow spoke]

bro wth

[pearl pond]

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[nova mortar]

why does the log become that ?

[merry carbon]

Change of base formula

[nova mortar]

wym

[dense plank]

in this case, the new base is e

[nova mortar]

oohh

wow thanks

appreciate it

.close

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[smoky saffron]

what this mean

[worldly glacier]

they are telling you to make a LI set that spans R^2

[smoky saffron]

do yk what a spanning set means?

[worldly glacier]

yes

[smoky saffron]

what is it

i dont konw

[worldly glacier]

do you know what the span of a set is

[smoky saffron]

nope

[unborn abyss]

are you in a linear algebra class?

[smoky saffron]

grade 12 calc

[pearl pond]

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[nocturne apex]

what is the formula for this?

[pearl pond]

@nocturne apex Has your question been resolved?

[nocturne apex]

<@&286206848099549185>

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[grave fjord]

ab^t no?

and the t is substituted for x as the input

a= the intial deposit, b = growth rate/decay, t= independent input variable (years)

[pearl pond]

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[hybrid basin]

Hello

[hybrid basin]

Hold on let me type

How do we know that (1, 1) gives the greatest increase

iirc ∇f(\vec a) is the steepest slope at a point

\vec a being (1, 1) as given in the question

[grave fjord]

start by plotting the vector at that point

[hybrid basin]

wdym plotting the vector?

[grave fjord]

then once u plot it u can find the slope

[grave fjord]

graph it starting at (1,1)?

like on a plane

messy graph but wtvr

[hybrid basin]

How does that help though

[grave fjord]

bc you can find the "end point of the vector" to find rate of change

[hybrid basin]

I'm confused

[grave fjord]

now just do the slope formula

[cinder flower]

[hybrid basin]

Not (2, 2)?

[grave fjord]

the position would technically be (3,2)

though the vector itself is 2,1

[cinder flower]

brielle i don't think this is right

[hybrid basin]

Also, how do you know multivariable calculus when you tagged yourself as pre-university math

[grave fjord]

😔

[cinder flower]

wdym by this

[hybrid basin]

^

2nd line solution

[cinder flower]

(1, 1) gives the greatest increase

you might be a little confused

[hybrid basin]

What am I missing?

[cinder flower]

at the point f(1,1)

you could move out from (1,1) in any direction in the plane

like move out in a straight line

[hybrid basin]

True

[cinder flower]

and the function behaves differently depending on what line you pick

along that line

[hybrid basin]

Are you talking about "∇f(\vec a) dot producted by directional vector"

[cinder flower]

i was never any good with the upside down triangle

[cinder flower]

but anyway when you pick a line, the function has a rate of change at (1,1) along that line

[hybrid basin]

Gradient sucks I feel you

[cinder flower]

kinda like a single variable function

since we're just looking at it over a line

[hybrid basin]

I feel like we are stepping the border of Linear Algebra and Calc 3

[cinder flower]

but anyway you can describe the line you pick with a direction vector

[hybrid basin]

I know that

[hybrid basin]

But like how

I'll ask my university cohorts

Thanks for the help though

.close

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[hybrid basin]

.reopen

[pearl pond]

✅

[cinder flower]

you deleted the stuff

[hybrid basin]

University course material can't stay outside 🥲

[cinder flower]

[hybrid basin]

But either way

The point was

How does one calculate the steepest slope

In a function

It's not like where we find the inflection point in a single variable function

Since we can't really find limits in multi

[cinder flower]

the direction vector that gives that is indeed the gradient of f at (1,1)

or any scalar multiple of the gradient of f at (1,1)

[hybrid basin]

?????

[cinder flower]

since those all prescribe the same direction

why ?????

[hybrid basin]

What does directional vector have to do

[quartz citrus]

Kim chaewon

[cinder flower]

m8of48

[hybrid basin]

https://tenor.com/view/chaewon-kim-chaewon-heart-wave-le-sserafim-gif-1186965009290811417

[quartz citrus]

slayla

[hybrid basin]

?

[quartz citrus]

?

[cinder flower]

chebyshev's infinite pee norm = m8of48

[cinder flower]

hi

[cinder flower]

i think i explained earlier

[hybrid basin]

I didn't get it

[cinder flower]

this

[hybrid basin]

I'll just wait for a FICE to help me

[cinder flower]

FICE?

[hybrid basin]

First in Class Engineering

Why do engineering have to learn calc 3 stuff in calc 2

sighs

[cinder flower]

[quartz citrus]

engineering must be hard

[hybrid basin]

https://tenor.com/view/waterloo-warriors-king-warrior-yeah-yes-mascot-gif-24019116

[cinder flower]

you must be engineering

[hybrid basin]

Which eng are you in

[sudden silo]

https://tenor.com/view/hcde-human-centered-design-human-centered-design-and-engineering-hcde-major-gif-25594252

[hybrid basin]

tf?

[quartz citrus]

I am but a lowly math dumbfuck

chaewon is the real gigachad

[hybrid basin]

You did not answer the question

[sudden silo]

1st thing that appared when I searched engineering

[hybrid basin]

Well, idk what HCDE is

[quartz citrus]

I am a math engineer

[hybrid basin]

That's a thing?

[sudden silo]

Apparently it's some type of engineering major

[cinder flower]

i'm also a math engineer

[topaz acorn]

hi is anyone good at lin alg here? i need some help with gram schmidt and inner product stuff

[hybrid basin]

Eigenvectors~~~~

[cinder flower]

i was never any good at linear algebra myself, sorry

[hybrid basin]

I got a shit schedule

Welp

[hybrid basin]

No one uses inner product

Stupid ass terminology

[topaz acorn]

uh well its in my course and i need help understanding it

[quartz citrus]

When is dance practice

[hybrid basin]

You won't see it in the midterm

Trust me

[hybrid basin]

In the next decade?

[topaz acorn]

uhh i don't care about that

i want to understand it still

[hybrid basin]

Hold on

[topaz acorn]

can you help me or not

[hybrid basin]

HOLD ON

LET ME BRING MY MEMORY BACK

[topaz acorn]

ok

[hybrid basin]

Plus, you shouldn't be asking in this channel

But whatever

[topaz acorn]

let me know when your memory is backk

[hybrid basin]

What is it about that you don't know about inner products

[topaz acorn]

ok basically its a specific section in my textbook

let me send screenshot

[cinder flower]

[topaz acorn]

inner products were first defined here

very simple and cool so its ok

[hybrid basin]

Read my notes if that helps

[topaz acorn]

the issue is

they introduce polynomial inner product here

and i get this too but here's where it gets worse

i don't get whats going on in example 5 at all

what are the first three vectors shown

and what in the world are they doing with them

[hybrid basin]

Okay

You lost me

I'm sorry

[topaz acorn]

oh

so u wont be able to help? 🥹

[hybrid basin]

Span and subspaces are long gone memories

Yes

My bad

My apologizes

[topaz acorn]

no worries

[hybrid basin]

.close

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[visual canyon]

What is the spread of the data set {4, 2, 6, 10, 8, 0}?

2.8

5.0

3.4

[visual canyon]

i dont understand

isnt spread the diff between the min and max value

isnt the max 10 and min 0

so shouldnt the spread be none of these options?

im obviously missing something..

[oblique river]

they're probably asking for standard deviation

[visual canyon]

no no

they are not

thats in a diff question too

i pasted directly idk dude

its def spread of the data set

[oblique river]

standard deviation is one of the measures of spread

along with range

if you calculate it for this set you get 3.4

[pearl pond]

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[wicked mortar]

You might want to get your own channel

Instructions in #❓how-to-get-help

[tardy path]

Oh really sorry

Didnt realize

[pearl pond]

@chrome flame Has your question been resolved?

[chrome flame]

How to find unit element?

[wicked mortar]

Consider what makes it impossible to find a unit element in modular arithmetic

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[main matrix]

I need some help with using elimination

[main matrix]

so

I have the equations

4x+3y=4
8x-y=1

so what I did is

multiply every number in equation 2 by -3

so it's balanced and now I can delete the 3ys

so it would suomthing like

4x+3y=4
-24x+3y=-12

wouldn't it be?

[light helm]

no

[main matrix]

how then

[light helm]

-3 * 1 isn't -12

[main matrix]

ah yeah ups

-6

[light helm]

isn't -6 either

[main matrix]

yeah

I got it now

so

[slender storm]

-3

[main matrix]

yeah

so

it would be

4x+3y=4
-24x+3y=-3

?

[light helm]

yes

[main matrix]

would it be

28x=1?

[light helm]

no

ensure that you're subtracting -3 from 4

[main matrix]

-7?

[light helm]

no

[main matrix]

[light helm]

that would be subtracting 4 from -3

what you're doing when subtracting equations like this is
LHS1 - LHS2 = RHS1 - RHS2
4x+3y - (24x + 3y) = 4 - (-3)

you've correctly simplified the left to 28x,
now simplify
4 - (-3)

[main matrix]

7?

I'm confused now

[light helm]

yes

4 - (-3) is 7

thus after subtracting the equations you would have
28x = 7

[main matrix]

so I would have to divide 28 into 7?

4

[light helm]

literally write 7
a fraction line
then 28 below it

[main matrix]

ah

[light helm]

you want 7/28, not 28/7

[main matrix]

divide 7 into 28

0.25

...

[light helm]

7/28 is 0.25, yes

[main matrix]

so now I can put that into any equation right? so

if I put it into 1

It'd be 4(0.25)+3y=4

which the final result is 1?

[light helm]

result of y is 1, yes

[main matrix]

so if I want to check it

I can put that into 2 maybe?

and it'd be 8(0.25)-1=1 ?

a yeah

it gave me 1=1

ty for your help a lot, ik I'm stupid but really thank you for your patience w me, so thanks a lot!

[pearl pond]

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[winter night]

so confused -- could somebody better phrase, or just simply explain the following question: Use a diagram to show that (A ∪ B)′ = A′∩ B′.

[light helm]

use venn digrams

[tall flint]

What about it confuses you?

[light helm]

draw it in stages, colour code if possible

indicate A U B on one leading to → (A U B)'

then same idea for the right side
shade in A', B' in different colours/patterns leading to A' ∩ B'

[pearl pond]

@winter night Has your question been resolved?

[winter night]

so, both (A ∪ B)′ and A′∩ B′ affect the same region of the venn diagram
affirming that (A ∪ B)′ does in fact equal A′∩ B′ ?

[warm current]

Correct

[winter night]

.close

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[dense plover]

can someone help me with a please

[dense plover]

is it requiring suvat

[pearl pond]

@dense plover Has your question been resolved?

[fallen acorn]

What's the formula for COR

[pearl pond]

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[nova mortar]

i don't understand how to resolve this

and how it becomes this

[thin sigil]

Through hard work and dedication

Ok, well first the 2's cancel out right?

[wraith hare]

that's actually what I love to say whenever my friends ask me how. I always respond with "dedication, skills, practice and hard work"

[nova mortar]

oh yeah

[thin sigil]

Then we can rewrite the bottom part like so

by squaring and rooting it

it's already a squared expression so the sign shouldn't be an issue here ( I think )

[nova mortar]

ohh so then u have

[thin sigil]

and then we can put it all under one square

[nova mortar]

huh

what's the 4

[thin sigil]

to the 4th degree

instead of 2

since we squared it

and then rooted it

[nova mortar]

ohhh yeah

[thin sigil]

and then under the same root

and the top part cancels with one of the bottom ones

so the exponent goes from 4 to 3

and there you have it

[nova mortar]

do i also have to square the x+1/x-1 then?

[thin sigil]

no

[nova mortar]

then why does x+1 go to the fourth power

sorry for stupid questions 😭

ohh nvm

i understand already

.close

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[smoky saffron]

when using the dot product formula and u have to find cos theta

[smoky saffron]

does the angle mean the tail to tail of the vectors ur trying to find?

not sure exactly what dot product does anyways

[gloomy scroll]

The angle theta in question is indeed the angle between the two vectors when they are in tail to tail position

[smoky saffron]

Oh okay tysm for clarifying

[gloomy scroll]

No worries. I'm trying to find a good explanation for what the dot product means, but I haven't found it yet

[smoky saffron]

If u do find it pls tell me

[gloomy scroll]

I mean, I did find this iamge, which shows what it does, but it's not really explaining it. I suppose that there isn't really a reasoning, it would be like asking why a+b is adding two numbers. It was just defined that way

but I could be wrong, it's been a bit since i've seen vectors

Hey Garlic here to save the day

[snow fossil]

yo

[vital estuary]

my way of understanding the dot product is if something is moving in the direction of one vector, how much will the other one "help" the other vector

[snow fossil]

(x + h ) at 3

?

[smoky saffron]

what is the something youre talking about?

like

a point?

[vital estuary]

a particle, a car, anything really

[smoky saffron]

ohh

[late prism]

The dot product also outputs 0 if two vectors are perpendicular and the product of their magnitudes if they are parallel

And it doesn't require finding the angle between the two vectors

Which is quite nice

[smoky saffron]

Oh ok

[pearl pond]

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[vestal pelican]

how do i go on about solving this

[vestal pelican]

i have ploted the points on a graph

what do i do from there

[thin sigil]

Are you familiar with integrals?

That is, 3d problem integrals?

[vestal pelican]

integrals yes double integrals yes 3d problem integrals no

[thin sigil]

yeah that's what I meant

Anway, all points lie on the xy plane, right?

[vestal pelican]

yes

they form a triangle

[thin sigil]

Since you need the volume of this solid, you'd basically do a double integral of this function

in the area of this triangle

Real question here is how to set up the boundaries

Drawing a sketch of the triangle might help

[vestal pelican]

i already did

[vestal pelican]

yep

[thin sigil]

Here's how I'd approach this

I'd break down this area into blue and green as shown

I'd also fine the line functions for the sides of the triangle

The first integral has boundaries from 0 to pi/2 on x and from purple to orange line on y

the second integral would have boundaries from pi/2 to pi on x and from brown to orange on y

and then just solve them and add them to get the full volume

[vestal pelican]

so basically like this

[thin sigil]

no

[vestal pelican]

how

[thin sigil]

Let's first find the equation for the purple line

It would be

y = -x + pi/2 right?

[vestal pelican]

why -x

[thin sigil]

The orange one would be y = 1/2x + 1/2 * pi

[thin sigil]

because the slope of the function would be (0 - pi/2) / (pi/2 - 0)

which is -1

[vestal pelican]

where is -1 there

[thin sigil]

and then the last line, brown, would be y = 2x - pi

[vestal pelican]

i only see -pi/2 with a minus

oh nvm

[thin sigil]

(0 - pi/2) / (pi/2 - 0) = -pi/2 / pi/2 = -1

[vestal pelican]

i see

[vestal pelican]

so this cam from (pi/2) / (pi)

[thin sigil]

yeah

[vestal pelican]

wouldnt that just give us 1/2

[thin sigil]

yes but that line would be centered at 0,0

we have to move it up

by pi/2

to put it at the point

[vestal pelican]

what

[thin sigil]

yeah it gives us 1/2

which is the slope factor with x

if that's what you meant

[vestal pelican]

ok

[thin sigil]

and then the last line similiarly

once we have the lines we can write the integral

[vestal pelican]

thats just 2

[thin sigil]

yes

but shifted by -pi

to move it

[vestal pelican]

ok thats where im lost

[thin sigil]

if you don't want to think about it

there's a formula

the line between 2 points A and B is always

(y - B_y) = ((B_y - A_y) / (B_x - A_x )) * (x - B_x)

[vestal pelican]

so if we were to plug it in which one would be B_y

[thin sigil]

the y coordinate of the second point

So if we look at points

(pi / 2, 0)

and

(pi, pi)

we'd have

A_x = pi/2

A_y = 0

B_x = pi

B_y = pi

[vestal pelican]

ohhhhhhh

so it will be
y-pi=(pi-0)/(pi-pi/2)*(x-pi)

[thin sigil]

Yeah and when you simplify that

you'll get what I wrote above

[vestal pelican]

y-pi=(pi-0)/(xpi)-(xpi/2)-(pi^2)+(pi^2)/2)

[thin sigil]

ummm

no

[vestal pelican]

what

[thin sigil]

Mind the parentheses

[vestal pelican]

ohhhhh

y-pi=((xpi)-(pi^2))/pi-(pi/2)

[thin sigil]

no

[vestal pelican]

what

[vestal pelican]

ohhhhh yea

i shouldve wrote it in my notepad

ok so we factored the pi's

but where did that additional pi come from

[thin sigil]

Which one?

[vestal pelican]

nvm got it

[vestal pelican]

so we use the same formula here?

[thin sigil]

yes

in all cases

the same one

[vestal pelican]

ok

[thin sigil]

anway, once you get the line functions

we basically have this integral

[vestal pelican]

yep

[thin sigil]

By plugging in everything we get

[vestal pelican]

why are we adding to double integrals

[thin sigil]

Because we split up the triangle into 2 parts

as I showed above

[vestal pelican]

ohhh yea true true

[thin sigil]

Now solve this and you're done

[vestal pelican]

wouldnt it be easier if we had dxdy instead of dydx?

[thin sigil]

would it?

[vestal pelican]

i feel like yes

[thin sigil]

how come?

[vestal pelican]

well i learned somewhere that if we have more y's than x's we start with dx and vise versa

[thin sigil]

not quite

here's the thing, you do the boundaries in order so that the last ones you do have only numbers

the boundaries for y have x in them

so we do dy first

then dx last

Like so

You could do it the other way I guess (maybe), but generally this is the easier path

At least as far as I've found

[vestal pelican]

so u think its easier to integrate wrt x after integrating first wrt y

[thin sigil]

yes

[vestal pelican]

ok

well this makes sense now

thanks

[thin sigil]

You should get about 5.68 if desmos is correct

[vestal pelican]

btw here

how do u know pi/2 is A_x and not B_x

[thin sigil]

Because I put that A is (pi/2, 0)

[vestal pelican]

what if u but B=(pi/2, 0)

we would get a different result

[thin sigil]

no

you'll get the same

[vestal pelican]

really even after plugging it to the equation?

[thin sigil]

yeah

[vestal pelican]

ok

[pearl pond]

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[lime radish]

can i get some help on this?

i can find that first bit easy but then when i try to find M i having trouble

refering to this

[pearl pond]

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[pearl pond]

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[pearl pond]

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[brittle comet]

Help

[brittle comet]

Number 18 and 19

[midnight haven]

18 yes

same common angle and the ratio of the two sides are identical

[brittle comet]

i need to say if its SAS or SA or wtv

that typa shi

[midnight haven]

SAS?

[brittle comet]

ye

[midnight haven]

what does that stand for

[brittle comet]

side angle side

[midnight haven]

wtv?

[brittle comet]

wtv = whatever

[midnight haven]

the two sides have the same ratios of lengths and same angle

if that helps

[brittle comet]

idek

[midnight haven]

use SAS in a sentence

[brittle comet]

Triangles ABC and DEF are similar by SAS

[midnight haven]

oh, yes

just replace the letters

idk what 19 is asking, its just a triangle lol

[brittle comet]

if theyre similar and why

i think they r both sunukar

similar

[midnight haven]

why do u think that

[brittle comet]

cuz it looks like it

[midnight haven]

more specific

[brittle comet]

the angles look the same

o shi

theyre parallel

so its like

congurent angles

[midnight haven]

yep. same thinking as 18. the ratios of the lengths will be equal and have a common angle

[pearl pond]

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[pearl pond]

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[clear orchid]

what have i done wrong, i don’t know if im missing something?

[rough stream]

Let u = sinh(x + y)
What's du/dx?

[pearl pond]

@clear orchid Has your question been resolved?

[clear orchid]

du/dx = cosh(x+y) right?

[pearl pond]

@clear orchid Has your question been resolved?

[pearl pond]

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[midnight coral]

how do i start with a

[pseudo oxide]

the limit def of the derivative

[wicked mortar]

Do you have the derivative at x=-3?

[midnight coral]

like the derivative of fx?

[pseudo oxide]

yes

[midnight coral]

12x+8?