help-10

[distant moth]

Have u done this?

[devout warren]

Because the inside of the square root will always be negative

What do you mean by a square common?

[distant moth]

Like x^2-a^2= a^2( (x^2/a^2)-1)

And then a ^2 comes out of the sq root

[devout warren]

I tried that before but it got me nowhere

[distant moth]

Trust me it works

[astral mantle]

use the sub x= a sec u

and see where it takes u

[distant moth]

Would that be more direct 🤔

[astral mantle]

wait no hold on

[devout warren]

@distant moth I tried your method

[distant moth]

Where did u end up

[devout warren]

But where do I go once I take it out?

[distant moth]

Then inside the square root there shud be a

(x/a)^2 term

Take x/a=p

And then it should work out

[devout warren]

Well now I get 1/xa*sqrt(p^2 -1)

But I have 3 unknowns

[distant moth]

but x/a=p

Can u show ur work

[distant moth]

U need to replace dx

x/a=p, find dp

[devout warren]

Dp is 1

So it's the same as dx

[distant moth]

dp isnt 1

x/a=p
dp/dx = 1/a
dp= dx/a

[devout warren]

Yeah I'm being braindead

[astral mantle]

my trig sub still works btw

if u want to try another approach

[devout warren]

X = asecu?

[astral mantle]

yeah

[devout warren]

Give me one moment I'll try it I'm in the car atm so it's hard to work anything out but I'm home in a min

[astral mantle]

okay np take ur time

[devout warren]

@distant moth I've expanded yours further to get this:

Is that looking right?

@astral mantle also what made you want to use a sec substitute instead of a cos or sin sub

In the previous questions for me I've only had to sub in either sin or cos or tan

Never sec or csc or cot

[astral mantle]

rmb the trig identity (tanx)^2 + 1 = (sec x)^2

[devout warren]

Yes

Ohh

Sex^2 -1 is tan^2

I didn't spot that

[astral mantle]

yes

[devout warren]

I was trying to get it to work with cos

Lol

[astral mantle]

and when u usub and get du

everything cancels out nicely

[devout warren]

But then I'd get cos^2 -1 which is -sin^2

Also when you differentiate sec

Is that the same as differentiating 1/cos

[distant moth]

Yes this is the derivative of an inverse trig function

[astral mantle]

yes it is

[distant moth]

If u dont know which one, memorize all of them id say

[astral mantle]

one good tip would be to memorize the derivatives of sin cos tan csc sec cot so that u can easily sub in when needed

when u see integrals with sqrt(a^2-x^2) or smth similar, using a trig sub is likely one way to find the answer

[devout warren]

Wait which one is it? It isn't sin because the sqrt would have (1-p^2), or cos for the same reason, nor tan

[distant moth]

Its sec inv derivative

[devout warren]

Ohh we haven't learned about those yet

[distant moth]

Actually the sec inv derivative the outside p would have an absolute value, but my teacher said to not worry about that during indefinite integration

[devout warren]

I will do, thank you!

[devout warren]

Ahh awesome got it

Thank you both for your help I really appreciate it

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[timid silo]

this is sort of a part 2 of my question (my question is on #help-3). So how do I get the x1 and x2 of the quadratic equation?

[kind hawk]

well if would be better if you didnt make us scroll through that channel to find what you are talking about

either repeat the whole question or give a link

[timid silo]

sorry sorry

[untold zenith]

if you are leaving it in the exact form you already have both roots

[timid silo]

so -3 + sqrt of 57 / 2 and -3 - sqrt of 57 / 2?

[untold zenith]

that is one

remember you had a ±

[timid silo]

ops wrong sign. let me change it

[untold zenith]

yea those would be the two roots

[timid silo]

thanks!!!

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[leaden turtle]

Whats the name of the formula being used on the right hand side?

[cedar lichen]

Law of cosines

[astral mantle]

law of cosines

[cedar lichen]

I assume that's what you're referring to

[leaden turtle]

oh i think thats the one

thanks

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[flat kestrel]

Hello, I am having trouble with the attached question

[astral mantle]

what happens when x=4?

[flat kestrel]

Then the function doesn't really exist

[versed cave]

(consider the numerator too)

[flat kestrel]

Since it's 0/0

The limit exists though, it's 1/8

Wait got it

That's the answer

Thanks

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[obtuse pebble]

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[flat kestrel]

Hello again, I am having trouble finding the domain of this function. I was able to find that t>sqrt(2) that way we don't have ln(0), but I don't know what to do beyond that.

[tranquil arch]

$2+t^2>0$ for all $x$ in $\mathbb{R}$, so the domain is $\mathbb{R}$

[warm shale]

秋水

[fierce lagoon]

^

[flat kestrel]

Wait what? I don't understand

We can't have 0 or lower in the ln()

[astral mantle]

t^2 is always positve

[fierce lagoon]

Yes but 2+t^2 is always greater than 0

[astral mantle]

2+t^2 is always equal or greater than 2

[flat kestrel]

Oh that would be right

[fierce lagoon]

So $\ln(2+t^2)$ is defined $\forall x$

[warm shale]

Umbraleviathan

[flat kestrel]

Gotcha, thanks

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[static echo]

ok im trusting you guys again

[static echo]

ok,, yk like this thing but opposite cuz im looking for the model instead

hm

you know what

nevermind.

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[warm olive]

could someone help me with the proof of the 1st question

[obtuse pebble]

@warm olive Has your question been resolved?

[obtuse pebble]

@warm olive Has your question been resolved?

[tardy epoch]

you mean 2?

[warm olive]

yes

[tardy epoch]

what's your definition of the inner product?

[warm olive]

< a I b > = < b I a >*

and

[tardy epoch]

that's not a full definition

what are a and b?

[warm olive]

scalars?

[tardy epoch]

don't think so

[warm olive]

oh

[tardy epoch]

go to your book/notes and share a picture/screenshot of it here

[tardy epoch]

Good

apply these two to your left hand side

expand this using the definition and properties

and this one

i guess you need to use all the properties haha

[warm olive]

the first image u sent

is the definition

?

[tardy epoch]

yes

[warm olive]

of a and b or the inner product?

[tardy epoch]

the inner product

[warm olive]

ah ok

[tardy epoch]

this is the definition of $\underline{a}$

[warm shale]

riemann

[warm olive]

that makes sense

woudlnt using the definition of a for this proof

make the question a bit more difficult

[tardy epoch]

it's not absolutely necessary, but you don't know what you're doing yet so you should use the definition

[warm olive]

ok

thank u

@tardy epoch is this correct

?

[tardy epoch]

[warm olive]

thank u smmm

:))

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[obtuse pebble]

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[hot gull]

Hi , I'm working on some elementary MacLaurin polynomials, I've got a doubt about this one:
1/(1+x^2), to be computed to the 6th grade

[hot gull]

in particular, in other cases I tried to simplify by substitution: for example instead of computing the polynomial of e^(-x^2), I substituted -x^2 with t

and then substituted -x^2 back in the MacLaurin polynomial of e^t

how should I proceed in the first case ? i.e. 1/(1+x^2) without simplifications it gets too burdensome

[tardy epoch]

just use geometric series expansion

$\frac{1}{1+y} = \sum_{k=0}^\infty (-y)^k$

[warm shale]

riemann

[hot gull]

don't know how to use this

any alternative? how would you substitute for t

[tardy epoch]

you use substitution to get it into your form

[tardy epoch]

similar to this substitution

[kind hawk]

what is wrong with just using the other trick and differentiating 1/(1+t)

the derivatives of that are easy

[obtuse pebble]

@hot gull Has your question been resolved?

[hot gull]

will try this thanks

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[grand trail]

i multiplies it by root 2

then i got root2/3

but thats the wrong answer

so what was i supposed to do??

anyone pls??

[viral blade]

did you multiply the whole thing by sqrt(2)?

or both sides

[grand trail]

wym ?

i did 1/5-root2 * root 2

OH WAIT I GET IT NOW I KNOW WHAT I DID WRONG

THANKS!!!

[viral blade]

ah np!

[grand trail]

lol

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[grand trail]

.reopen

[obtuse pebble]

✅

[grand trail]

@viral blade i was wrong...

i did ( 1/5-sqrt2) * sqrt 2

and i got sqrt 2/5sqrt2-2

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[viral blade]

.reopen

[obtuse pebble]

✅

[viral blade]

that's better

u gotta multiply by the conjugate of 5-root(2) tho

the conjugate will make it work

[grand trail]

k

ithink i got it now

thanks!

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[small rock]

Is ma + Ma equivalent to (m + M)(a^2)?

[royal shard]

no

use distributive rule

[small rock]

(m + M)(a) then?

[royal shard]

ma+Ma=(m+M)*a

yes

[small rock]

Ok for sure

[royal shard]

@opaque stag #❓how-to-get-help

[obtuse pebble]

@small rock Has your question been resolved?

[obtuse pebble]

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[agile robin]

will carry over when splitting right

[placid dagger]

hello

[agile robin]

?

[placid dagger]

idk cus im in 10th grade

[obtuse pebble]

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[hardy widget]

nice

[obtuse pebble]

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[warm olive]

how comes e1 (with hat) = (1 0)

[tardy epoch]

did you calculate $||e_1||$ ?

[warm shale]

riemann

[warm olive]

yep

its 1

[tardy epoch]

did you plug that into the formula for $\hat{e}_1$ ?

[warm shale]

riemann

[warm olive]

yes

so it becomes (1 0)/1

but how does that give

[tardy epoch]

and how do you simplify that?

[warm olive]

(1 0)

[tardy epoch]

right

[tardy epoch]

does that answer this question?

[warm olive]

can u kind of treat it like normal fraction

?

to calc ur answer

then put it back as a vector in the end

[tardy epoch]

if $\vec{v} = (v_1, v_2, ..., v_n)$ and $c\in \R$, then $c \vec{v} = (cv_1, cv_2, ..., cv_n)$

[warm shale]

riemann

[tardy epoch]

in your case, c = 1

[warm olive]

i meant (1 0) at the end

but is that a correct method

?

[tardy epoch]

yes

[warm olive]

ok

thank u very much

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[timid silo]

Could someone explain the remainder part?

[timid silo]

I don't understand the last sentence. Why is a_2017 =a_1 due to the remainder being 1?

[rigid lintel]

2017 mod 6 = 1

[timid silo]

Is there any other way of thinking about it without modular arithmetic? This question doesn't expect knowledge of that

[rigid lintel]

woops

well you know what dividing with remainder is right

thats all they do

[timid silo]

Wdym

[rigid lintel]

the remainder of 5 divided by 2 with remainder is 1

because 5 = 2*2 + 1

[timid silo]

Yep

could you please explain how that connects with this question? (Excuse my ignorance)

[rigid lintel]

well the sequence loops every 6 iterations

[timid silo]

Yeah

[rigid lintel]

so a_1 = a_7 = a_13 = a_19 = a_n*6+1

[timid silo]

yeah

I'm having trouble understanding how the remainder is useful for this question

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

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[rancid cliff]

1. How do you say in English the act of having a matrix with 0's in the bottom left

2.- Why is it so difficult to do what mentioned above when the matrix has parameters.

[rancid cliff]

I've been struggling with the same stupid matrix for the last 15 mins 😭

[timid silo]

upper triangular? https://en.wikipedia.org/wiki/Triangular_matrix#Description

[rancid cliff]

yeah

[rigid lintel]

theres some tricks you might want to know when you have variables

are you computing eigenvalues?

[rancid cliff]

what do you mean?

from the red I need to get to the blue

but idk what this guy is doing tbh

[rigid lintel]

that looks so sloppy

[rancid cliff]

idk its what I need

like I need to delete a column

[warm shale]

Chuti | Spanish

[rancid cliff]

but idk how to get to that last line :/

[obtuse pebble]

@rancid cliff Has your question been resolved?

[obtuse pebble]

@rancid cliff Has your question been resolved?

[obtuse pebble]

@rancid cliff Has your question been resolved?

[obtuse pebble]

@rancid cliff Has your question been resolved?

[obtuse pebble]

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[wicked tundra]

did this turn into a matrix

[wicked tundra]

I thought it will just be a vector in a vector

but it looks like here is a matrix

gradients make matrices?

guess I need to tell the difference between a gradient and a vector

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[timid silo]

Simple fraction question

WAIT

ya

how do u do that

cause the answer key says = 2t

but I keep getting -8

[random depot]

U sure it’s jusr 2t

[timid silo]

well its actually a whole equation

[random depot]

Ok what’s the whole thing

[timid silo]

solve by elimination

[random depot]

Ok

[timid silo]

im just confused by this part

cause we have to turn it into whole numbers

so im confused about the fraction times 6

im multiplying the first equation all by 6

[timid silo]

thats why I asked this

i keep on getting -8t instead of 2t

Multiply the whole of the first equation by 3 and then again by 2

uhuhuhuh

i thought u multiply like this
1-5 x 6

---

3 x 1

[random depot]

Multiply each term in first eqn by 6

[timid silo]

but i get -8

[timid silo]

ya thats what i dont get

how do i multiply it by the fraction

[random depot]

Factor 3 out of 6 then cancel common factor of 3

[timid silo]

It becomes 2(t-5) + 3(w+1) = 6

[timid silo]

Just expand and simplify

um

[timid silo]

i have like no idea what this means

when multiplying fractions, u multiply numerators, and u multiply denominators

SO HOW IS IT 2T AND NOT -8T

Oh

ugh nvm

u guys explained it so badly bye

i figured it out on my own

sorry

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[near mango]

Can anyone explain why a vector parallel to a plane and a point isn't enough to describe a plane?

[royal basin]

what's "the" plane passing through the origin and parallel to the vector (1,0,0)?

it could be the plane y=0.
but it could also be the plane z=0.
or it could be the plane 2y+7z=0.

or infinitely many more options

[near mango]

Sorry I don't understand why it could be the plane z=0, let me think about it for 30 seconds

Would it not be perpendicular?

Like if I have a line on the Z=0 plane, would that line not be perpendicular to the x axis?

[royal basin]

no

not necessarily

it could make any angle with the x axis

[near mango]

Wait i get it now

Thanks a lot lol

[royal basin]

the plane z=0 contains both the x and y axes

[near mango]

Got it, thanks for your help 🙂

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[south dome]

Q.29

[obtuse pebble]

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[winter oxide]

So there's this question in my math textbook
Maxwell earns a monthly salary of $4580 as a web developer. He is paid bi-weekly. How much is each pay in a 2-pay month? How much is each pay in a 3-pay month?
The answer in the back of the book is listed as $2113.85 for both the 2-pay month and 3-pay month (I assume the answer is gross pay as the textbook doesn't state otherwise)
I initially thought splitting the monthly salary evenly across each pay would work ($4580 / 2 for the 2-pay month for example), but it looks like I'm wrong. I'm not sure how the textbook got that answer
Is there something I'm missing? Are monthly salaries not split evenly when paid biweekly?

[winter oxide]

(Also that is the textbook wording exactly)

[obtuse pebble]

@winter oxide Has your question been resolved?

[winter oxide]

<@&286206848099549185>

[viral blade]

there's a little bit more than 4 weeks in the average month

still don't know if we're supposed to account for leap years

ig probably not?

[winter oxide]

Is that what the question is asking for?

[viral blade]

seems to be

otherwise there would be no 3-pay-months

[winter oxide]

huh

I would never have gotten that

[viral blade]

ye its a bit weird

[winter oxide]

I thought the question was asking for the amount of each pay in an example 2 pay month and an example 3 pay month

Thank you!

.close

[obtuse pebble]

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[viral blade]

np!

[obtuse pebble]

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[rancid cliff]

Who wants to tell me if my intersection of the plane is correct

Plane 1 : 2x + y + 2z = 4
Plane 2 : x - y + 3z = 5

Ans: k(-5, -12, 1) + (9, -14, 0)

[stable rain]

whats

working

[fossil crag]

The point (9, -14, 0) is not on plane 2 so it cant be in the intersection

[devout sable]

u can just ask wolfram

[fossil crag]

The only way you can solve this easily is :

1. Find all (x,y,z) that satisfy :
   2x + y + 2z = 0
   x - y + 3z = 0

[devout sable]

,w intersection of plane 2x+y+2z=4 and x-y +3z=5

[rancid cliff]

oh

[fossil crag]

Then, find a single triple (x0,y0,z0) that is in the intersection

[rancid cliff]

why = 0?

[warm shale]

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[fossil crag]

Because then you can "translate" by a particular solution

[rancid cliff]

well but the plane isnt equal 0

[fossil crag]

If you find all (x,y,z) that satisfy this, then find a particular (x0,y0,z0) on both planes (for example z0 =0), then all of the points on the intersection of planes are of the form (x+x0,y+y0,z+z0)

[rancid cliff]

I cant randomly change the result of the plane 🤷‍♂️

[fossil crag]

It works though

[rancid cliff]

for every plane in the world?

[fossil crag]

Yes

[rancid cliff]

cant I do it with the original plane?

[fossil crag]

You can, it's a bit more painful though

[rancid cliff]

so in that case

how would I solve the thing?

shouldnt be difficult to find the intersection between two planes but I clearly dont know

[fossil crag]

The solutions of this are of the form k(-5,4,3) with k any real number

[rancid cliff]

but I dont want to use = 0

I want the original plane if possible

[fossil crag]

Well, let's start from here

[rancid cliff]

ok

[fossil crag]

First : simplify the 2nd equation by the variable y. To do this, you keep the first equation as is, but you replace the second equation by "the first equation + the second equation"

[rancid cliff]

ok 1 sec please

y = -5 + 3z + x

[fossil crag]

Ok why not

Then ?

You have to substitute this value of y into the other equation

In the equation of the first plane, you can now replace "y" by "-5 + 3z + x"

[rancid cliff]

ok 1 sec please

for the moment I did the exact same thing

it gives me

x = (9-5z) / 3

now I replace that x in y = -5 + 3z + x right?

so that everything is z based

[fossil crag]

Ok but can you write down the steps just to make sure

[rancid cliff]

what do you mean by write down the steps 🤔

I mean

stupid question ik but I dont get it 🤣

I'm just replacing

[fossil crag]

Well just to make sure you didn't make any mistakes while calculating

[rancid cliff]

k

[fossil crag]

But I believe you, x = 3 - 5z/3

Then ?

[rancid cliff]

x = (9-5z) / 3

[fossil crag]

Yes, that's the same thing

9/3 = 3

[rancid cliff]

okay 🙂

yeah

u right

[fossil crag]

So afterwards ?

[rancid cliff]

I replace x in y = -5 + 3z + x

so I have now

y = -5 + 3z + (9 - 5z)/3

right?

[fossil crag]

Yep

Yes

[rancid cliff]

k

[fossil crag]

Now simplify

[rancid cliff]

1 sec

y = -2 + (4/3)z

[fossil crag]

Yessir

[rancid cliff]

so now I have the intersection right?

[fossil crag]

So let's recap :
x = 3 - (5/3)z
y = -2 + (4/3)z

And the final touch is to add z=z

[rancid cliff]

x = (9-5z)/3
y = -2 + (4/3)z
z = z

so the intersection is the following line

param(-5/3, 4/3, 1) + (3, -2, 1)

I did something wrong before

hahaha

[fossil crag]

Yes, and there is still one last thing

[rancid cliff]

whats that thing ? 🤔

[fossil crag]

z = 0 + z, not 1+z

[rancid cliff]

ohh thats right!!!!

omg

haha

my exam is in 1 hour 30 mins lmaoo

hahah

okok

thanks a lot rafilou

[fossil crag]

So the easiest point to find on the line has which coordinates ?

No problem

[rancid cliff]

with param = 1

(-5/3 + 3, 4/3 - 2, 1)

thats the easiest point

[fossil crag]

Nah, with z =0 is easier xd

[rancid cliff]

right lmao

the easiest point is (3, -2, 0)

[fossil crag]

Yep

[rancid cliff]

nice man

amazing

thanks a lot again

[fossil crag]

You're welcome :)

Good luck on your exam !

[rancid cliff]

haha thanks!

.close

[obtuse pebble]

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[obtuse pebble]

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[honest basin]

i'm doing an experiment to determine sodium in mg/100g bread. to find this standards were made and two bread samples prepared. bread samples were prepared by crumbing 5g of bread and adding it to 200mL of 1% HCL which was stirred on a magnetic stirrer for 30 minutes., then filtered under vacuum and filtrate collected. This was done in duplicate. I will just use 1 of the bread concentrations

From the standard curve line equation I got a concentration for 1 of the samples of 5.0630ppm or 5.0630ug/g. So i need to work this out from the dilution that was done above. Then 4mL of that filtrate was taken and diluted to 100mL using distilled water. So once the first part has been worked out I then need to work out what it would be from diluting 4mL with 96mL of distilled water. The final answer needs to be in mg/100g

[stable rain]

OMG

u actually did experiments?

[honest basin]

? lol

[stable rain]

ok well

i tried to read thru

but

thrs a bit too much stuff

maybe look up

dimensional analysis

[honest basin]

no worries, ty 🙂 yeah, my head is exploding haha

[stable rain]

aite

🥣

[honest basin]

do i close?

[obtuse pebble]

@honest basin Has your question been resolved?

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[hot storm]

How do I solve this

[hot storm]

The calculator doesn’t have steps

It’s not hw or exam

Also teach me how to solve not just give me the answer

<@&286206848099549185>

[tranquil quiver]

what does the subscript n mean

[hot storm]

It’s 1

It’s for Reuman hypothesis

[tranquil quiver]

ohh its the base of exponent

[hot storm]

Oh makes sense

Can u give me steps and teach?

Not professional teaching

[tranquil quiver]

what exactly do you want to be taught

[hot storm]

How to solve the equation

Delta formula shown with any s value

The big number is the s

@tranquil quiver

[tranquil quiver]

no idea sorry

[obtuse pebble]

@hot storm Has your question been resolved?

[obtuse pebble]

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[timid silo]

GUys, how is it that -2^2 = -4 BUT (-2)^2 = 4?

[brisk matrix]

-2^2 = -(2^2)

(-2)^2 = (-2)*(-2)=4

[honest cliff]

😑

[mint tendon]

monke

[honest cliff]

Y s

Yea*

[timid silo]

OHH lol

so easy

thanks

this is igcse level

so hard

.close

[obtuse pebble]

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[honest cliff]

Nooo

[timid silo]

.reopen

[obtuse pebble]

✅

[timid silo]

guys pls help me another question

[timid silo]

Whats the asnwer for part 2?

[timid silo]

?? i got part 1 whats part 2? I got 3 but idk

[honest cliff]

Idk lol

[timid silo]

nvm its correct yeah?

[brisk matrix]

it’s $\pm 3$

[timid silo]

i think correct

[warm shale]

maximo

[timid silo]

WHAT

[timid silo]

why is it +-?

[brisk matrix]

when you take the square root like that you create other solutions

you arrive at $9=t^2$

[warm shale]

maximo

[brisk matrix]

3^2 = 9 = (-3)^2

[timid silo]

whatt

[timid silo]

what i did when i got 9 = t^2 was

squareroot9 = t^2

squareroot of 9 is 3

so t = 3?

but how is it plus and minus

[brisk matrix]

it becomes $\sqrt{9} = \sqrt{t^2}=|t|$

[warm shale]

maximo

[brisk matrix]

so |t| = 3

[timid silo]

whats the /t/

[brisk matrix]

t = 3 or -3

absolute value

[timid silo]

|t|

ok

Omg i stil dont understand why its + or -

please

[brisk matrix]

this is why

when you take the square root

you dont get t

you get |t|

[timid silo]

i did not understand the |t|

[brisk matrix]

it’s the absolute value of t

[timid silo]

isnt t alreadey the absolute vcalue omg idk

i never learned about absolute value

[brisk matrix]

|x| makes x positive

so like

|-3| = 3

|-10| = 10

|4|=4

[timid silo]

in the asnwer box if i write the asnwer just: t = 3 will i get mark..?

[brisk matrix]

not sure, but the only answer isn’t t = 3

[timid silo]

ok

thanks

... i didnt understand but thanks

[brisk matrix]

which part

[timid silo]

On how its +3 or -3

wait

ill tell u my working out:

47 = 5t^2 + 2

i take away 2 from both sides

45 = 5t^2

then i divided by 5 on both sides

which is 9 = t^2

then i square root both so that i remove the squared...

then i get t = 3

[brisk matrix]

i told you already

$\sqrt{t^2}=|t|$

[warm shale]

maximo

[brisk matrix]

$\sqrt{t^2}\ne t$

[warm shale]

maximo

[olive swan]

if t^2 = 9

then 2 values of t

t = 3

or

t = (-3)

[timid silo]

but -3^2 gives u -9

not 9

[brisk matrix]

you plug in with parentheses

[timid silo]

i just want to know how there is 2 values

[brisk matrix]

(-3)^2

[timid silo]

bruh now why is there parenthesis

[brisk matrix]

i already explained to you why

if t = -3, then t * t = -3 * -3 = 9

,w plot y=x^2

[warm shale]

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Requested by maximo#5992

[brisk matrix]

if i asked you what x values make y = 1

is there 1 or 2?

[timid silo]

what does that even mean

sorry

[brisk matrix]

on here

do you know what a graph is

[timid silo]

yes

...

oh there is 2 right? because there is 1 and - 1 on the graph

...idk

[brisk matrix]

yes

exactly

so now

,w plot y=x^2 from x = -5 to 5

[warm shale]

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Requested by maximo#5992

[brisk matrix]

shoot

well

it’s the same idea

now look at this

,w plot abs(x)

[warm shale]

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Requested by maximo#5992

[brisk matrix]

this is the absolute value function

[timid silo]

ok

[olive swan]

(-3) x (-3) = 9

3 x 3 = 9

[brisk matrix]

so if we want to solve |t| = 3

[olive swan]

thats why two values

[brisk matrix]

we do t = 3, and -t = 3

[timid silo]

wait is it cause there is 5 behind the t in the equation so thats why we have to put brackets?

oh ok now kinda ez

[brisk matrix]

when you plug in you always use brackets

[timid silo]

ok thanks

idk why u waste ur time to help me

but i appreciate it

[brisk matrix]

it’s not just because of the 5

[timid silo]

your the real top g

[timid silo]

then what...

[brisk matrix]

.

[timid silo]

wiat but if there was no 5

wouldnt it be

h = 3^2 + 2

?

why would it be in brackets anyways?

[brisk matrix]

that’s a different equation altogether

but still

when you plug in

[timid silo]

ok ig

[brisk matrix]

always use brackets

[timid silo]

ok

thanks

ur so nice

thanks

.close

[obtuse pebble]

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[narrow shale]

how to prove that the number a is divisible by 9

?

[spice citrus]

is there anything given about a0, a1, a2 ... and an

that their sum might be divisible by 9 for example?

[proven zephyr]

Would you mind posting the original question?

[spice citrus]

what does montrer mean, to prove?

[narrow shale]

the original question is in french , the number a0, an are between 0 and 9, and they told to prove that the number a is divisible by 9, but i am blocked to fin it

[spice citrus]

okay, so you can write 10 as 9 + 1

and 100 as 99 + 1

do you see how that helps

[narrow shale]

yeah i already use this but i didn't find how to continue, i grouped all the 99 to one variable and it divisible by 9, but a0 + a1 +.... an not

[olive swan]

a is only divisible by 9 if a0 + a1 + a2 .................+an is divisible by 9

[spice citrus]

that is what he's trying to prove

[olive swan]

lol i misread

[spice citrus]

do you see that 100 * a_2 = 99 * a_2 + a_2, which means that it's only divisible by 9 if a_2 is divisible by 9 because 99 = 9 * 11

have you had modular arithmetic btw?

[olive swan]

N ≡ 0(mod9)

a0+a110+a2102+⋯+an10n ≡ 0(mod9)

a0+a11+a212+⋯+an1n ≡ 0(mod9) as 10≡1(mod9)

a0+a1+⋯+an ≡ 0(mod9)

[spice citrus]

$\sum_{i=0}^{n}10^{i}\cdot a_{i}=\sum_{i=0}^{n}\left(10^{i}-1\right)\cdot a_{i}+a_{i}$

[warm shale]

Jelle

[spice citrus]

since 10^i - 1 is always divisible by 1, the sum is only divisible by 9 if $$\sum_{i=0}^{n}a_{i}$$ is divisible by 9

idk

the sum of the digits is divisible by 9

10^i - 1 = 1^i - 1 = 0 mod 9

[narrow shale]

@spice citrus @olive swan thanks i understand, it is a chapter on number theory of computer science when of the mit

[spice citrus]

k

[narrow shale]

.close

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[cursive talon]

Can someone help me with this I’m really sick rn and can barely think but I need to submit my answer to part c by 12:00

[astral mantle]

can u express theta in terms of x

try using trig

[cursive talon]

@astral mantle how would you do that

[astral mantle]

think of what tan theta represent

it may help to draw a right triangle on the diagram

[obtuse pebble]

@cursive talon Has your question been resolved?

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@cursive talon Has your question been resolved?

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[dusk shore]

clarification on this problem

I started a little something but not sure if i am correct

some work https://magma.com/d/MUgX20WUUA

<@&286206848099549185> help 🙂

anyone here?

[timid silo]

I assume this is your problem?

[dusk shore]

that was my little approach

sorry yes that is the actual question

[timid silo]

Nah it’s cool, was just making sure before I went to try & solve it

[dusk shore]

could it be a recursive step of something like this p_{k+1} = p_k + 1, and q_{k+1} = q_{k} + 2*p_{k+1} - 1

[timid silo]

It may 🤔 but honestly I would say check out the python server, it’d be better help there

[obtuse pebble]

@dusk shore Has your question been resolved?

[obtuse pebble]

@dusk shore Has your question been resolved?

[obtuse pebble]

@dusk shore Has your question been resolved?

[viral blade]

I assume you have to prove the base case

I wrote that part on the right

[obtuse pebble]

@dusk shore Has your question been resolved?

[dusk shore]

@viral blade sorry say again

[viral blade]

the r(1) = s(1)

you have to prove it

"prove"

you just plug the values in really

[obtuse pebble]

@dusk shore Has your question been resolved?

[dusk shore]

.close

[obtuse pebble]

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[barren hound]

sum probability pair of four sided dice?

[worthy cargo]

well first start off with all possible sums

what are they?

[barren hound]

2 3 4 5 6 7 8

[worthy cargo]

great

now think about how many unique combinations of dice rolls there are

[barren hound]

so

[worthy cargo]

yeah

basically

[barren hound]

tysm

i’ll show the rest in a min

[worthy cargo]

np

[obtuse pebble]

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[rigid gust]

I have a problem finding answer to this problem.

[rigid gust]

This is my progress so far.

And I solved the final equation using the data given. But the answer is incorrect according to the answer sheet.

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

.close

[obtuse pebble]

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[stable rain]

i think yes

u can let the vectors be split into x y

then apply mvt separately

[regal igloo]

bet

how do u prove it

[wild swallow]

lol no

you have no guarantee that MVT will produce the same value

[stable rain]

[wild swallow]

the statement is probably true though

[stable rain]

probably-

sounds like what u said abt indenting contours

[wild swallow]

wait

no

it's false

[wild swallow]

exactly because of this reason

[stable rain]

how tho

like

counterexample

[wild swallow]

that's your job

[stable rain]

idk

well

gl

[regal igloo]

wait so how do u prove it

[wild swallow]

think about how MVT is proved for 1 variable

and how that fails for 2 variables

or more

[obtuse pebble]

@regal igloo Has your question been resolved?

[regal igloo]

wait wdym fails for 2 variables

[wild swallow]

i mean for the vector valued function

[regal igloo]

.close

[obtuse pebble]

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[vague saffron]

I am learning about dot products and cross products in matrices and vectors

[vague saffron]

Are they only different in this context?

And also

I do understand the difference between them now, but in what practical situation do you want to use one over the other?

[spice citrus]

in graphics programming they are quite useful

or in physics you could use the cross product to find torque

[vague saffron]

Right, but I mean, how would I know to use one over the other?

[simple marsh]

https://math.stackexchange.com/questions/77/understanding-dot-and-cross-product

[vague saffron]

If in a formula 2 vectors or matrices are multiplied for example

How do I know if they then want the dot product or the cross product

In my experience the dot product seems to be used more often

But thats a small sample size

[spice citrus]

if there is a dot then it's a dot product

[royal basin]

they should not "just be multiplied"

[spice citrus]

if there is a cross it's a cross product

nothing usually means dot product for vectors I think

[royal basin]

also cross product is ONLY defined in R^3 while dot products can exist in any number of dimensions

asking when you would use one or the other sounds about equally silly to "When do I use addition and when do I use multiplication?"

[vague saffron]

That is when both concepts are very familiar to the receiver of the question.

[vague saffron]

Right

However

When I get a formula like this

There is no specific dot and no specific cross

And in this case I had to use the dot product

[royal basin]

there is no multiplication of vector by vector either

[vague saffron]

let me adjust the vocabulary, it is just that previously the dot and the cross were used for multiplication, but in this contest its not I suppose

Or atleast in a different way

[royal basin]

there is no multiplication in this formula as written, at all

[spice citrus]

the dot product of a vector with itself is its length squared, if that's what you mean?

[vague saffron]

Sorry

Wrong forumla

I had to translate this

To this

And I use the dot product

[royal basin]

$w^T x$ is the multiplication (in the matrix sense) of a row by a column

[warm shale]

Ann

[royal basin]

er

wait, no. X is a matrix.

[vague saffron]

Indeed

[vague saffron]

So does this imply the dot product?

[royal basin]

if x were a vector then w^T x would be the dot product of w and x yes

in all honesty i think dot and cross products should not really be put on equal footing despite their apparently similar names.

[vague saffron]

I understand and I am not trying to, but its just that I want to distinguish them

[vague saffron]

So can I say

When getting the product of a row times a column I need to use the dot product?

[royal basin]

you can say that but it is kind of cringe imo

[vague saffron]

😂 😂

Love it

Also

Is the cross product of 2 vectors the same as the determinant?

[royal basin]

no

and don't ask me what the difference is

because i will preemptively say i will be unable to give a non bullshit, nontrivial answer to that

[vague saffron]

so tempting..

determinant = change in area

cross product = actual area

?

3blue1brown does seem to say its the same though

Ah here we go

[royal basin]

still bad

packaging n vectors in R^n into a matrix and calculating the determinant gives the volume* of the parallelepiped generated by them

[vague saffron]

Ah

He also now says

That the cross product is a vector and not a number

Which by definition would make it different from the determinant

[royal basin]

yes, very

[vague saffron]

x

What is the way to calculate determinants for non square matrices?

Ah got it

.close

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

Can anybody tell me what I did wrong here

[timid silo]

.close

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

The sequence (0,2,0,2...) neither converges to 0 nor to 2

I have to proof this using epsilon

Solution:

If e=1 then
|xn - x|=2 >1 for terms x2=2, x4=2...

Thus 0 isn't the limit and similar argument is true for 2

[timid silo]

I don't understand the solution can someone please help me

[novel knoll]

what dont you understand?

do you understand what you have to show

(the negation of converges to 0 is what?)

[timid silo]

I got that |xn-x|<e should help us identify that it doesn't converge and is divergent if that inequality doesn't hold

But I don't get why they wrote
|xn-x|=2

I know they wrote 2 cause they are considering even terms but didn't get why |xn-x| is "equal" to 2

[novel knoll]

because they wrote for even terms

[novel knoll]

do you understand this?

[novel knoll]

what is the negation?

[timid silo]

That it diverges?

[novel knoll]

write statement of convergent to 0

take the negation

and everything should be clear

[timid silo]

okay, I'm trying

For convergent to 0:
|xn -0|= xn<e
Where e>0

And negation would be:
|xn-0| =xn>e?

[novel knoll]

you are missing some quantifiers

[timid silo]

I'm not sure

What type of quantifiers?

[novel knoll]

$\forall \epsilon>0,\dots$

[warm shale]

ScapeProf

[novel knoll]

is the start of defintion of convergent

[timid silo]

Oh this

For all e>0 there exists a natural number K(e) s.t. xn satisfies

|xn-0| <e for all n>= K(e)

For convergent to 0

[novel knoll]

yep

and negation of that?

[timid silo]

And negation
There exist e>0 such that for any natural number K:
|xn-0|>e for some particular term n_k>= K

[novel knoll]

okay so now we pick epsilon=1

and argue that no matter what K is given to us

we can always find a term (pick an even term greater than K)

and the distance is greater than 1

[timid silo]

oh okay makes sense so we chose 2 (from even term) and 2 is n_k, right? Which is greater than 1 thus the negation is true

[novel knoll]

what

you can't choose 2

you can choose an even number greater than K

then x_{n_k}=2 for this even number n_k

[timid silo]

Oh in my sol they chose 2 so I thought they chose 2 from the sequence my bad

It is confusing. I'll read it again, thank you so much!

[novel knoll]

we pick epsilon=1

someone gives us a K, say K=100000001