help-27

[hybrid snow]

It's legit just manipulation

[quasi wasp]

I just don’t understand how it got to that form in the first place

[hybrid snow]

I'm turning x^2 into -kx^2 + (1+k)x^2

If you do the algebra, they're the exact same thing

[quasi wasp]

Yeah so why has that happened. Im sorry I’m just not getting that part

[hybrid snow]

Well it's because I notice that (x-k) * x^2 = x^3 - kx^2

So I take -kx^2 from x^2

[hybrid snow]

Hence this

To prove they're equal: -kx^2 + (1+k)x^2 = (1+k-k)x^2 = 1x^2 = x^2

But tbh that should be evident by the time you're doing polynomial division

[quasi wasp]

So I just looked at the solution and they approached it a whole different way, which I should’ve noticed at the start but failed to.

(X-k) is a factor of f(x)
F(k) = 0 => k^3 + k^2 - k + k = 0
K^3 + k^2 = 0
K^2(k+1) = 0
K = 0 or -1

[devout snow]

@quasi wasp Has your question been resolved?

[devout snow]

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[raven orchid]

every picture I draw of this supports the theorem, but I'm not sure how to start to prove it or how I would use the endpoint conditions

[manic condor]

Try considering a function h(x) = f(x) - g(x)

After that, mean value theorem is your friend.

[devout snow]

@raven orchid Has your question been resolved?

[raven orchid]

got you, thanks

[devout snow]

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[humble cobalt]

Kinda confused as to how the 13 ends up negative

[humble cobalt]

For more clarity it’s a conics question

Changing from standerd form to general and that’s a picture of the answer key

[topaz beacon]

Looks like the author made a mistake

[humble cobalt]

Kinda confusing cause that’s a website which has answers like detailed, but the textbook key has the same answer

Ima ask someone

Yesterday I spent hours tryna figure a question jus for the teacher to tell me to try graphing it because the function is too high degree and we haven’t learning that

[devout snow]

@humble cobalt Has your question been resolved?

[devout snow]

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[stray nova]

How do I solve this problem?

[brittle burrow]

$|2u-3v|=\sqrt{|2u-3v|^2}=\sqrt{(2u-3v)\cdot(2u-3v)}$

[woven radish]

chlamydia

[brittle burrow]

do you see how this works?

[neat solstice]

@stray nova
what chlamydia did is use the definition of the norm you are using
square it, then take the root
they then rewrote the squaring as multiplying it with itself

what we can then do is outmultiply the brackets
this will give us terms like u^2, u * v and v^2
the u^2 and v^2 are easily solved by using the definition of your norm again
for the u * v part, you will want to look at the definition of the scalarproducts

[stray nova]

ohhhh I see

[neat solstice]

there is an alternative to this, but this way is by far the easiest

[stray nova]

May I see it?

[neat solstice]

the alternative would be to notice that the exact orientation of the vectors is irelevant
thus we can just choose u=(1,0,0)
then we can look for a vector v=(x,0,0) such that the angle will be pi/3
then we can just calculate 2u-3v

[stray nova]

Is this a theorem?

[neat solstice]

a theorem i just made up

intuition basically

we will get a specific vector for 2u-3v which depends on our choice of u and v
however the length of that vector will always be the same if |u|, |v| and the angle are the same as was given

[stray nova]

but the V vector has to satisify the condition that the magnitude is 2 right

[neat solstice]

yes

[stray nova]

so we have two conditions, || v || =2, and the angle between them must be pi/3

I meant to type | | v | |

[devout snow]

@stray nova Has your question been resolved?

[devout snow]

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[tardy fossil]

hello, i have a question on algebra and just need some help

[main gull]

Post the question you are stuck on and patiently wait for help

[tardy fossil]

well, its not really a question, i just need help understanding the concept if that makes sense?

[main gull]

Then post it what it is

It's not like the people here have telepathy and can read your mind

[tardy fossil]

im sorry, im new to askin for help

.close

[devout snow]

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[devout snow]

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[next dock]

why dividing distance by time gives speed. please help me imagine the process of dividing distance by time

[jaunty mantle]

What is speed

[main gull]

Lightning McQueen /s

[next dock]

i don't know

[jaunty mantle]

How would you define speed?

[next dock]

i'm trying to define

i can define distance but not the other way around

[jaunty mantle]

Well what’s distance

[next dock]

speed times time

[jaunty mantle]

(This is actually a bit of a tricky question)

[next dock]

what do you mean

[jaunty mantle]

The distance is something that measures a property of 2 points

[next dock]

okay

[jaunty mantle]

Does that make sense?

[next dock]

.___________.

like this?

[jaunty mantle]

Kinda

[next dock]

oaky

[jaunty mantle]

If I gave you 2 point let’s say your home and your school

I can ask you about the distance between those 2 places

[next dock]

because we count the distance between my home and my school by arbitrary units that we made up ie meters

[jaunty mantle]

Sure

[next dock]

right?

[jaunty mantle]

Well the idea is that to go from point A to point B takes some time

Let’s say the points were 50 units apart

If it takes you 1 hour to get from A to B

Then every 1 hour you can travel 50 units

Does that make sense?

[next dock]

kinda

i'm trying to comprehend how are they connected to each other

[jaunty mantle]

Well if I asked you, how many times can you travel from A to B then to A then to B etc

In 3 hours

What would you say?

[next dock]

" how many times can you travel from A to B then to A then to B etc" can you elaborate this?

[jaunty mantle]

Like go back and forth between A and B

[next dock]

i would say 6 times but i wouldn't say that i understand what i'm doing

[jaunty mantle]

Well it takes 1 hour to get from A to B

[next dock]

then 3 times

[jaunty mantle]

Ah

But why 3

[next dock]

i'm thinking

[jaunty mantle]

You can try to describe it with words

The important thing here is to try express your thoughts

[next dock]

because we counted |AB| |BA| |AB| with 1 hour units and each distance was 1 hour unit?

[jaunty mantle]

Aha!

What if I told you it takes 1.5 hours to go from A to B

And I still only had 3 hours

[next dock]

yes it is 2

so

speed is counting travelled distance by time

is that right?

[jaunty mantle]

Kinda

We want to measure how far we can travel per some time

[next dock]

we defined traveled distance by hours, then when dividing that distance by time we were counting by that time unit?

[jaunty mantle]

Yes

That’s what “per” means

When we say 60kmph

That’s saying 60 km per hour

Or 60km/hr

Or every hour we travel 60km

[next dock]

4 cookies per person

8 cookies per 2 people

.... ....

this is so hard

[jaunty mantle]

What’s wrong with that

[next dock]

with what?

[jaunty mantle]

With what you just said

[next dock]

is something wrong?

[jaunty mantle]

Nothing is wrong

[next dock]

i don't know what's wrong

[jaunty mantle]

But you said it was hard

[next dock]

yes it is

[jaunty mantle]

Which part of that was hard?

[next dock]

trying to understand division

[jaunty mantle]

(I’m not saying it should be easy, just wondering where you are having difficulty)

Ah

Do you understand division in other contexts?

[next dock]

like what?

[jaunty mantle]

Like splitting a pizza between people

[next dock]

yes i can understand splitting a pizza

[jaunty mantle]

Do you also get that division is like the inverse of multiplication?

[next dock]

i know but i don't get

[next dock]

ring theory right?

[jaunty mantle]

$\div(*(a, b), a)=b$

[woven radish]

Frosst

[jaunty mantle]

Mhmm never mind

[next dock]

what do you want me to do

[jaunty mantle]

If you multiply something by a then divide by a

You get what you started

[next dock]

yes that's right

[jaunty mantle]

So in a sense it’s doing the opposite of multiplication

[next dock]

yes, i know that

but why "per"?

[jaunty mantle]

That’s just the word we use

“How much are the ice cream?”

“They are 3 dollar each”
This is the same as saying
“They are 3 dollars per ice cream”

[next dock]

why is it a division?

dollars/ice cream?

[jaunty mantle]

Yes

Precisely that

[next dock]

yes but i can't make a connection between (dollars/ice cream?) and (why is it a division?)

[jaunty mantle]

Because every 3 dollars gets you an ice cream

If I change the question

“How many ice cream can I buy per dollar?”

Now I want to know ice cream/dollar

I also just noticed I’ve used ice cream subconsciously because of your name lol

[next dock]

lol

[jaunty mantle]

Anyhow, now it is 0.3333… ice cream per dollar

Or 1 ice cream per 3 dollars

$\frac{0.333…}{1} = \frac{1}{3}$

[woven radish]

Frosst

[next dock]

okay

you divided 1 by 3 on top left

and divided 3 by 3 on bottom left?

[jaunty mantle]

No I just went $\frac{0.333…}{1}=0.333…=\frac{1}{3}$

[woven radish]

Frosst

[next dock]

yes

can't say i get what division means

[jaunty mantle]

Can you give an example where you don’t understand the meaning

[next dock]

okay

[next dock]

how are we dividing dollars by ice cream?

or binqilin i would say

[jaunty mantle]

What’s wrong with that

[next dock]

in a way every new division example looks like an alien concept but not multiplication

[jaunty mantle]

Ok let me give you a perhaps weird example

What is force

[next dock]

i don't know

wait

tiny atoms coming together

[jaunty mantle]

Have you seen F = ma before

[next dock]

yes countless times

[jaunty mantle]

What’s m measured in (typically)

[next dock]

kg in europe

[jaunty mantle]

What about a

[next dock]

m/s

[jaunty mantle]

How does it make sense to multiply kilograms with meters divided by seconds

It might be a useless thing to think about

[next dock]

mass go big, mass hit big

[jaunty mantle]

But this kind of measurement happens to be what force means

[jaunty mantle]

Also it’s m/s²

[next dock]

ah yes

m/s was speed

or velocity?

[jaunty mantle]

Similar to how we are dividing units here

It’s meaningless unless it tells us something

Dollars/ice cream tells us how much it costs to buy ice cream

kgm/s² tells us how much force something applies

If we want to measure work

We multiply F by distance

If we apply a force over some distance we do some work

In the same sense “if we apply some speed over some time we travel some distance”

It’s a very rough analogy but maybe it helps you understand the connections

[next dock]

why it is multiplication?

[jaunty mantle]

It just happens to be

[next dock]

why not force + distance

[jaunty mantle]

Because it doesn’t align with the real world

[next dock]

"for 5 unit distance we applied 1 unit force"

force+force+force+force

[jaunty mantle]

“We applied 1 unit of force over 5 units of distance”

That’s usually the way we phrase it

[jaunty mantle]

But this is fine as well

[next dock]

okay i got this

now all i need to do is understanding the inverse of this

aaah

[jaunty mantle]

Well what if I asked

How much force do I need to apply over some distance to do X work

I give you the distance and the work

How do you find the force

[next dock]

w = f.d

w/d = f

[jaunty mantle]

We usually use s for distance

[jaunty mantle]

It’s also a bit wrong but I don’t think the difference matters in our context

[next dock]

yes you are right

what's wrong

w = f * s

[jaunty mantle]

$W=\int_CF\cdot ,ds$

It’s more like this

[next dock]

what is c

[jaunty mantle]

The path

But honestly it’s not really the point of our discussion

If C is just some path from s = 0 to s = s then it’s just W = Fs

Fuck

[woven radish]

Frosst

[jaunty mantle]

It was weird when I started writing it

Or rather $W=\int_{s=0}^{s=d}F\cdot , ds = [Fs]_{s=0}^{s=d} = Fd - 0 = Fd$

[woven radish]

Frosst

[jaunty mantle]

So if we move from 0 to d (a force F applied over a distance d)

Then we did work equal to Fd

[jaunty mantle]

Which is what you have here

[next dock]

yes i remember from college

[jaunty mantle]

Anyhow it’s not really the point we’re focusing on

[jaunty mantle]

This is how division is helpful

[next dock]

well i just did algebra...

doesn't mean that i get it

work divided by distances

[jaunty mantle]

How much work did we do per distance?

[next dock]

1 work = |....| distance

i'm trying to visualise distance and work

in my mind

trying to visualise what would work per distance look like to be exact.

[jaunty mantle]

Work might be a bit abstract to think about

[next dock]

everything is abstract

okay if we have 100 human

10 humans*

and if they are paired with each other

how many group we have per pair

one pair is 2 humans

aah

this is where i got lost

group per pair

is there any division contexts than these?

[jaunty mantle]

You can ask this

But it might be useless to know

[next dock]

ask what about it?

[jaunty mantle]

There are 5 groups

There are 2 people per group

Or 1 group per 2 people

2 people is a pair

1 group per pair

Group per pair means how many pairs of people are in a group?

[jaunty mantle]

Since you defined here 1 group has 2 people paired together

You get 1 group per pair

[next dock]

but we have 10 people

why didn't we divide

[jaunty mantle]

But groups per pair answers the question: “How many groups can you make with 1 pair of people?”

[next dock]

can you give an easy example about permutation that includes division?

[jaunty mantle]

Why permutation

Permutation is usually not simple lol

[next dock]

okay then

[jaunty mantle]

Combinatorics is usually easier

[next dock]

maybe i'm mixing them

[jaunty mantle]

How many ways are there to pull 4 aces from a deck of cards?

[next dock]

1 way

[jaunty mantle]

Actually that’s probably too hard too

How many ways are there to pull 3 aces from 4 cards from a deck of cards

That’s better

The division in these question takes care of “over counting”

Honestly these are pretty shit examples 😦

I can’t think of a good one on the spot

[next dock]

my brain is about to explode

"PAPAYA" how many meaningless or meaningful words can we write, using each word each time

this requires division

nevermind this is too hard for me

[jaunty mantle]

Ah

That’s a good example

The A’s are indistinguishable

So whether the first, second or third A goes anywhere

It’s the same permutation

[next dock]

no i'm serious this is like phd level division nevermind

okay what about interpolation factor

x-x0/x1-x0

x0------x--------------x1

x0------x and
x0---------------------x1

.close

[devout snow]

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[next dock]

.reopen

[devout snow]

✅

[next dock]

thank you for your efforts @jaunty mantle

.close

[devout snow]

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[devout snow]

Available help channel!

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Remember:
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• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[stray socket]

i need to be taught 85,86,87

[rapid merlin]

What are the properties of two parallel lines on a graph?

@stray socket ?

[stray socket]

sorry

the same b value?

[rapid merlin]

You mean the same slope ?

[stray socket]

yes

same slope different b is what i meant

[rapid merlin]

Ok so get the function in the (a 85)
To be
y = mx + c
Form

Done?
@savageben.123#4537

[stray socket]

is it

y=1/4x+1

i was working it out

[rapid merlin]

Umm
You need to divide the 4 to the whole right side
Not just x

It will be like this
$$y=\frac14x+\frac14$$

[woven radish]

Sherif Player

[rapid merlin]

Ok ?

[stray socket]

got it yeah

[rapid merlin]

So the slope is 1/4

[stray socket]

i messed that up but i understand

[rapid merlin]

Now just get the derivative of the function and equation it to 1/4

[stray socket]

the deriv is just e^x right

[rapid merlin]

Yeah

[stray socket]

what would i do after getting deriv'

[rapid merlin]

Equate it to 1/4 and get the x and y values of each point that satisfies the slope

As you need to get a point in the derivative that its slope is equal to 1/4

[stray socket]

so itd be e^x=1/4?

im not following on this part

[rapid merlin]

Yes
Now just get the x value that satisfies this condition
And then substitute it to the original function to get the y value of the point that satisfies the conditions

[stray socket]

im confused on that part^

the x value that satisfies

[rapid merlin]

Do you know how to solve for x there ?

[stray socket]

no

[rapid merlin]

Did you get to know the logarithmic functions?

[stray socket]

no im afraid not

[rapid merlin]

Like
$$\log_2(8)$$
$$\ln(e^2)$$
Nothing of those ?

[woven radish]

Sherif Player

[rapid merlin]

@stray socket ?

[stray socket]

no i havent seen those before

[rapid merlin]

Then you need to learn about them to solve 85 and 86

[stray socket]

would it be ln1/4

x=ln(1/4)

[rapid merlin]

Did you just get that from an online calculator?

[stray socket]

no i looked at the notes from today

[rapid merlin]

So you learned about it today ?

[stray socket]

yes and no. he gave us 1 example using e^x

but in a different scenario

[rapid merlin]

I mean how do you don't even remember that you got those
And this is in your notes

[stray socket]

was it right?

anyway. when i get my x=ln(1/4) do i sub it into the original y=1/4x+1/4

[rapid merlin]

Yeah it was right but I am afraid that you just don't understand why it is the solution to it and how to get its value by your self in the future

[stray socket]

well my exam is tommow so i have to learn it by tonight

[rapid merlin]

https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs

[stray socket]

but i need to know how to solve the 85,86,87

[rapid merlin]

This is a really good unit there to learn about it

[stray socket]

well ill be checking it out tonight

[rapid merlin]

So now you got the value of x right

[rapid merlin]

What will you get when you substitute it to the original function

@stray socket ?
It should be easy

[stray socket]

ln1/4/4+1/4

or no?

[rapid merlin]

I said original function before taking the derivative

[stray socket]

ln(1/4)-4y=1

?

[rapid merlin]

We don't want anything from the equation of the line except knowing its slope
No need for anything else

We knew its slope so just throw it out of the window

[stray socket]

e^x?

[rapid merlin]

Wait
Do you understand what derivative mean?

[stray socket]

is that what your talking about

yes

[rapid merlin]

Like you now that it is about taking the slope of the function at any point x

[stray socket]

e^ln(1/4)

yeah i understand the derivatives

is there a way to like call you? if not its fine its just hard for me to type

[rapid merlin]

So to get the a line parallel to that line equation we need to find a point where the slope of the function equal the slope of the line
So we took the derivative of the function
F'(x) = e^x
And we equted it to the slope of the line
e^x = 1/4
To get
X = ln(1/4)

Now we need to know the y value of that point so we will substitute x back to the original function

F(x) = e^x
e^ln(1/4)

To get the value of y

That will output the same value 1/4

So the point will be (ln(1/4), 1/4)

So now you got a slope and a point right

Just make the equation of the line that has that slope and passes through the point

And you did it

@stray socket
All good ?

[stray socket]

Is this right.

?

wait whys it ln4+1 and not 1/4

did i do something wrong

oh i think i get it

[rapid merlin]

It should be
ln(4) not ln(4+1)

[stray socket]

okay gotcha

thank you

on 86 it gives u 2 points so would u sub in the x value into e^x?

[rapid merlin]

So you know that
$$\ln(\frac14) = -\ln(4)$$

[woven radish]

Sherif Player

[rapid merlin]

There is a point b in 85

If you didn't see it

[stray socket]

didnt see it good catch

would we have to make our why value 0?

[stray socket]

to find the origin

[rapid merlin]

So in your opinion what would you need to do

[rapid merlin]

What!!!

Come on tell me that you know what is the origin point

[stray socket]

i thought the origin was 0 on both axis

[rapid merlin]

Yes

[stray socket]

like point 0,0

[rapid merlin]

Yes

[stray socket]

how would i go about finding it?

id have to make a point 0,0

im going to move onto 86

[rapid merlin]

Sorry for being late

[stray socket]

no problem. im just preparing for my test

[rapid merlin]

@stray socket
First do you know a way to Express the equation of a line of some point in a function by knowing that its x co-ordinates is a and its y co-ordinates is f(a)

If you don't know this is a quick way just remember this rule
(y-f(a)) = f'(a) * (x - a)

[stray socket]

no i didnt know that

[rapid merlin]

This works for every function

If it is continuous in the point you are doing that of course

[stray socket]

and thats the equation of a line?

[rapid merlin]

Yeah that's the equation of the tangent of any point in a function

[stray socket]

okay gothca

im writing that down

[rapid merlin]

Now in our case
f(a) is just e^a
Right?

[stray socket]

your doing 86 right?

[rapid merlin]

85b

[stray socket]

yes then

[rapid merlin]

Then what is f'(a)

[stray socket]

would it just be e^a

[rapid merlin]

Yes

[stray socket]

wait so what is e^a in our problem

[rapid merlin]

It is just the value of a function knowing that its x coordinates is x
Meaning it is the value of y in the graph of the function

Now we want to get a line equation that passes through 0,0

[stray socket]

okay

would we use the equation u showed me

i dont think he taught us this way. or he may not have taught us at all because none of this is familiar

[rapid merlin]

Yes we just want to first separate it to the
y = mx + c
Form

To make it easier on us
So here we need c to be 0

[stray socket]

c?

oh i see

[rapid merlin]

Ok

$$y- e^a = e^ax-e^aa$$

[woven radish]

Sherif Player

[rapid merlin]

$$y=e^ax+e^a-e^aa$$

[woven radish]

Sherif Player

[rapid merlin]

So now we got it to the form

So now you should know which part we want to be zero here

[stray socket]

a?

[rapid merlin]

No

[rapid merlin]

Like what part represents the constant here

[stray socket]

do u mean which constant should be

[rapid merlin]

I mean which is the part that should be zero in that equation to make it look like
y = mx

[stray socket]

if we are trying to get mx+b

everything to the right of the addition sign

needs to go right

[rapid merlin]

Correct

So just say that
$$e^a - e^aa=0$$
And solve for a

[woven radish]

Sherif Player

[stray socket]

do i sub numbers in yet

or get the a to other side

[rapid merlin]

It is easy to solve tho
Just take e^a * a to the right side then divide by e^a

@stray socket
All good ?

[stray socket]

e^a/e^a

=a

[rapid merlin]

Yeah but you can simplfie it more

[stray socket]

a=1? or is that wrong lol

[rapid merlin]

Yes

[stray socket]

hell yea

[rapid merlin]

It is correct

Now just substitute it to the original line equation

To get the line equation

[stray socket]

which ones the original. the one u showed me

(y-f(a)) = f'(a) * (x - a)

[rapid merlin]

No this is the general one
To use this you need to substitute the f(a) and f'(a)

[rapid merlin]

I meant this

[rapid merlin]

Or this

Both of them will work

So did you got the final line equation?

[stray socket]

y=e^1x

is e^1 just e

so itd be y=ex

[rapid merlin]

Yeah

That's correct

[stray socket]

awesome

ill have to get some more help on that before my test tommorow

i learn much better in person

[rapid merlin]

Now to 86?

[stray socket]

think im gonna do some easier ones that i also need to know

il lsend u a pic

[rapid merlin]

86 actually uses the same equation I told you above

[stray socket]

52-56 will be on test

so 86 is similar?

[rapid merlin]

Not really but it uses it in another way

[stray socket]

on 52, 4sin^2x

what rule would be used for the derivative

[rapid merlin]

What do you think?

[stray socket]

would that be multiplication rule

uv^prime+vuprime

[rapid merlin]

Yeah that works

[stray socket]

let me work it out some

[rapid merlin]

But there is another way
Which is

[stray socket]

chain rule?

[rapid merlin]

$$\frac{d}{dx}F^n(x) = F^{n-1}(x) F'(x)$$

[woven radish]

Sherif Player

[stray socket]

os tjat chain rule?

[rapid merlin]

Yes

[stray socket]

would the 4 be considered outter function

[rapid merlin]

It is a constant that you can ignore and multiply by it in after getting the derivative

[stray socket]

is it -4cos^2x

[rapid merlin]

No

[stray socket]

what would be considered the outter function of sin^2x

[rapid merlin]

$$4 * sin^2(x)$$
$$4 * 2 * sin(x) * cos(x)$$

[woven radish]

Sherif Player

[rapid merlin]

Like this

[stray socket]

okay i see now

so it would be 8sinxcosx

[rapid merlin]

Yes
Then substitute the point

[stray socket]

8sinpi/6cospi/6

[rapid merlin]

Yeah what is the value

Remember that this is in rad

[stray socket]

would i need the unit circle?

[rapid merlin]

Not really

[stray socket]

what would u do

[rapid merlin]

If you remember them

π/6 is the same as 30 degree

[stray socket]

1/2?

would it be 8x1/2xsqr3/2

[rapid merlin]

Yeah

Which will result in?

[stray socket]

can i not leave it like that?

[rapid merlin]

You can but you can also simplify to be more easier
Like
2√3

[stray socket]

ohh gotcha

okay

so would that be the slope?

[rapid merlin]

Yeah

56 is not hard

[stray socket]

can i leave it in y-y-1=m(x-x1)

because i wont know how to simplify that tmr

[rapid merlin]

You can

[stray socket]

good

im gonna try 53

quotient rule first right

y=2x-1

did u work it out?

it says the answer is y=-1

[rapid merlin]

Yeah because you should have got a 0 instead of 2

[stray socket]

i see why now

messed up a neg. sign

[rapid merlin]

Happens a lot with new to average people in math:)

[stray socket]

wait actually i dont see my mistake

can u find hte4 problem?

[rapid merlin]

,rotate

[rapid merlin]

When you substituted zero there how did you get 2?

[stray socket]

1--1

am i missing something

2/1

[rapid merlin]

Zero times something is zero

• zero times something which is zero

[stray socket]

oh i see

i forgot to multipy by the zeros

silly mistake

im gonna try 54

[rapid merlin]

@stray socket sorry for that but I gotta sleep now so just use helpers tag here if you need any help

[stray socket]

okay thanks very much

[devout snow]

@stray socket Has your question been resolved?

[devout snow]

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[vivid quiver]

@drifting torrenter How do I solve the problem: "too+too+spot what is the value of "t"" I don't even know where to start?

[devout snow]

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.

[main gull]

And post an image of the problem

That makes no sense, what you have typed

[vivid quiver]

ok just a sec

[devout snow]

@vivid quiver Has your question been resolved?

[karmic prairie]

do you have any values for S or P?

[vivid quiver]

No

Idk how it works but I got it in a test so it must be possible

[karmic prairie]

are these variables?

[vivid quiver]

Do you mean as in the each hold a specific number value?

[karmic prairie]

yes

[vivid quiver]

Yes it is

[timid whale]

huh

thst looks to be impossible if they are all single digits

2x+1 can never have same parity as x

[vivid quiver]

@timid whale thats odd

I'll have to ask my math teacher about it

[timid whale]

its certainly impossiblr

[vivid quiver]

Because she says it's possible

[timid whale]

either that

[vivid quiver]

So idk

[timid whale]

if theres no carry over in first step then second should give t aswell

and if there is max carry is 1

so 2x+1 should give 10+x

wait lol

9

anyway

its doable im just dumb

o is 9

after that ig u can solve

t is 8

[vivid quiver]

Ok

Thanks so much

.close

[devout snow]

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[devout snow]

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[glad glen]

Help I'm having a mental health crisis
I just learned about this python package called sympy that lets you do all sorts of symbolic math
like differential equations and stuff
why am I trying to become a physicist when a calculator can do everything I could ever want to do

[glad glen]

can I have a reason that I need to understand how to math when I could just type it in a calculator

whats the point of doing anything other than compsci at this point

[livid geyser]

gl typing proofs into a calculator

There technically are formal proof verifiers but

[wooden zodiac]

Or finding new theories lol

[livid geyser]

They are messy af

[wooden zodiac]

Physicists' sole job is not computing stuff lol

[glad glen]

I get that the conceptual parts of the math is important

but why am I killing myself trying to understand DE

when I could just plug it in

a caluclator

[livid geyser]

oh intro DE is a useless class in 99% of schools tbh

Needs more proofs

[glad glen]

Does physics even use proofs

[livid geyser]

yes

Witten is a physicist and has a fields medal

[glad glen]

oh really

[livid geyser]

ye

[glad glen]

hmmmmm

ok

im still sad

[livid geyser]

But yeah intro DE is a joke class that they make u go through most of the time cus idek

some top schools don't even have it as a requirement for math major nowadays

[glad glen]

oh

well it still seems important to physics tho

[livid geyser]

DEs are very important

but intro DE isn't

[glad glen]

am I just failing at it because I skipped past calc 3

[livid geyser]

hmm it shouldn't require Calc 3 stuff

[glad glen]

well I guess im just stupid

[livid geyser]

Nah

Maybe ur just not the best at computations stuff

But we have computers for that nowadays

Like u pointed out

[glad glen]

yeah ur right

I guess its just been a long day

thanks

[livid geyser]

np

[glad glen]

.close

[devout snow]

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[shut elbow]

i was wondering why theta is at that angle

[supple knot]

https://www.brightstorm.com/math/trigonometry/advanced-trigonometry/angle-inclination-of-a-line/

[devout snow]

@shut elbow Has your question been resolved?

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[shut elbow]

not sure if my work is right for this question

[devout snow]

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[woven citrus]

What do i do i am stuck for 20 minuted

[rapid merlin]

, rotate

[rapid merlin]

What do you know about solving by substitution?

Nvm

[woven citrus]

I cant understand substitution

[rapid merlin]

Try getting the value of y in terms of x in the first equation and substitute it to the second equation

[woven citrus]

Yes i tried and it didnt work

[rapid merlin]

Or if you want to avoid square roots
You can get it from the second one and substitute it to the first one

[woven citrus]

Okay brb let me try it out

[rapid merlin]

Did you got
$$y=\frac{23-x}{1+x}$$
$$x^2 + \frac{23^2-46x+x^2}{x^2+2x+1} = 34$$
$$\frac{x^2(x^2+2x+1) +x^2 - 46x + 23^2}{x^2+2x-1} = 34$$
$$x^4+2x^3+2x^2-46x+23^2=34x^2+68x-34$$
$$x^4+2x^3 -32x^2 -114x + 563 = 0$$

[woven radish]

Sherif Player

[rapid merlin]

,calc 23*23 +34

[woven radish]

Result:

563

[rapid merlin]

,calc 114/2

[woven radish]

Result:

57

[rapid merlin]

,calc 563/114

[woven radish]

Result:

4.9385964912281

[rapid merlin]

,wolf solve x^4 + 2x^3 -32x^2 -114x + 563

[woven radish]

Results provided by WolframAlpha

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

Requested by sherif_player

[rapid merlin]

@woven citrus
Found an easier way yeah

[devout snow]

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[opal birch]

Helllo i need help with something

[hushed wraith]

[opal birch]

wait lemme send

I need to explain what Summation of a product is

and make 2 examples on how to do it

[devout snow]

@opal birch Has your question been resolved?

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[amber blade]

How can a) possibly be a d-system if u(X) is not promised to be v(X)? where X is the whole space

[stone stump]

that is indeed strange

[devout snow]

@amber blade Has your question been resolved?

[amber blade]

well I just ignored it for now

onto reproving the monotone class theorem

[devout snow]

@amber blade Has your question been resolved?

[devout snow]

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[viscid snow]

TRASLATED: Determine by calculating the interior angles if the triangle with vertices: ... Is a rectangle one

[viscid snow]

help, where to start

@wooden veldt could u help me?

[devout snow]

@viscid snow Has your question been resolved?

[supple knot]

don't ping individual helpers

[devout snow]

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[royal drift]

x^2013 + 1/x^2013 = 2. Find x^2022 + 1/x^2022

[lilac mango]

not sure if theres a fast way

but

you can let u = x^2013

so u + 1/u = 2

[royal drift]

i can provide you with options

[lilac mango]

go on

[royal drift]

the options are : 0, 1, 2 and 4

It must be any one of these

[lilac mango]

well

if you have

u = x^2013

and u + 1/u = 2

theres a bit of an obvious solution

for u which u can then use to solve for x

[royal drift]

Alright, ill try

[lilac mango]

have you worked out the value of u?

[royal drift]

yeah, u is 1

[lilac mango]

yep

so if you have

u = x^2013

1 = x^2013

so what would x be

[royal drift]

then the correct answer is also 1

sorry, 2

[lilac mango]

yep

great

👍🏻

[royal drift]

thanky you very much

[lilac mango]

no worries

[royal drift]

.close

[devout snow]

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[sinful inlet]

This is what I have so far

[devout snow]

@sinful inlet Has your question been resolved?

[sinful inlet]

<@&286206848099549185>

[devout snow]

@sinful inlet Has your question been resolved?

[sinful inlet]

<@&286206848099549185>

[devout snow]

@sinful inlet Has your question been resolved?

[sinful inlet]

.close

[devout snow]

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[west tinsel]

Hi

[west tinsel]

The product rule says that ... Explain why ....

I haven't begun yet because I don't know how but I have an idea that it might have something to do with the constant rule?

[lone ravine]

Do you need to show the rule for partial Integration?

[west tinsel]

ye

I need to figure it out

[lone ravine]

Nice, that is how I started my oral exam today 🙂

[west tinsel]

in uni?

[lone ravine]

How about bringing the two integrals on one side?

[lone ravine]

Yes

[west tinsel]

nice. first year?

[lone ravine]

Finals over first and second semester

[lone ravine]

Did you do that?

[west tinsel]

Yep

now we can put them together

nice¨

[lone ravine]

Yes 🙂

And then you just apply the identity above and you're done

[west tinsel]

nice

I didnt even know you could put them together like that until 10 seconds ago

I thought it would make sense and I guess it was right xD

[lone ravine]

That's just the linearity of the integral

[neat solstice]

can't we just differentiate everything?

that way, we will use the product rule and the fact that d/dx(integral(f))=f

assuming that f is integradable of course

[lone ravine]

Yes, that's another way of doing it !

[devout snow]

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[west tinsel]

Use partiel integration on f(x) = x and g(x) = 1/(1+x^2)^n to realize that:...

the differentiated of 1/(1+x^2)^n is really insane, I dont know if its necessary for me to calculate it here

[neon aspen]

it's not that insane

[west tinsel]

How would you do it?

And is it really necessary?

[neon aspen]

yes

[west tinsel]

shit

okt

okay

[west tinsel]

how would you do it?

by hand

idk where to go from here or even if I did it wrong

<@&286206848099549185>

[devout snow]

@west tinsel Has your question been resolved?

[devout snow]

@west tinsel Has your question been resolved?

[ancient ravine]

,rotate

[devout snow]

@west tinsel Has your question been resolved?

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[sharp wigeon]

is their a way to solve this? very confused

.close

[devout snow]

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[sharp wigeon]

.CLOSE

.clsoe

.close

[devout snow]

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[misty dirge]

I'm unsure if this is the correct approach

as i've also asked for AI's opinion and it gives something quite different althought similar taste

[livid geyser]

Bruh never ask an AI to do math for u

[winter patrol]

don't use chatgpt for math

[misty dirge]

XD

[rough swan]

$\lim_{n\to\infty} \tfrac{f(n)}{g(n)} = ?$
$\lim_{n\to\infty} \tfrac{g(n)}{f(n)} = ?$

[woven radish]

YouShouldBeHigher

[rough swan]

do you know Stirling's approximation to the factorial?

[misty dirge]

i think f(n) is still faster right

i do not

[rough swan]

ok so for large n, $n^44^n >> n^33^n$, follow?

[woven radish]

YouShouldBeHigher

[rough swan]

means "is very much bigger than"

[misty dirge]

yes

[rough swan]

so we can ignore the lesser term

[misty dirge]

ye we just look at n^4 * 4^n right

i put 4^n which is incorrect? should be the whole large expression

[rough swan]

yes

[misty dirge]

which is n^4 * 4^n

[rough swan]

y

$f(n)=2^n * \tfrac{n!}{3!(n-3)!} = \tfrac{2^n*n(n-1)(n-2)}{6}$

[woven radish]

YouShouldBeHigher

[misty dirge]

yes, and the numerator simplifies to 2^n * n^3 because we take the largest expression in the sum of expression of n(n-1)(n-1)?

[rough swan]

if we multiply out the factors, we will get a cubic polynomial n^3+...

when n is large, the n^3 term will dominate the lesser terms

[misty dirge]

In this case would we just be comparing degrees instead of factorials vs exponentials speed

[rough swan]

so now we only need consider

$\tfrac{f(n)}{g(n)} \approx \tfrac{2^nn^3}{6\sqrt{n^44^n}}$

[woven radish]

YouShouldBeHigher

[rough swan]

ready^

simplfy

$\tfrac{f(n)}{g(n)} \approx \tfrac{2^nn^3}{6n^22^n}$

[woven radish]

YouShouldBeHigher

[misty dirge]

infinity and 0 respectively?

[rough swan]

so you were right, f is faster

[misty dirge]

thank u for ur help bro!

[rough swan]

np

[misty dirge]

i would just check for f(n)/g(n) and g(n)/f(n) right?

and then since f(n)/g(n) is infinity and g(n)/f(n) is 0

i can conclude that f(n) growsfaster

after simplifying with heuristics

[rough swan]

what if they had been constants?

f(n)/g(n)->3.14159

say?

[misty dirge]

either wouldn't be fast?

im not sure

it'd just be a difference in numbers but the ratio would remain the same?

[rough swan]

they grow proportionally to each other

f(n) ~ c*g(n) where c is a constant

ok, we good?

[misty dirge]

ye i think so

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[torn lagoon]

try rewriting the fraction as a product of two

[thorn birch]

a product of 2?

[thick inlet]

hi

what DID I DO WRONG GUYSS

[thorn birch]

uh this is mine😭

u have to go to a new one

[devout snow]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[torn lagoon]

yeah, you can split the fraction up into a product of two numbers

ill give you the first part of it -> (5/6) * (? / ?)

[thick inlet]

oops my bad

ill change it

[thorn birch]

would it be the cube roots?

[torn lagoon]

hint: cbrt(24/3) is the same as cbrt(24)/cbrt(3)

[thorn birch]

ok chbe root (24/3)

[torn lagoon]

ye

[thorn birch]

So (5/6) cuberoot(24/3)

[torn lagoon]

yes, being multiplied. you can simplify the cube root further

[thorn birch]

cube root of 24 and 3?

[misty dirge]

How can u split cube root 24 to simplify it?

[torn lagoon]

you have cbrt(24/3)

what is 24/3?

[thorn birch]

12 and 2?

[thorn birch]

what r u talking abt division?

[torn lagoon]

if you have the cube root of (24/3), you can simplify the division in side. 24/3 is 8, so you would have the cube root of 8 or cbrt(8)

[thorn birch]

okay

[torn lagoon]

so your term now looks like (5 / 6) * cbrt(8)

[thorn birch]

okay

[torn lagoon]

do you know what number raised to the 3rd power is equal to 8?

or in other words, what is the cube root of 8?

[thorn birch]

3

uh

[torn lagoon]

it's actually 2, 2x2x2 = 8

oops

[thorn birch]

2 ?

[torn lagoon]

yes

[thorn birch]

yea

[torn lagoon]

so you should now have (5/6) * 2

[thorn birch]

okay

[torn lagoon]

one thing to note though is that you can only rewrite fractional roots like this if they have the same power (in this case, cbrt is power 3 root)

[thorn birch]

ok

[torn lagoon]

if you have sqrt(24)/cbrt(3), you would not be able to simplify any further

[thorn birch]

noticed

so A?

[torn lagoon]

what do you get when you do (5/6) * 2

that should be the answer

[thorn birch]

what is the star representing

[misty dirge]

Times

Right now u have 5 * 2 * cuberoot(3) / 6 * cuberoot(3)

U can simplify that

Anything divided by itself is what?

[thorn birch]

ur confusing me

can u just u like an x

so 5x2x cuberoot of 3/6

[torn lagoon]

its (5 / 6) x 2

you can write that as (5/6) + (5/6)

[thorn birch]

1.66666 ???? idk it came up with a bunch of 6

[torn lagoon]

you can do it without a calculator

[thorn birch]

1 2/3

[torn lagoon]

it will be 10/6

[thorn birch]

ok now what

[torn lagoon]

simplify

[misty dirge]

Simplify.

[torn lagoon]

10/6 can be condensed into a simpler fraction

[thorn birch]

1 4/6?

[torn lagoon]

do you know the factors of 10 and 6?

10: 1, 2, 5, 10
6: 1, 2, 3, 6

Notice they have a common factor of 2

[misty dirge]

5/10 is the same as 1/2

[thorn birch]

ok

[torn lagoon]

therefore, you can divide both terms by 2 to get the simplest fraction: 5/3

[thorn birch]

ok

is that all

[torn lagoon]

yes! it's as simple as it can get now

[thorn birch]

do u know how to find integer values

[torn lagoon]

when dealing with fractions and roots, try your best to simplify everything manually and without using a calculator until the end

[thorn birch]

ill try

[torn lagoon]

integer values? how so

[torn lagoon]

ah yeah, same principle!

so you can rewrite this one and combine the roots into one fraction, you should get the square root of (90/10)

[thorn birch]

okay

[torn lagoon]

and from the previous problem, you just need to do the division inside the root first, then the square root of the result

for this problem it should be pretty simple arithmetic, no calculator required

[thorn birch]

so do i find the square root then divide them

[torn lagoon]

divide first, then do the square root

so whats 90/10

[thorn birch]

9

[torn lagoon]

right, now take the square root

[thorn birch]

of 9?