help-28

[vivid berry]

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[west quiver]

the answer would be ln | 5x - 8 | + c

[hot herald]

you messed up when factoring 5 out if the integral

instead of 5, you wrote 1/5

[west quiver]

oh...

my bad, thanks

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[muted gate]

js

[muted gate]

help..

[shrewd hamlet]

[rose zephyr]

I don't think that's right?

Did math get an update or something

[vestal meadow]

[vestal meadow]

just to be clear, is that your textbook or your own work?

[muted gate]

scheme from my module

given the functions f(x)= 8 + 5x and g(x) = 4/x+2 find (fg)^-1(x)

@vestal meadow

<@&286206848099549185>

[rose zephyr]

Chill

Yeah, I would stop at line 3

And then do the inverse from there

Not sure how they have done that

[muted gate]

i think the scheme is just wrong…

[rose zephyr]

Yeah I think so

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[misty flare]

Hey guys, I need help with this question:

***A square building site is bounded by the following corners: A(3,2), B(-5,28), C(36,27) and D(38,11). All measurements are in m.

1. Calculate the lengths of the 4 sides of the building plot.***

Are there any special formulas I should use?

I have also drawn the square:

[vestal meadow]

Pythagoras' Theorem

[eternal summit]

Isn’t Pythagoras theorem only used in triangles that have one 90 degree corner?

[vestal meadow]

you can always form a right-angled triangle with the hypotenuse being the side you're interested in

for example, for the line AD, I can form a right-angled triangle like this (horrible drawing I know)

[eternal summit]

Oh!!

If someone can confirm it would be great, but imo I would solve this by using vectors. On the right side are the formulas

[misty flare]

I don't understand the last line

[eternal summit]

AB?

[misty flare]

yes, the line you underlined

[eternal summit]

I underlined the answer to AB

Are you asking how I got that answer?

[misty flare]

I would've asked, but I understand now

[eternal summit]

😂 ok

[misty flare]

So I should just do the same with the other lengths, right?

[eternal summit]

Yes

Same formulas

CD = (Dx - Cx ; Dy- Cy) and so on^-^

[misty flare]

ok, thank you very much for the help

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[hard crater]

I don't know if that's revelant, but have you tried to do +i -i on the numerator? It may help to simplify this division?

[thick hedge]

when x=0, it's easy

otherwise maybe multiply and divide by its conjugate

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[royal kiln]

How do I find the integral of this

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[royal kiln]

!helpers

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@royal kiln Has your question been resolved?

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@royal kiln Has your question been resolved?

[rose zephyr]

Done a ton of integrals but never seen one in this form but I did manage to solve it

First thing I did was try to remove the square root with a u-sub, I couldn't do that but ended up removing the denominator in the root

I set u = x - 3 to do the above

[royal kiln]

As far as I am concerned i should start with t=(2x+1)/(x-3)

But then it still seems to be kinda hard

[rose zephyr]

I'm not sure how helpful that u-sub is

[royal kiln]

I did ton of work gere

This were my only ideas

[rose zephyr]

Re checked my work

I actually did u^2 = x - 3

I guess that's sorta the same as t = x - 3 followed by u = sqrt(t)

[royal kiln]

Yeah but sth seemed to be wrong in my sollution

Couln't figurę it out tho

[rose zephyr]

You're missing a 2 before your u

[royal kiln]

And using substitution so many times seemd too complex

[rose zephyr]

2t => 2u^2

[rose zephyr]

It can be daunting but It's fine

[rose zephyr]

After correcting that

[royal kiln]

Here's the answear

I thought i was clouse but I have no idea how have there appeared 2x^2-5x+4

[rose zephyr]

Because you're not done yet

[royal kiln]

Which is (x+3)(2x+1)

[rose zephyr]

Could I suggest my next substitution

[royal kiln]

Right i still have to deal with u^2/sqrt7+u^2)

[royal kiln]

Of course

[rose zephyr]

Wait, how did you get here?

[royal kiln]

It is on the photo i have shared

[rose zephyr]

Actually nvm. In the second photo: you have the integral of sqrt(u^2 + 7)

You made a mistake when you subbed back in

You're missing the 2 before u^2

Look back and you'll see

Assuming all that is fine. The substitution is $u = \sqrt{\frac{7}{2}} tan w$

[royal kiln]

Yeah i see

[glossy valve]

StrangeQuarkAL

[royal kiln]

What is tan w ?

[rose zephyr]

w is a new variable

tan(w)

[royal kiln]

Should I do an cotangens with it?

[rose zephyr]

Hmm?

[royal kiln]

Does tan stands for tangens?

[rose zephyr]

Yes (tangent)

[royal kiln]

Deam never heard of tangent

So i might not now how to use it

[rose zephyr]

Oh

what about sin, cos

[royal kiln]

Yes

I am also familiar with tangens

But in my country the short for for this is tg

So I assume it is not that

[rose zephyr]

Ohh that's right I believe

Do you know about secant, sec

[royal kiln]

So I thought you meant tangens and the co function would he handfull

[royal kiln]

Nat, only co-function

And I hear about sinh

Cosh

But actually never used them

[rose zephyr]

Damn

Kinda makes it harder to explain why I used that substitution

[royal kiln]

The book i use also never mentioned them so there must be diffrent way

[royal kiln]

Definetely

[civic bay]

there might be a much easier way here

long division inside the radical?

wait never mind that still ends up being messy

[rose zephyr]

I popped it into integral calculator to find other ways

[royal kiln]

Yeah I Belive the t iquals to the inside of the root seems to be the most reliable idea

[rose zephyr]

Integral calculator did t = the reciprocal of the root

[rose zephyr]

Ah ok, it also does what you suggested

[royal kiln]

Yeah but then i reach this part

Looks like a lot od dirty work to do

[royal kiln]

It it smoother than this way

[rose zephyr]

Actually, that's great

[rose zephyr]

Nope not at all

[royal kiln]

Why great?

[rose zephyr]

Do you know how to decompose fractions

[royal kiln]

I belive i do

[rose zephyr]

You can express that as $\frac{A}{t^2 - 2} + \frac{Bt^2 + C} {(t^2 - 2)^2}$

[royal kiln]

Okey I will try

[rose zephyr]

Oh wait

One correction

Shit

[royal kiln]

Why did you this way

Yeah

Now I get it

[rose zephyr]

Nah still wrong

[glossy valve]

StrangeQuarkAL

[rose zephyr]

OK it's right now for sure

[royal kiln]

What did you change

[rose zephyr]

Added a square to the Bt

[royal kiln]

Okey so

I did

This

[rose zephyr]

Do Bt^2 instead

[royal kiln]

Okey but how do I know this soulf be this way?

[fallow coral]

,rotate

[royal kiln]

Shoul it be this way?

[rose zephyr]

You want both products to expand out to give terms of similar degrees(if one contains ax^n, the other should contain bx^n)

[rose zephyr]

Yep

[royal kiln]

But therw is no solution

It is like it is the same vector or the combinstion the the same vetros

[rose zephyr]

Huh, that's strange

[fallow coral]

the wolfram solution to this integral is a mess btw

[rose zephyr]

The reference solution is quite messy as well

[fallow coral]

$\sinh^{-1}$ type messy?

[glossy valve]

caspar

[rose zephyr]

Not looking very arsinhiny to me

[rose zephyr]

Bruh

Oh yeah I see it. I actually had two options for my second u-sub

u = sqrt(7/2) tan w and u = sqrt(7/2) sinh w

I just assumed regular trig would be easier

[rose zephyr]

Yeah I don't actually know. My decomposition is possibly not often

This is a perplexing integral

This leads you down 4 more partial fraction decompositions

[royal kiln]

I am about to return tomorow to this one can I DM you then?

[rose zephyr]

You may

[royal kiln]

I will

It is too Kate for this one to me

[rose zephyr]

It's alright. Get some rest

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[zealous plank]

<@&286206848099549185>

cant figure out the inequality

[languid panther]

If you plug three into the equation for be it shouldn’t equal 3

[zealous plank]

i figured out that one

tips on the inequality

and its not taking off the equal signs

[languid panther]

Plug 12 into the equation for B

[zealous plank]

i did that already genius how do u think i got the 80.41 figure

[languid panther]

80.41 isn’t what you’re supposed to get

Which is why I told you to do it again

I’m just trying to help dude

[zealous plank]

plugging B=12 returns 80.412

[languid panther]

Plugging B = 12 returns 3.26

[languid panther]

Your y isn’t 12 your x is 12

Your 6 is B

[zealous plank]

i am an idiot ty

is it 0 =< s =< 3.26?

[languid panther]

I think so

Try it I may be wrong

[zealous plank]

didnt work

[languid panther]

Dammit okay let me try something else

[zealous plank]

cant check anymore

i think it was 0.16 not 0

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[meager sedge]

What's the norm of (1+sqrt5) and why?

[pure spoke]

I'm confused do u mean a complex number?

Like a Norm of a vector space?

[meager sedge]

An intermediate step to determine if Z[sqrt 5]/(1+sqrt5) is a field

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[craggy tapir]

i have a velocity graph like this. if i want to calculate the total amount of distance traveled from the moment of movement start to end of moment, do i take the integral from 0 to 4 of this graph?

[craggy tapir]

additional information: this is a parabola, the axis of symmetry of the graph is parallel to the y axis

oh wait yeah its correct, i was thinking of something else

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[trail salmon]

!help

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[trail salmon]

56 = 2 * 2 * 2 * 7

how do you write this

like for example

112 = 2 * 2 * 2 * 2 * 7 = 4^2 * 7

is the first one written as

2^2 * 14?

[slate zenith]

$$56=2^3(7)$$

[trail salmon]

no

it has to be perfect square

[glossy valve]

Bestower

[trail salmon]

the exponent must be

2

[slate zenith]

ohh your asking

[trail salmon]

cause thats what the question wants

yes

hello

u there bestower

[brittle steeple]

2^2 * 14 ig yeah

the only motivation for doing this I can image is so you can say sqrt(56) is 2sqrt(14)

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[sharp stratus]

would someone help me with this

[sharp stratus]

I am really bad at probability

I feel like I would just add the 0.125 and 0.375 and the answer would be 0.5

[scarlet panther]

yes

[sharp stratus]

Yay

Thank you

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[plush egret]

whatd you try

[civic bay]

in general, multiplication by i corresponds to a 90 degree counterclockwise rotation in the complex plane

[sharp stratus]

I think it is B

Because -2i makes it go up two circle and 90 degree rotation counterclockwise right?

[plush egret]

I would say try this

[civic bay]

notice B is two circles above

[plush egret]

write z = a + ib

now is a > 0 or a < 0

[civic bay]

for this since you don't have specific points, you could honestly just eyeball it

like just call z something like -2 + i

[plush egret]

you dont have to know anything

you just need to write z = a + ib

figure out if a > 0 or a < 0

same with b

see what happens when you do -2iz

[civic bay]

^

[sharp stratus]

a<0

[plush egret]

yea

how about b

[wet patrol]

-i is a rotation clockwise

[sharp stratus]

b>0

[plush egret]

awesome

so a<0

and b>0

[sharp stratus]

ohhhhh

then multiply -2i

[plush egret]

now what is -2i(a+ib)

[sharp stratus]

a>0 and b<0

[plush egret]

i see $-2iz = -2ia -2i^2 b$

[sharp stratus]

so C is answer

[glossy valve]

jan Niku

[plush egret]

dont eyeball it

[sharp stratus]

oh

[plush egret]

simplify this

[sharp stratus]

z=a-ib

[plush egret]

no

z = a+ib

[sharp stratus]

oh yes

mb

[plush egret]

and a<0

and b>0

now we write $-2iz = -2ia-2i^2b$

[glossy valve]

jan Niku

[plush egret]

simplify this

[sharp stratus]

z=a+ib

[wet patrol]

all u have to know is that 2 will double its magnitude and -i will rotate it 90 degrees clockwise, its pretty simple knowing that.

[plush egret]

but what if u dont know that

[wet patrol]

well u can come to that conclusion quite easily

[plush egret]

so let them come to the conclusion

[civic bay]

you can also eyeball this by calling z = -2 + i, then (-2i)z = (-2i)(-2+i) = 4i + 2

[wet patrol]

a rotation by i is 90 degrees anticlockwise so a rotation by i^3 is 270 anticlockwise or rather 90 degrees clockwise

[plush egret]

or u could just feed them the answer

[sharp stratus]

Uhhh

I simplified it

[plush egret]

scraxzt dont let me drag u through the whole thing if you just want the trick lol

[sharp stratus]

I want the methodical process and trick

Both are good

[civic bay]

he's tryna give you the geometric intuition which is goo

d

[plush egret]

whatd you get when you simplified

[civic bay]

since each option is in a different quadrant, you can just check the signs of a and b like he's suggesting

[sharp stratus]

z=a+ib

[plush egret]

yea

and what is -2iz

[plush egret]

you could further do like compare a and b, if you needed to

[sharp stratus]

-2ia-2i^2b

[plush egret]

right

and this can be simplified

what is i^2?

[sharp stratus]

-1

[plush egret]

okay

[plush egret]

so rewrite this

[sharp stratus]

-2ia+2b

[plush egret]

yea

$-2zi = 2(b-ia)$, say, where $a<0$ and $b>0$

[glossy valve]

jan Niku

[sharp stratus]

ok

[plush egret]

what quadrant is it in?

whats the sign on the real and imaginary parts?

[sharp stratus]

so quadrant 4

[plush egret]

👀

what is $Re( b - ia)$

[glossy valve]

jan Niku

[sharp stratus]

I have to go

[plush egret]

okay

[sharp stratus]

But I will come back to this later

[plush egret]

sure

[sharp stratus]

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[twilit leaf]

!status

[full forum]

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

[torn jolt]

1 basically

what equation am I looking for to find the distance travelled

[twilit leaf]

integrate

[torn jolt]

that gives velocity

and then displacement

how to get spee

speed

[unkempt oak]

a tip for rate problems

think of it logically

u know the equation

so input every value into it

maybe i’m being stupid

😭😭🙏

[tame perch]

Feeling eepy so I'm just gonna leave this here

[unkempt oak]

he’s him

[tame perch]

Oh btw for he y = etc. you'd need to graph it and get 3.339 for 0 now gnnn

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[zinc turtle]

i have found values of p0,p1,p2 now how can i prove that they are equal?

[civic bay]

what did you get for p0, p1, and p2

my values?

the problem asks you for generic u and w

which means your expressions for p0, p1, and p2 will be in terms of u and w

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@zinc turtle Has your question been resolved?

[zinc turtle]

p0=1-u , p1=1-w and p2=2(1-w)

[native stratus]

how'd you get this

[zinc turtle]

since p(head)=u so p(no head)=1-u

this is my logic

[native stratus]

right, but its asking about the probability that you get 0 heads in total, so both the first and second coins are tails

[zinc turtle]

yes

[native stratus]

so surely your probability should depend on both u and w

[zinc turtle]

p0=(1-u)(1-w) since they are independent events

can we write like this

[native stratus]

yes

if $X_1,X_2$ is first and second flip respectively, $p_0=P(X_1=T\cap X_2=T)=P(X_1=T)P(X_2=T)$

[zinc turtle]

yes thats what (1-u)(1-w) is

[glossy valve]

Bair

[zinc turtle]

thats a lot 🙏🏻

[native stratus]

ok, what about the other ones?

[zinc turtle]

thanks

p2=u(1-w)

[native stratus]

what if the first coin is tails and the second is heads

[zinc turtle]

p1=(1-w)u+(1-u)w

[native stratus]

yes

ok now p2

[zinc turtle]

p2=u(1-w)

[native stratus]

what

how

[zinc turtle]

will it be p2=2*u

[native stratus]

no, i don't understand where you get these expressions from

what is probability of getting two heads? its the probability that the first is heads and the second is heads

so apply independence

[zinc turtle]

sorry no idea

🥲

[native stratus]

$p_2=P(X_1=H\cap X_2=H)=P(X_1=H)P(X_2=H)$

[glossy valve]

Bair

[native stratus]

what are P(X_1=H) and P(X_2=H)?

[zinc turtle]

P(X1=H)=u

but not sure about P(X2=H)

[native stratus]

what

you are given it

does the problem make sense?

x1 and x2 represent the values of the two coins

[zinc turtle]

sorry uw

p2=uw

[native stratus]

yes

ok now what do you need to find

[zinc turtle]

read the question wrong

my bad

now i just need to make p0=p1 and p2=p1

and solve the two equations i get

[native stratus]

yes

[zinc turtle]

okay i can do the rest

thanks for helping me

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[paper wedge]

anybody know how i should do this?

[sudden spear]

This is a good start

However, you still need to convert $\cos(\sin^{-1}(x))$ and $\sin(\sin^{-1}(x))$ into algebraic expressions

[glossy valve]

otheol

[sudden spear]

This can be done by drawing a triangle

[paper wedge]

how can i do that? They arent giving me specific numbers to work with

[sudden spear]

If you let $\theta=\sin^{-1}x\implies\sin\theta=x$, then you can figure out the expressions

[glossy valve]

otheol

[paper wedge]

yup i undertand that

[sudden spear]

You can simply let the hypotenuse be 1 and the opposite of the angle be x for simplicity

Since that satisfies the constraints of $\sin\theta=x$

[glossy valve]

otheol

[paper wedge]

oh i see

x/1 = x

how about adj?

[sudden spear]

That can be solved for

[paper wedge]

x^2 + ajd^2 = 1^2?

[sudden spear]

Indeed

[paper wedge]

ima give it a try, il lyk how it goes

[sudden spear]

Alright

[paper wedge]

thx

[sudden spear]

No problem

[paper wedge]

so adj would be

squareroot(1-x^2)

[sudden spear]

Indeed

So therefore $\cos(\sin^{-1}x)=\cos\theta=?$

[paper wedge]

squareroot(1-x^2)
/
1

[glossy valve]

otheol

[paper wedge]

= squareroot(1-x^2)

[sudden spear]

Indeed

[paper wedge]

so answer would be

1-x^2-x

i think

[sudden spear]

Dont forget that your sin is squared as well

[paper wedge]

oh ye

1-x^2-x^2

1-2x^2

[sudden spear]

I believe so

[paper wedge]

yup thank you!

have a good day

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[sudden spear]

Good day to you as well

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[foggy glade]

hi can anyone help me understand what is logarithmic regression i have no clue

[sudden spear]

Logarithmic regression is something used to fit a logarithmic curve to a set of data

[civic bay]

you assume your data fits some curve y = aln(x) + b

one way to tell if your data fits a logarithmic model is if you make a scatterplot that plots e^x against y, if your result looks linear then a logarithmic model is your go-to

apologies, that should be plotting x against e^y

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[fossil wedge]

hi guys i've just learnt about the harmonic series and i have a question

[fossil wedge]

so 1/k for k=1, ... inf diverges

but 1/k^p for p > 1 converges

for example

1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +... diverges, but (for p=2) 1 + 1/4 + 1/9 + 1/16 + ... converges

[sudden spear]

Yes

[subtle hatch]

what's your question?

[fossil wedge]

hold up im formulating my question lol

ok so this

1 + 1/4 + 1/9 + 1/16 + ... is a subsequence of 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +...

1 + 1/4 + 1/9 + 1/16 + ... converges, so 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +... should also converge by this theorem

what am i getting wrong?

why not?

[subtle hatch]

subsequence is formed by deleting the terms of the original sequence

[fossil wedge]

1 + 1/4 + 1/9 + 1/16 + ... is contained in 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +...

it's as if we eliminated 1/2, 1/3, 1/5, 1/6, 1/7, 1/8, 1/10...

[subtle hatch]

oh yeaa maybe it's got to do with the relative positions of the term

[fossil wedge]

hmm im not sure i understand

[subtle hatch]

I might be wrong, but we probably can't delete random terms of a sequence, and call it a subsequence, let A, B, C, D, E... be a sequence, then A, B, C , D is a subsequence because we don't disturb their relative positions but A, C, E is probably not a subsequence

also this definition makes sense because a subsequence that converges, means we can easily deduce that a super sequence (I just made that term up), also converges because the relative positions or order isn't affected

<@&286206848099549185>

[fossil wedge]

okay i think i get it now

so to have a subsequence you need to create a function from the original sequence to the subsequence itself in a certain sense?

i.e. you must have a "rule" on how to choose the terms to eliminate from the original sequence

[subtle hatch]

Yes, the rule is again probably that we shouldn't disturb order or relative positions, sorry for the unsureness, I'm a HS grad and trying to learn as much as possible before college lol

[fossil wedge]

dw you know better than me as a hs grad than me as a university student lol

thanks for the help btw

appreciate it

[subtle hatch]

you're wc

[cunning thistle]

Can somebody help me to solve my question

Here it is

[fossil wedge]

sorry to bother you but in the subsequence i created how are we disturbing the order of the positions?

i mean, if a sequence is in the form a1, a2, a3, a4, ..., an

in order not to disturb the order of the positions a subsequence of a1, a2, a3, a4, ..., an must be like a1, a5, a8, a9, ...

[cunning thistle]

<@&286206848099549185>

[cunning thistle]

Help me to solve this question

[fossil wedge]

in the original sequence we have that a1 comes before a5, a5 comes before a8, and so on... and similarly in the subsequence a1 still comes before a5 and a5 comes before a8

so we're still keeping the order of the elements

similarly in 1, 1/2, 1/3, 1/4, 1/5 ... the subsequence 1, 1/4, 1/9, 1/16... keeps the order of the elements

[subtle hatch]

There are various interpretations of order I think, what I mean by order is "this precedes that", eg: for a sequence a1, a2, a3..., so a sequence like a1, a5, ... here this breaks the rule "this precedes that", also more generally I think, a subsequence is something that preserves the rule of progression of the sequence, this not only does satisfies my definition of "this precedes that" but also guarantees the proposition you mentioned to be true. The rule "this precedes that" is probably a corollary of this definition.

whatever the definition, the proposition is def true, no one writes a false proposition, which guarantees that the definition of a subsequence is not what you had thought

hope this helps!

[cunning thistle]

@subtle hatch

Hey

Can you help me

In solving this

[subtle hatch]

!help

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[opaque nova]

try setting two variables for the speed of car and train,

you should get two linear equations

which you can then solve

[fossil wedge]

bruh wtf this is my channel 💀

[opaque nova]

but yes wrong channel

[fossil wedge]

okay so that "a subsequence preserves the rule of progression of the sequence"

this means that if we have the sequence (n) = 1, 2, 3, 4, 5, ...

[subtle hatch]

it's an arithmetic sequence with common difference 1

[fossil wedge]

and we define a sequence (p) that is characterized by all the prime numbers, so (p) = 2, 3, 5, 7, 11, ... then (p) is not a subsequence of (n) ?

the elements must be equally distanced?

[subtle hatch]

I said it preserves the rule of progression

I didn't say it changes it

so

yes it

is not a valid subsequence

according to me lol

[fossil wedge]

can you elaborate please

[subtle hatch]

so like most sequences are not random, right? Most sequences have a rule of progression, this makes their summation for example, to be written in the capital sigma notation. So, a sequence formed by deleting the terms of the sequence without altering it's rule of progression means another sequence with the same properties as of the original sequence. This makes the proposition that you mentioned guaranteed to be true. Because if the rule of progression is the same, the convergence property of the two sequences must be the same too.

<@&286206848099549185>, where are the helpers lol

[fossil wedge]

but well, in my example (p) has still the same properties as (n)

every prime number is still a number

https://youtu.be/KqX0mKcV_3A?si=_dXZGd0xd7FpmAJa&t=432 this guy says that 1, 1/4, 1/9, ... is a subsequence of 1, 1/2, 1/3, 1/4, ...

<@&286206848099549185>

[fossil wedge]

starts here

[subtle hatch]

that's like saying earth follows the same orbit as jupiter because they're both contained of matter, it's not considered a rule of progression, that would make every sequence with numbers subsequences of each other

[fossil wedge]

eh sorry if im dumb

this is so confusing

[subtle hatch]

no lol you're not don't worry

I might have just bullshitted a lot, if this all comes to be wrong lmao

[fossil wedge]

"that would make every sequence with numbers subsequences of each other" 1, 1/4, 1/9, 1/16 is not a subsequence of 1, 2, 3, 4, 5, ... though

[polar valve]

the sequence of all prime numbers is of course a subsequence of all (natural) numbers.

[fossil wedge]

mkay

[fossil wedge]

is 1, 1/4, 1/9, 1/16, ... a subsequence of 1, 1/2, 1/3, 1/4, 1/5, 1/6, ... ?

@polar valve

[polar valve]

of course.

[fossil wedge]

okay so going back to the original question

[fossil wedge]

.

[polar valve]

youre mixing up sequencies and sum of sequencies.

if b_n is a subsequence of a_n, you cant say sum(b_n) is a subsequence of sum(a_n).

[fossil wedge]

but sum(a_n) is defined as lim n->inf (a_n), correct?

[polar valve]

no.

if a_n = 1/n then lim a_n = 0 but sum(a_n) does not exist (or is infinity).

so sum of sequence and lim of a sequence are different things.

[fossil wedge]

sorry, what i meant is: if s_n is a partial sum of a series S, then S = lim n->inf (s_n)

[polar valve]

thats true.

[fossil wedge]

so a partial sum of S is not a subsequence of S, ok

[polar valve]

but dont name the series and the sum of the series with the same letter.

[polar valve]

this question doesnt make any sense. a partial sum is a value. and therefore it cant be a (sub)sequence.

[fossil wedge]

yeah right

[fossil wedge]

okay i think i get it now. thank you very much for the help

@subtle hatch thank you for the patience lol

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[raven needle]

i am confused is my answer wrong ?

[copper dome]

you might've mistook it for the derivative

[raven needle]

but isnt (tan^2(lnx)/x) the same as (sin^(x^2)* 2x ) in that case i know that we make u =x^2 or in the tan case lnx

not in the value the sam but in the integration method

like in sin(x^2 - x + 2) (2x-1)
u = x^2 -x + 2
du = 2x -1 dx
sin(u) 2x-1 (du / 2x-1)

= -cos u + c

[copper dome]

but here the sin isnt squared

thats why its -cos

[raven needle]

so in the case of squared i cant use this method right ?

[copper dome]

yeah there are usually trigonometric formulas that can simplify squared functions to make them easier to integrate

[raven needle]

oh ok thank you

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[rancid wraith]

hi :)
okay so i am a bit confused with these

[strange summit]

Look at logic gates

For exemple

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[copper dome]

In both the Massachusetts Number Game and the New Hampshire Lottery, a 4-digit number is drawn each night. On Tuesday night, September 9, 1981, the number 8 092 was drawn in both lotteries. The newspapers block lettered that the probability of both lotteries drawing the same number is only 1 in 100 million. Is this correct?

[copper dome]

heksbsheizjejekzkzkzkzkzkzlsnsns

i wanted to do this

answer is 0.01%

so 4 out of 10 possible digits

[idle zealot]

its not about digits drawn, they draw whole 4-digit numbers

[copper dome]

oh

[idle zealot]

So you just have to know how many 4 digit numbers there are

and then you can calculate the probability

of both drawing the same 4-digit number

[wet patrol]

think about how u would construct a 4 digit number, u have to pick from 10 numbers for the first digit, then u have to pick from another 10 for the second digit etc...

[copper dome]

why isnt it 1 in 100 million

bc id do that yeah LMAO

but its 0.01%

[wet patrol]

because what u are working out is the probability of them both getting a specific number

what do u think the probability of 2 people picking the same thing in rock paper scissors is?

[copper dome]

🤷‍♀️

[wet patrol]

well think

[copper dome]

why isnt it just ncr(1,1)^2/ncr(3,1)^2

[wet patrol]

that equates to 1/9

i can see what you're thinking

lets say the first guy picked rock, thats a 1/3 chance of him picking rock and 1/3 chance of the 2nd guy picking rock meaning there is a 1/9 chance of them both picking rock

but that doesnt help us work out the probability of them picking the same thing

because what if they both picked scissors? or what if they both picked paper?

[copper dome]

so 10000/100*10^6

but like i get that but

[copper dome]

here you know the first one picked rock and that was 1/3 and so the other one has a 1/3 chance to also get rock for it to be the same therefore itll be 1/9

[wet patrol]

right

[copper dome]

so shouldnt the same logic should apply to my problem when you already know they will pick 8092

because why are you viewing other possibilities for them to get the same number when you know its one

[idle zealot]

But it was about the probability that they both draw the same number not that they both specifically draw 8092

[wet patrol]

this

[copper dome]

hm ok

ty

[idle zealot]

If it was about the probability that they both draw 8092 you would be right with 1 in 100 million

[copper dome]

ok tyy

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[stray rock]

hi guys

[stray rock]

can someone explain this step please?

[torn jolt]

I don't understand that

[stray rock]

so first it says

[low echo]

This integration can be more easily solved by x = tan∅

[oak musk]

english pls

[torn jolt]

ok

[low echo]

So if if speak of the step

[torn jolt]

if if?

[low echo]

u² = (x+√x²+1)²

Or u² = x² + x² +1 + 2x√x²+1

[topaz valley]

[stray rock]

it says:

Let's define a new variable u implicitly with the expression:
...
From this relation, we can explicitly express both u and x to obtain:
...

[low echo]

Or u² = 2(x² + x√x²+1) +1

[topaz valley]

yes keep making a mess by squaring

[low echo]

Or u²-1 = 2ux

Or x = u²-1/2u

[topaz valley]

,, u - x = \s{x^2 + 1} \Implies (u - x)^2 = x^2 + 1

[topaz valley]

one then easily concludes the desired equality

[stray rock]

oh alright so x has to be alone?

[low echo]

I will suggest solving this by considering x = tan∅ though

[stray rock]

yeah but thats not what im studying

[low echo]

Yeah

[stray rock]

that

it says that for integrals of that type we can always by universal substitution to
translate the integral to a integral of a rational function. When choosing the new variable u, we distinguish two
examples:

and then those two above

anyways thank you @low echo , @topaz valley for taking the time

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[distant halo]

hello

[distant halo]

please

does anybody have any advice on how i can master trig triples

ive looked for questions

and i cant find any

[subtle hatch]

umm by trig triples, do you mean Pythagorean triples?

[glacial steeple]

triple angle identities?

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[cunning storm]

its more of an understanding questino really but it uses triangle similarity and optics

[cunning storm]

i have a solution i want checked

am asked to find the area of the shadow casted on the screen.
though wont the area of the shadow be the entire trapezoid formed by area A?
my question is, is the area of the shadow cased on the screen the area of A? (the trapezoid) or only the length of the dark part on the screen?

• here is the original question - suppose a Point light source that is located 4cm away from an obstacle (a side of a square) which its length is 6 cm. from Point light source we also set a screen located 8 cm away from it as the Point light source is located in front of the middle of the obstacle and the same length away from each other ( distance between the light source to the obstacle is equal to the distance between the obstacle to the screen = 4 cm). *

find the area of the shadow that is created on the screen

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@cunning storm Has your question been resolved?

[full sphinx]

I agree with your solution @cunning storm

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[ancient wyvern]

i know trapezium method

and i assume you use the disk method for volume

but what do they mean by that integral?

f(y) dy

this one

isnt that just integrade the curve?

and get the volume kind of

wheres the work

wait

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@ancient wyvern Has your question been resolved?

[brisk obsidian]

You need to make f(y).

[proven mango]

since you're rotating the graph around the y axis, you have to integrate it with respect to y

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@ancient wyvern Has your question been resolved?

[ancient wyvern]

huh?

yeah?

but dont i need like

the radius

smth like this

so the r value is x^2 no?

oh wait

yeah i integrate y

[ancient wyvern]

what exactly is f(y)?

is it not just x^2

[brisk obsidian]

No. f(y) is in terms of y.

[ancient wyvern]

ok

so like

y(y-4)?

for work?

since x^2 sub in 2 you get 4

wait no

its 4-y

[brisk obsidian]

Let's step back for a moment and consider what you are trying to calculate. What is the equation for Work?

[ancient wyvern]

mass* grav*height

oh yeah include grav and mass

the density

well its there in final so its basically there

[brisk obsidian]

But what is the actual equation?

[ancient wyvern]

f * distance

force *d sitance

height is distance

force is gravity*mass

[brisk obsidian]

W = F*d

So you need to find a way to evaluate this in terms of y.

W = F(y)*d(y)

Which you will then approximate with the Trapezoidal Rule.

[ancient wyvern]

oh

[brisk obsidian]

So you need to make an equation for the Force and an equation for the distance.

What is the physics equation for Force?

[ancient wyvern]

uh

mass*accelera

how to find mass with y

[torn jolt]

density * volume

[ancient wyvern]

ye

i wanna get volume with the uh

shell method

[brisk obsidian]

Ok, to find the mass, you need to know the density as well as the volume. This is where the y=x^2 comes into play.

[ancient wyvern]

not shell

disk

ok so at a certain y

i need the radius theres

which is sqrt(y)

and formula is pi(r^2)

so it becomes integral of pi(y) for the volume

then the distance is (4-y)

distance from top

so integral of pi * g * density *(y)(4-y)

i think this is correct

[brisk obsidian]

Be aware that you are moving disks of the paraboloid upwards. How would you calculate the volume of each of those disks?

How would youl calculate the volume of that slice?

[ancient wyvern]

y

y pi

y=x^2

x is the radius of slice

x^2pi= ypi

[brisk obsidian]

But it needs to be in terms of y.

[ancient wyvern]

ye

y pi

[brisk obsidian]

y = x^2

x= sqrt(y)

[ancient wyvern]

yeah

but you need the area

so x^2pi

[brisk obsidian]

Oh yeah. 🙂

[ancient wyvern]

is my formula wrong

oh ok nvm

[brisk obsidian]

No.

You were a step ahead of what I was thinking.

[ancient wyvern]

nice

[brisk obsidian]

So you have an expression for the volume, y*pi dy.

[ancient wyvern]

yeah

[brisk obsidian]

And you found the expression for the distance.

[ancient wyvern]

ye

i gotta make it trapezoid rule

now

1/2( 1 4 2 1

[brisk obsidian]

Put that all together with the density and you will have made your integral.

[ancient wyvern]

this right

[brisk obsidian]

From that integral, you can make your Trapezoidal approximation.

Yes.

pig density 😄

[ancient wyvern]

1/2 ( 1 22 1)

that correct?

trapezoid

ignore the 1 4 2 1 i was thinking of simpsons

[brisk obsidian]

The 1/2 isn't correct. (b-a)/2 iirc.

[ancient wyvern]

i meant interval/2 * (1+2+2+1)

1 was just placeholder

[brisk obsidian]

(b-a)/2*(1*f(x) + ...+ 1*f(x))

So yeah.

[ancient wyvern]

okay

i got the answer

tysm!

is 10 btw if you want to know

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[tidal bridge]

Can you explain this

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[torn jolt]

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[high mural]

Hi I need help

[high mural]

I'm doin the ch square and square roots

Help @full forum

Hello?

[hot wadi]

just post your question

[high mural]

How to do this question 5

[high mural]

Ok

I did but it's not responding

[hot wadi]

the bot doesn't help, people are meant to respond

bot only makes the channel

[hot wadi]

we know double digit numbers begin from 10 and end at 99

[high mural]

Yes

Yes I know

But how

Oh I get it thanks

My brain was not braining lol

[raw scarab]

😂

[high mural]

Question 6)How do I find it

[raw scarab]

100

10*10 lol

[high mural]

Wtf

Am I really that dumb

My brain does not work during maths

[raw scarab]

which grade r u?

[high mural]

8

[raw scarab]

ah aight

its fine ull get a hang of it

[high mural]

What abt question7 how do I solve this

[raw scarab]

first know squares for first 20

will help

[high mural]

Yes I know

[raw scarab]

memorize it

uk?

[high mural]

Done

What should I do then

*after that

[raw scarab]

nah u dont need those for this question

u have to take lcm for this sum if im not wrong

[high mural]

😑

[raw scarab]

for 8 9 10

[raw scarab]

lol no for the previous questions

u cud hav done it urself

[high mural]

Hehe

Let me solve LCM for 8,9,1/

*10

[raw scarab]

yeah then find the prime factors of the lcm

[high mural]

LCM is 360

[raw scarab]

ver good

what are the factors?

prime factors

[high mural]

Wait

6×6×10

[raw scarab]

yes but

[high mural]

Is it correct

[raw scarab]

it has to be perfect squares

so u do 2x2 3x3

[high mural]

Yes

[raw scarab]

2x5

2 and 5 aint perfect squares

so multiple it

u get 10

[high mural]

Wait let me do

[raw scarab]

now u multiply the lcm with 10

[high mural]

I don't understand

What should I do after finding the lcm

[raw scarab]

u write down the factors

u get

2x2x3x3x2x5

now group them

(2x2)

(3x3)

2 and 5 is unpaired prime factors

they are not perfect sqares are they?

[high mural]

No

[raw scarab]

yeah so u multiply them

[high mural]

Okk

Is the answer 60?

[raw scarab]

nahuh

wait

lemme clear it for u

2x2x3x3x2x5

group them

2x2

3x3

2 and 5 is left

what do u do to make these perfect squares?

multiply 2 by 2 to get 2x2

and multiply 5 by 5 to get 5x5

correct?

[high mural]

Yes

[raw scarab]

yeah so

the factors

2x2x3x3x2x5 is the lcm u found

now to make it a perfect square

u multiple another set of 2 and 5

so it becomes 2x2x3x3x2x2x5x5

correct?

[high mural]

Yess

I get it now

[raw scarab]

now all has paired numbers

yeas

now u do the math

ull get the answer

[high mural]

It's still 60

😭

[raw scarab]

-_-

what was the lcm

[high mural]

360

[raw scarab]

yes

now how does multiplying it with 10 make it 60

[raw scarab]

Calculate this again

do it properly

[high mural]

Ok

It's 3600

[raw scarab]

yessir

theres ur answer

[high mural]

Okk

Thank you very much

[raw scarab]

what root of 3600?

[high mural]

Wait

60?

[raw scarab]

yeas

very good

[high mural]

Yay

If I have more doubts can you explain it

[raw scarab]

sure

8th grade math hell yeah

[high mural]

I have sent friend request to you

[high mural]

Yay

[raw scarab]

i joined this server to get calculus help lmao ended up doing 8th grade work 💀