help-27

[odd peak]

What is the command to check equivalency?

@pulsar dock

[pulsar dock]

== should do it. It would help if you simplified your proposed derivative more

[odd peak]

(16e^x - 4e^2x)/(4+e^x)^3

@pulsar dock that any better?

[odd peak]

,w e^x((2e^(2x))/(4+e^x)^3 - (e^x)/(4+e^x)^2) + (e^x)/(4+e^x)-(2e^2x)/(4+e^x)^2 == (16e^x - 4e^2x)/(4+e^x)^3

[woven radish]

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Requested by tiberiusrox#6304

[odd peak]

Uh no that does not look like it is equivalent

I will try again

[novel totem]

It looks like you did fine. It is just simplifying further. At numerator, factor out 2e^x and you have [2(4+e^x)-4e^x] distribute and simplify this and you will get 2e^x(8-2e^x) distribute here if you want, but the answer do not have to be exactly like WalframAlpha

[devout snow]

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[atomic crystal]

hi! i have a question, it is: what is the probability of getting a king or a spade. so i have P(A or B)=4/52+13/52-1/52? I put 1/52 for the overlap because there is a king and a spade in the 13 spades.

[somber viper]

I think you are correct, since there are diamond king, heart king, clover king, and 13 spade cards
if the problem explicitly mentions it should only be a king or a spade then you have to sub 1/52 from it

[atomic crystal]

right, because you cant count it twice

[somber viper]

yes, it depends on the question though, I am not sure if spade king is allowed

[atomic crystal]

so if it were for multiplication can i do P(A and B)=4/52 * 13/52?

[somber viper]

no, thats a completely different thing

that would be the probability of picking a king and then picking a spade card consecutively

this question is asking about 1 time picking cards

[atomic crystal]

it would be 1/52

[somber viper]

that would be the possibility of picking a specific card from a deck, for example, spade 5

what you need to do for this question is just add possibility of getting spade + possibility of getting king - possibility of getting spade & king

[atomic crystal]

yeah i did P(A or B)= P(4/52)+P(13/52)-P(1/52)

[somber viper]

yep!

[atomic crystal]

yeah then it asks a king AND a spade so that would be P(A and B)=P(4/52) * P(13/52)=52/2704

[somber viper]

no, if it asks picking cards thats both king and a spade, then there is only one possibility: picking the spade king

out of 52 cards

[atomic crystal]

OH

im a bit iffy with cards so forgive me

[somber viper]

nah, probability is sometimes tricky

[atomic crystal]

so are we looking for the probability thats its a spade king?

[somber viper]

yes, if the question asks a king AND a spade

[atomic crystal]

because i interpreted it as a separate spade and a separate king

[somber viper]

what does the question exactly saying?

[atomic crystal]

Find the probability of selecting a king and a spade

[somber viper]

king and a spade

so that means picking ♠️ K

from 52-carded deck

[atomic crystal]

yes

im just confused on if i have to find the probability of both cards or if its asking for the probability of a king spade

[somber viper]

the question is asking a king and a spade
if it was what you understood, the question shouldve been like this: find the probability of selecting a king and then selecting a spade

[atomic crystal]

ohhhh it would be two separate events then

[somber viper]

exactly

[atomic crystal]

got it

[somber viper]

happy to hear that!

[atomic crystal]

yeah ive been reviewing this stuff quite a bit and looked thru my textbook and some resources and it still didnt really make sense

you helped me, thank you for your patience!

[somber viper]

np!

[atomic crystal]

how do i close this

[somber viper]

.close

[atomic crystal]

.close

[devout snow]

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[devout snow]

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[slim fossil]

Heya, currently trying to solve this equation by solving for x but I can't figure out how to actually write the equation so I can use logarithms

[graceful cosmos]

Start with the log of both sides

[slim fossil]

I've tried writing it as 4 x (2x+1)log3=(x)log5 x (x-1)log6

[graceful cosmos]

log(xy) ≠ log(x)log(y)

[slim fossil]

So I'm assigning logs incorrectly here?

Sorry my teacher does this thing where he assigns homework due before the class he teaches us how to do it so I struggle to understand exactly what this question is asking

Did I do log(xy) ≠ log(x)log(y) somewhere?

I thought you took down the exponents and assign the base to log ie 4 x (2x+1)log3 =

or should I be assigning log4 x (2x+1)log3=

[slim fossil]

I'm not sure what this is suppose to mean in regards to what I've posted

<@&286206848099549185>

Instead should I be writing it as log10(4x3^2x+1) for the left side?

[graceful cosmos]

So if you take the log of the left side, you get:
log(4•3^(2x+1))

Your 4 kind of escaped

The right side is similar, everything gets wrapped up by one big log

There's ways to break these logs down! You'll want to see your log rules

[slim fossil]

log(4x3^(2x+1) =log(5^x x 6^(x-1))

So like this?

[graceful cosmos]

Ye. Avoid x for multiplication, useless notation

[slim fossil]

Yeah I prefer the dot as well just helps me since I'm very weak at math

[devout snow]

@slim fossil Has your question been resolved?

[slim fossil]

So I'm at a point where it tells me to sub out 3^x with u; is this normal or is the guide I found weird? haha

I never seen u being used to stand for the exponent of a number

Or is the u arbitrary and it could have been any letter to represent what 3 to the power of _ = x

[devout snow]

@slim fossil Has your question been resolved?

[slim fossil]

.close

[devout snow]

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[visual mural]

Got a question with this function here and changing dy and dx. I do know the first integral will have to be constants and the second integral can be in terms of x or y and so wondered on how able to tell the limits for each one of them.

[supple knot]

got any work to show?

[visual mural]

Yes

need to do it pn phone

i thought if I solve for those three points then I can find the bounds

Have no idea if that is okay or not

[supple knot]

i typically draw "strips" of dx or dy

[visual mural]

Okay like the second queston above is the graphing I done

If can show demostratipn

[supple knot]

like his dotted lines here
https://www.youtube.com/watch?v=LUvynduoUX0

[visual mural]

Okay will look at it

[supple knot]

this looks right

[visual mural]

Do know

But for me feel like showing the three points he’ll show the upper and lower bound

Also self teaching myself for cal 3 and so not doing this for homework

If where to graph focus on the one section then

[supple knot]

it's tricky. sometimes you have to split the integral into multiple sections because the bounds change. e.g. for a trapezoid region

[visual mural]

Okay

looking a video about it

https://www.youtube.com/watch?v=6eac_VRb1x0&ab_channel=TheMathSorcerer

Thanks again for the help

[supple knot]

https://tutorial.math.lamar.edu/Classes/CalcIII/DIGeneralRegion.aspx

^ good examples too

[visual mural]

If you are still here as wondered for the second part do you think did the right way

For me hope to become better

[supple knot]

not sure. you should just follow a university's syllabus and stick to it

then take the exam on your own to test yourself

[visual mural]

Okay

Feel like did better with this one here

integral from 8 to 0 and second integral from 2 cube root y

Did you think did better at this as use the three points as well for this

@supple knot if still able to help me out

Did it correctly a technique is helping me out the three points with help finding the lower and upper bound

<@&286206848099549185>

Still if anybody is there

.close

[devout snow]

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[visual mural]

.reopen

[devout snow]

✅

[visual mural]

.close

[devout snow]

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[white rock]

😭 can someone help…

[thorny obsidian]

@white rock

Do you know the equation of a circle?

[white rock]

The formula? yes I do

[thorny obsidian]

Ok type it in here

[white rock]

Sure! I would use x^2 + y^2 = R^2

[thorny obsidian]

Ok

Good

Now do you know what we can substitute with the known information?

Also I would use

(x - a)^2 + (y - b)^2 = r^2

[white rock]

is that more easier!

?*

[thorny obsidian]

Sure

That’s the method I’m finials with

Espically when wuestions where it passes through

Now with that equation I gave you do you know what you can substitute ?

Would you rather me do the working out so you can understand

?

[white rock]

Yes please

[thorny obsidian]

Ok

So let me snow you

[white rock]

sure thing

[thorny obsidian]

Is this familiar so far?

[white rock]

so you basically just plugged in the points for both

[thorny obsidian]

Yes then solve r2

But you need to know the rules

The center point went from - to positive for example

However the pass point did nkt

I’m assuming you know tbis?

[white rock]

I do know the rules for positives and negatives yes

[thorny obsidian]

Ok good

Now solve for r2

And lmk what you get

[white rock]

Alrighty!

[thorny obsidian]

@white rock what did you get

[white rock]

almost done

[thorny obsidian]

R^2 = (-4)^2 + 8^2

[white rock]

I feel like I did something wrong

[thorny obsidian]

Ok

That’s right

But the 4 goes before square root

[white rock]

omg.. ok great

[thorny obsidian]

But it’s

Plus or minus 4 square root 5

Do you know how to write that?

[white rock]

uh wait plus or minus?

[thorny obsidian]

Wait let me snow you

[white rock]

oki

[thorny obsidian]

Understand?

[white rock]

Ohhh ok Yes yes

[thorny obsidian]

Ok now

We found r^2 because they gave us the passing point

Now we can ignore the passing point and use r instead

To write in general form

[white rock]

right right

[thorny obsidian]

Give it a go

And I’ll let you know if you did it rigjt

[white rock]

ok

idk

[thorny obsidian]

Ok for the first part of the picture

It’s = (+- bla bla bla)^2

[white rock]

right

[thorny obsidian]

And then you will be correct

Change that then show me

Then ylu would be correct

[white rock]

oh.. I just forgot to add those

[thorny obsidian]

Yea

Then that’s questjon 1 done

[white rock]

Thank youu!! apologies for taking too much of your time

[thorny obsidian]

It’s okay

Here to help

Do you know how to do question 2?

[white rock]

Not exactly no

[thorny obsidian]

Ok I’ll help you with that

Got nothing better to do

Do you know how to start ?

[white rock]

No

[thorny obsidian]

No problem

Wait

[white rock]

ofc

[thorny obsidian]

Are you familiar with complete the square?

[white rock]

no 😕

Can I guess the answer for no. 2 is it x+y+3x-2y-6

[thorny obsidian]

That’s the answer and working out

[white rock]

nvm I shouldn’t have guessed help-

[thorny obsidian]

Read through tbat and try understand

[white rock]

Oki!! is it okay if I ask questions on the way ( if i have any )

[thorny obsidian]

Yes

If your wondering where the random values came from

We add a value to be able to complete the square

So we add to both sides

And factorise the x side

I chose 9 for 6x as 3 goes in botj

I hope that’s easy to understand

[white rock]

what r those sorry

[thorny obsidian]

Ok

So

Let me write that seperste

And explain

Understand ?

[white rock]

Ohhh cause 3 can both go into 6 and 9

[thorny obsidian]

Yes

[white rock]

alrightyy

[thorny obsidian]

And since we added a 9 we also add it to the end of the equation

Understand?

[white rock]

yesyes

[thorny obsidian]

Perfect

Same thing goes for the 4y part

[white rock]

the rest I understood by the way.. I was just wondering about the 9

[thorny obsidian]

Yeah no worries

Ok understood questjon 2?

[white rock]

yesyes

[thorny obsidian]

Ok I have to go but someone else will help you with the rest

[white rock]

I can apply that with any similar questions right?

[thorny obsidian]

Yes

[white rock]

Thank you for your helppp :))

[thorny obsidian]

Question 1 and 2 helped with, 3,4,5 to be helped with

[thorny obsidian]

No problem

If nobody responds in 15 mins ping helpers

[white rock]

alrighty

wait i just pinged horribly wrong.. 😭 that was embarassing anyway..

<@&286206848099549185>

[devout snow]

@white rock Has your question been resolved?

[devout snow]

@white rock Has your question been resolved?

[devout snow]

@white rock Has your question been resolved?

[supple knot]

.close

[devout snow]

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[exotic marlin]

I have this math equation I have to answer but have no clue what the answer could be, help would be appreciated! the question is: I order 3 sparkling waters and 3 fantas and pay €13.05. The next round I order 5 sparkling waters and 2 fantas and pay €15. How much does a fanta and a sparkling water cost?

[wild creek]

do you know how to frame this sentence as equations?

[exotic marlin]

Not quite, it's a math question the teacher had given to us

[wild creek]

ok

lets call w the price of a water

and f the price of a fanta

[exotic marlin]

mhm

[wild creek]

3 sparkling waters and 3 fantas and pay €13.05

can you link f and w using this sentence

?

[exotic marlin]

What do you mean, Like make an equation?

[wild creek]

yep

[exotic marlin]

hmm

Bare with me, I suck at math haha

[wild creek]

go ahead

[exotic marlin]

Err, 3f + 3w = €13.05
5w + 2f = €15

The 5 cents in the first problem really confuses me as there is none in the second one

[wild creek]

thats right

you did step 1

now you have 2 linear equations

with 2 unknowns

[exotic marlin]

basically x

[wild creek]

there should be a method to solve these

in your textbook/notes

[exotic marlin]

Hmm

we would use something like

F(x) 3 . x + 3

F(x) 5 . x + 2

I'm pretty sure?

[pallid vector]

Not like that

[exotic marlin]

Oh- That's the only thing I can honestly remember we learn recently

I honestly wouldn't have a clue on what the other possibility might be

<@&286206848099549185> (i'm supposed to be pining you after 15 minutes I suppose?

[wild creek]

https://www.youtube.com/watch?v=YydLDj16fjs look this up

it explains the method to solve such systems of equations

[exotic marlin]

Nono it's alright, might aswell fail the question 🏃‍♂️ ty though!

.close

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[final raptor]

I've this problem and i'm not sure where to start, could anyone help me solve the first problem and how would you do that

[sand thorn]

@final raptor do you know how to add and scale vectors

[final raptor]

no clue, just back into the semester and have forgotten everything

[supple knot]

https://youtu.be/pNMrYACjHXQ

[final raptor]

thank you very much

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@final raptor Has your question been resolved?

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[torpid elbow]

how do i solve this by factoring?

[devout snow]

@torpid elbow Has your question been resolved?

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[final raptor]

Heya i was just wondering if someone could help me with this problem, i understand a bit but not two vectors

[wooden veldt]

do you know what $2x$ will be?

[woven radish]

iCaird

[final raptor]

would it be 2 * by (1, -2, 3, 4)

[wooden veldt]

which is?

[final raptor]

2, -4, 6, 8. Then do i add them together?

[wooden veldt]

no

[final raptor]

what would be the next step?

[wooden veldt]

now we need 3y?

[final raptor]

3*y= 12, -3, 6, 9

[wooden veldt]

now you add 2x and 3y together component by component

[final raptor]

so 16, -2 and 27, -3

[main gull]

How did you get that?

[final raptor]

added all of x's components that are positive and did the same for y

[main gull]

That doesn't make sense

Given a vector x = [x1, x2, x3] and y =[y1, y2, y3] then x + y = [x1 + y1, x2 + y2, x3 + y3]

So in your problem, you would do 2 + 12

[final raptor]

oohhhh

2 + 12, -4 + -3, 6 + 6, 8 + 9 = 14, -7, 12, 17

[main gull]

Yes

[final raptor]

and how would you then show it complete

[sand thorn]

wym

[final raptor]

like as an answer, would i do all the working then show it as 14, -7, 12, 17?

or would i summarise it

[main gull]

How much work does your teacher want?

[final raptor]

not sure, when it comes to vectors is it standard to add the sums together and summarise (like 14 + -7 + 12 + 17) = 36 or leave it at 14, -7, 12, 17

[sand thorn]

That’s odd, because that’s not at all what the answer is

You would write the answer as [14, -7, 12, 17]

[final raptor]

ah okay with the brackets too

[sand thorn]

Are you sure you know what a vector is

[final raptor]

and do the same route with multiplication?

[sand thorn]

No

[final raptor]

struggling to understand

[sand thorn]

I think we should really quickly go over what a vector is and how it works

[final raptor]

sounds good

[sand thorn]

A vector is an object that holds a list of numbers

The list can be however long you like (barring zero or infinitely many elements)

So for example, [1, 2, 3, 4, 5] is a vector, as is [pi] and [2^20, -17]

[final raptor]

oh i get ya

[sand thorn]

So you have to sort of imagine we’re mathematicians inventing this new “vector” object

Right now all it is is a list

But that’s not very interesting or useful

So let’s define some operations on it

I’ll write V = [1, 2, 3] to represent a vector. Here’s our new operation: scaling. When we scale a vector, we’re multiplying every element in the list by the same number. So for example, using V from before, we have 2V = [2, 4, 6]

Similarly, 5V = [5, 10, 15]

[final raptor]

Understood

[sand thorn]

So if k is the “scaling factor”, we can write kV = [k, 2k, 3k]

Capisce?

[final raptor]

Yes!

[sand thorn]

Awesome

Ok

Gimme one sec

Real quick, this is why we call it scaling

[final raptor]

ooohohhh

[sand thorn]

If you draw the vector V = [1,2] in a plane, scaling it by 3 is the same as tripling its size

Hence “scaling”

[final raptor]

so much more easier to understand

[sand thorn]

I’m glad

Ok, now let’s define a way to add vectors together

If I’ve got two vectors, A = [1,2] and B = [3,4], their sum is a new vector whose values are the sums of the corresponding values in A and B

So A + B = [1 + 3, 2 + 4] = [4, 6]

[main gull]

3B1B has some really good linear algebra/vector videos about scaling and stuff like this

[final raptor]

makes sense

thanks ill have a watch after

[sand thorn]

Yep I highly recommend this series it’s great

Ok

And gimme another sec

[final raptor]

with multiplying the two

algood

[sand thorn]

Vector addition also has a nice visual interpretation

When you add the corresponding x-components and y-components, you get this new vector that travels from the tail of A to the tip of B

[final raptor]

oooh i get ya

[sand thorn]

(By “component” I mean the position in the list)

Yeah cool

[final raptor]

so mulitplication of the same problem i had before

[sand thorn]

Well let’s go back to here

What is (a) — imagine you’re doing it for the first time again

[final raptor]

Okay

It would be 2x = [2, -4, 6, 8] and 3y = [12, -3, 6, 9]

And the components together and that would be [14, -7, 12, 17]

[sand thorn]

Yep, ok cool

Ok so you might think we could define such a thing as “vector multiplication,” where we would multiply the corresponding entries — and you’re right, you could invent that — but it turns out it isn’t very useful or interesting. Not only does it not have a good geometric interpretation, but it depends on the choice of coordinate system, which is always a bad sign.

Instead, mathematicians have defined something called a “dot product”, where you take two vectors, multiply their corresponding entries, and then add the resulting entries

Which means unlike scaling and addition, when you dot product two vectors you end up with a single number, not a vector

[final raptor]

Ooooohhh

[sand thorn]

Anyway, here’s an example of dot product

A = [1,2,3], B = [4,5,6]

Then A • B = 1(4) + 2(5) + 3(6) = 32

Got it?

[final raptor]

Ah yes, ur making it beyond easier for me. Thanks a lot

[sand thorn]

Np that’s great

Okay now try (b) on your own — show me your work and lmk what you get

[final raptor]

It would be 2x = [2, -4, 6, 8] and 3y = [12, -3, 6, 9] then would it just be 2(12), -4(-3), 6(6), 8(9).

[sand thorn]

Yep, but remember to add them all together

[final raptor]

So [24, -12, 36, 72] with the previous steps too

[sand thorn]

wdym previous steps

[final raptor]

With the 2(12), -4(-3) etc, just to explain the steps

[sand thorn]

Ah

So what’s the final answer

[final raptor]

Would it be 120?

[sand thorn]

144

I think you did -12 instead of +12

[final raptor]

Oh yeah my bad

[sand thorn]

Ye np

Ok cool

[final raptor]

Wait sorry why wouldn’t it be -12

[sand thorn]

It’s -4(-3), which is +12

[final raptor]

Oh mare by me

[sand thorn]

Ok (c)

Hmm

Oh

I’m pretty sure this involves something new

Wait hold up

Do you know what ||x|| means here

[final raptor]

It’s been a while

[sand thorn]

Ok no problem

Looking back at this

Let’s write A = [1,2]

||A|| denotes the length of the vector, which is typically called the “magnitude”

Do you have any ideas on how to find this length? @final raptor

Don’t worry if you don’t — it’s tricky

[final raptor]

No

[sand thorn]

Ok

Gimme a sec lol

[final raptor]

Algood

[main gull]

Magnitude is Pythagorean theorem based

[sand thorn]

The key is to imagine a right triangle like this, where the hypotenuse is the vector

[final raptor]

Gotchu

[sand thorn]

We already know the legs of the triangle — they’re simply the x and y coordinates of the vector

So we can find the length of the vector (hypotenuse) using the Pythagorean theorem, from geometry

Do you remember the Pythagorean theorem

[final raptor]

a^2 + b^2 = c^2 I think

[sand thorn]

Yep

In this case, we have 1^2 + 2^2 = c^2, where c is the hypotenuse

So we can rewrite it as c = sqrt(1^2 + 2^2), and this is exactly the length of the vector

Are you following so far

[final raptor]

Yep making easy sense of it 👍

[sand thorn]

Awesome

[final raptor]

ohhh sorta getting it

[woven radish]

abs_0

[sand thorn]

Ok cool

Now let me show you this amazing formula

If A and B are vectors, then

[woven radish]

abs_0

[sand thorn]

Here θ is the angle between A and B

So this is amazing because it relates the dot product, the magnitude, and the angle between the vectors

[final raptor]

ohhh

[sand thorn]

Not only is it very useful for computation but the connection between them is fascinating — the fact that an angle has anything to do with multiplying entries together or finding lengths

Anyway

So let’s see if we can use this for (c)

[final raptor]

okay sounds good

[sand thorn]

I will expand x • y to this formula

[woven radish]

abs_0

[sand thorn]

Hmm

Ah let me square both sides

I’m allowed to do that because both sides are positive

Ok here

[woven radish]

abs_0

[sand thorn]

Now we can divide both sides by ||x|| and ||y||

So we have $$\cos\theta \leq ||x||,||y||$$

[woven radish]

abs_0

[sand thorn]

Hm

[final raptor]

im sorta getting it

[sand thorn]

Ye

I don’t actually know how to do it

I’m solving it on the spot

Ok hm

[wooden veldt]

You don't need to involve cos here

you just need to work out $x \cdot y$ and square root it

[woven radish]

iCaird

[wooden veldt]

for this particular case

and compare it the RHS

[final raptor]

RHS?

[wooden veldt]

right hand side

[final raptor]

gotchu

[sand thorn]

Oh wait

Yeah we’re working with actual vectors here

@final raptor so what is x • y

[wooden veldt]

(yeah don't try proving it in general lol, do it for those vectors)

[sand thorn]

Is that hard

Seems dependent on the vectors

[wooden veldt]

its not that hard but i think its better for regnigquack to just prove it for these vectors

[final raptor]

yep yep

[sand thorn]

Ah

[sand thorn]

?

[final raptor]

[1, -2, 3, 4] * [4, -1, 2, 3]

[sand thorn]

Yeah what is that

[final raptor]

would that be [1(4), -2(-1), 3(2), 4(3)]. Which would equal [4, 2, 6, 12]

[sand thorn]

But remember you’re not just multiplying

You must also add them up at the end

[final raptor]

ah yes

24

[sand thorn]

Yep nice

Ok now

[final raptor]

then square root of 24 which is 4.8

[sand thorn]

Right

Now find ||x|| ||y||

[final raptor]

im not sure how to do that

[sand thorn]

How do you find just ||x||

[final raptor]

not to sure how to ||x||

do the |x|

[woven radish]

abs_0

[sand thorn]

Do you see how to do it

[final raptor]

yes!

[sand thorn]

Nice

Now find ||y||, and then ||x|| ||y||

[final raptor]

calculating it now

y= sqrt 18

sqrt of 30 is 5.47, then sqrt of 18 is 4.24. Do i multiply them together?

[sand thorn]

I got sqrt(30) for ||y||

Wait

16 + 1 + 4 + 9 = 30

Yeah I think it’s ||y|| = sqrt(30)

[final raptor]

idk how i got 18 but yep makes sense

[sand thorn]

Ok lit

So what’s ||x|| ||y||

[final raptor]

not sure do i add them together

[sand thorn]

When you write two things next to each other, it’s multiply

So ||x|| ||y|| = ||x|| * ||y||

And what does that come out to

[final raptor]

so sqrt 900

[sand thorn]

Yep, which is

[final raptor]

30

[sand thorn]

Yes

[final raptor]

boom

[sand thorn]

lol

So now the inequality is

[final raptor]

4.89 < 30

[sand thorn]

Yep

Which is true

And you’re done

[final raptor]

Ah easy as

[sand thorn]

pie

Yes

Try (d) on your own, let me know what you get

and show me your work

[final raptor]

sqrt (1)^2 + (-2)^2 + (3)^2 + (4)^2 + (4)^2 + (-1)^2 + (2)^2 + (3)^2 ?

[sand thorn]

Nah

Ok do the left side first

What is x+y

Then find the magnitude of that

[final raptor]

5, -3, 5, 6

[sand thorn]

7, not 6

But yeah

[5, -3, 5, 7]

[final raptor]

Oop yeah

[sand thorn]

So what’s the magnitude of that

[final raptor]

Sqrt (5)^2 + (-3)^2 + (5)^2 + (7)^2

[sand thorn]

Yep, which is

[final raptor]

90

[sand thorn]

25+9+25+49 = 108

sqrt108 = 10.392

I think

Oh you did 25 - 9 + 25 + 49, didn’t you

[final raptor]

...

[sand thorn]

Lol

Just always keep in mind that two negatives make a positive (when multiplying)

[final raptor]

always forget that

[sand thorn]

ah

Ok cool so we have 10.392 <= |x| + |y|

Now figure out the RHS

[final raptor]

wouldnt x and y just be 30 again?

[sand thorn]

sqrt(30), yeah

[final raptor]

then it would be sqrt 60

[sand thorn]

No, you can’t do that

[final raptor]

which is 7.7

cant do that

[woven radish]

abs_0

[final raptor]

gotchu

[sand thorn]

Just find sqrt(30) and double it

[final raptor]

10.94

[sand thorn]

Nice

And 10.392 < 10.94

So we’re done

[final raptor]

wowwwwww

[sand thorn]

Yup

[final raptor]

thank you so much

[sand thorn]

Np dude

[final raptor]

cheers have a good one

[sand thorn]

you too

remember to .close

[devout snow]

@final raptor Has your question been resolved?

[wooden veldt]

.close

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[indigo abyss]

how do i solve this?

[worn cloud]

What have you tried?

[devout snow]

@indigo abyss Has your question been resolved?

[devout snow]

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[leaden aurora]

Help me

[muted reef]

with what? you need to provide the question you are looking for help in

[devout snow]

@leaden aurora Has your question been resolved?

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[lucid gale]

Does anyone know how to do the Polynomial long divison of Power[z,3]+6z-20?

[lucid gale]

.close

[devout snow]

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[lucid gale]

Does anyone know how to do the Polynomial long divison of Power[z,3]+6z-20?

.reopen

[devout snow]

✅

[lucid gale]

Does anyone know how to do the Polynomial long divison of Power[z,3]+6z-20?

[atomic lintel]

By

What

(z³+6z+20)/(what?)

[lucid gale]

yeah its from Ars Magna written by Cardano

I am trying to find the complex roots

it goes through this but I don't know how to do polynomial long divison with no divison

<@&286206848099549185>

[devout snow]

@lucid gale Has your question been resolved?

[devout snow]

@lucid gale Has your question been resolved?

[mental bough]

You're basically dividing y^3 + 6y - 20 by y - 2, which gives you y^2 + 2y + 10.

[lucid gale]

oh right thanks for that

[mental bough]

No problem.

[lucid gale]

do you by chance know Cardona's Method

[mental bough]

I'm afraid not.

[lucid gale]

damn all good

[lucid gale]

.close

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[craggy quiver]

my question is, whats the difference between product moment correlation coefficient and population correlation coefficient

could i have wrote 'where p is the product moment population coefficient' there?

[weak tundra]

A hypothesis is a statement about a population. You must always state it in terms of population parameters

[craggy quiver]

i dont understand?

what exactly is the population correlation coefficient?

[weak tundra]

Correlation coefficient for the population

[craggy quiver]

is it different from product moment correlation coefficient?

is it just a general term which includes product moment correlation coefficient?

[weak tundra]

Population correlation coefficient means the correlation coefficient of the population.

Correlation coefficient here means product moment correlation coefficient

[craggy quiver]

oh

so basically its the same thing as

population product moment correlation coefficient

they just missed out product moment?

ohhh i get it now

thanks

.close

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[devout snow]

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[wooden veldt]

<@&268886789983436800>

[wicked rover]

ty

[devout snow]

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[pallid rain]

i dont know what i did wrong

[pseudo basin]

missing parentheses

around 2n in the denom and 4x in the num

though tbh you would've done better to separate the (4x)^(2n) into 4^(2n) * x^(2n) so that the other x factor could be incorporated

[devout snow]

@pallid rain Has your question been resolved?

[hard sequoia]

f(x) = Cos(4x)

= Cosx = 1 - x²/2! + x⁴/4! + x⁶/6!..... + (-1)^n × x^2n/(2n)!...

= Cos(4x) = 1 - (4x)²/2! + (4x)⁴/4! - (4x)⁶/6! +......+ (-1)^n × (4x)^2n/(2n)!

Now simplify this whole shii together

1 - 16x²/2! +256x⁴/4! - 4096x⁶/6!......

= (∞)Σ n->0 (-1)^n × (4x)^2n/(2n)!

Something like this

[hard sequoia]

Idk why you got that extra "x" so... maybe ig... that's where it went wrong

[devout snow]

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[steel comet]

When I put this in a calculator, it comes 4. Even tho my calculations are correct

Why?

[twin flame]

What are you putting into a calculator?

[twin flame]

I see

That's because your calculator is finding the exact integral

[steel comet]

According to me, As integeral is a approximation, so its not showing the EXACT ANSWER

[magic thicket]

The right riemann sum of an increasing function is an overestimate

[steel comet]

Oml my prediction was correct. Thanks

That means the calculator is converting it to indefinute integeral, simplifying it and finding the antiderivative right?

[magic thicket]

Just approximates well enough to basically not look like an approximation

[twin flame]

Or possibly using the trapezium rule or some better approximation

[steel comet]

Idk that. Maybe I will learn that later in the book

[magic thicket]

Most likely much better. Stuff you don't really learn about like Rhomberg's method and the like

[twin flame]

Trapezium rule is a better approximation than just a riemann sum which you may learn about in school

Yes what @magic thicket says

[magic thicket]

Actually the trapezium rule, IIRC, is just the average of the left and right Riemann sums

[twin flame]

That sounds right, but I mean that it is likely that they may learn it after what they are doing just now

[magic thicket]

Yes ofc

[steel comet]

Whats the antideruvatuve of x^4/4?

Real quick.

That should be the answer ig.

[twin flame]

To the integral question you posted?

[steel comet]

Yep

Is this correct?

[twin flame]

What you have written is the antiderivative of x^3

Antiderivative of x^3 is x^4/4

+c

[steel comet]

Oh yeahh

That + c i hate it

[twin flame]

Antiderivative (integral) of x^4/4 is not needed to integrate x^3, you have already found that integral

[twin flame]

It becomes very important when you start solving differential equations

It will be included in your solutions in very non trivial ways

[steel comet]

I put the problem in ms math calculator

But i still d9nt understand the last step

[twin flame]

Different values of the integration constant will havs very significant changes to the solution often not just a vertical translation

What is the last step?

[steel comet]

I see...

[steel comet]

The one in which we converted x^4/4 to some thing

[twin flame]

So that is doing the definite integral of x^3 from 0 to 2

So it is substituting the bounds of integration into the antiderivative after it has found it to get the area

[steel comet]

Ohhhh soooo we plug in 2 and 0 as X and solve it

Oml that makes it so much easier than calculating the reimmans sum specially for large untervals

Intervals*

Thankyou so much.

[twin flame]

No problem at all.

[steel comet]

.close

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[steel comet]

Explination of example 1 pls

How did, '''
1/3[x+x^3/3]2,-1 turn into 2?'''

[supple knot]

,rotate

[supple knot]

Do you know what that vertical line with 2 and -1 means?

[steel comet]

Yes.

It means we plug in 2, -1 both in the Given Equation.

[supple knot]

Show your algebra

[steel comet]

Oml

My calculation is so bad

I messes up basic arithmetic🗿💀

Thanks tho.

[supple knot]

[steel comet]

.close

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[full prawn]

Ella wants to buy ice cream. In the disk, there are 4 types of ice creams: Chocolate, blueberry, strawberry, and kiwi. How many combinations are possible if they would like to have 2 scoops?

Remember that blueberry and strawberry is the same as strawberry and blueberry. The combination does not matter

[full prawn]

The note below the question made me a bit confused, since I don't really know how to prevent combinations popping multiple times

usually, I would've simply solved the problem by doing 4*4

giving me 16, but in this case, it would count strawberry and blueberry as an individual combination and blueberry and strawberry as an individual, something that the question doesn't allow

Now, of course, you could list up all possible combinations and remove "duplicates", but this won't really work if the question gets more advanced

Is there any way of solving the problem without including repeated combinations?

[torpid wave]

u need to think how many ways a given combination, like strawberry and blueberry can appear

[polar bolt]

look up binomial coefficient (also called n choose k)

[devout snow]

@full prawn Has your question been resolved?

[devout snow]

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[sinful star]

hello

[sinful star]

how do I solve this?

[exotic stump]

what have you tried

[still pendant]

guys

I need help

In thermodynamic

s

_^

[main gull]

Not your channel
#❓how-to-get-help

[still pendant]

@floral vortexhelpers

[main gull]

This is a math server

[still pendant]

lmao

I still need help -^

[main gull]

Then go to a physics one

[still pendant]

Ur harsh

[main gull]

Did you read #❓how-to-get-help

[still pendant]

ur still crucial

[main gull]

Not really

[still pendant]

DUDE

THX anywaYSS

_((

[main gull]

Dude read #❓how-to-get-help

[devout snow]

@sinful star Has your question been resolved?

[devout snow]

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[devout snow]

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[full prawn]

I haven't quite understood how you can exactly get to know the area of the overlap between the four circles
What I know, however is that the radius of the smaller circles is equal to 1, considering that their diamter is equal to the radius of the yellow circle
With that info, I can confirm that these four smaller circles have an area of 4 pi, which is equal to the area of the entire yellow circle
...but i can't seem to know what the area of the blue area is, nor the area of the yellow area

[full prawn]

<@&286206848099549185>

[restive river]

the area of the yellow circle is 16 pi and its not equal to the sum of the area of the 4 circles

[full prawn]

once again, the radius of the yellow circle is equal to 2.. that's why the radius of the smaller circles is 1

[restive river]

your words " I can confirm that these four smaller circles have an area of 4 pi, which is equal to the area of the entire yellow circle"

[full prawn]

total area of 4 pi

area of one circle is pi
area of the 4 circles in total is 4 * pi = 4pi

i don't blame you though, it's my fault i haven't clarified my sentence

<@&286206848099549185>

[main gull]

https://mindyourdecisions.com/blog/2017/03/05/the-4-overlapping-circles-problem-sunday-puzzle/

@full prawn

[full prawn]

Lovely! Exactly what I've wanted

Thanks a lot, mate!

.close

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[restive river]

what is <A’s hypotenuse, opposite and adjacent?

[restive river]

i was thinking that BC would be <A’s hypotenuse because its the direction of which the 90° box thingy is pointing but then im confused because it also seems to be the only opposite

[tiny carbon]

BC is always the hypotenuse, no matter what angle

[restive river]

okayy but then which is the opposite and which is the adjacent??

[tiny carbon]

AC would be opposite

Then I think logically you know what the adjacent is

[restive river]

You can think of the hypotenuse as the longest side

can u explain why?? i thought that the opposite was the line that doesnt touch

[tiny carbon]

This is true as well

[tiny carbon]

AC doesn't touch the angle

If you look at the figure

[restive river]

And then the opposite side is the side opposite to the angle (in this case (30)

[tiny carbon]

Oh she said angle A

🤦‍♂️

[restive river]

Apologies

[tiny carbon]

I just saw the 30

[restive river]

*she 🙂

[tiny carbon]

My bad

Bad habits

[restive river]

its okay

i think i get it sorta

That applies for all right angled triangles anyway if you remember it like that

[tiny carbon]

<A's opposite is also the hypotenuse

[restive river]

see this is what i wzs confused about

[tiny carbon]

Which is why Sin(90) = 1, because its just Opposite/Hypotenuse where they are the same, anything divided by itself is 1

[restive river]

hmm

ohh i see it noww

thank u both

.close

[devout snow]

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[restive river]

.reopen

[devout snow]

✅

[tiny carbon]

Whats up?

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[toxic peak]

I'm trying to find the center of mass of a parabola and I'm a bit stuck. I have Z = p/m (pi*R^2 *h^2/3) I know the answer should be 2h/3. Can someone help with where I'm getting stuck?

[devout snow]

@toxic peak Has your question been resolved?

[toxic peak]

help

Is there anyone around who can assist me please? <@&286206848099549185>

Hello, I could really do with some help if anyone is available <@&286206848099549185>

[wooden zodiac]

no need to ping helpers right away after u pinged helpers

[toxic peak]

Sorry

[grave saffron]

u should prob show the problem so they can help u

[devout snow]

@toxic peak Has your question been resolved?

[devout snow]

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[restive river]

umm why is 2^2^2^2 different from ((2^2)^2)^2

[small field]

$$2^2^2^2, ((2^2)^2)^2$$

lol

[tiny carbon]

In the first one you start from the top, and then go down

With the parenthesis, you start at the bottom and then go up

[rare yoke]

Parenthesis priority.

[restive river]

ah

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[restive river]

When I integrate I get $\int\sqrt{4-x^2},dx=\arcsin\left(\frac{x}{2}\right)+C$. Why is this not true?

[woven radish]

Arr0w_04

[patent tartan]

because the derivative of arcsin(x/2) is 1/sqrt(4-x^2)

[restive river]

I let $x=2\sin(u)$ so that $dx=2\cos(u)$. I then divide this by the numerator of the integrand by the derivative ($2\cos(u)$) and everything cancels...

help

Actually nevermind redact I'm an idiot, sorry nvx lol I forgot how to do calc

[patent tartan]

you probably forgot to integrate a cos^2 term

[restive river]

Yep lol

[patent tartan]

@restive river open another channel

[restive river]

how

[patent tartan]

#❓how-to-get-help

[devout snow]

@restive river Has your question been resolved?

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[devout snow]

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[magic elk]

Help

[magic elk]

What am I doing wrong

[patent tartan]

in the denominator you suddenly changed pi into e

after the 4th equality sign

[magic elk]

thank you

answer is B

god bless you

I love you

so much

.close

[devout snow]

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[magic elk]

Help please

.reopen

[devout snow]

✅

[magic elk]

.CLOSE

[devout snow]

@magic elk Has your question been resolved?

[supple knot]

.close

[devout snow]

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[torpid horizon]

How can the diameter have 2 different measures

[rugged linden]

The first is that angle at S. The second is the length.

That is, the circle's diameter is 18 cm.

[torpid horizon]

Oh

[main gull]

Because one isn't the diameter

[torpid horizon]

🤦‍♂️

I wasn’t reading it right

Bruh moment

My b guys

[rugged linden]

that's a right angle triangle

[torpid horizon]

I can figure out now

Lemme close

.close

[devout snow]

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[torpid horizon]

Ty

[devout snow]

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[wooden bridge]

did i do this problem right?

[small field]

u want the solution to check?

bro you were literally here 30 seconds ago

[wooden bridge]

i wasnt here 30 seconds ago

[wooden bridge]

my last message was last night

[wooden bridge]

and yeah if possible

[small field]

,w solve 4x^2 - 8x + 16y^2 - 32y - 44 = 0

[woven radish]

Results provided by WolframAlpha

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

Requested by Chunkin#4952

[restive river]

Really it's on 6:28 am here and @small field reached back at 6:30

Ya 2 mins

Not 30 seconds

[small field]

nvm

[wooden bridge]

i'm confused lol

[small field]

u got the center right

[wooden bridge]

i'm also unsure about my c/foci

i thought it would be sqrt12 and not just 12

.close

[devout snow]

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[quick ferry]

Hey

[quick ferry]

So they human body can only use around 65% of muscle. If I were to use 100% how many times more would my power increase.

1.53846153846

?

[devout snow]

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[fervent jewel]

So I know that d|a and d|b, hence a=dm and b=dn for some m,n

Then I subbed it in gcd(a/d, b/d) = gcd(m,n)

Not sure how to continue

if I can somehow prove that m and n are relatively prime maybe?

Any hints?

[graceful cosmos]

In your proof so far, d is just some random number that divides a and b. That's not enough to complete this.

Are you allowed to use prime factorization yet? Haha

[fervent jewel]

nope

[fervent jewel]

im not sure what that means?

[graceful cosmos]

This line, while true, loses information. d is the largest such number.

[fervent jewel]

thats true

[graceful cosmos]

Let's say m and n were not coprime. That is, there's some extra number k such that, for new integers m' and n':
a = dkm'
b = dkn'

But then dk is now a larger common factor, and d itself was not the gcd

Ah sorry I got a bit carried away

[robust oar]

isnt m and n relatively prime?

d is the gcd of a and b so d contains all common factors of a and b

and gcd of two relatively prime numbers is 1 so your proof is done?

[fervent jewel]

Sorry to interupt, I think here m and n has to be prime right? Since d should contain all common factors of a and b?

^^

[robust oar]

yeah thats it thats all you need to write and you are done with the proof

[fervent jewel]

is that why u asked this? lol

[graceful cosmos]

Depends how much your course has covered. By writing something like this, you are conveying that this structure has been previously proven to exist

Prime factorization is not necessary, haha. I was just asking.

[fervent jewel]

Hm, i dont remember proving sth like this. I just thought it was "intuitive". maybe ill check with the prof when the course begins.

But this is suppose to be review, before getting introducted to groups haha

.close

[devout snow]

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[fervent jewel]

I gave it a second thought

[torn vessel]

and?

[fervent jewel]

From Bezout's identity, we know gcd(a,b)=d = ap+bq where d is the smallest positive integer in that form, and p,q are integers. We also know d|a and d|b. So if we divide by d on both sides. We get (a/d)p + (b/d)q = 1

And I thought I could use this corollary