so what is f(0)
#help-19
narrow crypt
hollow copper
what why do we put the number in the brackets
narrow crypt
oh dear
to represent what is our input
for the function
say f(x) = my rizz in x days after today
ocean bramble
the surface would be a depth of zero, not 1
narrow crypt
the surface would be a depth of zero, not 1
yes this
warped glacier
the surface is 0 millimeters below the surface
hollow copper
what
hollow copper
the surface is 0 millimeters below the surface
then why is it below the surface
shouldnt it be on the surface
warped glacier
shouldnt it be on the surface
well then that's a language issue, not a maths issue
on the surface is 0 millimeters below the surface if you think about it
narrow crypt
then why is it below the surface
0 milimeters below the surface is exactly at the surface
hollow copper
thats what im sayinnnn
ocean bramble
warped glacier
yeah so you have t = 0
ocean bramble
that's a glorious drawing of the beam going through the surface
and it has less particles the more it goes through it
because some particles get angry and say YOU KNOW WHAT, i'm tired of penetrating the surface
narrow crypt
yeah so you have t = 0
ok so we are calculating f(0) where f is teh function given in the question
ocean bramble
yes
copper quarry
the surface would be a depth of zero, not 1
thats what im thinkinn
narrow crypt
anything to the power of 0 is 1
yess
narrow crypt
yup
ocean bramble
anything to the power of 0 is 1
zero to the power of zero sometimes disagrees
hollow copper
narrow crypt
zero to the power of zero sometimes disagrees
lets keep that aside
hollow copper
YAY
narrow crypt
(for now)
copper quarry
k gaslighted u into thinking u were wrong 🤣
narrow crypt
me when physics
ocean bramble
"replace t for 0"
"physics"
bruh
copper quarry
ts just a skill issue not physics issue 💔
narrow crypt
physics just estimates everything
copper quarry
where is the estimation vro 🥀
narrow crypt
lets see
mircoscope magnification formula
wave interference formula is based on
[ \sin\theta \approx \tan\theta]
clever fjordBOT
k
narrow crypt
assume its parralel but its not actually parralel
copper quarry
bro its just a math question its not that deep
hollow copper
ohhhh
narrow crypt
when're u taking the sat 🥀
hollow copper
how many faces and edges are there on a cube
hollow copper
when're u taking the sat 🥀
august 23rd
narrow crypt
how many faces and edges are there on a cube
edges are not important
hollow copper
alrr
narrow crypt
august 23rd
great. u have time
hollow copper
even tho i dont know these questions that look so easy for u 😭 ??
narrow crypt
some ppl just come in here and say stuff like 'guys. i have my calc 3 exam in 12 hours how do i do calc1'
late sinew
narrow crypt
now 5 sides
hollow copper
so 841 + 145
narrow crypt
,calc (29^2)* 5
clever fjordBOT
Result:
4205
those vertical bars means "absolute value of"
hollow copper
oooo okay
hollow copper
|x - 9| = 18
narrow crypt
how split into two cases
hollow copper
two cases?
narrow crypt
no
case 1: x-9 = 18
case 2: -(x-9) = 18
or u can do
case 1: x-9=18
case 2: x-9=-18
depending on ur preferance
narrow crypt
find x
hollow copper
x = 37, x = 1
hollow copper
x - 19 = 18
narrow crypt
its not 19
clever fjordBOT
narrow crypt
well done
hollow copper
dude
copper quarry
x = 9 + 18e^i*n ✅
hollow copper
i cant enter two solutions
narrow crypt
so what is the full question asking
hollow copper
copper quarry
💀
narrow crypt
just add the two solutions together then
copper quarry
next time show the full question vro
hollow copper
narrow crypt
what are the choices 😭
hollow copper
what are the choices 😭
uhhhh
narrow crypt
hint: factor something out
hollow copper
oh man why is the sat so hard
english section is easy just the maths section is hard
narrow crypt
gang
hollow copper
anyways
narrow crypt
i beg to differ
hollow copper
hint: factor something out
is it k
narrow crypt
is it k
no it is not me
its something else
[ \frac{42 \cdot a}{k} + 42 \cdot a \cdot k]
clever fjordBOT
k
hollow copper
42
narrow crypt
just 42?
hollow copper
factor means to multiply them?
hollow copper
42a/k + 42ak
hollow copper
narrow crypt
[ 42a\left( \frac{1}{k} + k\right)]
clever fjordBOT
k
narrow crypt
ohh
hollow copper
but even with chatgpt im struggling so ig its skill issue
narrow crypt
if u try hard enough, ull understand it some day
hollow copper
narrow crypt
odd edgeBOT
@hollow copper Has your question been resolved?
amber veldt
(it sucks at calculus)
o4-mini-high sucks slightly less btw
odd edgeBOT
odd edgeBOT
Available help channel!
wanton bison
Say I have a complex function f(z). Can I always write f(z) as f(z) = f(x,y) = u(x,y) + iv(x,y). where u and v are real valued functions?
tepid pelican
Say I have a complex function f(z). Can I always write f(z) as f(z) = f(x,y) = u...
x, y are the real and imaginary components of z?
wanton bison
Yes
wanton bison
I actually think I figured it, given f is analytic we can express f as a power series...
Then we can group real and imaginary parts
tepid pelican
Why'd you need that
why not just literally take the real and imaginary part
that works for non-analytic functions
why go through that power series thing
wanton bison
What if you have something like cos(z) I thought or some nasty rational function where it's just hard
tepid pelican
u(x, y) = Re(cos(x + iy))
v(x, y) = Im(cos(x + iy))
both u and v are real valued
I see
odd edgeBOT
wanton bison
.unsolved
odd edgeBOT
✅
wanton bison
both u and v are real valued
Is it possible for a complex function that its real part or imaginary part is undefined?
Or does not exist, or am I tripping?
tepid pelican
Is it possible for a complex function that its real part or imaginary part is un...
only if f(z) itself is undefined at that point
wanton bison
Oh ok.
tepid pelican
if f(z) is defined and is complex, then the result will be a complex number
and every complex number consists of real and imaginary part
odd edgeBOT
odd edgeBOT
Available help channel!
analog raven
the probability that a student is chosen as the school prefct is 0.15,if ther are 11 males and only seniors can be elceted,how many females are there
can someone please help me?
amber veldt
the probability that a student is chosen as the school prefct is 0.15,if ther ar...
uh, is there a connection between gender and being a prefect?
analog raven
well you are supposed to find how many females there are based on the number of males and the probability that the person is female
amber veldt
I don't see how it's solvable unless there's some sort of relationship between gender and being a prefect
static totem
amber veldt
otheriwse it's like saying
the probability that a student is chosen as the school prefct is 0.15,if ther are 11 people who play Skyrim and only people over 2 meters tall can be elected,how many non-skyrim players are there?
rose coral
-# loving these pronouns
amber veldt
there's something missing about the way you presented the problem
because otherwise Skyrim and being over 2 meters tall are just as relevant as being male or female
amber veldt
oooh you miswrote the question
analog raven
oh,i did?
amber veldt
you said the probability that a student is elected
but it's specifically the probability of a female student
amber veldt
do you know the law of total probability?
analog raven
nope
amber veldt
it's when you divide something into categories such that:
no categories overlap
everything is in exactly one category
so for example
a high school can be partititioned in: freshmen, sophomore, junior, senior
analog raven
oh so that everyone belongs to oe group only
amber veldt
exactly
know what an "event" is in probability?
it just means a thing that can happen or not happen
here's the rule of total probability:
if the possible events are partitioned into categories P1,P2,...,Pn
then:
$$\mathbb{P}(X)=\mathbb{P}(X|P_1) + \mathbb{P}(X|P_2)+\cdots +\mathbb{P}(X|P_n)$$
clever fjordBOT
gfauxpas
amber veldt
let's give an example
analog raven
then?
amber veldt
suppose I have a collection of candies
they are either sour or sweet
and I want to know the probability that a candy is broken
then
$$\mathbb{P}(\text{broken})=\mathbb{P}(\text{broken}|\text{sour})+\mathbb{P}(\text{broken}|\text{sweet})$$
make sense?
clever fjordBOT
gfauxpas
amber veldt
do you understand the example?
analog raven
i think i do
amber veldt
actually i used the wrong notation
it's
$$\mathbb{P}(X)=\mathbb{P}(X \text{and} P_1) + \mathbb{P}(X \text{and} P_2)+\cdots +\mathbb{P}(X \text{and} P_n)$$
clever fjordBOT
gfauxpas
amber veldt
$$\mathbb{P}(\text{broken})=\mathbb{P}(\text{broken and sour})+\mathbb{P}(\text{broken and sweet})$$
clever fjordBOT
gfauxpas
amber veldt
I was using the | incorrectly, anyway
what's the probability of ANYONE being elected prefect?
presumably the prefect election has to have a winner
analog raven
oh so its like the probability that anyone is elected is ,the total of nominees,plus boys,plus the total nominees plus girls
?
amber veldt
you have the right idea but let's make it precise
assuming a candy is not both sour and sweet, and is either sour OR sweet and not neither
you can split up candies into sour candies and sweet candies
for the election, let's split up the people running for prefect into males and females
it's a partition because math problems don't deal with intersex people and the like
right?
analog raven
yh
amber veldt
$$\mathbb{P}(\text{prefect is elected})=$$
$$\mathbb{P}(\text{male prefect is elected}) + \mathbb{P}(\text{female prefect is elected})$$
clever fjordBOT
gfauxpas
amber veldt
you also know the probability that a prefect is elected
analog raven
you also know the probability that a prefect is elected
im confused,because they didnt state the probability for this
amber veldt
im confused,because they didnt state the probability for this
they didn't, but, you know it anyway
it's like saying
what's the probability that there will be a president/prime minister victorious in the next election?
analog raven
100 percent?
amber veldt
exactly
so the probability that a prefect is elected is 100%, or 1
the probability that a male prefect is elected? we dont know yet
prob that a female prefect is elected? they tell us
analog raven
oh ok
amber veldt
solve for the probability a male prefect is elected now
analog raven
99.75?
amber veldt
how'd you get that?
first of all, probabilities are always from 0 to 1, or from 0% to 100%
analog raven
how'd you get that?
well i did change of subject to get 100-0.15
idk if thats correct
amber veldt
1-0.15, not 100
analog raven
11
amber veldt
trying to think of how to do this the easiest, simplest way
analog raven
ok,ill be waiting
amber veldt
what does (SHORT WORK-10 Sec) mean?
youre supposed to do it in 10 seconds?
if you're supposed to do it in 10 seconds, there's some shortcut im not seeing
analog raven
if you're supposed to do it in 10 seconds, there's some shortcut im not seeing
yh,its a competition question
sample question
amber veldt
i'm going to pass this question to <@&286206848099549185> then because the way im thinking of is time consuming and im pretty sdure there's a shortcut im not seeing
analog raven
ok
but still continue tho so that ill get the answer
the shorter method can wait
@amber veldt
amber veldt
yeahokay
shortcut way
the probability that a female student is elected
okay
it has to be
the only way that I can see you do this problem
is to assume everyone has an equal chance of being elected
which is idiotic
tidal matrix
i might have another way: if only the senior students can be elected, 15% chance of being elected = 15% of total class
equivalently, 85% chance of being elected = 85% of the class = 11 males
does this work?
amber veldt
i might have another way: if only the senior students can be elected, 15% chance...
that's what im saying
the problem is only solvable if you assume every candidate has an equal chance to win
tidal matrix
ohh sorry, i thought you meant irrespective of gender
amber veldt
nope, you were on the nose
I was not assumign that because that's not how elections work but
anyway, haseeb will take over now
tidal matrix
unfortunately the mathematical world is idealized
tidal matrix
equivalently, 85% chance of being elected = 85% of the class = 11 males
so assuming equal chance of election, does this make sense? @analog raven
tidal matrix
well, if 85% of the class = 11 males, we can make an equation where x = size of entire class
do you see how?
analog raven
i think i do
tidal matrix
give it a try :)
analog raven
so basically,85/100 of x =11
85 when simplified is 17,100 is 20
so 17 over 20 of x =11
which gives 12.94?
tidal matrix
yep exactly! if you have a calculator, you could do 0.85x = 11 too
tidal matrix
which gives 12.94?
i got the same, you can round to 13 here or keep it for now
because next we need to find 15% of class, i.e. 0.15(x)
tidal matrix
no, that's the total class size
we need to find the number of women
if 15% of women can get elected, then 15% of the class is women, considering equal chance
tidal matrix
yeah 2 lol
i think considering it is short work, you can assume an equal chance and do something like this
analog raven
thnx
tidal matrix
you can also make it faster: we divided by 0.85 and multiplied by 0.15, so just do (11 / 0.85) * 0.15 in one step
but if thats too confusing, better to do it right than do it fast :)
odd edgeBOT
If you are done with this channel, please mark your problem as solved by typing .close
analog raven
.close
odd edgeBOT
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Available help channel!
limpid juniper
odd edgeBOT
limpid juniper
I js don understand this question
What is a term to term rule
There are no common difference
analog raven
there doesnt need to be
you just need to multiply each value given by the figures in the rule
limpid juniper
really
i thought there is always a common difference in arithmatic sequnce
analog raven
1*2+3=5
limpid juniper
you just need to multiply each value given by the figures in the rule
given by this rule how do u find 1st term
1?
analog raven
really
i thought there is always a common difference in arithmatic sequnce
only if you're not given a rule
analog raven
given by this rule how do u find 1st term
well it could be -1*2+3
=1
then 1*2+3 =5
and so on
limpid juniper
ic its totally different when u are given a rule
latent scaffold
ic its totally different when u are given a rule
This is a more general definition.
Arithmetic sequences are a special case where the term-to-term rule is "Add m" for some fixed m which is the common difference.
limpid juniper
its not nessecary that 1st term n = 1, 2nd term n = 2
limpid juniper
This is a more general definition.
Arithmetic sequences are a special case wher...
wdym 'add m'
analog raven
m is an integer that must be added,subtracted,divided or multiplied by the first given value to get the next number in the sequence i think
limpid juniper
ok so for 2nd term m = 1, for 3rd m = 2 like this
latent scaffold
That's not what I meant
analog raven
ok
limpid juniper
i can ask the answer but i want to understand it too, thats why im asking too many q
latent scaffold
m is fixed. For any m fixed, say m=4, the rule "Add 4" generates an arithmetic sequence
This is different from this problem, as the rule isn't "Add <insert fixed value here>"
But the idea is the same. You're given starting terms and the way to generate the next term from a previous term.
analog raven
so basically,you apply the same formula for every new value you find in the sequence
in order to find the next one
do you get it?
limpid juniper
yeah
analog raven
so whats the next numbr in the sequence
limpid juniper
we find the next term relative to the previous term
13 multiply 2 then add 3
29
thats it
odd edgeBOT
odd edgeBOT
Available help channel!
dreamy totem
How do I simplify this? The absolute value signs are so confusing
feral halo
let u = |x+1| ig
strange aspen
let u = |x+1| ig
How would that help ?
atomic void
@dreamy totem , notice that (-5)^2 = 5^2. Squaring doesnt depend on the sign
so u can safely yeet out the absolute value in the firsst term
feral halo
<@776570662831259679> , notice that (-5)^2 = 5^2. Squaring doesnt depend on the ...
oh i see
u cant factorise as quadratic but u can still just simplify
atomic void
yep
odd edgeBOT
@dreamy totem Has your question been resolved?
fathom orchid
Super confused on what I’m supposed to do cuz the answer I got for elasticity was like 13 sum that can’t be right!!!
fathom orchid
I think there’s sum wrong with those formulas at the end like why r we dividing by 2 here
odd edgeBOT
@fathom orchid Has your question been resolved?
haughty jungle
help
odd edgeBOT
help
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
haughty jungle
it was accounting
here is my progress, I am stuck in adjusted trial balance
our professor said, our ending balance should be same TOTAL and not unequal
odd edgeBOT
Please post images (such as PNGs or JPGs) of the question rather than other filetypes such as PDFs which have to be downloaded. Non-image downloads can potentially contain viruses or other security risks.
haughty jungle
I've already made journal entries, tried to recheck 3x as well.
Adjusting entries was correct as well.
Adjusting TRIAL Balance is correct as well
But in un-adjusted TRIAL BALANCE is i don't know why it is still not equal, and it must be
I'm stuck for about 2hours like wth
I'm done thank you for nothing, but still I don't know how i get the answer
I mistakenly put a utilities expense on cr side, that should be on dr side
I'm still confused AF, how 5k on service revenue add from its previous one
.close
odd edgeBOT
odd edgeBOT
Available help channel!
zenith crane
can someone check my answer i got 175pi+(2/3pi*125) for volume but that doesnt seem right
stable sequoia
can someone check my answer i got 175pi+(2/3pi*125) for volume but that doesnt s...
what did you do
zenith crane
i dont remember
mystic nova
Is the top part a half of Sphere
desert jolt
Is 6 the height?
zenith crane
yeah
desert jolt
Then why are there 2 side lengths
desert jolt
So we’re gonna ignore the 4?
zenith crane
yeah
desert jolt
How did you get your answer
desert jolt
@zenith crane
odd edgeBOT
@zenith crane Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
patent parcel
Question 10) is the answer of this question 5!•5!
odd edgeBOT
Question 10) is the answer of this question 5!•5!
patent parcel
Yea
mystic nova
Question 10) is the answer of this question 5!•5!
It's not, since 0 can be in front
narrow crypt
five spots for even. five for odds
mystic nova
can't
patent parcel
It's not, since 0 can be in front
Wdym
narrow crypt
why
patent parcel
five spots for even. five for odds
Right
narrow crypt
not u
patent parcel
Kk
mystic nova
I mean 0925476183 count?
patent parcel
O E O E O E ... count?
Ig no
narrow crypt
I mean 0925476183 count?
i think so
patent parcel
We r assuming 0 even here
patent parcel
i think so
So yeah
narrow crypt
if O E O E O E... counts too
patent parcel
Wait then again my answer is correct
mystic nova
should multiply by 2
Yeah
mystic nova
We have odd first and even first are two cases that why he say multiply by 2
patent parcel
Ok right
I get it
2•5!5!
Considering odd integer first can be case it doesn't violate anything in question
Thankyou guys
mystic nova
you are welcome
patent parcel
Could u guys check other question answer
Question 12) is it P(39,7)
The case is there's no club card in any lineup
So removeing 13 cards we get 39
mystic nova
I have no idea what a club is since I have never played card 😂
patent parcel
7-Permutations from 39 is P(39,7)
patent parcel
I have no idea what a club is since I have never played card 😂
Oh
I will give u some information about it not that much tho
There are 4 suits
each suits contains 13 cards
Hearts, diamonds , clubs and spades (they r actually four suits)
So clubs contains 13 cards
mystic nova
7-Permutations from 39 is P(39,7)
Oh okay, your look right, I'm thinking of a counterexample rn
patent parcel
I have no idea what a club is since I have never played card 😂
Neither i play it
mystic nova
Yeah, I think you're right, I can't think of any countercase
odd edgeBOT
odd edgeBOT
Available help channel!
kind smelt
odd edgeBOT
kind smelt
i tried expanding the denominator for both sin and cos but the 3 angles are ugh
iron current
i tried expanding the denominator for both sin and cos but the 3 angles are ugh
there might be a different approach
kind smelt
yeah
upbeat wharf
if you let $S = \alpha + \beta + \gamma$, you have $$\sin(\alpha) + \sin(\beta) + \sin(\gamma) = 2 \sin(S)$$
and likewise $$\cos(\alpha) + \cos(\beta) + \cos(\gamma) = 2 \cos(S)$$
clever fjordBOT
kind smelt
okay
upbeat wharf
try and wrestle this into the form $e^{i \theta} = \cos(\theta) + i \x \sin(\theta)$
so maybe multiply one of the equations by $i$
clever fjordBOT
kind smelt
Oh complex numbers
clever fjordBOT
kind smelt
isn't there a way to do this using Q.E, sequence and series, Trigo, basic maths?
kind smelt
ok yes
leaden karma
then expand and use the two identities
leaden karma
kind smelt
which two identities?
kind smelt
do you mean these two equations?
kind smelt
then expand and use the two identities
how do i exactly "use" the equations
i got 6 terms which i tried factorising
after expanding
kind smelt
after expanding
the thing we are looking for
leaden karma
how do i exactly "use" the equations
the sum in question looks like cos(S-alpha)+cos(S-beta)+cos(S-gamma)
Expand all the terms and group the terms with cos(S) and sin(S)
kind smelt
the sum in question looks like cos(S-alpha)+cos(S-beta)+cos(S-gamma)
Expand all ...
group ?
the terms ?
leaden karma
yes
kind smelt
the sum in question looks like cos(S-alpha)+cos(S-beta)+cos(S-gamma)
Expand all ...
ok yes i got the answer by this tho thank you
leaden karma
kind smelt
.close
odd edgeBOT
odd edgeBOT
Available help channel!
fleet lake
hi
narrow crypt
hi 
fleet lake
find max value of f(x)=|x+1|-2|x-1|
turbid comet
What have you tried
wooden python
do you know what piecewise functions are in general
fleet lake
like ik graphs
fleet lake
do you know what piecewise functions are in general
no
wooden python
bruh ok
then how were you taught the modulus function
like how was it introduced to you
fleet lake
u mean Cases like x>1 etc
turbid comet
do you know what piecewise functions are in general
I am pretty sure they know but not the terminology (piecewise)
fleet lake
true
wooden python
u mean Cases like x>1 etc
yes i mean cases.
write a definition for f(x) that doesnt involve absolute value but does use cases
fleet lake
done
turbid comet
The graph for each interval is different
fleet lake
yeah
fleet lake
done
wooden python
do you understand the meaning of the word "show"
fleet lake
x<-1
x-3
-1<=x<1
2-x
x>1
-x
wooden python
this looks wrong to me. show your work.
turbid comet
The graph ??
fleet lake
do you understand the meaning of the word "show"
sorry i was responding to that abput graph
turbid comet
There is an error in the last one
wooden python
i think all of his sub-expressions are wrong here
turbid comet
The first one is correct i think
fleet lake
yeah -1<=x<1
is 3x😅
nimble grove
x<-1
x-3
-1<=x<1
2-x
x>1
-x
for case 3, take x >= 1
wooden python
would have liked to see it on paper but given op's history of bad handwriting im afraid to ask
fleet lake
for case 3, take x >= 1
yeah
2-x
fleet lake
would have liked to see it on paper but given op's history of bad handwriting im...
my god
i just dont like decorating maths
it looks better when complex
fleet lake
shall i write it proper
nimble grove
just show it
fleet lake
first
wooden python
my god
i just dont like decorating maths
it looks better when complex
im not asking for any decoration
im asking to have x's that actually look like x and not n or u or h or k
magic ledge
ty
fleet lake
I'm sorry I was doing so rough work and silly mistakes
magic ledge
im having so much trouble w my goddamn monitor
whats the question bud
btw im Rao
Im 15
im now learning Tangents in circle
nimble grove
I'm sorry I was doing so rough work and silly mistakes
Check your case 3 !
turbid comet
In the third one it is +2
fleet lake
im not asking for any decoration
I feel lazy to get up and bring my phone to send u my work also I disconnect from the router and had to use hell slow internet
3-x now
For case-3
nimble grove
perfect
fleet lake
everyone here💀 know that
magic ledge
In the diagram below, PQRS is a cyclic quadrilateral.
Find the value of x.
68°
82°
106°
115°
turbid comet
!occupied
odd edgeBOT
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nimble grove
Now you have your 3 cases, check the slopes of those 3 cases respectively (the coeffecient of x in each case)
nimble grove
If its positive, its an increasing slope. If negative, its a decreasing slope
magic ledge
Now you have your 3 cases, check the slopes of those 3 cases respectively (the c...
wat??
magic ledge
The question???
yeh
magic ledge
If its positive, its an increasing slope. If negative, its a decreasing slope
i think id learn that in chapter 8 for me sam
nimble grove
Hey @turbid comet , so sorry for the ping and unrelated chat but this is my first time helping someone here as this question happened to be around my skill level and current knowledge. Is there anything I should note for further questions?
fleet lake
not you. please leave this channel as this one is already being used
I guess he just don't know the rules
Pls don't be rude explain him
nimble grove
I guess he just don't know the rules
Pls don't be rude explain him
oops i should've used emojis.. i didnt mean to come off as rude
fleet lake
Graphs drawn
nimble grove
now back to your question
nimble grove
Graphs drawn
Did you note the slopes?
nimble grove
Now you have your 3 cases, check the slopes of those 3 cases respectively (the c...
.
turbid comet
Hey <@1261742170835128382> , so sorry for the ping and unrelated chat but this i...
I don't think so
fleet lake
Did you note the slopes?
I can see angles right?
Instead of finding slope
It's just about find max
nimble grove
Yes, that works too
Now find where it's max and plug it into f(x)
That should be your answer!
nimble grove
plot the 3 cases and find if their graphs are increasing or decreasing
fleet lake
im saying taht 3x-1 graph is the most increasing
fleet lake
[-4,2)
nimble grove
so therefore it increases uptil 1 and then starts decreasing which implies your max is at x = 1 !
fleet lake
oh u mean domain
nimble grove
My terminology is getting rusty
Now just plug it into f(x)
That will give you max value
fleet lake
2
fleet lake
.close
odd edgeBOT
odd edgeBOT
Available help channel!
errant elk
can someone explain for me why a=b=t because we set t=a+b/2 first , im confused a bit
magic ledge
can someone explain for me why a=b=t because we set t=a+b/2 first , im confused ...
nah
wdh is this
errant elk
Its an inequality problem
atomic void
can someone explain for me why a=b=t because we set t=a+b/2 first , im confused ...
no u just plug in t, t, c into the formula
nimble grove
can someone explain for me why a=b=t because we set t=a+b/2 first , im confused ...
you're not assuming a = b = t. you're deliberately replacing a and b with two equal values t to simplify the inequality
errant elk
we already set a+b/2=t tho , I just don't get it 😅
atomic void
Imagine this,u have the function f(x) = x^2
obviously, f(a) = a^2 right? Just a change of variables anyways
then if u want to set t = a/2
f(t) = t^2 anyways
doesnt matter what u set t as
just now u can write f(t) = t^2 = (a/2)^2 = a^2 / 4
@errant elk u got it?
errant elk
I got it thank u sm😭
odd edgeBOT
If you are done with this channel, please mark your problem as solved by typing .close
errant elk
Close
errant elk
.close
odd edgeBOT
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Available help channel!
frosty sundial
odd edgeBOT
tepid pelican
Can you state the conditions in terms of decreasing/increasing and convex/concave
ivory grove
I needed help and 2 different ai gave 2 different answers
Please don't trust AI for any math-related tasks. They just suck ngl
frosty sundial
f'(x)>0 is increasing and less than is decreasing. f''(x)>0 is concave up and less than is concave down
frosty sundial
Please don't trust AI for any math-related tasks. They just suck ngl
its alr. they can be useful a lot of times but sometimes not so much
tepid pelican
f'(x)>0 is increasing and less than is decreasing. f''(x)>0 is concave up and le...
Okay, so our f must be increasing and concave down on the intervals
On which intervals is f increasing
Of A B C
frosty sundial
A?
tepid pelican
No
Increasing means that if you were walking from left to right, youd be walking uphill
frosty sundial
C
tepid pelican
Yeah
frosty sundial
but part of c is also cocave down
tepid pelican
F is increasing on both B and C
frosty sundial
like at the end
tepid pelican
like at the end
Yep
So f'' < 0 at C
What about B
Is f concave up or down there
tepid pelican
Yep
frosty sundial
ok
wait
ima check if i got it right
stay here
I DID
thanks for the help @tepid pelican
.close
odd edgeBOT
tepid pelican
Np
frosty sundial
im back
yo somebody help
basically
mach each graph, with the appropriate form of the function
ie f(x)=I, f'(x)=II, and f''(x)=III
thats the gist of it
yo
somebody
<@&286206848099549185>
yo
help
new problem
i got the other one wrong
.close
.close
.reopene
.reopen
odd edgeBOT
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Available help channel!
hidden escarp
Hello I need some help with this
odd edgeBOT
Hello I need some help with this
hidden escarp
narrow crypt
translate plz
strange aspen
translate plz
I dont think its that needed
hidden escarp
A numerical sequence with u0=2 as the first term and u(n+1) =....
Calculate the lim of Sn
solar peak
what have u tried
solar peak
limun?
solar peak
oh
hidden escarp
Yes
brittle beacon
(did you try working out some of the S_n's?)
solar peak
one second im trying something
solar peak
u can use the options
all the terms are positive
and it starts from 2
so it cant be option 1
or option 4
the 2nd term is very small but still it wont be 2
so by that logic i would say it has to be C
i hope u get a proper explanation tho, this is the best i could do
odd edgeBOT
solar peak
Ohh ok thats nice thanks
i suggest u keep this channel open cause this is a horrible way to solve the problem
hidden escarp
.reopen
odd edgeBOT
✅
hidden escarp
i suggest u keep this channel open cause this is a horrible way to solve the pro...
Yeah I guess but this exam doesn't require explanation
I didn't understand why it can't be 2 tho
hidden escarp
Yeah
solar peak
my thought process was its very unlikely that 2.27 + ... is approximated to 2
brittle plinth
the series starts from k=0
hidden escarp
Ohh ok
brittle plinth
and all the terms after it is positive
still doesnt really explain why it is divergent
solar peak
yeah
brittle plinth
unless there's some horrible way to write out the general term
bitter sleet
Why not use series convergence test
odd edgeBOT
@hidden escarp Has your question been resolved?
hidden escarp
Why not use series convergence test
Whats that ?
tropic vale
why are parabolas for conic sections specifically the parameters x=at^2 and y=2at or y^2=4ax?
narrow crypt
What😭
tropic vale
yk like for the focus and directrix of a parabola?
narrow crypt
y^2 = 4ax is from the defn that parabola is locus of points equidistant from directrix and focus
Derived from distance formula
tropic vale
what's the distance formula?
narrow crypt
[ D = \sqrt{(\Delta x)^2 + (\Delta y)^2} ]
clever fjordBOT
k
tropic vale
how does that derive to y^2 = 4ax?
narrow crypt
Consider the simplest case
narrow crypt
Focus is at (a, 0)
tropic vale
right?
narrow crypt
Ye
narrow crypt
**k**
Simply equate the distance
Since both are in the square root
And are never negative
It suffices to only consider the inside
elfin zodiac
writting correctly
tropic vale
thanks sherlock
tribal ingot
surround your latex with $
tropic vale
thank you
clever fjordBOT
satvik
tropic vale
$D = \sqrt{(x-a)^2 + (y)^2}$
tribal ingot
$D = \sqrt{(x-a)^2 + (y)^2}$
clever fjordBOT
satvik
clever fjordBOT
lm
narrow crypt
How abt the distance to the directrix?
narrow crypt
(x + a)^2
modest kite
a six sided dice is thrown twice. What is the expected value of:
$E(\max(X,Y)|Y=k)=\sum^6_{x=1}x\cdot P(\max(X,Y)=x|Y=k)$?
clever fjordBOT
McMake
modest kite
I only get a value with k as a result. I know the technical value with the chances of k, but dont know the formal way to get there
could someone help?
quasi sparrow
break it down into cases when x < k and x >= k
odd edgeBOT
@modest kite Has your question been resolved?
modest kite
hello. my internet went out. Its the same question:
a six sided dice is thrown twice. What is the expected value of:
$E(\max(X,Y)|Y=k)=\sum^6_{x=1}x\cdot P(\max(X,Y)=x|Y=k)$?
clever fjordBOT
McMake
quasi sparrow
break it down into cases when x < k and x >= k
.
modest kite
yeah but I get $\frac{k^2-k}{12}+3.5$
clever fjordBOT
McMake
modest kite
from $\frac{1}{6}\left(k^2+21-\frac{k^2+k}{2}\right)$
clever fjordBOT
McMake
modest kite
this is my seperation:
$\frac{1}{6}\left(\sum^k_{x=1}k+\sum^6_{x=k+1}x\right)$
clever fjordBOT
McMake
modest kite
I don't know how to formally get k in there
im basically asking how do I break this down?
$\sum^6_{x=1}x\frac{P[\max(X,Y)=x,Y=k]}{P[Y=k]}$
clever fjordBOT
McMake
