help-23

[safe radish]

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[topaz shard]

hey im tryna solve this problem. the second attachment is the formula im using but i got the wrong answer. pic 3 is what i got for the f gradient. pic 4 is after i put r(u,v) in, then i just simplified it and did the dot product with partial r/u at (u,v) pic 5 was my final answer but im not sure whats wrong

[topaz shard]

ah shit my gradient z is wrong

-close

.close

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[halcyon salmon]

Can someone help with this?

[safe radish]

@halcyon salmon Has your question been resolved?

[silver glade]

Since the limit results in an indeterminate form, we can apply L'hopital's rule

[halcyon salmon]

So i just have to do f'(x)/g'(x)

?

[silver glade]

yeah

i got like -sqrt(3)

[halcyon salmon]

I actually have to do 10 exercice for tomorrow..

Its 1am rn

[silver glade]

oh oof

Is -sqrt(3) right for this one

I'm practicing limits too haha

[halcyon salmon]

Lol i m actually in Last year everything feels so hard

[silver glade]

yep same lol

I'm taking calc next sem though

i self learned most of it over the summer

[halcyon salmon]

Math isn t my main i m better in subject like geography history science

[silver glade]

oh ok

I plan to pursue cs but i enjoy math

[halcyon salmon]

The way i wanna go to economy but i m suck at maths

[silver glade]

wait are you from the UK?

[halcyon salmon]

I m actually from France usa and ivory coast but i m actually in ivory coast

[silver glade]

ohh ok

[halcyon salmon]

In the school called the inphb

Best school of the country

Also the hardest

[silver glade]

Oh damnn

[halcyon salmon]

Ur from uk?

[silver glade]

nah, canada

[halcyon salmon]

Oh nice

[halcyon salmon]

Still can t find the result..

[silver glade]

Is the answer not -sqrt(3)?

[halcyon salmon]

I found 3/-sqrt3

[silver glade]

well the derivative of sin(3x) is 3cos(3x)

and the derivative of 1-2cosx is 2sinx

so the limit is
lim (x->pi/3) (3cos3x)/(2sinx)

substituting x=pi/3, you get cos(3x) = cos(pi) = -1
and sin(pi/3) = -sqrt(3)/2

so it becomes
(3*(-1))/(2*(-sqrt(3)/2)

= -3/sqrt(3)

= -sqrt(3)

[silver glade]

yes just simplify further

[halcyon salmon]

Oh alr

[silver glade]

specifically multiply both the numerator and denominator by sqrt(3)

[halcyon salmon]

Alr

Finally only 3 exercices left

[silver glade]

🎉

[safe radish]

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[native robin]

how do they get step 3

[median vigil]

the diagram shows a right triangle, they are writing a trig ratio from that

[native robin]

ohhhh

i thought they were using one of the dot product formulas

ty

.close

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[leaden harness]

Where do these values come from?

[lean otter]

these are the result of the values you added to the expression "y = sin x"

[leaden harness]

I don't quite understand

[pine horizon]

sin(x) is zero when x= 0, pi, 2pi, ...

[lean otter]

you should play around with this in desmos, its really fun to understand it yourself, as in graph sin x and then try graphing n * sinx and then (sin n * x)

[pine horizon]

sin(x) = 1 when x = pi/2, ...

and sin(x) = -1 when x = 3pi/2, ..

[lean otter]

or astar can explain it

[languid quest]

You’re looking for important x values such as x intercepts and amplitudes. Solve for x when y is 2 to get pi/8

And so on

[leaden harness]

Just tried playing it around with Desmos but still don't quite understand

[leaden harness]

I don't understand what this says

[pine horizon]

basically

you know graph of sin(x), right?

[leaden harness]

no not really

[pine horizon]

do you know for what x values is sin(x) equal to 0, 1, -1?

[leaden harness]

based on the unit circle?

[pine horizon]

yes

if u mean this (radian values)

[leaden harness]

yeah

sin(0) is 0

the other two im not sure

[pine horizon]

check this and tell

[leaden harness]

sin (-1) is 3pi/2
sin (1) is pi/2

[pine horizon]

correct

now

in your question you have y = 2sin(4x)

ignore the leading 2 for now

[leaden harness]

alright

[pine horizon]

when will be sin(4x) = 1?

sin(x) = 1 when x = pi/2

so for what x will 4x = pi/2

[leaden harness]

x = 1/45pi? I got this from 4 x pi/180

[pine horizon]

what

[leaden harness]

wait mb

Let me reread

[leaden harness]

I'm not sure

How do you get x?

[pine horizon]

$4x = \frac{\pi}{2}$

[flat frigate]

Astar777

[pine horizon]

what is x?

[leaden harness]

2pi

[pine horizon]

so $4(2\pi) = \frac{\pi}{2}$?

[flat frigate]

Astar777

[leaden harness]

no

[pine horizon]

then why is x = 2pi

[leaden harness]

x = pi/8? mb I'm like hallucinating rn on even basic algebra

[pine horizon]

yes

now do the same for -1

[leaden harness]

x = 3pi/8

[pine horizon]

yes

now for pi/4

do you know sin(x) = 0 when x = 0, pi, 2pi, ...?

[leaden harness]

no

what do you mean pi,2pi,....

Like continuing?

[pine horizon]

yes

3pi, 4pi and so on

[leaden harness]

I did not know that

[pine horizon]

well, now you know

[leaden harness]

yeah

[pine horizon]

so for what x is 4x = pi?

[leaden harness]

pi/4

[pine horizon]

there u go

all three points

[leaden harness]

so

whenever we're graphing sine

We use the values of 0, 1, -1 and the solved length?

or the period*

[safe radish]

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[safe radish]

@wicked swallow Has your question been resolved?

[wicked swallow]

I got A. 2 possible B. one C. two

<@&286206848099549185>

<@&286206848099549185> anyone?

.close

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[solar briar]

need help with this

[solar briar]

tried v*t to get d, wasn’t it

tried kinematics formula, wasn’t it either

[barren crane]

hi

[solar briar]

hi

<@&286206848099549185>

[versed isle]

well,, im not familiar with this topic yet, but in the kinematics equation wont ur intial velocity be the terminal velocity?

[solar briar]

isn’t that the final?

i start out with velocity of 0

and end at 45

[versed isle]

ohh
so the terminal is the final velocity

[solar briar]

yes, when it won’t exceed that speed in free fall anymore

also the answer would be like super large lol

[versed isle]

so the question is a simple kinematics in which

initial velocity is 0

final is 45

time is 1.5 sec

and distance is asked right??

[solar briar]

that’s what i did for the second patt i crossed out

and it was incorrect

[versed isle]

consider ur acceleration once again

[versed isle]

the acceleration i faulty here

[solar briar]

the question said to approximate it as 10, not 9.81

[versed isle]

and the time u considered here is 11.51?

[solar briar]

yes?

[versed isle]

i need u to give me the correct values as im not aware of terminal velocity

but can solve equation if u could present me with the values

[solar briar]

why’s time 1.5

the previous answer 11.51 is marked right

[versed isle]

so initial vel 0

final 45

time 11.51?

[solar briar]

yes

[versed isle]

are u aware of v = u + at?

[solar briar]

and that doesn’t give me distance fallen

[versed isle]

that gives u the acceleration

[solar briar]

which is 10

because gravity

[versed isle]

that is for free fall

and this is not a free fall condition

[solar briar]

ah

still wasn’t right

got d=258

acceleration=3.91

._.

[versed isle]

mmmmmmm

[solar briar]

well i’m dumb

i solved it

integrate v(t), set d(0)=0 to get C

plug in t=11.51, ended up with 350.5

thanks for uh, the slight support i guess

[versed isle]

😭

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[burnt junco]

hello
can i get some help ?

[safe radish]

@burnt junco Has your question been resolved?

[burnt junco]

<@&286206848099549185>

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@burnt junco Has your question been resolved?

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@burnt junco Has your question been resolved?

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[plucky lotus]

in taking a derivative of an inverse hyperbolic function, do i need to take into account its domain when differentiating?

[safe radish]

@plucky lotus Has your question been resolved?

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@plucky lotus Has your question been resolved?

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[lean otter]

I dont know what to do after

All i know for no 1

Guys pls help

<@&286206848099549185>

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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.

[lean otter]

ah ok

[frozen marlin]

jesus chr7st man you opened your channel 2 mins ago

[lean otter]

oh

yeah

can u help me with my question

[spark pier]

cant you just...

factor???????

Why are you dividing that

[frozen marlin]

what he said

[lean otter]

i dont know how to do that

[craggy sedge]

why did they not implement the rule?

[spark pier]

h u h

[plucky jasper]

is this polinomial?

[frozen marlin]

??

[lean otter]

yea

[frozen marlin]

polynomials, yes

[spark pier]

Wait youre learning that before FACTORING????

[lean otter]

yep

[frozen marlin]

not a good idea

[spark pier]

bro no forget dividing by polynomiols learn factoring first

[plucky jasper]

ohh, you just need to find the value that match the x²+5x+6 while multiply with x+3

[spark pier]

the answer is x+2 but that's not important

[safe radish]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[frozen marlin]

oops-

!nosols

[safe radish]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[frozen marlin]

wrong factoid 😭

[lean otter]

uhhh

how do you factor

[spark pier]

Well um.

[plucky jasper]

wait, i will divide it

[spark pier]

Factoring is not really a small little nuanced topic you can explain through text 😭

I suggest searching up video's about it

The basic idea is, you getting the common factor and grouping them together

For example

[plucky jasper]

do u got it?

[spark pier]

5x+15 = 0

You see how you can group the LHS by 5?

so it'll become 5(x+3) = 0

That's factoring at the most basic level\

[frozen marlin]

https://www.youtube.com/watch?v=9MUDAr1PnlE

[spark pier]

Factoring as a whole expands on this

[frozen marlin]

watch this and come back

[spark pier]

^

[frozen marlin]

use

[spark pier]

Im too lazy

hehe

Ill do it next time

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

no

I STILL DONT UNDERSTAND

what does x^2 have to do with x

what am i gonna do with 3 and 5x

whats up with the 6

[frozen marlin]

did you even watch this?

[lean otter]

I got it

So its 2x+6

For number 1 right

[spark pier]

Hi, do you understand factoring now?

[lean otter]

I did not use factoring

[lean otter]

Ok nvm this is wrong

.close

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[safe radish]

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[woven zodiac]

x ÷ 1 + 3/10=8/13

[woven zodiac]

I got 80/169

If I check it

I get 800/2197

Did I do something wrong

Tried cross multiplication

[digital sparrow]

What?

3/10 is not 8/13

[valid olive]

can you send the photo of the question

[woven zodiac]

My phrasing is wrong

Mb

x/(1+1/3)=8/13

[valid olive]

how are you getting 80/169

[woven zodiac]

Ok got it thanks

.close

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[raw schooner]

I Know we are supposed to use the product rule but I can't figure out the right answer

[raw schooner]

alright i got that one

i also had this one which was giving me a lot of trouble

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@raw schooner Has your question been resolved?

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[cobalt beacon]

Hello! I am currently studying hyperbolic geometry, and encountered the theorem that states "Two triangles are congruent if the three pairs of corresponding angles are congruent." I am confused, does congruent mean equal sides?

I am thinking of a triangle, wherein if you extend two of its side to make a similar triangle. Isn't it clear that the lengths of the sides of the bigger and smaller triangle are not equal.

[indigo valve]

its not about equal....

its about in proportion.....

[cobalt beacon]

does that guarantee that all sides grew by some constant k? the theorem alone

[indigo valve]

yeah

like a triangle zoomed in or out and rotated maybe

[cobalt beacon]

Thanks a lot!

.close

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[median vigil]

in the hyperbolic plane, magnifying a triangle would distort the angles

[cobalt beacon]

.reopen

[safe radish]

✅

[cobalt beacon]

but one could create a bigger triangle, proportional sides with the same angles? or no?

[median vigil]

in euclidean geometry, yes. but not in hyperbolic geometry

[cobalt beacon]

ic so congruence in the theorem i sent means equal sides.
RE: theorem. Two triangles are congruent if the three pairs of corresponding angles are congruent

[median vigil]

yes. so even though in plane geometry, similarity and congruence are different things, in hyperbolic geometry they are the same

[cobalt beacon]

Thanks!

.close

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[lean otter]

help

[safe radish]

@lean otter Has your question been resolved?

[plucky elk]

Try factoring the denominator and add subtract terms until you get a^2-a-3

[lean otter]

Okay

oh

i got the answer

it is

2/3

thansk for helping :))

.close

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[desert pasture]

so this is basically something like m equations in m variables?

[rustic goblet]

I don't see what you mean

[desert pasture]

So basically, what I mean is , what do we mean by each element in $\sum_{i=1}^{m} V_i$ has a unique representation

[flat frigate]

Veni, vidi, perii is $\R - \Q$

[rustic goblet]

it means that for any $v \in V_1 + \dots + V_m$, there is a unique way to write it as the sum of vectors $v_i \in V_k$

[desert pasture]

mhm

so it's basically a relation that isn't symmetric

[rustic goblet]

I don't know what you mean by this

[desert pasture]

,w symmetric relation

[flat frigate]

Results provided by WolframAlpha

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

Requested by physicsrocks

[rustic goblet]

I dunno what you're asking still >.<

[desert pasture]

nvm, my bad

[flat frigate]

higher!

[desert pasture]

basically there exists one and only one set of m vectors such that one vector comes from each of $V_i$, that satisfies the given condition

[flat frigate]

Veni, vidi, perii is $\R - \Q$

[rustic goblet]

that is a very confusing way to put it

if $v = v_1 + \dots + v_m = w_1 + \dots + w_m$, where $v_i, w_i \in V_i$ for $1 \leq i \leq m$, then $v_i = w_i$ for all $i$

[flat frigate]

higher!

[rustic goblet]

that's what uniqueness means

[desert pasture]

Hmm

I'll deal with this tomorrow

Sorry

,ti

Thanks

[flat frigate]

The current time for physicsrocks is 11:38 PM (IST) on Mon, 14/10/2024.

[desert pasture]

.close

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[candid ocean]

Can someone help me explaining my data management project?

[candid ocean]

Im confused about the "design the game to have an expected profit of up to $0.60"

but how can i do that if we're paying in dollars??? and how do i even calculate that

[digital sparrow]

i guess its like somone pays 1 to play

and you earn 1.6 on avg

so like 0.6 profit

[candid ocean]

but how do i earn 1.6 ov avg

[digital sparrow]

yeah not on avg

max profit is 1.6

[candid ocean]

oh

so if someone wins then i cant give them 2 dollars?

instead they win nothing???

im so lost tho how does this work

[digital sparrow]

i think its like

[candid ocean]

bc if they lose then they just lose their original dollar

[digital sparrow]

you pay 2 to play

4 outcomes

you lose evrything

you get 1 back (lose 1)

you break even (no loss)

jackpot you win 1

this is only an example, this prob not the ans they expect
i actually dont know what hypergeometric distribution is

and that sounds important

[candid ocean]

:p

[digital sparrow]

did i interpret your doubt correctly?

[candid ocean]

idk ill ask my teacher its ok

.close

[safe radish]

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[prisma helm]

how do I find the x int and y int of t his

[lean otter]

ppl dont know if file safe

[rustic light]

fr

send a ss

[prisma helm]

my bad

[solar hazel]

yes the classic download an image from a kid on discord looking for homework help and get a virus

[wispy monolith]

Somehow I dodged getting a virus there

[solar hazel]

shocking

[frozen veldt]

A bmp file can't contain a virus without a vulnerability in your OS/the app you use to open images

[prisma helm]

im so cooked I cant find the x and y int

[solar hazel]

same with pdfs for everyone’s information

[peak siren]

anyways to solve for your intercepts set x = 0 and solve for y and then set y = 0 and solve for x

[prisma helm]

I lost my my calculator is there any good online one

[peak siren]

i usually use desmos but that’ll give you the answers without doing the arithmetic

[safe radish]

@prisma helm Has your question been resolved?

[safe radish]

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[lavish silo]

1000 dollars is put on a bank account with a fixed interest rate of 2.5% per year.
How many years does it take for the value to double?
Round off to integer.
Solve without natural logarithms.

[lavish silo]

I tried 1000*(0.025^x)=2000 but that requires natural logarithms.

[lean otter]

do u know geometric sum ?

[lavish silo]

No.

That comes in 2 years.

[lean otter]

i meant sum of geometric sequence

same ?

[lavish silo]

like this I have no clue

[lean otter]

yes this

hm so idk

[lavish silo]

it just says solve with a calculator nothing else

[lavish silo]

Is this even the right equation in the first place?

Shouldn't be, because that equates to around -0.18790182

And it doesn't take -0.18 years for the rate to double the value lol

[lean otter]

ye sure

[lean otter]

idk because it is exactly this case tho

[lavish silo]

"Solve the problem with a digital tool.
We deposit $1,000 into a bank account with a fixed interest rate of 2.5% per annum.
How many years does it take for the value to double?
Round to whole numbers."
This is exactly what it says

I translated it to english, though.

<@&286206848099549185>

damn not even helpers can help 😭

[silver pelican]

we can write an equation for this

1000*(1+2.5%)^x=2000

[lavish silo]

Yeah, I tried $1000 \cdot 0,025^{\x} = 2000 (idk how to use texit) but that just ends up in -0.18

[lavish silo]

wait so you need the 1 I totally forgot about that 😭

[silver pelican]

think about it right

[silver pelican]

yeah

💀

that makes the 1000 get bigger with every year

is that all?

[lavish silo]

no like how many years does it take, round off

[silver pelican]

yeah

the x is the amount of years

so you would just solve the equation

do you want me to show you how to?

[lavish silo]

0 years don't think so

[lavish silo]

but it's not 0 years is it

[silver pelican]

no

it's (1+2.5%)^x

not

1+(2.5^x)

[lavish silo]

2.5% is the same as 0.025

[silver pelican]

the computer thinks that you're saying 1+(2.5^x) because of pemdas

[lavish silo]

but I still get natural logarithms which we haven't covered yet 😭

28 years that seems right

[silver pelican]

yeah, thats how I solved it

the only other way that I know would be to guess and check, which I think is too time consuming

[silver pelican]

yeah, that's what I got

[lavish silo]

so it's 1000*(1.025)^x=2000

[silver pelican]

essentially

do you understand how we got there?

just making sure

[lavish silo]

yeah I just forgot the 1 lol

[silver pelican]

alr

hope that helps

lmk if you have other questions about this

[lavish silo]

thanks

I think it was just an error made by the people who made the question cuz usually it says if we're allowed to use equation solvers

which it stated that we weren't here, and my teacher said that you have to use our equation solver when it comes to natural logarithms.

[silver pelican]

yeah

[silver pelican]

I mean you can do them manually, but it's easier to use a calculator when finding the values of the logarithms

[lavish silo]

I cannot do them as we haven't covered natural logs yet.

[silver pelican]

it's ok

you'll learn

[lavish silo]

yeh we'll cover it in the extracurriculum which comes in 2 years

[silver pelican]

👍

[lavish silo]

also why is ln(e)=1?

[silver pelican]

you know how log 10 of 10 is 1

like how log x is of a base x?

[lavish silo]

I did not know that lol

[silver pelican]

well natural logrithms just have a base of e

[lavish silo]

is log some kind of base conversion

[silver pelican]

it's kinda the inverse of an exponenet

[lavish silo]

but that's just root

[silver pelican]

like if 2^3=8, then log 2 8=3

[silver pelican]

yeah

[lavish silo]

wait why can I type log2(8) but not loge(e)

[solar hazel]

@lean otter did you ping me and delete it

[lavish silo]

he did

[silver pelican]

what do you mean?

[lavish silo]

he accidentally replied to you

[lavish silo]

like in google, maybe google isn't the best

[silver pelican]

yeah

google is weird sometimes i assume

[lavish silo]

answer is e right

[solar hazel]

don’t delete it next time

[lavish silo]

no the answer is 1

[silver pelican]

I think we're getting off topic here

[lavish silo]

that's true

[silver pelican]

if you don't have any questions, you should close this so other people can get help

[lavish silo]

that's true... I'm just curious to learn new things!

thanks for your help.

.close

[safe radish]

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[scarlet comet]

Any advice on 5c and 5d?

[raven heart]

nothing revolutionary

you can use the same hint as b) for c)

and in d) you're just summing two pieces you already know

@scarlet comet

[scarlet comet]

I honestly need help to check the previous ones tbh hold on

[scarlet comet]

5a is 2x simple right

5b im stuck at 2AxA

[scarlet comet]

what do you think about my 5b here

f(x) = ||Ax||_2 ^2 = g(h(x))
h(x) = Ax
g(z) = ||z||_2 ^2 = zTz
grad h(x) = A
grad g(z) = 2z
grad f(x) = grad g (h(x)) * grad h(x)
= 2(Ax) A = 2AxA

[safe radish]

@scarlet comet Has your question been resolved?

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@scarlet comet Has your question been resolved?

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[prisma helm]

is this the correct step

[plucky elk]

that's very hard to read

[safe radish]

@prisma helm Has your question been resolved?

[prisma helm]

.close

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[dusky dagger]

Hi so i need some guidance im going to have a mathematical logic half term exam in 2 days can you guys help me with tutorial videos to the kinds of problems that i need to solve. Please i would be really grateful if someone would help me. Also if you know anything that i need to learn on the side to understand these problems please tell me 🙂

[dusky dagger]

If the english is butchered on some problems thats my doing i just translated it from hungarian a minute ago

[safe radish]

@dusky dagger Has your question been resolved?

[dusky dagger]

<@&286206848099549185> I'm sorry for the ping i read the rules they said to ping after 15 minutes of no interaction. Soo umm any of you know mathematical logic and could help me out? :Ö

[safe radish]

@dusky dagger Has your question been resolved?

[dusky dagger]

fine ill deal with it myself

.close

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.close

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[modern bloom]

just want to confirm, so basically if the equation is in form of y'+ax=f(x), and the homogeneous solution is periodic, then the particular solution must be periodic? And the converse is not true?

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[prisma condor]

[\begin{aligned}
P(A\cup B) &= P(A) + P(B) - (A \cap B)
&= \frac{1}{2} + \frac{1}{4} - \frac{1}{8}
&= \frac{5}{8}
\end{aligned}
]

[flat frigate]

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

[storm maple]

What does the fact that C is a subset of B tells us?

[prisma condor]

Tells us that B union C = B

?

[storm maple]

Yes, so what about P(B U C)?

[prisma condor]

P(B U C) = P(B)?

[storm maple]

Yes, anyway you dont need that. My mistake

Do you know the principle of inclusion/exclusion?

P(A U B U C) = P(A) + P(B) + P(C) - P(A intersect B) - P(A intersect C) - P(B intersect C) + P(A intersect B intersect C)

[storm maple]

You already know P(A), P(B) and P(C). You need to find P(A intersect B), P(A intersect C), P(B intersect C) and P(A intersect B intersect C)

A and B are independent, so P(A intersect B) = ?

A and C are disjoint, so P(A intersect C) = ?

B is a subset of C, so P(B intersect C) = ?

And finally you can rewrite P(A intersect B intersect C) as P(A intersect (B intersect C))

[safe radish]

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[lavish rivet]

Can someone please help me with 9(3^x) = 27^(x-1)

[neat cypress]

Reduce all the numbers into a form with base 3, then use exponent rules to combine and solve for x

[lavish rivet]

I understand that, when I attempted to do it, it didnt align with the answer on the sheet. could you help me work through it?

[neat cypress]

Of course

What did you get

[lavish rivet]

0.125

ans is 5/2 or 2.5

[neat cypress]

Yeah I’m getting 5/2 so can you explain the steps you did

[lavish rivet]

starting off with the bases, ill start with making it 3^(9+x) = 3^9+x-1

aka 3^(9+x) = 3^8+x

Im confused on how to add the exponents, as I think thats where I was going wrong

I transposed the sides

so it would be 3^2x = 3^17

?

[neat cypress]

Not quite I think you’re having trouble dealing with 9 in this step

To start, how can we write the 9 so that it has a base of 3

[lavish rivet]

3^2

[neat cypress]

Yes, and what about the 27

[lavish rivet]

3^3

[neat cypress]

So now we have this right?

[lavish rivet]

Why is there a bracket on the 3^3?

[neat cypress]

Well we had 27^(x-1) so I replaced the 27 with 3^3 and then all of that to the power of x-1

[lavish rivet]

yep, but why is it in brackets?

[neat cypress]

I just wrote parenthesis to show that the x-1 exponent and the 3 exponent are different

[lavish rivet]

Ohh sorry I didnt see the ^3 there

nvm I understand that

[neat cypress]

Perfect

So now that we have all the same bases, how do we start combining them

[lavish rivet]

Start with the exponent in the brackets on the right side?

to see the full amt

[neat cypress]

Sure we can start with the exponent on the right side, how do we combine the 3 and x-1 exponents

[lavish rivet]

so it would turn into 3^3x-3

[neat cypress]

Exactly

[lavish rivet]

Im finding the left a bit more complicated, would I just use the product rule?

[neat cypress]

So the rule is that when you have two exponents with the same bases, in this case 3, being multiplied to each other, you add the exponents, in this 2+x

[lavish rivet]

yep

so its 3^2x?

[neat cypress]

Yes

Wait no

Sorry

It should be 3^(x+2)

We add the exponents not multiply then when the bases are being multiplied

[lavish rivet]

Sorry, my mistake, I can see why that is

yep

[neat cypress]

So now what

[lavish rivet]

so now we have 3^x+2 = 3^3x-3

[neat cypress]

Yep

[lavish rivet]

I would transpose next

[lavish rivet]

so 3^x-3x = 3^-3-2

[lean otter]

yoooo fern

my goat

[lavish rivet]

?

[lean otter]

please help

me with this one

[lavish rivet]

Sorry, please refer to an open channel to recieve support

[lean otter]

oh my bad

[lavish rivet]

so 3^2x = 3^-5

[neat cypress]

Yes

[lavish rivet]

so 2x = -5

x=-2.5?

[neat cypress]

Wait think you lost a negative

[lavish rivet]

probably

[neat cypress]

You get -2x

[lavish rivet]

ohh yep

[neat cypress]

And -5 for the exponents

[lavish rivet]

sorry I couldnt tell if i wrote a . or a - 😅

[neat cypress]

No worries

[lavish rivet]

so its -2x = -5

so -x = -2.5

[neat cypress]

Which comes out to the right answer if x= 5/2 or 2.5 yes

[lavish rivet]

Great, thanks alot!

Have a great day/night!

[neat cypress]

No problem, you too!

[lavish rivet]

.close

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[rustic summit]

I need help with discrete math, method of iteration, I have no clue on where I went wrong.

[rustic summit]

this is my work

I asked gpt to generate me a mock quiz for my quiz tmr and for some reason this question stumped me

<@&286206848099549185>

[wispy monolith]

How is r=2?

[rustic summit]

uhh wym

[wispy monolith]

r=2, n=n

[rustic summit]

r is the base, 2 is the base r = 2

u wanna see an example i did that was right

method of iteration, after we do all the iterations and we see that there is a pattern

of a number to a power

we can use the geometric formula

[wispy monolith]

I get till
2^n°3 + 2^n+2^(n-1).....+2

[rustic summit]

to find the explicit formula

uhh that photo is a bit old so i did kinda mess up there

but what i got

as a final answer

[wispy monolith]

Now you took (2^n+2^(n-1)...) as a gp

Right?

[rustic summit]

is 2^n x 3 + 2^n +1 -1

[rustic summit]

huh

[rustic summit]

yea so my prof explained that once u get to ur final iteration, and you see that there is powers, you can use the geometric formula, what I did was i found that the base was 2 so I replaced r with 2, then inputed everything else,

my work is a bit messy mb

the first bit at the top of the highlighted was just me writing the sequence

[wispy monolith]

2^(n+1)-1 ≠ 2^n -1

How did you reach to that

[rustic summit]

from 2^n all the way down to 2^o

[rustic summit]

i just plugged in

[wispy monolith]

Plugged in what

[rustic summit]

what I got from the iterations was that in the sequence, 2 was the base, apart from the 3 it always was followed by a base two to a power according to the iteration number(n) or n-1

so i used the formula for geometric sequences

and 2 being the base

r^(n+1) - 1 / r - 1

so i plugged in

all i had into the formula

[wispy monolith]

I get it and say as ratio , geometric series has ratio not base

[rustic summit]

the base is R

[rustic summit]

huh

[wispy monolith]

Yes you put r = 2 , so you get
2^(n+1)-1/(2-1)
But that is not equal to 2^n-1

[rustic summit]

yea I saw that error before i messaged this thing

i got 2^(n+1) - 1

so my final answer right now is (2^n x 3) + (2^(n+1) - 1)

but that answer is wrong

[wispy monolith]

You can simplify it more

[rustic summit]

not simplifying it more, it says that instead of that -1 it should be a -2

my classmate asked the same question, he got the answer 5 x 2^n - 2

when I asked it 3 times and being hella specific it kept saying that the answer is (2^n x 3) + (2^(n+1) - 2)

not -1

idk if gpt is trippin or i am

i been askin gpt for mock quizzes and its been fine til now

u see what i mean

or am i js trippin

[wispy monolith]

Yes

Wait

You used the sum formula of geometric series right?

[rustic summit]

yea

[wispy monolith]

It's
a(r^n-1)/(r-1)

Not
ar^n-1/(r-1)

[rustic summit]

wait

hold up

ur right

lemme look at my profs notes rq

ok so ig were not using geometric series sum formula

[wispy monolith]

You were using wrong formula

If you use right formula you will get -2

[rustic summit]

cause the formula at the end that were using is r^(n+1) - 1/ r -1

i mean

that is the geometric series sum formula

is it not

u use it without the first time

term

[wispy monolith]

Sum formula is
a1(r^n-1)/(r-1)

[rustic summit]

yea but if u dont have a first term u can express it as that no?

[wispy monolith]

How can you not have a first term

[rustic summit]

good question ngl

so wtf is that formula

[wispy monolith]

Wrong formula

Whoever has given

[rustic summit]

it cant be

lol

theres no way my prof fucked up for the past 2 weeks

the mf been teaching the same course for so long

[wispy monolith]

Well....

[rustic summit]

other questions that we do

either with him

or from a diff textbook

[wispy monolith]

Show me one and I will explain

[rustic summit]

alright

[wispy monolith]

Where he has used same formula

[rustic summit]

i didnt write it completely following him

but u see what

at the end he simplified it more

but i didnt write it down

but he uses that r = 4 n = n-1 this time

because the terms after the 2

is always 1 less

than the iteration number

i mean in this instance even if we added a1 then it would be 1 because the first term is 4^0

so everything stays the same

[wispy monolith]

What is the geometric series in this question, can you type it?

[rustic summit]

4^0 + 4^1 + 4^2 +..... 4^n

[wispy monolith]

Nope

Last term is 4^(n-1)

Not 4^n

[rustic summit]

uh ok

[wispy monolith]

4^0 + 4^1 + 4^2 +..... 4^n-1
Total terms = n
First number= 4⁰=1
Ratio is = 4

Sum = 1(4^n-1)/(4-1)

As per you
Sum = 1(4^(n+1)-1)/(4-1)```

Let me know which one is correct?

[rustic summit]

what

[wispy monolith]

Read it ,understand it. The last power is different for the question your professor has done versus the question you were solving.

[rustic summit]

alright hold up, this thing that Im going to send is way more clear than that one, this one i worked personally with my professor on

[wispy monolith]

For any general case of geometric series if you want to find the sum use below formula

When r >1```

[rustic summit]

the formula is at the bottom, i see the difference betweem two formulas

the geometric series formula vs whatever this is

2^n-1 is the final answer

[wispy monolith]

@rustic summit read this and understand this, don't use that r^n+1 formula or whatever

[rustic summit]

no i understand that, i used it during precalc

but

so

am i trippin or is my prof trippin

cuz we been using that formula for weeks

just practicing these iteration questions

and it always comes down to that formula usually

[wispy monolith]

Your prof is right, he is wrong that he didn't explain why that addition is happening at power

[rustic summit]

ohh ok

alright so was the original question

me being wrong

or the question being wrong

[rustic summit]

this

[wispy monolith]

Yes because the start term was not 1 and last term power was not (n-1)

If it was something like 2⁰+2¹.....2^(n-1)

[rustic summit]

because the original question last term was n was it not

[wispy monolith]

Then you could have used what your professor had taught, but eventually you would have ended at my solution

r^n-1+1 becomes r^n only

[rustic summit]

yea i understand that but that question im referring to the last term is 2^n

[wispy monolith]

If it was something like
1+2+²...2^(n-2), then it will be
2^(n-2+1)-1

[wispy monolith]

Yes and first term was not 2⁰ but 2¹

[rustic summit]

ohh

that makes alot of sense

ohh aight appreciate it

thanks

[wispy monolith]

No problem

[rustic summit]

.close

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[wraith swift]

ans key says d why is that?

[safe radish]

Please don't occupy multiple help channels.

@wraith swift Has your question been resolved?

[fossil depot]

Probability of A not happening is 16/24. Probability of B not happening is 6/24. They both sum up to 22/24, meaning the probability of either of them not happening cannot be larger than that, while the student's data suggests the probability of either of them not happening is 23/24

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[pure vector]

(iv)

I forgot how to do this

[rancid sand]

suppose gf(x) = g(f(x))

range of gf depends on the denominator from what I think

[obsidian ginkgo]

Did you find the expression?

[safe radish]

@pure vector Has your question been resolved?

[pure vector]

Can you explain a bit further?

[pure vector]

yeah,it's$\frac{2}{x^2-4x+6}$

[flat frigate]

e_waste

[pure vector]

so here's my solution

$\frac{-b}{2a} = 2,when\ x=2,y=x^2-4x+6=2$

[flat frigate]

e_waste

[pure vector]

so $x^2-4x+6 \geq 2,gf(x) \leq 1$

also,$x^2-4x+6>0$,$so\ gf(x) > 0$

and eventually the domain of gf(x) is $(0,1]$

[flat frigate]

e_waste

e_waste

e_waste

[pure vector]

<@&286206848099549185>

Am I right?

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[obsidian ginkgo]

Wdym

[main mural]

.reopen

[safe radish]

✅

[pure vector]

find the vertex

since a > 0 then the vertex should be the minimum point

[obsidian ginkgo]

Yup

[pure vector]

if I get the minimum point then I'm okay to prove that $x^2-4x+6 \leq 2$

I mean $\geq 2$

[flat frigate]

e_waste

[obsidian ginkgo]

Why?

I mean you want the range of gf()

[pure vector]

so $\frac{1}{x^2-4x+6} \leq \frac{1}{2}$

[flat frigate]

e_waste

[pure vector]

times 2 we get gf

[flat frigate]

e_waste

[obsidian ginkgo]

=

[pure vector]

oh sorry

[obsidian ginkgo]

Sure yea, this works

[pure vector]

also $x^2-4x+6 > 0$

[flat frigate]

e_waste

[pure vector]

then 1 over it must > 0 as well

[obsidian ginkgo]

No

[pure vector]

why?

[obsidian ginkgo]

I mean yea sorry

[pure vector]

so eventually the range of gf is $0 < gf(x) \leq 1$

[flat frigate]

e_waste

[pure vector]

I think it works

[obsidian ginkgo]

Yea!

[pure vector]

thx

.close

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[honest harbor]

am i just supposed to ignore the 3.25 since it doesn't line up with the graph?

[fathom jewel]

3.25?

[honest harbor]

pi + 0.11

did i solve for x incorrectly

[fathom jewel]

Also are you supposed to find all solutions, or within some interval

[honest harbor]

NAWHHH

i believe all solutions, no restrictions was provided

[fathom jewel]

the period is 2pi/3

[honest harbor]

right

[fathom jewel]

take your first solution x_1 = 3.598 + 2pi/3 * k

second

x_2 = 6.175 + 2pi/3 * k

k is an integer

[honest harbor]

right

so those would be my solutions?

[fathom jewel]

ya

[honest harbor]

ow i see what i did

LMAOOO

thank u

.close

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[pastel abyss]

suppose $A\Delta B = A\cap B \$ Prove $A=B=\emptyset$

[flat frigate]

Adam Ch.

[hearty egret]

you can the folw fact $A\Delta B\cap(A\cap B)=\emptyset$

[flat frigate]

everg

[hearty egret]

because of the assumption you can say that $(A\cap B)=\emptyset$ and $A\Delta B=\emptyset$

[flat frigate]

everg

[pastel abyss]

how did u get to that ?

[hearty egret]

just use the definition of $\Delta$ (the one that you told me earlier )

[flat frigate]

everg

[pastel abyss]

damn this is so smart

thnx

.close

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[prisma pecan]

Why are there more than one empty sets in the answer for this question???

[hearty egret]

it seems like it is using the property of being close under infinite unions to prove the property of being close under finite unions

now he wrote a finite union as an infinite union just by adding an inifite number of emptsets so the the final results wont change

[prisma pecan]

Oh alright cheers that makes sense

.close

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[stable kestrel]

hello guys, i came to this moment and don’t know what next

[covert yoke]

$\log_{1/3}(x+5)$ or $\log_{1/3}(x) + 5$?

[flat frigate]

OmnipotentEntity

[stable kestrel]

second one

wait

i’m dummy

[covert yoke]

Isolate log(x) then

[stable kestrel]

yeah

ty

i didn’t see it as it is

i dont know how to read

😅

[covert yoke]

Same

@stable kestrel if you don't have any other questions, please don't forget to .close the channel

[stable kestrel]

okay okay

.close

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[obtuse plover]

log_2

Nice

[severe pond]

Nice

[harsh mason]

is this question correct?

Log base 2 of what???

[severe pond]

exactly

log base 2

[boreal epoch]

base 2 of 5, my fault

[severe pond]

log rules sir

[harsh mason]

Log_2(5-a^3+9^(7/3))
correct me if I am wrong

[severe pond]

!nosols

[safe radish]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[severe pond]

and it’s wrong

[harsh mason]

lol

[severe pond]

log(a) + log(b) = log(ab) ≠ log(a+b)

[severe pond]

lol

[harsh mason]

ohh

[severe pond]

bruh do not type the answer

[harsh mason]

-Log_2(5(a^3)(3^7))
correct me if I am wrong

[severe pond]

brother

you’re wrong again

stop trying

[harsh mason]

damn that's hard

[severe pond]

it’s not

[harsh mason]

let me try again

[severe pond]

feel free to open your own help channel

[harsh mason]

got it

[severe pond]

instead of clogging up his

[covert yoke]

Putting this back up so that it's visible, first term should be log_2(5) https://media.discordapp.net/attachments/903481106819612714/1295760312368369857/20241015_164730.jpg?ex=670fd254&is=670e80d4&hm=9ed3bb9a78305922d5e246d631cf550043da8bddf685faac7853395e842da61c&

!status @boreal epoch

[safe radish]

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

[boreal epoch]

2

[covert yoke]

Can you show your work so far?

If I know where you are stuck, I might be able to help you with your next step