help-0

[verbal heart]

[vale wigeon]

read, understand and remember your own messages

this is an equation in k that you are trying to solve for k

[verbal heart]

Yes

[vale wigeon]

now that you have rewritten it so that the left-hand side is factored, and the right-hand side is still 0 as it was,

are you able to solve this equation?

[verbal heart]

Not actually

[vale wigeon]

have you solved quadratic equations by factoring before?

it sounds like you're either forgetting something or putting up a mental roadblock in front of yourself

[verbal heart]

Kind of

[vale wigeon]

if you were given the equation (x-11)(x+4) = 0, would you be able to solve it for x?

[verbal heart]

I remember solving this question. Here, we open the bracket and it goes like
x-11=0, x+4=0
x=11, x=-4

[vale wigeon]

notation could be better

but ok

why can't you do the same thing for 4k(k-6) = 0?

[verbal heart]

Oh wait....

So, will it goes like (4k+1)(k-6)=0?

[vale wigeon]

no

why add a +1 where it doesn't belong?

it's not (4k+1)(k-6) = 0, it's 4k(k-6) = 0

(4k)(k-6) = 0, if you are scared of the lack of parentheses where you're used to seeing them.

[verbal heart]

But during the question, if there is no number we add 1? Isn't it?

[vale wigeon]

if you memorized the rule "if there is no number we add 1" with the intention of applying it mindlessly without thinking about what it means then i am very sorry for you

[verbal heart]

I use to do this with find the coefficient

So I thought we need to do the same

[vale wigeon]

if you are looking at a term in an expression, and wish to find its coefficient, and no coefficient is written, THEN that means the coefficient is 1.

but phrasing this as "insert +1 wherever i please" is many levels of wrong.

[verbal heart]

Oh, I apologise

[vale wigeon]

don't

you have done nothing wrong and you have been apologizing too much in conversations with me

90% of it for things that didn't warrant an apology

[verbal heart]

I am sorry. Let's continue...

So, (4k)(k-6)=0

[vale wigeon]

yes, let's keep going.

when i prompted you with a different quadratic equation in factored form, you were able to set each factor to zero separately and obtain the two solutions this way.

do the same now.

[verbal heart]

4k = 0, k - 6 = 0
k = 0/4, k = 6

Is this okay? Because 4 is in multiplying, there it will be divided

[vale wigeon]

sure, but why write 0/4 and not 0?

[verbal heart]

Oh yes, we can write 0 too because 4 can divide 0

[vale wigeon]

0 divided by anything (other than itself, obviously) is 0.

[verbal heart]

So, k = 0, k = 6

[vale wigeon]

yes, and there you have your answer.

if you have anything left to ask about this problem, then ask it now. otherwise, close this channel and post any new problem(s) in a new channel

[verbal heart]

Thanks

[verbal heart]

Um, no, I have no question. Thanks a lot for helping me out miss.

.close

[lone heart]

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[alpine sable]

i need help doing equations of lines

[spark creek]

Post your q

[alpine sable]

for question c

i am quite confused

i ended up with -3/1

and i dont know whether

that means the answer is c

or d

[spark creek]

3/-1 = -3

[alpine sable]

okay so my second answer was correct

thank you man

.close

[lone heart]

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[lone heart]

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[cerulean vine]

aight so ye

[cerulean vine]

15,16,17,19

so now do i convert 27 in 3^3

and 3^2

hey?

guys?

[languid river]

You do ye

[cerulean vine]

so how do i procceed XD

[languid river]

You do it like this where you - the powers because it is divide

[cerulean vine]

wait is this the ans?

[languid river]

Ye

Or 27

[cerulean vine]

what did you do

to the denom

[cerulean vine]

so do we apply same principles in 16

[languid river]

You basically do the same ye

[cerulean vine]

(3^5)^2/5

[languid river]

So that’s why it’s 3^4

[cerulean vine]

oh so 1 x 4 = 4

[languid river]

For this you do 5 x 2/5

[cerulean vine]

what about 16?

[cerulean vine]

so 2?

3^2?

[languid river]

Ye

[cerulean vine]

and then for (2^5)^-3/5

[languid river]

Same sort of thing again, 5 x -3/5

2^answer

[cerulean vine]

so 2^-3

[languid river]

Ye

[cerulean vine]

17 i frl dont know

[languid river]

For 16 243^2/5 is just 9

[cerulean vine]

what ques this 16?

[cerulean vine]

is this ans?

[languid river]

No there is still more 1 sec

[cerulean vine]

aight so?

[languid river]

That’s 16 and 171

17*

[cerulean vine]

aight so what did you do exactly

[languid river]

For 16 I just did it the same as the first 2 but ignored the 9 until the end, for 17 I expanded the brackets by multiplying the powers just like we did before and then put it as 1 thing rather than 3 if that makes sense, then I just got for example the s from top and - it from the s on the bottom so s^2 / s^4 which is s^-2 and the same thing for the other letters

[cerulean vine]

i am an idiot i just realised

ive been overcomplicating stuff

i thought we had to apply the indices law bs

it technically is

but we basically ignore the base number for the majority

[narrow geyser]

@languid river can you help me when your done

[cerulean vine]

of the entire thing

[languid river]

Ah ok

[languid river]

If I can do it ye

[narrow geyser]

thanks

im help-13

[lone heart]

@cerulean vine Has your question been resolved?

[wet spindle]

you don't need a calculator to solve 17

243 is 3^5

32 is 2^5

and 4 is 2^2

now you have $$\frac{(3^5)^{\frac{2}{5}}\cdot(2^5)^{-\frac{3}{5}}}{(2^2)^{-\frac{5}{2}}}$$

[ocean seal]

hyperlix26

[lone heart]

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[craggy pelican]

🙏

[lone heart]

@craggy pelican Has your question been resolved?

[lone heart]

@craggy pelican Has your question been resolved?

[lone heart]

@craggy pelican Has your question been resolved?

[lone heart]

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[clear rapids]

i want to get the odds % of like 2 percentages

[clear rapids]

like i have a thing where its 25% actual odds, and the practical test i did showed 20%, how do i show the difference as a fraction or percentage?

like 25% and 25% would be 1/1 or 100%

[lone heart]

@clear rapids Has your question been resolved?

[chrome salmon]

Won't that be just 20/25

[clear rapids]

ye true ty

.close

[lone heart]

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[wet spindle]

what should you do to x to get 1/x?

[prime badge]

divide 1 by x

no other way

well you can do x ^ −1

[wet spindle]

hmm

[glass lichen]

take reciprocal

[pale lance]

What context is it in?

[wet spindle]

I have the value of $x_1+x_2+x_3$ which is 4

[ocean seal]

hyperlix26

[wet spindle]

but they ask for the value of $\frac{1}{x_1}+\frac{1}{x_2}+\frac{1}{x_3}$

[ocean seal]

hyperlix26

[wet spindle]

@pale lance

[pale lance]

Ahh

The way i'd do it (even if im pretty simple-minded) is find x1 = 4 - x2 -x3 then do 1 over that

Afterwards I'd make the denominator the same

Does that make sense lmao

[wet spindle]

this?

[pale lance]

That's how i'd do it

But the way i do it is very long

I wonder if anyone else has a solution

[wet spindle]

alright now what?

[wet spindle]

wait, so 1/4?

[glass lichen]

no

[wet spindle]

well I got it right

[glass lichen]

cause $\frac{1}{x+y+z}\neq\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$

[ocean seal]

Mosh

[wet spindle]

"The zeroes of $x^3-4x^2+x-4=0$ are $x_1$, $x_2$, and $x_3$. The value of $\frac{1}{x_1}+\frac{1}{x_2}+\frac{1}{x_3}$ is $\frac{1}{4}$"

[ocean seal]

hyperlix26

[glass lichen]

...

Thanks for finally giving the entire context

Apply vieta's results

[wet spindle]

yeah and $x_1+x_2+x_3=4$

[ocean seal]

hyperlix26

[glass lichen]

that is one of the results

though roots 1 at a time wont be as useful

roots 2 and 3 at a time will be more useful

[wet spindle]

oh so I got the right answer in coincidence

[glass lichen]

yes

[wet spindle]

cool

$\frac{1}{x_1}+\frac{1}{x_2}+\frac{1}{x_3}=\frac{x_2+x_1}{x_2x_1}+\frac{1}{x_3}$

[ocean seal]

hyperlix26

[wet spindle]

$\frac{x_2+x_1}{x_2x_1}+\frac{1}{x_3}=\frac{x_2x_3+x_1x_3+x_1x_2}{x_1x_2x_3}$

[ocean seal]

hyperlix26

[wet spindle]

oh yeah x_1+x_2+x_3=4 isn't useful at all

[glass lichen]

yeah

[wet spindle]

ok since it's a degree 3 polynomial

the product of the zeroes are gonna be negative

but we have a negative coefficient

so it's gonna be positive

[glass lichen]

yes, -(-4/1)=4

[wet spindle]

-(-4/1) = 4

ok I'm stuck with the numerator

how do you find it?

[glass lichen]

numerator is roots 2 at a time

[lone heart]

@wet spindle Has your question been resolved?

[lone heart]

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[alpine sable]

So i got an triangle with side a 11m side b 3 m and side c 10,9 m , i want to change side c to 10,88m and want to know how to calculate how much side a will tilt in cm how can i do that?

[alpine sable]

Got the degrees but not sure how to proceed

Is it even possible to calc that?

Am feeling stupid atm lol

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[slender bane]

My question for this is, how would I go about taking those top 2 limits, if one piece is undefined, yet the other piece is, how do I go about taking that limit

[slender bane]

ok I kinda figured it out I think

[merry depot]

the limit exists only when the left and right limits exist and are the same

[slender bane]

yeah

for the 1st one right

lim x -> 1

for the first one

limit is 1

bottom, limit is 1

right?

[merry depot]

yeah.

$\lim_{x\to1^-} 1 = 1$

[ocean seal]

Zybikron

[slender bane]

ok great

and the limit for 2 does not exist

[merry depot]

correct, why?

[slender bane]

because as x approaches 2 on the left side, the limit is less then 2, and approaching on the right side, the limit is 2

i believe on the left side the limit for approaching 2 is: 2 - 1/x

i think.

[merry depot]

yes

[merry depot]

no

[slender bane]

dang it

well

a limit doesnt exist for 2 on that side????

since its just not defined

[merry depot]

$\lim_{x\to2^-}f(x) = \lim_{x\to2^-}2-x$

[ocean seal]

Zybikron

[slender bane]

oh

OHHH

yep that makes sense

[merry depot]

so the left limit is 0, right limit is 2. So limit DNE

[slender bane]

yep

and then the second part of this is continuity

so its not continuous at 2

continuous at 1

and 0

[merry depot]

yep

[slender bane]

beautiful

thank you for the help

.close

[lone heart]

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[foggy acorn]

how do i find invertible matrix X such that XA=B

[foggy acorn]

also it is given that these two are row equivalent
as well as it seemed that the ff elementary matrices are to be used to answer this problem

[rustic jungle]

You can write down all the coefficients and make the system of equations to start (btw they are the same, so its just to illustrate)

[foggy acorn]

write down the systems of equations for XA=B?

[hybrid hearth]

As a better approach, you can consider the row operations that takes A to B

[foggy acorn]

the row operations that were used are as follows:
R1 = R1/3, R2=R2-5R1, and R2<->R3

[foggy acorn]

so like system of equations of matrix multiplication or some sort?

[rustic jungle]

Yes, you just list all of the single equations and analyse them as a system of equations and not as matrix

But at the end of the day matrix is always faster

[hybrid hearth]

You can represent every row operation as a matrix

Composition of row operations becomes multiplication of matrices

[foggy acorn]

i dont exactly get what this is meant

[hybrid hearth]

$\begin{pmatrix}1&0&0\-5&1&0\0&0&1\end{pmatrix}\begin{pmatrix}a\b\c\end{pmatrix} = \begin{pmatrix}a\-5a+b\c\end{pmatrix}$

[ocean seal]

ryker.chen

[foggy acorn]

Ohh

sry capslock

so the others will be the ff?

[hybrid hearth]

It is similar, but not the above. Recall matrix multiplication

The number of columns of the first matrix has to match the number of rows of the second

[foggy acorn]

but the matrices are initially 3x2 tho

i dont get it

[lone heart]

@foggy acorn Has your question been resolved?

[foggy acorn]

yeah but is it valid to change the dimensions of a 3x2 to a 3x3 matrix

or am i missing something

.close

[lone heart]

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[lone heart]

@timid prairie Has your question been resolved?

[lone heart]

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[alpine sable]

I am unsure how to solve this, do I need to do : 0.4/1.2 = 0.5/05+x ?
1.5 is wrong and the picture isnt in a right "scale"

.close

[lone heart]

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[fossil bluff]

is this not correct?

[lone heart]

@fossil bluff Has your question been resolved?

[tacit arch]

What is u_6

[glass lichen]

heaviside at t=6

[tacit arch]

Oh. Laplace transform then?

[fossil bluff]

yeah

[fossil bluff]

do you mind checking it? online calcs say the answer is much simpler but i dont see that i did anything wrong.

[lone heart]

@fossil bluff Has your question been resolved?

[lone heart]

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[fossil bluff]

can someone please check this? 🙂

[fossil bluff]

<@&286206848099549185>

[lone heart]

@fossil bluff Has your question been resolved?

[tight locust]

what is u_6(t)

[lone heart]

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[lone heart]

@pearl rover Has your question been resolved?

[fossil bluff]

step function

[lone heart]

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[alpine sable]

would I just let the least upper bound = $e$

[ocean seal]

Joseph Fourier

[alpine sable]

would the set be bounded to e ?

[trim plinth]

try bound it to π

${

${

${\frac{\pi}{4},\frac{\pi}{2},\frac{3 \pi}{4}, \pi}$

[ocean seal]

sunflame

[trim plinth]

wait

sequence of rational numbers, how come the upper bound is irrational

[alpine sable]

idk

thats just what the question asks @trim plinth

why pi

[glass lichen]

Pick rational numbers st the digits of an irrational number are correct up to the nth digit

[alpine sable]

does e not work

[glass lichen]

any irrational number works

[alpine sable]

ok but how big do I have to make the set

[glass lichen]

infinitely

it's a sequence

[alpine sable]

how do I show that its infinite

[glass lichen]

...

you're picking a set

you're tasked with just providing an example

[alpine sable]

so, the least upper bound is any irrational number

if I pick e for example

[glass lichen]

that's the goal yes.

if you pick e, you need to find a sequence in Q that converges to e

then the sup is e, which is not in Q

[alpine sable]

ok yeah but do I define the sequence

[glass lichen]

yes

you're providing the sequence.

[alpine sable]

do I just say a_n = {2, 2.7...etc}

[glass lichen]

yes, then probably use words in that construction

e does have a non-wordy sequence, it's the sequence of partial sums

[alpine sable]

how is it a sequence of partial sums

[glass lichen]

$\operatorname{sup}{a_n=\sum_{k=0}^n\frac{1}{k!}|n\in\mathbb{N}}=e$

[ocean seal]

Mosh

[glass lichen]

since we know a priori from calc that $e^x=\sum_{k=0}^\infty\frac{x^k}{k!}$

[ocean seal]

Mosh

[alpine sable]

x = 1

what would be another way to define the sequence

[glass lichen]

the typical limit definition of e I suppose

[alpine sable]

could I just say that $a_n$ is a sequence that gets infinitely close to $e$

hi

is this open

[glass lichen]

well no, cause that's a "no shit sherlock"

lol

[ocean seal]

Joseph Fourier

[glass lichen]

and a bit pedantic

[alpine sable]

mosh

[glass lichen]

$\lim_{n\to\infty}(1+\frac{1}{n})^n=e$

[ocean seal]

Mosh

[alpine sable]

you think you could help me on some geometry

bro

once you're done

[glass lichen]

so you define the sequence trivially

[alpine sable]

i got sent here ☠️

[glass lichen]

#❓how-to-get-help

[alpine sable]

holy fuck

stop

[alpine sable]

so this is a_n

[glass lichen]

the part you're taking the limit of, yes

[alpine sable]

is there any way to define the sequence how I originally proposed to

but with a paragraph definition

[glass lichen]

what was your original proposition?

[alpine sable]

a_n = {2, 2.7, 2.71...}

let least upper bound be e

[glass lichen]

no, you dont let it be e

the sup of that set will be e

[alpine sable]

could the least upper bound be the nth term in the sequence

if n = last term

[glass lichen]

if you have a finite set, the sup is in the set

so the sup would be rational

[alpine sable]

ok

but can I just define the set for 5 terms

and then just say supremum is e

[glass lichen]

{2,2.7,2.71,2.718,...}, where a_n is the 1st n digits of the decimal expansion of e

you need to define the sequence

then trivially sup = e

[alpine sable]

I dont think we learned those definitions of e

[glass lichen]

...

you're the one proposing it?

[alpine sable]

...

ok

so

idk

lets start from the beginning

the supremum is any irrational number

the sequence is finite

[glass lichen]

No

the sequence must be infinite

[alpine sable]

so how would I define a infinite sequence

[glass lichen]

else the supremum would be rational

..........

[glass lichen]

.

[glass lichen]

.

[glass lichen]

.

these are all infinite sequences

[alpine sable]

we didnt learn

[alpine sable]

we didnt learn

[glass lichen]

k.

Either way, everything we've discussed has only been infinite sequences

cause, again, a finite set of rational numbers will have a rational supremum (obviously)

[alpine sable]

ok and thats all I have to do

[glass lichen]

Yes

The question is "provide a sequence of rational numbers whose sup isnt rational"

nothing more, nothing less.

[alpine sable]

cool thanks

.close

[lone heart]

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[merry coral]

if the node at (5,2) weights 200 units

and gravity is like 9.5

how much upward force would the node at (3, 1) have to extert at a minimum

so the node would weigh 200 * 9.5

but like lol how does this work

[glass lichen]

exert at a minimum to do what?

[merry coral]

keep it stationary

(not falling down)

[glass lichen]

gravity is a central force, so the force it exerts would have to be away from the node

ie down and to the left

and what's the mass of the (3,1) node?

[merry coral]

it is locked in place

[glass lichen]

so then... no force lol?

If it can't move, it cant move

[merry coral]

like the line moves

like the line is an arm ig

💀

[glass lichen]

Yeah you're doing a poor job of explaining the setting

[merry coral]

true

so lets imagine that this is a bench press

ight

so the point (3,1) would be the start of the arm

the arm would be the black line that wants to move the bar at (5,2)

so how much force does it need to use to keep that bar from falling down due to gravity

[glass lichen]

does the bar have mass?

[merry coral]

yes

if the node at (5,2) weights 200 units

9.5 gravity

[glass lichen]

not the point-masses, the bar

[merry coral]

the bar is the point

[glass lichen]

.....

[merry coral]

I'm trying to make a 3d sceneraio 2d to make it simple lol

[glass lichen]

How are the 2 masses coupled then?

if there's no bar

[glass lichen]

That has a bar

you said there's no bar

[merry coral]

yeah

[glass lichen]

what is the flipping mass of the bar

[merry coral]

200 units

[glass lichen]

Ok

so the bar creates a torque, you want a force in the y^ direction that creates the same torque but opposite rotation

[merry coral]

uhm

I guess so sure

the whole point of this is to find the optimal bar bath for a bench press (which would not be a straight line cause that does not account for gravity)

if that clarifies anything

[lone heart]

@merry coral Has your question been resolved?

[lone heart]

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[gloomy ice]

hii this is more of a physics question- I= P/4(pi)(r^2)

[gloomy ice]

but

in the formula I= P/4(pi)(r^2)

how do we find the power of a sound source

[lone heart]

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@gloomy ice Has your question been resolved?

[lone heart]

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[tight locust]

i don't get it

it doesn't seem possible or sensical to write the triangular region as the sum of two different regions

[raven rover]

What if you somehow manifested a negative into the bounds by saying that the triangle in question = (large triangle) - (smaller triangle)

Large triangle: y = 2x, x = 5, y = 0
Small triangle: y = x, x = 5, y = 0

[tight locust]

yes but it won't let me do that. i can't subtract

unless i reverse the bounds or use a negative differential?

[raven rover]

try reversing the bounds - tbh I don't have a great idea as to how this would work

[tight locust]

@raven rover

i manifested the right answers somehow

just completely guessed at it, but that makes no sense at all why you'd do that

let me try writing this in latex

[raven rover]

Yeah I don't like that problem to be honest

[tight locust]

i mean i guess that works?

i don't see why you would choose the specific horizontal line y=5 though

to make the "cut"

that has no real justification

well i mean i guess it does. that's the only horizontal line which splits it into two different triangles

but i just don't like the problem

i reject the premise entirely

[raven rover]

same

[tight locust]

if it had explained which two regions it wanted i would have been fine with it actually

[lone heart]

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[quartz hinge]

how do i find

[quartz hinge]

i didn’t learn ab when it’s obtuse taking up two quadrants

[lone heart]

@quartz hinge Has your question been resolved?

[oblique spire]

What is the (-5, 12)

[lone heart]

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[quartz hinge]

the coordinate

[lone heart]

@quartz hinge Has your question been resolved?

[quartz hinge]

useless

.close

[lone heart]

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[formal vortex]

a car of mass 1000kg moves up an inclined plane of angle 30 to the horizontal at a constant speed of 20m/s. if the frictional force is 2000N. calculate the power developed by the engine

[oblique spire]

Is that a physics question

[formal vortex]

kinda

@median dirge h

hi

[median dirge]

Yea sorry im on my way to school so cant really help rn

[formal vortex]

ohh its okay

[median dirge]

So it probably is work done against frictional force in time t

So youll be resolving frictional force and gravitational force to their components

Sorry i cant really do the whole thing im travelling

[formal vortex]

ok

so

f net = speed - mgsin+fc?

wait

what sud i do with the speed

[lone heart]

@formal vortex Has your question been resolved?

[formal vortex]

.close

[lone heart]

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[ocean spindle]

i was looking at the notes

my tutor solved this question

but i dont understand where he got the 2 on the x axis

im looking for critcal value in this question

i get how he got max and min, and direction of graph increasing/decreasing

[lone heart]

@ocean spindle Has your question been resolved?

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[quaint mica]

can someone go on channel 2

[lone heart]

Please don't occupy multiple help channels.

[quaint mica]

the person isnt helping me

[wary stream]

Don't open another channel to try and get your other channel attention

You wait patiently

[quaint mica]

save me the scolding bruh

[wary stream]

Bruh, then don't open a different channel, like I said

[quaint mica]

breh bruh brah bravisimo

[oblique spire]

The mods will just warn u

[quaint mica]

@leave

.close

[lone heart]

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[wary stream]

You should read #❓how-to-get-help if you don't know how to do that

It does say

Did you even read #❓how-to-get-help ?

[lone heart]

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[wary stream]

Try to write both numbers as the same base

Don't tell the person that

You should teach the person how to get there

[atomic stirrup]

Yeah ur right sry

[wary stream]

You already know the base would be 2 because it's easier to work with the smaller numbers

So you need 16 to have a base of 2

So what power of 2 makes 16?

Powers are repeated multiplication of the same number, right?

So then what's 2^4, if you calculated that?

So then 16 = 2^4, right?

You can replace that in then problem, making 16 be 2^4

And don't forget parentheses

[lone heart]

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[frosty blaze]

hiya!

[frosty blaze]

i was hoping i could get a bit of help on this linear algebra homework question, i've been struggling with how to tackle it for about half an hour now

this is the question

do i need to convert the matrix to parameterized form?

i don't even know where to begin :/ any help would be appreciated!!

i can and will show all work along the way as i build an answer to this. at the moment though, i'm completely stuck and don't even know what to begin picking apart

my eyes are drawn to the matrix but i can't think of what to do with it off the top of my head. any guidance would surely go a long way for me!

is this on the right track or am i getting sidetracked with trying to do this

determinants have no role here, right?

[wary stream]

Trying asking in the more specific topic channel, #linear-algebra. The more specific channels, people who mainly know that topic will be there more, compared to general help because anyone can help

[oblique spire]

No ig

This is a help channel

So anything goes

[wary stream]

I'm saying the more specific channels, people who know that topic will mainly be there instead of being in general help channels

[oak perch]

Do it by definition, calculate that determinant

[frosty blaze]

how can i calculate the determinant of a matrix with variables in it

just do it manually?

ok one sec

i will do that and get back to you

also @wary stream i'm just concerned about it getting lost in #linear-algebra but i'm down to cross post i don't mind

so long as cross posting isn't frowned upon

[oak perch]

Just do it

Like xy_1 is the first term, there are 6 terms

[wary stream]

Won't get lost because majority of the people use general help and less frequently use the specific topic channels

[frosty blaze]

you saying that to the cross post, or the determinant thing? cause i'm doing the determinant rn

[frosty blaze]

so response time will take longer?

[frosty blaze]

yep am on it, will get back to you with an answer for the determinant

one moment

[wary stream]

Depends on traffic hours

[frosty blaze]

sorry for ping btw

am still getting used to this reply mechanism

[oak perch]

If you know Laplace expansion you can expand it in terms of the first row, if you don’t know it it doesn’t matter you just calculate it

[frosty blaze]

i don't know laplace expansion no :c

i calculate determinant one sec this is a process that i'm not used to bear with me i'm getting there

am writing it in notebook rn hol' up

[frosty blaze]

how's this?

fuck! sorry for ping

i really gotta get better at that :/

genuinely am sorry did not intend to ping

i know people get feisty about that shid

how does the determinant have to do with the line passing through the points? i'm a little lost on how the determinant comes into play here

i understand that the determinant is just the factor by which the area changes with some linear transformation

how does that play a role here

the fact that that matrix = 0, does that mean that the determinant = 0 too?

[frosty blaze]

can i slap an = 0 to the end of this?

or is that no bueno

[oak perch]

Good

x(y_1-y_2)+y(x_2-x_1)+(x_1y_2-x_2y_1)=0

It’s a line

So just prove that (x_1,y_1) and (x_2,y_2) are on it

[frosty blaze]

oh okay I SEE that is why the determinant is 0

because it's a line in R2

right?

[oak perch]

Yeah

[frosty blaze]

okay cool i'm following

[frosty blaze]

does this mean plug in values? iirc my professor doesn't want me plugging in random values for a proof, he only wants me doing that if i'm disproving something

[oak perch]

The geometric explanation is actually the volume of the parallelepiped expanded by (x,y,1),(x_1,y_1,1),(x_2,y_2,1) is 0 so (x,y) must be sitting on that line but it doesn’t matter

Yeah just plug in values

[frosty blaze]

parallelepiped
one sec i gotta google this word

[oak perch]

I googled it too, not my first language

[frosty blaze]

ok googled i have learned a thing

lmao

[frosty blaze]

so again, my prof only wants me plugging in values if i'm disproving something

like, he wants me to give explicit values if i'm providing a counterargument

but in a proof he wants me to be all wordy. for example, this is my answer to the next question in that homework

so i gotta tackle the proof formulaically in some sense

[oak perch]

?

[frosty blaze]

so i understand that the determinant of that matrix is 0 because it's a line in R2. that part i totally follow, i'm with you.

[oak perch]

It’s not specific values

[frosty blaze]

oh? what would i be plugging in?

[oak perch]

I mean let (x,y)=(x_1,y_1)

[frosty blaze]

if not specific values

OH

I SEE

[oak perch]

And let (x,y)=(x_2,y_2)

x(y_1-y_2)+y(x_2-x_1)+(x_1y_2-x_2y_1)=0

[frosty blaze]

okay thank you i will come back to you with what i have so you can lemme know if i'm on the right track with my logicbrain

[oak perch]

Let (x,y)=(x_1,y_1), you will find that it’s an equation

Okay

[frosty blaze]

i think i follow what you're saying, will get back to you if i run into an obstacle with my understanding as i type this out

gimme a few mins to think on this

i dearly appreciate all of your help thus far

[oak perch]

Sure

[frosty blaze]

ok so this is my answer thus far but i'm getting a little bit lost with this

i'm not sure how i can let (x, y) be two things at once

trying to incorporate

x(y_1-y_2)+y(x_2-x_1)+(x_1y_2-x_2y_1)=0
this into it is difficult for me because i am struggling with thinking about mapping (x, y) to two different things

wouldn't it be the same as saying (x, y) = (x_1, y_1) = (x_2, y_2)?

[oak perch]

No I mean respectively

[frosty blaze]

so, by doing that, i'm just able to say that because they're equal to each other then they fall on the line? my wires must be getting a bit crossed

[oak perch]

First you let (x,y)=(x_1,y_1)

x(y_1-y_2)+y(x_2-x_1)+(x_1y_2-x_2y_1)=0

Let (x,y)=(x_1,y_1)
x_1(y_1-y_2)+y_1(x_2-x_1)+(x_1y_2-x_2y_1)=0

So (x_1,y_1) is on this line

Got it?

[frosty blaze]

OHHHHHHHHHHHH I THINK SO

ok ok ok hold up am modifying this

[frosty blaze]

is this really all there is to it??

would it be better to rewrite the determinant line to be formatted like the others?

[oak perch]

Yeah

I mean that’s all

Nothing further

[oak perch]

This is clearly a line, it’s standard

[frosty blaze]

awesome

i modified it slightly further

just to add a line to the det thing

ok so this is the product of all this

looks good cog?

[oak perch]

Yeah

[frosty blaze]

awesome, thank you so so so much for your help, you've certainly helped me gain some understanding

i appreciate it a lot

[oak perch]

Np

[lone heart]

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[fickle dock]

Am I thinking about this wrong? I thought this is how these problems are supposed to be solved, I pick some values, and based on those, I find the last one, no?

[lone heart]

@fickle dock Has your question been resolved?

[oak perch]

Of course it’s wrong, the dimension is 3

Choose one variable for example x_1, then all other 3 variables are free

You can let them be (1 0 0) or (0 1 0) or (0 0 1) respectively to obtain a basis

[fickle dock]

but it worked for the previous one, that one had dimension 3 and the basis was dimension 3 as well 🤨

yeah it worked here

[oak perch]

No

Your new question dimension is 2

[fickle dock]

because there's 2 matrices?

[oak perch]

What? No

[fickle dock]

so the dimension of the basis is always 1 less than the original matrix?

[oak perch]

No

Dimension =n-rank(A)

Now your matrix A=(3,-4,-6,-8) whose rank is 1

So 4-1=3

[fickle dock]

so how do I know how many matrices I need then?

I need 3 because there are 3 free variables, right?

this still doesn't work tho :/

[chrome salmon]

Why such answer

[oak perch]

What?

Just one matrix

With one row

A=(3,-6,-4,-8)

Ax=0

[chrome salmon]

(x,y,z,w) st -4x+6y-6z-w=0

[oak perch]

Why you keep asking different questions

[chrome salmon]

Sorry

[oak perch]

I mean him

[chrome salmon]

Oh sorry

Now I see why they have lizard in their name

[fickle dock]

oh sorry my bad, I thought I had the other one pulled up 🤦‍♂️

[chrome salmon]

Ogay do u get it?

[fickle dock]

I'm re-reading it

so I choose 1 variable

x

that one's gonna have the formula that I came up with earlier

I don't understand this

so I pick x to be my computed variable based on the 3 free ones

which variables does the basis represent then?

[fickle dock]

oh THIS is what you meant

wow that was easy

thank you guys

.close

[lone heart]

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[noble rain]

hi, quick question. i forgot how to write the domain of a function that excludes a number

[spark creek]

N - {100}

[ocean seal]

moof

[noble rain]

ah my bad, it's been so long since I've used latex

[tall hearth]

R - {4}

[spark creek]

Put the number in curly braces

[noble rain]

Oh ya, forgot to put that in too

[noble rain]

If there are two numbers?
Is it going to be $R - {4 \cup 6}$

[ocean seal]

moof

[tall hearth]

R - {4, 6}

[noble rain]

Okay, thanks!

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[left frigate]

Can someone please explain the interpretation and use of a 'transition density' function in the context of a stochastic dynamical system?

[lone heart]

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[left frigate]

.reopen

[lone heart]

✅

[lone heart]

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[lone heart]

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[unique halo]

Does anyone know what x would be in “4x+5”

[safe pawn]

inner angle is same as outer angle

[ripe rain]

Wait is the question incomplete?

Ohh

I see

[unique halo]

Yeah I need to solve for X

[winter tangle]

This is using the arc length formula

[safe pawn]

no

4x + 5 = 85

solve for x

[ripe rain]

85=4x+5

Ya

[safe pawn]

no need for arclength

[winter tangle]

No

[ripe rain]

@winter tangle question is poorly designed

[winter tangle]

Ahhh

[ripe rain]

Anyways we need radius to find x by arc length method

Hence I thought question was incomplete

[unique halo]

So the answer would be B then ?

[winter tangle]

Yh didn’t see that there wasn’t radius

[unique halo]

Cuz if u put 20 into the variable X

4 x 20 + 5

= 85

Or is that not right

[ripe rain]

It is correct @unique halo

[unique halo]

Okay thank you

Does this server only let us have a couple questions or as much as we want

[lone heart]

@unique halo Has your question been resolved?

[unique halo]

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[timid mauve]

Hey people. I'm stuck with basic trig, I'm ashamed, ha! I totally used to know how to do this in high school. I guess my psychology teacher was right when she said: "Use it or lose it".

I'll start learning again with Khan academy. Could I get a reminder how this problem presented in the picture could be solved, please?

[timid mauve]

What I'm trying to find is - I have a mountain next to my house, but no sextant. I know the distance between the mountain and me, and the elevation of the mountain and mine elevation.

[safe pawn]

please dont use cursive for variable names

that is so cursed

[timid mauve]

The question that I have is - what's the alpha angle

[timid mauve]

Oh, sorry

Old habit heh

I also noticed a typo

546 isn't mm, it's just metres

and b is in kilometres, but that can easily be shifted to metres, just multiply by 1000

[fervent timber]

what sides do you know, relative to the alpha angle?

[timid mauve]

Well, I know all sides and the 90deg angle

[fervent timber]

depending on the sides you know, you'll be able to use either sine, cosine, or tangent

first, you have to determine which sides are the opposite, adjacent, and hypotenuse, relative to alpha

[timid mauve]

Ah, true

I know for a fact that the sum of L and B should be 90

So, to determine L, I'd go like

let me see if I remember correctly

[fervent timber]

you mean alpha and beta right?

[timid mauve]

Yeah

😄

[fervent timber]

yes, good

and it's a right triangle so you can use the trig functions to calculate the angles

since you know all 3 sides, you can use any trig function you desire

[timid mauve]

Be right back, I'm going to read up a bit on wikipedia

Can't remember fully

[fervent timber]

specifically, you would determine the equation, and find the inverse function to find the angle

[timid mauve]

Thank you for guiding me 😄

[fervent timber]

no problem

[slender gull]

Do you know stuff like what tan, sine, cosines are?

If you don't, I suggest that is what you look up.

[timid mauve]

Yep, gonna have to do some more reading but that should be more or less it

what's funny is I don't remember arcsin being a thing at all

aand it's wrong 😄

brb, need to recheck where I went wrong

okay uh

it's corect but.. I thought I was calculating sine for beta

¯_(ツ)_/¯

[fervent timber]

that looks great!

[timid mauve]

Figured it out! :p Thank you people ❤️

Wiki + some googling + this website to show me actual steps https://www.calculator.net/triangle-calculator.html?vc=90&vx=620&vy=2510&va=&vz=&vb=&angleunits=d&x=83&y=11

[fervent timber]

also, if you want to calculate alpha you would just do 90-beta

[timid mauve]

I'm gonna pick up a textbook with problems

Relearn everything

Got any nice ones to reccomend? 🙂

[fervent timber]

hmm, not sure

[timid mauve]

I might just go for the current reccomended one in schools

That seems like a safe choice

[fervent timber]

there might be a place in this server to ask; but I can't guide you specifically because I'm not really familiar with this server, sorry

[timid mauve]

No problem, thank you a lot for helping ❤️

[fervent timber]

yeah that seems sensible

no problem!

[timid mauve]

Welp, gonna close this now

Thanks once again ❤️

.close

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[mortal crest]

nvm

.vloae

.claoe

.cloae

.close

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[mortal crest]

.reopen

[lone heart]

✅

[mortal crest]

nvm again

thought i got it

[rigid smelt]

is this a test?

[mortal crest]

no

well

it is

but not a school one

[rigid smelt]

i dont know, i havent been programmed to deal with this, i'll let <@&268886789983436800> continue

[dreamy cedar]

What do you mean by not a school one

[mortal crest]

its a for fun test

[mortal crest]

programmed?

[dreamy cedar]

I see

[mortal crest]

why tho

are yall not supposed to help on school test?

[rigid smelt]

no, we're just askign because we are interested

[mortal crest]

oh well

so anyone know it?

[lone heart]

@mortal crest Has your question been resolved?

[lone heart]

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[alpine sable]

Hi I really need help

[crimson carbon]

okay

[alpine sable]

Those are the questions

[crimson carbon]

jesus

[alpine sable]

You can skip some questions

I really need help I've to send it to my tutor

[crimson carbon]

aight

So wanna begin with the first?

Okay so for 1(a)

It's asking for us to express the ratio 1min30s to 1hr in simplest form

We'll have to use the same units

[alpine sable]

Oh ok

[crimson carbon]

So it'll look like a:b

<1min30s>:<1hr> (we'll need to convert 1min30s to hrs)

[alpine sable]

Can I talk to you in DM for awhile

[crimson carbon]

I think

ye

[alpine sable]

.close

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[violet panther]

Hi, for this question, am I doing correct way?

[crimson carbon]

ye

[spark creek]

Si

[spark creek]

Yes

[violet panther]

I’m stuck….

It said largest domain, but I’m not sure how to find it

[spark creek]

You know what a domain is right?

[violet panther]

Yes

The x

[spark creek]

Yeah, specifically what values x can take

So this function (x+1)(x+9) is inside of a square root

[violet panther]

Ya

[spark creek]

Which puts a pretty strict constraint on what values it can take, what constraint is that?

[violet panther]

X can’t be -1 or -9

?

[crimson carbon]

the radicand can't be negative

[spark creek]

Those are the roots of the equation, if you put them, you'll get 0, which is an acceptable answer

[spark creek]

Yess

[crimson carbon]

i.e (x+5)^2-16>=0

[spark creek]

Yes

[violet panther]

What is radicand?

[spark creek]

The thing inside the root

The whole expression

[violet panther]

Oh ya

Can’t be negative

[spark creek]

Yup

I think you can solve it now

[violet panther]

Let me try first

[violet panther]

I think x can’t be the number between -9 and -1

Because if I put the number between them, I’ll get negative

So I think the x have to be less than -9 or more than. -1

And the largest domain one, I think the answer is ♾?

[crimson carbon]

-9 and -1 exlusive ye

(-infinity, -9] U [-1,+infinity)

[spark creek]

It can take -9 and -1 , so just exclude those 2

[violet panther]

Ya

[crimson carbon]

For the composition h(x)=f[g(x)]

[violet panther]

So is this the answer for it?

[crimson carbon]

ye the domain for

in interval notation

[violet panther]

Oh okay

Got it

Thank you both of you for helping me out

.close

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[weak harbor]

This is the integral given and i got to my answer.

[weak harbor]

now following that exercise i have to use this..

and one of this is the right answer

[limpid spade]

use

[glass lichen]

yeah, so apply the Pythagorean identity

[limpid spade]

per partes

[weak harbor]

so i know cos^2(x) is -sin^2(x)

so the last one is not right

[limpid spade]

1-sin^2x*

[weak harbor]

so sin^2(x)+cos^2(x)=1 becomes cos^2(x)=1-sin^2(x)

so the first one is correct?