help-10

[tall flint]

Okk

Me have more question

[timid silo]

https://byjus.com/maths/conditional-probability/

This is a good source.

[tall flint]

this one

me not sure

me not know how to do C and D

help pls

[obtuse pebble]

@tall flint Has your question been resolved?

[obtuse pebble]

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@frail dune Has your question been resolved?

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[shadow trellis]

besides l’hopital, any way to solve this?

[shadow trellis]

oh wait right rationalisation?

.close

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[livid imp]

can someone help me with part c

what is the h0 and h1 supposed to be

the null and alternate hypothesis

[obtuse pebble]

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[sturdy rune]

Why does this function not get a max value? (Weierstrass)

[night igloo]

What would that max value be, then?

[sturdy rune]

The value right next to the empty dot?

[night igloo]

And how about the value in between that value and the empty dot?

Isn't that a bigger number?

[sturdy rune]

Yes but then we can say thats the max value, right?

[night igloo]

No, because you can always find a y-value closer to the y-value of the empty dot without actually reaching it

[chilly raven]

both sets of points
the lower line segment and the other one not including a point
have infinitely many points
there are infinitely many points between any two different points on either line segment

[sturdy rune]

so it is because we cant know which value it would be because there's unlimited values that could be closer?

[chilly raven]

yes
the max doesnt exist

[sturdy rune]

okay

[obtuse pebble]

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[plucky temple]

how do I make n the subject

[maiden oar]

hi

[plucky temple]

hi

<@&286206848099549185>

[maiden oar]

hi

[plucky temple]

?

[maiden oar]

could you help me with a question

on math please

[plucky temple]

uh sure but my education level is until igcse

[maiden oar]

what?

[plucky temple]

i can try

[maiden oar]

ok i am grade 7

[plucky temple]

the question?

[maiden oar]

Pete is making 8 identical fruit baskets as gifts. Each basket contains some apples and 12 oranges. Pete uses a total of 168 pieces of fruit to make the baskets. Determine the number of apples that are in each basket.

here

[plucky temple]

so there are 8 identical fruit baskets with 12 oranges in each

hence there are 96 oranges

in total

which means 168-96=72 apples in 8 baskets

since each baskets have the same number of apples, each basket has 9 apples

72/8=9

[maiden oar]

ok thank you so much for your help

[plucky temple]

do you understand?

[maiden oar]

yes

[plucky temple]

nice

[plucky temple]

<@&286206848099549185>

[hazy marlin]

make n the subject? as in express n?

[plucky temple]

like n = somehting

like n be the subject

[hazy marlin]

well hmm

i'd start with getting rid of the fraction

im assuming this is a geometric series of some sort?

so i!=1

[plucky temple]

was doing part c

and I got that eqn and need to find n

but I'm not sure how to make n the subject

[hazy marlin]

you know the values of all the other variables?

i, R P, etc..

oh yea

well like I said, i'd start with getting rid of the fraction

also you forgot the e in increases

[plucky temple]

wait

i literally did that like 3 times

and i was careless 3 times

now i managed to do it

lmao im dum

[hazy marlin]

lol happens

[plucky temple]

ty tho

[hazy marlin]

np

[plucky temple]

i spent like 40 mins doing it again and again

i went back to part a and b

to seee if i was wrong

-__-

.close

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[plucky temple]

the answer is b

the equation can be rewritten as y = -(x-2)^2 +3

[wanton dagger]

Ok

[plucky temple]

since there is a minus in the front we know it is a n curve

so its either b or c

[wanton dagger]

Yep

How about the negative 2?

What can we get from that?

[plucky temple]

this is like a formula to remember

so treat -a as -2

[wanton dagger]

Ok

[plucky temple]

the point (a,b) lies on the line

[wanton dagger]

S0 -a becomes positive?

[plucky temple]

yep

and the one on the outside stays the same

[wanton dagger]

Oh right

Oky thanks

I have one more question I need help with

[royal basin]

forgot the ^2 there

pretty crucial part of the equation if you ask me

[royal basin]

also the square might have a coefficient in front of it

[plucky temple]

ah yes

[plucky temple]

yea mb I tried to simplify it

[wanton dagger]

How would I do this kind of question?

[royal basin]

you'd probably need to know enough calculus to make judgments about slope and concavity from graphs

[wanton dagger]

Oh

But I barely know calculus

[royal basin]

the alternative is to memorize what signs of coefficients correspond to which "shapes" of cubic functions... but that'll be very forgettable without calculus knowledge

personally idk how youre expected to do this without some calculus background

at least parabolas are simple enough, but cubics are much less so

like, ok
we're told a > 0, which means options C and D are ruled out as they have a negative leading term (as can be seen from their end behavior)

[wanton dagger]

Ok

[royal basin]

one could try looking at the y intercepts btw but you can't rule anything out from that in this problem as all options have it at -6

[wanton dagger]

True

[royal basin]

now i want to say that b = p''(0)/2 so the sign of b controls the concavity of the graph near its y-intercept

so one would want to say that our graph should be concave up there

which would be A

but if you haven't gotten to that point in your calculus studies, which iirc you haven't, then i don't know how you're expected to arrive at this

[wanton dagger]

Ok

So if I wanted to solve this question what should I learn In calculus I’m just curious?

[plucky temple]

the ans is b

[wanton dagger]

Oh

[plucky temple]

what grade are you

[wanton dagger]

10

[plucky temple]

ooh

[hazy marlin]

I think a is more likely

as x is closer to 0m the cube and square terms are much smaller than the first term

[plucky temple]

I tried substituting it

I'm assuming the way to find it is the info b is positive

[hazy marlin]

notice that for your second equation the coeff for x^2 is negative

you can try to imagine the rise and fall of the function as the negative coef, overpowering the positive coefficient in terms of size

for a more intuitive approach

[plucky temple]

ah yes

I just expanded it

[royal basin]

??

[plucky temple]

@wanton dagger mb the ans was a

[royal basin]

second derivatives and concavity

those are the keywords to look out for

[wanton dagger]

Ok

[wanton dagger]

It’s okay

[wanton dagger]

I don’t even know how to solve these question yet so it’s not that important

Anyways thanks for the help

[plucky temple]

I've never really seen these kind of qns

but I didn't really learn those in g10

[hazy marlin]

you can try to rule out a

I mean

b**

notice that in a, the function has 2 exterma points

[wanton dagger]

Ok

[hazy marlin]

on the poistive side of the x axis

[plucky temple]

maybe substitute values and try finding whetehr it's positive

that's my best bet now since you havent learnt calc

[hazy marlin]

now intuitively that would imply that the negative term of the function would be smaller at one positive interval and bigger at another positive interval

[wanton dagger]

Okay I’m understanding what you mean

[hazy marlin]

but given that your only possible negative coef is c

then once x^3 x^2 have managed to become bigger than c it will constantly stay on the rise

im obviously speaking very informally yea lol

[wanton dagger]

Lol

[plucky temple]

what grade do we learn this?

[royal basin]

dunno

different for everyone

[hazy marlin]

So how is it possible that all of a sudden your function has started decreasing after rising constantly on the positive intervals

[royal basin]

i never learned this type of exercise specifically

[plucky temple]

I'm in g11 and just finished ib am I supposed to know how to do it

wait not ib

finished igvse

igcse

[royal basin]

no fucking clue lmao

i am not in the know about what does and doesn't go into igcse

[plucky temple]

bruh xD I got through igcse without knowing this xD

[royal basin]

does igcse include concavity as a concept

[plucky temple]

nope

but I did learn calc

but I didn't learn limits

[royal basin]

okay then you're not supposed to know how to do it...

[hazy marlin]

Honestly as you advance in calculus and learn about deducing the behavior of a function through it's derivatives it will just come to you

[royal basin]

kind of strange you've learned calc but not concavity

[wanton dagger]

Wait I can tell you

[plucky temple]

the calc I learnt is like finding gradiant and finding a point on a curve with a specific gradiant

[plucky temple]

ah yes ok I haven't done it

my school started with apgp first

[wanton dagger]

So isn’t igcse like the US curriculum or something?

[plucky temple]

uh I'm not really sure

I'm from Singapore international school

so I just got back my igcse and now I'm doin ib

[wanton dagger]

Oh wow

[plucky temple]

extended as in hl math?

extension*

[wanton dagger]

What do you mean by hl maths?

[plucky temple]

higher level maths

wait are you doing igcse and ib?

[wanton dagger]

I don’t know i think I’m doing gcse or something

In Australia’s

Thingy

[plucky temple]

the I infront of gcse is international

[wanton dagger]

Oh ok

[wanton dagger]

Oh yeah by extension 1 we have like different levels, standard, advanced, ext 1 and ext 2

[plucky temple]

ah I see

for me in ib we choose 3 higher level and 3 standard level subjects

[wanton dagger]

So ext 1 and 2 is like the higher maths

[plucky temple]

ah I see

[wanton dagger]

Oh ok

[plucky temple]

so what exam do you take in g12?

[wanton dagger]

HSC it’s called

“Higher school certificate”

It’s like the main exam that tells your ATAR and of course yr 12 mark

[plucky temple]

yea I think it's the cert for g12 students

[wanton dagger]

So you just finished yr 11?

[plucky temple]

nope just started yr11

just finished g10 and got back my igcse

[wanton dagger]

Oh so you were yr 10 ok

I see.

[plucky temple]

yea yea 😂😂

[wanton dagger]

So was yr 10 better than yr 9

I mean as in difficulty

[plucky temple]

hm not sure we spent yr 9 and yr 10 preparing for igcse

[wanton dagger]

Oh ok

I still don’t understand what’s igcse

Actually nvm I got it

[plucky temple]

it's the level of achievement after grade 10

[wanton dagger]

Ok right

So any advice for me for yr 10 I can get from you?

[plucky temple]

hm

ig would be to not fall behind

[wanton dagger]

Ok

[plucky temple]

like practice the topics you are on don't leave it til later

I did that like twice and did badly for 2 terms

and bcuz of that my teacher gave me a very bad class score

[wanton dagger]

Ok

[plucky temple]

so if we got bad class score we can't take that subject in ib

so I went to study for it before igcse

[wanton dagger]

Oh no

[plucky temple]

was tiring

but isok got a*

mentally draining tho

[wanton dagger]

Oh nice

Lol

[plucky temple]

like g11 will be abit tiring also

[wanton dagger]

True

[plucky temple]

I like missed school for 2 weeks

and I have so much stuff to do

[wanton dagger]

Off

That’s annoying

[plucky temple]

yea all my teachers are expecting me to catch up with their subject first

[wanton dagger]

Yh

So any advice on how to perform good in like tests?

[plucky temple]

keep up with the work and revise the stuff u did in class

active recall too (this is the most impt)

[wanton dagger]

What do you mean by active recall like practice

[plucky temple]

go back to the stuff once in a while

[wanton dagger]

Ok

[plucky temple]

like after learning the concept go back and look through the same questions 1 week after you learn them

to make sure you memorise it

[wanton dagger]

Ok

[plucky temple]

sometimes I get lazy and don't do that as a result I forget and have to spend even more time on it

Chinese was the only subject I didn't keep up with

[wanton dagger]

Ok

[plucky temple]

I got a c for Chinese

it was the only thing not a* in my results +_+

[wanton dagger]

Still average

[wanton dagger]

Offfffff

[plucky temple]

my sch did well on average so I kinda got average in my school

[wanton dagger]

How do you get all a ‘s like I perform real well but I need advice

[wanton dagger]

Oh yh that also counts

[plucky temple]

I just really enjoy my subjects

except English literature and chinese

the rest I treat studying them like a hobby

[wanton dagger]

I don’t like English

[plucky temple]

so I'll just go and read and remember it

[royal basin]

-> #discussion?

[wanton dagger]

Ok

[plucky temple]

yea me too xD

let's go discussion

[wanton dagger]

Uhh yes you’re right

[plucky temple]

.close

[royal basin]

.close

[obtuse pebble]

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[obtuse pebble]

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[proper coyote]

I have to form the 1st one into a form “a cos (2x) + b sin (2x) + c”

[raven spire]

uhh

[proper coyote]

What do i do next i have no idea?

Because i cant use 2sinx times cosx rule because there is a root 3

[raven spire]

well, but you can multiply with 2

and write root 3 times 2sin x times cos x

[proper coyote]

So the whole equation times 2 right?

Lemme do the rule now too

Should c be “3p -2” then?

[raven spire]

yep

[proper coyote]

Okay ty

[raven spire]

Good job

[proper coyote]

Thx

Have a nice day i appreciate you helping me a lot!

.close

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[real scarab]

How do you find the area of the blue

[raven spire]

Is that the center? of the circle?

[real scarab]

X=8cm

I think, but it doesnt say

[raven spire]

well, we can show that it is indeed the center so for now, let's just go ahead

given x = 8cm

we have angle subtended by center = 90°

sum of all angles on the center = 360°
so the other angles except for the right angle = (360° - 90°)/2 = 135°

find the area of corresponding segments now that you've found the angle and know the radius

:D

[real scarab]

How do i find the radius?

[raven spire]

x = 8cm?

radius is given

[real scarab]

Oh shit, forgot sorry

My username is kinda a warning lol

.close

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[swift snow]

my homework. Give a geometric interpretation of the following first-order Differential Equations.

[swift snow]

need help interpretating the first one to do the other ones

c:

my answer is this:
is that slope of the curve at y

but im not sure

[stray cave]

like do you represent it with words?

or draw it out

[swift snow]

represent ir with words

[spiral maple]

well what's dy/dx and y in words?

[swift snow]

the change in y with respect to x?

[spiral maple]

not quite

as a function, what does dy/dx tell you about y?

[swift snow]

I really dont know

[spiral maple]

.

say this but more accurately

[swift snow]

oh I thought sometime else

[swift snow]

the slope of the curve with respect to x is equal to the ordinates?

[spiral maple]

the slope of the tangent

The slope of the tangent is equal to the height of the graph

[swift snow]

oh

why is it tangent?

I need to do the graph first?

[spiral maple]

dy/dx is, by definition, the slope of the tangent

[spiral maple]

no..

[swift snow]

thank you c:

this cleared all my questions, My teacher doesn't teach much

he says we should look for it

thank you! ❤️

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[winged kayak]

Can you help me out with this one?

At is the SYMETRIC matrix....

how do I make this one?

[tardy epoch]

A^t is the transpose, it's not symmetric

Matrix A is symmetric if a_{ij} = a_{ji} for all entries

[obtuse pebble]

@winged kayak Has your question been resolved?

[obtuse pebble]

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[stiff palm]

when I graph this I don't see any zero's

.close

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[lost glen]

Mrs ... gives a list of eight questions to the class out. In a query, she puts two of these questions to the student before. The student must answer one of these.

Jonas only has time to prepare for one of the eight questions. Calculate the probability that he is asked a question for which he has prepared himself.

I know that it's calculated like shown in the picture but I have no clue why.

[novel knoll]

Two ways to get the question he have prepared - either 1st question the one or 2nd question the one he prepared. Prob for 1st question to be the one is 1/8 * 7/7=1/8 and similar for 2nd question being the one, so 7/8 * 1/7=1/8. So prob is 1/8+1/8=1/4, which is the same as the answer they gave there

If you prefer a non combinatoric answer

But we need to choose the correct one, so 1 way to choose that and then choose one of the not correct, so 7 ways. In total there are {8 choose 2}=28

So 7/28=1/4

[obtuse pebble]

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[lost glen]

Thanks now

I understand it

[obtuse pebble]

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[shadow oriole]

I'm trying to solve the following Cauchy problem: $u_t+xtu_x=0,u(x,0)=\sin x$. I've found the general solution as $u=f(\frac{t^2}{2}-\ln{|x|}$, but when I try to solve for the boundary I run into problems.

[warm shale]

PhysMan

[shadow oriole]

Also curious if anyone knows of any symbolic math programs that can solve for general solutions of PDEs. It seems that Wolfram Alpha just gives the trivial solution.

[obtuse pebble]

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[obtuse pebble]

@west forge Has your question been resolved?

[obtuse pebble]

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[candid bay]

Hi I am doing this numerical reasoning test. When answering this question I am getting 165,000 I get this answer by multiplying 750k by 22% but I don't think this is correct unless there is some red herring information which I doubt. Can anyone help?

[short spruce]

Cheating on tests and exams, as well as other forms of academic dishonesty, will result in an immediate ban.

[candid bay]

it is a practice one

Just as evidence that I am not cheating on the actual one

Numeracy is not my strong point due to personal reasons growing up which is why I am asking if anyone can double check the answer that I got which is 165,000

[short spruce]

understandable

the 165,000 would be the entire sales for beauty

they've only hit 29%

[candid bay]

so would I do 100-29 = 71 then do 0.71*165000?

[short spruce]

looks good to me 👍

[candid bay]

Thanks! just one last question do I divide the computer issues by the total computers when doing this before multiplying it by 100%?

[short spruce]

👍

[candid bay]

so kind of like 280/5465*100

thank you again!

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[haughty finch]

there are four married couples at a party, how many ways can they sit around a circular table where the couples cannot sit next to each other? i know that the amount of ways they can sit around the table without restrictions is 5040, but how do i put it where the couples cannot sit next to each other when everyone in the party as a spouse? i cannot find a way to figure it out

[obtuse pebble]

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[golden pagoda]

can someone help me with this question

[golden pagoda]

I’m so confused on what I set x and y as and what the equation has to be

<@&286206848099549185>

[obtuse pebble]

@golden pagoda Has your question been resolved?

[golden pagoda]

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[timid silo]

Let n be an integer. Prove that either 4 | n^2, or there exists some integer k such that n^2= 4k+ 1.

Is it valid to state for n = 1,

1^2 = 4k + 1
k = 0

Therefore an integer k exists?

[quaint glen]

Yes

[timid silo]

like is that a complete proof?

[quaint glen]

Its a valid proof that the statement is true for n=1, but not a proof that its true for all integers n(which is what you're asked to prove)

[timid silo]

how would i go about proving it's true for all integers? was able to get 4 | n^2 for n being even but not for n being odd.

[quaint glen]

My league game is starting, I'll try help you after its done if noone else has/you ahvent figured it out by then. i can tell you to consider the cases where n is odd and where n is even in the meantime.

[timid silo]

like i think i got parts of the proof but not sure how to get it all together. like 4 | n^2 holds if n is even, but not odd. and n^2 = 4k + 1 for n being odd but not even.

gotcha, thank you.

i think i solved it. thank you for the help.

[quaint glen]

ok

[obtuse pebble]

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[dense moon]

<@&286206848099549185>

[real pewter]

Do you know midpoint theorem

[dense moon]

yes

the formula right?

(x1+x2)/2, (y1+y2)/2

lava

hola

[real pewter]

The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

and The converse of the midpoint theorem states that ” if a line is drawn through the midpoint of one side of a triangle, and parallel to the other side, it bisects the third side”

[dense moon]

didn't knew these

i was preparing for math olympiad but there was no solution to this problem

[real pewter]

can u see that DE= BF=BC/2=16

[dense moon]

yes

i can understand that

[real pewter]

DM=1/2DE=8

[dense moon]

how dm = 1/2?

[stray cave]

is E the midpoint of AC?

[stray cave]

DM = 1/2DE

which basically means DM is DE by a half

[real pewter]

By converse of midpoint, yes

[stray cave]

i see

i suppose we use the Thales theorem

[dense moon]

oh

got it

[stray cave]

here

this is how i would do this

since AB = BC

and AB is 32

then BC would be 32 also

[real pewter]

you can say midpoint a special case of thales

[stray cave]

use Thales theorem for DE // BC and EF // AB accordingly

[stray cave]

yep

from what lava said here we can say that DE = 1/2BC and EF = 1/2AB

[dense moon]

ok

DM = 4, MO =?

1/2 X DM X MO

mo? = ?

[stray cave]

hm

[dense moon]

mo = 1/3AB?

[stray cave]

yes, we have to find MO

[real pewter]

applying converse of midpoint in DEF, we get MO=1/2EF

[stray cave]

since D and F are midpoints of AB and B respectively, we can derive that BD=BF so DEFB is a square

[dense moon]

so MO = 8?

area of dmo = 16?

[real pewter]

no 32

1/2*8*8

[obtuse pebble]

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[mighty jackal]

how did it become that?

[mighty jackal]

Can someone give me the step by step explanation please

[raven spire]

You know about De Moivre's theorem? or roots of sin x > 1 existing in complex numbers in general?

Or are you just curious about it :o

[mighty jackal]

curious

[raven spire]

https://brilliant.org/wiki/de-moivres-theorem/

A good short read imo

[mighty jackal]

thank you so much

[raven spire]

From there, you can directly write $[e^{ix} - e^{-ix}] = 2i \sqrt{\frac{4}{3}}$ and solve using the normal methods

[warm shale]

Ansh

[mighty jackal]

thanks so much

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[warm zephyr]

<@&286206848099549185>

[timid silo]

What I always do is extract as much data as possible from the given question, and work around with the data.

We know $x, y \in \bN$

[warm shale]

Pencil

[timid silo]

@warm zephyr read the question and say what happens next

[warm zephyr]

If we divide by 4 remains a remainder

If we divide with 7 remains a remainder

[timid silo]

It leaves a remainder*

[warm zephyr]

What is the largest value of A+B

[timid silo]

Can you write it in terms of x and a for this

[timid silo]

And in terms of y and b for this

@warm zephyr

@warm zephyr I suggest using modular arithmetic for this

[upbeat plinth]

i muted this for the remaning duration too

.close

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[raven spire]

Sorry for the confusion Jintaro ^^"

[obtuse pebble]

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[placid hollow]

Hi! The problem Im struggling is in the picture. I've done thins until now and I think its correct:

[placid hollow]

i. the reason it's wrong is that the author assumes that A and B are "served" by the same upper bound - which they might not be

a value of M that works as a bound for A may not work for B

you need to have two different bounds, one for A and one for B, and to then take their maximum for the upper bound of A \cup B

however for ii

I havent been thought how to write proofs yet and this is my first assignment so I'm scared to mess it up

how would I write it correctly if my answer for i is correct?

[mental solstice]

sounds like a troll

anyway

back to this question

[placid hollow]

oh ok

[mental solstice]

you're right, A and B might have different bounds

say, M_1 and M_2

and you also rightly said you should take the maximum for the UB of A\cup B

so, that's $M = \max{M_1, M_2}$

[warm shale]

Camilleone

[mental solstice]

can you see how to continue?

[placid hollow]

Well i mean once I know this I can write why this would make the proof wrong but the problem is idk how to put it into 'math language'

[mental solstice]

ah i see, so you need help rephrasing (i)?

[placid hollow]

yes exactly!

[placid hollow]

this helps thought to start. I hadnt even thought about writing it this way

[mental solstice]

well, you can do something like saying that the definition of Cinderella liking a set only means that there exists such an M such that (copy the definition), but this M may differ for each set

so there is no reason to assume that the same value of M will work for both sets A and B simultaneously

it's wordy, yes, but it's also mathematical

[placid hollow]

ah ok so you dont think its bad if I write it like that? Since we havent seen many properly written proofs I thought that writing it like this would be okay but idk then I thought maybe it needs to look more mathematical hahaha

[mental solstice]

well, when it comes to proofs, there are often a lot of words

in the end it's all about logic, so as long as you express the logic properly, with the right words (i.e. you don't misuse terms), it counts as a proof

[placid hollow]

I see. Thank you so much sir! Logic and proofs are slowly starting to make sense haha

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[upbeat plinth]

w/e u do, pls dont write a sea of quantifiers /s

[obtuse pebble]

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[placid hollow]

Ok so I've got a similar question to my previous one

[placid hollow]

so for i. the proof is wrong because:

the proof asserts "M=1 is a non-example of a strict upper bound for [0,1], therefore Belle cannot like it!"

conveniently sweeping under the rug that Belle may well like it, but with a different strict upper bound

Cinderella likes sets with a nonstrict upper bound and Belle likes sets with a strict upper bound

.

To put it briefly

M=1 is not a witness for Belle liking A, but that alone does not mean Belle doesn't like A

however for ii. I'm struggling to first paraphrase what I'm trying to say

Idk how to put it into 'mathematical language'

oh and also, is my answer for i correct?

[obtuse pebble]

@placid hollow Has your question been resolved?

[placid hollow]

<@&286206848099549185>

[placid hollow]

<@&286206848099549185>

[novel knoll]

what are all those weird symbols in your text?

but yes sounds fine

for ii) you want to show there is an upper bound in the set if and only if there is an upper bound not in the set

[novel knoll]

I'm assuming some information is missing, for example [0,1) doesn't have this property (posting full questions are a good idea)

[royal basin]

all of this is copied from things i said with minimal alterations

[obtuse pebble]

@placid hollow Has your question been resolved?

[placid hollow]

Yeah but I needed help trying to paraphrase it cuz we haven’t learnt how to actually write proofs u know

[obtuse pebble]

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[tranquil topaz]

how many sections are in parallel

pairs

[obtuse pebble]

@tranquil topaz Has your question been resolved?

[obtuse pebble]

@tranquil topaz Has your question been resolved?

[tranquil topaz]

nobody wants to help

[obtuse pebble]

@tranquil topaz Has your question been resolved?

[raven spire]

What you confused about?

What's the issue with the question? I don't see

[obtuse pebble]

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[lean dragon]

hello

[lean dragon]

i need some help

can someone help me find a sine and cos equation for this trig function?

@here

[sage geode]

You can solve for the amplitude, period and initial angle using the graph

By recalling their visual definitions

[obtuse pebble]

@lean dragon Has your question been resolved?

[tranquil topaz]

not 6?

not F E and D C

?

[nocturne minnow]

FYI, this isn't your channel anymore

You need to open a new one

[tranquil topaz]

why tf it closed

i didnt get help lol

[nocturne minnow]

And it's too late to reopen since someone took the channel

[tranquil topaz]

bruh

alright then

that shouldn't work like that

[nocturne minnow]

The bot gave you another chance to keep it open, but you never reacted to it, so it closed, eventually

[obtuse pebble]

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[timid silo]

hey

[timid silo]

List the squares:

0, 1, 4, 9, 16, 25, 36, 49, …

Then take their successive differences:

1, 3, 5, 7, 9, 11, 13, …

Then take their successive differences again:

2, 2, 2, 2, 2, 2, …

So the 2nd successive differences are constant(!) and equal to 2.

OK, now list the cubes, and in a similar way, keep taking successive differences:

0, 1, 8, 27, 64, 125, 216, 343, 512, …
1, 7, 19, 37, 61, 91, 127, 169, …
6, 12, 18, 24, 30, 36, 42, …
6, 6, 6, 6, 6, 6, …

Gee, the 3rd successive differences are all constant(!) and equal to 6.
What happens when you take the 4th successive differences of 4th powers? Are they constant? What do they equal? (They’re all 24.) And the 5th successive differences of 5th powers?

Aren’t derivatives similar to differences? What do you think happens when you take the n-th derivative of xn?

i was reading about successive differences

and i was intrigued about the statement:"Aren’t derivatives similar to differences? What do you think happens when you take the n-th derivative of xn?"

is it really true?

because i was not able to give a concrete answer to it

and if it is true

how is it true

please some one help me

[civic zealot]

What's the first derivative of x^n?

[timid silo]

n times x^n-1

[civic zealot]

what's the second derivative

[timid silo]

ik where you are going, at the end we will get a constant

when i take the nth derivative

of x^n

[civic zealot]

specifically n-factorial or "n!"

[timid silo]

but isnt like n! different from n^ something

[civic zealot]

very different, yes.... I guess not 'very' different, but they are definitely not the same

[timid silo]

and my major question is how can i say derivatives are similar to differences, atleast in this situation

[civic zealot]

ok, so you're taking the difference of $x^n$ over an interval of length 1. So you're finding the average rate of change. The derivative is 'instantaneous rate of change'

[warm shale]

Zybikron

[timid silo]

yes, but if i take a normal polynomial, are the results of the average rate of change gonna be similar to instantaneous rate of change

[civic zealot]

yes, the instantaneous rate of change is the limit of average rate of change

[timid silo]

yes

so in all the cases it wont be same right

[civic zealot]

And the mean value theorem says on a given interval the average rate of change is equal to the derivative for some value in that interval

[timid silo]

ok

what is that some value

[civic zealot]

changes depending on the function

and the interval

[timid silo]

ok

i will try to check it out by finding some average rate of changes and

differentiate some polynomials

and see how similar can they be

[civic zealot]

So, what is happening here (i think)

for x^2, the integer values are where the derivative and average rate of change are the same

[timid silo]

ok

[civic zealot]

when you take the derivative of x^3, that's just x^2 times a constant

[timid silo]

but there are some other methods that i read and vaguely remember that involve something like 3! or something

like to find the terms of the polynomial describing the sum

i mean the co-efficients of the terms

[civic zealot]

yeah, $\sum_{k=1}^n 2k-1 = n^2$

[warm shale]

Zybikron

[timid silo]

sum of n odd numbers in n^2

[civic zealot]

yup

[timid silo]

but for adding up

[civic zealot]

there's a similar one for cubes, but I don't remember

[timid silo]

a series of

odd numbers

they have a common difference

where as for sums of cubes or squares or so one

on

the rate of changes are variable until a certain successive differnce

for n^3 it is (n(n+1)/2)^2

thats what i remember

[civic zealot]

ah, yeah that sounds right

[timid silo]

i want to get like a proper derivation of these kinds of sums, instead of proving them by using proof by induction

[timid silo]

ohh yeah fine then seems like i can take care, thanks for the help!

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[obtuse pebble]

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[timid silo]

What is the difference between a class and a set?

[civic zealot]

A class is a set with some criteria. A set is a set.

they're used pretty synonymously since most of the time you'll probably want some criteria on your set

[brave bramble]

Some objects can't be made into sets. This is made clear by a few paradoxes in set theory.

Classes are our attempt to build collections that don't need to also be sets

One of the most important things about classes is that they need not be sets, but are still collections of stuff.

[civic zealot]

isn't a set, at it's most basic definition, a collection of stuff?

[brave bramble]

Ye

Well, no. A set, at its most basic definition, is any object that obeys the rules in ZFC.

[civic zealot]

Right, it's a collection of stuff that doesn't create a paradox

but your last line basically says "A class doesn't need to be a set, but it's a set"

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

Ohh alright thanks everyone!!

[obtuse pebble]

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[silent adder]

since alpha and beta are roots, can you think of a way to write f(x) in terms of alpha and beta?

Hint: || f(x) = (x-alpha)(x-beta)||

[obtuse pebble]

@vital dew Has your question been resolved?

[tardy epoch]

do you know the quadratic formula?

you should understand why

[raven spire]

Given f(x) has only two real distinct roots $\alpha, , \beta$, do you know a way to write the polynomial f(x)?

[warm shale]

Ansh

[raven spire]

Okay, then... Do you know what does it mean for a polynomial to have a root?

what is it?

Right, put it there

put $f(\alpha) = 0$ and put $f(\beta) = 0$

[warm shale]

Ansh

[raven spire]

Then simplify and solve till you get $\alpha + \beta$ in terms of "a" and $\alpha \beta$ in terms of "b"

[warm shale]

Ansh

[raven spire]

nothing... wrong channel ^^"

try that and let me know

[vital dew]

Should I complete the square ? And find it ?

[raven spire]

Nope... Just plug in alpha and beta and tell me what you get

Yeah!

Now eliminate "b" first because you only want a relation in "a", "alpha" and "beta"

yep

$3\alpha^2 + 2a * \alpha + b = 0 \to (1)$

$3\beta^2 + 2a * \beta + b = 0 \to (2)$

[warm shale]

Ansh

[raven spire]

Subtract equation 1 from equation 2

$3(\beta^2 -\alpha^2) + 2a(\beta - \alpha) =0$

[warm shale]

Ansh

[raven spire]

factorize and you have

$(\beta - \alpha)(3(\beta + \alpha) + 2a) =0$

[warm shale]

Ansh

[raven spire]

So

$3(\beta + \alpha) + 2a =0$

[warm shale]

Ansh

[raven spire]

And

$\beta + \alpha = \frac{-2a}{3}$

[warm shale]

Ansh

[raven spire]

that's it

For $\alpha \beta$, you just eliminate "a" from the two equations, and you'll get "b" in terms of the roots

[warm shale]

Ansh

[vital dew]

@raven spire

[raven spire]

nope

$(\beta - \alpha)(3(\beta + \alpha) + 2a) =0$

[warm shale]

Ansh

[raven spire]

But questions says beta and alpha are distinct, so (beta - alpha) can't be 0

but the product is zero

then, what term in the product must be zero?

exactly

well done

Again

$3\alpha^2 + 2a * \alpha + b = 0 \to (1)$

$3\beta^2 + 2a * \beta + b = 0 \to (2)$

Right?

[warm shale]

Ansh

[raven spire]

Now, subtracting equation 1, from equation 2, eliminated "b", why?

Why did eqn. 2 - eqn. 1 work out though?

to eliminate b?

Partially true, but also because the coefficients of "b" were equal in both equation

coefficients is just a term coined to the "factors" multiplied with the term in concern at the moment

Divide eqn. (1) by alpha and eqn. (2) by beta

[warm shale]

Ansh

[raven spire]

Now can you eliminate "a" from equations 3 and 4?

Lol

You could just do Eqn. 4 - Eqn. 3, eliminate "a" and solve for "b"

We're quite literally done here

[raven spire]

wrong

3(alpha - beta) + b/alpha - b/beta = 0

now solve for "b"

$3(\alpha - \beta) + b/\alpha - b/\beta = 0$

[warm shale]

Ansh

[raven spire]

$\implies 3(\alpha - \beta) - \frac{b(\alpha - \beta)}{\alpha \beta}= 0$

[warm shale]

Ansh

[raven spire]

$\implies (\alpha - \beta)\qty[3 - \frac{b}{\alpha \beta}]= 0$

[warm shale]

Ansh

[raven spire]

$\implies 3 - \frac{b}{\alpha \beta}=0$

[warm shale]

Ansh

[raven spire]

Solve the rest

and go through all the steps till you can convince yourself

:D

[obtuse pebble]

@vital dew Has your question been resolved?

[obtuse pebble]

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[mint whale]

if a plane contains a line, does that mean the line lies in the plane or the line intersects the plane once?

[mint whale]

sorry for pinging @sage geode I was in class so the channel automatically closed. I reworded my question

[strong vale]

if a plane contains a line, does that mean the line lies in the plane

true

[mint whale]

for one of my homework though, the plane "contains" the line but only intersects it once?

[strong vale]

not possible

[mint whale]

that is so weird then if it is correct then

[obtuse pebble]

@mint whale Has your question been resolved?

[raven spire]

that's false. the dot product of direction vector of your "line" and the normal vector is 0, implying that the line lies in your plane

it's possibly just your weird imaginations

also, (3,1,5) lies in the plane -4x+3y+14=0 as well... so it just lies in the plane

not just parallel to it

[obtuse pebble]

@mint whale Has your question been resolved?

[mint whale]

the way I calculated this plane eq. Ax + By + Cz = Ax_0 + By_0 + Cz_0 where I plug x_0, y_0, z_0 as the point from the line equation so I guess that's where my confusion stemmed from

[raven spire]

Aaaahhhh

[mint whale]

if I just plug the line point in the plane equation, it just seems to me it magically becomes "contained"?

[raven spire]

Nope

the "point" is contained in the plane

but here, the set up was such that

you were given a line whose direction vector was normal to the normal vector of the family of plane Ax + By + Cz = d

[raven spire]

hence, just equating those two worked out

[mint whale]

ohhh I see, so it was just by chance then

if I were given this question that it was not by chance, I wouldn't know how to do it lol

[raven spire]

Nope, it was the question maker's intentions

Yeah you probably haven't read the equation of a plane in normal form yet, so that's why probably they didn't bother to complicate the problem

For a line to be contained in a plane:

1. You need at least 1 point common in the line and the plane
2. the dot product of the direction vector of the line and the normal vector to the plane must equal 0

[mint whale]

if you don't mind me asking, normal form is Ax + By + Cz = D? isn't that the same as Ax + By + Cz = Ax_0 + By_0 + Cz_0 and A(x-x_0) + B(y-y_0) + C(z-z_0) = 0?

[raven spire]

Nope, normal form in terms of normal vector is actually n.p = d

[mint whale]

OK! I see!!! Thank you so much for your time 🥰

.close

[obtuse pebble]

Channel closed

Closed by @mint whale

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
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• 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.

[fickle cave]

Trigonometry 65 degrees find the value

[spiral maple]

65=65

[fickle cave]

huh?

lol

[spiral maple]

You asked what's the value of 65 degrees

[fickle cave]

like

cos 65

[spiral maple]

use a calculator

[fickle cave]

can I share my screen and show you what is going on?

[spiral maple]

you can take a screenshot, sure.

[fickle cave]

uhh ok ok

gimme second

hey is there a way I can get help in a voice call

?

[spiral maple]

Sure, won't be from me though

I don't do vcs to help

[flat anvil]

most people won't say yes to that questoin

the rules also say that you shouldn't ask that

[fickle cave]

oh ok

sorry

[flat anvil]

use windows + shift + s to take a screneshot using snipping tool if ur on windows

then u can just ctrl + v and paste the image here

[fickle cave]

alright I'll do that now

[flat anvil]

also do you mean find the exact value of cos(65 degrees)? b/c then you would have to use a half angle formula

or something like that

[fickle cave]

I'll send 1 more

give me second

[flat anvil]

then mosh was right

u just wanna plug that into a calculator and use sig figs

[fickle cave]

I'm just wondering how the decimal system works

[spiral maple]

refer to the table

and it'll tell you

[fickle cave]

yeh

that's what I'm confused about

[flat anvil]

well for 68.4 degrees you know that you wouldw ant 3 sig figs

as the table says

[fickle cave]

so 68.4 degrees I would use the 3rd significant digit?

[flat anvil]

you would use 3 total sig figs

[fickle cave]

what about the sin 44

I got that 1 wrong

[flat anvil]

you would use 2

b/c it says use 2

on the table

[fickle cave]

ohh I thought it depends on the answer when I do the math haha

silly me

but it's really up to the number before doing the math right?

[spiral maple]

44 is to the nearest degree, so you use 2sf

[fickle cave]

so the sin 44 = 0.69465837

which 1 would I use?

[flat anvil]

2 sig figs

and make sure you round correctly

[fickle cave]

I think I understand

[flat anvil]

it should be 0.69

[fickle cave]

alr

lemme try do another question from the homework

ok yes I have another question lemme take a snip

shouldn't the answer be 47.23?

degrees

I did Shift cos on calculator then put in 0.6791

[high lily]

,W arccos(0.6791)*180/pi

[warm shale]

Results provided by WolframAlpha

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Requested by ramonov#0921

[high lily]

yes

[fickle cave]

so with the rounding thing it's 47.23?

because it's over 4 significant digits right?

[high lily]

0.6791 has 4 Sig figs
and according to the table the degree value should be to the nearest hundredth (2 dp)

[fickle cave]

alr 47.23 it is

[leaden ibex]

it might be easier to count the amount of sig figs if you write it as 6.791 * 10^(-1)

[thick socket]

hi

i have a question

[leaden ibex]

#❓how-to-get-help

[fickle cave]

hi petter

lol

Ramonov your so smart!! alr lemme do some more

[thick socket]

what is the double of a number that we have decreased by one half?

😳

[high lily]

#❓how-to-get-help

[fickle cave]

1+1=2

.5+.5=1

so 2+1=3 lo

l

[high lily]

this channel is occupied, reserve your own

[thick socket]

ohh sorry

[leaden ibex]

it's not like there is a shortage of available channels

[fickle cave]

I got an answer of 76.15930451 and it says round to the first decimal place

so would it be 76.2 or 76.1

?

Ramavas?

[hazy marlin]

76.2 would be more appropriate

[fickle cave]

alright thanks

I got it right 😄 it is 76.2

lemme try some more

[hazy marlin]

i rounded it like that because .159 is closes to 2 than 1 btw

[obtuse pebble]

@fickle cave Has your question been resolved?

[fickle cave]

yes but I got more questions

I'm working on them now

on this 1

I seem to got it wrong?

can you explain why I got it wrong

[high lily]

you put an m in the 3rd answer box

snd

[fickle cave]

ok

[high lily]

you didn't actually identify side

[fickle cave]

other than that everything looks right?

oh

[high lily]

a properly

from conventional labelling, side a is opposite which vertex/angle ?

[fickle cave]

I'm not sure

so the answer would be 20, 70, 9.4, 3.42?

[high lily]

no

from conventional labelling, side a is opposite which vertex/angle ?

this is very important to understand

[fickle cave]

oh ok ok

[high lily]

and similarly
side b is opposite which vertex/angle?
side c is opposite which vertex/angle?
these should be quite intuitive

[fickle cave]

so side b is 10

and c is 9.4

and a is 3.42

right?

[high lily]

yes

[fickle cave]

that helps so much thank yu

so the answer is 20/70/3.42/9.4?

[high lily]

yes

[fickle cave]

basically I am stuck on this because when I put it in on my calculator it says math error

I did Shift cos (15.79 divided by 9.61)=

I used soh cah toa and it was COS= A over H

[nocturne minnow]

Yes cos = a/h

[fickle cave]

so I shouldn't use second function cos?

[nocturne minnow]

But in respect to where the angle is

Second function?

[fickle cave]

ohh

the shift button

on calculator

[nocturne minnow]

You mean inverse?

[fickle cave]

yeh

inverse cos

then brackets

then I put in the numbers

math error

[nocturne minnow]

What is the 15.79?

What side of the triangle is that?

[fickle cave]

15.79 because I know the H side is 15.79 cm

so I did right angle triangle

homework

btw

I used soh cah toa

[nocturne minnow]

If the ratio is cos = a/h, and you put 15.79/9.61, you're saying a = 15.79

[fickle cave]

not sure it said math error

[nocturne minnow]

I'm pointing out the mistake

You're saying a = 15.79

But you said it was h

[fickle cave]

oh umm

I'm not sure anymore

lol

I'm pretty sure it's Cos