help-33

[velvet yarrow]

then im cooked for final exams

cause then all the "probabilty" questions are wrong

[spark otter]

the solution is wrong

I'll briefly reexplain why

when you do (cases that work)/(total number of cases)

this gives you the probability ONLY if each case has the same probability of happening

[velvet yarrow]

right

[spark otter]

this is the "plane crash into my house" example all over again

[velvet yarrow]

so MMII does not have the same probability as M I N U

[spark otter]

for example yes

[velvet yarrow]

right

yeah

fair enough

it makes sense now

what about this noe

is it just 8C4 - 5C1 / 8C4

[spark otter]

uh

with parentheses?

[velvet yarrow]

yeah

[spark otter]

are there really only 5 equally likely scenarios where this is false?

out of the 8C4 choices?

[velvet yarrow]

oh wait its 5C2/8C4

[spark otter]

yeah exactly

[velvet yarrow]

is there some wack probability mistake here

cause theres an equsl cahcen of each thing

oh right

[spark otter]

here there is an equal chance of every combination of 4 students happening

considering each student is different

[velvet yarrow]

so that previous question is an anomali

[velvet yarrow]

yh ok

[spark otter]

yeah, it's teacher's fault for that mistake

or whoever wrote the previous solution

[velvet yarrow]

idk found it online

well ok

thanks a lot then

.close

[marsh citrus]

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[marsh citrus]

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[hollow dune]

I have problem with the question number d)

What am I supposed to do

I have the solution sheet but I don't understand the next step and the other steps

Can you explain the concepts in a way that I can generate the answer here and in similar questions to this or very different but basically be able to apply the concepts

[main idol]

find all ways X1 + X2 can add up to 5

[marsh citrus]

@hollow dune Has your question been resolved?

[marsh citrus]

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[hollow dune]

.reopen

[marsh citrus]

✅

[hollow dune]

What is X_1 and X_2 from the question

X1 and X2 value

[main idol]

X1 and X2 are copies of X

[hollow dune]

So they have the same probabilities for each x value

[main idol]

right

[hollow dune]

Based on the x values

they can't add up to 5

based on the distribution table I mean

So I take both those probabilities and say = 0 bcz they are not 3 or 2 but

4+1 is possible so maybe there is 1

Ya but as an individual value there is no 1

So its basically asking the probability of any of the 2 random variables sum being 5

But that is not possible even if we add any 2 random variables

[hollow dune]

But what is the intersection part then

[hollow dune]

^

[hollow dune]

Why in the solution sheet only 2 ways have been considered 3 2 and 2 3 why not 4 1

[main idol]

which x value gives X1 or X2 equal to 4

[hollow dune]

no value

This is so abstract

[main idol]

so why do you think this is possible

[hollow dune]

But then 3 and 2 is also not possible

so why we consider that

[main idol]

2 is certainly possible

[hollow dune]

how?

[main idol]

oh you're right it has probability zero

but it takes some checking because x=2 is part of the definition

[hollow dune]

takes som checking meaning

[main idol]

i guess that's all the solution is saying

[hollow dune]

Definition of what?

[main idol]

verifying that when x=2 that that's 0

whereas for x=4, there's nothing to check

since this is 0 when x=4

[hollow dune]

Oh so we have to always take x values which are there in the distribution

as the random variables

[hollow dune]

So what is the intersection part meaning

is that just the addition rule

So there are two independent observations so that's why 2 3 3 2

[main idol]

yes

[hollow dune]

If based on probability we have an independent observation

it can be 2 3 2 3 twice as well

right

[main idol]

no idea what you mean

[hollow dune]

or because of the same value that observation would be same

[hollow dune]

In the solution sheet

[main idol]

(X1=3) and (X2=2) is different from (X1=2) and (X2=3)

[hollow dune]

It says P(X 2 intersection 3 ) + P (X 3 intersection 2)

[hollow dune]

Got it and what about the intersection part

[main idol]

i don't know what you're confused about

[hollow dune]

This

like the P (X_1=2 intersection X_2=3)

[main idol]

uh huh what about it

[hollow dune]

and the other way around

So how did intersection come here

What's the conceptual reason of it being here

[main idol]

2 + 3 = 5

[hollow dune]

I have not conceptually connected probability rules with discrete random variables that well I feel

So the value of probability

But why intersection

intersection is plus

But union is plus right?

[hollow dune]

Is intersection plus or union plus or both of them are plus?

[main idol]

intersection means "and"

[hollow dune]

Is it possible I could have done the question just like this without the intersection signs like
P(X1=3)+P(X2=2)= 0+0= 0

[main idol]

union means "or"

[hollow dune]

So both cases we add?

[main idol]

no this is not true in general

If $A = [X_1 = 3], B = [X_2=2]$, then $P(X_1 =3 \cap X_2 =2) = P(A \cap B) = P(A) * P(B)$ by independence

[elfin berry]

riemann

[hollow dune]

How do we know they are independent

But if its independent then it will 3*2 = 6

[main idol]

read your problem more carefully

[hollow dune]

I am so sorry

for a useless question

[main idol]

nowhere did i say P(A) = 3

[hollow dune]

so why in the solution sheet the probability is added is that a mistake

because it should 0*0

=0

[main idol]

it's not wrong, just skipped a step. 0 * 0 + 0 * 0 = 0

[hollow dune]

Oh

makes sense

For the next part of the question

I just add the random variable probability values to make y

[hollow dune]

So have spent some time doing this question and understanding more

Is y=3 wrong because that is possible if $$P(X_1=2) \times P(X_2=1) +P(X_1=1) \times P(X_2=2)= 0 \times 0.25+0 \times 0.25=0$$

[elfin berry]

Educo

[hollow dune]

I think this question is almost done just this last knowledge gap

So is my working correct for y= 3 the end one

[marsh citrus]

@hollow dune Has your question been resolved?

[marsh citrus]

@hollow dune Has your question been resolved?

[hollow dune]

<@&286206848099549185>

[hollow dune]

<@&286206848099549185>

[hollow dune]

<@&286206848099549185>

[hollow dune]

its not correct I am not getting the answer but for the same process I am getting the previous answers

[hollow dune]

<@&286206848099549185>

[still temple]

if no one is answering cant you just try chatgpt or something

[hollow dune]

tried chatgpt didn't understand

Are you a helper?

[still temple]

oop-

[still temple]

i try 😶

[hollow dune]

Got it you will get there

[still temple]

but i dont know how to solve it

[still temple]

thank you

[hollow dune]

Your Welcome

[still temple]

i hope you find your answer tho

[hollow dune]

Thank You

[still temple]

is it an assignment

[hollow dune]

Its a practice Q topical stats

A level Maths

[still temple]

have you asked a teacher

[hollow dune]

I have no teacher since doing maths a levels for the first time as I am going in CS quit medicine so not in a school anymore already graduated

[still temple]

oohhh welp idk anymore uhm wow

have you tried photomath thats my last suggestion ig

[hollow dune]

Ya didn't check that let me check Ty for the suggestion

[still temple]

👍

[hollow dune]

.close

[marsh citrus]

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[marsh citrus]

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[slim nest]

Two identical rectangular prisms each have a height of 90 centimeters (cm). The base of each prism is a square, and the surface area of each prism is Kcm. If the prisms are glued together along a square base, the resulting prism has a surface area of 92/47 ​K cm2. What is the side length, in cm, of each square base?

[marsh citrus]

@slim nest Has your question been resolved?

[limpid pond]

When we combine the 2 rectangular prisms we get 2K-2s^2
the reason behind -2s^2 is because when we combined the 2 rectangular prisms we lost the area of the square base at the end
And we know the surface area of the two prisms combined is 92/47K so 2K-2s^2=92/47K

[marsh citrus]

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[upbeat tree]

hello

[upbeat tree]

how does $1/a+b * (1/a+1/b)$

[elfin berry]

3rdWorldHero

[upbeat tree]

can someone tell me how to make $ a/1$ make numerator and denom on bottom ?

$x//y$ test

[elfin berry]

3rdWorldHero

[upbeat tree]

.close

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[slim nest]

Okay, how can I find side length s?

Can I substitute 'k' for 2s^2+4sh? It will then become like this 2(2s^2+4sh) -2s^2=(92/47)K

Is that correct?

[limpid pond]

yes but it’s preferred to keep K as K

It’ll make solving the equation easier

[slim nest]

Okay

[marsh citrus]

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[arctic bison]

Is that right?

[marsh citrus]

@arctic bison Has your question been resolved?

[still temple]

What are u trying to do

Just take the derivative of those terms?

[arctic bison]

Im on the second derivative

Wanted confirmation these were the rules for the next derivative

[still temple]

6cos(x^2) + 12x^2(-sin(x^2)) first derivative, yes

df/du du/dx

[arctic bison]

Idk the d format well.

I was just asking someone how important is it to learn because I only know the f(u) format. 😅

[still temple]

Say you have a function of x:

cos(x^2).

You define u as x^2.
f(u)=cos(u)

df/du means take the derivative of cos(u) with respect to u

du/dx means take the derivative of u with respect to x. So it’s the derivative of x^2

[arctic bison]

Oh youre just saying I need to chain rule.

I think I know how to do the rules I wrote down. Just wanted to make sure I wasnt missing one.

[still temple]

Looks all good

[arctic bison]

Ayy, thats good to hear. Identifying when to use them has been my biggest issue. Thanks for the verification before I do all the math for it.

Hopefully wont be back to ask where I messed the math up. 😂

.close

[marsh citrus]

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[molten ferry]

what does $\frac{\partial^2}{\partial x\partial y}$ mean

[elfin berry]

Jash

[fervent rampart]

,, \pdv{}{x,y} = \pdv{}x \pdv{}y

[elfin berry]

cloud

[fervent rampart]

so it's the second partial derivative, first with respect to y and then with respect to x

[molten ferry]

so does this mean to multiply the partial derivative with x with partial derivative with y

[fervent rampart]

no, it means take the partial derivative with respect to y, then take the partial derivative of that with respect to x

[molten ferry]

ohh

[main idol]

Should do a couple examples to get accustomed to the notation

[molten ferry]

ye cuz im tryna figure out hessian determinant

[main idol]

Try evaluating this for f(x,y) = sin(x) * e^y

[molten ferry]

f^(0,1)(x,y)=sinx e^y

partial derivative of that wrt x is e^y cosx

[molten ferry]

is it e^y cosx

im stuck

[main idol]

That's not readable

[molten ferry]

im trying to find if a function has a global extrema

or global minimum

or neither

and the function given is $f(x,y)=\frac{\sin x+\sin y}{x^2+y^2+2}$

[elfin berry]

Jash

[molten ferry]

i tried solving $\nabla f(x,y)=(0,0)$

but mathematica couldnt solve it

[elfin berry]

Jash

[main idol]

Yea find one partial at a time then

[marsh citrus]

@molten ferry Has your question been resolved?

[marsh citrus]

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[swift olive]

I simplified it to

$\frac{x^4-a^4}{x-a}$

[elfin berry]

smeagol

[swift olive]

Then put a = 1

.close

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[swift olive]

i gtg I'll be back later

[marsh citrus]

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[buoyant jetty]

.close

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[boreal pine]

Me and some of my friends are having trouble understanding what to do on this question. We were told to use laws of sin or cos

[clever spade]

what does FR represent?

[boreal pine]

The resultant

[clever spade]

well given you don't know the angle

you will most likely be using inverse trigonometric functions

You could put each vector tip to tail and redraw (which is often useful in force questions)

[boreal pine]

like this? or with 2 vector meeting at 1 point

or perhaps this way?

[marsh citrus]

@boreal pine Has your question been resolved?

[boreal pine]

After trying to use cos to find the angle i got 1.709 degrees would that be correct?

i'll try again another time as Im having a headache

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[inland prawn]

How do I even start

[marsh citrus]

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[compact sentinel]

hello

[compact sentinel]

quick question

how is this not right

shouldnt it be a right triangle, with the left leg as some variable h, the bottom leg as 7, and the hypotenuse as 25?

doing pythagorean theorem gives 24 as the left leg initally

and then shouldnt you be losing 2 per second since it falls 2 feet per second?

[sinful skiff]

Well it stays a right triangle so you can use Pythagoras theorem I guess, do something like y(t)^2+x(t)^2=25^2

Then solve for y in terms of t after plugging in x

[compact sentinel]

thta makes sense

lemme try

so like

$y(t) = \sqrt{625-(7+2t)^2}$

[elfin berry]

j

[compact sentinel]

would this be like rightg

[sinful skiff]

I mean you could maybe try to simplify

[compact sentinel]

Ok

[sinful skiff]

See if it’s possible

But that does look good to me at least until the ladder is perfectly flat

Then it would break down

Since Pythagorean theorem breaks

[compact sentinel]

$2\sqrt{144-7t-t^2}$

[sinful skiff]

But it also doesn’t matter much since that’s at the end of the motion

[elfin berry]

j

[compact sentinel]

this is the most simplified it gets

it worked

thank you my beo

[sinful skiff]

👍

Did it make sense how I got that

[compact sentinel]

wait why would this not be 24 tho

[compact sentinel]

Yea

I forgot that part we learned it last year

[sinful skiff]

Well try plugging 24 into that

[compact sentinel]

It makes sense so Thank you my friend

[sinful skiff]

Tell me what happens

[compact sentinel]

oh its imaginary

[sinful skiff]

Yess

So try to solve the inequality 144-7t-t^2 >= 0

[compact sentinel]

$-16\le :t\le :9$

[elfin berry]

j

[sinful skiff]

Remember that it’s not the range but the domain

That’s why 24 doesn’t make sense here

[compact sentinel]

Ah

But since it cant be negative

[sinful skiff]

It doesn’t take 24 seconds to fall

[compact sentinel]

0<=t<=9?

[sinful skiff]

Yeah time would be positive generally

[compact sentinel]

Wonderful

[sinful skiff]

At t=0 it’s at its peak

22 ft I guess

[compact sentinel]

Thank you very much Bro

[sinful skiff]

24*

[compact sentinel]

Ahhh Oh i was confusing range with it earlier too

I see what i did wrong

[sinful skiff]

Yeah exactly

[compact sentinel]

Thank you so much

[compact sentinel]

Wait 9 was wrong

[sinful skiff]

,w t^2+7t-144

[elfin berry]

Results provided by WolframAlpha

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

Requested by llspacebarll

[sinful skiff]

Hmm

,w -t^2-7t+144

[elfin berry]

Results provided by WolframAlpha

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

Requested by llspacebarll

[sinful skiff]

I mean I don’t know what else it would be then

The y function is correct

[compact sentinel]

yeah

[sinful skiff]

And at t=0 it outputs 24 and at t=9 it goes to 0

[compact sentinel]

yea

[sinful skiff]

So that should be the time elapsed for the motion

Maybe do -16 to 9

Because it just ask about the range of t values for the function

Not necessarily referencing the physics

[compact sentinel]

I cant change my answer from 0 as the first one since its correct

[sinful skiff]

Oh lol I’m blind I see

[compact sentinel]

lol

i might just ask other people if they got it

but i have to wait until monday then

but this is so stupid

[sinful skiff]

I don’t think we did anything wrong and I can’t see anything in the problem statement that’s tricky

Could it be a quirk with the program maybe

Like does it want 9.0 or something dumb like that

Do you have unlimited attempts?

[compact sentinel]

nope

i think if i miss it once more I lose points for the question

[sinful skiff]

That’s unlucky

Then I would wait

[compact sentinel]

yeah this program we use sucks

[sinful skiff]

This should be right so maybe talk to your teacher about it

[compact sentinel]

i lost two points earlier for rounding differently than them.. even tho i was correct

[compact sentinel]

Ok

Thank you for helping

[sinful skiff]

No problem good luck

[marsh citrus]

@compact sentinel Has your question been resolved?

[marsh citrus]

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[humble lichen]

Just wanted some confirmation if I'm doing this right, basically all I want to do here is integrate right? the position is just whatever(t) which is already there on the right just naturally and then the initial condition would basically just be the integrated version + c which would make the initial condition 1 = c

[humble lichen]

.close

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[terse vine]

This is gr 12 math

And we’re doing long division with polynomials

Except I’m confused on the next step

Like what do I do

Should I bring the -2x^2 down?

Because I have 3x^3 - 7x^2

Oh nvm

.Close

.close

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[still temple]

We're trying to find a way to make the number 1 go up and down by 10% and 20% stackable modifiers using this equation where a is a 10% stackable modified, b is a 20% stackable modifier, and c is a stackable 10% modifier but we keep finding ourselves with a loss after a couple of stacks

1*((a/5) + 1) * ((b/10) + 1) *1/(c/10) +1

if a=1 , b = 1 , c = 1:
1*((a/5) + 1) * ((b/10) + 1) *1/(c/10) +1 = 1.2 (Good)

if a=-1 , b = 1 , c = 1
1*((a/5) + 1) * ((b/10) + 1) *1/(c/10) +1 = 0.8 (Good)

if a = 2, b = 2, c = 1
1*((a/5) + 1) * ((b/10) + 1) *1/(c/10) +1 = 1.52727272727 (Bad)

Is there a better way to do this?

[marsh citrus]

@still temple Has your question been resolved?

[chilly spoke]

why's 1.52727 bad?
what do you want it to be?

[marsh citrus]

@still temple Has your question been resolved?

[still temple]

I think the original equation will actually give us a better idea of what we're trying to do , I may have biffed the explanation a lot because I'm really tired right now , sorry

[still temple]

the one i just sent is the original equation , we tried to play around with it to figure out something a little better and we figured that first one i sent here was a better equation for what we were trying to do

[chilly spoke]

so do you want it to be like 9 instead of 9.0909...?
if so, you can use b*(1 - x/10) instead

you want this to be additive stackable right?

[still temple]

i believe so yeah

i also just kind of want to know why the final number is doing that in the first place

because maybe we can also just figure it out from there

[chilly spoke]

it's doing that because multiplying by 1/1.1 is equivalent to solving what base so that a +10% modifier would make it 10
and it's not 9 bc 9*1.1 is just 9.9

[marsh citrus]

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[marsh citrus]

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[marsh citrus]

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[compact crescent]

heelo

[still temple]

heeelo

just ask

[compact crescent]

I have a geometric question.

[still temple]

just ask

[vernal forge]

ask

[quaint elm]

pcmg you've done this so many times. When you start a new channel, you should ask your question in the first message.

[compact crescent]

I'm discouraged to ask question. I had a negative feedback which makes me feel sad

I will send you the link

#help-9 message

people told me to close my channel and then left me

Anyway.

Given a point, let's say P, on the xy plane such that PB/PA=3/1
Would the trail of P be a circle?

[quaint elm]

what have you tried?

[compact crescent]

my approach makes me sad

I assume P=(x,y)

I cannot see the graph of P

furry animal!

[compact crescent]

until I got that very bottom line and realized it is a circle.

furry animal!

[compact crescent]

why?

why

I do not like the algebra-based solution

it is bulls

I should see the graph at the first sight like a robot

and I DO NOT HAVE TO BE A ROBOT TO RECOGNIZE THE GRAPH AT THE FIRST SIGHT

just gives me the tip.

Newton could achieve that

Why we cannot solve it like an ellipse

Like some rope and stuff

[marsh citrus]

@compact crescent Has your question been resolved?

[crystal lintel]

furry animal

[cold pecan]

Bro

It's just that you don't have to ask your question in multiple channel.

One channel is enough

If you open a new one, close the previous one

That's how things work here

[marsh citrus]

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[cold pecan]

Point P is (x,y). Let the point A be (x1, y1) and B be (x2, y2).

We know that PB/PA = 3
Then how about putting the PB and PA in it. For ex : PB = √(x²-x2²) - (y²-y2²). Then solve the equation you will get a final equation in a form

(x-h)² + (y-k)² = r²
Where h,k are the centre of the circle and r is the radius.

Hence proved that Trail of P will be a circle

[cold pecan]

Sheesh

. close

.close

[marsh citrus]

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[slate yarrow]

[fleet fossil]

Sheeesh

[cold pecan]

@compact crescent try this and if you get stuck feel free to open a channel here and ask

[marsh citrus]

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[flat bear]

Is the best way to solve this just to use the quotient rule to find the derivative and then solve for which values of x are roots to the polynomial in the nominator in the derivative? (See 2nd picture for derivative)

[red nimbus]

yea it's a good approach

[flat bear]

One more thing

in the product rule you can forget which is f(x) and g(x) kinda as the order doesn't matter. Is it the same for quotient rule or do i have to memorize in its entirety so i dont take g'(x) * f(x) - f'(x)*g(x) in the nominator by accident?

[lofty gyro]

you have to memorize cuz they cant be flipped 😦 🙃
or for me, i will usually only use product rule

[lofty gyro]

Hiii bacc,ooo new name

[red nimbus]

tabaco

[lofty gyro]

e.g. for this question
I'll take f(x) as (x²-2x+5)(1-x)^(-1)

so that i only have to remember product rule

(i always forgot the ordering of quotient rules)

[flat bear]

ohh ok will memorize then, but its just a result from the product rule right? so i could "derive" the qoutient rule if i needed/wanted to?

[flat bear]

ohh thats smart

[lofty gyro]

you're right!

[flat bear]

Last thing if i can be a bit shameless 🙂 i've never used a sign table(mbe?) so do i just look that up and solve b and c or is there some trick to those?

[lofty gyro]

let's see

god i hate those tables lol

[flat bear]

do i just try numbers around my stationary points?

and see if the deriv is pos/neg

ok wbout c then

[lofty gyro]

yea, just plug neighbouring numbers to the calcuator lol

oh

convex and concave

its about 2nd derivative

[flat bear]

convexity and concavity is always hard to remember my teacher taught me conCAVE as it looks like a cave opening or downward smile, while convex is the opposite right? 🙂

[lofty gyro]

yea, i remember it using the word cave too

[flat bear]

Oh ok i can calculate the 2nd deriv but is it a similar process where i try numbers or something?

how do i find the interval of -inf to 1 and 1 to inf

[lofty gyro]

yea, but before that you can simplify your f'(x) first

[flat bear]

really?

[lofty gyro]

oh, you'll have to see where the f''(x) = 0 or DNE

and it's the case x=1

so we check when x<1 and x>1

tables again lol

[flat bear]

wait so as the 2nd deriv is negative when x > 1 it is concave there on out and convex when 2nd deriv is positive when x < 1?

and for 1 it is not defined

[lofty gyro]

lemme double check

,w f(x)=(x^2-2x+5)/(1-x), find f''(x)

[flat bear]

How do you get the 2nd deriv is it just quotient rule or prod rule again?

[elfin berry]

Results provided by WolframAlpha

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

Requested by biscuityxd

[lofty gyro]

yep

[lofty gyro]

correct

[flat bear]

ok will verify this by hand so i get practice with the rules

tysm

❤️

.close

[marsh citrus]

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[lofty gyro]

cheers!

[marsh citrus]

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[rocky veldt]

What is the error in this

[marsh citrus]

@rocky veldt Has your question been resolved?

[rocky veldt]

nope

Here, if you see in point 1, f(X) = X^3, why have they taken the expectation value of that when it is clearly mentioned it should be just X^3

You can verify this in point 2. where they have subsituted the RV directly instead of the Expectation of the f(X) or g(X)

Please tell me where I am going wrong

<@&286206848099549185>

[marsh citrus]

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[spark otter]

If you multiply a row or a column by 6, the determinant is multiplied by 6

so if you multiply both rows by 6...

nonono

take any matrix M that is 2*2

if you multiply one row of M by 6

the determinant becomes 6* det(M)

if you multiplied the whole matrix by 6

then yeah having 3 rows the determinant is multiplied by 6^3

no that wasn't it

it's actually constant^n * det(M)

since the matrix is 2*2, n = 2

[marsh citrus]

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[charred vine]

I have some problems with Binomial Formulars
My main problem is number 4.I dont really get how I should calculate the results of those equations.

(My English is bad so might’ve used the wrong words-)

[marsh citrus]

@charred vine Has your question been resolved?

[marsh citrus]

@charred vine Has your question been resolved?

[main idol]

,rccw

[marsh citrus]

@charred vine Has your question been resolved?

[marsh citrus]

@charred vine Has your question been resolved?

[charred vine]

Yall pls

,rccw

[elfin berry]

faiyrose

[cold pecan]

For q6 do middle term splitting 👍

[red nimbus]

Als ob diese channel immer noch offen ist

[brisk laurel]

j

T + J

= TJ

[marsh citrus]

@charred vine Has your question been resolved?

[marsh citrus]

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[orchid shore]

Is this correct?

[orchid shore]

Remainder is 75/(2x-5)

[dreamy pollen]

No

[orchid shore]

Where did I go wrong

[dreamy pollen]

+10x

-5 * -2x

[orchid shore]

Ohh

[dreamy pollen]

+8x

[orchid shore]

Ok thx

.close

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[mystic lark]

can someone help me visualize this summation for matrix multiplication, i know how to do matrix multiplication but i cannot visualize this summation

[mystic lark]

and i think i am bad at reading summation notation in general

[marsh citrus]

@mystic lark Has your question been resolved?

[marsh citrus]

@mystic lark Has your question been resolved?

[sand kindle]

you go over the row of A (from left to right) and the column of B (from top to bottom) and multiply the corresponding terms, and the result is the sum

there are plenty of visualizations of this around; here's one from Wikipedia/Wikimedia

https://upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Matrix_multiplication_diagram_2.svg/2331px-Matrix_multiplication_diagram_2.svg.png

so for example the red middle cell in the top row has value (a_{1,1} b_{1,2} + a_{1,2} b_{2,2})

[elfin berry]

Invariance

[marsh citrus]

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[crisp kraken]

i don't understand this

[crisp kraken]

isnt this the same as writing
x^t = x ?

if i have Ax i get some vector b
if i trnspose Ax i get
x^tA^t = b^t

why it says they are equal?

oh because there is a third vector and it result in a 1 by 1 matrix . ok

[stray fern]

When you transpose a product, the order reverses

[marsh citrus]

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[small stream]

how to integrate this?

[small stream]

Thx !

.close

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[novel bear]

I'm not too sure what I'm supposed to do here to show my work as my understanding of this is just put on the value that's on the x-axis.

[cloud field]

write the functions that are in that domain

[novel bear]

(-∞,3)
(2,3]
(3,6]
like in that format?

<@&286206848099549185>

[eager tinsel]

What Shioshi wanted to say was that write the equation for the function illustrated in the graph in the respective domain

[novel bear]

okay

y=0x+3
y=0x+2
y=-1/3x+3

[novel bear]

like this?

[eager tinsel]

erm the form is correct but the equation aren't quiet correct

[eager tinsel]

the second one y=2 is fine but other two aren't

[novel bear]

one sec i'll rework em

y=5/2x+8
y=0x+2
y=-1.5/3x+2.5

[novel bear]

how's this?

[eager tinsel]

seems alright
but 1.5/3 could be simplified further

I am not quite sure about the y=0x+2 thing

I mean it is correct

But idk if it will be accepted as an answer or y=2 or both

mathematically it is correct

[novel bear]

I'm still getting this error I'm a little confued because the privous question ^ was like this a lot simpler is it not the same format?

[eager tinsel]

you're supposed to enter the whole thing not the intercept
(which all really aren't in the graph)

[eager tinsel]

here they're demanding the intervals of the domain

[eager tinsel]

but here domains are given and you have to enter the equation

[novel bear]

ah

I see I'll give it a shot

[eager tinsel]

juts write the right hand side of the equation

so y=something

[novel bear]

like this right?

[eager tinsel]

1.5/3 can be simplified further

[eager tinsel]

0.5 is 1/2

that also that's -1/2

[eager tinsel]

nice

[novel bear]

Thank you, I need to learn to read better been at this for hours

[eager tinsel]

nw

[novel bear]

have a good night/evening/morning

[eager tinsel]

you too

[novel bear]

.close

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[junior lintel]

Hi

[severe tree]

hey

[junior lintel]

I need help guys i will do anything

[severe tree]

now mention helpers here

[junior lintel]

<@&286206848099549185>

Ok bro

[severe tree]

it's fine

[junior lintel]

Guys i havent slept for 2 days istg

Im so so so tired

[marsh citrus]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[junior lintel]

Help me out

I have asked my friends but no one is helping me

Help me pls pls pls pls

[raw hawk]

Yeah

What question

[junior lintel]

This

[raw hawk]

Everythin?

[eager tinsel]

even a mod came to help you dude

[junior lintel]

Yeah maybe just do one and explain to me and ill do the others

Idk what to do i never took this in class ong

[raw hawk]

Do you know what end behavior is

[junior lintel]

No sorry

[raw hawk]

Okay

[slate yarrow]

when did a mod come?

[eager tinsel]

https://discord.com/channels/268882317391429632/1289920695471570945

[fleet fossil]

In the help forum

[raw hawk]

https://study.com/academy/lesson/end-behavior-in-math-definition-rules.html

[junior lintel]

Oh ok

Now i know what is end behavior

X = + infinity
X = - infinity

Right?

[raw hawk]

As x tends to ±∞

What is the effect on f(x)

[junior lintel]

What is f x

[raw hawk]

A function of x

[junior lintel]

Oh

I think f(x) is negative

[raw hawk]

In 1 what happens to f(x) as x->-∞

[junior lintel]

It decreases

Cause there is a negative

[raw hawk]

It approaches -> ∞

[junior lintel]

Ohhhh yeahh

Mb i forgot

Oh positive

I knew it

I think i know what to do now for end behavior

Im gonna write smt and tell me if its true

[junior lintel]

Tell me if this is right

@raw hawk

[raw hawk]

,rccw

[raw hawk]

Yup

[junior lintel]

Fr?

Bruh no way

I got this in the first try

[raw hawk]

Lol

[junior lintel]

Ok i finished a

Now i need to do domain and range ( b, c)

What is domain and range

I think domain is x and range is y

[raw hawk]

Domain is all values for which a function has a 'definite' result

[junior lintel]

Oh

So what exactly do i do

[raw hawk]

Range is the set of the results

[junior lintel]

Oh

So like

Bruh

This shit is hard

Can u help me @raw hawk

@raw hawk u there?

I figured smt out

Domain is left to right
And range is down to up

<@&286206848099549185> i need help

This is what i wrote so far

I hope its right

Now they want the domain and range

I figured smt out

Domain is left tor ight
And range is down to up

Bruh why is no one helping me

What did i do wrong 🥲

Bruh yall are mean

.close

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[opal valve]

part 2 please. i have no idea what to do

[raw hawk]

Open new channel

[marsh citrus]

@opal valve Has your question been resolved?

[marsh citrus]

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[glass silo]

e.g. "cube the inverse matrix"

[lone heart]

Aka (A^-1)^3

Ideally it would be B * B * B, not each element cubed, I believe

[glass silo]

-1/27

[marsh citrus]

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[stuck geode]

<@&286206848099549185>

[mellow kraken]

! status

[marsh citrus]

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

[stuck geode]

None of the above

[stuck geode]

None of the above

(16x² sin(y) Σ 1 dxdy)=1+2 coth(r) 12 00 M 127 Σ n=1 + 5 = 69

[marsh citrus]

@stuck geode Has your question been resolved?

[main idol]

Show the entire question and choices

[main idol]

What is this supposed to be

[marsh citrus]

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

Show your work, and if possible, explain where you are stuck.

Show your work, and if possible, explain where you are stuck.

[wise lance]

It didn't mention that the building is 40m

It just said that it took 2 seconds to fall the last 40m

Meaning that it could have initial velocity

Use kinematic equation

Yeah but he didn't mention the height of the building
Meaning that the building could be 100m
And at the final 40m it took 2 seconds to fall

When you use Vi = 0 for these 40m you are saying that the ball is released at the 40m mark

Yeah
Use the formula
Yf = Yi + Vi * t + (1/2)a t^2

[marsh citrus]

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[marsh citrus]

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[still temple]

hello everyone, I have this number sequence to study : u0 is in ]0,2[ and Un+1 = sqrt(2+Un*(-1)^n) I have to tell wether it converges or not and I can't find like I find that when n is even, it converges but when its odd it doesnt, pls help me

[marsh citrus]

@still temple Has your question been resolved?

[marsh citrus]

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[still temple]

hello everyone, I have this number sequence to study : u0 is in ]0,2[ and Un+1 = sqrt(2+Un*(-1)^n) I have to tell wether it converges or not and I can't find like I find that when n is even, it converges but when its odd it doesnt, pls help me

[sinful thistle]

you mean

[still temple]

yes thx

[potent fog]

I think it was supposed to be (0,2)

[sinful thistle]

idk man

he used ] [ which is neither ( ) nor [ ]

[still temple]

well ][ means the intervall is open

its french notation

[sinful thistle]

ahk

[still temple]

idk if its same in english

[potent fog]

This is bourbaki notation for the open interval

[sinful thistle]

it's ( ) in english

[sinful thistle]

ahk

[still temple]

oh ok i didn't know

thx

[elfin berry]

ren

[marsh citrus]

@still temple Has your question been resolved?

[still temple]

<@&286206848099549185>

please

[main idol]

Did you find the first few terms of the sequence

In terms of u_0

[still temple]

well Uo is between 0 and 2 so i can't find U1

i mean I don't have the value of U0

[marsh citrus]

@still temple Has your question been resolved?

[marsh citrus]

@still temple Has your question been resolved?

[restive torrent]

So you found that for n even the subsequence converges to 2 , and for n odd it doesnt converge to 2 right?

[still temple]

Yes

[restive torrent]

well you know that a sequence converges if and only if all of it s subsequences also converge to the same number

since you found 2 that dont, the main sequence can not converge

[marsh citrus]

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[marsh citrus]

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[marsh citrus]

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[molten ferry]

why is it plotting 3 planes

[marsh citrus]

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[manic gyro]

My quesiton is soemthing related to trig

[manic gyro]

i am

solving for section A_3

and have already foudn the areas for section A_1 and A_2

I am using a triangle approach but not sure how to strart solving for A_3

[marsh citrus]

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[vague jasper]

Is it possible to make a function that is continuous at all rational numbers, and discontinuous at all irrational numbers?

[sand fable]

no

[tight furnace]

There's probably a way to assign every number a value based on how close it is to a rational number with a small denominator

[vague jasper]

is there a way to prove this (or has it been proved)?

[tight furnace]

but maybe we'd always be able to find an irrational which gets a score of 0

and maybe the function is continuous there

[marsh citrus]

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[sand fable]

https://en.wikipedia.org/wiki/Gδ_set#Examples

[marsh citrus]

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[stray agate]

Find the no. of arrangements of the letters of the word EQUATIONS in such a way that no 2 vowels are together.

[stray agate]

Can anyone tell me how to solve this?

Anyone ?😞

[marsh citrus]

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[echo garnet]

how do I find the accumulation point of a complex set?

[echo garnet]

i.e. let's say I have something like $z_n = i^n, n = 1, 2, 3...;$

[elfin berry]

jv

[echo garnet]

how can I find all the accumulation points of said set?

[glass silo]

Can you do it for the real sequence (-1)^n?

[echo garnet]

so, whenever n % 2 is 0 we get 1 and n % 2 is 1 we get -1, correct?

so... there are acummulation points in every point? lol

sorry I've never had an analysis class lol this is for intro to complex analysis

[glass silo]

If by “every point” you mean both 1 and -1, then yes, both of those are accumulation points

[echo garnet]

mhm, I see

so for i^n then it's -1, i, -i, 1?

[glass silo]

Yep, there you go you have subsequences that converge to each of those points

[echo garnet]

thank you, got it!

[marsh citrus]

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[somber sable]

if the limit of a function is a number divided by 0 is it DNE?

[potent fog]

Depends (strictly speaking, the limit cannot literally be a number divided by 0, because that isn't defined, but I think I understand what you're asking)

[marsh citrus]

@somber sable Has your question been resolved?

[echo garnet]

not necessarily, the condition for a limit to exist is when its neighborhood converges to the value of the limit

[marsh citrus]

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[mental walrus]

can someone help with this question? I get the general idea of related rates but the relation between the height and radius is tripping me up

[severe tree]

hey

okayy

do you know the formula for the volume of a cone?

[mental walrus]

yes

[severe tree]

alright

now the question gives us the relation that h = 3r

[mental walrus]

I think I figured it out I ultimately got -2/3pi for the rate of change of the radius

but im not positive on that

[severe tree]

that's right

[mental walrus]

ah ok good

thanks

[severe tree]

if this was your working process

you've done it right

any other questions-?

[mental walrus]

no thats all I had

thank you

[severe tree]

okay have a good one

[mental walrus]

you too

.close

[marsh citrus]

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[copper basin]

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[copper basin]

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[twilit geyser]

what have you tried?

[copper basin]

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[twilit geyser]

well why not

[copper basin]

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[twilit geyser]

usually you want to do a little something to show, even just a little or people won't want to put in any effort if you haven't

I'll give you a hint though, try to combine the fractions in the numerator

make 3/x-3/c have the same denominator specifically, if that makes sense

[copper basin]

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[twilit geyser]

here it's not really a conjugate, but maybe similar kind of idea

[copper basin]

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[twilit geyser]

conjugate is like when you have 3+5sqrt(2) and the conjugate is 3-5sqrt(2)

[copper basin]

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[twilit geyser]

here we're just making like denominators to add fractions

just focus on 3/x - 3/c to have the same denominator, what do we need to do

[copper basin]

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[twilit geyser]

yeah I think I see what you're saying

yeah try that and show what you get and I'll help where it needs fixed as you go

[copper basin]

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[twilit geyser]

good you caught that you missed a piece, I'll let you cook

yeah perfect, keep going with it if you can

[copper basin]

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[twilit geyser]

yeah

[copper basin]

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[twilit geyser]

almost

[copper basin]

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[twilit geyser]

-(c-x) = -c+x = (x-c)

[copper basin]

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[twilit geyser]

wait I think you have a slight mistake there in the denominator

$$\frac{\frac{3(c-x)}{xc}}{x-c}$$

[elfin berry]

Merosity

[copper basin]

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[twilit geyser]

the top one, the denom in the numerator

cause the denominator you just made there was xc not x-c

[copper basin]

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[twilit geyser]

so back up here

you have xc in the denominator

[copper basin]

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[twilit geyser]

but here you lost the xc

cool cool

[copper basin]

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[twilit geyser]

nice ok

[copper basin]

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[twilit geyser]

so I would combine the denominators now, since dividing 3(c-x)/xc by (x-c) will put it in the denominator

$$\frac{3(c-x)}{xc(x-c)}$$

[elfin berry]

Merosity

[twilit geyser]

that step make sense? we're nearly there

[copper basin]

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[twilit geyser]

nope no foil

that'd be for like multiplying not dividing

so how is c-x related to x-c? it's actually the negative of it

one way to see that is multiply -1 by (x-c) and see what you get

the point is once we have (x-c) in the numerator and denominator, you can cancel them out

[copper basin]

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[twilit geyser]

yeah distribute the -1

[copper basin]

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[twilit geyser]

yeah a useful trick you'll see this again so good to remember how that works

[copper basin]

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[twilit geyser]

is that supposed to be *(-1)?

[copper basin]

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[twilit geyser]

yup

you got it

[copper basin]

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[twilit geyser]

I had already typed it up if it's clear to see

so replacing (c-x) with (-1)(x-c) in the numerator

[copper basin]

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