help-13

[dire geode]

x^2 = 4 has two solutions on the real line

[prisma bluff]

Oh okay thanks

.CLOSE

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[austere plume]

How do I answer 3?

[cedar kiln]

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[gusty rain]

Can someone help me understand a few algebra questions? I'm reviewing for a big exam tomorrow and I forgot a lot from Algebra

[gusty rain]

<@&286206848099549185>

[fiery whale]

what are you confused about?

[gusty rain]

Everything, I have no idea what to do

[fiery whale]

😭

alright

do you know what a gradient is

[gusty rain]

Sadly no 💀

[fiery whale]

or slope ig

same thing

[gusty rain]

I remember slope but not what it means

I forgot it

[fiery whale]

it means how steep a line is

you calculate by taking the change in y divided by the change in x between two points on a line

so like in the first problem, you can find the slope by taking two points on the line, finding the height difference and width difference between them, and slope = height divided by width

thats slope

negatives matter by the way

were you not taught this?

[gusty rain]

I learned it in 8th grade and now I'm taking an exam in 11th grade to graduate

On a weeks notice

If I don't pass I won't be able to grad next year

[fiery whale]

ah

gl then

khan academy has good stuff to relearn all this

[topaz epoch]

Remember the formula y=mx+c when finding the intercept

As @fiery whale said you can quickly relearn them online. A simple Google search would be enough

[gusty rain]

Alright, thank you

[topaz epoch]

For the equation of the line with two points you find the slope first, then the intercept using the two given points. All the best tomorrow

It's pretty easy stuff, you can reach out if you need more help

[gusty rain]

Good to know, thanks

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[open vine]

Why does the example say to use the 20 degree angle when calculating the rectangular components but then in the answers for another similar question they want me to use the 60 degree angle instead of the 30 degree one

[cedar kiln]

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@open vine Has your question been resolved?

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[crimson sedge]

i want to see if im undeerstanding something correctly

[crimson sedge]

can i ask about some notation here

is this line division

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[solar geode]

Geometry

[wheat pendant]

Hey

Can someone help me with my algebra, completing the square and I’m not good at this at all so can you tell me it simply please

[solar geode]

O

[autumn current]

mate wrong channel

[wheat pendant]

Oop

[autumn current]

dont bomb other peoples channels

[wheat pendant]

I went to algerbra and gem and it bought me here Srry

[autumn current]

go back to #help-4

[autumn current]

meanwhile, just visualise a barrel

since diameter of barrel = diameter of lid

just get radius of lid

and you have your answer via simple pi * r^2

[solar geode]

I need the formula to get r

[twilit sapphire]

Radius is half the diameter

[solar geode]

So 11.5

[twilit sapphire]

11.5 inches yes

$\pi r^2 = \pi * 11.5^2$

[wraith dagger]

rip_uwu

[solar geode]

So

I do

[twilit sapphire]

Question says take 3.14 as value for pi

[solar geode]

415.265

So 415.27?

[twilit sapphire]

Yes that's the answer I got

[solar geode]

Ok thanks

Also I may need help with the next one so don’t close it yet

Ok so I learned some of this in class

B4 bell rung

8.7 is the diameter

[silver parcel]

it's half a circle, so use the formula for area of circle and divide by 2

[twilit sapphire]

Area of circle is pi r^2. Area of semicircle would be half that

[solar geode]

And you said the radius would be d/2

[twilit sapphire]

Yes

[silver parcel]

indeed, the radius is half the diameter, by definition

[solar geode]

So I get 4.35

[twilit sapphire]

As the radius

[solar geode]

Yea

[twilit sapphire]

So square that and multiply what you get by 3.14 to find area of circle

[solar geode]

So I got 59.42

And I divide that by 2

Because it’s a semi circle

[twilit sapphire]

Wait I'll check

[twilit sapphire]

Yes that's area of circle

[twilit sapphire]

What did you get as your final answer

[solar geode]

29.71

Tysm

I learned a bit from this

[twilit sapphire]

No problem

[solar geode]

🙏🏾

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[exotic verge]

Can someone help me solve this question?

[cedar kiln]

@exotic verge Has your question been resolved?

[dire geode]

!show

[cedar kiln]

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

[silent bobcat]

You have shown way too many occurrences of using the help channels without saying anything about what you think, what you did, your approach, there is nothing about it. It's still the same as the other times, we're still waiting for you to actually do something about it. And it's only going to get worse if someone already helped you beforehand on the same topic (Hello that's me )

[cedar kiln]

@exotic verge Has your question been resolved?

[exotic verge]

Is this allowed and do I just solve for b next by using quadratic formula?

[exotic verge]

^

[exotic verge]

<@&286206848099549185>

[cosmic spindle]

yes

[exotic verge]

?

[cosmic spindle]

use qudratic formula to solve for b

[exotic verge]

Were my steps that i showed correct?

[cosmic spindle]

yea they look about right

[exotic verge]

about...? lol

does that mean there is a mistake somewhere?

[cosmic spindle]

no

[exotic verge]

ok ty

appreciate it!

.close

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[crimson sedge]

@earnest mulch obviously, more than

[cedar kiln]

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.

[crimson sedge]

So what is there to explain?

√121 = 11 < 11.986...

[cedar kiln]

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[clever pendant]

can someon explain how to integrate dx/xsqrt(lnx)

[sturdy shoal]

$\int\frac{\mathrm{d}x}{x\sqrt{\ln(x)}}$?

[earnest socket]

substitution

[wraith dagger]

Stumpman

[clever pendant]

is this setup right

[earnest socket]

,rccw

[clever pendant]

i split it up so when i did u sub for lnx it would cancel out the dx and 1/x

so i was left with 1/sqrt(lnx) du

[earnest socket]

well after you perform the change of variables, everything should be in terms of u

[clever pendant]

oh yea mb i meant 1/sqrt(u)

is that right so far?

[earnest socket]

yes

[clever pendant]

ok so then i do the power rule thing for it and lemme send my work rq

What should I do instead of this?

,rccw

[earnest socket]

you applied power rule incorrectly

you want to integrate u^(-1/2)

[clever pendant]

2sqrt(lnx)?

yup it was

thank you brother @earnest socket

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[spare turtle]

How do I figure this out

[royal loom]

Can you multiply together a 2x2 and a 4x4 matrix?

[cold knoll]

when multiplying an nxm matrix and an axb matrix, 'm' and 'a' must be the same number and the resulting matrix will have the dimensions nxb.

[spare turtle]

Ok thanks

What about (ii)

[cold knoll]

do you know how to do the transpose of a matrix

[spare turtle]

Yes

[cold knoll]

so you essentially apply the same thing to part 2

but B is now its transpose

so B^T would be bxa instead of axb

AB is a 3xb matrix because 3x5 * axb gives you a resulting matrix of dimensions 3xb

[spare turtle]

Ok I get it thanks

B^tC is bxm?

[cold knoll]

correct

[spare turtle]

yayy thanks man

[cold knoll]

np

[spare turtle]

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[frozen dome]

I know its not math but it uses derivatives to solve the question and i need help with that

[frozen dome]

its just finding the derivative of 5t sin(4pie t)

i cant get my answer to 20pie t

and yes i used product rule

i got the 5 sin (4pie t)

ow wait

nvm

i understood my mistake

.close

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[naive plinth]

anyone know>> im so confused

[heavy mulch]

Draw a triangle

[naive plinth]

ok

and then what

[heavy mulch]

find the leg lengths of those triangles

use trig to figure out the angle of a

you know what sin cos and tan do right?

pick one to solve your problem

[naive plinth]

wait but how do i find how long the legs r

[heavy mulch]

by drawing a triangle

[naive plinth]

bc i know i can count but what abt the sideways ones

no ik

[heavy mulch]

draw the triangle first

then look at the graph

[heavy mulch]

the sideways one?

the hypotenuse

[naive plinth]

wait is it like 5 4 3 ??

do u think??

[heavy mulch]

yes

[naive plinth]

Ok ty

[heavy mulch]

Pythagorean theorem or distance formula for this. (but you already figured it out)

[naive plinth]

ok so now that i have the lengths

i do trig??

[heavy mulch]

yes

use sin, cos or tan

to find the angle of a

[naive plinth]

ok so sin cos and tan are trig right

[heavy mulch]

do you not know what they are?

[naive plinth]

mmm kinda

i mean

i did it in class

i just kind of forgot

so im gonna take that as a yes i think

ok this is too hard im just gonna do a different question

thanks anyways

[heavy mulch]

don't

go relearn trig

stop doing problems

https://www.khanacademy.org/math/trigonometry

[naive plinth]

mmmm i might

i gotta do a bunch of problems by an hour soooooo ill go back to this one

ill let u know if I have time to come back to this one and relearn trig

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[modern rune]

without directly evaluating, prove that :

[heavy mulch]

without evaluating?

[modern rune]

i don't know if there is a property for this problem

[heavy mulch]

maybe set a variable

like

d = (a+1+b+c)

[modern rune]

like without a method

[heavy mulch]

then to get detriminate

[cerulean star]

They can't mean don't do any algebra?

[heavy mulch]

its would be 3d-3d

[violet flume]

they mean use some equivalent statement

[cerulean star]

First row, first col:
Det(matrix) = (b+c)(b-c) = b^2 - c^2

[radiant topaz]

Get a row 0

You have to perform row operations and get a zero row

[violet flume]

https://mathworld.wolfram.com/InvertibleMatrixTheorem.html

[modern rune]

isn't a row 1 equal to a det= 0?

[violet flume]

note 19

[radiant topaz]

No

[violet flume]

any negation of any other number is equivalent

[radiant topaz]

@heavy mulch what's the matter bozo

[heavy mulch]

🤨

[radiant topaz]

You can see that R1+R2 = (a+b+c) R3 , so the rows are dependent and hence determinant is 0

[modern rune]

i dont understand the relation between note 19 and the problem

[cerulean star]

@modern rune I can confirm that at least two rows can be transformed to the same thing

Through row operations

[modern rune]

.close

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[lone linden]

can anyone explain where inertia block came from

[cedar kiln]

@lone linden Has your question been resolved?

[dire geode]

#old-network for physics server

[lone linden]

thx

[cedar kiln]

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[simple summit]

Hello, I'm looking for some help with this problem on integration by parts. I understand the first method, but I tried a different method and I don't understand why it doesn't give the same answer. Have I made a mistake somewhere?

[radiant topaz]

Yes there's a mistake

e^(ln x) = x

[simple summit]

Ah, thank you. Let me try it again.

[radiant topaz]

Just change last line

[simple summit]

So the last line looks like this:

[wraith dagger]

Romulus

[simple summit]

I think that's still different than the answer given by method 1:

[wraith dagger]

Romulus

[radiant topaz]

Maybe you missed a sign somewhere

Check that

[simple summit]

Yeah, I'll check it over. Thanks!

[radiant topaz]

I think I've brought you pretty close to god

You're welcome dear

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[umbral ravine]

How to find equation of parabola if there are no X or Y intercepts?

[umbral ravine]

(I have data points which look like a parabola, and I need to find its equation)

[tropic oxide]

show data points...?

[umbral ravine]

(-60, 12.4)

(-80, 25.4)

(-90, 18.1167)

do you want more?

[lapis maple]

we should be able to work with those

12.4 = 3600a -60b +c
25.4 = 6400a -80b +c
18.1167 = 8100a -90b + c

13 = 2800a -20b

go on

[cedar kiln]

@umbral ravine Has your question been resolved?

[umbral ravine]

ok all good ty

.close

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[ivory flare]

Question 4 please help

[cedar kiln]

@ivory flare Has your question been resolved?

[vague rapids]

The diagram is wrong

When the base is pulled away, the top will be placed downwards from its earlier position

@ivory flare

[ivory flare]

Oh

That makes it even harder

[vague rapids]

make a new diagram and send a pic of it

[vague rapids]

We'll use the fact that the hypotenuse (length of ladder) remains same

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[crimson sedge]

t

[crimson sedge]

so i am tryna find the area of this shape i know it’s a trapezium but idk why

and i tried splitting the triangle and the rectangle apart to find separate areas and add them but apparently ai got a different answer bc it used the trapezium formula

this is what i did

<@&286206848099549185>

[cedar kiln]

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

[uneven crater]

,rotate

[nocturne flower]

8.5 - 5.5

[uneven crater]

I am getting the same answer by both ways, maybe you can check your calculations

[nocturne flower]

tes yes

pythagurum yes yes

cm^2

**

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[tall knot]

I really need help answering this question. Algebra.

[robust pagoda]

The first equation has a y, the second equation has a y, therefore because they are both equal you can put them together in one equation

This wll give the point of intersections

For example 2 = 1+1 and 2 = 2 - 0... This can be written as 1+1 = 2-0

So in your case you would do, they will interesect when the equations are equal... you would do 3x-3 = -2x + 7

[tall knot]

Ahh.. ok ok

[robust pagoda]

Solve for x, it will give you the x - cord then you can easily find the y cord by using either equation

[tall knot]

Okay got it thanks

[robust pagoda]

once you are confident you get it do .close to close the help channel

[tall knot]

.close

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[keen fiber]

hello, i would like to ask how would i solve this question (question 7).

[vague rapids]

Circles have same radius

These arcs have same length

[keen fiber]

oh so the ones going in would be the same as going out

[vague rapids]

Yes

[keen fiber]

so it would be 2pi

[vague rapids]

Yes

[keen fiber]

ok i understand now tysm

.close

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[nova snow]

how do I simplify cot^2(x) + 1

[nova snow]

oh

wait

i just figured it out

lol

.close

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[viral tartan]

Hi guys need some help with this

[viral tartan]

Stuck at square 1

[cedar kiln]

@viral tartan Has your question been resolved?

[viral tartan]

<@&286206848099549185>

[lethal jackal]

well there are a few ideas you can try here

one of them involves picking a value for something like e, and then seeing if you can pick the values for f and d that makes both equations true

and then compute e/f

ofc that's a little bit cheap because you're assuming that these equations uniquely define e/f

but the other way probably involves trying to get rid of the d in the second equation and rearranging to get something like e/f = something

[odd snow]

cross multiply

all you need

[viral tartan]

How so?

[odd snow]

d=2f

write 2f instead of d

and then cross multiply

[viral tartan]

If i’m being honest, i’m still confused

[odd snow]

(e-f)/(d-e)

can you write it without using d

it says d=2f

[viral tartan]

So 2f?

(e-f)/(2f-e)

[odd snow]

yeah

[viral tartan]

Right

[odd snow]

okay now, can you cross multiply

(e-f)/2f-e)=1/4

do you know what cross multiplying is i assume you know

[viral tartan]

I do and i’m cross multiplying the (e-f)/(2f-e) part?

[odd snow]

can you tell me what cross multiplying means

[viral tartan]

Multipling one corner to another?

[odd snow]

yeah so do it

[odd snow]

.

here

[viral tartan]

My brain is not working please just show it to me

[odd snow]

multiply 4 with (e-f) and multiply 1 with (2f-e), they are equal

[viral tartan]

So it’s (4e-4f)/(2f-e)

[odd snow]

4e-4f=2f-e

add e to both sides

5e-4f=2f

add 4f to both sides

5e=6f

divide both sides with f

5e/f=6

divide both sides with 5

e/f=6/5

you struggle a bit at cross multiplying and ratios

i strongly recommend solving more problems about this

[viral tartan]

Thank you! I get it now

[crimson sedge]

.Thank you! @nocturne flower

[viral tartan]

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[jolly sable]

A set R is closed in binary operations
If a subset of R is q compliment will be closed? Or only binary satisfied

[crimson sedge]

do you have an example in mind?

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[gritty shore]

Help

[south narwhal]

!status

[cedar kiln]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[gritty shore]

Ahh ok

[hazy scaffold]

!status

[cedar kiln]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[hazy scaffold]

3

!3

IDK ¯_(ツ)_/¯

[jolly sable]

Q compliment

It is subset of R

. reopen

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[autumn coral]

My college is hosting a maths competition and this is one of the questions

I went ahead and solved it using pythagoras and other theorems

and in the end got an area of 2 for the smallest, 4 for the one in the middle and 8 for the large one

and that totals to an area of 14units sq

but that is not one of the options

wait nvm root 196 is 14

i guess that would be the answer

[tribal kite]

2u^2+4u^2+8u^2 yeah it's 14 ur right, pythag works

U can close since u realised alr

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[clever bough]

How can I calculate altitude and vertical velocity using angle and horizontal velocity? (m/s)

[clever bough]

Example: Calculating the vertical velocity of an aircraft using the speed and angle values.

[crude gale]

draw a right-angled triangle with length of hypothenuse being the speed of the aircraft

the vertical velocity is the height of that triangle/the opposite side of the triangle

^do the above make sense? If it does, are you able to proceed to use trigo to solve for the opposite side?

[clever bough]

sorry, I forgot to mention I'm an 8th grader...

I just need the formula

or something like that

[crude gale]

vertical velocity = speed x sin θ

I think its extremely important to understand where the above comes from though, which is precisely from drawing out a triangle

[clever bough]

alright, thanks. is that all I need to know?

[crude gale]

yes and for the horiozntal velocity its speed x cos θ

[clever bough]

thanks.

how do I close the discussion?

oh

.close

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[clever bough]

.reopen

[cedar kiln]

✅

[clever bough]

hey

is the speed in m/s?

[vernal holly]

Yes. Because sin and cos do not have units, multiplying by them does not change the units

[clever bough]

hey I'm an 8th grader and don't know what sin and cos are.

I just need a way to use this formula in my code and stuff

where is angle in this formula?

[crude gale]

angle is θ

[clever bough]

okay.

[vernal holly]

does this make sense?

[clever bough]

wait there are two people sorry

[vernal holly]

now if you do some basic algebra you get this

[clever bough]

sin theta is sin(20°)? theta = 20°

[vernal holly]

This is where the horizontal and vertical components come from

[vernal holly]

correct

theta is 20 degrees, not 20

[clever bough]

thanks for the images

[vernal holly]

thats kinda important

[clever bough]

so i'll use a calculator. am I supposed to do 789m/s x sin(20°) ?

789m/s = horizontal vel
20° = angle

[vernal holly]

Assuming 789 m/s is H and you are solving for the vertical component, yes

[clever bough]

could I add gravity to this calculation or is that another thing?

that's just physics sorry nvm

[vernal holly]

mhm

different formula

[clever bough]

i'll try to understand this and implement a gravity system because i'm writing code not calculating real scenarios

the pyhsics engine probably will do the work for me

[vernal holly]

also note that this only works for right triangles

i forgot to draw the little box

[vernal holly]

cool

[clever bough]

have a nice day and i'm sorry i don't know sin and stuff so yeah

[vernal holly]

no all g

coders are cool

[clever bough]

haha thanks

[vernal holly]

i just thought the triangles would help you visualize it better

have a good one as well

[clever bough]

yeah thanks for that

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[rugged tusk]

Joe sells books. He has them all stacked on one big pile, one on top of the other, mixed up in different ways. He knows that price of each book is p_i. One by one, customers come to him, each of them wants to buy one book, they don't even care which one, because they're in a hurry. Joe has a good eye for people, and for each customer he can tell from a glance
the value of z_i, which indicates how busy the person is. And that's a good thing, because it gives Joe ability to maximize profit.

But Joe doesn't have time to rummage through the whole pile of books, he can offer each customer only one of the top three books.
At the end of the day, when he has sold all the books, Joe wonders if he has offered them as best as he could. Help
help him find out.

Input format
On the first line of the input is the number n (1 ≤ n ≤ 500) - the number of books Joe has and also the number of customers.On the second line is n space-separated numbers p_i (1 ≤ p_i ≤ 1000) - the prices of each book in turn, in the order in which they are stacked on the pile. The book with price p_1 is at the top of the pile, below it is book p_2, and so on.On the third line, there are n space-separated numbers z_i (1 ≤ z_i ≤ 1000) - the desperation of customers in the order in which they came to Joe.

Output format
List one number - the largest possible amount of money Joe could make if he offered customers books optimally. For selling book j to customer i, Joe gets p_j - z_i of the money and each customer he can sell only one of the top three books.

Example input:
4
16 6 2 10
3 8 12 9

Example output:
336
First customer got third book in a row for a total price of 6. To the second before the second book
in the order for the price of 48 (at this point he could also sell the second book, which is now with
third on the kicker at 80, which is not optimal).
The third loser leaves with the first book and the last one is left with the one priced 10, which is already at the top of the pile.

[rugged tusk]

can someone help me how to come up with an optimization function? I have tried to calculate minimum price for last 3 books, but it does not product optimal result

[cedar kiln]

@rugged tusk Has your question been resolved?

[cedar kiln]

@rugged tusk Has your question been resolved?

[cedar kiln]

@rugged tusk Has your question been resolved?

[heavy mulch]

Sir this is not discord.gg/programming

[cedar kiln]

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[thick vessel]

I'm confused what order you condense this logarithm. Also in general what order do you expand a logarithm

[dire geode]

a + b - c = (a+b) - c = a + (b - c)

[thick vessel]

do you go from right to left or from left to right

[dire geode]

it doesn't matter

[thick vessel]

This website said you do

[dire geode]

that's not telling you the order

it's telling you what "expanding" means

and what "condensing or compressing" means

[thick vessel]

oh i see

.ticket close

.close

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[thick vessel]

Im really confused on how you would solve condense this

[royal loom]

Can you send the entire question?

[thick vessel]

thats it

[dire geode]

simplify how? as a single log?

[thick vessel]

yea

[dire geode]

log(e) = 1

[royal loom]

send log properties textit

log(a)-log(b)=log(a/b)

[livid hound]

dies your book use log with unspecified base as
common log of base 10
or the natural log?

[royal loom]

could simplify it further

[thick vessel]

im pretty sure its the common log of base 10

[dire geode]

log(10) = 1

[royal loom]

^

[dire geode]

hurts me to type that

[thick vessel]

the key says log base 5/2

.close

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[livid hound]

you've improperly use the word base there

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[crimson sedge]

is sin θ = 8/17, 0deg < θ < 90deg called a quadrant problem

[crimson sedge]

i just want to know what sin θ = 8/17, 0deg < θ < 90deg is called

if its called anything

[crimson sedge]

probably not

nvm

.close

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[royal loom]

if it is called anything specific, I'm pretty sure it is not important to know what it is called. If I was to call this anything, I'd call it a "trigonometry question"

[crimson sedge]

ok

[cedar kiln]

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[lunar radish]

how do you convert 1/11 to base 3 and other bases

[cedar kiln]

@lunar radish Has your question been resolved?

[lunar radish]

<@&286206848099549185>

[weary vessel]

Let's consider base 3

1/11 is something like 0.0909090909

Since we are in base 3, you know that the only digits in this base are: 0, 1, and 2

Right?

[sacred canopy]

hi

[weary vessel]

Hello Hiro!

[surreal cave]

First, how do we convert base 10 to base 3? Firstly, consider $101_{10}$ to rewrite this as $n_{3}$ we must consider the remainders after it dividing by 3. View the following table:\~\

\begin{tabular}{||c|c||}
\hline
\textbf{Number} & \textbf{Remainder} \
\hline
101 & 2 \
\hline
33 & 0 \
\hline
11 & 2 \
\hline
3 & 0 \
\hline
1 & \verb|NaN|\
\hline
\end{tabular}

To get the number in base 3 we consider the remainders—starting from 1—going up the list, and hence we get $1,0,2,0,2$.\~\

Hence the number is converted into base 3: $101_{10}=10202_{3}$. Now, can you repeat this exercise for $\frac{1}{11}_{10}$?

[wraith dagger]

XxMrFancyu2xX

[sacred canopy]

what is this

[surreal cave]

converted numbers from base 10 into base 3

[sacred canopy]

oh okay

[weary vessel]

Efficient and lovely algorithm!

[sacred canopy]

you love math luna?

[weary vessel]

i do!

[sacred canopy]

math is a good thing to love

[surreal cave]

math is awesome

[surreal cave]

didn't Leibniz make it?

[weary vessel]

No idea

[sacred canopy]

idk ever

igot to go bye

[surreal cave]

Can the algorithm be generalized?\~\

Say, converting $n=m_{\beta}$\~\

Note: I am called $r(x)$ the round function which takes any input and floors because im too lazy to type \verb|\floor| every time ;-;\~\

\begin{tabular}{||c|c||}
\hline
\textbf{Number} & \textbf{Remainder} \
\hline
$n$ & $n\mod{\beta}$ \
\hline
$r\left(\frac{n}{\beta}\right)$ & $r\left(\frac{n}{\beta}\right)\mod{\beta}$ \
\hline
$r\left(\frac{r\left(\frac{n}{\beta}\right)}{\beta}\right)$ & $r\left(\frac{r\left(\frac{n}{\beta}\right)}{\beta}\right)\mod{\beta}$ \
\hline
$\ldots$ & $\ldots$ \
\hline
\end{tabular}\~\

$m=\ldots+r\left(\frac{r\left(\frac{n}{\beta}\right)}{\beta}\right)\mod{\beta}+r\left(\frac{n}{\beta}\right)\mod{\beta}+n\mod{\beta}$?

[wraith dagger]

XxMrFancyu2xX

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[nova snow]

How do I prove this?

[nova snow]

,rcw

[nova snow]

ignore the stuff above

I don’t suppose cancelling cos terms on LHS will get me anywhere

[iron saffron]

What did you do?

Do you have anything written about the problem?

[nova snow]

I’m asking how I should approach it

Should I be cancelling cos terms

[vernal holly]

You see RHS is two separate terms and LHS is not

your first step is to separate the fraction

[nova snow]

Oh

[iron saffron]

You can start with this and the steps you need will be shorter

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[royal orchid]

How this wrong

[royal orchid]

sin(3) / (1 - sin(3)) is the decimal

[rain drift]

so remember that the convergent series sum starts at n = 0

which means for n to start at 1 we simply just need to subtract the 1st term from the sum to get the answer

[royal orchid]

?

Thats what I did but its wrong

I also checked my answer by using calculator and it gives my answer

[earnest socket]

\infty

[rain drift]

lol thanks

[royal orchid]

huh

[rain drift]

oh ffs

[iron saffron]

not that

[royal orchid]

is that the asnwer?

doesnt seem like it

[rain drift]

oh wait sorry the forumla is wrong

one moment

[iron saffron]

1-r

sin(3) / (1-sin(3))

[earnest socket]

pretty sure you calculated it wrong

,calc sin(3) / (1 - sin(3))

[wraith dagger]

Result:

0.16430701539698

[royal orchid]

oh what

[iron saffron]

no i did not calculated wrong

[earnest socket]

your answer corresponds with 3 degrees

answer wants 3 radians

[royal orchid]

Am I using wrong calc thing

oh yea

oops

[earnest socket]

not you

[iron saffron]

oh ok

[royal orchid]

Thank you

.close

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[crimson sedge]

what am i doing wrong

[crimson sedge]

$cosx(tanx+2)(2tanx+1) = 2secx+5sinx$

[wraith dagger]

Ilvvus

[crimson sedge]

Base equation

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[honest shale]

for this one, the markscheme doesnt use cauchy, but is it possible to go about using cauchy?

[dire geode]

Maybe but it's harder to use Cauchy when you only have recursively defined sequences

[honest shale]

i found this thing called a contractive sequence which kind of looked similar to this problem

and which uses cauchy

does the above argument work though?

[dire geode]

You don't have r

Do you?

[honest shale]

i dont, so this is not contractive, im just trying to make a similar argument to show its cauchy

by chaining together inequalities like that

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[cedar kiln]

@honest shale Has your question been resolved?

[cedar kiln]

@honest shale Has your question been resolved?

[tranquil oracle]

you can set r=0.5

you have enough information in your conditions to allow for that

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[fossil flame]

exponential form of : 1+2i

[cedar kiln]

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

[fossil flame]

i couldn't get there

[cosmic spindle]

Find the magnitude first

[cedar kiln]

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[livid hound]

the notation is super dodgy

that second = sign shouldn't be there
instead you should have a new line

what you've written implies that
2^3/3^3 is equal to 2/3
which is clearly false

to get from
$$k^6 = \frac{2^3}{3^3}$$
to
$$k^2 = \frac23$$
take the cube root of each side

[wraith dagger]

ℝamonov

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[half quiver]

Can someone explain to me why the result of u × (v × w) (cross product of those vectors) lies in the plane determined by v and w? I don't understand it well because I know that the result of (v × w) is perpendicular to the plane determined by v and w, but if we multiply it again by u, why does the result lie in the plane determined by v and w?

[dense hornet]

you just said it yourself, (v** x w) gives you a vector that is perpendicular to the plane that spans v and w. Hence u x (v x w) will produce a vector that is both perpendicular to u and (v x w). And we know that any vector that is perpendicular to (v x **w) will lie in the space spanned by these two vectors

here's a simple visulisation, the blue vector is the cross product of v and w

and as we can see, any vectors that is perpendicular to the blue vector must also lie on the plane pi

[cedar kiln]

@half quiver Has your question been resolved?

[half quiver]

I might be really confused but

the purple one here is perpendicular to v x w and not on the plane of v and w right?..

[dense hornet]

yes, but that purple one would be impossible to be the cross product of u x (v x w)

or well, a more accurate way of saying would be it wouldnt make much sense to be representing the cross product in that way

[half quiver]

sorry for asking so many q's imjust still not sure why purple wouldnt be right

[dense hornet]

wait a second, im trying to think of a nice example

[half quiver]

thank you sm

[dense hornet]

ok i cant really think of any simple application of a vector triple product right now, but the main catch is that most of the time, triple product will be used in rotational motion, or probably tension problems, and in those problems, say the rotational motion problem, you can actually describe geometrically the centripetal acceleration using triple product. But anyway, the main thing that im saying is, all of these vectors are drawn starting from a particular point in order for them to make sense of. For example, with the centripetal acceleration case, we use the triple product consisting of the angular velocity and the vector position from a point to the particle in observation. both vectors are spanned from the particle, in order to make sense of the product.

so all in all, back to you original question, the purple vector drawn in your diagram could not be a result of any triple product involving v and w and another vector

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[half quiver]

thank you!

.close

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[analog lichen]

I help with (b) probabilities of 1 white and 1 red

[cedar kiln]

@analog lichen Has your question been resolved?

[cedar kiln]

@analog lichen Has your question been resolved?

[rustic roost]

find the chance of every white + red occuring and then add them together

[analog lichen]

So for white I’ll need to multiply 1/7 x 0/7 x 1/6 x 1/6

And for red it’s

4/7 x 4/6 x 3/6 x 4/6

Is this correct????

[deep oriole]

So what you need to do is the chances that 1 white and 1 red is pulled

There are 2 occasions where this occurs

Picking red then white

And picking white then red

Find those probabilities and addd them together

So 1/7 * 4/6 and 4/7 * 1/6

And add them together

[analog lichen]

What about the denominator since they are two different numbers

[deep oriole]

When you multiply two number multiply the numerators and then the denominators

So 1/7 * 4/6 = 4/42

[analog lichen]

Oh so multiply them not add them ?

[deep oriole]

We’ll multiply to find the chances of one of them happening and then add the two together

Say if we had 2 things that could happen

Picking a red ball and then picking a white ball

Or picking a white ball then picking a red ball

If we want to find the probability of one of each being chosen, we want to consider both

So find the chance of one of them happening by multiplying the probability and the do that to the other one and then add the two results together

[analog lichen]

Both of them equals 4/42

[deep oriole]

Yes so add them together

[analog lichen]

So it’s 8/42

[deep oriole]

Yeah

That’s the probability of getting one of each

[analog lichen]

Oh

Alright thank you so much

Sorry for the trouble

[deep oriole]

np

Happy to help

[analog lichen]

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[cedar kiln]

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[rich fulcrum]

hii, would this statistical exercise be solved like this?

[cedar kiln]

Please don't occupy multiple help channels.

[drifting marlin]

The random variable measures time in thousands of hours

So no

[rich fulcrum]

ohh so 5 instead of 5000?

[drifting marlin]

Yes

[rich fulcrum]

alright thanks 🙂

can I ask another question?

[rich fulcrum]

(also just realized I should be doing 1- all that)

.close

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[quick flume]

How do I solve this?

[quick flume]

I am kinda lost after 2nd step

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[crystal raptor]

<@&268886789983436800>

.close

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[barren parcel]

yo

[barren parcel]

[\sqrt[n]{n} \cdot x + y]

[wraith dagger]

madmike

[barren parcel]

now imagine n -> infty

I know that the root converges at 1 (in a vacuum)

but can I assume the same here when it's multiplied with something else?

[buoyant perch]

yes

any limit on (an * bn) = lim(an) * lim(bn) i believe

[barren parcel]

can I actually go ahead and remove the root because it doesn't affect the limit anyway?

so I have it easier to figure out the other things

[buoyant perch]

should be able to yes

[barren parcel]

ok thanks

.close

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[lucid turtle]

Stuck at the second part - 2(2^k-1)

[cosmic steppe]

Simplify 2^(k-1)

In the form ab^k

[lucid turtle]

So…. 2^k - 2^1

[cosmic steppe]

No

That's not how exponents work

[lucid turtle]

Ummm I don’t remember

[cosmic steppe]

Don't forget.

It's concerning you're forgetting basic exponent rules if you're doing summations

[lucid turtle]

Oh divide

🤦‍♂️

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[old monolith]

Hey all! Calc 3 question

[old monolith]

I'm in the doctors office btw. It could be a while to see them, but if they appear I'll have to vanish

Anyway — I know how to solve for the cross product, and I know how its computed from the determinant of the matrix. I'm not really sure, though, what I'm being asked to show

Could someone explain this to me a bit?

[dire geode]

don't take up a help channel if you're just gonna ghost

[old monolith]

Well, odds of being seen in the next 15 minutes are pretty slim

[cedar kiln]

@old monolith Has your question been resolved?

[old monolith]

Not remotely XD

[cedar kiln]

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[keen hawk]

this is not a problem but I'm trying to learn math by myself and don't know what to learn after learning calc? any recommendations?

[buoyant perch]

analysis and algebra courses?

[crude gale]

i think there might be better channels for this but did you learn calc at a hs-level or at a college level

[keen hawk]

im sorry if I used the wrong channel but thought it would be fast anyway, but i learned it at a college level

[dire geode]

Try #book-recommendations

#calculus will also be better

[keen hawk]

alright thanks!

.close

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[finite badger]

hey mechanics question with angular moment, anyone got a similar question with detailed answer by a chance?

[finite badger]

video would be awesome as well

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[cyan void]

is c, 1.5?

[cyan void]

@dull oxide teach

[simple sable]

do you know the rules for a 30 / 60 / 90 triangle?

[cyan void]

kinda

[simple sable]

so the side that is opposite of the 30 degree angle we can call x

[cyan void]

is opposite of 30, 3

[simple sable]

yeah that’s given

[cyan void]

alr

[simple sable]

so knowing what x is

Do you remember what the opposite of 60 degrees would be in terms of x?

[cyan void]

longe rleg

longer leg

[simple sable]

yeah it is longer

do you know by how much?

[cyan void]

uhh

[dull oxide]

What kind of triangle is ACD?

[cyan void]

60 30 90

[dull oxide]

ACD, not ABD

[cyan void]

60 60 30

[dull oxide]

That does not add up to 180. That is not a triangle

<ADB=<CDB=30, so what is the measure of <ADC?

[cyan void]

60 60 60

[dull oxide]

Yes

Do you know the name of this kind of triangle?

[cyan void]

30 60 90

[dull oxide]

How does that work? You just called it 60 60 60

[cyan void]

oh

[dull oxide]

I'm still talking about triangle ACD.

Still around, @cyan void?

[cedar kiln]

@cyan void Has your question been resolved?

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[dull oxide]

bruh why did I even bother helping

[cedar kiln]

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[heady spindle]

The solid that the triple integral in cylindrical coordinates representated is the green one?

[dire geode]

yea that looks right. the z=0 plane would be the floor

[heady spindle]

yay :D

but I have a question

why 0 <= z <= 4-r^2

[dire geode]

that's the dz integral limits

[heady spindle]

and no 3 <= z <= 4 - r^2?

[dire geode]

wot

where did 3 come from

aren't you trying to calculate this integral?

[heady spindle]

my mistake, is z=2

if the solid that the integrate representate is the green one of the image above, why z goes to 0 and no to 2?

[heady spindle]

I have to draw the solid and change it to cartesian coordinates

[dire geode]

why are you plotting z = 2?

[heady spindle]

the solid is not this?

[dire geode]

0 <= r <= 2

[heady spindle]

yes, then the radious of the cylinder will be 2

oh

wait a minute

this is the solid?

[cedar kiln]

@heady spindle Has your question been resolved?

[heady spindle]

<@&286206848099549185>

[cedar kiln]

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✅

[cerulean sail]

.reopen

Oh someone did it already

[cedar kiln]

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[verbal kettle]

Can you help me guys

[cedar kiln]

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[thick kiln]

Does this like correct? If not, give me a hint! If there was an easier way to do it, mention it!

[runic garnet]

Ur looking for h’ it seems

[thick kiln]

I am

[thick kiln]

I used the quotient rule

[runic garnet]

On the last line how’d u get from the first to the second numerator

[thick kiln]

You you rewrite that

I don't understand

1^2 cos^2(t) = 1 + cos^ t right?

[runic garnet]

U went from cos t + 1 to simply 1 in the numerator

[thick kiln]

oooooooo

[runic garnet]

What

[thick kiln]

I had a cost T + 1 in the num and denom

so I canceled one of them out

[runic garnet]

U have a 1 + cos^2 (t) in denom, Not 1 + cos t

#❓how-to-get-help

[fading narwhal]

you gotta open your own channel...

[thick kiln]

isn't cos^2 just cos * cos ?

[runic garnet]

Yes

[thick kiln]

x^2 / x can be reduced to x / 1

oh wait

why do I feel like that doesn't work

if it was x / x^2

[runic garnet]

U have $\frac {x+1}{x^2 + 1}$

[wraith dagger]

Stephen

[thick kiln]

hmm

yeah true

okay nvm

I don't need to reduce the fraction anymore than it is then

right?

[runic garnet]

Uh

1 sec

Oh wait yea I see where u messed up

U changed $(1+\cos x)^2 \rightarrow 1+\cos^2 x$

[wraith dagger]

Stephen

[runic garnet]

In the denominator

[thick kiln]

yeah

is that wrong

[runic garnet]

Freshman’s dream

[thick kiln]

huh?

[wraith dagger]

Stephen

[thick kiln]

ah

gotcha

.close

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[crimson sedge]

how would u use this triangle as a trick