help-38

[nova spire]

and you're interested in the outcomes above 2* the expectation

suppose all outcomes are equally likely in this example

well you can't have more than half of the outcomes above 2*the expectation

otherwise when you compute the expectation

you get more than 1/2 * (2*expectation)

so the expectation is bigger than the expectation

which doesn't make sense

in general, if you're interested about how likely it is that you're above m*the expectation

it happens in at MOST 1/m of the case

[quaint ruin]

X ~ # of heads in 4 tosses.
E[X] = 4*1/2 = 2

P(X >= 3) <= E[X]/3=2/3

So, the probability that you get at least 3 heads, is below 2/3?

Is this not correct understood with an example?

[nova spire]

yeah it's exactly that

3 heads is 1.5 * the expected number of heads

so you can only get 3 heads or more in at most 1/1.5 of the cases

take another example

say you have a distance of 100m to travel in 100 seconds

and X(n) is your average speed on the n-th second

well E[X] = 1m/s

since your total average speed is 1 meter per second

so for example

the time you spend at 4m/s or more

has to be less than 1/4th of your trip

so less than 25 seconds are spent at 4m/s+ speed

does this example make things clearer?

[quaint ruin]

the time you spend at 4m/s or more

P(X >= 4m/s) <= (1m/s) / (4 m/s)

So, yes when i plug it in it does

[quaint ruin]

but I do see what ur saying as well in the logic

like otherwise we would go over the amount of seconds i think

so it has to be less than 1/4

🤔 i think xD

[trim jolt]

@quaint ruin Has your question been resolved?

[nova spire]

yeah that's kinda it

so

just adding the "f" thing

you just apply Markov

to the new non-negative random variable Y = f(X)

and a "new epsilon" $\varepsilon' = f(\varepsilon)$

[solid kiln]

rafilou2003

[nova spire]

so $\mathbb P(Y\geq \varepsilon') \leq ...$

[solid kiln]

rafilou2003

[nova spire]

and P(X >= epsilon) is less than that

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[craggy dirge]

Hello

[craggy dirge]

In a lottery of 100 tickets
there are three winning tickets.
What is the probability of winning one prize by buying two tickets

<@&286206848099549185>

1)b

Part b

In 1)a irs 3/100

[zinc ginkgo]

!15m

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[craggy dirge]

Oh sorryy

I thought we can ping once we enter the help session

[tawny bone]

Think about how many ways in total can you pick 2 tickets first

[cosmic meadow]

Get the probablity of not winning them

[craggy dirge]

But guys

[cosmic meadow]

And do 1-that

[craggy dirge]

1)a is 3/100 right? Its for winning one ticket

[tawny bone]

Or that

[craggy dirge]

But for winning 2 tickets
Cant we just multiply by 2
Thus makes it 6/100

[tawny bone]

Yes cause you have 3 ways of picking a winning ticket and 100 ways in total

[craggy dirge]

100 ways to?

[tawny bone]

You've got 100 ways to pick the first ticket

[craggy dirge]

And 99 the second

[tawny bone]

Exactly

And how many ways can you pick 1 winning and 1 not-winning ticket?

[craggy dirge]

3/100 + 3/99 ? 😅😅

3/100 + 3/99 + 2/99

What if the ticket was a winning

[cosmic meadow]

You are not reading the hint

[tawny bone]

Nonono

[cosmic meadow]

You calculate not winning

And subtract to the total

[craggy dirge]

Your way i got it but in trying to see jurism

[tawny bone]

But you also can't pick 2 winning tickets

You only get 1 prize

You'd have to subtract that too

[cosmic meadow]

Yes

[craggy dirge]

Yr way is
Total ways - not winning
1-97/100

Right?

[cosmic meadow]

No

[tawny bone]

That'd be for 1 ticket

[cosmic meadow]

That is only

Exactly

[craggy dirge]

Ahh right

For 2 its hmm

[cosmic meadow]

For the second u calculate getting the two tickets

And subtract to what ubhave

[tawny bone]

But also the order doesn't matter

[craggy dirge]

1-2/100

Ir no thats wrong

[cosmic meadow]

1-(winning 0 tickets + winning 2 tickets)

[tawny bone]

So it's not 100*99 but rather 100 choose 2
Which is 100*99/2

[tawny bone]

This is probably easier than what i'm saying

[craggy dirge]

1- 97/100 - 2/3

[cosmic meadow]

What are those numbers? They are too off

[craggy dirge]

We shuffle since order matters?

[craggy dirge]

Total minus winning nothing minus winning 2

[tawny bone]

Well if you ever have that thought think it through a little and you'll see it's negative
You can't have a negative probability

[cosmic meadow]

You did not understand

[craggy dirge]

So sorry guys its my first day in probability and my teacher told us to solve that

🥲

[tawny bone]

Let's only focus on samuel's method for now

[cosmic meadow]

1-(winning 0 tickets by taking 2 tickets + winning 2 tickets by taking 2 tickets)

[craggy dirge]

Ok but pls show me ur method too after samuel

[cosmic meadow]

You repeat the method, dont overdo

[craggy dirge]

I didnt understand

Whyby taking 2 tickets + winning ticketd by taking 2

[tawny bone]

Wait, have you gone over combinations/binomial symbol?

[craggy dirge]

We did them yeah

I know how they work

[tawny bone]

Ok then i think my way might be slightly easier tbh

[craggy dirge]

Its the question maybe a bjt tricky for me

[cosmic meadow]

You have to understand the question

They are asking u to get exactly 1 winning ticket

[craggy dirge]

Probability if getting 2 winning tickets out of 100

[cosmic meadow]

With 2 opportunities

[craggy dirge]

How? They said 2 tickets

[cosmic meadow]

You said 1 winning ticked before

[craggy dirge]

Its oart A

I done that

Now part B

[cosmic meadow]

Read

[tawny bone]

You buy 2 tickets
Only 1 wins

[slim hornet]

I need help with statistics

[craggy dirge]

Omg

[slim hornet]

and trigonometry

[craggy dirge]

I thought its 2 prizes 🥲

[slim hornet]

plzzzzzzzzz

[craggy dirge]

Okok getting 1 prize

[cosmic meadow]

!occupied

[craggy dirge]

Lets continue

[trim jolt]

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

[cosmic meadow]

So ok now

Think about all outcomes

You buy 2 tickets

Maybe you get 0 prizes

Maybe 1 prize

[craggy dirge]

Ok

[cosmic meadow]

Maybe 2 prizes

[craggy dirge]

Maybe 1 or maybe 2

[cosmic meadow]

You have 3 outcomes

[craggy dirge]

Ahhh thats why u subtracted

2 win 2 loss and 0

[cosmic meadow]

Instead of calculating 1 prize

[craggy dirge]

So it gets u 1 ticket only

[cosmic meadow]

You calculate 0 prizes and 2 prizes

Cause it is easier

[craggy dirge]

From subtracting the total

Right?

[craggy dirge]

^

[cosmic meadow]

Yes

[craggy dirge]

We use combination right?

[cosmic meadow]

You can use whatwver you want ñ

[craggy dirge]

1 - 2/100 - 97/100 - 3/100

[slim hornet]

guys

[craggy dirge]

Truee?? Pls say yes

[slim hornet]

I need help with trig graphs

[craggy dirge]

!occupied

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

[craggy dirge]

Samuel

Answer is negative

Something is wrong let me see

Hm

[craggy dirge]

My bad
1-2/100 - 97/100 = 0.01

But samuel
The probability of winning with one ticket is 3/100 which is 0.03
Probability of winning with 2 tickets is 0.01
Which is less
Shouldnt more tickets = higher chance @cosmic meadow sorry for tagging

Maybe this is correct?

@tawny bone any 😭where r u guys

[tawny bone]

Oh

I was gonna let Samuel take it

[craggy dirge]

Thats fine but samuel is busy idk

Here is the question again

[tawny bone]

Ok i'll just say my method then

[craggy dirge]

But this works???

[tawny bone]

You know how the probability of something (for simple exercises) is n/m right

[craggy dirge]

Yes

[tawny bone]

Right
So just find your n and your m
And you're set

[craggy dirge]

M is 100

N is what

[tawny bone]

M isn't 100

You're buying 2 tickets

[craggy dirge]

M is total

[tawny bone]

Yes

[craggy dirge]

98 is M?

[tawny bone]

But the total isn't 100

That'd be if you're buying 1 ticket

You're buying 2

[craggy dirge]

Hmm total tickets is not 100?

[tawny bone]

So the total number of ways you can buy 2 tickets is your total

That's 100 choose 2

Makes sense?

[craggy dirge]

2/100

🥲

[tawny bone]

Combinations

No
100C2

[craggy dirge]

Oh

[tawny bone]

Cause you're choosing 2 things out of 100 things

[craggy dirge]

That us 4950

[tawny bone]

Yes

Good

So that's the total

Then you have to find the amount of ways you have exactly 1 winning ticket

[craggy dirge]

Sorry to ask
But total of what?

[tawny bone]

Ways to buy 2 ticketd

M

M = 4950

[craggy dirge]

We dont have repitition here

And order doesnt matter

[tawny bone]

Which is why you're using combinations and not variations

[craggy dirge]

Ahhh

Yes

I get u now

[tawny bone]

Exactly

[craggy dirge]

Bcz lets say
T1 t2 t3…
T1 and t3 = 1 combo
…

Till 100

[tawny bone]

Yes

[craggy dirge]

Okok continue mister

[tawny bone]

Ok

So now N

N is the number of ways you can pick one winning and one losing ticket right

[craggy dirge]

2c3 + 100c97 out of 2c100?

[tawny bone]

Idek what 2c3 would mean but

[craggy dirge]

Like this

Combination

[tawny bone]

Bigger number first

[craggy dirge]

Oh i flipped

[tawny bone]

Like you wrote 100c97

[craggy dirge]

Yeah

[tawny bone]

But

It's simpler

Basically

You have 3c1 ways of picking a winning ticket, right?

[craggy dirge]

Yea

[tawny bone]

And for every winning ticket, you have 97c1 losing tickets you can pair it with, since you're buying 2 tickets and 97 are losing

[craggy dirge]

Oh not 100C97

[tawny bone]

So for every way you can pick a winning ticket

You have 97 ways to pick a losing ticket

Imagine W1 W2 W3 are the winners

And L1, L2, ..., L97 are the losers

[craggy dirge]

Like this?

[tawny bone]

Close
You have to multiply, not add

3c1×97c1

[craggy dirge]

Why this

[tawny bone]

Because

[craggy dirge]

Tho*

[tawny bone]

Look back at this

[craggy dirge]

Omg

[tawny bone]

W1 can go with L1, L2, ..., L97
So

[craggy dirge]

I got the same anawer as i did with samuel

[tawny bone]

You have 97 ways if you pick W1

[craggy dirge]

But samuel still didntt reply

[tawny bone]

If you pick W2, you can also pick L1, L2... so again 97

3*97

[craggy dirge]

Both ways correct right?

[tawny bone]

Huh

[craggy dirge]

Broo thank u so much 😭😭can u become my friend???

[tawny bone]

Why are you doing 2-something?

[craggy dirge]

Where

[tawny bone]

Oh

That's a 1

Nevermind

Handwriting

[craggy dirge]

😅

[tawny bone]

Yes that's right

Altho it looks like you wrote 1650 in the denominator

[craggy dirge]

🤣🤣

[craggy dirge]

Pls

Now 2a and b

Let me check

[tawny bone]

You can ping me if you need help, but I'm not very active on discord

[craggy dirge]

Instagram? Idk

Not for math

Like friends in life

Also math friends why not
I wanna major in maths cuz i like it

[tawny bone]

I've got to drive somewhere rn, try yourself first and/or ask others

[craggy dirge]

Thats Okay dude?

[craggy dirge]

Oh okok

[tawny bone]

Not really looking for friends right now, sorry, things are pretty hectic as it is

[craggy dirge]

Not friends
U become my math helper or idk

😭😭😭

But i actually would like to

Idk do whats comfortable with u

Go drive bro have fun

.close

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Closed by @craggy dirge

Use .reopen if this was a mistake.

[craggy dirge]

.reopen

[trim jolt]

✅

[craggy dirge]

<@&286206848099549185> exercise 4

What would it change in the equation if we used probability for the fake die

Odd and even

Found different ways but im lost

Multiply by 2

Idk

Its been 15 min <@&286206848099549185>

[zinc ginkgo]

this is entirely too small to read

[craggy dirge]

Let me fix it

Better!?

[craggy dirge]

Ex 4

[zinc ginkgo]

did you find the probabilities

P(even) = 2 * P(odd)

use sum of all probs = 1

[craggy dirge]

I did
P(even)/2 = p(odd)

[craggy dirge]

But the one thing i couldn’t understand is

How to get each probability for each case of sum of faces

Like i know we will get multiple

[zinc ginkgo]

.

prob of odd are all equal and prob of even are all equal

[craggy dirge]

2,4
4,2
In this case r they the same or we need to get each too

[zinc ginkgo]

what does 2,4 mean

[craggy dirge]

When we roll the dice

We get example : 4 then 2

We roll the dice again

We get 2 then 4

Are they considered the same

Like does order matter?

[zinc ginkgo]

this is the question you should be answering first

[craggy dirge]

Oh nope 😅

[zinc ginkgo]

.

[craggy dirge]

Okok

Thx

.close

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• Show your work, and if possible, explain where you are stuck.
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[icy nova]

for part C) would the answer be China or India? China increases a lot (about from 1 to 11) but India goes from like (0 to 2.5)
and for part D) do I add together (all others, China, and the US)?? or do I not include "all others"

[hallow spruce]

for part C) would the answer be China or India? China increases a lot (about from 1 to 11) but India goes from like (0 to 2.5)
I'm not sure what about this would cause confusion
and for part D) do I add together (all others, China, and the US)?? or do I not include "all others"
"all others" is every other country combined. The top 3 countries are all named in the graph

[icy nova]

.close

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• 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!

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[gritty mountain]

can anyone help me how to do this?

[ancient edge]

Ok

So we know at f’(-3) there’s a horizontal tangent right

Cause it’s given

Meaning that f’(-3) = 0

[gritty mountain]

yes

[ancient edge]

I’ve also drawn out the derivatives at the given point

We can see that f’(0) has a negative slope, meaning that f’(0) will be negative

And we see that f’(4) has a positive slope

[gritty mountain]

how did you get the new line?

[ancient edge]

Meaning that f’(4) will be posivie

Well cause you know derivative is the slope at that given point right

[gritty mountain]

yes

is that the same as x=-3?

[ancient edge]

X=-3 would look like that

[gritty mountain]

yes

but how did you get the other lines?

[ancient edge]

Do u notice at 0

If u draw a tangent line at x=0 that line will be negative

[gritty mountain]

alright

so the deravitive will be a negative slope?

[ancient edge]

Yes

[gritty mountain]

but why did you pick zero

[ancient edge]

Because

The mcq options

[gritty mountain]

so it cant be 0?

[ancient edge]

There was only f’(0), f’(-3), f’(4) listed

Wdym

[gritty mountain]

so how will the order play out?

[ancient edge]

Like this

F’(0) < f’(-3) < f’(4)

[gritty mountain]

i see

f'0 is negative

f'-3 is 0

or nuetral

and f'4 is positive?

[ancient edge]

Yes

[gritty mountain]

why would it give a horizontal tangent of x=-3, was it to trick you?

[ancient edge]

Just for our information

Not meant to be a trick

[gritty mountain]

i see

it just tells us the horizontal tangent?

[ancient edge]

sometimes

is this ap calc?

I rmb on the test it was given

But if its not given u can also see it

[gritty mountain]

yes

so it would be A?

[ancient edge]

yes

[gritty mountain]

i have a another question

i dont understand this

particulary because of the ln

do you understand how this goes?

[ancient edge]

Are u allowed to use derivative rules to evuaate this

or do u have to use the limit def

[gritty mountain]

i can use derravitive rules like

power rule and quotient rule

[ancient edge]

we can see that f(x) in this case is ln(x)

and its evulating the derivative of ln(x) at the point x = 3

so we just have to derive ln(x)

and then plug in 3

[gritty mountain]

derive of lnx is e^x

[ancient edge]

no

[gritty mountain]

is it not?

[ancient edge]

1/x

[gritty mountain]

what

i though ln x is e^x

oh bruh

it is 1/x

my bad i got mixed up

so it would be 1/2x?

[ancient edge]

wel u have 1/x now

and it wants to find derivative at x = 3

so u plug in 3 for x

[gritty mountain]

but it is gonna give 0

[ancient edge]

1/x ?

1/3

[gritty mountain]

wont it give 0 when plug in?

[ancient edge]

oh not into that

[ancient edge]

into this

into the 1/x

because we found that the function they were deriving was ln(x)

and they were evulating it at x = 3

And we knwo the deriviative of ln(x) is 1/x

[ancient edge]

all we have to do now is plug in 3 for the x

[gritty mountain]

1/3?

[ancient edge]

Yes

[gritty mountain]

i stiil dont understand how

what about the bottom

wait now i ge tit

@ancient edge but why didnt we use product rule?

[ancient edge]

There aren’t 2 products

[gritty mountain]

i mean power rule

[ancient edge]

Power rule for ln(x)

?

Doesn’t work

Cause power rule only applies to functions being raised to a power

[gritty mountain]

i think i get it

my brain is being fried

<@&286206848099549185>

[pearl thicket]

Okay so they want you to find the derivative of f evaluated on 1

[gritty mountain]

i dont know how to get a derravtive of a graph

[pearl thicket]

And you know f(x) is a product of two functions

[gritty mountain]

yes

[pearl thicket]

Did they teach you rules of getting derivates of functions?

[gritty mountain]

yes

power rule

[pearl thicket]

And with products of functions?

[gritty mountain]

yes product rukle

[pearl thicket]

So if f(x) = g(x)×h(x) what would the derivative function look like

[gritty mountain]

it would be g'(x)h(x)+g(x)h'(x)

[pearl thicket]

So f'(x) equals that

Thus f'(1) = g'(1)h(1)+g(1)h'(1)

h(1), h'(1) is given

The rest you gotta take from.the graph

What is g(1)?

[gritty mountain]

how do i find derravtive of g(1)

2?

[pearl thicket]

Nope

Oh well g(1) = 2 yes

But the derivative

Do you know what the derivative exactly is

[gritty mountain]

i dont know the derravtive of a the graph

no

[pearl thicket]

The derivate is way to show how much a function is 'increasing' at some point

or 'decreasing'

[gritty mountain]

looks like its decreasing

[pearl thicket]

Correct

And its decreasing at a linear pace

Right?

[gritty mountain]

yes

[pearl thicket]

Do you remember how to calculate how much a linear function increases or decreases?

[gritty mountain]

rise over run?

[pearl thicket]

I dont know if you call it that in english, i was in a german school

[gritty mountain]

ohi see

is it -2?

[pearl thicket]

Yes!

[gritty mountain]

oh i se

then we do the multip;ocatpom

[pearl thicket]

Now put it all together and youll get your answer

[gritty mountain]

i see will do

[pearl thicket]

What did you get?

[gritty mountain]

is it 8?

[pearl thicket]

It should be 10

g'(1)×h(1) = (-2)×3 = -6

[gritty mountain]

oops

i think i made a miscalcultion

thank you summi

i am studying for my unit 2 exam for calc

[pearl thicket]

No problem, do you have any further questions?

[gritty mountain]

yes

a diffcult ome

[pearl thicket]

Well you can ask me

I want you to be able to understand what this is about

Did you understand all the steps we took to solve the problem from before?

[gritty mountain]

yes out of noewhere the teacher gives us hard questions on exam

yes i understood the g'

whcih is the slop

this is it

it tells me nothing

i hate table and graphs so hard to understand

[pearl thicket]

Dont worry Ill make sure you will understand

[gritty mountain]

thank you summi

you are the best

[pearl thicket]

Okay we have no idea how f really looks like but they have given us some information

So where they want us to estimate f'(3)

[gritty mountain]

somewhere in the middle of 5 and 8

[pearl thicket]

Yes

We know from 2 to 4 the function changes its value from 5 to 8

[gritty mountain]

yes

if it is differentiable

does it mean it will probably be going up only

[pearl thicket]

Could be the case or it could not we dont know

[gritty mountain]

?

oops had some lag

[pearl thicket]

So lets take a small step back

[gritty mountain]

alright

[pearl thicket]

So you understand how derivatives work

[gritty mountain]

yes

slope

[pearl thicket]

Okay do you remember the last problem

How we calculated g'(1)

[gritty mountain]

we used the slope

[pearl thicket]

Yes

[gritty mountain]

oh wait

the poijt slope formula?

[pearl thicket]

;)

[gritty mountain]

y-y1=m(x-1)

[pearl thicket]

Yes

Derivates started off by creating a slope between two points

And then we fix one point amd shift the other closer to the former point

[gritty mountain]

i say 8-5=m(4-2)

[pearl thicket]

So we gain a better estimation

[gritty mountain]

3/2?

[pearl thicket]

So what would m be

Yes

[gritty mountain]

but how does it apply to f'(3)?

[pearl thicket]

Because we are looking at for 4 and 2

And 3 is inbetween

[gritty mountain]

oh i see

man these are so complicated

[pearl thicket]

So our best estimation is to look how much our function changes from 2 to 4

[gritty mountain]

i see

so 3/2

[pearl thicket]

Yes

Its like average value

[gritty mountain]

i have another question

[pearl thicket]

Okay

[gritty mountain]

i thought it would be 6 but it is not even a answer

[pearl thicket]

Do you know what continouos means?

[gritty mountain]

yes

no holes

[pearl thicket]

Pretty much yes

[gritty mountain]

and same left and right

[pearl thicket]

Now what is differentiable

[gritty mountain]

if there is no cusp

or a sharp turn

or if vertical is 0

none of these

[pearl thicket]

There is a sharp turn though

In this function

[gritty mountain]

but it is at 6

and 4 i dont really kmow

it doesnt seem to sharp

[pearl thicket]

but 4 is the answer

[gritty mountain]

i see, so i am correct?

[pearl thicket]

With 4 yes

[gritty mountain]

but it is baret any sharp

[pearl thicket]

And with 6 too

It doesnt matter

It has to be smooth

[gritty mountain]

i see

[pearl thicket]

It doesnt matter if its a tiny bit sharp

[gritty mountain]

like curves right

[pearl thicket]

Yea

Because the issue would be that the f'(4) (for an example) would have two values

If you come from right and from left

You would gain two different values

Do you understand?

[gritty mountain]

i see

[pearl thicket]

But do you get what Im saying?

[gritty mountain]

yes i am pretty srue

[pearl thicket]

Do have anymore questions?

I have time, you can ask me anything

[gritty mountain]

yes

i think i got this can you tell me if id o antyhing wrong

[pearl thicket]

Well then suggest me how you would do it

[gritty mountain]

i would take f prime and g(x) and multiply

then add f(x) and g'(x)

i got 9

[pearl thicket]

Okay this is a case of right answer but not the right idea of solving

Look again how is k defined

[gritty mountain]

my bad i would add the prodcurt of f(x)g'(x)

[pearl thicket]

I think you mean the right thing

What rule are you using for this?

[gritty mountain]

i am using the product rule

[pearl thicket]

Yes

[gritty mountain]

i see so it would be correct?

[pearl thicket]

9 would be the correct answer, you just gotta apply product rule and read the values from.the table

[gritty mountain]

yes

that is what i did

[pearl thicket]

Oh then its perfect

[gritty mountain]

wait i hva enoather question

[pearl thicket]

I thought you just multiplied f'(x) and g'(x) before

[gritty mountain]

i stil dont understand this

[gritty mountain]

oh lol

i worded it a little bad

sorry

[pearl thicket]

Oh god this brings back memories

[gritty mountain]

lol these things make me so mad

limits and fractions not my strong suite

[pearl thicket]

Uhmmm idk how advanced you are in calc, is tjis school level or university level?

[gritty mountain]

school bc

calculus bc

[pearl thicket]

Did you hear of l'hospital?

Okay now lets make this simple

Do you know what exactly happens here

[gritty mountain]

i have not head of lhopital yet

we were not taught

[pearl thicket]

Do you know what happens im this formula thing?

[gritty mountain]

all i know this is a altternate derravtice formula

[pearl thicket]

Exactly

Its a formula to calculate the derivative of ln(x) at 3

[gritty mountain]

i dont know how to do the bottom

since 3-3 will equal 0

[pearl thicket]

Thats why you dont bother about it

The trick is

That you realise that this is how the derivative is defined

If f(x) = ln(x)

[gritty mountain]

so i dont have to be worried about the denominator?

i get 1/x

[pearl thicket]

Then this expression is equal to f'(3)

Yes

You dont have to do calculations there

[gritty mountain]

so all i need is the numerator?

[pearl thicket]

Yes and no, yoi are doing no calculations there

Again

The trick is that you have to realise that this is the derivative of ln(x) at 3

You dont have to do anything further with this

[gritty mountain]

i see

[pearl thicket]

All you gotta think is what is the derivative of ln(x) at 3

Do you know this?

[gritty mountain]

which is 1/3

[pearl thicket]

Exactly

Thats it

[gritty mountain]

so i dont have to worry about bottom?

[pearl thicket]

Nope

Its all about realising that this is the definition of a derivative

[gritty mountain]

hopefully i do good in the unit 2 test

[pearl thicket]

Just keep a cool head

[gritty mountain]

i keep on going crazy

during the test

[pearl thicket]

The solutions are simpler than you at first expect

[gritty mountain]

and time goes so fast

[pearl thicket]

Do want to ask anything more

[gritty mountain]

yes

this would be d right?

[pearl thicket]

Imma be honest i forgot what the derivative of sec(x) and csc(x) are

[gritty mountain]

i think it should be correct

[pearl thicket]

Just looked it up

D is correct

[gritty mountain]

sweet

ok i am gonna do this

is it 0?

[pearl thicket]

No

[gritty mountain]

oh wait

it is 2

[pearl thicket]

Yes

[gritty mountain]

sweer

i think i have a few more questions left for the review

[pearl thicket]

Im still here if you need more help

[gritty mountain]

alright i got three more questions left

i will do this on m own

i got 6/25

gona tr again

[pearl thicket]

Look up the quotient rule again

[zinc ginkgo]

,tex .diff rules

[solid kiln]

pizzanator

[pearl thicket]

Oh shit thats neat

Thank you

[gritty mountain]

i got it

2/16 simplified

which is 1/8

[pearl thicket]

Correct

[gritty mountain]

nicee!!

now doing this

i got

A

[pearl thicket]

Yes

[gritty mountain]

now gonna try this

i got -2

[pearl thicket]

Try again, there must be one small mistake

If you want to yoi can show me yoir calculations

[gritty mountain]

oh wait i think i forgot something

[pearl thicket]

And I think I know what you forgot

[gritty mountain]

it was the bottom

i fotgot the lo^2

[pearl thicket]

Yes

[gritty mountain]

i got -1/2

[pearl thicket]

And thats the correct answer

[gritty mountain]

lets goooooooo!!!!!

ok time to check

i got 5 wrong

i am pretty sure i did this correcrly

[pearl thicket]

What did you do to solve this

[gritty mountain]

first

i made the top and bottom to equal eachother

which it did

then i got the derrravtives

[pearl thicket]

What the the derivative of the first function

[gritty mountain]

x

[pearl thicket]

No

[gritty mountain]

oh wait it is 1

[pearl thicket]

Yes

[gritty mountain]

that is the mistake i made

so it wouldve been b

[pearl thicket]

Yes

Continuous but not differentiable

[gritty mountain]

i got this wrong

i see what i did wrong

i forgot the second derravtive

[pearl thicket]

Im this task or a different one?

[gritty mountain]

a difgfernet one

how did we get rthis wrong

[pearl thicket]

HUH

WHAT AM I A FAILURE

WHAT IS THE RIGHT ANSWER?

[gritty mountain]

it was 2

A

[pearl thicket]

Okay gimme a sec

Oh yeah it is 2

What the fuck did i calculate

Oh I realised my mistake

[gritty mountain]

how

[pearl thicket]

I took g(1) = 4 when in reality is 2

[gritty mountain]

oh i see

this graph is a litle werid looking

[pearl thicket]

Its f(1) = g'(1)×h(1)+g(1)×h'(1) = -2×3 + 2*4 = -6 + 8 = 2

[pearl thicket]

Nah it was me being dumb

Dont be like me :D

Wanna move to the next one

[gritty mountain]

YES

oops caps lock

[pearl thicket]

I can already tell what your mistake was

[gritty mountain]

i didnt do the producrt rule

[pearl thicket]

Yes

[gritty mountain]

i wa sbeign to quick

how ddi i get this wrong

i thought this was corect

[pearl thicket]

Okay lets do it step by step

What is f'(x)

[gritty mountain]

it is

1/x

[pearl thicket]

Not just 1/x

[gritty mountain]

1/3

[pearl thicket]

1/x + 2

[gritty mountain]

oh yes

i forgot

it is 1/3 + 2

2*3

[pearl thicket]

And that simplifies to...

[gritty mountain]

7/3

breh

my brain is fried

i think i am going to take a smallbreak

my brain is about to explode

thank you summi

can i dm you if i have any more questions

?

[pearl thicket]

No problem, if you have questions you can dm me

Yes :D

Ill be awake for 1 more hour though

[gritty mountain]

thank you man you are the GOAT!!

[pearl thicket]

Maybe longer

[gritty mountain]

🐐

i see thank you

time to give my head a little rest

.close

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[native coral]

Can someone pls check if my answers is correct or no

[trim jolt]

@native coral Has your question been resolved?

[native coral]

I’m sorry I didn’t get what you mean😅

[somber ginkgo]

looks about fine

[somber ginkgo]

small correction: q5 asks for the square of 7, not the square root of 7

[somber ginkgo]

also note that you can do the very last part (arrange in correct order) without finding out the values of the square roots

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[marsh forum]

We now attempt to prove that A mapping from a. higher dimension to a lower dimension wherein 0 is the only element mapping to $0$ isn't possible.
\
\
Consider the following Transformation T from $\mathbb{R}^n$ to $\mathbb{R}^m$, given by the generall matrix
\
\
$$\begin{bmatrix}
a_{11} & a_{12} & \cdots & a_{1n} \
a_{21} & a_{22} & \cdots & a_{2n} \
\vdots & \vdots & \ddots & \vdots \
a_{m1} & a_{m2} & \cdots & a_{mn}
\end{bmatrix}$$

so
$ \begin{bmatrix}
a_{11} & a_{12} & \cdots & a_{1n} \
a_{21} & a_{22} & \cdots & a_{2n} \
\vdots & \vdots & \ddots & \vdots \
a_{m1} & a_{m2} & \cdots & a_{mn}
\end{bmatrix} \cdot \begin{bmatrix}
a_{11} \
a_{21} \
\vdots \
a_{n1}
\end{bmatrix}= \begin{bmatrix} \sum_{i=1}^{n} a_{1i}x_i \ \sum_{i=1}^{n} a_{2i}x_i \ \vdots \ \sum_{i=1}^{n}a_{mi}x_i \end{bmatrix}$
\
\
We now solve

$\begin{bmatrix} \sum_{i=1}^{n} a_{1i}x_i \ \sum_{i=1}^{n} a_{2i}x_i \ \vdots \ \sum_{i=1}^{n}a_{mi}x_i \end{bmatrix}= \begin{bmatrix} 0 \ 0\ 0 \ \vdots \ 0\end{bmatrix}$
\
\
Which gives us a solution set consisting of a non -finite number of elements proving our result .

[marsh forum]

Can I have this checked?

[solid kiln]

Veni, vidi, perii

[ionic pendant]

why does the solution set necessarily consist of a non-finite number of elements?

[marsh forum]

there are more variables than equations

[ionic pendant]

well that shows that the linear mapping is equivalent to an overdetermined homogeneous system of linear equations, although you should probably expand on why that necessarily has nontrival solutions (or invoke some theorem)

[marsh forum]

Got it

Thanks

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[dapper wedge]

As a lone expression, would -2^2 be 4 or -4

[dapper wedge]

Not assuming there are any brackets

[hearty plank]

I'd say -2^2 = -(2^2) = 4

That's what calculators assume

[dapper wedge]

Calculators assume -(2•2)

Which would be -4

From everything I know

-2^2 would be -2 × -2

But I'm arguing with people right now that are hell bent on -(2×2)

[unique minnow]

If we assume calculators use usual order of operations, which they commonly do to avoid ambiguity, the exponent latches on the 2, so it's interpreted as -(2^2) = -4, yes.

[hearty plank]

You know that (-2)^2 is 4 which is correct

[unique minnow]

Now it also depends on how your calculator works to begin with. Some will not have a minus sign per say, but rather will flip the sign of whatever you input, so if you press - then 2 then ^2, it might treat it as (-2)^2 = 4.

This is somewhat uncommon in scientific calculators and programming languages.

At the end of the day, if it's on paper, order of operation dictates -4.

[dapper wedge]

Except outside of a calculator

How are you supposed to interpret it

[unique minnow]

At the end of the day, if it's on paper, order of operation dictates -4.

[hearty plank]

The same way really

[dapper wedge]

I read that after yea

[unique minnow]

-2^2 = - (2^2) = -4

That's the "legit" way.

[dapper wedge]

Literally every teacher I have ever had has done -2^2 = 4

[hearty plank]

The second behaviour is seen more commonly of the older style scientific calculators

[dapper wedge]

Maybe it's a regional thing?

[hearty plank]

Or the ones we are supposed to use in the exams

[unique minnow]

The whole point of giving priority to certain operation is to be able to write things more concisely without sacrificing any meaning in the operation. If it's ambiguous, then there's no point debating it since either can be right. You're just better off using brackets to make things clear.

However, in any context where BODMAS or PEDMAS or whatever you call it is assumed, I have a hard time reconciling -2^2 = 4.

[hearty plank]

Agreed

Cause then what's the point of the minus

[dapper wedge]

The way I see it is since it's not an equation the - is already attached to the the number, it's a negative number, so the negative sign wouldn't be left out and you go to do the exponent

But maybe it's just a matter of perspective ig

Obv it would be different if it was y^2 -y^2

Or something

[unique minnow]

The thing is in BODMAS if you wanted to treat it as a negative number squared, you'd explicitly write it as (-2)^2 to unambiguously say "see this number -2? I'm taking its square."
Your last example is actually a good argument for -2^2 = -4, because I'm pretty sure in most cases, -x^2 is parsed as - (x^2) and not (-x)^2.

Now nothing stops you from hereby declaring that -2^2 = 4, and some people might agree, but you then have to be consistent with that choice across the board, because otherwise what is the point?

[dapper wedge]

My last example was to show the difference of when the expression is alone vs when it's in an equation

Meaning you would need the parentheses when it's an equation as the negative could be seen a minus too

But when it's alone I personally see it as a negative number, not separate

[unique minnow]

Yes I know what you meant, but the point is it becomes inconsistent if you see it that way.
Technically it should work for any value that -2^2 = 4 (like -3^2 = 9), but then for a placeholder like x it doesn't

[hearty plank]

I mean, if want to see it like that personally, we can't really convince you out of it

But generally you'd find that unary negation is a lower precedence operations in maths and computer science than exponential

I think that was mentioned by Azy (sorry to shorten you name)

[unique minnow]

Like for instance, this is an edge case that you don't need to deal with if you stick with some convention for order of operations.
Now it doesn't mean that it's completely devoid of meaning, although it does seem to overcomplicate things for me. Regardless, if you make it clear whenever you're writing maths that this is what you mean, then so be it it'll just be interpreted as such; you just have to keep in mind that this is usually not the adopted convention.

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[pseudo shoal]

I need help with this question I am not sure if the process I am using is correct

Here is the work for it

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[frail sierra]

i need help figuring out what I’m doing wrong. i’ve checked with synthetic division and long division and i got the same answer 😕😕😕😕

[bronze sigil]

ur answer isn't wrong?

[frail sierra]

yeah that’s what i’m thinking, but answer key says otherwise i guess

[bronze sigil]

that third picture is the guide right?

[frail sierra]

yeah

doesn’t show how they did it

[bronze sigil]

so ur answer isn't wrong

they just did difference of squares on x^2 - 5

[frail sierra]

Wait

Pmg

i’m blind

I thought it said imaginary numbers

Errr

😭😭😭

[bronze sigil]

only if the minus was a plus

it would be imaginary

[frail sierra]

yeah i was thinking the square root was imaginary numgers

oops

[bronze sigil]

oh

[frail sierra]

My bad thank u 😭😭😭

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[buoyant ivy]

I’m taking some time to practice transformations

But I’m struggling to remember the shifts

That’s what I got so far

I know for certain that the -8 has to make the entire thing shift down 8 units

But what about the x-3? Did I plot the points correctly passed on the chart? I’m so lost

[stray drum]

If -8 makes it shift down by 8 then does it make sense that x-3 make it shift down by 3

[buoyant ivy]

So they both make the entire function shift down?

Once by -3 and once by -8?

[stray drum]

No thats not what im saying

[buoyant ivy]

Oh

Then no it doesn’t make sense

Cuz it’s not correct

And yet it’s what I did

Damn😭😭

My fault

So it’s a shift to the left by 3 units?

[stray drum]

To the right

[buoyant ivy]

But if it was adding its to the left right? Just wanna make sure

[stray drum]

Yes it seem kinda confusing

So think abt it this way

[buoyant ivy]

My new point is going to be (3,1) for the first transformation essentially

And then (3,7) for the final

[stray drum]

If you have a y=x, and y =x-3, the second equation is 3 units ahead of the first, because you would need x=0 for y to be 0 in the first one, but x=3 for y to be 0 in the second

[buoyant ivy]

Huh😭😭 im sorry I don’t understand

[stray drum]

So like

Find x intercept for y=x

Then find x intercept for y=x-3

You’ll see that the x intercept for the second equation is 3 units to the right of the first

And so is the entire graph

[buoyant ivy]

I get it finally

And after that I simply shift down 8 units?

[stray drum]

Yep

[buoyant ivy]

Lemme rewrite it and lmk if I understand it

Gimme 2 seconds

Ignore the chart

But is that good? I feel like I rly understand it now

[stray drum]

Looks good

[buoyant ivy]

ayyyyyy

You the goat

Thank you

[stray drum]

Np

[buoyant ivy]

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[buoyant ivy]

.reopen

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✅

[buoyant ivy]

Hi @stray drum

Sorry real quick I just had a idea

I used to see some questions last year when the x-3 is not an exponent but it’s in parenthesis, how would the shift move? If I’m not mistaken wouldn’t it just be a vertical shift up by 3 units?

Sorry a shift down 3 units

Or would it still be to the right

[stray drum]

Vertical shifts are always the last term

[buoyant ivy]

So that means it would still be 3 units to the right even though it’s not a exponent

[stray drum]

No

[buoyant ivy]

Oh

Lemme see if I have a old paper that shows this

Gimme a second

I might have a sample

BAM!!

Ok so in some cases like that

[stray drum]

Thats logarithm

[buoyant ivy]

oh

I’m blind now apparently

Sry

So the basic function is at (0,1) then a horizontal shift by 2 units to the left

[stray drum]

I think so

[buoyant ivy]

Do you want me to solve it and just show it to you? If that’s ok wit you

[stray drum]

Its prolly easier if you just say the thought process here

[buoyant ivy]

Ok

So the basic transformation is just the basic log function which is (1,0)

1st transformation is going to move it 2 units to the left which makes our point (-1,0)

And the final transformation is down 4 units so our final point is (-1,4)

That’s what I got

Like this

[stray drum]

Yeah that looks right

[buoyant ivy]

Bro ur giving me powers or something ur Goated

Aight then

I’m chilling

Byeee

[stray drum]

Cya

[buoyant ivy]

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[lean thunder]

Let 𝑓(𝑛) = 𝑛 + ⌊√𝑛⌋. Prove that, for every positive integer 𝑚, the
sequence,

𝑚, 𝑓(𝑚), 𝑓(𝑓(𝑚)), 𝑓(𝑓(𝑓(𝑚))), …

contains the square of an integer

[lean thunder]

There are a lots of things to experiment on this problem. I also can't get into any algebraic relation.

No contest math

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@lean thunder Has your question been resolved?

[lean thunder]

<@&286206848099549185>

[ripe valley]

Nice question hmmm have you tried induction?

It might just help

[lean thunder]

Yes

But didn’t help

[ripe valley]

I see

[ripe valley]

Hmm sqrt(n)<= (n+1)/2 implies its floor is...

Try thinking along these lines

[lean thunder]

I think I need to experiment a lot with this problem. Like creating a table with bunch of numbers and calculating them roughly

[ripe valley]

You could try that