help-10

[timid silo]

hopefully u get an idea of what i mean from this example^

[slim relic]

that makes sense yes!

ahh so there are 3 ways, am i right?

[timid silo]

so now apply it to your question

[timid silo]

bingo

what are they

[slim relic]

correct answers

so they have three different ways

[timid silo]

yep the person could get the first question right then proceed to get the second and third wrong

or they could get the first wrong, second right and third wrong

[slim relic]

yea i get that

[timid silo]

of first and second wrong and third wrong

so you’ll need to work out the probability of each of these 3 by multiplying across the tree diagram

[slim relic]

how would i do that?

[timid silo]

so lets do the first way of the person getting one q right

[slim relic]

yep

[timid silo]

^ this one

[slim relic]

ok!

[timid silo]

whats probability of getting first q correct

[slim relic]

1/3

the others are 2/3

[timid silo]

whats probability of getting 2nd wrong

[slim relic]

so 1/3, 2/3, 2/3

[timid silo]

yes exactly

so multiply them

[slim relic]

i got 4/27

[timid silo]

yep

[slim relic]

but that still isnt right

[timid silo]

now do the other two ways of the person getting one q right

[timid silo]

not done yet

[timid silo]

^

[timid silo]

^

[slim relic]

i still dont quite get it || sorry im dumb || what do i do with the 1/3 x 2/3 x 2/3

oh do you mean do 2/3 x 1/3 x 2/3

[timid silo]

this u got as 4/27 and it was the probability that the person gets the first q right and second and third wrong

[timid silo]

yes this would be the probability that the person gets the first q wrong second right and third wrong

[slim relic]

yea ok :d

yea i understand that

wait

[timid silo]

notice a pattern 😆

[slim relic]

does that mean 2/3 x 2/3 x 2/3 would mean they got zero questions right?

[timid silo]

yes

[slim relic]

ahh

[timid silo]

so that would be ur answer for d

[slim relic]

8/27 cool i understand that

and 1/3 x 1/3 x 1/3 = 1/27 (answer to c)

that means that 1/3 x 1/3 x 2/3 = 2/27 (answer to b)

but 1/3 x 2/3 x 2/3 = 4/27 which is wrong..?

[timid silo]

yep b and c answers right

[timid silo]

we not done yet for a

[slim relic]

why is a different from b c d?

why wouldnt it use the same method for solving?

[timid silo]

^ whats ur answer for this

[timid silo]

because theres 3 different ways of getting one question right

either first q right other two wrong

or first right second wrong last right

[slim relic]

so you'd multiply this for each question (3)?

[timid silo]

or first and second wrong last right

[timid silo]

after u have found the probabilities for the three ways of getting 1 question right u add them up

so what did u get as the probability for each way of getting 1 q right

[slim relic]

4/27

wait

would you do 4/27 + 4/27 + 4/27 = 4/9 because each is a different way to get it right?

[timid silo]

exactly

u add the probabilities of each way up

and u got 4/9 which is right

[slim relic]

omg

it actually all makes sense now

[timid silo]

lol

ur school teacher must be shit

[slim relic]

i cant thank you enough and you deserve a promotion

[timid silo]

im not a teacher lmao

[slim relic]

no actually, he is really good but i have a test tomorrow and i have been sick the last few days so nobody has been able to teach me this stuff

[timid silo]

make sure u pass the test then

[slim relic]

well the test is meant to be today

everyone is doing it right now but im sick

so i get a little extra time now to study :>

[timid silo]

heres pics of the three ways of getting 1 q right if it helps u visualise it and understand better maybe

[slim relic]

yea i see now

[timid silo]

best tip for probability questions is draw tree

[slim relic]

yea well probability isnt my forte so this has been really helpful

i appreciate the help so much, im not joking

i guess i will stop annoying you now but thanks sm!

[timid silo]

no its np i like helping ppl

[slim relic]

have a great rest of your day - you have made mine :)

.close

[obtuse pebble]

Channel closed

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Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
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[warped bane]

How do i solve this

[warped bane]

Im stuck

[tired shell]

let's label the 3 areas '

(1) is -4, (2) is unknown, and (3) is -5

that integral from 0 to 4 tells you (2)+(3)=15 right?

so see if you can figure out the area of (2)

[warped bane]

i-

c-cant

[tired shell]

(2) + -5 = 15

[mild ocean]

you know the area of 2 and 3 combined, and you know the area of 3

[warped bane]

damm we just started this topic and im alr brain dead

[mild ocean]

it took me a minute to figure it out too

i considered saying there’s not enough information lol

[warped bane]

So its unsolvable

[mild ocean]

no

it’s definitely possible to solve

[warped bane]

i cant im too dumb

[mild ocean]

area 2 + area 3 = 15, area 3 = -5

surely you can do that

[warped bane]

yup

But i dont understand point 3

Is that what u call discrimination or smth

[mild ocean]

that’s an integral sign

[warped bane]

Oo

[mild ocean]

from x = 0 to x = 4

[warped bane]

Ohh

How about dx

Ik fx is function

[mild ocean]

basically what it’s asking is what’s the area of area 1 + area 2, also area 1 = -4

even though it says 4

this is because it’s under the x axis

have you done the definition of an integral

or is this like your first introduction to this

[warped bane]

no yes

[mild ocean]

oof

[warped bane]

its next year topic welp

im learning in advanced

[oak locust]

You know the meaning of area under the curve with respect to definite integrals? @warped bane

[mild ocean]

no they don’t

[warped bane]

WHAT?

[mild ocean]

they don’t even know what an integral really is

[warped bane]

yea

im dumb

[oak locust]

It's alright

[mild ocean]

do you know what a derivative is

[oak locust]

It isn't that hard to be frank

[warped bane]

no

[mild ocean]

i’m not sure why your teacher is introducing integrals before derivatives

[warped bane]

i learnt till trigonormetry

math teachers are insane

theats why

[fervent cradle]

there's something wrong here

[mild ocean]

definitely

they didn’t even label the areas right in the problem

it’s positive when it should be negative

[warped bane]

With me or the question

[oak locust]

They're not 😆
You must have skipped both differentiation and integration

[mild ocean]

have you learnt limits @warped bane

[warped bane]

u mean limits in

[mild ocean]

lim as x->a of f(x)

[warped bane]

Whats the anserr

[mild ocean]

no clue

that’s an example

and i’ll take that as a no

so you probably skipped a lot of stuff

[warped bane]

So unsolvable

[oak locust]

Never worry about answers while learning concepts 🙂

[warped bane]

But answer = full marks

[mild ocean]

well i don’t know what to tell you honestly, since you’re learning something when you’re missing required prerequisites

[oak locust]

Not while you're at your home/class and you're learning for the first time

[warped bane]

whats preraussiteus

[mild ocean]

a prerequisite is something you should learn before learning something

[oak locust]

Limits, derivatives, indefinite integrals and definite integrals in this case

[warped bane]

[mild ocean]

like before learning algebra 2 you know algebra 1

algebra 1 is a prerequisite

[warped bane]

theres different algebra?

bruh

I learn it as a whole

Not 1

And 2

Ok so whats the anser

Ill workd backwads

[mild ocean]

@oak locust even if i was to give them the answer the info they have on there is wrong

so i have no clue what to say

[warped bane]

Just say the answer

Ill check

With teacher

[mild ocean]

the area of the first section and the last section is negative

although they say it’s positive

[warped bane]

Ill start WW3 with them if they give fake question

[oak locust]

No bro. The info given there is on point @mild ocean

Take a closer look

[warped bane]

so u guys cant solve

[mild ocean]

no it’s not

it’s under the x axis

wait a second

i might be dumb

ok the area of the last section is negative

[oak locust]

No you're not

[oak locust]

I can solve it even before you could read these entire problem. But that's not the point here

[warped bane]

aow

[mild ocean]

isn’t the area of the third section negative?

[warped bane]

thats enlighting

[mild ocean]

x is positive and y is negative

so the area should be negative

[warped bane]

16?

Why whole number

Shouldnt it be decimal

Or smrh

Pls show the working

[oak locust]

Bro. The area can never be negative

[mild ocean]

according to integrals it can

[fervent cradle]

signed area

actual area is positive

[mild ocean]

oh

[warped bane]

do y guys have working on paper

should i call albert einstein in

[oak locust]

The value of integrating can be negative
If the value of integral is positive then it means the region is above x-axis and if it's negative then it means the region is below x-axis
But always remember, the area can never be negative
@mild ocean

[mild ocean]

yeah i remember

[oak locust]

Rookie mistake, it's common

The question is entirely perfect. It's just that our guy here skipped all the required concepts to solve it and directly jumped to the definite integral and applications of integration questions

You still there? @warped bane

[warped bane]

Yea

[warped bane]

nice criticism

So the answer is 16

But whata the working

[oak locust]

Dude. You don't get it, do you?

[warped bane]

What

Whats the working

Is the anser 16

[mild ocean]

you don’t know how to do the question

is this assigned work or just a problem you want an answer too

[oak locust]

Read the server rules.
We just don't give out the answers here
We don't give out the working written solutions
That's cheating and it ain't gonna do you any better
But instead we can help you with the step where you got stuck
Or we can clear any doubts that you've regarding the question or concepts @warped bane

[mild ocean]

you should have been taught a lot of stuff before learning this

this is like the end of calculus 1, when you haven’t learned the beginning of it

well that’s exactly what it is

talk to your teacher and say i don’t know how to do this

[unique solstice]

[mild ocean]

that didn’t ping mods if you were wondering

hi @unique solstice

[oak locust]

You can check if I'm wrong or making this up
If you think I'm making stuff up then please do ping @moderators @warped bane

[unique solstice]

Hello

[visual kelp]

Sadly not even f(x) needs to be known for this question... I don't see the point of plotting it

[oak locust]

One suggestion @warped bane
Please go through #❓how-to-get-help once again and close this channel if you're not using it 🙂
Have a good day

[obtuse pebble]

@warped bane Has your question been resolved?

[obtuse pebble]

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[polar gulch]

why CDF doesn't have an C?

and another question i'm integrating PDF

and getting CDF/beta + C

what i did wrong?

or i simple ignore C ?

[jolly ginkgo]

While solving you will be getting the limits of integration

For ex P(1<X<2)

[warm shale]

it's Sam

[polar gulch]

so i ignore C cause when i do definite integration they cancel out

ok,

but what do i do about 1/Beta

[jolly ginkgo]

What bout it

[polar gulch]

i'm integrating $\int{\frac{e^{-(z+e^{-z})}}}{{\beta}}dz$

where $z = \frac{x - y}{\beta}

[jolly ginkgo]

Isn't beta in denominator

Wait I'll type out integration in some time

[polar gulch]

https://wikimedia.org/api/rest_v1/media/math/render/svg/e09e74a68cf5035d35d98a8a7effacd2b3ffd854

here

i'm integrating this

where

[jolly ginkgo]

And what's the problem you are facing

[polar gulch]

and gettin this divided by beta

[jolly ginkgo]

Ok can you show workings

[polar gulch]

yeah

wiat a sec

[polar gulch]

,rotate

[polar gulch]

here

[jolly ginkgo]

Ok

We have pdf of x right

So we have to integrate wrt x

[polar gulch]

oooooooo

[jolly ginkgo]

If you do dz then you have to find dz/dx = 1/beta

[polar gulch]

i thought that integrating why respesct do z would be the same thing

[jolly ginkgo]

Nope u either use this or do wrt x

[polar gulch]

ooooo ok

ty

so, imaging that i started with the function with x and not z

[jolly ginkgo]

dz = dx/ beta

[polar gulch]

i would do 2 subs

?

one for dz

and another for du

[jolly ginkgo]

Wait lemme just show you with text

[warm shale]

it's Sam

[jolly ginkgo]

@polar gulch

You started CDF like integration of some f(z) dz

Which is not the case

[polar gulch]

oooooo ok, now makes more sense

it's a sub

[jolly ginkgo]

Yes you can think it that we or you can say it's a transformation too

[polar gulch]

never heard of that, good to learn

[jolly ginkgo]

Just keep in mind where your starting point is

[polar gulch]

always on X

really thankss

https://tenor.com/view/chick-pio-cute-penguin-pinguino-gif-12847009

[jolly ginkgo]

If your doubt is done we can close the channel you're welcome 😊

Type .colse

.close

[polar gulch]

.close

[obtuse pebble]

Channel closed

Closed by @polar gulch

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[timid silo]

Determine if an ordered pair is a solution to the system of linear inequalities. Show your solution.

[short spruce]

#❓how-to-get-help

[short spruce]

what exactly do you need help with?

[polar glacier]

bru

ques 2

pls

[short spruce]

how many faces does a cube have?

[polar glacier]

6

[short spruce]

and each face is 49 cm^2

so how would you go about getting the total surface area?

[polar glacier]

6*49?

[short spruce]

precisely

[polar glacier]

also what's a net

in ques 3

[short spruce]

it's like the thing shown in question 3

oh

i scrolled up before you said the 2nd part lmao

it's just the picture to the right of it

[short spruce]

kinda like a piece of paper that you could fold into the original shape

if that makes sense

[polar glacier]

ohh]

[unique solstice]

Ive never heard of that called a net

But ig its assumed from the pic

[polar glacier]

Lmao

is it the rectangular?

@short spruce

[unique solstice]

Do you think so

[polar glacier]

no

[short spruce]

why don't you think so lol

[polar glacier]

lmao

bc they asked that

now i feel like it's not right

[short spruce]

it is right

[unique solstice]

Hmm

[polar glacier]

OKk

[unique solstice]

Thats a valid point

[polar glacier]

what do i do in ques 5

multiply all?

@unique solstice

[unique solstice]

Uhhhhh

Well think of a cylinder unwrapped

Like the weird net thing

Itd be two circles on the top and bottom kinda just hanging out

Then a big flat surface for the curvy side

[polar glacier]

nvm]

[unique solstice]

Like wrapping a piece of paper around a can

[polar glacier]

i meant ques 4

[unique solstice]

Oo

[polar glacier]

sorry

[unique solstice]

Yeah youd just multiply

[polar glacier]

ok

@unique solstice so what do i do for ques 5

multiply

[unique solstice]

Well going back to the wrapping a piece of paper around a can

[polar glacier]

yeah

[unique solstice]

If the piece of paper fit the can perfectly around

Whatd be its length

In terms of the can

Think of a circle

[polar glacier]

2πrh+2πr2

[unique solstice]

Well yes

But thats a lot of nasty stuff to remember

If you think of wrapping a piece of paper around the can

Its dimensions would be

The height of the can

And the circumference of the can

Does that make sense

[polar glacier]

yeah but what do i do

idk how the formula works

cuz it might be on the quiz

and i' too dumb

[unique solstice]

The first part of the formula is the edge side of the cylinder

[polar glacier]

width?

[unique solstice]

And the second part is just 2 times the circle area formula

Because theres a circle on the top and on the bottom

Well do you understand the circle part

[polar glacier]

yeah

top and bottom

[unique solstice]

Ye

So then the other part

Is just the rectangle formula with special lengths to wrap perfectly around the cylinder

Base*height

Where height is of course the height of the cylinder

And base is the circumference of the circle

Cause thats the distance it has to wrap around

[polar glacier]

oh ok

what the area

again

[unique solstice]

For the edge?

[polar glacier]

it says

[unique solstice]

Oh the question

[polar glacier]

surface area

yeah

[unique solstice]

Well you can get the top and bottom right

Just the circles

Then do you remember the circumference formula?

[polar glacier]

3.14

[unique solstice]

Thats part of it

The other part is just * diameter

So pi * diameter

[polar glacier]

what's the dismtere

so i do 30.5*3?

@unique solstice

[unique solstice]

30.5 is the length

Diameter is just twice the radius so 6

[polar glacier]

6*30.5?

[unique solstice]

6*pi finds the circumference

Which is remember the width of that rectangle that wraps around the cylinder

[timid silo]

mp[

[unique solstice]

Then the height of the rectangle that wraps around is 30.5

[polar glacier]

i still don't get it

shit

srry

for wasting ur tie

time

idk what to do

i have a quiz trw

[unique solstice]

Its alright

[polar glacier]

can u help with

6

ques 6

[unique solstice]

Are you good on question 5?

[polar glacier]

yeah ut's ok

[unique solstice]

I mean it seems like a quiz question

[polar glacier]

true

[unique solstice]

Lemme draw a pic

[polar glacier]

ok

tysm'

[unique solstice]

So heres your cylinder right

Top and bottom are pi r^2

So the first part of the area is just 2pi r^2

Then the second part

Is the piece of paper wrapping around

As you can see in this poorly drawn picture

Of a blue piece of paper partially wrapped around the cylinder

And the width of that piece of paper is the circumference

And the height of the piece of paper is the height of the cylinder

Yes?

[polar glacier]

ok

what is radius again?

[unique solstice]

The distance from the center of the circle to the edge

[polar glacier]

oh ok

[unique solstice]

Then the diameter is edge to edge

Or twice radius

[polar glacier]

the whole is 30.5 right?

thing*

[unique solstice]

The height yes

[polar glacier]

ok

what is that sign

[polar glacier]

?

that's the radius?

[unique solstice]

r is radius yes

And ^2 is just squared

[polar glacier]

ok

[unique solstice]

$\pi r^2$

[warm shale]

PapaBread

[polar glacier]

so what do i do with the radius

[unique solstice]

Youll use the radius to find the circle areas

On the top and bottom

[polar glacier]

it's 2?

[unique solstice]

The radius is 3

If thats what you mean

[polar glacier]

oh ok

[unique solstice]

Or do you mean like

2 circles

[polar glacier]

so what exactly do i do

[polar glacier]

2 square thing

[unique solstice]

Oo

Ye

[polar glacier]

what do i do with ques 6

[unique solstice]

The sketch of the building?

[polar glacier]

yes

[unique solstice]

Uhhhh

Thats kinda a weird question

Would you know how to start

[polar glacier]

true

like wym sketch

[unique solstice]

I think they just want you to draw different views of the outline of the building

[polar glacier]

ok'

help with question 10 pls

i meant 9

[unique solstice]

Do you know how to find the area of a single side

Just like the first one you asked about but opposite

[polar glacier]

no

NO IDEA

but it's asking for length right?

[unique solstice]

Ye

You gotta break it down into smaller pieces though

So a cube has 6 equally sized sides

And all of the sides areas together is 1014

How would you find a single sides area

[polar glacier]

oh yeah'

is it divide

@unique solstice

[unique solstice]

Ye

[polar glacier]

how do i do it

1014 divided by 6?

[unique solstice]

Yes

[polar glacier]

okkkkkk

[unique solstice]

So then

You know that the area is 1014/6 or 169

[polar glacier]

169?

yeah

[unique solstice]

Yes

So then whatd be a single side length

Of a square with that area

[polar glacier]

what

idk

what do i do

with

169

[unique solstice]

So squares obviously have equal side lengths yes

So what number times itself equals 169

[polar glacier]

yes

[unique solstice]

What math operator gives you this

[polar glacier]

1

169?

[unique solstice]

Non

Theres a math operator just for this

[polar glacier]

rlly??

[unique solstice]

Like what number multiplies with itself to get 4 for example

2*2=4

Which operator would give you that

[polar glacier]

oh yeah

so is it just 169?

[unique solstice]

Non

Square root of 169

[polar glacier]

whatt

so what is the answer

[unique solstice]

You havent learned square root?

[polar glacier]

no

[unique solstice]

Hmm

[polar glacier]

i'm ded

failing '

[unique solstice]

The $\sqrt{}$ symbol?

[warm shale]

PapaBread

[polar glacier]

oh yeah

[unique solstice]

Like uhh

$\sqrt{9}$

[warm shale]

PapaBread

[polar glacier]

how is the side cube 13m??

[unique solstice]

Cause using base * height

If the base and height are 13

Then the area is

13*13

Or 169

[polar glacier]

but the answer will be 169 right?

[unique solstice]

Its asking for the side length

So itd be the 13

169 is the area of a single face of the cube

While 13 is the length of a single edge of the cube

[polar glacier]

oh ok

got. it'

ok what abt ques 10

[unique solstice]

Do you get stuck at a specific spot

[polar glacier]

yeah i'm r;;y dumb

[unique solstice]

Where do you get stuck

[polar glacier]

i don't get the ques soeties

sometimes

[unique solstice]

I mean they dont make it particularly easy

Theyre just asking you to make a new shape out of two of the shapes they give you

So two wedges

[polar glacier]

oh ok

how do i make a new shape like what

[unique solstice]

Just like uhh

Building blocks I guess they want

Just glue two of them together however you want

And answer the questions about the glued together shape

[polar glacier]

do i have to make a new shape out of the givin shape

or make my own?

[unique solstice]

You make your own shape out of two of the given shapes

So kinda both

[polar glacier]

oh ok

can u help me with ques 11

@unique solstice

[unique solstice]

Youd just use that same formula

[polar glacier]

SHITTTT

can u pls show me on paper

if u can

@unique solstice

[obtuse pebble]

@polar glacier Has your question been resolved?

[polar glacier]

@unique solstice where'd u go

[unique solstice]

Oh sorry I didnt notice that you pinged

The area question?

Sorry Im really tired

If you have to just memorize the formula

But you should try to conceptually know what it means

Heres the formula

$\underbrace{2\pi r^2}{\text{this is 2 times the area of the circles on top and below}} + \underbrace{\pi d h}{\text{this is the area of the rectangle that wraps around the side}}$

[warm shale]

PapaBread

[unique solstice]

$2\pi r^2 + \pi d h$

Here it is without the explanation

[warm shale]

PapaBread

[unique solstice]

r is the radius

d is the diameter (or 2 times the radius)

h is the height

[polar glacier]

ok

[polar glacier]

@unique solstice u there?

[obtuse pebble]

@polar glacier Has your question been resolved?

[obtuse pebble]

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[weary sail]

hello

I'd like help with find the constraints of t?

i know how to set of the indefinite integral

just don't know where on t im supposed to integrate over

thank uuu

.close

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[magic bay]

Second Quarter
DLP 1
Directions: A. Find the quotient. Differentiate the quotient as terminating or repeating
decimal by putting a check (/) under the corresponding column.
Equation Quotient Terminating Repeating
Ex. 5 ÷ 15 =
0.33̅ √

1. 3 ÷ 15 =
2. 4 ÷ 45 =
3. 9 ÷ 12 =
4. 8 ÷ 12 =
5. 2 ÷ 4 =
   B. Give the equivalent value in decimal form.

1
5

2
3

1
4

B. Write the following decimals to fraction.

1. 0.66̅
2. 0.8
   Attachment URL: https://drive.google.com/file/d/1SUQBq4jQHZks2M2DNa7d4Ii2dn3tEnsp/view

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[mystic plaza]

wait when I get a 0 while using sign charts to determine if max or min and I get 0 does that count as increasing?

[naive fossil]

I'm assuming you mean for a function - the first derivative indicates slope so if you get a 0, it means your slope is neither increasing nor decreasing. Think a horizontal line.

[obtuse pebble]

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[languid pebble]

hello

[languid pebble]

lookin for some trig help if anyone is free it would be much appreciated

[unique solstice]

It depends on the question

[languid pebble]

okay hold on i get a picture

we've been doing online school and its making it difficult sorry if its a dumb question

[unique solstice]

Have you learned law of sines and law of cosines

[languid pebble]

yeah

im just having trouble with the calculater part

[unique solstice]

Try using one of those

[languid pebble]

sorry about the shitty typing i trying to do multiple thing. yeah i know the law of sines but i cant remember how to put it in my calculator, im using my phone so i dont know if its a logical or illogical calculator

thats all im having issues with right now

[unique solstice]

Wdym by logical or illogical

[languid pebble]

well theres two different types of calculators a logical one with mean you can put the equation in exactly how its read and illogcal means thats its put in differently, so basically i just dont know which one my calculator is because i get a possible answer for my question whenever i use either way

but i dont know which answer is the right one, im not asking for the answer to the whole question just if you could help me figure it out even give me a different questions to do to figure it out

[unique solstice]

All calculators should be able to just have numbers plugged into them

That should be the same across all calculators

[languid pebble]

no you have different steps for every calculator depend on the parts used in manufacturing and coding

hence logical and illogical calculators

[unique solstice]

Do you mean like

An algebraic calculator

Vs just simple math

Cause no two calculators should be so different that you can't solve a problem with it

[languid pebble]

if i had a logical calculator and i punched in the equation into it i would get the right answers, but if i were too punch the exact same equation into an illogical calculator it would give me a different answer because it requires different steps other than the one used in the logical calculators. my problem is that when i punch in the numbers with the right equation for each calculator into mine i get a different answer for each but they are both similar look like they could be used in the answer

[unique solstice]

Does both calculators evaluate values of sin the same

sin(50) for example

[languid pebble]

I appreciate that you did all you could to help but my teacher just became available to help me thanks a lot

.close

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[tribal jetty]

how do i show that $\circ: M \times M \rightarrow M, \quad((a, b),(c, d)) \mapsto(a d+b c, b d)$ is well-defined?

[warm shale]

˞˞˞˞˞˞˞˞˞˞˞˞˞˞˞˞˞˞˞

[tribal jetty]

it's a bit weird to me

forgot to mention that $\mathcal{M}=\mathbb{Z} \times \mathbb{Z} \backslash{0}$

[warm shale]

˞˞˞˞˞˞˞˞˞˞˞˞˞˞˞˞˞˞˞

[lethal crest]

well defined you say?

[tribal jetty]

yeah

well-defined operation

on M

[lethal crest]

because all the individual +s and *s are well defined

[tribal jetty]

well, it's quite obvious that it is, but how would i formulate it tho

[lethal crest]

yeah it is quite obvious

the definition says if $a=b$ then $f(a)=f(b)$

[warm shale]

Ryuzaki

[lethal crest]

u can maybe try something like (a,b) = (c, d) means a=c and b=d

and now proceed

honestly it's trivially trivial

[tribal jetty]

yeah, true

[jolly ginkgo]

((1,2),(4,2)) = (10 , 4)
((2,1),(2,4))=(10 , 4)
@tribal jetty

[tribal jetty]

arent those just specific examples

[jolly ginkgo]

One example is enough

[lethal crest]

no it's not

[tribal jetty]

no?

[jolly ginkgo]

There are more if it satisfies condition bd=ac

[jolly ginkgo]

Wdym to show that it's not well defined we need more than that

[lethal crest]

of course

[tribal jetty]

i need to show that it is well-defined

[jolly ginkgo]

Oh yes I did other way round thing so it isn't valid

[tribal jetty]

doesnt matter tho, ill just not show it, it wasnt really the point of the question ig

.close

[obtuse pebble]

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[lethal crest]

Left as an exercise to the reader

[obtuse pebble]

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[deep hollow]

Could somone walk me through the steps to prove this?

[craggy flame]

What have you tried to do in order to prove this?

[deep hollow]

first I broke up the top part of the left side of the equation to get (sin^2x - cos^2x)(sin^2x + cos^2x)

Then used the pythagorean Idenities to get 1 for both of them

[craggy flame]

Both!?

[deep hollow]

which i think is where Im wrong

yep I figured I was wrong

[craggy flame]

You are in the right direction. But which one can be eliminated by the pythagorean identity?

[deep hollow]

the one that adds sin and cos squared?

[craggy flame]

Good. Now, what else can be done to conclude your proof?

[deep hollow]

now we are left with 1 (sin^2x - cos^2x)

[craggy flame]

divided by...

[deep hollow]

sinx cosx...

would the (sin^2x - cos^2x) be able to be broken up again to be cancelled out?

I think im overthinking it

[craggy flame]

note that this is (sin x)(sin x) - (cos x)(cos x)

[deep hollow]

Ohh so it can be broke up?

or I guess simplified would be the correct term

[craggy flame]

Yes, the cos^2 x is a confusing expression. but it means (cos x) (cos x) not (cos (cos (x)))

[deep hollow]

gotcha ok

so then we would be left with sinx - cosx

then for the tanx - cotx we could use the quotient identity to get sinx / cosx - cosx / sin x

[craggy flame]

You can go from (sin4 - cos4 )/sin cos directly to sin/cos - cos/sin. (i'm droping the x's because it is easier to write here...)

Since you will be manipulating equalities all over, the proof will go directly from the first to the last expression.

[deep hollow]

oh so then we could keep that sin2 - cos2 because on the right side you need a common denominator and would have to multiply to get sin2 - cos2?

[craggy flame]

Yes, but I would argue from the left expression and conclude on the right expression.
Left expression = ... (expand the diff of squares)
= ... (eliminate the pythagorean)
= ... (symplify)
= right side (using the definitions).

This is a clear way to structure the proof that those expressions are equal.

[deep hollow]

oh ok, so how could we break down the right side then?

if we've simplifed the left all we can which would be sinx - cosx

[craggy flame]

The left expression is (s^2 - c^2) / (s * c) = (s^2)/sc - (c^2)/sc, right?

[deep hollow]

Yes

because you would have to multiply the get the common denominator

[craggy flame]

Great, then (s^2)/sc - (c^2)/sc = s/c - c/s (which by definition are...)

[deep hollow]

tan and cot?

[craggy flame]

Yes. You have proved that the right side equals the left side.

[deep hollow]

gotcha, thank you so so much

Walking me through it really helped me

[craggy flame]

You will get used with this kind of argument, don't worry.

[deep hollow]

I hope so, just gotta keep working at it!

Thank you again!

.close

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[obtuse pebble]

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[timid silo]

can i please understand how to find a counter example to a^3 = b^3 => a = b in complex numbers?

[timid silo]

if you can provide an example and explain how did you come to it (through experience, deduction, ...?)

[cobalt sage]

Well

1 has 3 cubic roots

They're all different from each other

But when you add the third power to them they become equal to 1

So that's a counter example

[timid silo]

cubic roots are you talking about principle roots?

[cobalt sage]

I'm talking about the nth roots of unity in complex numbers

3rd roots in this case

[timid silo]

im sorry i lost you

whats an nth roots of unity

[cobalt sage]

We call Z a nth root of unity if Z^n = 1

3rd roots of unity would be written as Z^3 = 1

[timid silo]

Z is a + bi?

[cobalt sage]

Yeah it's a complex number

[timid silo]

oh okay

[cobalt sage]

Are you familiar with the exponential notation for complex numbers?

[timid silo]

no it wasn't mentioned in our course

[cobalt sage]

I see

Well it's known that the 3rd roots of unity are 1, -1/2 + i√3/2 and -1/2 - i√3/2

They're not equal

But

1³ = (-1/2 + i√3/2)³ = (-1/2 - i√3/2)³ = 1

Even though they're not equal their cubes are equal

And that's a counter example

When trying to find a counter example for these kinds of questions, just try to think of something simple

Of small numbers

Like 1 in this case

[timid silo]

interesting but i didn't know about nth roots of unity

do you think that was what i would have been missing to find such example?

i mean when i am asked about a complex number i straightaway think about a+bi form

oh looking at the script now i see they did mention z = re^{i alpha}

saying that alpha is an angle and r is the magnitude

thats all

[cobalt sage]

Yes that's the exponential notation I was talking about

Learning it is really crucial when working with complex numbers

It makes things way easier

You should also learn the trigonometric form of a complex number

[timid silo]

but how do I deduce from that z = re^{i alpha} that nth roots of unity is 1

thing is, they just gave us a very small intro about it

[cobalt sage]

The nth roots of unity aren't 1

The nth roots of unity are the nth roots of 1

Unity means 1

It's not straight forward for you since you don't know a lot about exponential and trigonometric forms of complex numbers

[timid silo]

yeah

im still confused tbh

[cobalt sage]

Just look it up on youtube

[timid silo]

i skipped the question and just worked on the other assignments

[cobalt sage]

It'll help you a lot

[timid silo]

but def im going to look this up

you suggest to look up complex numbers in general or specific points ?

because you mentioned this "You should also learn the trigonometric form of a complex number"

im lowkey triggered the fact i wasn't able to find the solution straight up

like through the whole day i've spent in total 6 hours thinking about a solution and absolutely no clue

i thought that z = a+bi is a direction to a point and every time you ^n it rotates counter clockwise so whats the number that when you set it ^3 will get the same value at the end

it def came to me this angle stuff but nothing was mentioned in my course that talks about it so if start writing stuff outside the script it will be sus

[cobalt sage]

Some problems can't be solved just by using the algebraic expression of a complex number which is a +bi

They told you a complex number is written as re^theta

re^theta is the same as r^theta+2π

[timid silo]

wait a sec i think they mentioned another way to find out about this 1^3

they gave a lemma with

$g: \mathbb{R} \rightarrow \mathbb{C}, \ g(a) = a+0i$

[warm shale]

mhD

[timid silo]

mentioned some operation to show that we can use real numbers to make it seems like we using real numbers but instead its a complex number

also it says that the function is injective

next lemma after this one talks about

[cobalt sage]

Just work with e theta they talked about

[timid silo]

nah there is no theta

this is what they have written into

saying that alpha is an angle and it is irrelevant when |z| = 0

thank you very much for the help though @cobalt sage

[cobalt sage]

Give a sec

[timid silo]

yeah im still around

[cobalt sage]

these are the different ways to express a complex number

If you know trignometry you'll understand why a = rcos(alpha) and b= r×isin(alpha)

And then from this we can deduce that re^i(alpha) is the same as re^i(alpha + 2π)

Because we would just turn counter clock wise and reach the angle alpha again

We would have the same number Z

[timid silo]

like I might get why (-1/2 + i√3/2)³ = 1^3

because if we ^3 the left side then it will counter clockwise and probably the angle is so small that it becomes flat on the a line

but how is this supposed to be equal (-1/2 - i√3/2)³ = 1^3?

[obtuse pebble]

@timid silo Has your question been resolved?

[cobalt sage]

Here I showed that even tho we have z³ = z'³

z doesn't equal z

Because alpha/3 and (alpha/3 + 2π/3) is not the same angle

While alpha and (alpha + 2π) is the "same" angle

[unique solstice]

,rotate

[unique solstice]

😎

[cobalt sage]

😱

[obtuse pebble]

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@lavish zinc Has your question been resolved?

[obtuse pebble]

@lavish zinc Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

✅

[obtuse pebble]

@lavish zinc Has your question been resolved?

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[brisk arrow]

Can I convert it into equation and find the x, y, z

[obtuse pebble]

@brisk arrow Has your question been resolved?

[brisk arrow]

<@&286206848099549185>

[jolly ginkgo]

Is this chemistry?

[obtuse pebble]

@brisk arrow Has your question been resolved?

[obtuse pebble]

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[brisk arrow]

.reopen

[obtuse pebble]

✅

[brisk arrow]

i think yes, but consider it as a application math question

[jolly ginkgo]

See

Isolated terms with S

Like x=y

3x=2y+2z

[brisk arrow]

what it means, isolate the S?

ohh

[jolly ginkgo]

I mean don't think about O just observe
xS -> yS

[brisk arrow]

X(S+3O)=Y(S+2O)+Z(2O)

[jolly ginkgo]

Yes

[brisk arrow]

then what should i do next it looks terrible

[jolly ginkgo]

Look at thia

[brisk arrow]

i can't follow

[jolly ginkgo]

Treat S and O as different variables

[brisk arrow]

ok

should i do expanding them

[jolly ginkgo]

Do you know number of S on right should be equal to number of S in left

[brisk arrow]

yes

[jolly ginkgo]

So u don't have to do this much

[brisk arrow]

so x must be equals to y

am i right

[jolly ginkgo]

On left there are x S and on right there are y S
So x=y

[brisk arrow]

ohhh

let me write it down

x=2, y=2, z=1

am i right

[jolly ginkgo]

I wont give answer

[brisk arrow]

6O=4O+2O

[jolly ginkgo]

[brisk arrow]

x=y=2,z=1

and that's it

[brisk arrow]

is there anything wrong

maybe its the way i approaching to it?

[jolly ginkgo]

Wait

I don't get whachu did

[brisk arrow]

make a table of x=y and z

then put the numbers in

[jolly ginkgo]

Wait I'll just write it

[brisk arrow]

ok

[warm shale]

it's Sam

[obtuse pebble]

@brisk arrow Has your question been resolved?

[obtuse pebble]

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[flint kelp]

Why is the answer +200 at the end and not +2?

wouldn't you just take that 3i + 2

[daring tide]

because you do it 100 times

[flint kelp]

and sub out i for the formula?

hmm, why wouldn't you multiply i by 3 100 times as well?

[warm shale]

it's Sam

[flint kelp]

oh wow I didn't know that initial property

Thanks!

.close

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[lime magnet]

hey! I've been able to find the implicit derivative of this function, but how to I solve for x=1?

[lime magnet]

I got this for the derivative

[obtuse pebble]

@lime magnet Has your question been resolved?

[lethal crest]

put x=1 in your original equation and solve for y(x=1). then substitute in dy/dx

[lime magnet]

can anyone confirm my answer of -7? thanks 😊

x=1 in the original function gives -4

(-6(1)+4-5)/1
(-2-5)/1
-7

[lime magnet]

<@&286206848099549185> is this the correct way to solve this problem?

[obtuse pebble]

@lime magnet Has your question been resolved?

[daring tide]

it is -7

[daring tide]

Theres many ways you can solve it but the way you did works ↑

[lime magnet]

thank you !!!

.close

[obtuse pebble]

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[proper relic]

Hello I am stuck on this question, I do not know how to proceed.

[proper relic]

This is all I could do.

Oh no it's tilted.

There we go.

[warm shale]

kiid

[daring tide]

none of solutions to choose from are in good form

ln(e) = 1 but they didn't factor that

[proper relic]

Wait what.

Oh.

[undone geyser]

? one of them is correct

[daring tide]

oh yeah i see im blind

[proper relic]

lne just becomes 1 right?

Because log(e)e = 1.

[undone geyser]

use $\log_a b^c = c \log_a b$ and $a^{\log_a k}=k$ to simplify $e^{x\ln a}$

[warm shale]

kiid

[undone geyser]

why did you do it for them 😦

[proper relic]

e^ln(ax) = a^x?

[daring tide]

to explain it in concrete numbers

[daring tide]

no

$$e^{a \cdot ln{x}} = e^{ln{(x^a)}}$$

[warm shale]

MattDog_222

[proper relic]

If there is a log anywhere in the equation I can bring the exponent to the front?

[daring tide]

it goes both ways with this formula, idk what you mean by "anywhere"

the entire quantity is to said power

[proper relic]

Oh uhh.

[daring tide]

$$e^{3 \cdot ln{(3x^2+7x)}} = e^{ln{((3x^2+7x)^3)}} = (3x^2+7x)^3$$

[proper relic]

Those are equivalent?

[daring tide]

yes

[proper relic]

I thought the 3 wouldn't affect the numbers inside like the cube does.

[warm shale]

MattDog_222

[daring tide]

all 3 of those are equal

[proper relic]

Wait so the e or the ln is irrelevant here?

[plucky jewel]

Basically

[proper relic]

Because the second and third one are basically the same except the third doesn't have ln or e.

[daring tide]

because they cancel each other out since they share the natural base

[proper relic]

OH because ln = loge, and it's basically the same as log base e (e)?

[daring tide]

$$ ln \neq log(e) $$

[warm shale]

MattDog_222

[daring tide]

$$ln(x) = log_e(x)$$

[warm shale]

MattDog_222

[proper relic]

This is 1 right?

Wait nvm.

[proper relic]

Due to this the majority of the first bit is taken away, leaving us with a^x?

[daring tide]

wdym

[proper relic]

In here.

[daring tide]

$$e^{x \cdot ln(a)} = e^{ln(a^x)}$$

[proper relic]

You went from e^xlna to e^ln(a^x) so I assumed that you brought ln to the front.

[warm shale]

MattDog_222

[daring tide]

this is a logarithm law

[proper relic]

Oh.

[daring tide]

well

[proper relic]

So it can never be x^a?

[daring tide]

$$x \cdot ln(a) = ln(a^x)$$

[warm shale]

MattDog_222

[daring tide]

is the law

it just occures inside the exponent

[proper relic]

Oh.

[daring tide]

and we need to do that so we can cancel the e and the ln

[proper relic]

So we take the last number and raise it to the power of first number?

[daring tide]

huh?

[proper relic]

Like we take a, and raise it to x.

[daring tide]

yes because its being multiplied on the outside, so its the same as raising to the power on the inside

$$z \cdot ln(x+y) = ln((x+y)^z)$$

[warm shale]

MattDog_222

[daring tide]

it applies to the entire value of the expression