help-26

[misty sand]

No is 2.65 right

cause thats the first year

[mint crescent]

Yeah

[misty sand]

how did u find this

[craggy haven]

no

pay attention to the equation and the text

[mint crescent]

Did I mess up

[craggy haven]

t is time in years since 2010 not 2018

oh

bro why do they put them out of order

i read 2020 for the second date

nvm... No = 2.65 is correct

[misty sand]

😭

alright

wait so to find a

i just divide

3.0 by 2.65

but that would be for 8 years

its 9:11 btw

thought that was funny.

if i plug in

[late token]

How does an integral work

[mint crescent]

!occupied

[topaz sinew]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[misty sand]

N = 2.65 x a ^ 0

so a ^ 0 would be 1

so that goes away

wait no

but i gotta find a

n = 3.0 x a ^ 8

8 root (n/3.0) = a

[mint crescent]

??

Where did this come from

[misty sand]

i plugged in

3.0 million

for N8

and then t is 8

[mint crescent]

Then it would be $3.0=2.65 a^8$

[thorny flame]

Civil Service Pigeon

[mint crescent]

Read the question again

[misty sand]

OHHHHHHHHHHHHHH

i see

ok lemme do it rq

[misty sand]

is it 0.4329

for a

[mint crescent]

,w (3/2.65)^(1/8)

[thorny flame]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon

[misty sand]

oh

[mint crescent]

!show

[topaz sinew]

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

[misty sand]

i did it like this

8 sq root 3

and then i divided that by 2.65

[mint crescent]

$\sqrt[8]{3.0}=a \sqrt[8]{2.65}$

[thorny flame]

Civil Service Pigeon

[mint crescent]

This is what you get if you do that

[misty sand]

oh

ok

i got it now

ok so for the last question

N = 2.65 x 1.015627432 ^ -10

is that correct?

[mint crescent]

No

[misty sand]

uh

[mint crescent]

!show

[topaz sinew]

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

[misty sand]

alr so

N = N0 x a ^ t

N0 is 2.65

a is 1.015...

and then t goes backwards cause its in 2000

so it becomes -10

is t something else?

[mint crescent]

Omg I thought you were writing it in scientific notation for a minute

Never mind you’re fine

[misty sand]

oh alr

alright i got it right

thanks @mint crescent

i might need more help ill have to see

[mint crescent]

[misty sand]

yeah

heres what i think

the first one is

because i need the half life

ill divide t by 2

so t/2/30

so

t/15

oh

wait

do i divide everything by 2

on the right

f(t/2) would be the half life i think

so everything should get divided by 2?

[mint crescent]

Think of it like this

How much does t have to increase by for the sample mass to be divided by 2

Look at the exponent

That’s all I’m going to say

[misty sand]

30?

cause 30/30 would be 1

and then 80/2 would be 40 which is half of the sample mass

oh i see

as more time goes by the sample decreases

is the rate of decay

0.0228

cause i plugged in

1 for t

[mint crescent]

I’m pretty sure they want the value of $r$ when you rewrite the exponential factor in the form $e^{rt}$

[misty sand]

so i did 1/2 ^1/30

[thorny flame]

Civil Service Pigeon

[misty sand]

whats r

oh rate of decay

[misty sand]

im not sure how to start

i know e is 2. something

my teacher was talking about it today

i forgot though

[mint crescent]

Set up an equation based on this

What is equal to what

[misty sand]

ok i got E

its 2.718...

r is the unknown

and im not sure about t

its it just 1/30?

[mint crescent]

Can you answer the question please

[misty sand]

e is 2.718

wait so if rate of decay is 30

no

[mint crescent]

That’s … not what I’m asking

[mint crescent]

.

[misty sand]

im confused

[misty sand]

wait so

i rewrite it to get r alone?

[mint crescent]

Idk what “it” is, but if you have an idea, go ahead

[misty sand]

e^rt

[mint crescent]

And what is that equal to?

[misty sand]

is it equal to r

[mint crescent]

Dude

[mint crescent]

Here’s your exponential factor

[mint crescent]

$e^{rt}=\left(\frac{1}{2} \right)^{\frac{t}{30}}$

[thorny flame]

Civil Service Pigeon

[mint crescent]

Solve for r

[misty sand]

wait so why is the 80 not in there

ill do it rq

[mint crescent]

It cancels anyway

[misty sand]

how do i separate rt

[mint crescent]

Both sides are raised to the power of t

Take that as you will

[misty sand]

oh i see

ok so if i cancel both

e^r = 1/2 ^1/30

can i just swap the exponents

wait

lemme do 1/2 ^ 1/30

0.977...

[mint crescent]

I would advise you to not round until the end

[misty sand]

got it

its saved in the calculator

[mint crescent]

Take the ln (natural log) of both sides

[mint crescent]

Recall that ln(x) is the inverse of the exponential (e^x)

[misty sand]

uhh

wait so if i log it

it just becomes e x r?

and the other side becomes 1/2 x 1/30

[mint crescent]

I think you forgot to write the ln

[misty sand]

im confused

so ln (e^r) = ln (1/2 ^ 1/30)

?

[mint crescent]

$r \ln(e)=\frac{1}{30}\ln(2)$

[thorny flame]

Civil Service Pigeon

[mint crescent]

$r=\frac{1}{30}\ln(2)$

[misty sand]

but how do i change it by log

[thorny flame]

Civil Service Pigeon

[misty sand]

wait

so log just brought the r down?

and what happened to the ln (e)

[mint crescent]

$\ln(e)=\log_e (e)=1$

[thorny flame]

Civil Service Pigeon

[mint crescent]

$\log(a^b)=b \log a$ for $a>0$ (this is true for any base, including $e$)

[thorny flame]

Civil Service Pigeon

[misty sand]

wait so e was just 1?

or did it get cancelled out by the log

[mint crescent]

.

e^1 = e -> ln(e)=1

[misty sand]

nah i dont get it

i think u gotta dumb it down for me

if you log e^x it inverses so it just becomes e times ln (x)?

[mint crescent]

Yk what inverse functions are, right?

[misty sand]

i forgot

[mint crescent]

Yeah brush up on that later

[mint crescent]

Anyway, you’re done

[misty sand]

got it

where do u think i should go

to refresh my memory

on stuff

[mint crescent]

Google

[misty sand]

oh alright

ok i think im good

my brain is fried

thank you

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[strong sable]

I really dont understand how did they get there

[hollow hedge]

did you understand why F'(0) is the directional derivative of f at a in the direction v?

[strong sable]

hmm

no

[hollow hedge]

alright, so let's start with this definition they gave for F(t)

I'm suppose you are familiar with what f(a+tv) means in this context?

[strong sable]

yes, it's adding to it a small amount t in the v-direction

[hollow hedge]

right, but what I want to focus on is, the composition is essentially f(a+tv_1, b+tv_2)

[strong sable]

yes, ik

[hollow hedge]

alright, so the derivative of F(0) using the limit theorem is given above. Can you see how f(a+tv) and f(a) appears in the limit?

as in can you spot that this is just a substitution?

[strong sable]

yes

f(g(t))-f(g(0))

[hollow hedge]

right, g(0)=a as explained above. And the limit on the right is just the directional derivative of f at a in the direction v

[strong sable]

ye but i still dont understand this part

[hollow hedge]

yeah, we're getting there now

so as above we know that F'(0) is the directional derivative and expressed it using the limit definition. However, we can express that using the differential operator

so we have $F'(t) = \frac{d}{dt} F(t) = \frac{d}{dt}f(\textbf{a}+t\textbf{v})$

[thorny flame]

waler

[hollow hedge]

do you follow this?

[strong sable]

yes

[hollow hedge]

right, and f(a+tv) is essentially just f(x(t),y(t))

and $\frac{d}{dt}f(x(t),y(t)) = \nabla f(x(t),y(t)) \cdot (x'(t), y'(t))$

do you agree with this?

[strong sable]

this is just a notation thing i guess?

[hollow hedge]

more than just notation, if f(x,y) is parameterise by x(t) and y(t). Then the derivative of f(x,y) wrt t is the gradient of f at (x(t),y(t))

[strong sable]

I see

[hollow hedge]

oh oops I forgot a dot product with (x'(t),y'(t))

[thorny flame]

waler

[hollow hedge]

right there you go, sorry about that

essentially, just total derivative

you might have seen something like this before [\frac{df}{dt} = \frac{\partial f}{x}\frac{dx}{dt} + \frac{\partial f}{y}\frac{dy}{dt}]

[thorny flame]

waler

[strong sable]

Yes

[hollow hedge]

oops forgot the partial symbol in the denom

anyway, that in of itself is the dot product between the gradient of f at (x(t),y(t)) and (x'(t),y'(t))

which is exactly this

here (x(t),y(t)) is defined by the function g(t). Hence (x'(t),y'(t)) = g'(t)

and Df is your textbook notation for the gradient

because we care about F'(0), hence we substitute t=0 in the expression

[strong sable]

Why did they choose 0

[hollow hedge]

because F'(0) is the directional derivative of f at a in the direction v

they can choose any other value t as well, but we wouldn't get that nice equality

the point of the last line is that apart from the limit definition of directional derivative. You now also have a nice algebraic way to calculate the directional derivative. That is by applying the dot product between the gradient of f at the point a and the directional vector v

[strong sable]

I see...

This is hard😢 but thank you!!

[hollow hedge]

np, take your time. The most important thing to remember is this. The computation stuff is just to provide some working

[strong sable]

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[radiant rose]

Hey just a quick question im not asking about alpha but is the angle that I drew 130 degrees?

[wispy pier]

Bro

They r on the same segment

So equal

[radiant rose]

I didnt ask about alpha

[carmine lynx]

hes asking about the black one blud

i think we cant know if they are 130

[flint stump]

No, black angles dont have to be 130

They can be any number, depending on the locations of the 4 points on the circle

[wispy pier]

This marked angle is also alpha

[radiant rose]

Yeah thats what I thought but using angle bisector or whatever I dont what its called in english can you not solve it?

[wispy pier]

Not enough info

[radiant rose]

how so? It forms a 180-12,5-90=77,5

180-77,5*2=155

180-155=25

180-25-90=65

[craggy haven]

where in the world are these numbers coming from

[radiant rose]

wait I dont know these math terms in english so its gonna take a second to translate

but basically the angle bisectors meet in the middle and if you put a circle there. Then you always have a 90 degree angle to calculate with

this is basically what I mean

You cut the 25 in half you get 12,5 to calculate the the middle of the circle angles. And with the circle can you not calculate to the end? I dont get how you couldnt?

you have those two at 77,5. The one on the wall is 90 degrees. So you can calculate 180-77,5*2=25 and 180-90-25=65

[radiant rose]

?

I thought you couldnt know them at first either but then I remembered that the angle bisector whatever always makes a right angle on the side. So this should work no?

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[shell orbit]

I have a question about how to write your answer in exams

For part A of this question, we learned that f(x) = 0 gives x = 3pi

For part B of this question we learned that f(x)^2 = g(x)

for part C of this question we need to find the solid of revolution of f(x) in the diagram

So to find the solid of revolution we first need the x axis intercept, and to square f(x)

Both of which we found in the previous questions

If I was in an exam, what would I write? Would I just write x = 0 and 3pi, and not explain how I got it? Do I need to make some kinda note that I got it from part A or something?

What exactly would that note be?

This is just for if im in an exam, not for homework or whatever, what am I supposed to write

[shell orbit]

Same for squaring f(x) (for the solid of revolution)

[flint stump]

You can mention something along the lines 'using the results obtained in problem a, we can ...'

[shell orbit]

Ok cool

[flint stump]

Ofcourse, the problem a has to be the part of the exams as well

[shell orbit]

I dont know much about what to do and what not to do in exams, things like this

Like how much 'english' I can write, instead of maths, if that makes any sense

[flint stump]

Dont reference anything you proved outside of the syllabus

[flint stump]

As much as you want, but without ignoring the necessary maths notation that comes with it.

Like you should make sure that if someone reads only the maths notation, they should still be able to comprehend the entire thing logically

[shell orbit]

Ah ok thats a good rule to follow

[flint stump]

Do not put maths results inside english statements

[shell orbit]

Can you give an example sry

[flint stump]

Lets say you are going to use pythagoras theorem, you can mention it within the english textyou write, but whereever you use it, always mention the name right after the use

like:
So, in a right triangle, we know that the sides squared sum up to the square of the hypotenuse according to the pythagotas theorem. So we can use this in our solution since we have proven that the triangle ABC is right triangle. So, we obtain
a^2 + b^2 = c^2 ....... From Pythagoras Theorem

Instead of simply putting:
So, in a right triangle, we know that the sides squared sum up to the square of the hypotenuse according to the pythagotas theorem. So we can use this in our solution since we have proven that the triangle ABC is right triangle. So, we obtain
a^2 + b^2 = c^2

[shell orbit]

Damn ok so you can actually write a lot

I didnt realize haha

[flint stump]

You dont get your marks reduced for too much english

but you do get them reduced for too less maths notation

[shell orbit]

So for our original question we would say 'using the results obtained in problem a, we can see that

Therefore

[flint stump]

yes

[shell orbit]

is equal to

[flint stump]

Fun fact: You can still use it even if you havent solved it in exam (as long the result is stated in the previous problem)

[shell orbit]

Ahh ok cool

[flint stump]

because ithe problem goes like "Show that", implicitly acknowledging the veracity of the statement

[shell orbit]

Yeah that makes sense

Do you have any other advice for me or rules I should follow, regarding writing words in exams or whatever

Or maths notation or whatever

I literally learned nothing about this I just learned the course

Like what was on the actual exam

[flint stump]

idk dude, whatever I said, none of that is an exact written rule. Its all the experience ive had being part of the both sides of examinations

[shell orbit]

Yeye that's all I wanted haha some advice

But OK I guess I already understand a lot more now with what you just told me

Thank you!

[flint stump]

npnp

[shell orbit]

❤️

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[autumn plaza]

what does it mean by

[autumn plaza]

smallest positive rational number

[neon iron]

a number that is the smallest and positive and rational

rational numbers are numbers that can be written the form of p/q

[acoustic pecan]

where p and q are integers

[neon iron]

yes yes

[autumn plaza]

wow

how does it expect me to know that

[autumn plaza]

and q not equal to 0?

oh nvm

[acoustic pecan]

correct

[autumn plaza]

0 isnt an integer

[neon iron]

it is..

[autumn plaza]

oh...

so...

um..

how do i do it..

[neon iron]

i dont know how to write a formal proof, i'll just tell you why this is true

[autumn plaza]

its just contradiction

[neon iron]

dude i have never written a proof in my life

i skipped it

[autumn plaza]

what da freak

[neon iron]

yeah

[autumn plaza]

they made me do 4 types of proofs

[neon iron]

i was like "i dont care about my score"

but thats irrelevant now

[azure grove]

well, if you have to solve via contradiction, start by seeing what happens when u assume there is a smallest positive rational number and see what contradictions there are as you go

[neon iron]

@autumn plaza lets assume there is a smallest positive rational number

let it be n

[autumn plaza]

idek what smallest positive raitonal number is

[neon iron]

but then you can just write n/2

and n/2 is obviously smaller

and you can do this infinite times

there's no stopping

[autumn plaza]

oh

so theres infinite

so there is no smallest positive rational number

omg

[neon iron]

yess

and also

[autumn plaza]

am i smart

[autumn plaza]

how do i write that though..

[neon iron]

that i dont know

ask duck

[azure grove]

Let there be a number, p/q where p/q is the smallest positive rational number

Now, suppose a new number, p/2q, this number has to be 2 times smaller than the previous p/q

However, p/q was suppose to be the smallest positive rational number

There lies the contradiction

[autumn plaza]

ohhh

wow i hate this

why do we have to know this

[azure grove]

its a usefull proof technique

[autumn plaza]

WHAT IS A PRIME NUMBER 😭

[azure grove]

a prime number is a number that is only divisible by itself and 1

[autumn plaza]

oh

ok lemme try

[azure grove]

gl

[neon iron]

is that a test

[autumn plaza]

why would a test have check answer

[neon iron]

right, my bad

[azure grove]

this looks right

[autumn plaza]

wow that was kind of easy

nvm i like this

[azure grove]

lmaoo

[autumn plaza]

do u know physics

im doing waves rn but i dont understand this phase shift quesdtion

[azure grove]

nah, i haven't done physics

[autumn plaza]

rip

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[autumn junco]

why did dy/dx not become 0 tho-

[acoustic pecan]

im not sure what you mean

[neon iron]

because it isnt?

dy/dx refers to the slope of the function

[autumn junco]

y's a constant right

[acoustic pecan]

no

[neon iron]

no

[autumn junco]

shi

alr

[neon iron]

damn

[autumn junco]

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[mortal heart]

guys, for letter c, am i wrong?

i checked the answer key and it says (2, -2) is the answer. but the answer key on my book might be wrong

[trail hemlock]

WHAT?

[wary tulip]

i didn't read through it but this caught my eye

so that's at least one mistake

wait but

the answer you got is (2, - 2) lol

but (2, - 2) isn't right because log_4(2 - 2 + 9) isn't 0

[mortal heart]

ohhhhyesss

[wary tulip]

if you fix that then you'll find a solution when x = 4

the book answer isn't right

[mortal heart]

wait my bad

the answer key says x=4,y=−12

i got it alreadyyy

[wary tulip]

loll then yea that's right

[mortal heart]

thank youuu

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[golden trail]

how to show f is continous everwhere

[neon iron]

Have you shown it is continuous at (0,0)?

[golden trail]

yes

[neon iron]

Can you see that it is continuous at (x,y) whenever x is not 0?

[golden trail]

yes ,

[neon iron]

How did you show it is continuous at (0,0)?

You need to do something similar to show it's continuous at the point of form (0,y)

[golden trail]

like i found the function value at (0,0) and limit value at (0,0) and both values where same so i concluded at (0,0) its continous

[neon iron]

Can you compute the limit at (0,y)?

[golden trail]

yes i would get cosy

[neon iron]

And the value at (0,y) is cosy too

So it is continuous at (0,y)

[golden trail]

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[muted folio]

do you know synthetic division?

[pallid harness]

Yes

[muted folio]

then what is your problem here?

[pallid harness]

I need a form like this

What I am getting from synthetic division is not giving it me this form

This is what I get from synthetic division

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@pallid harness Has your question been resolved?

[pallid harness]

<@&286206848099549185>

[reef ermine]

Take the original polynomial

Divide it by (x-3)
The residue will be the coefficient for the constant.

Take the result of the division- divide it again by (x-3)

The remainder is the coefficient for (x-3) in the expression you're looking for

Take the result of the previous division and repeat- divide by (x-3)

The remainder this time will be the coefficient for (x-3)²

Proceed that way till the polynomial is constant

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[olive citrus]

so what is the difference between parts b and c of the question??

[olive citrus]

i know that the answers are b) -33.3 and c) -33 1/3 but i dont know why c is what it is. are they just asking for slope again and if so why is it not the same answer as b

[vernal matrix]

For part c, assumedly they want you to plot those points, join them up and try and draw a tangent, and find what its gradient is (as opposed to b, where you just need to pick two pairs of points, figure out the gradient in the pairs, and average those)

[olive citrus]

oh ok. we havent learned gradients i think

[vernal matrix]

Same thing as "slope" (I just prefer the word gradient personally)

Also just noticed you did the "pick two pairs of points..." as part a, so pick two of the values there and average those, which hopefully works out as 33.3

[olive citrus]

ohhh..well heck! thats what i did for part b also

because it wants the slope for the tangent line of point P, i used the points surrounding point P and averaged their msec's

but for c i am taking random points and averaging them?

[vernal matrix]

For part c, you're plotting those points out and joining them

(ideally, if you had graph paper or something )

[olive citrus]

you mean join as in connect the dots per se? and lol yeah im in my notebook

this textbook is stupid. if it wanted me to just plot the points for this function it shouldve just said so. why ask me to find slope AGAIN when i just found it

thank u for ur help

its the first day of class this fall so im overthinking btw lol byeeee

🩷

[vernal matrix]

(the idea is that they want you to try different methods, I presume, before they get you to derivatives )

[olive citrus]

funnnn

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[vale hemlock]

Hi, can someone explain to me what degree of freedom is? I'm confused.

[jade thunder]

it could mean a lot of things, what topic are you looking at?

[vale hemlock]

in stats

or like chi squares

[jade thunder]

it's just a parameter

like µ or σ² is a parameter for the normal distribution

but there are some important transformations that affect the degrees of freedom

the main one being if $X \sim \mathsf{N}(0, 1)$, then $X^2 \sim \chi^2_1$

[thorny flame]

frosst

[vale hemlock]

im confused...?

if theres like a coin right, whats the degree of freedom

im using this for chi squares in bio so im not sure about many of the stat stuff

[jade thunder]

the second one being if $X_1, ..., X_n \overset{\text{i.i.d}}{\sim}\mathsf{N}(0, 1)$, then $X_1^2 + ... + X_n^2 \sim \chi^2_n$

[thorny flame]

frosst

[jade thunder]

there is far too little information in here to understand what you're asking

coin flips are usually modelled as bernoulli or binomial distributions

these do not have the parameter "degrees of freedom"

[vale hemlock]

so like in chi squares, there a die and u roll 1s and 2s like 80% of the time where as like 3s 4s and 5s make up a collective 20% ur supposed to find how random it is

but then they use degrees of freedom and i just got confused

we get this chart thing but idk how to use it

[jade thunder]

what's the particular hypothesis test you're doing?

[vale hemlock]

ours was like on people taking sick days on mon/fri vs mid week and find out if it is random or more intentional

[jade thunder]

ah, it's called pearson's chi-squared test

[vale hemlock]

so like

[vale hemlock]

ohh

so what does degree of freedom play a part?

[jade thunder]

i think here due to how they set it up the degrees of freedom (dof) is just 1, since you only are looking at 2 categories, and you just minus 1 from that

[vale hemlock]

oh ok

[jade thunder]

if they set it up to be (in the rows of the table)
mon ...
tues ...
wed ...
thurs ...
fri ...

you'd have 5 categories

each with expected value of 20

then you'd have 4 degrees of freedom

[vale hemlock]

oh i see

[jade thunder]

it's sort of because you know how many people you interviewed/surveyed

[vale hemlock]

and then when i solve for my chi-square calc then i'd put it into this chart, correct?

[jade thunder]

if you tell me how many people was "sick" for 4 of the 5 days

i can already tell what the 5th cell says

[vale hemlock]

OH I GET IT

thanks so much this makes a lot more sense now

[jade thunder]

so you "lose" that degree of freedom of the last category

[vale hemlock]

tysm

[jade thunder]

right so you look at this table

calculate your "pearson's chi-squared goodness of fit test statistic" (very long name i know)

should be this

[vale hemlock]

oh i see

[jade thunder]

O_i is obviously the observed cell

E_i is the expected cell

[vale hemlock]

👍

[jade thunder]

the i just iterates through the rows of the table

[jade thunder]

after you put this into your calculator you have a number

[jade thunder]

you go to this table and find the row with your degree of freedom

and compare the number from your calculator to the number in the table

if the number in your calculator is bigger you reject the null hypothesis (THIS IS ONLY FOR CHI-SQUARED TESTS)

[vale hemlock]

oh i see!

tysm you helped so much

[jade thunder]

❤️

[vale hemlock]

i understand now

❤️

[jade thunder]

awesome!

[vale hemlock]

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[glossy cipher]

how to solve

[restive inlet]

angle addition

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@glossy cipher Has your question been resolved?

[grizzled obsidian]

You have both angles, ∠DCN = 8x-1, and ∠NCB = 42°. Also, ∠DCB = 12x+13

You would use the Algebra you learned previously (Solving equations with variables on both sides) to get your solution?

Got it, or need more help?

[glossy cipher]

got it tysm

[grizzled obsidian]

Happy to help!

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[fiery sigil]

I dont understand what happened over here

[fiery sigil]

Its confusing because logically and mathematically i sorta understand it but it clashes

How come we have h=y+3 but when we try making 2 variables then (y-0) becomes (h+3). should it not become (h-3 instead of h+3)

[topaz sinew]

@fiery sigil Has your question been resolved?

[fiery sigil]

<@&286206848099549185>

[timid umbra]

geometry?

[timid umbra]

wouldn’t you have to find the volume and divide it?

by 2?

[thick jay]

need help?

[fiery sigil]

no the equivalent integrals

Im so confused on whats what

[thick jay]

umm

the tank is the hemisphere provided right?

[fiery sigil]

idk

I think so

I dont know if the tank is a sphere

And its showed the cut in half one

[thick jay]

ok

h=2

r=2

so its a hemisphere

:/

[fiery sigil]

ok

[thick jay]

hmm

Ill try renormalising

[thick jay]

whats the equation for work given?

[fiery sigil]

the two shown above

[thick jay]

py?

what is py

what is py(y-0)

???

[fiery sigil]

lift

[thick jay]

lift?

[fiery sigil]

height of lifting from origin

yes

[thick jay]

wot

[fiery sigil]

bruh

[thick jay]

Youre doing work

but theres nothing related to the mass of the objects youre lifting?

Id expect the equation to be like:integral of( mgy*area of a crossection of the hemisphere at hieght y)

[thick jay]

shouldve been y=3+h

[fiery sigil]

yeah thats what i was thinking

theres mistakes in these videos honestly i dont like them

thanks

ima close now nothing else i can do

.close

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[wheat osprey]

hablen en spanish

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[uncut dome]

I need someone else's answer on this, I got 14.5 and 19.5 but my teacher doesn't seem to think so

[brave coral]

I got 14.5 as well as

[prisma mesa]

if i understand it correctly, i have same answer as you

[brave coral]

The bit about them saving was a little unclear but I assumed the 60 and 20 were the total savings after some number of weeks

[uncut dome]

The question it self was a bit unclear for me too, I might have to ask my teacher again

Can you go through your process for me if possible

[brave coral]

Sure

Let x be Megan's allowance per week then
x + 5 is Sally's
They spend £12 a week so in a week Sally saves (x + 5 - 12) = (x - 7) while Megan saves x - 12

After n weeks, Sally and Megan save 60 and 20 respectively

60 = n(x - 7)
20 = n(x - 12)

Solving that equation for x gives 14.5

@uncut dome

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[uncut dome]

Yeah yours seem to match up with mine, thanks for your pov

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[bitter python]

Why is cube root of 7100 = 10 cube root 71 and not 7.1

[brave coral]

Nah you're right. It's just a typo

Notice how the substitution give 8 - 9(0.1) = 7.1

[bitter python]

The reason I asked is because I fucked it up and got -0.1

I thought 7.1 = 8-9x would mean x=-0.1?

Ohhhh wait

Divide by -9

That might be it

[brave coral]

Didn't understand the last bits of your message but 8 - 9(0.1) = 8 - 0.9 = 7.1

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[limpid gate]

When dividing

[limpid gate]

Would this equation

(B-ac-c)/a, would I just divide and get b-2c or would it be like reverse distribution and like (b/a)-c-(c/a)

[restive inlet]

it'd be distribution, but you didn't distribute properly

ac/a isn't 1

[limpid gate]

Forgot

Alr tyy

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[hushed geyser]

idek what to do after this

[sudden temple]

you missed a negative in du/dx line

[hushed geyser]

yea i realised

[fallow heart]

!nosols

[topaz sinew]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[fallow heart]

!nosols

[topaz sinew]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[fallow heart]

Ups

[sudden temple]

lol

just guide helpee to the solution

not "give them"

huh?

I don't get what you mean

[cedar wagon]

He is not the one asking for help

[hushed geyser]

.close

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[exotic torrent]

Can someone check if I’m doing this correct?

[pearl fog]

1.ii looks incorrect

im not sure what the function g(x) is, but if its -x^2 then number 2 looks correct

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[exotic torrent]

oh ok thank you

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[chilly bough]

i have these two equations

[chilly bough]

that together produce this butterfly

how can i merge them into one equation?

here's what i've tried

while this works for most functions, in this particular case each function is undefined on some set of inputs so together they cancel each other out

[ruby tree]

Share the link?

[chilly bough]

is there a way to avoid it?

gimme a sec

https://www.desmos.com/calculator/80umddmm8s

[ruby tree]

\left(\left\{y\ge0:\ x\cdot0.8,\ x\right\}\right)^{8}+y^{8}-\left(7xy\right)^{2}=0

Or, if you don't want the conditional ({...}),
\left(\left(-\frac{y}{10\left|y\right|}+\frac{9}{10}\right)x\right)^{8}+y^{8}-\left(7xy\right)^{2}=0

https://www.desmos.com/calculator/bve4oymmpr

[chilly bough]

ummm im actually trying to do it without any conditionals 👉👈

sorry i should've mentioned that earlier

[ruby tree]

Do you consider |y| a conditional?

[chilly bough]

no since it can be defined as sqrt(y^2)

[ruby tree]

So this should be ok

[chilly bough]

oh wait i haven't noticed the second equation

thank you

.solved

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[shell peak]

why is it important that the diameter of the wire is measured accurately than its length

[steady escarp]

Because the diameter is a smaller number

Say actual diameter is 0.05 mm, but u measure it to be 0.08 mm, and its actual length is 1.42 m, but u measure it to be 1.43 m

[flint stump]

an error of 1mm in diameter is a lot higher in comparison to its diameter than the error of 1 mm in length wrt the length

[steady escarp]

Ull be "more wrong" in saying the diameter is 0.08 than in saying that the length is 1.43

It's the relative error

[flint stump]

Another less trivial point (but more significant in terms of which error you consider) is that we care more about cross sectional area of wire so, error in diameter gets amplified when you use diameter squared. On the other hand we are happy with using the length directly

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[ruby dagger]

to solve x?? i can end to a=-b but im pretty sure its wrong that way

[ruby dagger]

nvm i got it i was jst being dumb

[inner wren]

nice

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[somber cairn]

can someone please explain how to show this and why it is true?

.close

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[lost crater]

do you still need help?

I just finished writing an explanation

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[thorny meadow]

i need help with like two questions please

[junior fable]

!da2a

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[thorny meadow]

okayyy

need help with this

[raven sparrow]

What is confusing you?

[thorny meadow]

8 i forgot how to do it

[raven sparrow]

What is it asking for?

[thorny meadow]

find slope

[cunning kayak]

compare with y=mx+c

m is the slope

[thorny meadow]

so its -5/3

[cunning kayak]

yup

[thorny meadow]

oh wow

thanksss

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[mild wolf]

i have a physics question but its mostly algebra

[mild wolf]

my class keeps getting different things but i swear my answer makes sense

i used quadratic formula with the two eqations: q1 + q2 = 2 and q1 x q2 = 1/4

does my logic make sense??? my class makes it seem like im tripping

[loud oasis]

that seems to work, although it would help if you included the working on applying the quadratic formula

and you could also simplify the ratio

[mild wolf]

here’s the quadratic setup

my classmate tried to correct me saying the ratio is 0.5 when it literally says what ratio >0.5

theyre all convinced you have to use derivation

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[slate current]

A committee of four is to be chosen at random from a group of six men and six women who have volunteered for the committee.

What is the probability that there is more than one man on the committe, given that there is at least one man on the committe?

[slate current]

I think im close to the answer

I got 0.75, the answer was 0.7419

the question has given in it, so the probability will be intersection/whats given

the intersection between more than one man and at least one man is 2,3 or 4 men

to solve for this, i did 1 - 1 man - 0 men

[cursive patrol]

where does it say the answer is 0.7419?

[slate current]

in the booklet thing i have

[cursive patrol]

i get 0.75

[slate current]

i mean the booklet might not be completely error proof

i hope its wrong because i feel like im doing everything right on this question lol

[cursive patrol]

i am fairly convinced it is wrong yes

[slate current]

ok thanks

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[dire oak]

how does it get -1

[dire oak]

i thought it would be 0

[lean pebble]

the x's cancel

and you get -1

[dire oak]

but aren't you supposed to sub in 0

before

wait

im stupid

why did i even post this

dont judge plz

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[low scroll]

I'm not sure how to approach this question - I understand the basic logic of the mean value theorum, but I'm not sure how the sin(f(x)) composition affects it all and how to work through it

[unreal bronze]

what does the mean vaue theorem say about sin f(x)?

if you want, let g(x) = sin(f(x))

[low scroll]

that there is some point of sin(f(x)) in the interval [0,pi] that has the same gradient as the line connecting the points (0,sin(f(0)), and (pi, sin(f(pi))

[unreal bronze]

then apply the mean value theorem to g(x) over [0, pi]

[unreal bronze]

so write it down

the equation, I mean

[low scroll]

okay so following what i wrote earlier gives me pi*f'(c) = 1

but i dont get how i know what the values of f(c) are in the multiple choice answers as i only know f'(c)?

never mind i see

.close

[topaz sinew]

Channel closed

Closed by @low scroll

Use .reopen if this was a mistake.

[topaz sinew]

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>.
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• 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.

[tepid glacier]

,rrcw

,rrcw

,rrcw

[tough nest]

,rccw

[tepid glacier]

Hacker fr

,rrcw

[tough nest]

;P

[tepid glacier]

Whatever

[tough nest]

two cs

[tepid glacier]

are u able to help me

[tough nest]

not two r's

[tepid glacier]

Oh

[tough nest]

rotate counter clockwise

[tepid glacier]

Whoops

[tough nest]

is what it means

[tepid glacier]

,rccw

[thorny flame]

Couldn't find an attached image in the last 10 messages.

Aug 21, 2024, 11:45 PM

[tepid glacier]

,rccw

[tepid glacier]

Some one help

I genuinely cannot find the mistake idk if I am blind

[pearl fog]

can you try to graph it?

[tepid glacier]

Ok

I’m on mobile right now

Ig I willl graph it on paper

[tough nest]

actually try to do it yourself

you'll get more insight

[tepid glacier]

,rccw

[tepid glacier]

I did it @tough nest @pearl fog

[pearl fog]

hm, the right graph is for the translation, could you try to graph g(x), completely ignoring the translation?

[tepid glacier]

?

Like removing the right 4 for it

[pearl fog]

er

[tepid glacier]

And only focusing on horizontal compression

[pearl fog]

ok lemme rephrase it
g(x) is incorrect

[tepid glacier]

How so

[pearl fog]

vertex is incorrect

|2x-4|=0
2x-4=0

[tepid glacier]

Isn’t it just 4 to the right

[pearl fog]

ignore the translation first

i want you to try to graph f(x) and g(x) ans try to graph the translation

[tepid glacier]

No translation?

[craggy haven]

bad question imo

[tepid glacier]

?

[craggy haven]

here, try this: make a table of values x and g(x)

[tepid glacier]

Huh

[craggy haven]

so like

x   |  g(x)
-----------
0   |
1   |
2   |
3   |
4   |
5   |

and then you can graph the function easily

[tepid glacier]

Uh

[craggy haven]

so in the first row you'd calculate g(0)

do you know how to calculate a function like that?

[tepid glacier]

Ye but I feel like the question is much easier

I don’t need to do all this

[craggy haven]

you said that the vertex was at x = 4?

[tepid glacier]

Well the function says that

[craggy haven]

does it

[tepid glacier]

Is -4 not h = 4

[craggy haven]

so if i calculated g(4) i'd get 0?

[tepid glacier]

Idk

[craggy haven]

you should make that chart

[tepid glacier]

But why is h = 2

[craggy haven]

what's h

[tepid glacier]

When it doesn’t say 2

[tepid glacier]

You know h and k

[craggy haven]

uh

[tepid glacier]

In this example h is 4

H moves left and right

K moves up and down

[craggy haven]

so ultimately h is 2 because the equation is g(x) = 2|x-2|

https://www.desmos.com/calculator/jvn861kqza

[tepid glacier]

Yea I looked at Desmos

[tepid glacier]

But the 2 is inside of the absolute value

[craggy haven]

yeah, it's written as g(x) = |2x - 4|

so it might help to think about this in terms of stages

first, we start with |x|

then we replace x with x - 4; this means the graph is shifted 4 to the right. our equation is g(x) = |x - 4|

[tepid glacier]

Yes

[craggy haven]

we then replace x with 2x; this means the entire graph is squished closer to the y axis. this makes our equation g(x) = |2x - 4|

in particular, it's being squished down towards the y axis, not towards its centerline

[tepid glacier]

Ok

[craggy haven]

so since the sharp point was at (4,0), it gets squished down to (2,0)

[tepid glacier]

Hm

[craggy haven]

here, try this: https://www.desmos.com/calculator/no6ovnetru

and play with the sliders

in particular, try adjusting a

and see that the sharp point moves around

[tepid glacier]

Ye but why does it happen

[craggy haven]

because you're replacing x with ax, so the entire graph gets squished down closer to the y axis

[tepid glacier]

Why does horizontal compression affect

[craggy haven]

why wouldn't it? it affects every part of the graph

[tepid glacier]

Isn’t it just slope

[craggy haven]

well, yes

you'll note that the y-intercept stays the same when you move a

[tepid glacier]

Like if it was 2x then at vertex 4,0 wouldn’t it just go 2/1

[craggy haven]

the reason i think this is a bad question is because Monisha described exactly what happened to the graph of f -- it was translated horizontally by 4 units, and then it was squashed horizontally by a factor of 2

[tepid glacier]

So she did not finish her answer

?

[topaz sinew]

@tepid glacier Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

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.

[lapis lava]

I don’t know how to do this statistics problem:

[lapis lava]

@glacial adder

This is the linked table, but I don’t know how to use it

<@&286206848099549185>

[late quiver]

no

[lapis lava]

No worries bro, I’m sure someone who knows how to solve the problem will come and teach us

[verbal crater]

df?

[lapis lava]

I also don’t know

No worries maybe a 3rd person who knows will come and help

[verbal crater]

!xy

[topaz sinew]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[lapis lava]

That’s all of it from the beginning

[verbal crater]

well you have 5 categories in your test

the df is just n-1

so 4

[lapis lava]

Then do I do 96/4 and look it up on the table?

[verbal crater]

96/4?

[lapis lava]

96.336/4

[verbal crater]

why do you need to do that

[lapis lava]

How do I find the p value?

[verbal crater]

p value is just the area to the right of your test statistic

so you just look up 96.336 in the table with df = 4

[lapis lava]

They don’t have it

Goes to 13.227

I posted the table

[verbal crater]

the area gets smaller if the test statistic gets larger right?

[lapis lava]

Yes

[verbal crater]

so 96 is bigger than 13

what does that tell you

[lapis lava]

Is it p<.001?

[verbal crater]

not sure about that

but definitely <0.01

[lapis lava]

How could I eliminate .001 and get .01?

[verbal crater]

?

[lapis lava]

P <.01 and <.001 are both options

It’s multiple choice

Which one do I pick and why?

[verbal crater]

actually <0.001 is also possible

but your table doesnt really go that far

[lapis lava]

Do I take the square root of 96?

[verbal crater]

no

honestly <0.01 <0.05 and <0.001 are all possible answers

[lapis lava]

Only 1 is correct though

[verbal crater]

then <0.01 is more suitable i suppose

because your table doesnt go to 0.001

so you cant really be sure

[lapis lava]

The difference between .1 and .01 is 6

On the table

So that’s a factor of ten

Would it make sense that to get from .01 to .001 would be another 6?

Actually hold on

.01 is 13.227

Are you sure I don’t take the square root of 96 and then look that up in the table under 4df?

[verbal crater]

no

the tables are all chi squared values

never take the square root

[lapis lava]

Will it be .001 because 96 is bigger than 13.227?

[verbal crater]

13.227 is 0.01

[lapis lava]

Right

[verbal crater]

that only tell you its less than 0.01