help-0

[thorn niche]

Do i use x or dot

[unkempt robin]

Honestly

Whatever makes you feel better currently

But I am just saying that you'll most likely start to see dots for multiplication

As you get older

Because we use x, the letter, very often for variables

[thorn niche]

okay

[unkempt robin]

Okay, anyway

You can kick the 2 out, because $\frac{2a}{b} = 2 \cdot \frac{a}{b}$

[ocean seal]

USS-Enterprise

[unkempt robin]

Do you get this now?

The dot resembles multiplication

[thorn niche]

yep

[unkempt robin]

Okay

So after "kicking the 2 out"

We have $2 \cdot \frac{10^{18}}{10^3}$

[ocean seal]

USS-Enterprise

[thorn niche]

Where did that fraction come from

[unkempt robin]

Now, you can either simplify this fraction by canceling factors or using the division property of exponents

It's been there the whole time

We had $\frac{2 \cdot 10^{18}}{10^3}$

[ocean seal]

USS-Enterprise

[unkempt robin]

We just kicked the 2 out

[thorn niche]

What about this

Oh it was just an example

My bad sorry

[unkempt robin]

Yeah 😄

Anyway

We have $2 \cdot \frac{10^{18}}{10^3}$

[ocean seal]

USS-Enterprise

[unkempt robin]

What do you pick

[thorn niche]

10 18 - 10 3 = 10 15

[unkempt robin]

Canceling factors or using the division property for exponents

Ok so the second

Yes

[thorn niche]

2 x 10 15

[unkempt robin]

$\frac{a^m}{a^n} = a^{m-n}$

[ocean seal]

USS-Enterprise

[unkempt robin]

So $2 \cdot \frac{10^{18}}{10^3} = 2 \cdot 10^{18-3} = 2 \cdot 10^{15}$

[ocean seal]

USS-Enterprise

[unkempt robin]

And that's your answer

You could have also gone the other way

[thorn niche]

Okay

[unkempt robin]

What we talked about way back in the beginning

[thorn niche]

Can you please summarise it

[unkempt robin]

Canceling out common factors

You can rewrite 10^3 and 10^18 as multiplication

[thorn niche]

Wait so lets summarise this

8x10 18

divided by 4x10 3

[unkempt robin]

We had $\frac{2 \cdot 10 \cdot 10 \cdot 10 \cdot 10^{15}}{10 \cdot 10 \cdot 10}$

[ocean seal]

USS-Enterprise

[unkempt robin]

And csncel out the three 10s

And you end up with the same answer

[unkempt robin]

Yep

[thorn niche]

So we do 8/4

Which is 2

[unkempt robin]

You write as a fraction

You notice the main operation is multiplication

[thorn niche]

I think i get it

[unkempt robin]

So you are free to cancel whatever you can

So you cancel the common factor of 4 in 8/4

[thorn niche]

i have a question

[unkempt robin]

And end up with just 2 in the numerator and 1 in the denominator (though we don't write 1 in multiplication)

[thorn niche]

ok

[unkempt robin]

Sure

[thorn niche]

ok

So

Would this work for all questions

[unkempt robin]

Then you use the division property of exponents

[thorn niche]

It asks us to divide them bith

So

Do we do 8 divided by 4

And

18 - 3 = 15 so 10 15

[unkempt robin]

Yeah

[thorn niche]

Or is it only a coincidence

Are you sure it works with every question with division

[unkempt robin]

Of course! It depends on what you have to do though

[thorn niche]

Wdym

[unkempt robin]

What we did is called simplifying the fraction

[thorn niche]

ok

[unkempt robin]

Well sometimes you might have addition in there

Or substraction

Or even more division!

[thorn niche]

Can you give an example and we try to solve it

Oh wait I have one

@unkempt robin

Here is an example

[unkempt robin]

Sure thing

[thorn niche]

Ok here

Though its +

But

Wait do i give divide one

uhm

for addition

im pretty sure you do 1.7 + 4.2

then 10 8 + 10 8 which is 10 16

meaning the answer would be 5.9 x 10 16

@unkempt robin is that correct?

[unkempt robin]

Almost

You collect like terms

You add coefficients

10^8 remains the same

Not 10^16

[thorn niche]

Do they only add for multiplication

[umbral portal]

Maybe factor 10^8 out

[unkempt robin]

I doubt they are far enough for factoring yet

It's the same thing

But probably haven't heard of factoring

[unkempt robin]

Yes.

[thorn niche]

So the + one just stays the same?

[unkempt robin]

If we had $2^{9} \cdot 2^{9}$

[ocean seal]

USS-Enterprise

[unkempt robin]

You would add the exponents

$2^{18}$

[ocean seal]

USS-Enterprise

[thorn niche]

ok

[unkempt robin]

This is not the same as addition though

$2^9 + 2^9$

[ocean seal]

USS-Enterprise

[unkempt robin]

This implies multiplication!

Remember what I said before

Powers are multiplication and multiplication is addition

You are adding $a + a$

[ocean seal]

USS-Enterprise

[unkempt robin]

Which is just $2a$

[ocean seal]

USS-Enterprise

[unkempt robin]

So $2 \cdot 2^9$

[ocean seal]

USS-Enterprise

[unkempt robin]

Because you have two times 2^9

Or 2^9 plus 2^9

[thorn niche]

ok

[unkempt robin]

Yeah

So in your case, $1.7 \cdot 10^8 + 4.2 \cdot 10^8$

[ocean seal]

USS-Enterprise

[unkempt robin]

Notice the dot on the bottom are decimals

In the middle it's multiplication

Just means $1.7 \cdot a + 4.2 \cdot a$

[ocean seal]

USS-Enterprise

[unkempt robin]

And you collect like terms (add coefficients)

$5.9 \cdot a$

[ocean seal]

USS-Enterprise

[unkempt robin]

So $5.9 \cdot 10^8$

[ocean seal]

USS-Enterprise

[thorn niche]

ok

[unkempt robin]

Yep

Addition, substraction, multiplication, division all have their own rules 🙂

[thorn niche]

what about subtraction

[unkempt robin]

$1.7 \cdot 10^8 - 4.2 \cdot 10^8$

[ocean seal]

USS-Enterprise

[unkempt robin]

Same thing as addition, you just substract coefficients

So 1.7 - 4.2

$-2.5 \cdot 10^8$

[ocean seal]

USS-Enterprise

[thorn niche]

And thats the answer?

[unkempt robin]

Yes, that's the most simplified answer

You can of course calculate it

[thorn niche]

Wow thats easier than I thought

[unkempt robin]

But I doubt you want -250000000 written as the answer

😄

[thorn niche]

Ye how can u simplify

[thorn niche]

Without getting that 😂

[unkempt robin]

You can't

$-2.5 \cdot 10^8$

[ocean seal]

USS-Enterprise

[unkempt robin]

Is the most you can do

[thorn niche]

ok

.close

[lone heart]

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[manic hearth]

Hello i Need a help in French please

[manic hearth]

@vale crag dsl le sang vrm j’avais plus de Connection a la bibliothèque

[wispy ibex]

[wispy ibex]

Je suis français peut être que je peux aider pas sûr

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[sharp moat]

ا

[sharp moat]

help

i proved that p^p * q^q is bigger than 1 using Jensen theorem on xln(x)

but i cant get the other one to work

[open urchin]

is it possible to prove that p^p*(2-p)^(2-p) is concave

[sharp moat]

which function?

concavity is a property of functions not numbers

[open urchin]

not concave convex

[open urchin]

I meant this as a function of p

[sharp moat]

i think it will be tedious

to prove it convex

[open urchin]

couldn't you just take second derivative

it seems kinda painful but it should be pretty straightforward

[sharp moat]

sure

@open urchin yes its convex

for x between 0 and 2

so what should i do now?

[open urchin]

well once you know that it's convex

you can plug in p=0 and p=2

and see what you can do from there

[sharp moat]

but isnt 0^0 undefined?

[open urchin]

you can take the limit and define it to be 1

[sharp moat]

but how these values will help me?

it's 4 but i dont if the function is increasing or decreasing

[open urchin]

so you got f(0)=f(2)=4

but by definition of convexity

f(x) is under the secant line

[sharp moat]

oh

yeah thats true

thx

.close

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[lucid skiff]

Consider the list: g, f, z, v, x, p. Use insertion sort to sort this list, showing the list you get in every step. (Discrete math)

[alpine sable]

Start by making ur sorted portion

[lucid skiff]

Can you guide me through the process

[alpine sable]

so basically u do it in multiple steps

you parse thru every element

so for example

for the the list 7,4,5,2

step 1: you start at 7, you notice no elements left of 7, so you dont do anything

step 2: you check on 4, you notice one element left of 4 which is 7

as 7>4, 7 will be moved one position forward

so you have 4,7

step 3: you check on 5, the element left of it is 7

and as 7 >5, you move 7 one position forward

to have

4,5,7

step 4: you check on 2, all the elements left of it are greater than it itself

so you move it all the way to the left

so 2,4,5,7

apply the same process to your list but you are expected to make it alphabetically ordered

@lucid skiff

[lucid skiff]

Ohhhhhg

Thank you

[lone heart]

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[crimson crag]

yo

[crimson crag]

when there is a question like

calculate the ratio between a sphere and a cone

how do i know whether to divide sphere/cone or cone/sphere

[wild umbra]

!occupied

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[wild umbra]

between what?

[crimson crag]

like

[wild umbra]

sphere and cone's area? or volume

[crimson crag]

volume

[worn fox]

i would just do it in the order they're written

sphere/cone

[wild umbra]

yes

[crimson crag]

yeah but

does it matter which order

[wild umbra]

yes it matter

[crimson crag]

then how do i know for sure

[wild umbra]

this is right way

[worn fox]

the order theyre written

[crimson crag]

aight

thx

.close

[lone heart]

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[mystic nebula]

how do i solve this

(2x-3)(x-(1-4i))(x-(1+4i))?

do i put an x in front or something?

[alpine sable]

where did 2x-3 come from

[lofty gorge]

multiplicity 2 here means 3 is a root 'twice'

e.g. x^2 has root 0 with multiplicity 2

[mystic nebula]

so squared

[lofty gorge]

basically

[mystic nebula]

(x-3)^2

?

[lofty gorge]

yep

[mystic nebula]

so (x-3)^2)(x-(1-4i))(x-(1+4i))

[lofty gorge]

yep

[mystic nebula]

"Find the polynomial of lowest degree having leading coefficient​ 1,"

[alpine sable]

yes

[mystic nebula]

what does this part mean

[lofty gorge]

it means the coefficient of the highest power

[mystic nebula]

like how does it translate into a number

[lofty gorge]

is 1

[alpine sable]

it means that the 'a_n' in a_n*x^n + .... is 1

[lofty gorge]

in this case there are at least 4 roots, counted with multiplicity, so you need at least a polynomial of degree 4 / a quartic

and the 'lowest' degree bit means choose precisely degree 4

aka don't add any extra roots

[lofty gorge]

so precisely this

[lofty gorge]

and this highest power will then be 4, so make the x^4 coefficient 1

[fickle heath]

which is free because all the x's have coefficient 1

[mystic nebula]

so the significance is that the coefficient for x will be 1?

[fickle heath]

For x^4

[mystic nebula]

because there are four roots

[lone heart]

@mystic nebula Has your question been resolved?

[lone heart]

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[queen sentinel]

did i do this derivative correctly?

[normal pecan]

Is there any numbers than when multiplied gives -32 but also gives -25 when aditioned together?

[normal pecan]

1 sec

[worn fox]

this channel belongs to muody you other two need to get your own channel

[grand gorge]

I don’t have my own

[worn fox]

,w diff (x-5)^(2/3)

[ocean seal]

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Requested by icaird

[normal pecan]

A ) 21,73684211

[worn fox]

wait for one to become available, dont clog someone elses channel

[normal pecan]

B ) 10,56716418

[worn fox]

!nosols

[lone heart]

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.

[queen sentinel]

Is the () unnecessary in the answer?

[worn fox]

in the cube root? yeah its not necessary

[normal pecan]

Man a question is a question....

[queen sentinel]

i mean cube root(x-5)

[grand gorge]

Broooo😂

[queen sentinel]

Alright thank you boss !!!! @worn fox

How do i close this now

[worn fox]

.close

[queen sentinel]

.close

[lone heart]

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[small cypress]

To find the determinant of a 4x4 matrix, do u use solve it like how u would solve it when u find the detrmienant of a 3x3 matrix?

[lone heart]

@small cypress Has your question been resolved?

[remote heron]

3x3 determinant is a sub problem, yea

it generalizes up like you might expect if you had to guess

[small cypress]

wait wdym by this?

[worn fox]

https://en.wikipedia.org/wiki/Laplace_expansion

it works the same way for any size matrix

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[mystic nebula]

got it wrong again

(x-4)^2(x-3+3i)(x-3-3i)

x^2-3x-3ix-3x+9+9i+3ix-9i+9

(x^2-8x+16)(x^2-6x+9)

x^4-6x^3+9x^2-8x^3+48x^2-72x+16x^2-96x+144

x^4-14x^3+73x^2-168x+144

im so mad bruh 😭

why does a single 5 question quiz take me 3 hours to figure out

[fickle heath]

(x-4)^2=x^2??

Did you forget a few terms? nvm, next line has them

[worn fox]

you should be doing it like $x^2 -[(3-3i)(3+3i)]x + (3-3i)(3+3i)$

[ocean seal]

ΣΑCu

[worn fox]

treat the complex numbers as their own entity when you're initially expanding

[mystic nebula]

this looks more confusing

i initially have (x-3+3i)(x-3-3i)

is my expansion correct?

cause it looks way more simple

[worn fox]

youre looking for the word expand

[mystic nebula]

,w expand (x-4)(x-(3+3i)(x-3-3i)

[ocean seal]

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Requested by pom#7134

[mystic nebula]

what confuses it when i ask it to expand?

that's not expanded

[fickle heath]

x-3+3i, not x-(3+3i)

I mean you just have an extra parenthesis

[mystic nebula]

,w expand (x-4)(x-3-3i)(x-3+3i)

okay well this is the correct answer

[fickle heath]

You forgot the ^2

[mystic nebula]

😭

,w expand (x-4)^2(x-3-3i)(x-3+3i)

[ocean seal]

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Requested by pom#7134

[mystic nebula]

what did i do wrong

[fickle heath]

?

That's the answer

[mystic nebula]

why am i not getting the right answer when i expand it

(x-4)^2(x-3+3i)(x-3-3i)
x^2-3x-3ix-3x+9+9i+3ix-9i+9
(x^2-8x+16)(x^2-6x+9)
x^4-6x^3+9x^2-8x^3+48x^2-72x+16x^2-96x+144
x^4-14x^3+73x^2-168x+144

this was my process

[fickle heath]

Why is the second line already expanded?

[mystic nebula]

didnt organize it mb

second line is (x-3+3i)(x-3-3i)

(x-3+3i)(x-3-3i)--->(x^2-8x+16)
(x-4)(x-4)----> (x^2-6x+9)

[fickle heath]

Surely you mean (x-4)(x-4) = (x^2-8x+16) and (x-3+3i)(x-3-3i) = (x^2-6x+9)

[mystic nebula]

sure same thing

[fickle heath]

You missed a 9

[mystic nebula]

= or --->

hm where

[fickle heath]

x^2-3x-3ix-3x+9+9i+3ix-9i+9 = x^2-3x-3x-3ix+3ix+9+9+9i-9i

[mystic nebula]

,w expand (x^2-8x+16)(x^2-6x+18)

[ocean seal]

Results provided by WolframAlpha

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Requested by pom#7134

[mystic nebula]

oh i just missed a 9

[lone heart]

@mystic nebula Has your question been resolved?

[lone heart]

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[teal herald]

for the derivative can i rewrite this sqrt as (f(x))^1/2

[teal herald]

and then power rule chain rule bla bla bla

[fervent timber]

yeah, why not

[teal herald]

gas

.close

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[spark cairn]

I need help with Number c) , any kind of hint for the solution of this problem is appreciated.

Translation:

Consider the set
K:=ℚ[√2]:=ℚ^2, together with the addition and multiplication defined for (x1, y1),(x2, y2) ∈ K
(like in the image)

Then (K, +, ×) is a field. (You don't have to prove this)

c) Define when an Element (x, y) ∈ K is positive (notation (x, y) > 0), such that for all x ∈ ℚ with x ≥ 0

(x, 0) < (0, 1) ⇔ x^2<2

is satisfied and show that your definition is Axiom of order (O.1) is fulfilled.

Hint:
Define √2 as (0, 1) ∈ K and interpret (x, y) as x + y * √2
Important: You must not assume √2 ∈ ℝ as known!

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[spark cairn]

<@&286206848099549185>

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@spark cairn Has your question been resolved?

[half sonnet]

sin^3 x)/(cos x) + (cos^3 x)/(sin x) - 2sin x * cos x = 2 can anyone help me with this?

[lone heart]

@spark cairn Has your question been resolved?

[lone heart]

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[drowsy sedge]

if I have two complex numbers z_1, z_2 is (z1/z2)* = z1*/z2 conjugate, sorry discord formatting is weird and cant put a star there

[vale wigeon]

yes conjugate factors through division as well

[drowsy sedge]

sweet ty

.close

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[lone heart]

@dull tiger Has your question been resolved?

[dull tiger]

<@&286206848099549185> can you please help me?

[storm musk]

What is x if y = 3?

[upper zealot]

Can't you just use y first so u can find x?

[dull tiger]

you need to do derivatives and everything

and then do an equation like (y-y1)=m(x-x1)

[upper zealot]

You can just say
-3+2=0
Put the positive 2 to 0 in negative
-3=0-2
-3=-2
Then you put -3÷-2
It will equal fraction 3over 2

[upper zealot]

Ohh ok got it
Let me think about

[pearl hamlet]

first, write the equation in terms of one variable

you can write it in terms of y so that it is in the form x=

then, take the derivative wrt to y

then, plug in y=3

[dull tiger]

i still cant find the answer

[upper zealot]

Wait I think I got it
Well I think

[pearl hamlet]

go through the steps

did you write the equation in terms of y, so that its in the form x= ?

you want all y on one side and all x on the other side

[dull tiger]

but i already have the value of y

its 3

[pearl hamlet]

no, thats just one possible value of y

you're given the equation -xy-2+x=0, right?

and they want the equation of the lines tangent to that curve AT y=3

y=3 is just a point on this curve

does that make sense

[dull tiger]

....no

im still so confused

[pearl hamlet]

which part

explain

[upper zealot]

Ok here it is

All you need is to swipe the question

Since we have 2 X
We do this
-xy-2+x=0
Do it like this
Y=(x-2) ÷(X)

You can't find the x
You will make x be a x power 2

Then do a fraction of y over x
Equals 2 over X power 2 - 3 over X to the power of two

The answer will be -1 over X power 2
Change the X to the power of two and make it 3 to the power of 2 it will equal negative the fraction 1 over 9

Then make
Y-3= negative fraction 1 over 9
(X-X0)
Where (x-0, y-0)
Is the point of the curve where y=3

Then do
3= the fraction x-2 over x

Simplify it
It will equal
X to the power of 2 - 3X + 6=0

[pearl hamlet]

you didn't find the equation for the tangent lines

[upper zealot]

Just a second

I know my hand writing looks weird

[pearl hamlet]

what is a and b supposed to represent

[upper zealot]

It's the point
You got the square root negative or positive 3

[pearl hamlet]

not sure how you got that

if you plug in y=3 there should just be one corresponding x

[upper zealot]

Just use a
And put the positive square root 3
b
Put the negative square root 3

[pearl hamlet]

huh?

where is this squar root 3 coming fronm

[upper zealot]

Bro I am trying to help here 🥲🥲😭
I am not sure if I said it right

[pearl hamlet]

your answer isn't making much sense

[upper zealot]

My brain stopped working

[pearl hamlet]

what you should do is take the derivative of the function, then plug in the point

[upper zealot]

Oh yeah you right
I think I calculated wrong 😭

Anyway
I was trying my best to help

Although my brain isn't working anymore
(ಥ ͜ʖಥ)

[pearl hamlet]

First, rewrite the equation in terms of $y$: $$ -xy-2+x = 0 \implies x(1-y)=2 \implies x = \frac{2}{1-y}$$

[ocean seal]

Kaiser

[pearl hamlet]

Then, take the derivative w.r.t. $y$: $$\frac{\dd x}{\dd y} = -2(1-y)^{-2} \cdot -1 = \frac{2}{(1-y)^2}$$

[ocean seal]

Kaiser

[pearl hamlet]

Evaluate the derivative at $y=3$: $$\left.\frac{\dd x}{\dd y}\right|_{y=3} = \frac{2}{(1-3)^2} = \frac{1}{2}$$

[ocean seal]

Kaiser

[pearl hamlet]

That gives the slope of the equation w.r.t. y, so we can take the reciprocal to get the slope of the actual function, i.e. $$\left.\frac{\dd y}{\dd x}\right|_{y=3} = 2$$

[ocean seal]

Kaiser

[pearl hamlet]

Now, just use point-slope form to determine the actual equation of the line

@dull tiger@upper zealot make sense?

[upper zealot]

Actually yeah

Bro you are so damn good

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@dull tiger Has your question been resolved?

[lone heart]

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[zenith jasper]

I am given these two functions. After simplifying f(x) = g(x), I get this (2nd pic). From here, how would I go about determining a, so that the two functions would cross the abscissa in the same point?

[storm musk]

The hell is an abscissa

Don't use other channels

[zenith jasper]

the x coordinate

[storm musk]

So you want to find?

a that makes both functions cross each other?

[zenith jasper]

i want to find a, so that the graphs of the functions would cross x at the same point

[pearl hamlet]

if you have two quadratics, they will intersect

so the point of intersection will change based on a

[zenith jasper]

okay but how do i find the value of a for which the graphs of the two functions will cross the x-coordinate at the same point?

[pearl hamlet]

wdym by x-coordinate

if the graphs intersect, thats the same x-coordinate

[zenith jasper]

the x line on a standard graph

[pearl hamlet]

you mean the x-axis?

[zenith jasper]

yeah

[pearl hamlet]

x-coordinate means just the x-point

[zenith jasper]

okay, so the point at which they cross the x-axis is when y = 0, right?

[pearl hamlet]

yes

find where it happens for the equation that doesn't have a in it, and use that to solve for a in the other

[zenith jasper]

right

[zenith jasper]

that was easier than i thought

thanks!

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[meager sable]

is it true that $$\lim_{(x,y) \to (a,b)} f(x,y) = \lim_{y \to b} \left( \lim_{x \to a} f(x,y) \right)$$

[ocean seal]

LemonLime

[hushed locust]

no. that essentially amounts to taking a directional limit

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@meager sable Has your question been resolved?

[lone heart]

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[forest horizon]

im just confused on the bit at the bottom

if someone can help?

[upbeat hornet]

what are you confused about?

[forest horizon]

why you add it to pi

i got the answer as 0.76 pi radians but i dont understand that half line arg etc why you do that

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[pure pagoda]

i cant find anywhere what clicks are or cliques

[lone heart]

Please don't occupy multiple help channels.

[zealous lichen]

I'm no expert but Wikipedia says cliques are sets of vertices that are adjacent to each other

[upbeat hornet]

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[pure pagoda]

if thats the case can u help me

[zealous lichen]

basically count all complete subgraphs

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[empty spade]

idk how to do c

[slow wraith]

I think the equation is $\sqrt{(x-1)^2+(y-4)^2}=y$

[ocean seal]

Louis B

[lone heart]

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.

[slow wraith]

The right part is the distance between A and P

And the left part the distance between P and the x-axis

Oh sorry it's the other way around

[empty spade]

okay yeah that makes sense

thanks!

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[drifting seal]

Math concept question: f:N+ -> N+, does it mean f(x) is not continious?

[exotic canopy]

yes

[drifting seal]

thx

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[severe olive]

Dunno what to do on a question that says
Hence solve x^2+2x-24=0

[exotic canopy]

'hence' implies that you were solving some other question before

[severe olive]

yea

[exotic canopy]

show the full task

[severe olive]

gimme a sec, need to find phone

how u rotate it?

[exotic canopy]

,rotate 180

[severe olive]

i got (x+6)(x-4)

[exotic canopy]

great

what can you conclude from that? what are the solutions?

hint: if $ab=0$, then either $a=0$ or $b=0$

[ocean seal]

artemetra

[severe olive]

x=0?

[exotic canopy]

nope

your a=x+6, and your b=x-4

[severe olive]

ohhhh

so i pop in (x+6) in the 0 spot?

[exotic canopy]

yes

solve x+6=0 and x-4=0

[severe olive]

isnt it just (x+6)

cuz it = 0

[cobalt swallow]

No, you substitute a with x+6

[severe olive]

so x=-6?

[cobalt swallow]

Yes

[exotic canopy]

yes

that's one of the solutions

[severe olive]

ahh right, havent done factorising and that sorta stuff in 3 years, srry

[exotic canopy]

the other one is x-4=0

[severe olive]

so x=4?

[exotic canopy]

yes

here you go

[severe olive]

sick

thank you :D

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[wary nacelle]

Hi I need an explanation / refresher on how the eigenvalues are obtained for this DE problem

[wary nacelle]

I'm not very sure why the eigen values of the DE problem is simply the eigenvalues of the matrix itself

[vague coral]

the eigenvalues are the zeros of the characteristic polynomial

basically you solve this polynomial :
det(A - λI) = 0

where A is your matrix and I the identity matrix

[wary nacelle]

Are we sort of treating the DE as vectors?

[vale crag]

yeah

you're writing a 2nd order equation as 2 linked 1st order equations

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[rancid jay]

why is (1 + (1/∞))^∞ = e?

[golden canyon]

You can't really write an infinity symbol like that

[vale wigeon]

this is bad notation

[ocean seal]

Jelle

[rancid jay]

im sry

[rancid jay]

ig this is more accurate

so why is it?

[vale wigeon]

are you asking why it's a finite number at all, or why it's e specifically?

[echo socket]

(And also mention which definition of e are you using)

[lone heart]

@rancid jay Has your question been resolved?

[rancid jay]

why its specifically e

eulers number

[lone heart]

@rancid jay Has your question been resolved?

[charred jewel]

because thats what the limit of that thing is

[rancid jay]

but how do u get to that

[charred jewel]

you could try plugging in larger and larger numbers into n

and see that it slowly converges to a certain number

[glacial patrol]

Well one answer is that that's literally the definition of $e$

[ocean seal]

992qqoloy

[glacial patrol]

The answer to this question depends on what definition of e you start from

Here are a few of them (well it defines e^x but ye) https://math.stackexchange.com/questions/833962/how-many-different-definitions-of-e-are-there

Includes some proofs relating their equivalences in definition

[rancid jay]

uhm

ok

but idt it includes that proof

[glacial patrol]

It does for one of them

First answer

"$1 \iff 4$"

[ocean seal]

992qqoloy

[lone heart]

@rancid jay Has your question been resolved?

[pallid scarab]

The more usual definition of e is exp(1) where exp is the reciprocal of natural logarithm (log or ln)

[pallid scarab]

so to get back to why this is e

we write $\Big(1+\frac{1}{n}\Big)^n = \exp(n\log\Big(1+\frac{1}{n}\Big))$

[ocean seal]

rafilou2003

[pallid scarab]

if we let x = 1/n

we know that $\frac{\log(1+x)}{x}\longrightarrow 1$ when $x\to 0$

[ocean seal]

rafilou2003

[serene heath]

what grade is this?

[pallid scarab]

(Either l'hôpital, etc...)

[pallid scarab]

can be 12th grade ish or later

[serene heath]

woah thats like a a couple years ahead

[pallid scarab]

so, $\lim_{n\to\infty}\exp(n\log\Big(1+\frac{1}{n}\Big)) = \exp(1) = e$

[ocean seal]

rafilou2003

[pallid scarab]

so our original limit is indeed e

[rancid jay]

oh k

thank u

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[opaque heart]

Question about polynomials and multiplicity, why is this wrong?

[lone heart]

@opaque heart Has your question been resolved?

[lone heart]

@opaque heart Has your question been resolved?

[silver zinc]

v

[lone heart]

@opaque heart Has your question been resolved?

[glacial patrol]

I mean your reasoning of bouncing isn't super rigorous but other than that ur answer is correct so idk

Assuming

Ur allowed to assume poly is of degree 3

If not then maybe that's the problem?

[lone heart]

@opaque heart Has your question been resolved?

[opaque heart]

The problem might be that I'm not assuming degree of 3?

[glacial patrol]

Hmm you technically can't determine the degree of the polynomial from the graph alone, cus it's made up of a finite number of points (the image is made up of pixels, so it's discrete), which means there are technically infinitely many polynomials which fit it

you can say the multiplicity of -2 is even and of 1 is odd ig

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[winter ivy]

can someone help me understand this graph?

[winter ivy]

I understand everythings else

the green one is just a -cosine function but why does it correspond to lamda=1?

[tacit arch]

What do you mean why

Did you plug in lambda=1 into the function y(x)?

[winter ivy]

where do I see I have to plug in lambda=1 and lambda=0?

[tacit arch]

"first two eigenfunctions"

[winter ivy]

right, thanks

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[winter ivy]

.reopen

but @tacit arch would the eigenfunctions always look like this as long as were assuming l=0 and l>0? how would the function change for a different boundary value broblem?

[limpid turret]

This won't work

[winter ivy]

oh ok nevermind then

sorry

[raw kayak]

Hi

[raw kayak]

Quick question

My teacher went to water loo and told me to see these notes and tell me what they mean

[jagged cobalt]

interesting

[jagged cobalt]

lmao

[raw kayak]

Tf this shit even mean

[jagged cobalt]

nice bit oh engineering and physics

[raw kayak]

Physics?

[jagged cobalt]

third picture is physics

second is engineering

in any case, nice

also

[rose pasture]

the first picture expresses sums and products, the second is something with engineering...

[jagged cobalt]

.close

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[rose pasture]

lol

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[waxen turtle]

Idk what to do

[tacit arch]

g(r) = q

That's what "outputs a value q" means

So in your given equation, solve for q

[waxen turtle]

Wat

[waxen turtle]

How

Uhh I think it works if r and q are 2

[tacit arch]

Plugging in random points isn't the goal of the problem

The goal is to use algebra to write q=(...)

,tex .alg lesson

[ocean seal]

riemann

[hot bluff]

is there a list of those commands somewhere? sorry for off-topic.

[waxen turtle]

Uhh

[jagged cobalt]

theyre individual to each user

[waxen turtle]

q=(3/10)r+1.4

Idk

[tacit arch]

Correct

The right side is g(r)

[waxen turtle]

Yay

Ty

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[frosty nest]

I am stuck on 1d, I am confused how to prove whether the divergence is significant or not, and how to use the slutsky elasticity equation

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@frosty nest Has your question been resolved?

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@frosty nest Has your question been resolved?

[frosty nest]

.close

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[summer dirge]

!status

[lone heart]

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

[summer dirge]

1

I don't know how to use the dimension (rank-nullity) theorem here at all

any suggestions?

<@&286206848099549185>

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[steep reef]

How would I go about solving this?

[charred jewel]

sub t = 100 in B(t), then using your result from B(t) and put it in E(B)

[jagged cobalt]

nope

[steep reef]

B(100)=39.1 but idk how to do the derivative of E

wouldnt it just be 0

[jagged cobalt]

dE/dt = dE/dB * dB/t

[charred jewel]

oh rate of decreasing huh

[steep reef]

is that chain rule?

[jagged cobalt]

yeah

[steep reef]

E'(B) = 2(B+1)
B'(t)=2cos(t/10)

right?

[jagged cobalt]

seems so

[steep reef]

how would you deal with the function in E'(B)

[jagged cobalt]

deal with it?

E'(t)=E'(B)*B'(t)

then just sub in your t value

if you mean the B thats still in E'(B) just replace it with B(t)

[steep reef]

would dE/dt be $E'(20sin(10)+50) * 2cos(10)$

[ocean seal]

ycty

[jagged cobalt]

if thats a t/10, then yeah

[steep reef]

oh ok i figured it out

thank you so much!

[jagged cobalt]

no worries

[steep reef]

sorry i was kinda dumb

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[main tapir]

hi i was just wondering how to tackle this question and if anyone could help that would be greatly appreciated

[lone heart]

@main tapir Has your question been resolved?

[main tapir]

<@&286206848099549185>

um hello?

<@&286206848099549185>

[fossil mauve]

Okay so if V is the the speed and T represents time
then 2VT+VT=36
Or 3VT=36 VT=12
And the first bulldozer went 2VT distance or 24 units

[main tapir]

wait but why does 2VT + VT = 36

oh wait

im stupid

sorry

[fossil mauve]

Because the first bulldozer moves twice the speed so it's speed is doubled
And they add up to the total x

[fossil mauve]

It's okay happens all the time

[main tapir]

thanks

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[lone heart]

@hallow light Has your question been resolved?

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@hallow light Has your question been resolved?

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[unkempt birch]

I'm confused why my answer is incorrect

by fundamental theorem of line integrals

it should just be f(B)-f(A)

which is this:

which is equal to 14...

[tacit arch]

,calc (2)(3)(-6)

[ocean seal]

Result:

-36

[unkempt birch]

yeah

i just realized that

lmfao

woops

addition isnt the same as multiplication

im doing this very late at night lol my brain isnt braining

alright thank you

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[limpid spade]

Go touch grass

[unkempt birch]

lmfao

tell them to jump in one place

a couple

thousand

times

[unkempt robin]

Probably can just squeeze them together

Like a sponge you know

Just use my suggestion

😒

Is that how potholes are formed

🤯

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@alpine sable Has your question been resolved?

[full oyster]

ok

[lone heart]

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[wet lagoon]

Help

[wet lagoon]

Whats the formula for range and maximum height cant remember

[shadow wasp]

search it up on internet

[wet lagoon]

I cant find a specific one

can someone possible dhare

[lone heart]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

@wet lagoon Has your question been resolved?

[swift saffron]

Range and height of what

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[errant dagger]

a = prices go up
b = housing will be plentiful
c = housing will be expensive
is it
a => b ∧ c, ~c => b

[errant dagger]

the "but" is throwing me off

[placid zinc]

Better thought of as "and" here

(a → b n c) n (~c → b)

[errant dagger]

i seeeeeeeeeeee okay ok

and then for part b)

a = going to bed
b = going swimming
c = changing clothes

(a ∨ b -> c) ∧ (c -/-> b)

[errant dagger]

is there a not arrow?

[placid zinc]

There is not a not arrow. I like that idea though

[errant dagger]

what would it be then>

would it just be (a ∨ b -> c)

[placid zinc]

a → b is the same as ~a n b

So if we NOT that, we get a u ~b

[errant dagger]

wait why are we notting

are we NOT changing clothe implies going swimming?

[placid zinc]

But tbh you could just leave at as ~(c → b)

[errant dagger]

(a ∨ b -> c) ∧ ~(c → b) ?

woyuld be the ful result

[placid zinc]

Yeah I like it

[errant dagger]

chers

and for part d

would that not just be

c

she will be tired regardles

a = janet wins
b = she is tired

(a → b) ∧ (~a → b)?

[lone heart]

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[lone heart]

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[neat copper]

I’ve been trying to do this question for ages but I can’t figure it out. You’re supposed to use trig identities I’m pretty sure

[charred jewel]

do you know the half angle identity for tan?

[neat copper]

Oh yeah I think so

Is that this?

[charred jewel]

not really

we want tan(A/2) = something

[neat copper]

Oh wow okay I don’t think we ever learnt that

That’s all I need to know, thank you

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[ebon hornet]

12bii

[fickle sandal]

note that $(x+2i)(x-2i)=x^2+4$

[ocean seal]

chlamydia

[ebon hornet]

i know that

but idk how to do this iwth remainder theorem

[mortal trellis]

what does the remainder theorem state

[ebon hornet]

when you sub in a value

the remainder is what you get when you sub that in right?

[mortal trellis]

well more or less

if you divide P(x) by x^2+4, is the remainder a number?

[ebon hornet]

i got 65 so idk

my working was mad wrong

[mortal trellis]

we divide p(x) by x^2+4, we get p(x)=q(x)*(x^2+4)+r(x) where r is our remainder

r is a polynomial of degree <= 1

[ebon hornet]

true

so at least 65 is plausible

[mortal trellis]

well generally speaking pretty unlikely to actually have only degree 0. most of the time it will be degree = 1

but we dont know yet

we know that we can plug in 2i on both sides

if we plug in 2i into x^2+4 we get 0

so p(2i)=r(2i)

and p(-2i)=r(-2i)

yes?

[ebon hornet]

i think so?

[mortal trellis]

what are those two values?

[ebon hornet]

-7 +- 4i

[mortal trellis]

so we know r(x) is a polynomial of degree <= 1 and we know r(2i)=-7+4i and r(-2i)=-7-4i

can you determine r(x) from that information?

[ebon hornet]

2x - 7

[mortal trellis]

yes

[ebon hornet]

holy crap thats so smart

thanks so much mate

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[eager iron]

trigonometry - just making sure i understand this without all the hard math lingo from my uni text book

[eager iron]

i should also mention that i had a 5 year break from math and remember 0 whatsoever

if we have sin(2x) = 1/2

is it correct that what we're really saying is that sin(x) = 1/2 which is 30 degrees

and then we take half of that..?

so 15 degrees?

so instead of pi/6 we get pi/12?

[proven rune]

2x = pi/6
x = pi/12

[eager iron]

and we would also have to calculate the other values so sin(2x) = pi/6 + 2pin

[vale wigeon]

and 5pi/6 + 2pin

[eager iron]

and we just get x = pi/12 + pi * n?

ah yeah that one too sorry

just thinking in the first quadrant to not make this any harder

but is that essentially what we're saying?

[vale wigeon]

if you're thinking periodically you gotta take everything into account ;p

[eager iron]

like what's half the angle (because of the 2) of sin(x) = 1/2?

yes ;D

[vale wigeon]

but yes

u := 2x or whatever

[eager iron]

ok that makes sense then

[vale wigeon]

and then x = u/2

[eager iron]

got it

thank you a ton

actually think im starting to understand this

wishing you an amazing day <33

ok wait last thing

so previously I had a question where sin(3x) = cos(5x)

and i got help with the conversion to say

ah nevermind

figured it out myself

thank you!

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[slow grail]

Can someone help me answer this

Im confused

<@&286206848099549185>

Helooooo

[alpine sable]

hi

[slow grail]

Hiii

[alpine sable]

okay lets first start by making an augmented matrix of this

[slow grail]

Mhm

[alpine sable]

do you know how to

[slow grail]

Yess

[alpine sable]

good good text it

$$\begin{pmatrix}
1 & 2 & 3\
a & b & c\
\end{pmatrix}$$

[ocean seal]

$$\begin{pmatrix}
1 & 2 & 3\\
a & b & c\\
\end{pmatrix}$$

[slow grail]

This is where iv reached

[alpine sable]

okay so you started with

$$\begin{pmatrix}
1 & 2 & -3 & 2\
2 & 3 & 1 & 4\
3 & 4 & 5 & 8
\end{pmatrix}$$

[ocean seal]

okay so you started with 

$$\begin{pmatrix}
1 & 2 & -3 & 2\\
2 & 3 & 1 & 4\\
3 & 4 & 5 & 8
\end{pmatrix}$$

[alpine sable]

did row reduction to end up

1 0 11 0
0 1 -7 0
0 0 0 1

[slow grail]

Precisely

[alpine sable]

you reduced to

$$\begin{pmatrix}
1 & 2 & -3 & 2\
0 & 1 & -7 & 0\
0 & 0 & 0 & 2
\end{pmatrix}$$

can you already identify the pivots here

[slow grail]

No wait

[alpine sable]

dw

this was mine