help-39

[faint onyx]

theres many

scenarios

u could get a different head/tail at the n-1th try

or the 3rd try

[rustic gate]

X_ij tells you to add 1 to the total tally

[faint onyx]

so we need to sum up all these to get the expected value

[rustic gate]

well not try but like

pairs of tries

like

X_46 is if the 4th and 6th try match

[faint onyx]

wait

oh

right

wait i didnt even realise were throwing 2 coins

wait no

were throwing one

[rustic gate]

we're throwing a coin multiple times

it doesn't really matter if it's the same coin or multiple coins

there are just many coin tosses happening

ordered from 1 to n

[faint onyx]

oh so like

lets say

throw 1: heads

throw 2: tail
throw 3: tail
throw 4: heads

we wanna find out if throw 1 = throw 3 for example

so X_13 = 0

cuz theyre different

[rustic gate]

yes

[faint onyx]

OH

[rustic gate]

it's just a true/false value

[faint onyx]

so we define X_ij first

then P(X_ij) = 1/2

[rustic gate]

well X_ij is a random variable

[faint onyx]

because of the probability tree

[rustic gate]

so like

its value depends on the world state

[faint onyx]

whats tyat

[rustic gate]

and there are many potential worlds

like

imagine many different parallel universes

one for each possible outcome of the coin tosses

then X_ij will take on different values in each universe

depending on what the outcome is

that's a random variable

[faint onyx]

okay

that somewhat makes sense

[rustic gate]

but like

we can still do math on X_ij

cuz ultimately it'll just be a concrete value

once you realise which world you're in

but it's "random"

so like

P(X_ij = 1) = 1/2

the number of worlds in which X_ij is 1 (i, j match) is exactly half of them

[faint onyx]

okay i get it

v nic

[rustic gate]

okay good

so

to get the total number of matching pairs

we sum all the X_ijs

just like a tally

[faint onyx]

yes

[rustic gate]

good good

[faint onyx]

v nic

[rustic gate]

so it's gonna be like

E[sum X_ij]

yes?

[faint onyx]

hmm

yes

[rustic gate]

okay

so now

the most powerful trick in probability

use linearity of expectation to bring the sum outside

E[sum X_ij] = sum E[X_ij]

[faint onyx]

OH

HOW MANY times tho

like the sum

[rustic gate]

yes exactly

that's the question you need to ask yourself

[faint onyx]

hmm

[rustic gate]

because every E[X_ij] will be the same

[faint onyx]

ill just guess

[rustic gate]

it's just 1/2

[faint onyx]

idk nc2 or smth lmao

[rustic gate]

LOL

yeah

that's right

[faint onyx]

cus like

OH WAT

[rustic gate]

there are C(n,2) pairs

you just choose 2 out of the n

[faint onyx]

OH

very nice

[rustic gate]

oh wait we were doing when i,j don't match

i misread the question

[faint onyx]

hm but its the same right

[rustic gate]

yeah

which is trippy

but makes sense

[faint onyx]

i call that sus

[rustic gate]

it makes sense

[faint onyx]

next qn yes

[rustic gate]

because like

if you don't not match

then you gotta match

[faint onyx]

yes

1/2 1/2

[rustic gate]

and so match + don't match = total

ye

i gotta go tho

[faint onyx]

yes

[rustic gate]

can't stay sorry

[faint onyx]

nooooo

okay

thanks madam snow

[rustic gate]

[faint onyx]

.close

[pearl pond]

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[pearl pond]

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[lost sigil]

i need help with this

[buoyant ridge]

use the point you are given (the y-intercept) to solve for c

[lost sigil]

like
-3=2x+c?

or 10=2x+c

[dusky perch]

C is -3

10=2x-3

[lost sigil]

x=13/2

thats the answer?

[dusky perch]

Pretty sure it is

[lost sigil]

okay thanks alot

.close

[pearl pond]

Channel closed

Closed by @lost sigil

Use .reopen if this was a mistake.

[lost sigil]

.reopen

[pearl pond]

✅

[lost sigil]

it says its wrong for some reason

@dusky perch

[mortal island]

enter as a decimal

6.5

[lost sigil]

oh okay

wait lemme try

How about this

[dusky perch]

For this enter the x value for when Y is 0

[lost sigil]

so the answer in the first one is gonna be
x=0
x=1?

[pearl pond]

@lost sigil Has your question been resolved?

[lost sigil]

.close

[pearl pond]

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[left zephyr]

hi guys i have quick question, how do i transform this to cosine π/something

[plush bramble]

do you know arccos or inverse cos?

[left zephyr]

i know arccos, but im not sure how i can use it here

[plush bramble]

cos(x) = y implies x = arccos(y)

[plush bramble]

if this number is in the domain of arccos, then you can just take the arccos of it to find x

[pearl pond]

@left zephyr Has your question been resolved?

[left zephyr]

still no idea what to do with arccos -(sqr2 /4 + sqr3 /4)

[plush bramble]

,calc acos(-(sqrt(2) /4 + sqrt(3) /4))

[jolly parrot]

Result:

2.476024530295

[plush bramble]

that's your x

your 6 changed to a 3 magically

[left zephyr]

oh yea so soryy

[plush bramble]

x is your pi/something

so solve for something

[plush bramble]

type the correct version using this as a template

[left zephyr]

,calc acos(-(sqrt(2) /4 + sqrt(6) /4))

[jolly parrot]

Result:

2.8797932657906

[left zephyr]

thank you for your help, but i dont think im able to understand this right now

.close

[pearl pond]

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[proud bloom]

how does he go from 2^n+ 4 * 2^n to 5*2^n?

https://www.youtube.com/watch?v=KKjIRSnzKOM&feature=youtu.be

[supple spindle]

a(b+c) = ab + ac

a = 2^n, b = 1, c = 4

he just factored a 2^n on both terms

so 2^n * (4+1) = 5*2^n

[proud bloom]

but how did you go from 2^n + 4 * 2^n to 2^n*(4+1)

ohh wait I get it now

was just confused by the way its formatted

[supple spindle]

sorry for rearranging it weirdly

[proud bloom]

its ok now!

yea just didn't make the connection

that it was 2^n + 4*2^n = 2^n (1+4)

[supple spindle]

yh

[proud bloom]

fun questions tho

[supple spindle]

true

[proud bloom]

thx for help

.close

[pearl pond]

Channel closed

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[pearl pond]

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[fallen lotus]

!status

[pearl pond]

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

[frail slate]

um

5

[earnest stratus]

Might as well post that.

[frail slate]

yah my question is

whats the answer

[earnest stratus]

Huh?

I have a question about someone else's worked solution is what you opted for.

What is it?

[frail slate]

oh i thought it said do u have a question

well 6

[earnest stratus]

So you just want an answer?

[frail slate]

I dont mean to like

yk remove the importance of what u do fr

but yes I just want the answer because im not learning this shit either way

[earnest stratus]

Wrong server.

[frail slate]

alright

tell me how to do it then

[earnest stratus]

How familiar are you with congruent triangles?

[frail slate]

zero

[earnest stratus]

Do you know what congruent means?

[frail slate]

yes

[earnest stratus]

Good.

Do you know there are some criteria for congruence.

There's not many.

SSS, AAS, ASA, SAS...

Does that seem familiar?

[frail slate]

Yes

Except for the fact that i dont know what any of them mean

[earnest stratus]

That's alright.

S stands for Side.

A for angle.

So strictly in order if your triangles have corresponding S or A as stated in the criteria equal, then your triangles are congruent.

[frail slate]

mhm

[earnest stratus]

Example.

[frail slate]

corresponding

forgot what that meant in math

[earnest stratus]

Corresponding is the key word.

I'll illustrate using an example.

Consider the third problem in what you posted.

UV = XY

Yes?

[frail slate]

oh

so

[earnest stratus]

That's an "S" that's equal.

As you move.

To the other information they've provided about the triangle.

[frail slate]

so its congruent?

[earnest stratus]

You'll reach the included angle.

Well it is.

But what criteria do you think?

[frail slate]

criteria?

what do you mean

[earnest stratus]

Here.

[frail slate]

ok

[earnest stratus]

You need to show, which one of these you're using to get to conclusion the triangles are congruent.

[frail slate]

so if its side thats congruent is prolly SAS

[earnest stratus]

It's sas.

Good.

I think you roughly get the idea.

How about the second example?

[frail slate]

i think so

i just figured this

[earnest stratus]

Yeah that ones sas.

[frail slate]

sense v and x are angles?

[earnest stratus]

X and V

Yes.

[frail slate]

cool

[earnest stratus]

Second problem?

Can you tell if they're congruent?

If yes, how?

[frail slate]

well

they look congruent

[earnest stratus]

Look congruent is not the way to go.

Try to think what criteria this matches if it matches any.

[frail slate]

well

i could say

QP equals MN

[earnest stratus]

Yes.

What else could you say?

That's one thing you can say. But that doesn't make them congruent.

[frail slate]

MO = QR?

[frail slate]

then what does?

[earnest stratus]

QR you mean.

[frail slate]

yes my bad

[earnest stratus]

As the criteria mentioned above states.
There's a few condition.
Either you want all sides to be equal. That makes them congruent. (SSS)
You can also have a side, an angle and a side to be equal such that the angle is included between those two sides. (SAS)
You can have two angles to be equal and one side to be equal. Like this, angle, angle and then the equal side. (AAS)
Or you could have angle side angle.(ASA)

In the second example, you'd say they are congruent because all their sides are equal.

SSS.

[frail slate]

oh

so how was number 3 different?

[earnest stratus]

We didn't know if all three sides were equal.

Did we?

We knew, Side, angle and then side.

[frail slate]

yes

but there are no numbers

[earnest stratus]

SAS

You need no numbers.

the check mark on side means they are equal.

Single check = single check.

Double check = double check.

That's convention.

[frail slate]

So really, your just seeing what is equal? like if the sides are equal its SSS

[earnest stratus]

Yes.

You don't need to measure them or anything. Just see what equals what.

Can you try 1?

[frail slate]

wait

but whats number 2

because if were whats equal

[earnest stratus]

This one's third.

[frail slate]

whos to say that all these are not equal?

[earnest stratus]

Wdym

MN has double check

So does QP

They're equal.

That's how you show they're equal.

Same for the other two sides.

[frail slate]

ohh

so

if there all equal wouldnt that be SSS?

[earnest stratus]

And it is SSS

[frail slate]

ohh

lol

[earnest stratus]

Yes!

A thing to note

If two triangles are congruent, then all angles are equal too.

Then why did we not use angles to show congruence?

Because we didn't know if they were equal.

Only now we know after we've proved then congruent.

So however you prove them congruent, doesn't matter. After you've done that, you can claim corresponding sides are equal or angles.

Also, when you say two triangles are congruent. You need to kind of write the triangle in order so that you match the corresponding sides. What does that mean?
Well, in the third triangle
UV = YX
VW = XZ
So you'd say UVW is congruent to YXZ
Now here this is the only right way to write them.

[frail slate]

ohh yah

it asks for that as well

[earnest stratus]

I know

[frail slate]

and number 1 is not congruent right?

[earnest stratus]

It's actually not!

Why so?

[frail slate]

Because

it has a marker on different sides of the triangle

meaning one side is equal on triangle but not equal on the other

meaning their no congruent?

[earnest stratus]

Well, they are not congruent. They would have been if angle L was equal to angle G. Instead of J.

[frail slate]

yah thats what i mean

[earnest stratus]

Yeah.

You're right.

[frail slate]

there in different spots

[earnest stratus]

J isn't a side though, it's a vertex.

[frail slate]

oh

whats that

wait ik what that is

so this is correct?

[earnest stratus]

Not correct.

[frail slate]

[earnest stratus]

You've written MNO is congruent to QRP

When you say that, you mean MN is equal to QR, NO is equal to RP, and OM is equal to PQ

But is that really the case?

[frail slate]

ohh no

[earnest stratus]

That's what corresponding is for.

Sides are equal, but only the corresponding sides.

[frail slate]

so

[earnest stratus]

Think for yourself what you'd write.

I'll check your work.

[frail slate]

its

[earnest stratus]

Lmk.

[frail slate]

RPQ

?

[earnest stratus]

MNO and RPQ?

MN equal to RP you mean?

[frail slate]

yes

[earnest stratus]

MN and RP equal?

Try again.

[frail slate]

wait hold on

So

QPR

[earnest stratus]

That one's right.

Although it just might be that you tried so many times that it's a fluke.

So do the next one.

[frail slate]

Wait that's wrong too?

[earnest stratus]

Yes, XD.

Not that they're congruent. Or the criteria.

[frail slate]

Lol k

[earnest stratus]

But the triangle order.

[frail slate]

Zxy smh

It's ZXY isn't it?

Wait no

It's YXZ

[earnest stratus]

Final answer.

[frail slate]

YXZ

[earnest stratus]

Alright you're good.

Have fun.

[frail slate]

Def

[earnest stratus]

On an ending note, if you still want to master this. Totally a choice. You should watch a video on congruent triangles.

[frail slate]

Oh 💀 thank you so much

[frail slate]

Yah imma do that too

[earnest stratus]

.close

[pearl pond]

Channel closed

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[midnight haven]

why is e the answer not a

[merry carbon]

How did you get a?

[midnight haven]

4(t-3.25)

[modern fjord]

it says speed not velocity

[plush bramble]

,w plot abs(12t^2-78t+108) for 0 < t < 6

[jolly parrot]

Results provided by WolframAlpha

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

Requested by riemann#2529

[plush bramble]

i see

[midnight haven]

riemann what have you figured out?

[plush bramble]

ed rightly pointed out speed is absolute value of velocity

[modern fjord]

the answer is a if you think the word it said was velocity but it says speed

so either do what riemann did and just use abs value or consider concavity

[plush bramble]

just continuing this. use the definition of absolute value to differentiate speed (not velocity) and find where the derivative is positive

[midnight haven]

.close

[pearl pond]

Channel closed

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[frail slate]

.close

[pearl pond]

Channel closed

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[vast dune]

how tf do these vectors go to v?

[turbid moss]

Are you curious why w-u = v?

[vast dune]

yeah

wouldnt w-u look like this?

[turbid moss]

yup

now you do tail to head

[vast dune]

ok

[turbid moss]

when you connect the tail of w to the head of the red line this gives you w-u

[vast dune]

but how would it be = to v

[wind wigeon]

you kind of forget where the vector starts

it doesnt matter

[turbid moss]

you have to imagine the vectors are being drawn from the origin

[wind wigeon]

the only properties of a vector are direction and length

so you can forget about where you put the tail because you can put the tail anywhere and its still the same vector

[vast dune]

so if you were looking at it from the origin

isnt this just blatantly not equal

[vast dune]

i mean i guess that would make sense

[turbid moss]

i really meant moving the vector from where it is so that its tail starts from the origin

because as heavy said it doesnt matter where you start the vector all that matters is the length and the direction

also i think you've misinterpreted what w-u is

[pearl pond]

@vast dune Has your question been resolved?

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[midnight haven]

A kite string is let out 120 ft and is held 3.5 ft off the ground. If the string makes an angle of 42 degrees with the horizontal, how far above the ground is the kite?

[midnight haven]

I got approximately 5.23 ft.

Is that correct?

[old geyser]

Def not

Your answer implies that the kite didn't go really far up: only about 2.3 feet from your hands

What have you tried

[midnight haven]

@old geyser

Wait 120 ft would be the hypotenuse

?

[midnight haven]

I just tried again and got ~83.8 ft.

[old geyser]

yeah

[midnight haven]

wth

[old geyser]

120 is your hyp

[midnight haven]

why is this channel still open

[old geyser]

epic

[midnight haven]

Welp

I have another problem

Could you help me with it?

You and a friend are standing on balconies of nearby builings. Your balcony is 40 ft above the ground andd your friends is 28 ft above the ground. When you loo kat your friend the angle of declination is 18.5 degrees. When you look at the top of your friend's building the angle of inclination is 44.2. Note: These angles are also called the angles of depression and elevation respectively. Use right triangles to determine the height of your friend's building.

.close

[pearl pond]

Channel closed

Closed by @honest linden

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[quick epoch]

need help

[cosmic basin]

turn it into simple shapess then sum the area of them

so turn it into a 2 rectangles and a triangle

[quick epoch]

I drew it

[cosmic basin]

sso first rectangle has sides of 8 and 4

2nd hass sides of 6 and 3

and the triangle has base of 6 and a hieght of 8

[quick epoch]

8 x 4

[cosmic basin]

sso solve for the areas of each then sum or add them all

[quick epoch]

32 + 18

the triangle

[cosmic basin]

base times height times .5

its essentially the rectangle formula but you cut it in half

[quick epoch]

for triangle?

[cosmic basin]

yeah

so 6 times 8 times .5

[quick epoch]

48 x 0.5?

[cosmic basin]

yup

[quick epoch]

24

32 + 18 + 24?

[cosmic basin]

yup

formulas that you'd use for that

[quick epoch]

74

[cosmic basin]

yea

[quick epoch]

i got it wrong

[cosmic basin]

how bruh

[quick epoch]

i have another one

[cosmic basin]

you get the process or no ?

[quick epoch]

yea move to the next question

[cosmic basin]

oh

because the hiehgt iss 8 plus 4

thats dumb

[quick epoch]

its alright ig

[cosmic basin]

you have to solve for stuff

first rectangle is 6 * 4 2nd is 3 * 2 then the triangle is (6+3) * 5 * .5

[quick epoch]

i dont see a 3 on the 2nd rectangle

[cosmic basin]

sorry 2

[quick epoch]

9 x 5

45/2

[cosmic basin]

imma be honest ixl is like the most infuriating thing ever

[quick epoch]

it is

i have to get to a 80 to pass

is it 24 + 6 + 22.5?

[cosmic basin]

id write it out like each shape seperatly on paper

yea

then add em all together

[quick epoch]

52.5

[cosmic basin]

yea

[quick epoch]

yup correct

if your cool about helping with me again ok if not ill move channels

[cosmic basin]

sure

[quick epoch]

i think i cut it incorrectly

[cosmic basin]

no you can do it like that

just as long as you can solve for the area of each shape you make

[quick epoch]

kk

[cosmic basin]

so 1st triangle has a base of 6 and height of 4

rectangle is 2 by 9

and 2nd rectangle is 3 by 5

[quick epoch]

24/2

12 + 18 + 15?

[cosmic basin]

yea

[quick epoch]

45

[cosmic basin]

yup

[quick epoch]

yup

again or

[cosmic basin]

sure

[cosmic basin]

so you'd get rectangle 9 by 5 2nd rectangle 9 by 4 triangle 21 by 18

[quick epoch]

21 x 18 /2?

[cosmic basin]

yup

[quick epoch]

189

45 + 36 + 189

[cosmic basin]

yea

[quick epoch]

270

yup

[cosmic basin]

bruh im in shock right now

were doing dynamics in ap physics

and i got a question about the drag coeffcient of a parachute

this aint even a formula on the reference table

[quick epoch]

what grade you in

[cosmic basin]

11th

[quick epoch]

wow thats how hard it is

[cosmic basin]

the other stuff is a lot eaiser in this like review sheet

but i just got a question that we dindt even begin to go over

[quick epoch]

always happens

[cosmic basin]

so

9 by 2
4 by 13
and 3 by 7 times .5

[quick epoch]

18 + 52 + 10.5

[cosmic basin]

yea

[quick epoch]

80.5

[cosmic basin]

yup

[quick epoch]

yup

and thats a 80

[cosmic basin]

nice

[quick epoch]

thanku

[cosmic basin]

i looked it up and i got it so im good

ap physics just angers me when they like ask you to only write in terms of other variables and put equation into equations

[lucid vine]

48 + 36 + 8*6/2

[quick epoch]

? already got it

[lucid vine]

Close?

[quick epoch]

yea make it solved

[quick epoch]

it stresses you?

[cosmic basin]

not really

just really dumb questions they write like a whole essay for each question

heres one i have right now

An object is thrown with a fixed initial speed v0 at various angles α relative to the horizon. At some constant
height h above the launch point the speed v of the object is measured as a function of the initial angle α. Which
of the following best describes the dependence of v on α? (Assume that the height h is achieved, and assume
that there is no air resistance.)

im fairly good at it

but its one of the hardest courses but its also one with like the biggest curve

so getting a 70 is like a perfect sscore

for ap

5

[pearl pond]

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[pearl pond]

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[solar gyro]

For #7, how do I know whether it’s 64/24 or 24/64? <@&286206848099549185>

[solar gyro]

Srry i meant 32 not 24

[midnight haven]

what part

[pearl pond]

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

[cosmic basin]

you just have to show its proportional

[solar gyro]

Wait no

[cosmic basin]

because itss the same rectangle

[solar gyro]

How do i know what sides r corresponding

[cosmic basin]

so RS/RU = ZY/ZW

[solar gyro]

But how do yk that

[cosmic basin]

then you do 2nd divided by 1st for scale factor

id write how to go from 1st to 2nd times .5

[solar gyro]

Wait what

I’m so confused

How do yk what sides r corresponding

[cosmic basin]

bigger goes with bigger side so 64 goes with 32

[solar gyro]

This is so confusing

Ohh

[cosmic basin]

its just rotated

[solar gyro]

Nvm

The sides r larger

I get it

Ty

And does the bigger number always belong in the numerator? @cosmic basin

[cosmic basin]

no

it depends

[solar gyro]

On what?

<@&286206848099549185>

[pearl pond]

@solar gyro Has your question been resolved?

[solar gyro]

???

@cosmic basin

[pearl pond]

@solar gyro Has your question been resolved?

[pearl pond]

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[edgy wigeon]

physics but still same idea

geometry

does this mean a+b is 270 degrees?

.close

[pearl pond]

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[versed needle]

Hi! can i have some help with rotation of conics

[vital estuary]

do you have a specific question?

[versed needle]

Prove that the unit hyperbola (x ^2-y^2)=1 is actually just a rotation of the function f(x)= 1/2x

[vital estuary]

that is very much not true

oh 1/(2x)

no thats not right

[versed needle]

why?

the graph looks right on desmos

[pearl pond]

@versed needle Has your question been resolved?

[pearl pond]

@versed needle Has your question been resolved?

[warm current]

@versed needle do you still need help

[pearl pond]

@versed needle Has your question been resolved?

[pearl pond]

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[coarse sage]

Number of factors of p is

[jolly parrot]

Result:

480

[coarse sage]

Number of factors of q is

[jolly parrot]

Result:

300

[coarse sage]

Number of factors common to both p and q will be 48.

How do I proceed further?

[glacial sequoia]

Numbers that can divide p + Numbers that can divide q - Numbers that can divide both

$A \cup B = (A + B) - (A \cap B)$

[jolly parrot]

NEONPerseus

[glacial sequoia]

You said you never used set theory

[coarse sage]

This was so simple, and I'm dumb

[glacial sequoia]

Brainfart

Happens to the best of us

[coarse sage]

Congrats, you're green now

[glacial sequoia]

🥳

[coarse sage]

.close

[pearl pond]

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[pearl pond]

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[shut panther]

i have this pharse:
0 = cos(2x) - 2sinx
how do i solve this?

[old marsh]

Do u know ur double angle identities

[midnight haven]

$\cos^2{x} - \sin^2{x} = \cos{2x}$

[jolly parrot]

n!

[midnight haven]

Use this identity

[old marsh]

^

[midnight haven]

(You can derive another one using this)

[old marsh]

Wait

^

[shut panther]

yes

[old marsh]

Ok see which one would be most applicable for this situation

[shut panther]

this one i think

[old marsh]

Ok, but ultimately, u want everything in terms of sinx

How can we change that identity accordingly

[shut panther]

maybe there's an identity to change cos^2x?

[old marsh]

Yes there is

sin^2 + cos^2 = 1, remember this?

[shut panther]

yes

[old marsh]

So change this accordingly

[shut panther]

oh yeah

so i can do

cos^2 = sin^2 - 1?

[old marsh]

Yes

[shut panther]

great

[old marsh]

Wait

No

1-sin^2

[shut panther]

-*

yes

thank u so much

❤️

[old marsh]

Np

[shut panther]

.close

[pearl pond]

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[pearl pond]

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[north mauve]

Hi guys, I just want some clarification on ln vs logs. I have a formula here ill write it

[north mauve]

Is there a reason why the log turns into an ln?

I've seen this with another formula or two aswell and I dont get why that happens

Or are they just used interchangeably?

[feral sedge]

ln is log with base e

have you seen $\log_b(a)=\f{\log_c(a)}{\log_c(b)}$

[jolly parrot]

monikanicity

[pearl pond]

@north mauve Has your question been resolved?

[pearl pond]

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[vale kindle]

Just making sure here, v(t) would be s' and a(t) would be s'', correct?

[vital estuary]

Ye

[vale kindle]

Coolio, thanks

.close

[pearl pond]

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[vale kindle]

Hello, having problems here with this problem. I can't find where my error is

[light helm]

you used the derivative function for the y coord instead of the original function

[vale kindle]

Ah. So I plug the x values I find into the original?

[light helm]

yes

[wicked flicker]

can someone help me understand why its that answer?

and not y-x^2/y^3?

bruh mb

sry

didn't know thsi was occupied

[vale kindle]

I forgot to close, no worries

.close

[pearl pond]

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[wicked flicker]

hi

[pearl pond]

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[north mauve]

Sorry i had to go do something

[north mauve]

But yes i have seen it

And i understand that ln is just log with a base e

But i don't understand if they're interchangeable here it seems like they might be but then i don't get why

[feral sedge]

$\log_b(x) =\f{\ln(x)}{\ln(b)}$

[jolly parrot]

monikanicity

[feral sedge]

then derive it

[north mauve]

Is this different than saying the same as what's written there except replacing the lns with logs?

Do you always have to evaluate the log with dividing the lns of the numbers? Or can you do it with normal log?

[karmic fern]

all of the log rules apply to all of the logs

ln x = log_b x / log_b e for example

[north mauve]

I don't understand

[karmic fern]

write out the log rules

the bases don't matter

or rather

the log rules apply to logs of any base

[north mauve]

I understand the log rules but i don't get it where it uses ln and log

Why does it change

In the same formula

[feral sedge]

It's applying the log rule with c being e

[north mauve]

I dont get it

Sorry

[feral sedge]

This rule

Set c equal to e (2.718...)

ln is only log_e, its not interchangeable with log in general

[north mauve]

If it isnt interchangeable why does it change in the formula?

[north mauve]

But they give me the same answer

So doesnt that mean theyre interchangeable?

[feral sedge]

Because there's a specific rule that says you can

???

[karmic fern]

do you understand that ln is simply log_e?

[north mauve]

Yes

[karmic fern]

then what's the issue

[north mauve]

I dont get why it changes in the formula

[karmic fern]

what formula

write it out

say where it changes

[north mauve]

On the left side its log

And on the right side its ln

[karmic fern]

there's no "change" here

what you've written is just simply a true statement

do you want to know why it's true or something?

[north mauve]

But it changes

[karmic fern]

no it doesn't

there's no "change"

[north mauve]

On the left it says log

On the right it says ln

[karmic fern]

that's like asking why 1 changes to 2 because 1+1=2

makes no sense

what is written there is just a mathematical equation that turns out to be true

it's not derived from just "changing" some symbols on the left side to the right side

[north mauve]

Are these two the same thing

[karmic fern]

what base is the log in the second equation

[north mauve]

b

They both have a base of b

[karmic fern]

so you mean to ask whether $\dv{}{x} \log_b x = \frac{1}{x \log_b b}$ is the same equation as the first?

[jolly parrot]

Saccharine

[north mauve]

I dont know

I just dont get why it changes

I know you said it doesnt change but i dont know how else to say it

[karmic fern]

is what I wrote what you meant by the second equation

[north mauve]

In the one i wrote there isnt a b on the bottom right part

[karmic fern]

then what does "log b" mean?

[jaunty stratus]

How would I find these measurements with the info I have already written down?

[karmic fern]

you need to be specific about what you're writing

[small fractal]

Claim a new channel

[north mauve]

I dont know how else to say it im sorry

[karmic fern]

no

you need to be specifc

what does "log b" mean?

[north mauve]

I dont know

There was an ln b before

[karmic fern]

then how is anyone else supposed to know?

[north mauve]

I made the the ln into log

Cause thats what it does

[karmic fern]

when you write something, the meaning has to be clear to everyone else

you're basically asking me the equivalent of "h afdskjhadskfjhaksjd fnfnma kfhdsajhkfjkhfjdhkaj" what does that mean?

I changed the letters

and then I ask you "what does h afdskjhadskfjhaksjd fnfnma kfhdsajhkfjkhfjdhkaj mean?" and you tell me "I don't know"

when people write mathematical symbols down, it is basically a language for communicating the underlying mathematics

you can't just change random letters and symbols around and then ask "why isn't the equation this" without actually saying what any of those symbols mean

it would be like "why didn't Lincoln write his Emancipation Proclamation like this: akdshfkdsafdsambtemnberbntertkjfdsahkj" and then when asked what "akdshfkdsafdsambtemnberbntertkjfdsahkj" means you say "I don't know"

[north mauve]

How would I evaluate this derivitive, so it's like the same as the derivitive of ln 17 but we rewrite it as log base e

Is this how it would do

[karmic fern]

log base e is the exact same thing as ln

I thought we were clear on this before?

[north mauve]

Yes

[karmic fern]

it's literally like saying "hi" in English or "hola" in Spanish

[north mauve]

I understand

[karmic fern]

so what are you asking then

[north mauve]

I just wanted to write it with log so that it can be clear that the base is e

Would that be the right way to evaluate the derivitive

[karmic fern]

huh????

[north mauve]

How would i evaluate

The derivitive of

ln 17

[karmic fern]

$\dv{}{x} \log_e x \vert_{x=17} = \frac{1}{x} \vert_{x=17} = \frac{1}{17}$

it's literally just writing it in a slightly different way

do you not recognize

[north mauve]

How is it just rewriting it

[karmic fern]

wtf now you're making me write wrong shit

[karmic fern]

this is absolutely not true

[north mauve]

Then how would i do it

What is the long line

[jolly parrot]

Saccharine

[karmic fern]

evaluated at

doesn't matter

you have more pressing misconceptions to fix

[north mauve]

Whats that

[karmic fern]

it doesn't matter

do you understand that $\log_b x = \frac{\ln x}{\ln b}$?

[jolly parrot]

Saccharine

[north mauve]

I dont get why its ln on the right side and log on the left

Why not just keep it as log for everything

If we have like log base 5 of 12

Can we evaluate it as log base 9812 of 12 / log base 9812 of 5 and it'll still be the same thing as long as its the same base?

[karmic fern]

yes you can

[north mauve]

So the point here is that it doesnt matter what the base is on the right side as long as its the same in the top and the bottom?

[karmic fern]

what, does $\log_b x = \frac{\log_e x}{\log_e b}$ make you happier?

[jolly parrot]

Saccharine

[karmic fern]

a more accurate thing to say would be that $\log_b x = \frac{\log_2 x}{\log_2 b} = \frac{\log_3 x}{\log_3 b} = \frac{\log_4 x}{\log_4 b} = ... = \frac{\log_{3423} x}{\log_{3423} b} = ...$

[jolly parrot]

Saccharine

[karmic fern]

i.e. $\log_b x = \frac{\log_c x}{\log_c b}, c > 1$

[jolly parrot]

Saccharine

[north mauve]

Yes thats it that makes sense

Also why does c have to be greater than 1

[karmic fern]

I think c can actually be less than 1 and it works

but it just can't be 1

and honestly couldn't be bothered

[north mauve]

What happens if its 1? I dont see why 1 would cause a problem

[karmic fern]

log of 1 is 0

you're dividing by 0

[pearl pond]

@north mauve Has your question been resolved?

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[opaque hearth]

Is there an easy way to apply a arithmetic operation to every element in a list on a TI-84?

[opaque hearth]

For example if I wanted to add 5 to every element of a list without manually adding 5 to each one, what would be a good way to do that?

[pearl pond]

@opaque hearth Has your question been resolved?

[pearl pond]

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[mellow basin]

f is continous function on [a,b] and diffenrialble on (a,b)

show that for all x (a,b) f´(x)=0 that f(x ) is constant on [a,b]

[old geyser]

use FTC

What happens when you evaluate $\int 0 dx$?

Well

[jolly parrot]

Umbraleviathan

[old geyser]

@mellow basin

[pearl pond]

@mellow basin Has your question been resolved?

[mellow basin]

0?

oh

i see

so your saying that f(x) is constant on (a,b) cause f´(x)=0 and integral of 0 is also constant

hmm but with constant it means like f(x)= c on [a,b] but if integral of a non diffentiable function is 0 it hasnt have to be c , no? @old geyser

[old geyser]

Well it means that f = 0x + C

[mellow basin]

right

but that c hasnt have to be the c of (a,b) right

@old geyser

[old geyser]

Well $\forall x \in (a, b), f(x) = C$ where $C \in \bR$

[jolly parrot]

Umbraleviathan

[old geyser]

C can be anything

[mellow basin]

hmm

ok thanks

[pearl pond]

@mellow basin Has your question been resolved?

[pearl pond]

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[hard crystal]

A={1,2,...,10}
B and C are subsets of A such that B and C has no common elements and B U C=A

[hard crystal]

find no. of ways to select B and C if ordering is ignored

[jolly parrot]

Anagh

[hard crystal]

Is this answer correct?

[keen cradle]

yes

[hard crystal]

Ok thanks

.close

[pearl pond]

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[rustic owl]

does B simply equal to rhs?

[rustic owl]

or am i wrong?

[tacit mulch]

Not necessarily. Is there more information?

[rustic owl]

no

[merry carbon]

Remember the question we did earlier, and the preimage stuff, it’s similar here

[rustic owl]

🤔

i would say is must be equal

[merry carbon]

Remember the preimage isn’t necessarily the same as the image under the inverse (and the function need not be invertible!)

[rustic owl]

in case of A [ ] f^-1(f(A)) it would be an inclusion though

[merry carbon]

And here too!

[rustic owl]

but there cannot be x1 = x2 such that f(x1) != f(x2), can it?

[merry carbon]

[remember how we took some function g : A -> {0,1}, g(a)=0 for all a in A, then g^{-1}({0,1}) is A but g(A)={0}]

[merry carbon]

Nope, that’s the definition of a function being well defined

[rustic owl]

but it would mean that for x there might be few y

so it wouldn't be a function

in would be a relation instead

wouldn't it?

[tacit mulch]

Consider that if f is not surjective, then it is possible for f^-1(B) to be empty, even if B is not.

For example f: R -> R where f(x) = x^2.
And let B = {-1}, a subset of the codomain.

Then f^-1(B) is the empty set

so f(f^-1(B)) is also the empty set

[rustic owl]

oh, okay, now I get it

[rustic owl]

ok, now it makes sense

i was thinking in the wrong direction

thanks for help

.close

[pearl pond]

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[keen ore]

Let (X, d) and (Y, p) be two metric spaces, and f be a mapping from X to Y.

[keen ore]

prove f is continuous iff $f(cl(A)) \subset cl(f(A))$

[jolly parrot]

rikusp2002

[keen ore]

I posted this problem yesterday but I am still not sure on how to do the backward direction

it's easy to show if continuous then the result

But from the result I can't seem to get the continuity back

Even contrapositive doesn't work

Actually my bad.

.close

[pearl pond]

Channel closed

Closed by @keen ore

Use .reopen if this was a mistake.

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[turbid moss]

f:R-> R and f'(x) is continuous at some point x_0. Does f'(x_0) exist?

[snow skiff]

do you know definition of continuous

[turbid moss]

yeah

[snow skiff]

ok

[turbid moss]

oh sorry

[snow skiff]

then it should follow quite fast

[turbid moss]

i just assumed it was continuous

[snow skiff]

$\original$

[jolly parrot]

active mental mutilation liker

[turbid moss]

ok one sec

Let $f$ be some function with $f:R\to R$ such that $\lim_{x\to x_0} f'(x_0) = L$. Is it necessarily true that $f'(x_0)$ exists?

[jolly parrot]

please request a new nickname

[snow skiff]

is it differentiable at x_0?

[turbid moss]

That isnt given

[snow skiff]

okay

where is f differentiable at

[turbid moss]

idk this is the only thing that it says

[snow skiff]

the usage of f' seems to imply it is differentiable everywhere

like without any other context

Anyway

do you have a picture of the original question

because the usage of

[near echo]

i want to say they're implying it is differentiable about x_0

[snow skiff]

lim x-> x_0 f'(x_0)

did you mean f(x)?

[turbid moss]

what would change if it were differentiable

[snow skiff]

if it is differentiable at x_0 f'(x_0) certainly exists by definition

[turbid moss]

oh well that seems obvious im gonna assume that it may or may not be differentiable at x_0

[snow skiff]

$\lim_{x\to x_0} f'(x_0) = L$