help-28

[quartz gale]

7 - 5x is wrong

[dense edge]

ohhh

ty

[quartz gale]

Appart from that, this is the way to go

Just try again with the right value instead of 7 - 5x

[dense edge]

would you leave this as the answer?

x =
y =

[quartz gale]

What do they ask for ?

[dense edge]

it sounds like it's asking for matrices

[quartz gale]

yes

[dense edge]

so maybe i just replace this with values?

[quartz gale]

So give them the matrices

[quartz gale]

Exactly

Let’s check your calculations

[dense edge]

so this is the final answer? it asks for matrice(s) plural

i will check now

[quartz gale]

There is also A

[dense edge]

something went wrong

[quartz gale]

There is a mistake

[dense edge]

i'm getting different answers

this for AB

this for BA

[quartz gale]

Yes

A 5 became a 15

[dense edge]

always something so trivial

i'll have to be careful

tyvm

at least i have the method now

[quartz gale]

For big calculation be careful yes

But you did great

[dense edge]

but you are saying maybe there can be more than 1 matrix for the answer?

or only one matrix

[quartz gale]

Only two mistakes with all that

[dense edge]

i am not sure how i would get more than one matrix for the answer if this is the only matrix with variables

[quartz gale]

Here they ask for A and B. If you would have found 5 différents ( x,y) you would have to give all the matrices A and B associated to each couple (x,y)

But you found only one couple (x,y) so just give A and B for this couple

[dense edge]

oh like if somehow it was x^2

i would have to find roots for that and get 2 answers

[quartz gale]

Yes for example

But even more simple

If you had to resolve x = y +4

There is not a finite amount of solution (x,y)

[dense edge]

i have only seen higher powers with diagonalisation, not matrix multiplication

i thought the idea with matrices is that they are supposed to be linear

[quartz gale]

They are indeed linear

A(zB + C) = zAB + AC

So it’s linear

[quartz gale]

But you did a multiplication of two matrice though ?

[dense edge]

hmmm, OK..
A - (lambda)*Identity is the only time I have seen polynomials

[quartz gale]

Are you talking about x^2 ?

[dense edge]

which is kinda the point, to find the eigenvalues

yeah, to have multiplicity with a variable

[quartz gale]

Oh okay so here don’t think about it

It’s not a good example of finding more than 1 x

[dense edge]

like for example if both matrices had an x

[quartz gale]

Yes

[dense edge]

find all matrices AB = BA

this type of question could still be asked? or impossible to solve

[quartz gale]

Yes it could be asked

[dense edge]

and you would solve it same way I just used?

[quartz gale]

You would just probably have to solve a second degree equation

[quartz gale]

Almost

[dense edge]

OK

[quartz gale]

I just don’t get why you sum up the line

[dense edge]

i guess you just factor out both x values

oh, to make it = 0?

you would do it differently?

[quartz gale]

Look at what you sent me

[quartz gale]

.

[quartz gale]

Yes

[dense edge]

that doesn't make sense?

[quartz gale]

You don’t have to sum

[dense edge]

oh ok

[quartz gale]

It does

[dense edge]

what would you do instead?

[quartz gale]

Just do coefficient by coefficient

[dense edge]

ahh OK

[quartz gale]

So 4 equation

[dense edge]

22 = 7 + 5x

like that

yeah that's easier

[quartz gale]

But there is 2 unknown so you would only need of 2 equation

[dense edge]

i think that's where i messed up

x should equal 3

[dense edge]

based on this

[quartz gale]

It is

[dense edge]

somehow i got x = -3/5

probably from that full summation

extra work and causes error

[quartz gale]

.

Look at the end of the page

At the left part of the equation

There is two 15

Because a 5 became a 15

[dense edge]

oooops

good catch

[quartz gale]

Yes exactly

I’m used to look for mistake in my work or work of my friends

[dense edge]

i'm trying to go as fast as possible.. for final exams it helps

but it's easy to make mistakes

if not careful

[quartz gale]

Sure but always reread what you wrote

It’s the only way

Just reread it one time because you don’t have time for more

[dense edge]

i guess so 🙂 i'm so drained by the end, i have 10 mins left to check over all my work it's usually never enough time

[quartz gale]

And at the end if you still have time left never hand back your work

Check for the 4th time your work

But only at the end

[dense edge]

yeah

i never hand in early

[quartz gale]

During the exercice just 2 times is good

[dense edge]

always use full time

OK

[quartz gale]

At least when you don’t get 20/20

When you’ll get that feel free to hand out early

[dense edge]

tyvm, i'll try this problem again

this should save time avoiding full sum

[quartz gale]

No problem

[dense edge]

I will check my work now

crap

something went wrong again lol

this part looks fine

i used the first column entries to solve for x and y

[mighty ridge]

7+5x = 22
5x = 15
x = 3

[dense edge]

LOL

i even double checked that, thinking "wait, isn't that supposed to be 3?"

i thought maybe with my new vaues corrected it might change

wow

tyvm, i will check again now

[mighty ridge]

x = 3 and y = 10 should be the only possibility

since -35+5y = 15

[dense edge]

LOL

[mighty ridge]

y is not -4

[dense edge]

y=10

holy moly

i think my brain is cooked

too much math today

i will give this one last check

AB

BA

https://tenor.com/view/the-rock-wwe-wrestling-gif-9720992

tyvm everyone

appreciate it

[quartz gale]

Well done

[dense edge]

crawl before walking

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[misty zinc]

How would i do this with excel

[undone vector]

=T.INV.2T(1-conf,df)

[misty zinc]

=T.INV.2T(1-0.95,10)

for a.)?

[undone vector]

Yeah

[misty zinc]

Could you explain why it wouldn't be =T.INV.2T(0.025, 10)

because i thought we divide alpha by 2

[undone vector]

The .2T is for two tail test so it auto divides by 2. You could drop the .2T and do alpha/2 instead

[misty zinc]

I see

Fair

Thank you

[undone vector]

np

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[dense edge]

How can this be the basis? Don’t we need linear set of vectors in R^6?

[narrow ermine]

Isn't it a basis of the range?

[dense edge]

Oh.. Set of vectors actually

So that makes more sense I guess

But why are they not written as rows in augmented matrix form?

I had no idea the origin vectors are the ones to use. I thought the basis had to be taken after doing REF or RREF and using those same row values with column pivots

[narrow ermine]

The augmented matrix represents trying to solve for the coefficients in the linear dependence relation.

But the vectors aren't linearly dependent, so there's infinitely many solutions.

[dense edge]

If it asks for basis how do you know if it wants column basis or row basis?

[narrow ermine]

They just want a basis of the vectors. If you had a linear dependence relation, you would solve so that all the components add up to 0

That's what the matrix does.

[dense edge]

*basis of column space
Or
*basis of row space

They are different basis right?

[narrow ermine]

Yes.

[dense edge]

By default is it one or the other? When referring to basis of a matrix

[narrow ermine]

But here we want a basis of the column space

[dense edge]

The question will always ask? Basis of something

[narrow ermine]

i.e. a basis of the space spanned by the vectors that make up the columns

[dense edge]

It will never just ask for the basis? Because it doesn’t explain basis of what

like here is matrix A

“find the basis”

Nobody would never phrase a question like that?

It needs more context on what basis?

[narrow ermine]

But the question asks for the basis of the vectors.

[dense edge]

No I mean in general

Not with this question

[narrow ermine]

In general they would have to ask

[kindred grove]

a basis of a vector space is completely unambiguous

[dense edge]

OK

[kindred grove]

the way you rephrase that as a matrix equation or whatever is completely your call

you're responsible for that

[dense edge]

Wdym?

You can choose if you see it written on a test unambiguously?

Or you do all forms

Row basis, column basis

Null space basis

“Find the basis of the vector space”

What basis(s) would you personally solve for?

[kindred grove]

well you do one form, no need to find the same thing twice

[dense edge]

But each would be different

[kindred grove]

you could completely put each vector as a row of a matrix if you want

the real question is

what do you do with that matrix ?

and how do you interpret your matrix after what you did ?

[dense edge]

Linear independence (basis of column vectors) and linear dependence (basis of null space column vectors)

Not sure what basis of row vectors tells us tbh… Linear independence after matrix transpose? Basis of row vectors still feels weird for me

I think I get it finally

I should say, I think I mixed up my definition of row and column

Column basis is actually the transpose of a normal matrix

Because typically a matrix is written in this form for RREF:
x, y, z

The amount of columns indicate the space

for x, y, z the space is R^3

The amount of rows indicate how many equations are in the system

So after RREF if I get
1 0 0
0 1 0
0 0 1

Does that mean the basis is
1 0 0
0 1 0
0, 0, 1
?

3 vectors

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[raw ruin]

In number 1, how do you compute for p7?

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@raw ruin Has your question been resolved?

[inland moth]

isnt there a formula for percentiles

[raw ruin]

I don't know how to solve it

The formula that our teacher gave us can't be applied to this certain assignment

Idk why

[inland moth]

what

then what do they want you to do

draw an ogive?

[raw ruin]

This is the formula

[inland moth]

yeah

you cant use this?

[raw ruin]

I tried for p7 but it just doesn't work. I solved for 7(30)/100 which is 2.1 but the problem is that there's no cf lesser than 2.1

In the given table for the problem

[raw ruin]

The least cf on table 1 is 3, which isn't greater than 2.1

cf shouldn't be greater than (k(n)/100), atleast that's what our teacher told us

[inland moth]

cf is cumulative frequency before 10-14?

in this context

[raw ruin]

I guess?
I tried this formula that I found online which is
P_7 = 10 + 5/3 x 2.1 = 13.5

[inland moth]

isnt that just 0

theres nothing before the 10-14 class

so its just 0 all the way down

[raw ruin]

So cf = 0?

[inland moth]

yeah

[raw ruin]

I see

Thanks

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[marsh tusk]

Differentiate tan(-x)

[marsh tusk]

I used the chain rule

so

=sec^2(-x) * -1

=-sec^2(-x)

but for some reason the answer was -sec^2(x)

why did the x turn positive

[tight mortar]

it shouldn’t be

or I’m tripping and need to go to sleep

[umbral dome]

that answer is correct, but sec(x) is an even function so they are equivalent

[marsh tusk]

huh?

im not sure i understand what u say

[tight mortar]

they are the same

[narrow helm]

even if there was an odd function there, the square would've compensated the negative

[marsh tusk]

are you talking about the -f(x) = f(-x)

[narrow helm]

yes

thats odd

[craggy tapir]

an even function is a function that satisfies $f(-x)=f(x)$

[marsh tusk]

how do you know sec is a odd function

[glossy valve]

فطر

[craggy tapir]

cosx is an even function

[narrow helm]

its not

[craggy tapir]

and since secx is just 1/cosx, so secx is also an even function

[marsh tusk]

wait

[torn jolt]

He's saying it's even

[marsh tusk]

all trig functions are even right

[torn jolt]

So positive = negative

[torn jolt]

Sin isnt

[marsh tusk]

oh yeah

yeah

so -sec^2(-x) = -sec^2(x)

f(x)=f(-x)

yeah

ok thanks

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[red wasp]

Hi I need help with this question

[red wasp]

I don't really know where to even start

This chapter is differentiation but I don't really know what to do

[tribal flax]

do you mind typing it out?

i cant really read it

[red wasp]

OK wait a minute

profile picture
in the diagram shows a metal hemisphere with radius of 10 cm. Water is poured into the hemisphere such that the water level from its base. H cm increases at a rate of 0.2 cm persecond/

prove the area of the water surface is pi(20h-h^2)

[red wasp]

This is a rough translation from another language so I'm sorry if it's confusing

[tribal flax]

its ok dont worry

im also doing differentiation so ill try my best

ok

[red wasp]

OK thanks

[tribal flax]

ok so 0.2x where x is the time is the velocity of how fast its filling up correct?

no sorry its acceleration

[red wasp]

I don't understand

[tribal flax]

im a bit confused, does "H cm increases at a rate of 0.2cm per second" mean that the height is increasing or the speed at which the water is rising increases?

ok

so h is how high the water level is

[red wasp]

Yea

[tribal flax]

and every second it increases by 0.2 cm

[red wasp]

Yeap

[tribal flax]

so if a second is x

then after 2 seconds its 0.2 x 2 = 0.4 cm higher

[red wasp]

Yea

[tribal flax]

so it gives you the displacement of the height of the water

because at 0 seconds its empty

[red wasp]

Yea

[tribal flax]

have you been doing rectilinear motion yet?

[red wasp]

I don't know what that is so I guess no?

[tribal flax]

so basically, displacement, velocity and acceleration are all related to each other and you can use differentiation/integration to find out the equation of one if you know the other

[red wasp]

Oh ook, I think I should say this probably has nothing to do with integration cuz this practice question is before learning integration

And do I have to use the acceleration to find the area?

[tribal flax]

does this say i) prove that the area of the water surface, 2cm, is given by 2 = pi (20h - h^2)

it might not have to do with integration

i just cant read it properly so im not sure

[red wasp]

Oh sorry, it's L cm

My bad

[tribal flax]

ok

Lcm or 2cm?

[red wasp]

L cm

[tribal flax]

ok so you can use the area of a circle to find this

with a hemispherical sphere, the radius between each sides is the same from top to bottom

[red wasp]

What do you mean by this?

[tribal flax]

so at the top of the bowl, h = r

[red wasp]

Ohhhh okok I get it now

[tribal flax]

2 secs

try your best from here while im gone

[red wasp]

Ok

[red wasp]

Wait nvm I don't know what to do with the info given.

[tribal flax]

you got it?

ok

so if the formula is pi (20h - h^2) and h = r when its at the top

then h = 10 at the very top

and 20x10 - 10^2 is the same as 10^2

so thats the equivalent of pi r^2 which is the area of a circle

[red wasp]

But h does not decrease the same as r right?

[tribal flax]

because the distance from the bottom of the circle is not going to be the same as the sides we have to do the 20h to make up for the diameter of the circle vs the distance to the bottom

yes exactly

thats why its not just pi r^2

to find the actual radius, its 20h - h^2

this is hard to explain

[red wasp]

Where do we get this from tho? I mean we should just take from the itself right?

[tribal flax]

yes

[red wasp]

Shouldn't

[tribal flax]

its hard to explain

[red wasp]

Wait?

[tribal flax]

i just need a sec

[red wasp]

What

OK I'll wait

[tribal flax]

ok so you get that pi h^2 is like the vertical circle and its not the same as the horizontal thats pi a^2?

so to calculate the circumference of a circle its 2πr

[red wasp]

Cuzco they have different radius?

[tribal flax]

yes

but we arent calculating the circumference of a circle from the middle correct?

[red wasp]

I thought we're finding the area?

[red wasp]

Yea

[tribal flax]

this is so hard to say

have you done chords?

segments of a circle

[red wasp]

For example? Like finding the length of chords?

[tribal flax]

yes kind of

[red wasp]

Do we're trying to find thr formula that relates r to h?

[tribal flax]

if you use pythagorus's theorum to find a (which is our r in the area calculation)

its 10^2 - (r - h) ^2

which is 10^2 - r^2 - h^2 + 2rh

[red wasp]

So we're doing a²= R²-(10-h)²

[tribal flax]

and because r^2 is also 10^2

its 2rh - h^2

which is 20h - h^2

so its pi a^2 so π(20h - h^2)

im sorry that took so long to explain

idk what was going on in my head

[red wasp]

Oh it's fine I get it let me try doing for a sec I'll get back at you in a few secs thanks

So like this?

[tribal flax]

yes

[red wasp]

Thank you for helping and for having patience with me. Thank you very much I can continue by myself from here.

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[vague siren]

how can i solve this?

i have no idea

ping me pls

[hot herald]

there is no question

[vague siren]

find x value

[hot herald]

such that?

[vague siren]

we no to substitute f(x) for the function

and then resolve the equation

[hot herald]

so that what happens

[vague siren]

what?

[hot herald]

can you state the exact instructions of the question

[vague siren]

ok

here is the equation

and we need to find x value

you understand?

@hot herald

[hot herald]

the stuff in the original question seems to be for two different questions
why are those being set equal to each other?
why is stuff getting covered in red

can you please show an unedited image of the original from the book

[vague siren]

i covered because it is another question

[hot herald]

the stuff in the original question seems to be for two different questions
why are those being set equal to each other?

[vague siren]

its to resolve

[hot herald]

where are the word instructions telling you what to do with these functions

[vague siren]

listen

we have a equation

and the instructions is to find x value

just this

through simplifactions, transformations, eg...

[hot herald]

indulge me,
uncover the stuff you covered in red
and let me see for myself

[vague siren]

its in portuguese btw

i just got doubts on (b)

[hot herald]

ok, now what you're doing makes more sense

have you done anything else so far?

[vague siren]

so far no

[hot herald]

subtract 1 from both sides

[vague siren]

ok

[hot herald]

on the right side
factor out 2, then the double angle identity for cosine can be applied

[vague siren]

can you do it on a notepad and send a print?

its easy to understand

[hot herald]

try to do the work following my instructions to the best of your ability

i'll provide the necessary adjustments/improvements/input if needed

[vague siren]

ok

im here

forget it

i arrive the answer

.solved

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[bold tinsel]

Couldn't solve it out in my exam

I kinda know how to do (1)

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[bold tinsel]

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[icy pendant]

confused on how to work out 3

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[icy pendant]

<@&286206848099549185>

[coral coral]

if you have the answer for (ii), you can find that the probability of getting flu is 1 minus that answer

the expected number of students catching the flu is the probability of getting flu times the total number of students

just plug everything in and you'll find the total number of students

[icy pendant]

i got 17/49

dunno if thts correct

[coral coral]

(5/7)(34/35) + (2/7)(5/14)

(Probability of not catching the flu after vaccinated) plus (probability of not catching the flue as a not vaccinated student)

[icy pendant]

oh alr

39/49

[icy pendant]

whats the reasoning for this

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[tranquil stag]

Can anyone help I've been stuck for a while. Ive retried this question multiple times with different limits each time and cant seem to get the right answer

[tranquil stag]

points of intersection are (0.5, π/6) and (0.5, 5π/6)

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@tranquil stag Has your question been resolved?

[wheat vault]

what if we find the white area first, then subtract that from the whole circle area

ofc using integrals

[tranquil stag]

The white area at the top?

[tranquil stag]

I thought about doing that but surely it would be really complicated

Surely u would have to integrate from pi/6 to 5pi/6 then subtract the little bits from the other curve twice

Then subtract all of that from the whole circle area

[tiny terrace]

@tranquil stag hello again
Have sleep now
Similar to yesterday, you need to use the red line for one part of the interval and the blue for the other part

Overall, you should have integrated over the whole circle

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@tranquil stag Has your question been resolved?

[wheat vault]

how complicated?

its much easier this way

other than geting the area directly

[wheat vault]

for R, u will integrate from $1-sin(\theta)$ to $\frac{1}{2}$

[glossy valve]

CowCat

[tranquil stag]

What?

[wheat vault]

$\int_{\pi/6}^{5\pi/6}\int_{1-\sin(\theta)}^{1/2}rdrd\theta$

[thin flint]

you're forgetting an r

and also the lower bound is the 1-sin

cowcat is saying calculate this

and subtract that from the simple calculation of $\pi r^2 = \pi \frac{1}{2}^2$

[glossy valve]

CowCat

Katharine

[wheat vault]

what r?

[thin flint]

idk how much you know about coordinate transformations

but the determinant of the jacobian of the transformation from cartesian to polar is r

another way of saying it

[wheat vault]

thats not transformation, im directly integrating over r and theta

[thin flint]

you want to calculate the surface area no?

you generally do that by integrating over x and y

dx dy

but we're doing it in polar

[wheat vault]

no 2d

[thin flint]

so instead we have

dr and r dtheta

[wheat vault]

i know that dxdy = rdrd(theta) but thats when u transform from one to another, however here we are directly integrating in the polar coords

[thin flint]

you still require that r

[wheat vault]

yes, ur correct

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[timid lotus]

is this answered

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[ripe valley]

Does anyone know how to calculate standard error using this table and formula

[ripe valley]

If i fill in the formula I get 7,4207 which seems way too high for a SE

This is a cry for help

[ancient folio]

You might want to ask in #probability-statistics

[ripe valley]

Oh thank you

[ancient folio]

Lowkey just forgot everything I learnt from statistic course

[ripe valley]

np haha thanks

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[viral kayak]

Arne is going to fence in a dog kennel against his barn, for his two labradors – Einstein and Newton.
He has 64 meters of fence, which should be enough for three sides of a rectangular dog yard. The fourth
the wall consists of the barn. See figure.

Draw an expression for the area and determine the dimensions that the kennel can have for the dogs
get as much surface as possible to play on.

[viral kayak]

<@&286206848099549185>

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[torn jolt]

<@&286206848099549185>

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[modest trellis]

stop pigning god damn bro

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@viral kayak Has your question been resolved?

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@viral kayak Has your question been resolved?

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@viral kayak Has your question been resolved?

[timid lotus]

ur tryna maximize area

you know the perimeter must be 2(width) + length

and that must be 64

and ur tryna maximize area aka A = xy or (width)(length)

assuming u dont know calculus, the area function should be a quadratic and max is just the vertex

assuming the function concaves down ofc

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[finite burrow]

why is 19 wrong?

[steady fiber]

how did you get 19?

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[oak otter]

someone help me,

my teacher didnt discuss this smh

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@torn jolt Has your question been resolved?

[torn jolt]

<@&286206848099549185>

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[paper cove]

The price increase from 1967 to 2015 was 817.4 %. Determine the krone value in 1967. Give the answer to two decimal places.

[celest pewter]

you'd need the 2015 value to solve this

[somber niche]

That's like saying I grew 50% from ages 10 to 20, how tall was I at 10?

Missing data

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@paper cove Has your question been resolved?

[paper cove]

its the basis year

aka 100

[celest pewter]

ah

can you find an equation for 1967

[paper cove]

uhh

no💯

[celest pewter]

something like $P_{1967} \cdot x = P_{2015}$

[glossy valve]

b

[paper cove]

but how do i find out x

i have to find the price in 1967

and the price in 1967 is 817.4 % less than 100

the answer is 9,17

but how

[hazy lance]

which part are you confused about

[paper cove]

how do i find the index in 1967

actually I'm confused about the whole question😭 🙏

[hazy lance]

so if 2015 is the basis year, ie P = 100

and delta P = 817.4, then its just P + delta P = 917.4

divide by 100 you get 9.17

[paper cove]

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[steep garden]

can someone help me find ED ?

[low echo]

Hii

[analog raptor]

similar triangles

[steep garden]

heyo

[low echo]

Yeah

[analog raptor]

use their properties

[low echo]

9/6 = (2x+4)/x+4

[analog raptor]

||6/9 = x+4/2x+4||

[analog raptor]

hint

[steep garden]

so x is 2?

im new to this

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[restive quiver]

do i have to put the determinant equal 0

[torn jolt]

yes

wait

nvm

[ancient folio]

???

[torn jolt]

no

i thought it was a 3 variable equation

[restive quiver]

how am i gonna evaluate this determinant

i need to do it using matrices btw

@torn jolt

[torn jolt]

you can find determinant for only a square matrix only

[restive quiver]

yea

what do i do then

find lambda from this?

[torn jolt]

i am busy

please ask someone else

[restive quiver]

no worries

[regal shuttle]

ad-bc = det

[restive quiver]

yea but what bout this

[regal shuttle]

thats not square

[restive quiver]

yea

[regal shuttle]

u cant then

[echo marsh]

or you can just use that condition a1/a2 = b1/b2 = c1/c2

[restive quiver]

dont i have to include the other side of the equations too

[echo marsh]

(for infinite solutions)

[restive quiver]

i need to do it using matrices

@daring bay help me plz

[echo marsh]

write the system of equations as matrix equation

[restive quiver]

here

just put equal to 0

[echo marsh]

[[1,2], [2, λ]] . [x,y] = [4,-3]

now this system has a unique solution when coefficient matrix ([[1,2], [2, λ]]) is non singular (det != 0)

so for not unique solutions

it must be zero

so | [[1,2], [2, λ]] | = 0

on solving this you get λ = 4

[echo marsh]

no

[echo marsh]

this is correct

[restive quiver]

if i was given 3 equations

then would you still say that i have to include coeffeicent part only

[echo marsh]

if you had 3 equations with each having 2 variables

then you could just use any 2

so it'd still be same

thats how you convert system of linear equations to matrix equation

[restive quiver]

ok ok i got it

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[restive quiver]

@echo marsh

.reopen

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✅

[echo marsh]

what

[restive quiver]

3 n 4

[echo marsh]

(b)

and for 4th its (a) i think

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[night lion]

Please check and let me know if the series tests used for each question is right

[night lion]

also for this question where does the 2x-sin x come from?

[regal shuttle]

chain rule

its sin(x^2+cosx)*(2x-sinx)

when inputting the first bound

[night lion]

oh

so Im derivating this?

[regal shuttle]

yeah

[night lion]

ok thank u

[night lion]

also could u check this pls

[regal shuttle]

first one u apply divergence test

as lim goes inf, the sequence converges to 1

hence the series diverges

third one

split the sum

and apply ratio test for n/5^n

do the same with 5/5^n

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@night lion Has your question been resolved?

[night lion]

oh ok ty

after finding if its convergent or not how do I find the interval of convergence and also radius of convergence

<@&286206848099549185>

[devout valley]

The radius of convergence are basically the values you'll find for which the series must converge in and outside of which, you certainly won't converge in (for this one you should find something "interesting")
interval of convergence also considers the endpoints too and whether you converge at them, if you happen to get a finite nonzero ROC

[night lion]

I see, so I just do the limits and find out the sum of the series?

[devout valley]

how do you mean "do the limits"?

[night lion]

I mean like lets say I use a certain series test to find out if a series converges or not right

so some of them make use of limits

so in this case I would use the root test

which makes use of limit as well

but to find the value of x where it converges would be the limit where n approaches inifinite right??

[devout valley]

Well, you'd e.g. consider where the limit becomes less than 1 to find out the value(s) of x that would give you convergence

[night lion]

oh ok

alright that makes it clear

thank u

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[torn jolt]

Under steady current conditions, the current density vector field, $\vj J$, is both solenoidal and irrotational. Meaning: [
\div \vj J = 0 \q \curl \vj J = 0
]
but im a bit unsure what this implies to the geometric interpretation of the vector field? would love some elaboration

[viral jasper]

Hard to say geometrically because it is subtle

But it means you won't see a magnetic field coming from any particular sources. It's just kind of "everywhere"

This is where we conclude that no monopoles exist

[torn jolt]

hmm

[viral jasper]

Irrotational is pretty hard to describe, because it does not mean that the field can't bend. More that it can't spin.

Like, imagine putting a boat in water and how it's always pointing in its direction of motion. If it does that, then the vector field of the water current would be considered irrotational

[torn jolt]

i can kinda imagine that

but i want to ask

does solenoidal here imply that the field lines always begin and terminate where they started from?

or go to infinity in the space i suppose

[viral jasper]

Yes

Solenoidal means zero divergence

Hence, no monopoles

[torn jolt]

very very interesting okay

thanks a bunch!

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[wary tendon]

why do we need to cut it in half as the marking scheme says and not just do the whole triangle

[shrewd hamlet]

provide some more context

cut what in half

which triangle

[wary tendon]

the abc triangle

[wary tendon]

instead of 9 i got 12.7 because i did the whole triangle

[quaint prawn]

ABCD

[wary tendon]

wdym

[leaden ermine]

ABCD

[wary tendon]

what?

[quaint prawn]

Show your work

[wary tendon]

k

[quaint prawn]

Are you mad at me?

[wary tendon]

no

why should i? 😉

this formula is 1/2 * base * height

omg im so stu..

ty bro

tysm

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[shrewd hamlet]

man this is a tough one

[torn jolt]

Reee

[glossy valve]

fredthebread69
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[torn jolt]

Finally

Still shows error

Should I put stuff in tan and ln in curly brackets

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[torn jolt]

Bro nooo

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[torn wadi]

I need help with this, I found the curl to be (0,0,-1)

then i have to find the normal vector

so i paramtertic the surface\

r(x,y) = (x,y,x-y+3)

did cross product of the derivative x, y respectivly got (1,1,1)

(0,0,-1) dot (1,1,1) = -1

take the double integral with bound of y= 0 to 1 and x = 0 to 1-x

got 1/2

which is wrong

this is stokes theorem

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@torn wadi Has your question been resolved?

[torn wadi]

i also need help with this question

i calcualte the curl but im stuck with finding that paramertization.

im confused because z is not a function

its a range

(r,theta) = (rcos(theta), rsin(tehta), z)

i then take the gradient of this

but im just lost with stokes theorem

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[torn jolt]

how do i get started on this:

[torn jolt]

find the interval of convergence

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[versed ibex]

so this is about discrete random variables, something to do with binomial distribution idk

[versed ibex]

the probability of throwing a 5 with a biased die is p. an experiement consists of throwing this die n ties and recording the number of 5's thrown.

when this experiment is repeated a large number of times, the mean number of 5's is 60 and the standard deviation is 6. calculate the value of p and of n

[devout valley]

Sure binomial distribution do you know how to find the mean and variance (equiv. standard deviation) of a binomial distribution?

[versed ibex]

so apparently mean is given by 'np' and sd by 'npq'

[devout valley]

variance* for the latter, sd is the square root of that

But yep, mean is np and variance is np(1 - p)

Can you figure out how you can find n and p from there?

[versed ibex]

lemme think

mean = 60 = np

variance = 6 = sq rt (np(1-p))

i can solve simultaneously??

[devout valley]

Yep

[devout valley]

But variance is 6^2 and no square root (or standard deviation is as you've said)

[it's most likely a better idea to use the variance here, there should be something nice you see!]

[versed ibex]

okah so 6^2 = np(1-p) ?

[versed ibex]

i think its easier to solve that way

[versed ibex]

thank you!!

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[echo rock]

Would this be DNE or just 3?

[echo rock]

supposed to be negative one this was an old picture

[umbral dome]

,rotate

[echo rock]

that's my bad it's supposed to be negative 1 not positive

<@&286206848099549185>

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[crisp peak]

In Diagram 1 PQRST is a square pentagon and PRVW is a square quadrilateral. Find x

i forgot how

[devout valley]

"square pentagon"
"square quadrilateral"
Can you elaborate what those mean please? Feel like there may be a mistranslation there

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@crisp peak Has your question been resolved?

[crisp peak]

oh yea

mb i just copy pasted from google translate

[devout valley]

That's fine, as long as you can kind of describe them and we can try to figure out what you mean?

Maybe regular pentagon?

[crisp peak]

yes

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[patent lynx]

hi i am currently going over linear algebra and i need help w understanding column row factorization A=CR

[patent lynx]

https://www.norbertwiener.umd.edu/FFT/2020/Faraway Slides/Faraway Strang.pdf

(moving to linear algebra channel)

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[sullen grotto]

How to do

[hoary ember]

(159-(-1))/5+1=n

[tribal viper]

You use arithmetic sequence formula
a_n= a_1(n-1)d

[sullen grotto]

What is a_n

Is it just a then small n under

[hoary ember]

you can derive this from
$$159=-1+5(n-1)$$
$$159+1=5(n-1)$$
$$\frac{159+1}{5}=n-1$$
$$\frac{159+1}{5}+1=n$$

[tribal viper]

a_n is final term a_1 is beginning term n is number of terms d is common difference

[glossy valve]

Skill_Issue

[tribal viper]

Yea

[hoary ember]

$a_{n}=a_{1}+(n-1)d$

[glossy valve]

Skill_Issue

[tribal viper]

Yea

[sullen grotto]

Ai hol up lemme try to solve

So 159 is n right

Wait no

Nvm

trying to find n

Is it 33

@tribal viper

@hoary ember

[hoary ember]

think so

[tribal viper]

Yeah

[sullen grotto]

YES

THANK YOU

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[torn jolt]

how do u reas this

if all output values of function x are greater or equal to 0 then absoluting the output values of the function x will be equivalent the output values of the function x

???

[echo marsh]

yes

[viral jasper]

"If f of x is greater than or equal to zero, then absolute value of f of x equals f of x."

[viral jasper]

No

There is no mention of every x

[torn jolt]

y not

why not huh

[echo marsh]

f(x) > 0 -> |f(x)| = f(x)

thats true

[torn jolt]

whtpythrfucjnot

[viral jasper]

Nowhere here does it say that every x is being considered

Why? Because we have an explicit operator for that

[echo marsh]

it already said f(x) is greater than or equal to 0

[torn jolt]

ye

[torn jolt]

exacrly

[viral jasper]

$\forall x$

[glossy valve]

SWR

[echo marsh]

yes i know that

[viral jasper]

<@&268886789983436800> spam?

[torn jolt]

so?

[viral jasper]

But it's not saying explicitly that it's true for every x. It happens to be true, yes, but it's not actually written

[echo marsh]

maybe they just didnt write it

but its implied

[dull seal]

No

[torn jolt]

it is implied

[torn jolt]

to what

[echo marsh]

to this ig

[torn jolt]

aint no wayy

[torn jolt]

what is it

also

[echo marsh]

this

[torn jolt]

f(x) is the output or is it function of x maps to etc

heeeelp

<@&286206848099549185>

[torn jolt]

??

[torn jolt]

and how to reqd this

):

😩

.close

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[steady flicker]

hello! I have a stats test tmr and I wasn’t there for this lecture.

[steady flicker]

I have no idea how to get those answers listed

I have no clue how to find the % of the sample that has ppl under 60 inches

the table is for the z-score stuff we’re supposed to apply

pls help 😭

[tender nacelle]

5 ft = 60 inches.

The average student is 65 inches, and there is a standard deviation of 3 inches. That means that someone who is less than 60 inches whill be 5/3=1.67 standard deviations below average. This (1.67) is the z-score.

[steady flicker]

should i round that up?

to 1.7

[tender nacelle]

I would interpolate if i were you

[steady flicker]

got it

i think i see where i went wrong

as for the 62 inches on the bell curve, is that a single standard deviation? i don't know how to properly define/classify that marking

[tender nacelle]

yes, 62 inches is -1 standard deviation, while 68 is 1 standard deviation

[steady flicker]

gotcha

[tender nacelle]

a rule of thumb is that about 68% of people (looking at your table, 34.135*2) is within 1 standard deviation of the mean. For janky z scores like 1.67, you need to use the table you posted. If you interpolate for A(1.67) you should get something around 0.451 (do the interpolation, I'm just eyeballing it). This means that 45.1%x2= 90.2% of people are within -1.67 and 1.67 standard deviations.

and the complement, 9.8% is outside. However, we only want the subset of people below -1.67 standard deviations (not above 1.67), and since this distribution is symmetric (normal), 4.9% of the students will be below -1.67 standard deviations from the mean.

My numbers are probably imprecise since I didn't interpolate by hand, but that's the approach to take.

[steady flicker]

um i think im a lil behind 😭

i just plugged the value into the equation

i used 1.7 since i think that's what my teacher would want us to do

should the σ value be negative?

since the area we're focusing has negative deviations

[tender nacelle]

yes

however, the distribution is symmetric, so the number of people below -1.7 std will be equal to the number above 1.7 stds

[steady flicker]

Gotcha

I got a value of 59.9

[tender nacelle]

59.9 what?

students?

[steady flicker]

Inches

I think

[tender nacelle]

what

[steady flicker]

I’m referring to my notes I took

😭

[tender nacelle]

what's that 59.9 supposed to describe?

[steady flicker]

I’m gonna be honest I have no idea

I wasn’t there in class

[tender nacelle]

Yeah, I mean, we already know that

we want to find the number of people below 5 ft

aka 60 inches

we want the proportion of the shaded area to the whole area

The table tells us between the mean (65 inches) and 1.7 standard deviations (70 in, just the opposite of 60), the area is 45.54% of the total area under the curve.

With that in mind, and knowing that the distribution is symmetric, can you figure out what percentage of the total area under the curve is red (ie. below 60 inches)?

[steady flicker]

the blue area is 45.54% right?

[tender nacelle]

yes, do you understand why?

[steady flicker]

Referring to the table

The 1.7 is the standard deviation value

And the corresponding val is 45.54

[tender nacelle]

yep

[steady flicker]

The red portion is 4.46%

[tender nacelle]

si