help-0

[undone hornet]

Calc and vectors :D

So this wouldn't be valid since we are talking about the vectors themselves, not their magnitudes

[wet bane]

Are u saying that |u| = sqrt(x² + y²)

[undone hornet]

Yes, if we are working in 2D space

[wet bane]

Wich I hope we are cause that's as far as can go😅

[undone hornet]

Hahaha

Well the answer is a scalar quantity so it shouldn't matter what space we are working in anyways

[limpid turret]

Do you have answer key by chance?

[undone hornet]

Yeah

The answer is supposed to 41.3

[limpid turret]

41.5 you mean?

[undone hornet]

Oops yeah

[limpid turret]

I got 83/2, but the process ain't pretty

[undone hornet]

At least there is a process

I don't even have a start

[limpid turret]

Not sure if this is sufficient enough of a hint for you

Basically, I broke u and v down into their vector projections and rejections on w

[undone hornet]

yeah i havent learned projections or rejections

[limpid turret]

Yikes then I have no idea how to solve the problem without it

I can at least give you a crash course

[undone hornet]

I can learn it right now probably

[limpid turret]

a vector projection is kind of like treating w as an axis, so projection asks "how far along the w axis does u or v go"

But you need to understand it deep enough to get to this part:

where theta_u and theta_v are the angles that the u and v vector make with the w vector

If you're good at trig, you can solve for both angles in the equations of the last two lines

That's how I arrived at 83/2

There may be a more efficient method

But I am and could only find a brute force approach

[undone hornet]

yeah my friend did it in a different way and I don't understand it at all

[undone hornet]

LMFAO

[undone hornet]

Alright

I will watch some videos on projections

Lemme send his solution so maybe you can explain what he did

[limpid turret]

k

[wet bane]

When are u supposed to learn that in the curriculum?😂

[limpid turret]

in vector projections

[wet bane]

Lol I meant what year?

[undone hornet]

Grade 12 ideally

I haven't learned it yet though

[limpid turret]

Oh your friend had a genius solution

[undone hornet]

damn.

I get everything but u + v + w

I don't understand how that is achieved

[limpid turret]

Actually yeah...

hold on

Let me read more before I send praise

[undone hornet]

Alright

[limpid turret]

Oh ok I get it

It is genius

[limpid turret]

Do you understand this first image?

Or need I explain?

[undone hornet]

I understand everything but the first line

[limpid turret]

He's just evaluating (u+v+w)*(u+v+w)

Why he chose u+v+w will be made clear later

Is that a reasonable answer for you?

[undone hornet]

I still don't get it

Like at all

[limpid turret]

Your friend is basically like "omg hmmm... what is the dot product of u+v+w with itself? Lemme find out lol tiktok moment"

(I don't know how kids talk these days)

[undone hornet]

LOOOL

[limpid turret]

But yeah, the whole first image is just the solution to the question to "what is dot product of u+v+w with itself?"

yeah?

[wet bane]

could he have reverse engineered it somehow?

[undone hornet]

alright

I don't get the purpose but sure

That makes sense

I just was confused on why he did that

[limpid turret]

Yeah. He just showed that this is true:

Okay, next! We are given u+v-w=0, yeah?

[undone hornet]

Yeah

[limpid turret]

add 2w to both sides

What do you get?

[undone hornet]

u + v + w = 2w

[limpid turret]

yup

[undone hornet]

oh myu god

[limpid turret]

Genius, right?

Your friend is smart. I'm egotistical and don't like admitting when people are smarter than me

So give him pat on the back for that solution

Or punch him the stomach

Whichever feels right to you

[undone hornet]

The latter seems better

[limpid turret]

At least it's nice to see my approach works

[undone hornet]

I appreciate it, I am still a little confused on something

[limpid turret]

tell me

[undone hornet]

For this, he just plugs in the magnitudes of the vectors

and just to confirm

u + v + w was just for the fun of it?

[limpid turret]

Nah it was necessary

[undone hornet]

if so, I don't know how I am supposed to figure that out on a test

[limpid turret]

That's what makes it genius

It's hard to figure out intuitively

[undone hornet]

Yeah I couldn't

Alright so u + v + w was to solve the later steps?

[limpid turret]

mhm

[undone hornet]

How does he know u.v + v.w + w.u = (|u + v + w|^2)/2 - 61

[undone hornet]

Damn, thanks

I think thats all the help I need, although I got more than a little help. Thanks for your time.

.close

[lone heart]

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[arctic mortar]

5c

[arctic mortar]

Can you take the magnitude of a scalar?

I thought the magnitude notation was reserved for vectors and the dot product of 2 vectors is a scalar

but the answer key says this

[undone hornet]

Well technically |a| is just the absolute value

That is correct

You cannot dot a scalar and a vector

you can do 5v

But that's a scalar multiple

Vectors cannot be multiplied like scalars

[arctic mortar]

ok thanks

.close

[lone heart]

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[dark fern]

this is what I was thinking

but how would I prove it?

[slate monolith]

just compare the limit of the derivative

[dark fern]

what do you mean? solve the derivative and prove its discontinous at 3?

[slate monolith]

if the limits dont match for a value it doesnt exist

if this value is f(x) then not continous

if the value is f'(x) then not differntiable

[dark fern]

isn't f(3) continous?

both lhs and rhs would approach 0

[slate monolith]

yes but we are trying to show thats its not differewntiabvle at x = 3

[dark fern]

what do you mean by compare the limits?

[slate monolith]

if the limits dont match for a value it doesnt exist
if this value is f(x) then not continous
if the value is f'(x) then not differntiable

[dark fern]

so find the limit for x->3 for f(x) and f'(x)?

[slate monolith]

yeah

[round trellis]

I get but how do u prove for a continuous function

[slate monolith]

??

[dark fern]

ok, how come that proves its non-defierentiable?

[slate monolith]

think about a curve

if you come in from LHS and RHS

as the dist between those goes to 0

they reach the same value

if you have a kink

where it has like a sharp turn

the RHS for f' and LHS for f' dont match

[dark fern]

oh so the derivative does not exist

at 3

if its not-continous at 3

wouldn't the derivative be 1?

[slate monolith]

let me explain again

[dark fern]

I understand, you're saying that if the derivative

doesn't exist at 3, then it is not differentiatble at 3

and to prove

that

you prove the limit doesn't exist, so it is not continous?

[slate monolith]

no no no

it can be continious but not differentiable at a point

thats what the question is asking

[dark fern]

the limit of the derivative I mean

[slate monolith]

yeah

okay so what was your question

test for continuity

[dark fern]

what would the derivative of |x-3| be?

[slate monolith]

then test for non-differntiablity

split it up

into two lines

i gtg but you can figure it out from there

[dark fern]

thx

.close

[lone heart]

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[alpine sable]

Hello

[alpine sable]

I’m a freshman in highschool

in algebra 1

and I was just thinking about speed and stuff

and a question came to my head that my teacher couldn’t answer

so, when you see a sprinter run on the track, you know he is moving because he is going past the track on the ground

you can see the speed of something by comparing it to something else

So in the scenario that there is an object in space

with nothing else but that item

How can someone tell it is moving if there is nothing to compare it to?

[vapid shuttle]

speed is determined by distance / time

if an object is in space and there are no reference objects to compare it too, the reference object would become the observer

[alpine sable]

How can someone find it’s distance if it’s in empty space with nothing to compare itself to

[vapid shuttle]

if you are watching something move in space

it may be infront of a black sky

[alpine sable]

and if there is no observer?

[vapid shuttle]

you are asking, " how can someone tell it is moving ?"

so if no one is watching then no one could see ? lol

[alpine sable]

I’m just making a hypothetical scenario where the observer is not there to be a comparable object

[vapid shuttle]

then in that scenario no one would be able to tell they are moving, since no one is observing their movement

[alpine sable]

Thank you

oh and uh

what type of math would this be?

This type of question

[vapid shuttle]

this isn't really math, it might be classified as physics?

kind of just a logic question

[alpine sable]

oh wow that’s quite advanced

oh and

I heard about this temperature called kelvin

Hey does anyone know how to calculate a test grade score?

And when something reaches 0 kelvin

[vapid shuttle]

read #rules this channel is occupied

and #❓how-to-get-help

[alpine sable]

and when something reaches 0 kelvin

[lone heart]

Please read #❓how-to-get-help

[alpine sable]

it stops movin

mofo

If y’all don’t get out my math help channel

AustinU? Ya there?

[vapid shuttle]

yes

[alpine sable]

okay great

So

In the future if there is “the big freeze”

where does all the energy go

If everything is frozen in place

[vapid shuttle]

By the third law of thermodynamics, a system has temperature of absolute zero if and only if its entropy is zero, i.e., if it is in a pure state. Because of the unavoidable interaction with its environment, this is impossible to achieve.

[slate monolith]

That is now pure physics

0 kelvin is a theoretical thing

[vapid shuttle]

Also, it isn't possible for quantum particles to have a definite velocity and position (which would be required to be at 0 kelvin) by the Heisenberg uncertainty principal

but yes

this is not math help

[alpine sable]

Heisenberg?

[slate monolith]

From breaking bad

[alpine sable]

BREAKING BAD REFERENCE???

okay so

Uhh

What’s thermodynamics

[slate monolith]

That’s a google question

[alpine sable]

Can you dumb it down for me pls

[vapid shuttle]

the branch of physical science that deals with the relations between heat and other forms of energy (such as mechanical, electrical, or chemical energy), and, by extension, of the relationships between all forms of energy.

^ google

[alpine sable]

ohhh

I get it

temperature scienc

[slate monolith]

No

Heat science

That’s what thermo means

[alpine sable]

oh

[slate monolith]

Dynamics is motion

Motion of heat

[alpine sable]

So when something gets hotter

What’s the little molecules that are shaking fast

[vapid shuttle]

atoms?

this is way off topic of math

[slate monolith]

Yeah lol

[alpine sable]

sorry but

Idk where to ask these questions

[alpine sable]

If I shake myself really fast will I get hotter

[slate monolith]

No

[alpine sable]

oh

[slate monolith]

Temperature causes the speed

Not the other way around

[vapid shuttle]

you will be giving off energy by creating the motion

so no

[alpine sable]

what if a machine moves my hand for me

and I’m not doing anything

[slate monolith]

You cant apply molecular motion to humans

[vapid shuttle]

on an atomic level that wouldn't affect the speed of the atoms

[alpine sable]

If heat makes atoms move

why don’t we use it for energy

like wind moves windmills

[vapid shuttle]

this is the last non-math response I will give

https://kids.frontiersin.org/articles/10.3389/frym.2019.00105

[alpine sable]

Thank you

And now I have a really really really simple math question

if y=mx+b

and y-y1=m(x-x1)

and m=y2-y1/x2-x1

Does that mean y-y1=y2-y1/x2-x1(x-x1)

?

[vapid shuttle]

no

the equations are seperate

the first two are used to represent lines

one using the slope and intercept of the line

one using the slope and a point on the line

the third equation represents the slope of a line

where y2, y1, x2, x1 are related but arbitrary points on that line

they are not the same as the arbitrary point used for point-slope form equation

[alpine sable]

oh okay thank you

So my teacher said I’m not able to do this in math

A trick I do to make algebra easier

there would be an equation like

-y=7x+3

[slate monolith]

What if you make them the same though

[alpine sable]

So I’d just switch it to y=-7x-3

and she’d be like “you can’t do that”

[vapid shuttle]

you could, but that isn't what they were asking (and that's unnecessary in like all scenarios)

[slate monolith]

You can do that

[vapid shuttle]

you can

dividing both sides of the equation by -1

so long as you perform the same operation to both sides of an equality

[slate monolith]

Or multiplying by -1

[vapid shuttle]

it remains the same

because the = sign literally means they are the same thing

so if you do the same thing, to the same thing

it is still the same

[alpine sable]

Oh

Thanks

Y’all are smart

[slate monolith]

We’ve just been doing this for a while

Your curiosity will get your far

[alpine sable]

yay

[slate monolith]

Keep doing what you’re doing

[alpine sable]

My dad don’t like my questions

I have a lot of them

[slate monolith]

They’re great questions

Not everyone has the patience to answer them though

[alpine sable]

oh I have a question idk if it’s math tho

I think it is

Could be physics too tho

if I throw a ball into the air

does the height I throw it at affect it’s distance?

I have multiple questions so you can just put yes or no if you’d like

[slate monolith]

Yes

[vapid shuttle]

not necessarily

[alpine sable]

velocity?

[slate monolith]

If they throw it not straight up

And they start on a cliff

[slate monolith]

What

[alpine sable]

nvm

What about acceleration

[slate monolith]

That’s always a constant

[alpine sable]

Thank you

[slate monolith]

9.8m/s^2

[alpine sable]

what about air quality

Like humidity

[slate monolith]

Uh

I guess yeah

[alpine sable]

wind?

[slate monolith]

More particles more drag

For sure

[alpine sable]

the part of the world they throw it on?

[slate monolith]

Yeah

Gravity is just a tiny bit different

[alpine sable]

for gravity reasons right?

[slate monolith]

Yea

[alpine sable]

what about if my school is slightly slanted

Like for example

My apartment is at an 11 degree angle

constantly

[slate monolith]

You’re still standing straight up though

Doesn’t matter how the ground looks like

[alpine sable]

Does the material of the ball matter?

[slate monolith]

Yes

But not in a vacuum

[alpine sable]

Would an object that’s shaped as a Ferrari have a better time going through the air compared to an object shaped like a truck (they are the same weight)

[slate monolith]

Yes

[alpine sable]

and what would be the proper word for how easily air can pass on it

[slate monolith]

Drag coefficient

[alpine sable]

like how race cars are low to the ground for something in the air

[slate monolith]

That’s center of mass

Thats for traction

Not drag

[alpine sable]

and what is the equation for peak velocity based off body weight?

[slate monolith]

That’s something I don’t have memorized

It’s called terminal velocity

You can look up equations online

[alpine sable]

yes I’ve heard of terminal velocity but-

Wait

YOU HAD ALL THIS MEMORIZED?

[slate monolith]

I mean yeah just from life experience

You’ll learn these things too

[alpine sable]

the Magnus Carlsen of math

[slate monolith]

I wish

You’d cover almost all of this in an intro physics class

Which you should be able to take in a few years

[alpine sable]

does high school have physics

[slate monolith]

Yes

Some middle schools too

[alpine sable]

Yay

I don’t get it

[slate monolith]

That’s fluids

Look up terminal velocity

Technically if you’re going on the road you can reach near light speed

For free fall it’s terminal because gravity is only so strong

[alpine sable]

How do I find my mass

[slate monolith]

Weight divided by gravity

[alpine sable]

What’s the gravity?

[slate monolith]

9.8

But the scale already does that

[alpine sable]

146x9.8….

[slate monolith]

So just what it says on the scale

[alpine sable]

1430.8

So my mass is 1430.8

[vapid shuttle]

your weight on earth is different than your weight on other planets

your mass is the same everywhere

[alpine sable]

1430.8 what though

Oh my god

I’m so dumb

[slate monolith]

Your mass is 146 kg

[alpine sable]

Pounds bro😭

bro thinks I’m Eric cartman💀

so 146/9.8

14.8979

Is my mass

so how would I calculate my peak velocity from this?

[slate monolith]

What do you mean by velocity

Which direction

[slate monolith]

No I was wrong

Just convert lb to kg

Don’t /9.8

[alpine sable]

I just wanna know

How fast I can go free falling

[slate monolith]

It depends how you fall

[alpine sable]

Watchu mean

[slate monolith]

If you’re vertical the drag is a lot lower than if you lay down

The higher the drag the lower the terminal belocify

[alpine sable]

in the position that causes minimum drag

[slate monolith]

So standing up

Look it up

[alpine sable]

Ye

[slate monolith]

I have no idea lol

Look up terminal velocity for humans standing up

I’m at 1%

[alpine sable]

120mph

Oh

[slate monolith]

Cool

[alpine sable]

So sorry

[lone heart]

@alpine sable Has your question been resolved?

[slate monolith]

Any other questions

@alpine sable

Actually I realized that mass doesn’t affect the terminal velocity, density does

But since all humans have roughly the same density it’s the same

[lone heart]

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[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[lone heart]

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[deep prawn]

i dont think im getting the right answer and could use some assistance

I'm getting 14 .17 witch doesn't seem like a logical answer to me.

[lone heart]

@deep prawn Has your question been resolved?

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[sweet wolf]

can somebody pls help me

[sweet wolf]

i need to graph this

i need to graph all of these in one graph

<@&286206848099549185>

[wild trail]

what is h(x)?

[gray isle]

seems to be a function they need to make

what have you tried so far?

[lone heart]

@sweet wolf Has your question been resolved?

[lone heart]

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[hasty shale]

what is the actual proper way to solve limits of trigonometric equation?

[hasty shale]

what is the actual proper way to solve limits of trigonometric equation?
like this video he is using this weird swapping numerator and denominator

https://www.youtube.com/watch?v=HbtuSC_WOW0&ab_channel=TheOrganicChemistryTutor

is this just a shortcut?

I've also read that you should find the derivatives of the trigonometric functions to solve these kind of limit problems, which one is better? I want the more "raw" method

[vale wigeon]

do you have a timestamp of the numerator-denominator switching that you mean? @hasty shale

[hasty shale]

3:18 for example

he is using 5/5 and swap the denominator around

I feel like this method is somewhat limited?

[vale wigeon]

let's see here.

this looks fairly benign to me...

do i understand correctly that you don't like shuffling around factors in a product of fractions in the manner shown here?

[hasty shale]

so my understanding is if you want to find limits of trigonometric functions you should find the derivatives right?

https://www.youtube.com/watch?v=Gh48aOvWcxw&ab_channel=TheOrganicChemistryTutor
like in this video (3:33) he is using derivatives

[hasty shale]

yes, don't really like it. If there is a more formal/proper method i'd use it

[vale wigeon]

well, tough luck. that's fairly standard fare imo.

i mean like

you can, if you really want to, write this out as a big product

like sin(5x) * 1/x * 5 * 1/5 and then regroup the 1/x * 1/5 as 1/(5x) and then with the sine as sin(5x)/(5x)

if you want to subject yourself to that

there's nothing improper about doing it the way he does

it is certainly more "raw" than l'hôpital's rule...

[hasty shale]

wait I'll try to solve some problems with derivatives first

it says that it uses l hopital's rule but suddenly tan^2 appears

where does it comes from?

@vale wigeon

Am stuck

[vale wigeon]

eugghhhhhhh

multiple things wrong with all that

first off, you should take everything online solvers tell you with a MASSIVE grain of salt. a boulder of it, even.

second, you don't need l'hôpital here. it's overkill.

third, even if we concede the use of l'hôpital, you are not doing it correctly. you have misremembered the product rule AND you have fucked up the chain rule.

[lone heart]

@hasty shale Has your question been resolved?

[hasty shale]

@vale wigeon honestly all the resources online I found has their own techniques and "tricks", each question has it's own "tricks". Where the way you solve and think about the question is completely different, this course is so hard

[lone heart]

Channel closed

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Use .reopen if this was a mistake.

[wild trail]

.reopen

[hasty shale]

.reopen

[lone heart]

✅

[wild trail]

ah, my bad

.close

[lone heart]

Channel closed

Closed by @wild trail

Use .reopen if this was a mistake.

[hasty shale]

.reopen

[lone heart]

✅

[wild trail]

Also, basic thing to solve trig limits are to remember that

[hasty shale]

there is no general rule to solve trigonometric limits

it's all trial and error

so frustating

sometimes you get lucky and it works sometimes it doesn't

pisses me off

[wild trail]

$\lim_{x \to 0} \frac{\sin x}{x} = 1$ and $\lim_{x \to 0} {\cos x} = 0$

rest is just manipulation

[vale wigeon]

that first limit

[ocean seal]

numbpy

[hasty shale]

@vale wigeon do you know any database of questions and solutions other than youtube videos?

[vale wigeon]

i know of a textbook that has a lot of limit problems, not sure how much of it is this type specifically

demidovich

[hasty shale]

hmm, e books, alright

ill close this for now thx for the help before

.close

[lone heart]

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[wild trail]

for finding the intersection point, just equate them and solve

[lone heart]

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[uncut depot]

how do we know if they are sub-spaces

the definition is there needs to be addition and scalar multiplication over all x in the subspace

and additive identity needs to be there

[wild trail]

yeah so just check those properties

[uncut depot]

but

so the first one had addition, scalar multiplication and since 0 is present does it give way for additive identity

does that make it a sub-space

[wild trail]

the first one looks like a plane passing through origin

[uncut depot]

yes

so its a subspace

[wild trail]

yes

[uncut depot]

3rd one seems to be the same

all of them can be 0

right

what about (b) and (d)

[wild trail]

notice that 0 doesn't belong to (b)

[uncut depot]

thinking of these variables as planes and lines seems to help a lot

[uncut depot]

yes

wait

what

oh

yeah

[wild trail]

does 0 vector satisfy the condition given?

[uncut depot]

no

0 as in (0, 0, 0)

yes

it doesn't

so its not a subspace

[wild trail]

exactly

[uncut depot]

but d is

right

x - 5y = 0

the line passes through the origin

so it must be a subspace?

[wild trail]

I mean, there's a straightforward way to check if the given subset is a subspace (say S)

[uncut depot]

what's the way?

[wild trail]

(1) check if it contains the 0 vector
(2) check if ax + y belongs to the subset S for arbitrary x, y in S and a from the field

[uncut depot]

very nice

so (a), (c) and (d) are the answers

ahhhh

thanks

this was bugging me for a long time

.close

[lone heart]

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[dawn topaz]

-4√6 - √6

[dawn topaz]

Do we also minus 6 and 6?

Then we'll get zero

Riigght?

Or it stays

???

[near plover]

Don't understand what are you asking

[dawn topaz]

.

$-4 sqrt6 - sqrt6$

$-4 sqrt 6 - sqrt 6$

[near plover]

Ok but what is the question...

[dawn topaz]

What is -4√6 - √6

[near plover]

Oh

Do you know the Distributive property?

[dawn topaz]

No im in grade 9

[near plover]

This law

[dawn topaz]

Yes, but my question doesnt has parentesis

[near plover]

Exactly, you have to do the opposite

[dawn topaz]

Ok i just wanna know what happens to the both √6

Cuz i know the -4 will be -5

[near plover]

Yup

[dawn topaz]

Does the both six stays?

[near plover]

So -5√6 since (-4-1)√6

[dawn topaz]

Ok thanks

[near plover]

-4√6 - √6= (-4-1)√6 = -5√6

[dawn topaz]

But

What about -3√27 -3√27 -3√27

?

[near plover]

Same logic

[dawn topaz]

(-3 -3 -3)?

[near plover]

Yup

[dawn topaz]

Coolswagaliciousauce

[near plover]

But here you can even simplify it more

-3√27 -3√27 -3√27 = (-3-3-3)√27 = -9√27 = -9√9√3

-9*3√3 =-27√3

[lone heart]

@dawn topaz Has your question been resolved?

[vague mirage]

@dawn topaz what's your question?

[lone heart]

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[next ivy]

hello

[next ivy]

Can you help me how to solve Corresponding Parts of Congruent ?

[next flame]

No, i dont know what that is

[next ivy]

Oh

Okay 😦

[next flame]

Oh that

[next ivy]

The thing that i dont understand is the "find the values of a,b,c,d and e"

[next flame]

I don't have technical vocabulary knowledge to help but its about calculating crossing path angles

[next ivy]

oh

ok

im gonna try to search it ig (i might get wrong answer 😦 )

byee

ty

.close

[lone heart]

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[karmic wharf]

The Standard Cost of Chemical mixture ‘PQ’ is as follows:
40% of material P @ Rs.400 per kg. 60% of material Q @ Rs.600 per kg.
A standard loss of 10% is normally anticipated in production.
The following particulars are available for the month of March, 2004.
180 kgs of material P have been used @ Rs.680 per kg
220 kgs of material Q have been used @ Rs.360 per kg.
The actual of production of ‘PQ’ was 369 kgs.
Calculate the following variances:
a) Material Price Variance
b) Material Usage Variance
c) Material Mix Variance
d) Material Yield Variance

3. Following in the Trial Balance of a limited Company as at 31st December, 2021
   Particulars Debit Credit
   Share Capital 4,00,000
   Cash in hand 6,200
   Rent 5,300
   Prepaid Expenses 4,600
   Repairs & Maintenance 8,600
   Advances from Customers 50,000
   General Reserve 3,00,000
   Raw Materials at Cost 2,67,000
   Sundry Creditors 3,40,000
   Plant and Machinery 4,30,000
   Power 8,800
   Travelling and Conveyance 4,100
   Auditors’ Fees 1,500
   Cash at Bank 8,000
   Land 30,000
   Provision for Taxation 2,10,000
   Furniture 12,200
   Staff advances 5,300
   Sundry Debtors 1,40,000
   Misc. Income 54,600
   Finished Goods at cost 3,10,000
   Income-tax Advances 3,00,000
   Misc. Expenses 61,400
   Raw Materials Consumption 28,60,000
   Sales 42,30,000
   Development Rebate Reserve 1,00,000
   Building 74,100
   Salaries, Wages &Bonus 11,60,000
   Cash Credit from Bank 12,500
   Total 56,97,100 56,97,100
   The following additional information is also available:
   (20)
   i) The authorized capital of the company is 80,000 equity shares of Rs. 10 each
   of which 50% has been issued and has been recommended by the directors.
   ii) A dividend of 15% on the paid-up capital has been recommended by the
   directors.
   iii) The closing stock of finished goods at cost is Rs. 5,60,000.
   iv) The development rebate reserve is no longer required.
   v) Depreciation on plant and machinery amounting to Rs. 43,000 on furniture
   amounting to Rs. 1,300 and on building amounting to Rs. 3,800 has been
   debited to miscellaneous expenses.
   vi) Surplus in profit and loss account after proposed dividends, is to be transferred
   to general reserve.
   vii) Income-tax assessment for a prior year has been completed, fixing the income
   tax liability at Rs. 1,55,000 (against which a provision of Rs. 80,000 and
   advances of income tax of Rs. 70,000 exists in the books).
   You are required to prepare:
   i. Profit and loss account for the year ended 31st December, 2004; and
   ii. Balance sheet in the prescribed form as on that date.

The Standard Cost of Chemical mixture ‘PQ’ is as follows:
40% of material P @ Rs.400 per kg. 60% of material Q @ Rs.600 per kg.
A standard loss of 10% is normally anticipated in production.
The following particulars are available for the month of March, 2004.
180 kgs of material P have been used @ Rs.680 per kg
220 kgs of material Q have been used @ Rs.360 per kg.
The actual of production of ‘PQ’ was 369 kgs.
Calculate the following variances:
a) Material Price Variance
b) Material Usage Variance
c) Material Mix Variance
d) Material Yield Variance

[next flame]

Imo its about Thales Therorem. You have to search about it more how angles stay the same and caluclate missing angles by values you know (like how triangle and straight line have 180 degrees)

[karmic wharf]

The Standard Cost of Chemical mixture ‘PQ’ is as follows:
40% of material P @ Rs.400 per kg. 60% of material Q @ Rs.600 per kg.
A standard loss of 10% is normally anticipated in production.
The following particulars are available for the month of March, 2004.
180 kgs of material P have been used @ Rs.680 per kg
220 kgs of material Q have been used @ Rs.360 per kg.
The actual of production of ‘PQ’ was 369 kgs.
Calculate the following variances:
a) Material Price Variance
b) Material Usage Variance
c) Material Mix Variance
d) Material Yield Variance

Please this one

[next ivy]

o i got it now

[lone heart]

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[next ivy]

the other sides (left and right) have the value for abcde which is the numbers

[next ivy]

oop

[pseudo ice]

Did you want to open the channel again? (if not, please .close it )

[karmic wharf]

10+10 how much

20+20 equal to =

hey anyone here

[mortal trellis]

dont troll in help channels

[next ivy]

.close

[lone heart]

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[raven haven]

.coose

.omg you can type anything if you dontt

[lone heart]

@fickle oyster Has your question been resolved?

[lone heart]

@fickle oyster Has your question been resolved?

[pseudo ice]

Where have you gotten to? any ideas at all?

[lone heart]

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[misty sparrow]

How to combine 4 and 1/6? The calculator says when you combine the whole and fraction parts it will be 3 and 5/6

[lunar palm]

write 4 as an improper fraction over 6

you can add and subtract fractions only if the denominator is the same

[gray isle]

the ideal route would depend on your end goal

if you goal is to get a mixed fraction

then you can first express the 4 as 3 + 1 to get
$$4 - \frac 16 = 3 + \blue{1 - \frac 16}$$
then simplify the part in blue. go through the process of getting a common denominator etc.

[ocean seal]

ℝamonov

[misty sparrow]

Wasn't the 4 and 1/6 already a mixed numbers? The calcu and I both got the same answer of 4 and 1/6 then I wonder why it needs to do combining. Same goes to the book that I'm using to study

[gray isle]

mixed numbers would be stuff like
$$3 \frac 23$$
$$-2 \frac37$$

[ocean seal]

ℝamonov

[gray isle]

4 - 1/6 isn't in a form like that

ideally, you'd simplify as much as possible

[misty sparrow]

where did the - after 4 came from?

because my answer in the paper was 4 and 1/6 not 4 - 1/6

ohh maybe I know, because I subtracted lower number (1 - 2)

[quaint sinew]

they are different

4 - 1/6 means you are removing 1/6 from 4

4 and 1/6 means theres 4 and 1/6 more

[misty sparrow]

Yeah

[misty sparrow]

Though I still can't understand this part

[near plover]

Why?

[quaint sinew]

4 just becomes 3+1

[misty sparrow]

Thank you for the help guys, I still can't figure it out. I'm closing this thread.

.close

[lone heart]

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[slate solar]

How come the matrix's above became the ones below?

[slate solar]

Whats the calculation to simplify the matrix?

[sand pawn]

wdym?

It's just some simple matrix multiplication

[slate solar]

Can you explain it

Or like tell me what to search

"Matrix multiplication"?

[sand pawn]

They just substituted the value of Matrix A and Identity matrix

in that equation

BTW, do you actually know what a matrix is?

[slate solar]

Yeah

Have not encohntered the multiplication yet

Well i have now ig

Well thanks

.close

[lone heart]

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[sand pawn]

tell me the definition of matrix

[slate solar]

An array of matrices, consists of rows and columns defined as K x L, k for rows and L for columns, there ate many types of matrix such as zero matrix which consists of only 0's , row or column vector

Identity matrix,

Diagonal of a matrix

There is also the tranpose

Basically you replacd the column and make it a row and exc.

[sand pawn]

That is not how you define it

[lone heart]

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[slate solar]

Then bless me with the definition

[sand pawn]

Matrix is a mathematical entity that performs linear transformation upon a bijective function

[slate solar]

I see, i tried to teach to myself informally, like 15 minutes ago, so thank you for the information

[sand pawn]

let me give you a headstart on this

https://youtube.com/playlist?list=PL0-GT3co4r2y2YErbmuJw2L5tW4Ew2O5B

@slate solar you shall follow this playlist

it will give you the deepest of the insights and intuition available on the internet

@slate solar you should close this channel

[lone heart]

@slate solar Has your question been resolved?

[lone heart]

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[chrome depot]

I have to solve this equation

[chrome depot]

10x + 9y = 1009

x, y >= 0 (integers)

The idea is that I would like to solve this nicely without brute forcing combinations

Modular arithmetic here is at play

I know that

1009 - 10x should be divisible by 9

Am I right?

[dense blaze]

theres this thing called Diophantine equations

which may help

[chrome depot]

Let me check it out

[lone heart]

@chrome depot Has your question been resolved?

[quasi vector]

yes

you can simplify that expression

using the rules of modular arithmetic

[chrome depot]

How could that be done

[quasi vector]

you can reduce 1009 to 1

as 1009 is congruent to 1 (mod 9)

[chrome depot]

okay so what do I get on the left side?

10x + 9y = to what ?

[quasi vector]

well

first

[chrome depot]

9y will be 0

[quasi vector]

you take mod 9 on both sides

yes

and 10x will be?

[chrome depot]

but what about 10x hmmm

that doesn't have to be 1 necessarily

that can vary depending on x

[quasi vector]

can't you simplify 10x to x?

since you're given that x is an integer

[chrome depot]

yes x is an integer

but how do I simplify ... 10x to x wdym xd ?

substitution or smth ?

t = 10x

[quasi vector]

you are doing 10x mod 9

correct?

[chrome depot]

indeed

[quasi vector]

you can write 10x as 9x + x

and 9x will always be a multiple of 9

since x is an integer

[chrome depot]

oh

now ...

that's an interesting observation

so we have (9x + x) mod 9 = x mod 9

since 9x mod 9 = 0

[quasi vector]

yes

[chrome depot]

but x mod 9 varies because x varies too

and there are no additional rules

[quasi vector]

and what would you get on the right hand side

[chrome depot]

1009 mod 9 is 1

x mod 9 = 1 ?

[quasi vector]

yes

so

can you write x as 9k + 1?

[chrome depot]

indeed I can

[quasi vector]

so

put that expression into the original expression

90k + 10 + 9y = 1009

[chrome depot]

90k + 9y = 999
9(10k + y) = 999
10k + y = 111

[quasi vector]

that works

now how can you find a similar expression for y

[chrome depot]

I am not really sure how do you want me to do that since 9y is 0 mod 9

[quasi vector]

what about mod 10?

since 10k would just go down to 0

[chrome depot]

Ohhhh

You meant

This new equation

Not the first one

Well then yes mod 10 could work

and y mod 10 would stay 1 mod 10

while 111 would be 1

k + (y mod 10) = 1

[quasi vector]

why do you have k?

10k would just be 0

wouldn't it

[chrome depot]

Oh yes we are doing mod not division

Absolutely right you are

10k + y = 111 (mod 10)
y mod 10 = 1

hmmmmm

[quasi vector]

yes

so

[chrome depot]

I see

Now that simplifies a lot of stuff

[quasi vector]

try writing y in terms of a different variable

perhaps m

[chrome depot]

y = 10m + 1

[quasi vector]

so y = 10m + 1

yes

put that in the original equation again

and you will get a lot less cases

[chrome depot]

10k + 10m + 1 = 111

[quasi vector]

you will get 10k + 10m + 1 = 111 which simplifies to k + m = 11

[chrome depot]

Does it ?

10k + 10m = 110

10(k+m) = 110

Oh

yeah it does

Had to check myself

k + m = 11

Now that's legendary stuff

It's easy to test it out now

[quasi vector]

you have x = 9k + 1 and y = 10m + 1

so

k and m can take values of 0 as well

one small thing to keep in mind

[chrome depot]

Makes sense

I will do whatever rest I have myself and go through the process once again

Thank you kindly for your nice and detailed help!

[quasi vector]

no worries

[chrome depot]

Is there any resource on modular arithmetic you would suggest

[quasi vector]

https://www.youtube.com/watch?v=lJ3CD9M3nEQ

you could watch this video

it doesn't really go into any theory but it can give you a good understanding of modular arithmetic

[chrome depot]

Alright

Thank you very much for that too 😄

.close

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[hidden pike]

I have been trying to understand the proof of gaussian integral using Polar Coordinates (i don't know much about multivariable calculus, learning things by myself and internet + ChatGPT), and so now, the issue is, they considered x^2 + y^2 = r^2
now i didn't got how'd they got dxdy = rdrdθ
PS: I know about polar coordinates (basics i guess)

[quasi vector]

it comes from the jacobian matrix

[hidden pike]

yes yes

i used ChatGPT to find what did they do

it replied something like Jacobian matrix

what exactly is it?

[quasi vector]

that's...

not a good idea

do not use ChatGPT to understand any topic, especially mathematics

[hidden pike]

yeah

right

[quasi vector]

https://www.youtube.com/watch?v=wUF-lyyWpUc

[hidden pike]

i was just stuck so did that
then i remember this server exists

[quasi vector]

this is a good video on the jacobian matrices

[hidden pike]

oh ok sure

[hidden pike]

i didn't understood what happened here?

[lone heart]

@hidden pike Has your question been resolved?

[lone heart]

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[opal ruin]

for a parametrix equation that describes a plane, is 'q' and 'r' just two vectors parrallel to the plane?

[lone heart]

@opal ruin Has your question been resolved?

[opal ruin]

.close

[lone heart]

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[nova linden]

can someone help me with this?

[onyx storm]

ok you understand that s=3 as i see right?

[nova linden]

yep

[onyx storm]

also if we add all the values up it also equals to 25 right?

p+q+r+s=25 i mean

[nova linden]

I would assume so yes

[onyx storm]

do you also get that equation?

ok so

[nova linden]

yeah makes sense

[onyx storm]

if we subtract the value of s we are left with

p+r+q=22

[nova linden]

yea

[onyx storm]

which 2 numbers correspond to the number of chemistry students?

[nova linden]

in terms of what it gives us?

[onyx storm]

yeah

[nova linden]

18 and 12?

[onyx storm]

in the diagram chemistry students are at p and r

yea?

[nova linden]

i mean r is also in p

sorry q

[onyx storm]

physics students are at r and q then?

[nova linden]

yeah

[onyx storm]

if we add em up we get p+2r+q=30

[nova linden]

which isnt right

[onyx storm]

in that we are counting students that got both chem and physics 2 times

[nova linden]

ahh

[onyx storm]

and we found out p+r+q = 22

[nova linden]

yeah

[onyx storm]

what is the value of r?

[nova linden]

6?

[onyx storm]

nope

try again

p+2r+q = 30
p+r+q = 22

[nova linden]

2r?

[onyx storm]

the value of r, what is it?

[nova linden]

im not sure how to get there, is it something in the middle of 18 and 12?

[onyx storm]

so you know how some students got both lessons and some only 1?

[nova linden]

yeah

[onyx storm]

r is the number of students that got both lessons

[nova linden]

yeah

[onyx storm]

we found out the number of students that got lessons to be 22 yea?

[nova linden]

yep

wait

[onyx storm]

and the number of physics students to be 12, chem to be 18

[nova linden]

yeah

[onyx storm]

if we add those up we get 30 but we count each group seperatly

[nova linden]

8?

[onyx storm]

so we accidentally add the students that got both 2 times

[nova linden]

get tf out

[onyx storm]

as an atheist you need god in your life please get a life

[nova linden]

as an atheist, i can whole heartedly agree

[onyx storm]

yeah thats the amount of students that got both lessons

[nova linden]

yeah

then subtract from each each group?

[onyx storm]

yeah and you get the number of p and q with it

<@&268886789983436800>

[nova linden]

bro im tryna learn math with @onyx storm i dont need your 1+1=2in humor

sorry moderator potato

thank you mods

[sleek gyro]

the guy with the pfp?

[nova linden]

yep

[sleek gyro]

ok, done

[nova linden]

ty

[onyx storm]

yeah thanks

[nova linden]

ok so

[onyx storm]

you found out s and r now for p and q

[nova linden]

ok hang on

[onyx storm]

can you resend the photo if its not a problem? its a pain scrolling up

[nova linden]

chem is 10 and 12 is 4?

no problem

[onyx storm]

yep! chem only students are 10 people

physics only are 4

[nova linden]

cool!

[onyx storm]

which are p and q accordingly

[nova linden]

yeah

[onyx storm]

good job you found it out, i wish you luck on your journey

[nova linden]

so is there a formula for that or just figuring it out?

[onyx storm]

you just gotta run your mind on it,

[nova linden]

cool

[onyx storm]

find the p+r+q and p+2r+q for these types of questions

go to find r and then p or q whichever needed

[nova linden]

yeah

cool thanks!

[onyx storm]

np!

[nova linden]

👍

[onyx storm]

type with .

instead of !

[nova linden]

got it

.close

[lone heart]

Channel closed

Closed by @nova linden

Use .reopen if this was a mistake.

[lone heart]

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[tribal falcon]

I have a question about the ZF pair set axiom. Are the amounts A and B only containing one element each, two or more?

[tribal falcon]

It says for all A, B there exists a C, and for all D that D is an element of C and that's equivalent to D = A or D = B

A = [1], B = [3], C = [1,3], D = [1] or [3]?

[lone heart]

@tribal falcon Has your question been resolved?

[sly mantle]

@tribal falcon A,B are to be thought of as objects not sets

essentially it says if a,b are objects then the pair set {a,b} exists

or more formally there exists C (the pair set {a,b}) such that x is in C iff x=a or x=b

[tribal falcon]

I was afk, but great thank you, that makes a lot more sense! ❤️

.close

[lone heart]

Channel closed

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Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[uneven folio]

I got x^2 - x = 2

[uneven folio]

i can make it to x^2 -x - 2 but i am stuck here

[quasi vector]

try splitting the middle term

so that you can factorise the expression

[uneven folio]

i am not sure if i heard about splitting a term

[quasi vector]

i would suggest looking up a youtube video on the topic

[modern sedge]

how do you factor quadratic equations?

[uneven folio]

ax^2 + bx + c?

[modern sedge]

yep, how do you solve it?

[quasi vector]

explaining the process of factoring quadratic equations through discord is both tedious and ineffective. look up a youtube video

[subtle birch]

Have you heard of the quadratuc formula or shreedharaycharya's formula

[uneven folio]

I think you are atalking about -p/2 √(p/2)^2 - c

[modern sedge]

do you mean sridhara's?

[uneven folio]

I am not sure that is the one you are talking about casue im swedish so i dont use the same words

[quasi vector]

what?

[subtle birch]

(-b±(b^2-4ac)^(1/2))/2

[quasi vector]

https://www.youtube.com/watch?v=YMBjk_v-0j8

please

watch this video

or any other video

[modern sedge]

I've never heard it before

[uneven folio]

I solved it useing a thing called "Kvadratkompletering" i dont know the english word

.close

[lone heart]

Channel closed

Closed by @uneven folio

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Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[proper quiver]

Im supposed to evaluate how to calculate epsilon using trig functions. The answer I came up with is arctan((H-a)/d)+arctan(a/d). Which looks correct for me, but I seem to be missing something. My books solution tells me it is arctan((H*d)/(a^2-H*a-d^2)) What am I missing?

[minor needle]

reason might be usage of identity

[proper quiver]

Sorry if this is a stupid question, but what is that?

[minor needle]

,w ((H-a)/d+a/d)/(1-((H-a)/d)*(a/d)) simplify