help-36

[tranquil pine]

[grim nebula]

so you can just calculate the potential

since it should be very easy for all of these

idk what you're saying

it's just contrapositive

curl not 0 => not closed => not exact

[tranquil pine]

idk i feel like i got mixed information

ok lets recap

ok hear me out dawg

big dawg

we have exact => closed

so

i need to find a potential function

so solve the system of PDEs

find that

if i can find it

ok cool

then

and we are done?

[grim nebula]

so like

1. check curl = 0
2. if curl is 0 then you might be able to find a potential
3. if you can't find a potential, try to find a loop over which the integral is nonzero

[tranquil pine]

ok the last one seems conservative

i mean

closed at least ig

[grim nebula]

irrotational

not conservative

conservative means is the grad of something

usually called exact

irrotational means curl = 0

usually called closed

[tranquil pine]

huh

no wait bruh

i think im fucking up mathematica

[grim nebula]

bro

just calculate it by hand

[tranquil pine]

Are we checking curl = 0 because it is necessary for exactnesS?

[grim nebula]

yes

if curl isn't 0 then you can bail out immediately

[tranquil pine]

ok i calculated it by hand

uh

yep seems 0

so curl f

= 0

so this is irrotantional

irrotiatonal

irrotational

so now the PDEs

just do the thing and boom boom it idk

u get xyz

ok

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[sturdy cloak]

could someone explain to me plz how they iterated this

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[tranquil pine]

I dont get the choice of increments for the function

as in, why not the bottom is F(x + delta x, y)?

oh nvm

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[austere snow]

this is the book answer

did they just divide 8 by 2?

[tranquil pine]

yes

[austere snow]

alright thanks

just wanted to makesure

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[wraith merlin]

A 415kg container is dropped at an altitude of 300m, ignoring air resistance, how long will it take to reach the ground

[wraith merlin]

1/2Vf*t = 300

idk what to do from here

[merry steppe]

use
s = ut + 1/2 gt^2

[wraith merlin]

sqrt(61.2)seconds?

also if this is the answer, would the speed of the container just before it hits the ground be 76.7m/s?

[merry steppe]

yeah

[merry steppe]

yep

[wraith merlin]

if the container is attached to a parachute designed to produce a drag force that allows the container to reach a constant downward velocity at 6.0m/s, the magnitude of the drag force is 4070N?

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[zenith kelp]

can you differentiate inequalities

[inland kettle]

i think so

actually wait--no nvm

you can't

[tiny gorge]

not if you want the inequality to remain true

[inland kettle]

depends on the function points

[inland kettle]

lmao

[inland kettle]

so not usually

[tiny gorge]

say f(x) < g(x), that's equivalent to g(x) - f(x) > 0, so you're basically asking, if a function is positive, does that mean its derivative is positive?
e^(-x) is a counterexample

[inland kettle]

https://math.stackexchange.com/questions/2294397/do-inequalities-hold-under-differentiation#:~:text=Note you can never differentiate,function is increasing or decreasing.

found something

also, if g(x) is always larger than f(x), it doesn't necessarily mean that the derivative is larger

if g(x) = f(x) + c, g'(x) = f'(x) while g(x) might be greater/less than f(x)

(just one example)

[inland kettle]

^

1/x as well

!done

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[zenith kelp]

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[zenith kelp]

.reopen

[final saddle]

✅

[inland kettle]

hello again

what's your question

[inland kettle]

what the hell

we can't conclude that

FTC

[zenith kelp]

apparently you can actually differentiate inequalities

[inland kettle]

no

not if, as bungo said, you want the inequality to remain

let's say f(x) > g(x), where f(x) = g(x) + 2

if you differentiate that

f'(x) > g'(x)

[gritty solar]

$\cos x > \sin x \implies -\sin x > \cos x$

[soft zealot]

NEON

[inland kettle]

BUT f'(x) = g'(x(

[gritty solar]

does that make sense

[inland kettle]

doesn't always hold

[gritty solar]

exactly

[gritty solar]

you can take a definite integral though

[inland kettle]

no i mean the original statement doesn't hold

[gritty solar]

thats fine

provided t > 0

[inland kettle]

hmm

yea

definites are alright

[gritty solar]

on some restricted domain

[zenith kelp]

oh

[inland kettle]

indefinites no

[inland kettle]

yes

[zenith kelp]

aha

[inland kettle]

definites bc area under curve, remember

[zenith kelp]

so you can do definite integrals

[inland kettle]

yes

[zenith kelp]

but indefinite integrals and differentiation don't make sense here

[inland kettle]

yes

[zenith kelp]

thx all

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[mossy scroll]

Do not bother about the French text. I'm stuck on question 3. (b). Here is what is written before:
"We want to show that among random variables of given variance, those with the greatest entropy are those that follow a normal distribution. Let X1 → N(0, σ²) have density φ and X2 be a centered variable of density ƒ and variance σ². For simplicity we assume that ƒ is strictly positive on |R." (translated).

I've tried using the fact that they have the same expected value of 0 and the same variance, but I get nowhere. I don't get how we can find that considering there is no information on the position of f related to φ.

[mossy scroll]

Wait I'm onto something

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[warm python]

if $f(x)$ is a periodic function on an interval say $[-T/2, T/2]$ with a period T , prove $\int_a^Tf\left(x\right)dx$ is periodic with the same period

[soft zealot]

Why am. I here

[warm python]

can I have a hint

not even sure where I would start TBH

oh

[desert mantle]

!original

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Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[signal vector]

If you prove that $\int_{0}^{T}f(x)dx = \int_{0}^{2T}f(x)dx$, you are donr

[warm python]

just a min

made a mistake while posting the problem

It is known that $f(x)$ is an odd function in the interval $[-T/2, T/2]$ with period T. Prove $\int_a^xf\left(t\right)dt$ is also a periodic function with the same period

[soft zealot]

Why am. I here

[signal vector]

You need to do two things in order to prove that the integral is periodic with period T.

1. prove that integral from a to x = integral from a to x+T
2. prove that T is the smallest such positive number

When you prove the second condition, you are showing that T is the "fundamental period"

[warm python]

hmm, let me think about this, I'll reopen it if I need help

thanks!

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[cursive rain]

I am trying to prove the Cauchy-Schwarz inequality for complex numbers by algebraic manipulation.
the inequality states, for $z_1,\dots,z_n,w_1,\dots,w_n\in\mathbb{C}$ it holds that\
${\vert\sum\limits_{j=1}^n z_j\cdot w_j\vert}^2\leq\sum\limits_{j=1}^n\vert z_j\vert^2\cdot\sum\limits_{j=1}^n\vert w_j\vert^2.$

[soft zealot]

🇵🇸Mína🔆

[cursive rain]

i used that $z\cdot\overline{z}=\vert z\vert^2$

[soft zealot]

🇵🇸Mína🔆

[cursive rain]

basically two sides, on either one a product of two sums, which should yield a sum of $n^2$ terms. I don't understand how that is always not an equality?

[soft zealot]

🇵🇸Mína🔆

[oblique turret]

Because the terms are different in each side

[oblique turret]

In the left they will look like $z_iw_i\overline{z_j}\overline{w_j}$ and in the right like $z_i\overline{z_i}w_j\overline{w_j}$

[soft zealot]

d

[cursive rain]

and how can i shoe one is bigger than the other?

[oblique turret]

I don't remember the proof by algebraic manipulation, sorry

[oblique turret]

Well I found a proof

It is for real numbers

You just have to change a few things so that it works in the complex case

[cursive rain]

I'll try using that ^^ thanks for the help .close

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[pastel cosmos]

I don't understand (G:H) = |G|/|H| if G is finite

doesn't |G|/|H| mean the number of all cosets?

But (G:H) means the number of "left" cosets

I'm confused

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@pastel cosmos Has your question been resolved?

[pastel cosmos]

<@&286206848099549185>

[royal gust]

|G| / |H| is just the number |G| divided by the number |H|

It's indeed the same as G:H, the number of left cosets, which is also the same as the number of right cosets

[pastel cosmos]

yes therefore |G|/|H| is the number of all cosets

so then

are all left cosets also right cosets?

does there exist b in G such that aH = Hb?

oh I see

If G is divided into some cosets

In the partition, they are either all left cosets or all right cosets

Is this right?

left cosets and right cosets cannot be mixed when I make a partiton of G

[royal gust]

Not necessarily saying this. I'm just saying the following:

• The amount of aH
• The amount of Ha
  Are the same number

They need not actually be the same cosets, but you'll find the same number of cosets. This number can quickly be found as |G| / |H|

[pastel cosmos]

I see I see

Thanks for your help

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[rugged fiber]

is my steps right to evaluate this limit?

sin(4x+4) = sin(4)cos(4x) + cos(4)sin(4x)

(sin(4)cos(4x) + cos(4)sin(4x))/sin(4x) = sin(4)/tan(4x) + cos(4)

lim sin(4)/tan(4x) = sin(4)/pi/2

so final ans is 2sin(4)/pi + cos(4)

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[rugged fiber]

it looks very wrong though

is it because

tan(4x) limit doesnt exist

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[gritty solar]

yeah youre right

doesnt exist

[rugged fiber]

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[wind wedge]

I believe I got Q1 and 2 but Im struggling on 3 and 4, I dont really know what to do.

[wind wedge]

Q1 I got 1/6(sin^6(x)) + 2x^3 + 1/3 e^3x + C

and Q2 I got 1

Idk of those two are even right

I have this as an example

but its not the same I dont think

unless L3 means 3 rectangles?

<@&286206848099549185>

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[native valve]

guys someone help me with this please

[native valve]

bro first one iseasy

1st eqn, 3x+3=4y+8
so 3x-4y=5

but the 2nd one is weird

cnt i write (1/2)3+x to the power of 2 cuz 1/2 squared is 1/4

so 6+2x=3y

[robust mulch]

you plug in (1/2)^2 into 1/4

so you have it flipped

[native valve]

bro but why, techincally 1/2)^2 is 1/4

[robust mulch]

yes

so where should you put the (1/2)^2

[native valve]

wait that feels correct but is wrong

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[abstract summit]

i'd use ${(\frac{1}{2})}^{3+z}={(\frac{1}{2})}^{2*(3y)}\
3+z=2*(3y)$

[robust mulch]

3?

*3y?

[soft zealot]

nico

[robust mulch]

also its x

not z

but yeah

[abstract summit]

yeah...

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[tropic birch]

My goal is to model the relationship between the track the front wheel produces and rear wheel of a bicycle in terms of functions. I have used a tractrix formula and derived it and found a paper online who had the following function but gloss over how they found it. How do I arive at that function from the tractrix function? This is what im stuck at -

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[vital crag]

don't open multiple channels

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[tropic birch]

I dont see my other channel sorry

[vital crag]

look in your history

[tropic birch]

nvm found it thank you .close

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[tranquil pine]

.reopen

[karmic needle]

How do i make a equation of a circle out of 3 points

[karmic needle]

nm figured it out

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[steel ether]

The arithmetic mean of the number of employees per floor in a given commercial building is equal to 45 employees. The first two floors of this building will undergo renovation and the employees on these floors will
will be distributed across the other floors. If during
reform, the arithmetic mean of the number of employees
per floor that is not under renovation will be equal to 50
employees, the number of employees in this building is...?

[neon slate]

consider two unknowns, total number of employees, call it T and number of floors, call it n, can you write two equations relating these two quantities from the given info?

@steel ether ?

[steel ether]

T = (A1 + An) . n / 2 The total number of employees is the sum of A.P.?

[neon slate]

if we have n floors and there are an average of 45 people per floor, how many total people?

i'm not sure what you are trying to do there, but it is a lot simpler than that

[steel ether]

I need to find the total number of employees but I just have the Middle term, basically

Can you do a step by step?

[neon slate]

so if we have n floors and an average of 45 people per floor, we have this equation for the total people:
45n = T

i think you are overthinking this

now for the case where 2 floors are being cleaned, if we have 2 less floors in that case we have how many floors in terms of n?

[steel ether]

n - 2

?

[neon slate]

yes

and we have an average of 50 people per floor

so we have 50(n-2) = T

so now this becomes easy to solve: we have
45n = T
50(n-2) = T
so we can set:
45n = 50(n - 2)

what is n?

[steel ether]

20

[neon slate]

yeah exactly, so the question is asking for the total number of people which is T, now we can finally solve for T by plugging n into the first equation

T = ?

[steel ether]

900?

[neon slate]

yeah, you can double check if the number seems to make sense and we can see that yeah if we have 900 total and 20 floors then we will have 900 / 20 = 45 average people per floor
and if 2 floors are getting cleaned, we have 900 / 18 = 50 average people per floor, numbers seem to check out

[steel ether]

Awesome! Thanks a lot for help!

[neon slate]

sure just remember this relationship between total = number of containers x average

in this case the floors are the "containers"

!done

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[steel ether]

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[tranquil pine]

hiiii

[tranquil pine]

“The position function of an object moving along a straight line is represented by the
function s(t) = 2t^3 - 3t^2 - 36t + 6, where t
is in seconds and s is in metres.”
When is the object slowing down?

do i just use inequalities here?

idk

fixed

[tiny gorge]

look at the sign of the appropriate derivative?

[tranquil pine]

wdym by sign?

6t^2 - 6t - 36

[tiny gorge]

whether it's positive or negative

[tranquil pine]

positive?

[neon slate]

what does slowing down mean? what is happening with the velocity?

[tiny gorge]

which derivative tells you whether the object is slowing down or speeding up?

[tranquil pine]

when its below zero?

oh whoops

[neon slate]

if i am going 60 miles an hour and slowing down to 40 miles an hour in my car, is my velocity negative at any point?

[tranquil pine]

when acceleration drops below zero then

okk

[tranquil pine]

but on desmos after t = 0.5 it goes up

so its slowing down bsckwards?

the acceleration goes up

[tiny gorge]

,w second derivative of 2t^3 - 3t^2 - 36t + 6

[soft zealot]

Results provided by WolframAlpha

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

Requested by bungo.the.original

[tiny gorge]

is it speeding up or slowing down when t < 0.5?

[neon slate]

you might have to consider signs here since for example if something has velocity in the negative direction and the acceleration also has a negative sign then technically it is "speeding up" in the negative direction

[tiny gorge]

yea this is rather poorly worded

[tranquil pine]

velocity is going down right?

so when less then 0.5

speeding up

[tiny gorge]

should probably be examining the derivative of |v(t)|

[neon slate]

yeah, something like that or look for cases where: v is positive and a is negative OR v is negative and a is positive

[tranquil pine]

how would i show this on paper that it’s slowing down

a

at t = 1/2

[neon slate]

at t = 1/2, a = 0 right?

[tranquil pine]

like with math

[tranquil pine]

yes

[neon slate]

so at that instant it isn't slowing down, the reason you solve for that is because you want to examine intervals on either side of that, since you are working with polynomials which are continuous everywhere we know that the sign of a will not change for the interval t < 1/2 and it also won't change on the interval t > 1/2

so you can pick some random t in either of those intervals and use that to know the sign for all t in the interval

this is something you would have learned in some chapter discussing derivatives and continuity and whatnot

[tranquil pine]

okay so should i plug in a t value bigger than 0 and then do v(t) * a(t)?

my teacher said when v(t)*a(t) is negative, its slowing down

bigger than 0.5

[neon slate]

that's kind of a bad way nonintuitive way (at least if you don't understand the reasoning behind it) to think of it but yeah what they are saying is what i said here in so many other words:

"yeah, something like that or look for cases where: v is positive and a is negative OR v is negative and a is positive"

basically if you are traveling in the negative direction, then slowing down means accelerating in the positive direction right?
and traveling in the positive direction, then slowing down means accelerating in the negative direction right?

v(t) * a(t) will be negative when the signs of v(t) and a(t) are NOT the same i.e. what i said above

so yeah you can do that or just check sign of v(t) and compare against a(t)

[tranquil pine]

okk so i plug in 0.5 for both and compare

ok

[neon slate]

no...i...don't have energy for this rn 😛

[tranquil pine]

ok i will reread then

ty tho

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[clever lagoon]

What did I do wrong

[minor nexus]

you want to bring 5 to the other side to make it equal to 0#

[tawdry storm]

You're missing an x = 0

[tawdry storm]

That, too

[clever lagoon]

Oh I didn't know I'm supposed to do that

[tawdry storm]

Also, you've written out your work incorrectly... one sec

This makes it look like you're multiplying (x^2-x) with (3x-3)

The end result would have a 3x^3, which is why I thought you were missing an x=0

(you aren't, by the way - but the ones you have are wrong, because of the 5 mentioned earlier)

Also, why did you separate your 2x into -1x and +3x?

To get them back together, you'd need an addition sign here..

one set of parentheses butted up against another is for multiplication, not addition

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[tranquil pine]

Hi so I got the correct magnitude and angle but the answer says above the horizontal. Using component method how would I know the it’s above the horizontal

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[vocal grove]

the left one has the right values

[vocal grove]

how do i solve this?

<@&286206848099549185>

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[rotund ruin]

Any good way to solve #39 mentally?

[final tangle]

do you know trig/ ratios of sides of special triangles

[rotund ruin]

No, do u need trig for this?

[final tangle]

no, you don't but its one of the simplest ways to do it mentally if you do

[rotund ruin]

Oh ok

Could u show me? I’m learning trig in school in the next few wks so I wouldn’t mind learning

[final tangle]

look up special triangles

[rotund ruin]

Ok

I get the idea now, thanks!

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[pale spindle]

Hellooo

[pale spindle]

Can I get help on this one please

[static fractal]

you can subtract the curve from the line, which is the same as translating it up

then its just a normal disc integral

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[barren hound]

@ember zodiac Has your question been resolved?

[lofty gazelle]

just wanna say u made me think i opened a channel lmao

[heavy plaza]

:o hows the wife biggus

[warm python]

is your username a monty python reference ?

[trail mango]

my favorite scene

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[clever lagoon]

Don't you have to make one side =0 so you would subtract 3??

So that means the rest of it is wrong

so how am I going to see what they did "right" if they messed up in the first line

[pallid basin]

because x^2 is the only instance of x in the problem youre able to directly solve for x rather than factoring

this is probably a better explanation actually

[clever lagoon]

I know how to do the math but I dont understand when

Cause like idk when I have to isolate the x or isolate the 0 or make the square root variables for the final line

Like it could go 4 different ways

[pallid basin]

so like if you had for example

ax^2 + bx = -c

you would watch to move the c over and set everything equal to zero

(ax^2 + bx + c = 0)

because x appears twice in the problem and theyre not like terms so they cant be combined

bx + c = 0

you would want to move the c over (bx = -c)

and then divide both sides by b to find x

idk if that was clear because the variables make it slightly confusing

lets say you have x^2 + 5x - 6 = 0

[clever lagoon]

Can you put it in numbers

[pallid basin]

in this case you wouldnt want to move anything around because you have 2 instances of x that arent like terms

[clever lagoon]

I dont understand this ajy+494

[pallid basin]

what specific part do you not understand?

i can try to like better explain it

[clever lagoon]

Okay so why dont I make it =0

[pallid basin]

so in your specific problem

-4x^2 + 19 = 3

so do you see how like

theres an x^2

and thats the only time that any variable appears in the problem

[clever lagoon]

I made it 0

[pallid basin]

ohh okay so

youre essentially adding an extra step

[clever lagoon]

oh and I forgot the x squared

[pallid basin]

so do you see how in step 1 you initially subtracted 3 to make the equation equal 0

[clever lagoon]

yeah

[pallid basin]

instead of that you could have subtracted 19 from both sides

which would have gotten you to the same place you are at in step 3

[clever lagoon]

oh

[pallid basin]

do you see what im saying

[clever lagoon]

Yeah

I did this at the end

How would I make it x=-2 and x=2 though

Make the 4 negative?

[pallid basin]

so basically

im not sure how to like explain this super well

but

if you square 2 what do you get

4

[clever lagoon]

1.414

oh

not square root

4

[pallid basin]

yes okay so

if you square

-2

what do you get

[clever lagoon]

4

[pallid basin]

so everytime you take the square root of a number

the answer is positive or negative

because both -2^2 and 2^2 equal 4

[clever lagoon]

Oh

That makes sense

[pallid basin]

also

i dont know if youre doing cubing as well

but

for like

even roots (square root, fourth root, sixth root, etc.)

the answer is pos or neg

[clever lagoon]

For each cube is an equal amount of variables as well right

[pallid basin]

but that rule doesnt apply to odd roots

[pallid basin]

wdym

[clever lagoon]

if its ^3 theres 3 x's

what my math teacher said

[pallid basin]

can you give like an example of what youre sayig

saying*

[clever lagoon]

x^3-4x^2-9x+36=0

You automatically know its cubed cause theres 3

3 x's

[pallid basin]

you automatically know that its cubed because the highest exponent is 3

[clever lagoon]

oh

This problem looks like sooo much fun

[pallid basin]

do you need help w/ that one as well or do you know how to do it

[clever lagoon]

im trying to do it right now

[pallid basin]

alright if you get stuck lmk

[clever lagoon]

Is this right

since theres no perfect square in the square root of 27 it just stays

Hope I did it right

Wait it asks for x=

I dont think I did it right

[pallid basin]

9 * 3

[clever lagoon]

oh

9 is 3

So

[pallid basin]

7 - 3x = sqrt27
7 - 3x = 3sqrt3

the way i was going to work it was

[clever lagoon]

3 times square root of 3 is like 5

[pallid basin]

wait okay r u allowed to use a calculator

[clever lagoon]

ya

[pallid basin]

alright

i was doing it like

(7-3x)(7-3x)
49 - 21x - 21x + 9x^2
49 - 42x + 9x^2
9x^2 - 42x + 49 - 27 = 0
9x^2 - 42x + 22 = 0

[clever lagoon]

Isnt squared just cancelled

so isnt square root of 7-3x^2 just 7-3x

[pallid basin]

yes

[clever lagoon]

So how is that wrong

[pallid basin]

the way youre doing it isnt wring

wrong

[clever lagoon]

Is it 3 times square root of 9

[pallid basin]

i just think it might be more complex

[pallid basin]

wdym

[clever lagoon]

I dont undestand like the number times square root stuff

And idek how to get the answer to this

It says x=

Idk how im going to get square root of 27 out

[pallid basin]

okay so

youre original equation was
(7-3x)^2 - 27 = 0

so

if youre wanting to do the square root method

you would move the 27 over

[clever lagoon]

I did that

[pallid basin]

(7-3x)^2 = 27

yes

and then sqrt both sides

[clever lagoon]

i did that

[pallid basin]

7-3x = sqrt27

yes

and okay so

with sqrt27

within 27 theres 9 which is a perfect square

so that gets to come out of the radical

sqrt of 9 is 3

so we bring a 3 out

[clever lagoon]

wait what

So the 3 just disappears

[pallid basin]

no okay so

basically

sqrt27

is the same thing as

sqrt(9*3)

do you see why

[clever lagoon]

no

[pallid basin]

9 times 3 is 27

[clever lagoon]

but if you square 9 and 3 it doesnt equal 27

[pallid basin]

well like

sqrt27 = sqrt(9*3)

if you ignore the sqrt

27 = (9*3)

right

[clever lagoon]

ya

[pallid basin]

so if you put the sqrt back its still true

[clever lagoon]

ookaayy

[pallid basin]

does that make sense

[clever lagoon]

well what do I do with the 27

I know its 9 and 3

[pallid basin]

so okay

because its 9 and 3

so we have

sqrt(9*3)

well we can take the square root of 9

and get 3

[clever lagoon]

Square root of 9x3 is 5.196152423

[pallid basin]

dont multiply them back

we started with sqrt27

and we said okay well 9*3 equals 27

right

[clever lagoon]

oik

[pallid basin]

so we have sqrt(9*3)

so

we can take the sqrt of the 9

and get 3

rigt

right*

[pallid basin]

yes 27 is 333

ok it

ok discord made it odd

3 times 3 times 3 is 27

yes

so when we have sqrt(9*3)

if we take the sqrt of the 9

and we get 3

we can now take that 3 out from under the sqrt

so we now have

3sqrt3

do you see how i got there

[clever lagoon]

So you took the 3 out

Which one

theres 3 of them

[pallid basin]

well ok so

sqrt(27) = sqrt(9*3) = sqrt(3 times 3 times 3)

right

all the same thing

[clever lagoon]

yea

[pallid basin]

so

square root

when you square something you raise it to the second power

right

[clever lagoon]

yeah

[pallid basin]

so second power

2

those go together

right

[clever lagoon]

yeah if you take a number square it and then square root it is the same

[pallid basin]

okay so like

2 goes with squaring

[clever lagoon]

4

[pallid basin]

3 goes with cubing

do you get what im saying

[clever lagoon]

yeah

[pallid basin]

like the number goes with the word

okay we want the square root

and we have 3 3s

so

we can take 2 of those 3s

out

because

squaring goes with the number 2

so u need a group of 2 of the same number

[pallid basin]

do you get what im saying

[clever lagoon]

I took 2 out

now what

[pallid basin]

we took 2 of the threes and moved them outside of the radical

[clever lagoon]

I dont think its supposed to be this deep

im in 9th grade

if this was what it was actually about none of my class would know a thing

[pallid basin]

this is in fact what youre doing 😭

i did pass ninth grade

[clever lagoon]

3 times the square root of 3 is 5

So how do that equal (3x3)x3

[pallid basin]

ok the parentheses are to show that that is a group of 2

ok so like

normally in math

if you have a number that isnt a perfect square

like 3

and you have that as a part of your solution

unless they say to give it in decimals

they normally want you to just leave it as sqrt3

okay

[clever lagoon]

yeah

[pallid basin]

so thats why you have to simplify the radical

[pallid basin]

instead of doing

[clever lagoon]

Bro my teacher cannot be real

[pallid basin]

okay wait what r u confused on ab this

[clever lagoon]

How to solve square roots that arent perfect

Like if it got square root of 36

What do I do

[pallid basin]

okay 36 is a perfect square

so its just positive or negative 6

[clever lagoon]

what the hell

3 times square root of 3 is 5

So 7-3x is like

7-3(5.1961)

[pallid basin]

3 times square root of 3 is just 3 times square root of 3

because they dont want you to make it into a decial

decimal

they want you to leave it as 3 times square root of 3

[clever lagoon]

But how does that equal 27

[pallid basin]

it equals square root 27

not 27

[clever lagoon]

cause 3x3=27

or cause

[pallid basin]

no

[clever lagoon]

i'd have no idea

[pallid basin]

3 square root 3

okay

so

to put that 3

that is on the outside

back under the radical

you have to square it

because square and square root are opposites

[clever lagoon]

under?

[pallid basin]

back into the root bar

back under the root bar

whatever word

idk

[pallid basin]

no

hold on

you have to square the outside 3

to put it back inside

[clever lagoon]

wait

that makes sense

Now how do I get that from square root of 27

Like if I got 3 times 9

then 3 x 3

[pallid basin]

u see the 9 and the 3

right

[clever lagoon]

ya

[pallid basin]

in my pic u see 9 and 3

and the little dot between them

that means multiply

9 times 3

[clever lagoon]

wait a second

[pallid basin]

27

[clever lagoon]

So the answer of square root of 27 would be 9 square root of 3

Is this right

[pallid basin]

it would be 3 square root of 3

[clever lagoon]

why

[pallid basin]

you did step 1 right

[clever lagoon]

that would be 9

[pallid basin]

3 square root three

we just said

to get the outside three

back on the inside

we have to square it

right

so then we have 9 • 3 on the inside not 3 • 3

[clever lagoon]

cause 9 square root of 3 would be 81 x 3

[pallid basin]

step 1 is correct
step 2 you should have divided both sides by negative 4, and gotten x^2 = 4
and then you would take square root of both sides

[pallid basin]

9 square root of 3 would be the square root of 81 * 3

[clever lagoon]

I thought we have to square both sides

[pallid basin]

wdym

[clever lagoon]

or is that only when it has parenthesis

[pallid basin]

wdym

[clever lagoon]

When its like ex : (x+x)^2

You got to square root both sides

to get rid of the square

[pallid basin]

whats the other side

[clever lagoon]

Idk its just an example

[pallid basin]

well like

[clever lagoon]

Like if it has parenthesis

I have to do the square root to both sides

[pallid basin]

if u said (x+y)^2 = 4

[clever lagoon]

but if it doesnt then I dont because it doesnt habe the parenthesis

[pallid basin]

then yes ud sqrt both sides

if it doesnt have parentheses

wdym like if it said x+ y^2 = 4

[clever lagoon]

Then you would subtract x

[pallid basin]

mhm

[clever lagoon]

You would not have to do square root

Cause theres no parenthesis

[pallid basin]

well like

if u were trying to solve for y

you would subtract x from both sides

and get y^2 = 4 - x

and then sqrt both sides

[pallid basin]

y = 2 - sqrtx

[clever lagoon]

This has got to be right

Cause 1x2 = 2 x2 = 4

so square root of 4 is 1 square root of 2

Its got to be

[pallid basin]

the square root of 4 is 2

[clever lagoon]

Is that the same thing

[pallid basin]

no

[clever lagoon]

How?
Cause thats2x2

[pallid basin]

1 square root 2 is the same as square root 2

[clever lagoon]

And you get 2x2 once you get it on the inside

[pallid basin]

okay if you have sqrt4

[clever lagoon]

How??

[pallid basin]

2 times 2 is four

right

[clever lagoon]

id hope so

[pallid basin]

okay so

[clever lagoon]

oh wait

1x1 is not 2

nvm

[pallid basin]

okay like

sqrt4

2 times 2 is 4

yes

okay

so

sqrt4 = sqrt(2*2)

right

[clever lagoon]

uh huh

[pallid basin]

so we have a pair of twos

do u see that

[clever lagoon]

where

[pallid basin]

look at the yellow parentheses

pair of twos

[clever lagoon]

Oh yeah I see tyhat

How did they go from -4x^2 to -2x

Why didnt they just divide by -4

then it would be x^2=4

then square root both sides

[pallid basin]

they did that wrong

[clever lagoon]

to get x=-2, 2

[pallid basin]

they should have divided by -4

[pallid basin]

ok so because we have a pair of 2s

they get to leave the radical

and then theres nothing left under the radical

so we just have

2

the answer is just 2

sqrt4 is 2

[clever lagoon]

Yeah

That makes sense

[pallid basin]

woooo

[clever lagoon]

This wording is so dumb

[pallid basin]

it is kinda wack

[clever lagoon]

" Took the square root of a negative value on each side of the equation "

Wow a negative value that really helps

[pallid basin]

you cant take rhe square root of a negative

[clever lagoon]

no sol

its not A

Wait

it could be A

But it says select the errors the student made

But answer A says the student should have

so how does that make sense 😭

[pallid basin]

its not A

[clever lagoon]

i dont get B

Cause you cant take negative square root

[pallid basin]

yes correct

so if the student tried to do that

then that would be something they did wrong

[clever lagoon]

C is wrong

[pallid basin]

because you cant do that

[clever lagoon]

Cause they are multiply by -2 not 2

[pallid basin]

its not C

[clever lagoon]

its gotta be D and E

nvm

[pallid basin]

B is right

and E is right

[clever lagoon]

HUH

Oh its asking for their errors

not what they should have done

Wait I got x=2,-2 by myself

[pallid basin]

yes

the right answers r 2 and -2

[clever lagoon]

should be light

[pallid basin]

okay so u move 18 over

and take the square root of both sides

u get that right

[clever lagoon]

Yeah im trying to do square root of 18 rn

[pallid basin]

so

what numbers

multiply

to make 18

[clever lagoon]

3 6

[pallid basin]

okay so

[clever lagoon]

but since none of them are perfect squares its kept the same

[pallid basin]

no

okay so

3*6

3 is prime right

yk that rifht

[clever lagoon]

no

but continue

[pallid basin]

okay so

u can only make 3 by doing 3*1

right

[clever lagoon]

ya

[pallid basin]

but to make 6

what can u do

[clever lagoon]

1 2 3

[pallid basin]

aside from 6*1

what two nums can u multiply

to make six

[clever lagoon]

23

2 3

[pallid basin]

yes

okay so

since 3*6 is 18

3*3 times 2 is also 18

do u see how i got there

[clever lagoon]

Yeah

[pallid basin]

so

we have

sqrt(3 • 3 • 2)

do u see how we got there

[clever lagoon]

yeah kind of

[pallid basin]

okay so what do we have a pair of

[pallid basin]

yes

so when we have

sqrt(3•3•2)

what number do we have a pair of

[clever lagoon]

3s

[pallid basin]

yes

so they get to leave the radical

[clever lagoon]

so 3 square root of 6?

oh nvm

[pallid basin]

3 square root 2

[clever lagoon]

ooh

[pallid basin]

do u understand

[clever lagoon]

yeah

[pallid basin]

how we got there

woooo

okay so we have

[clever lagoon]

Alright alright

[pallid basin]

7 - 3x = 3sqrt2

rifht

[clever lagoon]

yeah

[pallid basin]

whats it asking u to do

[clever lagoon]

x=

so

wait a second

Do i subtract 7

and leave it alone

[pallid basin]

if u subtract 7 from both sides

u get

-3x = 3sqrt2 - 7

right okay

u understand how i got there right

[clever lagoon]

Yeah I did it before you typed it

what abt that scary -3

[pallid basin]

so now u need to divide both sides by -3

which im gonna write out

hold on

[clever lagoon]

How lovely

[pallid basin]

yes

but ud right it like that

because

wait

yeah ok

[clever lagoon]

isnt that just 7/3

2 negatives

[pallid basin]

yeah its just + 7/3

but um

[clever lagoon]

ok

[pallid basin]

the other part

u can divide 3 out of the top and bottom of the other fraction

do u see that

[clever lagoon]

yeah

[pallid basin]

it would make it jus

t

• sqrt2

negative

sqrt2

[clever lagoon]

yeah

what if it was like divide by -4

What would you do

[pallid basin]

then youd just leave it as -3sqrt2/4

[clever lagoon]

alr

So it turns into

[pallid basin]

so u have