help-0

[pearl solar]

Finding cube roots

Trying to find a good method for decimal approximations

[wind bane]

newton’s method is a good way to go

[pearl solar]

I want to calculate by hand and would like the method that takes least time

So does newton's method satisfy that

[onyx pawn]

no

[pearl solar]

So would you suggest a better way would you?

[onyx pawn]

range reduction and something ad-hoc for a range probably

[pearl solar]

I request ellaboration

[ionic jewel]

fancy guess and check

[pearl solar]

Should work for one decimal place i guess

[ionic jewel]

it takes at most 4 guesses for a decimal ppace

you can keep going

[pearl solar]

Yeah thanks

[weary hazel]

What would a displacement- time graph look like for a guy walking at a constant speed in a field after jumping off a gate?

[glass lichen]

Depends on where he walks, where 0 is

[glass lichen]

No

[weary hazel]

Help

[glass lichen]

What displacement anyway?

Hor or vertical?

[weary hazel]

Lemme send you the whole question

[glass lichen]

Good idea...

[weary hazel]

11

[glass lichen]

Yeah... poorly phrased imo

Unclear if you include the event of jumping off the gate

But there's 4 portions: 1st walk, pause, 2nd walk, running back

[weary hazel]

?

[glass lichen]

Yes except for the parabolic portion at the front

Cause he wouldn't get that far from the gate if you jump off it

[weary hazel]

So should I make it smaller or eliminate the hell out of that parabolic part?

[glass lichen]

Like.. that displacement would be neglible imo

[weary hazel]

Ohhh

[weary hazel]

Makes sense actually

[glass lichen]

So either an extremely small parabola... or just start the graph a bit further in time

[weary hazel]

Alright

Thanks 🙏

[glass lichen]

Also don't do math in pen

[weary hazel]

Just rough work, no worries

[warped phoenix]

so in the function of f(x) = A * sin(bt) + d

b is always = 2pi/period

how do i figure out the period?

[glass lichen]

Isolate for it

Since you just wrote the eqn for it...

[warped phoenix]

$\frac{2\pi }{p}=A\cdot sin\left(t\right)+d$?

[ocean seal]

TheMane3

[glass lichen]

No.....

b=2pi/P means P=2pi/b

[warped phoenix]

$A\cdot sin\left(\frac{2\pi }{p}:t\right)+d$

[ocean seal]

TheMane3

[warped phoenix]

ok so i have this then

now what 😦

get p by itself?

[glass lichen]

What????

[warped phoenix]

you said b = 2pi/p

so i replaced b with 2pi/p

[glass lichen]

You asked how to solve for P

I told you

Then you posted nonsense

[warped phoenix]

if p = 2pi/b

how do i solve it if idk what b is

[glass lichen]

b was a number in the equation........

[warped phoenix]

im not given b though im supposed to find it

[glass lichen]

.

That b...

[glass lichen]

Ok so then are you given the period....?

[warped phoenix]

this is what im given

[glass lichen]

The period is a year

[warped phoenix]

how would i find the period if it was in some unit other than time then

[glass lichen]

Period is how long something takes....

[warped phoenix]

so should i always just do 4 times x of the maximum point? @glass lichen

the maximum point here is (91.25, 8.2)

and 4*91.25 = 365

[fickle dew]

How can I calculate how likely a 1% event is going to happen after 40 tries?

I'm assuming its not as simple as 1*40 = 40%

[fair vine]

you do it over the reverse - chance it never happens which is 99%^40 and then its 100%- never happening so 100% - 99%^40

[fickle dew]

I see, thank you!

[sterile beacon]

can someone help me with this permutation problem? how do I find t?

[placid zinc]

Consider τ = (1,8,2,9,3,10...) @sterile beacon

[sterile beacon]

what? from where did you got this?

oh

you mapped it

like 1 to 8

2 to 9

[placid zinc]

Honestly from staring for a while. I realized it's impossible to do if you do the two parts separately, so I had to mix them

Actually, do the numbers work out that way?

[sterile beacon]

what do you mean?

[placid zinc]

(1,8,2,9,3,10,4,11,5,12,6,13,7,14

Yeah no it breaks because there's more numbers in the second permutation

[sterile beacon]

yeah...

[placid zinc]

(8,1,9,2,10,3,11,4,12,5,13,6,14,7,15???

Doesn't work either

[sterile beacon]

it has to be a straight solving 😦 it can have multiple solutions from what I understand in my testpaper

[oak chasm]

,w permutation ((1, 5, 2, 6, 3, 7, 4)(8, 13, 9, 14, 10, 15, 11, 16, 12))^2

[sterile beacon]

so.. what do I do with this?

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[placid zinc]

Very nice solution

[sterile beacon]

ok.. but how did you calculated?

[oak chasm]

You have 7 elements in the first one.

You want to add 2 times a certain number and end up adding 1.

[ocean seal]

Chai T. Rex

[oak chasm]

The modular inverse of 2 modulo 7 is 4.

Also, you can do it this way.

• 1 = + 7 + 1 = + 8

So, half of that is 4.

So, you start with 1 and start adding 4.

(1, 5, 2, ...)

Same with the second cycle.

9 long.

• 1 = + 1 + 9 = + 10

So, you add 5.

(8, 13, 9, ...)

[sterile beacon]

so.. If I have 11 on another group of () I just add 1 at the length and do the trick with adding one by one

and map them

[oak chasm]

Adding the length of the cycle doesn't affect anything because it wraps around.

So, if you're adding 1, that's the same as adding 1 + 11 = 12. If you want to do half as much, that's 6.

So, add 6 twice to add 1.

[sterile beacon]

oh, you add half

ok

but, what if it's an odd number ?

like 11

[oak chasm]

Yeah, if you add 11 + 1, it'll go round the cycle once with the 11 and then just add 1.

Then there's no square root.

Hmm, let's see.

You can add n times cycle length plus one to get the same effect as adding one.

This is because each cycle length just wraps around to where you started.

So, if c is the cycle length, 2 | cn + 1

Or replace 2 with whatever root you want.

If c is even, you can't get a square root.

2 | cn + 1
2 | (2a)n + 1
2 | 2an + 1
2b = 2an + 1
2(b - an) = 1
2 | 1
False

[sterile beacon]

oh.. no please no.. this is too much already

if I would have something else on the power of t like t^3 how would I do that? 3x = 1 ( mod 7 ) ?

[oak chasm]

Yes, that's right.

If you want to move 1 in 3 equal steps of length x, then 3x should be 1.

[sterile beacon]

ok, thank you so much for the explanation. You are a great math guy ❤️

[oak chasm]

You're welcome.

[proud eagle]

imagine solving this

[wind bane]

its 57

[solar cradle]

Well the second term is a very famous result so

[wind bane]

i imagined it

i solved it

what now

[solar cradle]

lol

[proud eagle]

innit 69?

[wind bane]

yea

[solar cradle]

yea it is

lol

[wind bane]

i messed up

what now

indian hitler

somebody elses head, thats why it was wrong tbh

[oak chasm]

,w Sum[1/n^2, {n, 1, Infinity}]

[ocean seal]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by Chai T. Rex#7323

[oak chasm]

,w Table[Sum[1/n^k, {n, 1, Infinity}], {k, 2, 10}]

[ocean seal]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by Chai T. Rex#7323

[plush quest]

Ik this is incredibly easy I just forgot how to divide over the summer for some reason.

[oak chasm]

Well, for the first one, dividing is multiplying by the reciprocal.

What's the reciprocal of 9/5?

[plush quest]

I’m back sorry lol

9/5 is 5/9?

[oak chasm]

What's 2 times 5/9?

[plush quest]

Oh 10/18

[oak chasm]

Nope.

[plush quest]

Bruh

[oak chasm]

When you multiply a nonfraction by a fraction.

The nonfraction gets multiplied into the top.

Like multiplying by 2, it should get bigger.

[plush quest]

Yeah, wouldn’t it be 2/1?

[oak chasm]

Yeah, that's right.

[plush quest]

Ok I figured out that part

I just forgot how dividing fractions is different than multiplying them

[oak chasm]

Oh, OK, yeah you just multiply by the reciprocal of the second one.

[plush quest]

The reciprocal is the opposite fraction that is either the numerator or denominator?

[oak chasm]

It's the top and bottom switched.

[plush quest]

Yeah

[oak chasm]

It's the opposite in terms of multiplication.

Like 2/5 times 5/2 (reciprocals of each other) is 1.

[unborn dome]

hey guys is this correct or am i missing a step...

[oak chasm]

@unborn dome Sorry, channel is busy.

[unborn dome]

oh sorry

[plush quest]

So do I flip each of the two fractions of only one?

Like 2/1 and 9/5 or just one

[oak chasm]

Just the one you're dividing by.

The second one.

[plush quest]

K

So the finale answer simplified would be 1 1/9?

[oak chasm]

Yes, that's right.

[gentle phoenix]

This is kind of hard to put into words but;
Is there a formula that can find a number that is a specific percent between two numbers?

For example, 2 and 4.
3 would be 50% in between 2 and 4

[oak chasm]

Yes, you get the distance.

You get a percentage of the distance.

[surreal meadow]

n/2(a+b)? no that makes no sense nvm

[oak chasm]

You add that to the low number.

2 and 4 are 2 apart.

[sudden crypt]

λa + (1-λ)b gets you the lambda-th part between a and b

[gentle phoenix]

Ah I see, thank you

[oak chasm]

30% of that distance is 0.6.

Low number plus 0.6 is 2.6

2.6 is 30% of the way from 2 to 4.

[surreal meadow]

(b-n)/(b-a) i think?

[gentle phoenix]

Got it.

[surreal meadow]

where the range is a to b and the number you want the percentage for is n

[shell drift]

Um i forgot how you can find a percentage of a specific number out of a different number

[surreal meadow]

n% of m = n*m/100

[shell drift]

Uhm lets say i wanna find the percentage 2 out of 7

How do i do that again?

Oh nvm i found it

Yes

Thanks now i remember

[gentle phoenix]

oh I figured out the formula
d= -n(a-b)+a

n is the percent that d will be between a and b
0 is just a,
1 is just b, and anywhere in between is there too, like 0.5 is the midpoint

bruh now i forgot what i was gonna use this for, but thanks for the help lol

[stray pagoda]

I feel like this is really simple but I can't. get it

The last part ^

[surreal meadow]

what function f(x) is its own derivative?

[stray pagoda]

you're not allowed to use that fact

[surreal meadow]

i see

[solar cradle]

Have you tried just using the product and chain rules?

[stray pagoda]

yes, and that worked for the first part of the question

I'm not sure how to use it for the second part

[glass lichen]

well f(a-x)f(x) you know is a constant

[wind bane]

?

a is assumed to be fixed, no?

[glass lichen]

fix it at 0 done

[stray pagoda]

that wouldn't work

omg

what if a = x+y

[wind bane]

there ya go

[stray pagoda]

nah wouldn't work I think

lemme try

[glass lichen]

yes it would

[stray pagoda]

where would you get f(x+y) from in the final expression

[glass lichen]

show that f(a-x)f(x)=f(a)

then a=x+y QED

[stray pagoda]

I have tried doing this to no avail

[glass lichen]

want a hint?

[stray pagoda]

yes please

[glass lichen]

look at your givens/assumptions about f

[stray pagoda]

f(0) = 1

[glass lichen]

yes

so we know f(a-x)f(x) is a constant, c, so show now that c=f(a)

[wind bane]

derivative of f(a-x)f(x) is f(a-x)f(x) - f(a-x)f(x) = 0 by product rule. then f(a-x)f(x) is constant, so f(a-x)f(x) = c for some constant c. then f(a-0)f(0) = f(a) = c, so f(a-x)f(x) = f(a)

[stray pagoda]

GENIUS

THANK YOUUUU

BOTH OF YOU

[glass lichen]

$f(a-x)f(x)=c \ f(a-0)f(0)=c \ f(a)=c \ a=x+y\implies f(y)f(x)=f(x+y)\qed$

[ocean seal]

Mosh

[glass lichen]

there's mine

[surreal sinew]

why does multiplying by the matrix
\begin{bmatrix}
\frac{3}{5} & -\frac{4}{5} \
\frac{4}{5} & \frac{3}{5}
\end{bmatrix}
cause a rotation of $53^\circ?$

i made a typo

[ocean seal]

TheToadSage
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[surreal sinew]

this

[keen jasper]

that's a normalized matrix. try using the arcsin and arccos functions as used in the 2d rotation matrix

[surreal sinew]

could you clarify?

[alpine sable]

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

[wind bane]

because cos(53) = 3/5 and sin(53) = 4/5

[stray pagoda]

well I only have a basic knowledge of linear algebra but the new basis vectors will become (3/5, 4/5) and (-4/5, 3/5). The determinant is 1 so there is no area change. And you will be able to see a right angled triangle. Arctan(4/3) = 53 degrees

[wind bane]

your matrix is a rotation matrix by definition

[keen jasper]

this is the 2d rotation matrix

since you're given the coordinate points (normalized), you can use arcsin and arccos instead

to get the angle

[alpine sable]

it can also be shown with eigenvectors if you already know them

[keen jasper]

for example, X_0,0, is cos(theta). which means, the corresponding value 3/5 is cos(theta)

[surreal sinew]

because $\cos(127) \approx -0.602$ shouldnt the top left be -3/5 and not 3/5?

[ocean seal]

TheToadSage

[surreal sinew]

wait is this in raidans or degrees

[keen jasper]

i mean, they're the same angle anyway

depends on what your calculator takes as input

or what convention you follow

[surreal sinew]

then why does it say -sin(theta) and not just sin(theta) if theyre the same

[keen jasper]

sorry, do you understand why matrix multiplication corresponds to rotation?

[surreal sinew]

yeah kind of

[keen jasper]

let's say you start with the identity matrix

you rotate it by 90 degrees

[surreal sinew]

yeah

[keen jasper]

what are the new coordinates in matrix form?

90 degrees counter clockwise btw

[surreal sinew]

counterclocwise?

kk

\begin{bmatrix}
0 & -1 \
1 & 0
\end{bmatrix}

[keen jasper]

you sure that's correct?

[surreal sinew]

oh i did clockwis

oop

[ocean seal]

TheToadSage
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[surreal sinew]

this should be right?

[keen jasper]

do it counterclockwise. that should explain why it's -sin(theta) and not sin(theta)

yep

[surreal sinew]

also about my previous question yeah i realized my mistake

[keen jasper]

well, the easy way to explain that is

[surreal sinew]

cos is an even function so cos(x)=cos(-x)

[keen jasper]

the value at y axis (1) switches to the x axis

and since it is counter clockwise, the value becomes negative (negative side of the x axis)

[surreal sinew]

yeah i understand why that works

i know matrix multiplication and stuff like that

but i dont understand why this works

[keen jasper]

you know what the trig function represents, right?

sin() represents the y coordinate, and cos() represents the x coordinate

[surreal sinew]

i dont get that

[keen jasper]

put in the theta value of 90 in the rotation matrix, and you'll get this output

[keen jasper]

which part?

[surreal sinew]

this part

[keen jasper]

ah, well, you know the unit circle?

[surreal sinew]

yeah

i know the unit circle and the trig functions on it

just not sure how that applies here

or well, i dont see how it applies outside the unit circle

[keen jasper]

alright. you know what's the 90 degree rotation of the identity matrix is. what happens if you multiply that matrix with another matrix?

[surreal sinew]

i get on the unit circle the x coordinate is cos and the y coordinate is sin

[surreal sinew]

you rotate the matrix 90 degrees

rotate the figure the second matrix represents^

[keen jasper]

it's not bound to the unit circle exactly. it's about the cartesian coordinate system in general

[glass lichen]

note that the canonical basis vectors of R^2 are on the unit circle

[surreal sinew]

i dont know what canonical basis vectors are

this is from a precalc class

[glass lichen]

a thorough explanation of the matrix requires linear algebra

[surreal sinew]

damn

well im reading axler rn but i havent gotten to that part

[alpine sable]

Let’s rotate a point. You know polar coordinates, yes?

[surreal sinew]

yes i do know that

[alpine sable]

Okay! So, every point can be described with an angle and distance, yes?

[surreal sinew]

yep

[alpine sable]

Ach, I have to go, my apologies

[keen jasper]

aight, let's think of this without the matrix

[surreal sinew]

np

[keen jasper]

let's say you have a vector in polar coordinates, which is (1, 45)

[surreal sinew]

yes

[keen jasper]

it's on the unit circle. can you represent it's x and y coordinate with trig functions

[surreal sinew]

yes

so far i understand

[keen jasper]

alright, what if the length was 2 instead of 1. would the same method work?

[surreal sinew]

so polar coordinate (2,45)?

[keen jasper]

try verifying it using the pythagoras theorem

the polar coordinate represents the hypotenuse and the angle. the cartesian coordinate represents the height and the base

so, if you had a vector (1, 45), it's cartesian coordinate would be (1/sqrt(2), 1/sqrt(2))

[surreal sinew]

i get a side length/2

not cos(x)

not sure why the same method hodls

[keen jasper]

ah, well

2 is just a scaled version of 1

if you understand the geometric interpretation of the trig functions, that should make sense

[surreal sinew]

i think i see it now

so its x and y are cos and sin

[keen jasper]

yep

now, what happens if you multiply a matrix by another matrix. it both "rotates" and "scales" the basis vectors

[glass lichen]

The linear algebra approach:
We want to show that rotation by an angle $\theta$ counterclockwise is equivalent to matrix-vector multiplying the point and that matrix.
To find matrix representations of transformations, we note what happens to the basis vectors under the transformation.
$e_1=[1,0]^T$ will be rotated by $\theta$ to the vector $[\cos(\theta),\sin(\theta)]^T$ so we make the first column of the matrix the transformed vector
Repeat for $e_2=[0,1]^T$ and you get the matrix

[ocean seal]

Mosh

[keen jasper]

"unless" the matrix you multiply with is normalized

[glass lichen]

massively condensed but the tl;dr is just find the matrix that represents the transformation of the plane

[keen jasper]

in which case, it only rotates

[surreal sinew]

yeah

@keen jasper i think i get the matrix now, but why can we write 3/5 instead of -3/5 for the top left element?

[keen jasper]

why would you get -3/5?

[surreal sinew]

[cos(127^\circ) \approx -3/5]

[ocean seal]

TheToadSage

[keen jasper]

for sure. you'll get -3/5 if you rotate 127 degrees

[surreal sinew]

yes but then the teacher put 3/5 for the top left entry

[keen jasper]

that means you're not rotating 127 degrees

if the cos() is positive, your angle is either at the first or the fourth quadrant

127 is at the 2nd quadrant

[surreal sinew]

oh ok

so the matrix is for clockwise or counter clockwise btw?

[keen jasper]

counter clockwise, always

[surreal sinew]

ohh ok

[keen jasper]

unless the angle is negative

[surreal sinew]

ok i get it now thanks but just 1 laast question: on our quiz we dont get calculators so how do i compute these without one?

also half my class dosent even know trig so im not sure how we do this on the quiz without a calculator

the teacher opened this problem when she was teaching and then she said "i forgot how to do this but this is the answer"

[keen jasper]

there are ways to approximate trig angles without a calculator, but i don't see why they'd ask such problems without letting you use calculators

[surreal sinew]

yeah

half the class prolly dosent know what sin means so im really confused

the teacher did this problem in the class, but there was no trig in the class and there wasnt really any rotational matrix or anything

so im confused whether or not this will be on the quiz, and if it is then how do i do it without a calc

approximating sin(x) should be possible but im not sure how to approximate the inverse functions

[keen jasper]

you'll only be asked to approximate, not calculate. the value at the top left corresponds with the cos(theta), if it's positive/0, then theta is between -90/270 and 90.. then you check the value at the bottom left, which corresponds to sin(theta). if it's also positive, then theta is in the first quadrant, or [0, 90]. if sin(theta) = cos(theta), then theta is 45 degrees. if sin(theta) > cos(theta), then the angle is >45 degrees and vice versa

[fleet glacier]

cos(x) = 3/5 is relatively well known. However, if your teacher gave you this on a test, that would be extremely uncool

[stray pagoda]

This is very similar to my previous question, but I've tried using that same method and it didn't work. I feel stoopid

I know it's just about getting one right substitution

[jagged raptor]

c(x) = cos(x) and s(x) = sin(x)

are you allowed to use the angle sum formula for cosine or do they want you to prove that

[stray pagoda]

you're not meant to use any properties of trigonometric functions

just the info they give in the question

[jagged raptor]

o

[glass lichen]

it's prove cos(x+y) without using the fact it's cosine and sine, similar to stuff you do with e^x and ln(x)

[stray pagoda]

howww

last time we substituted a = x+y

over here we don't have an a

[ornate rover]

Can anyone help me

[stray pagoda]

occupied

[stray pagoda]

Could you kindly elaborate

[glass lichen]

Ill be honest, no clue how to go about that either

that was just explaining to michael what the goal was

[stray pagoda]

Oh ok

[misty pebble]

I'm working with trig identities. How do I find the exact value of sin(x) if cos(x) = -3/5 and x is in the third quadrant

Would I just use the Pythagorean identity?

[stray pagoda]

That’s what I would do

[ocean seal]

Salah

[warped phoenix]

i was told you can figure out to use cos or sin depending on where the graph starts, if it starts at an extreme, you use cos, if it starts at the midline, you use sin

how did he know how to use cos here tho? the info given doesnt let us know where we start on the graph righr?

unless im just being dumb

[wise sigil]

They start counting from June 21, which is stated to be the maximum at the beginning of the problem

[warped phoenix]

oh ok so its just using the words in the text to see which piece of info came first?

so like if the sentence was "The shortest days in Alaska are about 382.5 mins. long, half a year before the shortest days is the longest day, June 21st, ~1096.5 mins. long."

id still use cos because before that first part of info would be where we begin, which is the max, right? @wise sigil

[wise sigil]

I'm not sure I understand your confusion, the order that the information is given doesn't matter

Like you said: if it starts at an extreme, you use cos

The problem tells you that June 21 is an extreme, and the person writing the solution has chosen to start at June 21. So by your own reasoning, it makes sense to use cosine

[warped phoenix]

we know they start at june 21 because we're only given info for after june 21 and not for before it basically is what you're saying?

[wise sigil]

The person writing the solution starts at June 21 for convenience

[warped phoenix]

ah right because we're not given a specific date for the shortest days, so it makes sense to start where we're given all info

i see

[wise sigil]

You are given a date for the shortest day

But you can't start at both lol

Well, you're given "half a year later" rather than a specific date, so I guess it is a little simpler to start at the maximum rather than the minimum, so yeah you're not wrong

[warped phoenix]

ahhhhh

right

ok

yeah ig im looking to deep into this sorry 😅

ty!!!

[alpine sable]

How do you do a problem like this?

[rigid smelt]

Ratios

Similar shapes imply similar ratio (between corresponding sides)

[alpine sable]

I'm thinking that since in the first one, CB is 2, and CD is 6, that's 2 x 6

so in the bigger one, I should multiply 3.6 by 2

and that will give me x

[surreal meadow]

think ratios

[rigid smelt]

Definitely not

[alpine sable]

oh woops I mean to say by 3

6 is 3 times bigger than 2

[rigid smelt]

Still no

Again try to establish a ratio

[alpine sable]

that is what I am trying to do

I'm looking at the left side

left side is 3x smaller than the top

3:1

[rigid smelt]

So the ratio of the right hand side shape is?

[alpine sable]

it should be the same if they're a consistent ratio

if all that's happen is it's scaled up

[rigid smelt]

Yes

But we could also write it in other terms except than 3:1

[alpine sable]

so x = 3.6 * 3?

[rigid smelt]

Yeah

Oh yeah

[alpine sable]

ah okay that's what I was saying lol

[rigid smelt]

No

[alpine sable]

oh

lol

im confused then

[rigid smelt]

Wrong operation

You have 3:1= x:3.6

Actually nvm, havign brain strokes again

x=3.6 * 3

[alpine sable]

ahk so my first guess was right then

cool, is that what you would have done, or a different method?

[surreal meadow]

the usual way to solve it is side ratios like you did, so 6/2 = x/3.6

[peak gorge]

I need help solving $2e-4 = erfc(sqrt(4\times t \times1e-4))$

[ocean seal]

Speedrow

[jaunty thicket]

what vid is this

i need to learn this topic too

[surreal meadow]

$2e-4 = erfc(\sqrt{4\times t \times e-4})$

[ocean seal]

maximo

[warped phoenix]

https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:trig/x2ec2f6f830c9fb89:sinusoidal-models/v/modeling-periodic-function-with-shift

[jaunty thicket]

thanks

[surreal meadow]

is this it @peak gorge ?

[peak gorge]

Yes

[surreal meadow]

what are you solving for?

[gray isle]

is erfc supposed to be error function or something?

[peak gorge]

Actually, complementary error function

Solving for real t

$erfc(z) = 1-erf(z)$

[ocean seal]

Speedrow

[peak gorge]

Any suggestions?

[high pasture]

What does a determinant of 1 mean in cramer's rule
I think it means that the system of equation will not have a unique solution but i'm not sure

[peak gorge]

Guys, my mistake. It was $2e-4 = erfc(\sqrt{4\times t \times e+4})$

[ocean seal]

Speedrow

[peak gorge]

Nevermind, it's only solvable through computational methods

[alpine sable]

o

[indigo slate]

if we have a simple closed curve $\alpha: [0,2\pi]\to \mathbb R^2, \alpha(t) = (x(t),y(t))$ and we know there is no $t$ such that $y'(t)=y''(t) = 0$. How to show that there exists at least a critical point of index 1 and one of -1. Then further how to show that infact ther number of crit points index 1 is equal to that of index -1

[ocean seal]

barry.

[alpine sable]

i dont want to interrupt but like did u memorise the code thingies

lmao

[indigo slate]

Im thinking take the derivative, $T = (x'(t),y'(t))$ and then $T' = \kappa N$

[ocean seal]

barry.

[indigo slate]

uh its called latex, good typesetting for maths

[alpine sable]

ohh

ok

[indigo slate]

then a critical point is at $\kappa = 0$ and like use EVT to say that $\kappa$ obtains both a max and a min on $[0,2\pi]$

[ocean seal]

barry.

[lone wraith]

How do i find E[(a.b),k] when I know the vertices of ABC and A'B'C'?

How?

Is there a formula?

[marble yarrow]

@elfin fern

[marble yarrow]

that’s so easy

[alpine sable]

@elfin fern @marble yarrow Hey lol

[marble yarrow]

buy me v bucks

tryna get arina grande skin😩

[low topaz]

If sine is the opposite side over the hypotenuse, what is arcsine

[marble yarrow]

she got a fattie

[marble yarrow]

20

[lone wraith]

...

[marble yarrow]

dummy bruh

[low topaz]

No its 5

[marble yarrow]

it clearly y=xy+b

[wind bane]

bro down bad 💀

[marble yarrow]

aye bro got to see it through

no shame in my game

[wind bane]

dawg

pause??

[marble yarrow]

no it’s 20

[keen jewel]

Forgot the s in the beginning

[low topaz]

NO ITS 5

[marble yarrow]

he packing i alr saw

[marble yarrow]

NO 20

[wind bane]

sheesh

[wind bane]

you wasn't lying tho

[alpine sable]

Uhhhhhhhhhh

[low topaz]

No its 5

[marble yarrow]

@low topaz u a girl

[low topaz]

Yes why

[marble yarrow]

u tryna tutor me

i’m failing math

[alpine sable]

Tryna find what does (2747388264+27479268)-(2695x375926)-2649572+2649562) is

[low topaz]

No its 5

5

[marble yarrow]

my tutor @low topaz can help u

[low topaz]

5

[wind bane]

,w (2747388264+27479268)-(2695x375926)-2649572+2649562

[alpine sable]

[marble yarrow]

@low topaz ignoring me🤧

[low topaz]

5

[marble yarrow]

be my tutor and it’s 20 btw

[ocean seal]

Results provided by WolframAlpha

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

Requested by coycoy#4831

[low topaz]

Ok

[marble yarrow]

add me

u can tutor me

pls

[wind bane]

what does this mean tho?

[low topaz]

15

[wind bane]

i mean, hinata is obviously a waifu, but the pillow itself is aight tbh

[low topaz]

Looks like a bed

O

K

[peak kite]

Um

ㅤ

ㅤ

ㅤ

ㅤ

ㅤ

[low topaz]

Ok

[peak kite]

Hmm

[wind bane]

sir?

[alpine sable]

i need help

[wind bane]

so does nana.kai

[alpine sable]

oh

[wind bane]

that was kind of a joke, but kind of not.
anyway, just ask

[low topaz]

Why

[alpine sable]

how do i find the TSA of a triangualr prism?

[low topaz]

Do math

[wind bane]

what is TSA

[alpine sable]

total surface area

[low topaz]

Do math

[alpine sable]

😐

[low topaz]

https://www.desmos.com/scientific

[wind bane]

it depends on what initial information you are given

[low topaz]

Same

[dense blaze]

i find the idea of vacuously true statements very counterintuitive and mind boggling i dont get why if the condition is false, whatever the hypothesis is, the statement is always true

eg. If the moon is made of barbecue and spare ribs, then I'm smarter than Ramanujan.

This is vacuously true; that is, logically it is true, but it really doesn't mean anything. The moon is obviously not made of barbecue and spare ribs; thus, whatever statement I have is true in no meaningful way (i.e., the statement is vacuously true). like i cant really grasp what this means, jus cuz its insignificant/ trivial doesnt mean it's true?

[low topaz]

The moon is made of ribs

[placid zinc]

So note that a mathematical definition of "true" doesn't need to match your preconceived notion of "true". In math, a statement is true unless a counter-example exists.

So, unless you can find me a moon made of bbq, and show me that you're not as smart as Ramanujan, that's a true statement

(I think it would be hard to prove there's no bbq moon though)

.
Yeah, this isn't how we often use "true" in normal life, but it does work in math.

[alpine sable]

.

[low topaz]

.

[dense blaze]

oh i see then for the example
if 1 = 0, then 1 = 1,
here, we can prove that 1 =/= 0, and 1 = 1 but it's still vacuously true

if 1 = 0, then 1 = 2, it's also true i think base on the truth table

[dense blaze]

sry i jus copied a random eg. on the web lol

[placid zinc]

Find me an example where 1 ≠ 0, and 1 = 1.
Since you know we can't, the statement is true

[low topaz]

No, the moon is made of ribs

[dense blaze]

wait im very confuse do u have like an analogy

i dont rly get wdym by we can't

[placid zinc]

Specifically, A → B is true unless there's an example where A is false, and B is true

A good example is the empty set:
If A is empty, then every element in it is a number.

Want to prove me wrong? Find me an element in A that isn't a number

That's right you can't

[dense blaze]

like what if we can find an example A is false and B is true, would it still be vacuously true? by an example, do u mean like if A is glass can't break, then i show u that i can break glass (sry very non mathematical)

[placid zinc]

No it wouldn't be. It would be false.

The big deal is that a statement is true if no examples exist. That's a vacuous truth

[dense blaze]

so this is true? cuz there's nothing in A to prove u wrong

[placid zinc]

If a moon is made of cheese, then it's also edible

If you want to prove me wrong, you must first find a moon made of cheese

[dense blaze]

this is false right? cuz man can test the substance of moon to prove it's not cheese

[dense blaze]

wait find whether a moon is made of cheese or not cheese

[placid zinc]

I didn't say that any moons are made of cheese. I said that if one is, then it is edible

[dense blaze]

oh

[placid zinc]

If you think the statement is false, you need a counter example. That is, you need to prove there exists a moon that is made of cheese, but isn't edible

Since that obviously can't happen, the statement is true

[dense blaze]

ahh okk

i see

[placid zinc]

(I'm assuming no moons out there are actually made of cheese)

[dense blaze]

wait but i feel like ive seen eg. that even tho the hypothesis can be proven false, it's still vacuously true

if sun rises in the north then everyone gets 100 percent in final exam, is a true statement since the proposition "sun rises in the north" is false

like we can prove that the sun doesn't rise in the north

[placid zinc]

Give me an example where the sun rises in the North, and someone didn't get 100%

Since that has never happened, this statement is not false

[dense blaze]

there's no example where the sun rises in the north so can we prove that's false?

and lets say for a test, everyone got 100% so it's true

[dark granite]

if the antecedent of an implication is false, the whole implication is true because implications are really about when the antecedent is true, so if it (the antecedent) were ever false, that would be besides the point and we can just say the conditional statement (i.e., the whole implication) still holds

[placid zinc]

You're answering something I didn't ask haha

[haughty falcon]

One message removed from a suspended account.

[dark granite]

This channel is busy

please go somewhere else @haughty falcon

[haughty falcon]

One message removed from a suspended account.

[haughty falcon]

One message removed from a suspended account.

[dense blaze]

so is it correct to say that the definition of a true if-then statement isnt for the hypothesis to lead to the same conclusion? like idk how to phrase it what does true even mean if the hypothesis (false) leads to a different conclusion (true) (which is false in our everyday definition) but it is still technically true

[dark granite]

that first sentence you asked "so is it correct to say...?" doesn't make sense. Could you rephrase?

If you're having trouble seeing how this makes sense from a straight up english perspective, think about truth tables. p implies q is true iff p is false or q is true. So you see that if p is false, (~p or q) is true (regardless of q's truth value). So, by logical equivalence, p implies q must be true (regardless of q's truth value).

[dense blaze]

cuz instinctively i take a if-then statement to be true if the hypothesis leads to the same conclusion

eg. if something is true then implies something is true, it is true
or

if something is false then implies something is false, it is true cuz the hypothesis and conclusion is the same

but now i learn that is wrong in math, where if a condition is false that implies a true conclusion, would still be considered true

[dark granite]

I need to be honest @dense blaze . I'm completely lost with what you're saying.

[dense blaze]

yeap i understand this
we can rephrase if p implies q, to either ~p or q, and if p is false, yeah ~p or q is always true

[dense blaze]

uhh sry i think it's not vv important what i previously thought, cuz it was wrong

[dark granite]

okay, no apology necessary.

my advice then would be to stick with truth tables

[dense blaze]

yup i think so too, i think using common sense/ english method doesn't work for me. so i'll do it with truth tables

thankss

[dark granite]

you're welcome

[jade flame]

Help..am stuck with this

There are 10 students in a class, all with different heights. They want to form a queue so that no person stands directly between two people shorter than them. How many ways are there to form the queue?

[alpine sable]

pls help with integration of this one

[rigid smelt]

See that cos(x) is a common factor

Try to factor it out

Then you will see a verry nice substitution

[zealous fractal]

having trouble with this one...

[wind bane]

do you know what the discriminant is?

[zealous fractal]

nope

[ocean seal]

logician

[zealous fractal]

ohhhh yeahh yeah

so you would just put the value in there and solve for m?

[wind bane]

well, first observation, can you see why m must be less than zero?

[zealous fractal]

yea

[wind bane]

ok, so factoring out an m, we require that

mx^2 + 3x - 4 = m(x^2 + (3/m)x - (4/m)) < 0

we already know that m < 0, so we must have that the expression x^2 + (3/m)x - (4/m) be greater than zero

is that much clear?

[zealous fractal]

ohhh yeahh thanks you soo much

i forgot about the discriminant i started doing the full quadratic equation then yeah i was soo clueless

[wind bane]

lol. so just to finish, ||you need m < 0 such that the discriminant of x^2 + (3/m)x - (4/m) is always negative||

[zealous fractal]

yeah thank you soo much!!!!!!!!!!!!!!!!

[gray isle]

there was no need to factor / divide m out

[wind bane]

good point, dont know why i did that

[shut tartan]

@gray islecan u help me

[gray isle]

#❓how-to-get-help

don't randomly ping people

[shut tartan]

i have an equation of 12x^2-560x-2000=0

i cant factor it out becasue 12 dosent divide into a whole number with 560 or 2000

[ionic jewel]

if ur ever unsure

quadratic eqn

[gray isle]

12 isn't the only integer factor of 12

[shut tartan]

can i show u guys a pic of my work so far?

[gray isle]

that would be ideal

[wind bane]

,rccw

[alpine sable]

thank u uwu

[gray isle]

i thought you meant your attempt at solving the equation you posted

[rigid smelt]

btw factor out cos^2(x) (referring to arcilla)

its easier

[woeful pulsar]

can apply quadratic formula directly, or factor out the common factor first then apply

[shut tartan]

oh so the common factor is 10 not 12?

[gray isle]

no

10 is not an integer factor of 12

[woeful pulsar]

@shut tartan what is the largest common factor of 12, 560, 2000

[gray isle]

or just a common factor would suffice,
and keep going if needed

[shut tartan]

i dont know

[gray isle]

any common factor

you do notice that they're all even numbers right?

[shut tartan]

yeah i do

[high pasture]

What does a determinant of 1 mean in cramer's rule
I think it means that the system of equation will not have a unique solution but i'm not sure

[gray isle]

so what does that tell you about a common factor that they all have?

[shut tartan]

its an even number im guessing

[gray isle]

don't overthing this

all even numbers have "this number" as a factor

(other than 1)

[wind bane]

why are we dealing with common factors tho, this is irrelevant to the problem

[gray isle]

its very relevant

[shut tartan]

its 4 lol

[woeful pulsar]

yeah, so you can simply divide by it

[gray isle]

factorisation can help with reducing the values in the question leading to less tedious calculations

[fleet pollen]

is the calculus and vectors and vector calculus the same ?

[shut tartan]

4 would be the greatest common factor ?

[gray isle]

yes.

4 would be the gcd here

[shut tartan]

i then have to find 2 numbers that when multiplied get -50 and when added equels to -140

[woeful pulsar]

no that doesn't work

[shut tartan]

i mean -500

[woeful pulsar]

that only works when the leading coefficient is 1

[gray isle]

you could use something similar like the ac + splitting/grouping method

[woeful pulsar]

yeah but i think i'll probably just do quadratic formula and not spend time factorising too much

these numbers are biggg

[gray isle]

i.e. find two numbers that multiply to ac = 3 * -500 = -1500
and sum to b = -140

which isn't actually that bad

[shut tartan]

i havnt learned that i have to do guess and check

is thier even 2 numbers that do that?

[woeful pulsar]

there are, try guessing them

[shut tartan]

just tell me please i cant do it

ill do the rest myself after

[woeful pulsar]

worst case just apply the quadratic formula if you are stuck

[gray isle]

look for a factor of -1500 relatively close to -140

[shut tartan]

i found 25x20 but it dosent add to 140

[gray isle]

20*25 doesn't multiply to -1500

[shut tartan]

no i meant -500

2000/4 is 500

[woeful pulsar]

you need to do -1500 because there is a leading coefficient which is not 1

[gray isle]

read our recent comments

[shut tartan]

im doing rational equations

[gray isle]

we know

well quadratic to be exact

[shut tartan]

im stuck my brain hurts rn

[gray isle]

did you read my comment earlier?

[shut tartan]

this one?

[gray isle]

yes

[shut tartan]

yes but how do i put my equation on the formula

[gray isle]

wdym

were you able to first find two numbers satisfying that property?

[shut tartan]

no

[gray isle]

look for a factor of -1500 relatively close to -140

[shut tartan]

i really dont know

[gray isle]

can you identify any obvious factors of -1500

[shut tartan]

-100

[gray isle]

any others?

[shut tartan]

-1, -2, -3, -4, -5, -6, -10, -12, -15, -20, -25, -30, -50, -60, -75, -100, -125, -150, -250, -300, -375, -500, -750, -1500

[gray isle]

one of those is very close to -140

[shut tartan]

-125

[gray isle]

there's something closer that is more useful

[shut tartan]

-150?

[gray isle]

yes

-150 * 10 = -1500

and -150 + 10 = -140
which is what you wanted

applying that you can manipulate your equation to:
$$(3x^2 - 150x) + (10x - 500) = 0$$

[ocean seal]

ℝamonov

[gray isle]

and factorise by grouping

[shut tartan]

Janet sells books for a living. She bought boxes of the first Harry Potter book for $400. She gave 5 away to friends and sold the rest for $900. If she made a profit of $12 per book, how many books did Janet purchase?

heres the full question

so if my math is right she bought 50 books?

[gray isle]

yes

[woeful pulsar]

teach me your ways (honestly i never learnt this trick before)

[gray isle]

ac method

oh the finding part?

that's mainly intuition based on the values present in this specific question

[woeful pulsar]

oh lol i thought it's just magic observation but i see you manage to phrase it quite well

[dawn galleon]

<@&286206848099549185>

how will i start

[rigid smelt]

please ping after a minimum of 15min

and start by finding what f''(x) is

[dawn galleon]

🆗

[dawn galleon]

replace x with -1 and thn work it out
basically
(-1-3)(-1^2 + 1)
(-4)(2) = -8

like that

[rigid smelt]

uh definitely no

and not what i suggested

i suggested finding what f''(x) is

not what f(-1) is

do you know what f''(x) represent?

[dawn galleon]

no why i wrong

[rigid smelt]

i suppose this part of the conversation is invisible to you

so lemme explain it again

its wrong because its not what i suggested
i suggested finding what f''(x) is
not what f(-1) is
do you know what f''(x) represent?

[dawn galleon]

oh ye u dont get -8

[dawn galleon]

ima do it again 1 min

[dawn galleon]

f(x)= (x-3)(x^2+1) expanding
= x^3 -3x^2 +3 -3
then you can differentiate twice and then sub x=-1
= -12

[rigid smelt]

= x^3 -3x^2 +3 -3
this is not expanded correctly

[dawn galleon]

oh

[rigid smelt]

tho i suppose that might have been a typo

[dawn galleon]

ye ill fix it tho did u get the same answer as mine

[rigid smelt]

idk, lemme see

[gaunt magnet]

hi

[rigid smelt]

yes -12 is correct

[gaunt magnet]

<@&268886789983436800> i cant change my name why?

[dawn galleon]

ty

[rigid smelt]

,rotate

[rigid smelt]

hmmm tricky

[solemn oar]

Yea actually I m having problem with that denominator

[rigid smelt]

first impression was to probably take some logarithm, but that wont simplify anything

[wind bane]

$\frac{a^x-1}{\log_a(x+1)}=\frac{a^x-1}{x}\cdot\frac{x}{\log_a(x+1)}$ and $\lim_{x\to 0}\frac{a^x-1}{x}=\frac{d}{dx}a^x\bigg|_{x=0}$

[ocean seal]

c squared

[rigid smelt]

ah

[wind bane]

the latter limit should be easier to deal with

just lhopital

[rigid smelt]

wait if you are goign to do l'hopital anyway then you might just as well do that from the beginning

[wind bane]

yea but its gross from the beginning imo

[rigid smelt]

tho the second limit seems doable without l'hopital

[wind bane]

it does, i just didnt feel like thinking about it lol

[solemn oar]

Also I have a little doubt
How can we say that l hospital is applicable in this?
Sorry I m bit confused

[rigid smelt]

indeterminate form 0/0

but i will want to stay away from l'hopital

[solemn oar]

Yea but we have a constant a? In log

[wind bane]

second limit is doable without lhopitals and converges to ln(a)

[rigid smelt]

log_a(1) is 0 for any a in (0, infty)/{1}

[wind bane]

log_a(x) = ln(x)/ln(a)

[solemn oar]

Ohhh thankss this was actually my problem

[solemn oar]

Thanks a lot

Also I have its solution can u guys explain me the solution?

I was a bit confused with how the denominator is expanded

[wind bane]

oh yea thats what i was just about to type up

[solemn oar]

Yeaa can u explain me the denominator part

[rigid smelt]

actually dont we already know ln(x+1)/x as x tends to 0 equals 1?

[wind bane]

its because $\frac{a}{b}=\frac{a\cdot\frac{1}{c}}{b\cdot\frac{1}{c}}$

[ocean seal]

c squared

[rigid smelt]

thats how you should do the second limit then

[wind bane]

it is the derivative of ln(x+1) at x = 0

[rigid smelt]

yeah

or basically

[wind bane]

just some sneaky derivatives in here

[rigid smelt]

eulers number limit definition but in different terms

[wind bane]

hrm...

[rigid smelt]

just saying, because i would want to stay away from l'hopitals

[solemn oar]

Can u show how to apply this in the equation sorry I m a beginner

[wind bane]

lol whats wrong with lhopitals

[rigid smelt]

i mean why rely on it lol, we can do it without that

i just dont want to be so dependent on it

[wind bane]

#free-me-from-the-l'hopital

[solemn oar]

Can u guys send me detailed solution
I really want to get this question I m still a bit in confusion with that log expansion

[wind bane]

do you agree that for any non-zero x, we have x/x = 1?

[solemn oar]

Yes

[wind bane]

this is just an application of this. $\frac{a}{b}=\frac{a}{b}\cdot 1=\frac{a}{b}\cdot\frac{x}{x}$ for any non-zero $x$.

[ocean seal]

c squared

[solemn oar]

Yess but how to apply it in the equation?

[wind bane]

in this picture, they just said, here, watch this:
$\frac{a^x-1}{\log_a(x+1)}=\frac{a^x-1}{\log_a(x+1)}\cdot 1=\frac{a^x-1}{\log_a(x+1)}\cdot\frac{(1/x)}{(1/x)}=\frac{\frac{a^x-1}{x}}{\frac{\log_a(x+1)}{x}}$

[ocean seal]

c squared

[solemn oar]

Yess

I GOT I GOT

YAYY

[wind bane]

YAYY!!!

[solemn oar]

I applied the series expansion to

Ln(x+1)

[wind bane]

wha... why you dont need it

but okay it works YAY

[solemn oar]

Wait I still didnt get 😭
Tho it was helpful but I m stuck with that ln(1+x).loga e/x expansion

[wind bane]

latex is an art form, my child

[solemn oar]

If I do the series expansion

Then the x and ln(1+x) can be eliminated to get logae

[rigid smelt]

you can evaluate ln(1+x)/x using the famous euler's number limit

[wind bane]

not sure which one you're thinking of lol

[solemn oar]

Yeaa I think its series expansion??

[rigid smelt]

well that can be rewritten as ln((1+x)^(1/x))

and then assuming the limit exists

or the function is continuous at x=0

you can bring the limit inside

and (1+x)^(1/x) as x tends to 0 is kind of recognisable imo

[solemn oar]

The solution u gave has gone c squared I wasnt able to look

[wind bane]

didnt want to interrupt waler's explanation

but i accidentally did

[rigid smelt]

im done, go ahead :)

[wind bane]

what do you think of this:
$$\lim_{x\to 0}\frac{\ln(x+1)}{x}=\lim_{x\to 0}\frac{\ln(x+1)-\ln(0+1)}{x-0}=\frac{d}{dx}\ln(x+1)\bigg|_{x=0}=1$$

[ocean seal]

c squared

[solemn oar]

The bot is not showing the picture is it broken

[wind bane]

i dont think so; its showing up for me

[solemn oar]

Yes now its showing

[solemn oar]

Yess I did this with series expansion as ln(1+x)= x-x^2/2+x^3/3-.......infinity
We will take x common and
We can cancel the x in num and denominator so in numerator we will be left with 1 - terms of x which will get zero
Hence answer is one

I got this part

I wanted to know where that log base a^e came from

[wind bane]

do you mean log_a(e)?

[solemn oar]

Yes yes

Log_a(e) in denominator

[wind bane]

because $\log_a(b)\log_b(c) = \log_a(c)$

[ocean seal]

c squared

[solemn oar]

Thankssssss

Nowwww I got the solution

[wind bane]

take $a=a, b=e, \text{ and } c=x+1$

[ocean seal]

c squared

[solemn oar]

I wasnt able to remember this property of log
Phew thanks a lot sir 😁

[wind bane]

np

[wind bane]

what have u tried?

[dawn galleon]

,w derivative (-x+2x^2) (x-6) wrt x

[ocean seal]

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[wind bane]

well, thats one way

[dawn galleon]

,w z=36t^2 - 12t + 14, t = 3

[ocean seal]

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[dawn galleon]

do u get 302 that what i did

[thorn kindle]

,w d^2/dt^2 3t4 - 2t3 + 7t2 + t - 2

[ocean seal]

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[narrow elm]

Why does the sin(t) turn to one?

[woeful pulsar]

it's integration by substitution, do you understand how it works?

[narrow elm]

Wait, you need to differentiate the part your substituting or something?

[sage bronze]

$$\int \frac {\sin t} { 1 - \cos t} dt$$ Let u = $1 - \cos t$ $$u = 1 - \cos t \implies \frac {du}{dt} = \sin t$$ Therefore, the integral becomes - $$ \int \frac {\frac {du}{dt}}{u} dt = \int \frac {du}{u}$$

[ocean seal]

HELLOBELLO

[woeful pulsar]

integration by substitution is like chain rule

[narrow elm]

Yea I got it, just confusing cause yea maths

[woeful pulsar]

think about what differentiating ln (1-cos(t)) gets you

[hollow quarry]

Why do you guys use weird symbols for math?
Like * and ^

[hollow swift]

Can anyone helps me this question?

[placid zinc]

Vieta comes to mind. Possible to do here?

Pain to expand all of it

Actually, fairly sure the sum is 0

[strong carbon]

What I thought was that we won't get x^20 and x^19 on the other side

[placid zinc]

Yeah if no x^19 appears anywhere, the answer is 0. Any way to easily justify that?

[hollow swift]

I try to solve with Vieta but I can’t.

[placid zinc]

Let a20 be the coefficient on x²⁰ of the simplified polynomial

Let a19 be the coefficient on x¹⁹ of the simplified polynomial

Sum of all roots is -a19 / a20

I'm thinking a19 = 0. So sum of all roots = 0

[hollow swift]

Oh I think so

[placid zinc]

Doesn't seem like any x¹⁹ comes out anywhere.

[hollow swift]

I have another problems that I can’t solve

[stray pagoda]

Just a reminder as this still hasn't been solved

[hollow swift]

👀

[ivory otter]

How do i integrate x^-1

is this correct?

[gray isle]

no

i don't understand your work

[ivory otter]

x^-1 = 1/x

so i just used 1/x

1/(1/x) = 1/x

[gray isle]

1/(1/x) is not 1/x

[ivory otter]

wait

then idk

[gray isle]

it looks like you're making some attempt to apply power rule to integrate this,|
(note that power rule can't actually be used here)
while also inappropriately using = signs

[ivory otter]

ok

[gray isle]

if you've done derivatives before, you should recognise the integral

[ivory otter]

i have done ye

[gray isle]

$\int x^{-1} \dd{x} = \ln|x| + c$

[ocean seal]

ℝamonov

[ivory otter]

hmm ok

but if i apply

x^n formula

to this i cant

so am i just supposed to know its ln x ?

[gray isle]

yes

[ivory otter]

ah ok

[gray isle]

ln**|x|** specifically, not just ln(x)

[ivory otter]

oh ok

thank you

[ivory otter]

so im confused

[golden falcon]

You technically can derive it, but it's easier to just remember it because it's very common.

[narrow elm]

For my maths course we have that integral on the a formula sheet

[ivory otter]

oh i see

So look at that rule

im confused because

doesnt integral of 5x fit to that?

like lets say i have

[glad aspen]

speaking of integrals, why is the integral of y'/y = log(y)?

[ivory otter]

confused on how to work with rule 3 here

[golden falcon]

just apply linearity and split it into two integrals, throw a constant outside the integral and finally integrate it

[ivory otter]

like this?

[placid zinc]

You're thinking backwards. What's the derivative of ln(y), taken in terms of x?

Also note that you can get that integral with u-sub. But the derivative thing is much more enlightening

[golden falcon]

because you can substitute $u = y(t)$, which gives you $du = y'dt $ and get $\int{\frac{y'dt}{y}} = \int{\frac{du}{u}} = \ln{u} + C = \ln(y(t)) + C$. That's essentially because of invariance of the first differential.

[ocean seal]

Dmytr

[golden falcon]

Don't forget the arbitrary constant C(or whatever letter you like) and it'll be just fine

[ivory otter]

ah shit ye, this is supposed to be a definite integral forgot to add it

forgot to add the limits

[golden falcon]

oh, then, assuming you substituted the boundaries, it's good

[ivory otter]

cool! thank you

[delicate tinsel]

Can someone tell me how to approach this question? thanks!

[alpine sable]

have you had any thoughts on how to tackle it?

[delicate tinsel]

i tried rationalising it but realise it wouldn't work

can you give me like a hint?

[alpine sable]

consider factoring a x^(1/5) or an x^(1/3) and see if you are able to continue from there.

[delicate tinsel]

hey, I managed to get it. Thanks for the hint!

I just realised you could divide by x^1/3 for both numerator and denominator. thanks anyway!

[young tendon]

how would you do (37 + z) times (11 + x) or any question with this sort of arrangment

[gray isle]

are you familiar with the distributive property?

[young tendon]

which on is that one

is that one like 2x ( 3x + 4) = 4x*2 + 8x

[young tendon]

not sure if i did that right

[gray isle]

not quite

a(b+c) = ab + ac

[young tendon]

yeah thats the one i was thinking

how would you apply it to (37 + z) times (11 + x)

[gray isle]

same idea

[young tendon]

so would it be that but double

[gray isle]

you could treat one of the expressions in parentheses as your a

[young tendon]

like 37 ( 11 + x)

then z ( 11 +x)

[gray isle]

with a + in between

[young tendon]

i see

so it'd look like

[gray isle]

=37(11+x) + z(11+x)
and expand further

[young tendon]

alright i get it now

thanks

hey

if you are there

could you tell me what these rules mean

and by rules its stuff like

C standard:

1. introduction to index notation teminology (can idetify base and power)

i dont exactly understand what they all mean and would like to know

[woeful pulsar]

usually we write powers using ^

[young tendon]

how do you get that symbol on a keyboard?

[woeful pulsar]

shift 6