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#help-39
pearl pondBOT
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pearl pondBOT
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agile wyvern
how do you solve this without discriminant of cubic or calculus
dapper kraken
how do you solve this without discriminant of cubic or calculus
could you take a clearer screenshot
jolly parrotBOT
Edmund Cloudsley
agile wyvern
yes
midnight haven
okay brilliant so there is something you must understand about cubic functions with positive coefficients
agile wyvern
does vietas work
midnight haven
midnight haven
does vietas work
I am not entirely sure
but there is a method I have used for a question that looks like this
agile wyvern
kk
agile wyvern
yea
midnight haven
okay so when the function has at most 2 real solutions, either the minima or the maxima must correspond with the x-intercept
agile wyvern
mhm
midnight haven
okay so when the function has **at most** 2 real solutions, *either the minima o...
or both must be below / above the x-axis
agile wyvern
if this is true
midnight haven
agile wyvern
does it only mean there can be one?
agile wyvern
ah
midnight haven
we are not working with the complex domain
midnight haven
https://www.desmos.com/calculator/e33supd3xk
if you go to this graph, and play with the c value, you will see that the function has at most -> which basically means exactly 2 or exactly 1 root if and only if one of the maximas or the minimas touches the x-axis or both the maxima and the minima are above the x-axis
agile wyvern
yes
midnight haven
So first things first, let's find out
--> the cubic in the form of ax^3 + bx^2 + cx + d
--> the derivative of the cubic
--> the x-coordinate of the minima
--> the x-coordinate of the maxima
can you do this for me?
agile wyvern
im not allowed to use derviatives
Sry i didnt clarify this earlier
no derivaitves or discriminant of cubic functions allowed
midnight haven
is it an instruction from the teacher?
midnight haven
**Edmund Cloudsley**
$$x(x^2 + 180) = r + 24x^3$$
$$x^3 + 180x = r + 24x^3$$
$$-23x^3 + 180x - r = 0$$
jolly parrotBOT
Edmund Cloudsley
midnight haven
put this in a graphing calculator
change the value of r
and kaboom kabam you are done
midnight haven
no problem
pearl pondBOT
Available help channel!
quartz rampart
can someone tell my why the life is that expression, isnt it supposed to be just t?
plush bramble
t is an integration variable so after integration the answer doesn't depend on t anymore
quartz rampart
t is an integration variable so after integration the answer doesn't depend on t...
I meant like the expression for total life in the para above the integral
plush bramble
what "expression"
quartz rampart
what "expression"
plush bramble
did you read eqn 13.14
quartz rampart
did you read eqn 13.14
it gives the number of nuclei at a given time t
also there another equation saying R=lambda*N
Where R is rate and lambda is radioactivity decay constant
so simplifying i get total life = time * Rate * interval for decay
which doesnt make sense to me
plush bramble
"total life" is relative to the interval [t, t + delta t]
quartz rampart
"total life" is relative to the interval [t, t + delta t]
oh wait is it like rate time delta t gives me the number of nuclei decayed in that interval and t is the life for one of the nuclei, so total in the sense their adding up the life of each nuclei
yeah that makes sense
thanks a lot!
.close
pearl pondBOT
pearl pondBOT
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bronze canyon
pearl pondBOT
bronze canyon
Is the answer (32,\ 53,\ 54,\ 73,\ 74,\ 83,\ 84,\ 89,\ 90,\ 91,\ 92)
bronze canyon
This
frozen lantern
oh sorry
frozen lantern
Is the answer (32,\ 53,\ 54,\ 73,\ 74,\ 83,\ 84,\ 89,\ 90,\ 91,\ 92)
whats your work
bronze canyon
This answer is my friends I didnt do it yet
bronze canyon
Cuz if its wrong im going to try it after I get home
frozen lantern
and if it's not? 
bronze canyon
And if mine is not right im gonna come back but for myself then help my friend
pearl pondBOT
pearl pondBOT
Available help channel!
desert solar
$z^3=-i$
jolly parrotBOT
Task Bot
frozen lantern
ok
eager jewel
whats ur question
frozen lantern
eager jewel
I Don't Know Why
can you do z^3 = 1?
desert solar
Yes
eager jewel
huh wait
celest cedar
i × -1
celest cedar
? = -1
jolly parrotBOT
Task Bot
desert solar
$\rho=1$
jolly parrotBOT
Task Bot
frozen lantern
the hell is rho
desert solar
Radius
eager jewel
the hell is rho
i think that is |z|
desert solar
Yes
desert solar
$\sin(\theta)=-1/1=-1$
frozen lantern
WHY ARE YOU DOING THIS LMAO
jolly parrotBOT
Task Bot
frozen lantern
if you have to use euler's form, proceed with de moivre's?
eager jewel
WHY ARE YOU DOING THIS LMAO
1+1 = 100-98
desert solar
$\cos (\theta) = 0/1 = 0$
frozen lantern
yeah okay dont listen
jolly parrotBOT
Task Bot
jolly parrotBOT
Task Bot
desert solar
What
desert solar
yeah okay dont listen
You first say "what you tried" and then write to me that I have to do other things
👍
fringe robin
can you write $-i$ in the form $Re^{i\theta}$
desert solar
No
jolly parrotBOT
Xetrov
frozen lantern
You first say "what you tried" and then write to me that I have to do other thin...
oh is this wht you tried
okay
desert solar
Okay I will do it alone
fringe robin
You don't know how to?
pearl pondBOT
desert solar
<@&268886789983436800>
eager jewel
You first say "what you tried" and then write to me that I have to do other thin...
dude we have been telling dont do this from that time and u are continuing to expand on what you have done? how are we supposed to help you?
desert solar
https://tenor.com/view/white-guy-blinking-white-guy-blinking-wtf-gif-7831341
Look
= troll
eager jewel
yes and then after you told us what u did..we told u not to do that
and instead of listening u are wasting our time
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sudden badger
Write the vector (1, -2, 5) as a linear combination of the vectors (1,1,1) ; (1,2,3) ; (2,-1, 1)
frozen lantern
Write the vector (1, -2, 5) as a linear combination of the vectors (1,1,1) ; (1,...
sudden badger
i dont understand what linear combination is
full agate
sudden badger
huh
steep saddle
i dont understand what linear combination is
a sum of the vectors given with scalar multipliers such that it equals the target
sudden badger
so the first vector + the second vector + the third vector
should give me the vector that is a linear combination of them
steep saddle
well you need to find the scalars for them
sudden badger
oh scalars
ok yeah i understand that how to do that
but i dont understand the question
write the vector as the linear combination of
do i just need to find the scalars
frozen lantern
do i just need to find the scalars
yep
sudden badger
and is the answer the scalars?
steep saddle
and is the answer the scalars?
the sum of the vectors with the scalars
write that expression or possible an equation
sudden badger
sudden badger
pearl pondBOT
sudden badger
asking me to prove if these are linear dependent or independent
i know its a linear combination because if i multiply the second one by 3 i get the first vector
does that mean it cannot be independent or dependent
mossy galleon
i think its dependent because one can be expressed in terms of the other, therefore its redundant information
open rivet
i know its a linear combination because if i multiply the second one by 3 i get ...
linear combination, thus not independent
pearl pondBOT
@sudden badger Has your question been resolved?
pearl pondBOT
pearl pondBOT
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dusky willow
Square based pyramid
pearl pondBOT
Square based pyramid
dusky willow
What does it mean by find the size of obtuse angle between plane OAB and OBC?
dusky willow
What does it mean by find the size of obtuse angle between plane OAB and OBC?
Like wouldn’t that just be 360-90?
gray lantern
360 - whatever the internal angle is
dusky willow
360 - whatever the internal angle is
Would it be 90?
Cuz it is square pyramid
(And it is 4mark question no way it is just that💀)
gray lantern
well depends on pyramid height i believe
since the inner angle would change based on height
dusky willow
Hmmm
gray lantern
(though im no expert at square pyramids)
dusky willow
I don’t think it will for square pyramid
gray lantern
id just calculate the inner angle in case
pearl pondBOT
pearl pondBOT
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fast heron
hello
fast heron
quick question
gamma is the circle centered at 2 wth radius 1
what is the value of this
celest cedar
$\frac{1 + z}{z} = \frac{1}{z} + 1$
jolly parrotBOT
╰ 𝕊 𝕃 𝔸 ℕ 𝔻 𝔼 ℝ ╮
celest cedar
Idk if that's helpful
fast heron
and then
celest cedar
$\int \frac{1}{z} + 1$ dz = $[ln(z) + z]$
jolly parrotBOT
╰ 𝕊 𝕃 𝔸 ℕ 𝔻 𝔼 ℝ ╮
fast heron
but i think it doesnt work?
iron arch
oh yea i didnt see
fast heron
oh hum okk
iron arch
https://www.youtube.com/watch?v=WLRrNhDdGuc actually this might be more helpful i feel like cuz you might be able to directly use cauchy's formula 
pearl pondBOT
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sharp glade
I dont know how to do this question
pearl pondBOT
I dont know how to do this question
pure pelican
have you tried drawing it so you can understand it better?
pure pelican
i don't think there is
sharp glade
can you give hint
pure pelican
have you drawn AB parallel to CD and everything right? where are you stuck?
sharp glade
i dont know how to do it
cuz like i feel like i need to know more legnths
<@&286206848099549185> can i have hint
help
mossy galleon
I dont know how to do this question
here is my approach. i would find the lengths of the left and right vertical segments (which should both be equal to MN) in terms of x and y using pythagorean theorem. using that equality and the fact that 12 - x - y = 7, i would get a system of equations that i can use to solve for one of the variables and get the length of MN. i dont know if this is the easiest way but maybe try it out?
sorry that is long lol
pearl pondBOT
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modest tartan
i don't get what they did in 2nd step on solution
pearl pondBOT
i don't get what they did in 2nd step on solution
modest tartan
plz help
modest tartan
yes
frozen lantern
me either
rough forge
it's the discriminant
frozen lantern
id just take cases and do wavy curvy though
rough forge
they investigated whether the denominator becomes 0
modest tartan
how did they remove mod with d?
frozen lantern
splish splash boom bam
rough forge
which is not the case since D < 0 implies no real roots
modest tartan
which is not the case since D < 0 implies no real roots
i get that but how did they remove mod
rough forge
and since it's facing upwards the parabola is always positive which means you can remove the abs value
modest tartan
o so they used the graph studf
stuff*
i forgot all the graph stuff for polynomials
when parabola open upwards
rough forge
it's easier to understand things geomtrically
modest tartan
so upwards parabola need positive x squared
rough forge
positive coefficient
modest tartan
ok got it
modest tartan
yes I know all that I just forgot how to represent graphically
well ig ima go do more questions bow
now*
bye and thx
.close
pearl pondBOT
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lunar parrot
so its a physics question but i need to find the length of AC, at first i tried splitting the triangle into two so i can subtract the radius of the circle and get AC but i got around 5,5 meters whereas the answer for AC is 5,95 meters. I asked my assistant professor and i was said to use the circle's equation but im not sure how to use it to find AC can someone help?(to find the length it doesnt require any physics btw)
pearl pondBOT
so its a physics question but i need to find the length of AC, at first i tried ...
@lunar parrot Has your question been resolved?
fair creek
so its a physics question but i need to find the length of AC, at first i tried ...
notice how angle EAD is 25°, while not rigorous, suggests that AD might equal AC
lunar parrot
.close
flat cedar
A group of 9 students, s1, s2,..., s9, is to be divided to form three teams X, Y, and Z of sizes 2,3, and 4, respectively. Suppose that s₁ cannot be selected for the team X, and s₂ cannot be selected for the team Y. Then the number of ways to form such teams, is
flat cedar
I tried it by forming cases, but I think I formed too many
This is my work if someone can understand it:
tepid mesa
You know nCr?
flat cedar
Np
flat cedar
Selecting S2 for Z
flat cedar
did you force s_2 to be in z?
Yes
toxic lichen
got a feeling there is a more straightforward way to do this
flat cedar
Yeah I assume so too
clever zenith
I think I have a way to solve this with generating functions
toxic lichen
count the following:
- total rosters, not caring about s1 and s2's restrictions
- rosters which violate the "s1 can't go in X" rule
- rosters which violate the "s2 can't go in Y" rule
- rosters which violate BOTH rules
flat cedar
Rosters? It means ways right?
toxic lichen
by a "roster" here i mean of course an assignment of all students to teams
flat cedar
Ohk
toxic lichen
like imagine you're the tournament organizer
and you write down on a sheet of paper somewhere who goes into what team
that's a roster
flat cedar
count the following:
- total rosters, not caring about s1 and s2's restrictions
...
So total is 1260 rosters, whithout any restrictions?
clever zenith
$\frac{(x^2+x^4+x^8+x^{16}+x^{32}+x^{64}+x^{128}+x^{256})^2}{2!} \frac{(x^1+x^4+x^8+x^{16}+x^{32}+x^{64}+x^{128}+x^{256})^3}{3!} \frac{(x^1+x^2+x^4+x^8+x^{16}+x^{32}+x^{64}+x^{128}+x^{256})^4}{4!}$
toxic lichen
$\frac{(x^2+x^4+x^8+x^{16}+x^{32}+x^{64}+x^{128}+x^{256})^2}{2!} \frac{(x^1+x^4+...
this is overkill for sure
toxic lichen
So total is 1260 rosters, whithout any restrictions?
correct
flat cedar
980 for violating s1
flat cedar
$\frac{(x^2+x^4+x^8+x^{16}+x^{32}+x^{64}+x^{128}+x^{256})^2}{2!} \frac{(x^1+x^4+...
I don't even want to understand it sry, it just feels to complicated
jolly parrotBOT
Horsi135
clever zenith
I don't even want to understand it sry, it just feels to complicated
the idea is simple it just looks big
flat cedar
count the following:
- total rosters, not caring about s1 and s2's restrictions
...
Okay:
So violating S1=280
Violating S2=140
Both=120?
open rivet
is there a easy way to learn logs
!occupied
pearl pondBOT
is there a easy way to learn logs
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).
open rivet
is there a easy way to learn logs
!help
pearl pondBOT
is there a easy way to learn logs
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
flat cedar
Okay:
So violating S1=280
Violating S2=140
Both=120?
So the total wrong ways =140+280-120=420-120=300
So the total ways is 1260-300=960??
It's wrong
toxic lichen
It's wrong
says who
gimme a minute...
violating s1 means automatically putting him in X, so we essentially get 8 people to be distributed into teams of 1, 3 and 4
toxic lichen
,calc 8!/(3!*4!)
jolly parrotBOT
Result:
280
Yup
And to violate S2, we divide 8 people in groups of 2,2 and 4
Which is 420
I was wrong there
And violating both means 7 people divided into groups of 1,2,4
Which is 105
I was so wrong
toxic lichen
yeah looks like you spotted it
flat cedar
Yh I got the correct answer now
I don't know what I was doing then
Thanks Ann and horsi
.close
humble ether
Hi. I'm confused about this binomial, how do you split it up in this way?
minor ibex
is this correct? i solved for sin61
pearl pondBOT
is this correct? i solved for sin61
fallow jay
yeah its correct
jolly parrotBOT
quick star
,calc 12/5
jolly parrotBOT
Result:
2.4
pearl pondBOT
@minor ibex Has your question been resolved?
pearl pondBOT
sharp vigil
<@&268886789983436800>
pearl pondBOT
frozen lantern
<@&268886789983436800>
next forum
im embarassed to be right back here but all i need help here is finding ho to rite these equations
jovial kiln
do you know the equations for compound interest and simple interest
next forum
I forgot them 😭
if you have a formula for them i think i can fill them out
jovial kiln
okay simple interest is:
A = P(1+rt)
compound continuously is:
A=Pe^(rt)
compounded yearly is:
A=P(1+r)^t
next forum
Thank you, ill try to fill them in
next forum
okay simple interest is:
A = P(1+rt)
compound continuously is:
A=Pe^(rt)
c...
hat does r and t standfor again?
next forum
i guessed that t as time after i thought a little harder r as trikckier tofind out
prime bramble
r for interest rate, or something
jovial kiln
yeah
jovial kiln
the interest rates vary with the type of interest, look at the question
also those r in percentages so u divide by 100
for instance, first one would be
A = 8000(1+0.05*6)
second one has interest rate 4.5%
pearl pondBOT
@next forum Has your question been resolved?
pearl pondBOT
next forum
lol
pearl pondBOT
Available help channel!
dusky oak
I have to look if its an arithmetic or a geometric progression
indigo pewter
what are the definitions of an arithmetic and geometric progression?
dusky oak
what are the definitions of an arithmetic and geometric progression?
An arithmetic progression is a sequence of numbers in which each term after the first is obtained by adding a constant value
A geometric progression is a sequence of numbers in which each term after the first is obtained by multiplying the preceding term by a constant value
oh and also when its arithmetic or geometric I have to calculate the diffrence the constant and whats on place 1 - 20
yea sorry I was 2 weeks :)
chilly iron
hi guys can someone help me out
dusky oak
hi guys can someone help me out
Please use a channel thats open
chilly iron
Please use a channel thats open
sorry didnt notice im new on the server
dusky oak
@indigo pewter Oh how nvm I think I got it
I have to devide the next term with the current term right?
c) constant = -1/3
indigo pewter
c) constant = -1/3
yeah thats right
indigo pewter
<@1113777722372673586> Oh how nvm I think I got it
I have to devide the next te...
thats for a geometric progression
dusky oak
thats for a geometric progression
I know because a and b have non
only c had a geometric
indigo pewter
yes thats correct
a and b are neither arithmetic nor geometric
c is geometric
what about d,e,f?
dusky oak
ah arithmetic wiht diffrence V2
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Available help channel!
atomic python
Im having some trouble with part 2 of this problem
pearl pondBOT
Im having some trouble with part 2 of this problem
atomic python
.close
pearl pondBOT
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).
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lilac jackal
lilac jackal
@compact palm sry dude i was busy, u still alive?
plush moss
<@384202982259949571> sry dude i was busy, u still alive?
Hallo
lilac jackal
Hallo
sup
ok gonna post my reply anyway and hope u see it when ur alive @compact palm
$f$ has a local max at $c$ if there exists $\delta>0$ such that $f(x)\le f(c)$ whenever $x\in D$ and $|x-c|<\delta$
jolly parrotBOT
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lilac jackal
$f$ has a local min at $c$ if there exists $\delta>0$ such that $f(x)\ge f(c)$ whenever $x\in D$ and $|x-c|<\delta$
jolly parrotBOT
ロケットジャンプ
lilac jackal
these definitions are more rigorous than "x near c"
using these definitions we can prove that c=-1 is a local min but not local max
pearl pondBOT
@lilac jackal Has your question been resolved?
compact palm
ok gonna post my reply anyway and hope u see it when ur alive <@3842029822599495...
Oh sorry thank you for the in depth explanation
That makes a lot of sense now thank you
pearl pondBOT
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latent quail
pearl pondBOT
tropic saddle
u sub
sharp smelt
tan(x)= u
pearl pondBOT
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dapper kraken
find the three smallest positive integer solutions (x,y) for x^2-3y^2=1
pure rapids
Pells ahh equation
eager jewel
can u do hit and trial
pure rapids
Theres a wikipedia page which states the recurrences for the solution of pells equation
Also hello 🙂
dapper kraken
rearrange it i got x^2-1=3y^2
dapper kraken
Also hello 🙂
hi
eager jewel
find the three smallest positive integer solutions (x,y) for x^2-3y^2=1
wait isnt this a hyperbola?
so 2 solutions are the vertices
1,0 and -1,0
dapper kraken
rearrange it i got x^2-1=3y^2
by trial and error, the first 2 is (2,1) (7,4)
eager jewel
.
dapper kraken
1,0 and -1,0
well they are positive integers
pure rapids
This is a case of pells equation when D = 3
eager jewel
This is a case of pells equation when D = 3
ok thought i could do this but no idea what this shit is
imma dip
pure rapids
Its a common equation in oly nt
eager jewel
what is oly nt
pure rapids
what is oly nt
Olympiad number theory
eager jewel
oh
dapper kraken
Theres a wikipedia page which states the recurrences for the solution of pells e...
is this it?
pure rapids
is this it?
Yes
pearl pondBOT
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brisk pike
gm people, a question from my module is here
pearl pondBOT
gm people, a question from my module is here
brisk pike
For what values of $a$ does $f(x) = \frac{ax^2+x-2}{a+x-2x^2}$ have the range $\mathbb{R}$, where $x \in \mathbb{R}$ and $\mathbb{R}$ are the real numbers
jolly parrotBOT
rak³en
brisk pike
Now my module suggests that answer is $a \in \left(1, 3 \right)$
jolly parrotBOT
rak³en
brisk pike
but the polynomials in the numerator and denominator have the same discriminant
and clearly if f(x) has to take every value in R, it must be 0 as well so its D must be > 0
BUT the denominator can never be 0, and since it has the same discriminant , we obtain D<0
clearly, either i am going crazy or this is genuinely wrong
flat cedar
BUT the denominator can never be 0, and since it has the same discriminant , we ...
Huh?
tardy reef
Whats the problem if the denominator is 0?
tardy reef
and?
brisk pike
R doesnt contain 1/0?
brisk pike
what did you think the domain was 💀
tardy reef
I was thinking we can just remove those points from the domain
brisk pike
I was thinking we can just remove those points from the domain
oh well everything would be nice and easy if that was true
tardy reef
I just wanted to make the range be R, I didnt care about the domain
brisk pike
I just wanted to make the range be R, I didnt care about the domain
well thats what my module did
thats precisely the problem
i have a similar question in my workbook, and it has the same exact problem
sharp smelt
**rak³en**
For it to have range $\R$ first note that $D<0.$
\
Here $D = 4-4a<0 \implies a<1$
jolly parrotBOT
What a wonderful world !
sharp smelt
wait, that or you want asymptote
brisk pike
**What a wonderful world !**
no
sharp smelt
yea
brisk pike
ur D is wrong
sharp smelt
wait, that or you want asymptote
this
brisk pike
wait, that or you want asymptote
i want the range of a ...
brisk pike
where are asymptotes coming from ...
sharp smelt
ensuring the denom goes to zero and doens't cancel out with the num
brisk pike
ensuring the denom goes to zero and doens't cancel out with the num
we dont want that?
right
sharp smelt
we dont want that?
we don't want it to cancel out at possible asymptotes
,w factorise ax^2+x-2
brisk pike
.............
sharp smelt
.............
yes?
sharp smelt
yeah, sorry
sharp smelt
BUT the denominator can never be 0, and since it has the same discriminant , we ...
okay, could you explain why the denominator can't be 0
brisk pike
okay, could you explain why the denominator can't be 0
because i assume that 1/0 is not a part of R
sharp smelt
like the domain will become R - that point
sharp smelt
because i assume that 1/0 is not a part of R
yea, but the function will quickly blow up, assuming all values of R( you want it such that you have two vertical asymptotes at that point in both directions
brisk pike
yea, but the function will quickly blow up, assuming all values of R( you want i...
i guess so but at those points it literally becomes infinity
it does not blow up
those points are the problem
i think they assume that
1/0 = infinity
and somehow infinity is a part of R?
sharp smelt
I may be playing teh devils advocate here , but they haven't mentioned forll x in R, so the domain isn't R. Unless I;m understanding you wrong that was a problem you had , right
brisk pike
so x in R and forall x in R are being treated as different which does make sense
but a finite number of x in R
can never achieve all R
so clearly x in R is a problem in itself is a problem
Well isnt it R
brisk pike
k
sharp smelt
wait, just a thought, consider 1/x+x^2, is discontinuous at 0, but it's domain is R, or so wolfram says
*range is E
*R
so work along that?
brisk pike
but its domain isnt R which is clearly what they meant
sharp smelt
how is it clear they meant that?
brisk pike
clearly, either i am going crazy or this is genuinely wrong
<@&286206848099549185>
brisk pike
how is it clear they meant that?
because well x in R can only forall x or finitely many x
brisk pike
not the domain
u use x in R to show pre-images?
brisk pike
because well x in R can only forall x or finitely many x
and finitely many real x is not possible
lilac jackal
too much to read, whats wrong?
brisk pike
i ll type it again
For what values of $a$ does $f(x) = \frac{ax^2+x-2}{a+x-2x^2}$ have the range $\mathbb{R}$, where $x \in \mathbb{R}$ and $\mathbb{R}$ are the real numbers.
the polynomials in the numerator and denominator have the same discriminant.
f(x) has to take every value in R, it must be 0 too so D>0
BUT the denominator can never be 0, and since it has the same discriminant , we obtain D<0
jolly parrotBOT
rak³en
lilac jackal
For what values of $a$ does $f(x) = \frac{ax^2+x-2}{a+x-2x^2}$ have the range $\...
wanting the domain to be R puts a contraint on a
brisk pike
wanting the domain to be R puts a contraint on a
which is what i wrote right?
lilac jackal
which is what i wrote right?
yes
well the logic is more like this
the top and bottom have the same discrim D. wanting domain R forces bottom to never be 0, forcing D<0, which forces the top to never be 0, so f is never 0
brisk pike
the top and bottom have the same discrim D. wanting domain R forces bottom to ne...
but it has to be 0 for the range to be R?
lilac jackal
but it has to be 0 for the range to be R?
yes so having domain R makes f nonsurjective
lilac jackal
its not worded as true false. it says find values of a
brisk pike
its not worded as true false. it says find values of a
well there is no value of a such that f can have the range R while also having the domain R
inland ivy
the denominator has to go to 0 at some value, otherwise the range can't be R
you can just remove the actual points from the domain
lilac jackal
well there is no value of a such that f can have the range R while also having t...
mhm
inland ivy
why does the domain have to be R?
brisk pike
why does the domain have to be R?
well isnt that what x in R is supposed to mean?
rok san suggested that it might mean pre-image
inland ivy
!xy
pearl pondBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
brisk pike
**rak³en**
exactly how it was stated.
lilac jackal
am i rok san
brisk pike
am i rok san
no i meant math_rocks
inland ivy
well isnt that what x in R is supposed to mean?
it means that the domain is a subset of the real numbers
I don't see why you can't just set y = f(x) and then solve for x in terms of y
lilac jackal
it means that the domain is a subset of the real numbers
thats a very unusual interpretation
brisk pike
it means that the domain is a subset of the real numbers
but thats what we were taught....
inland ivy
thats a very unusual interpretation
well
the wording of the question isn't great but clearly that is what's implied
lilac jackal
when we say "f(x)=.. with x in R" the near universal interpretation is f with domain R
inland ivy
I know, but that's clearly not what the question requires
And in general JEE questions are not worded well, so I'm just telling OP to not think too deep into this stuff
brisk pike
And in general JEE questions are not worded well, so I'm just telling OP to not ...
alright, fine
another question
lilac jackal
JEE strikes again
brisk pike
JEE strikes again
it will keep striking me for the next 2 years 
inland ivy
wait, you just came into 11th?
brisk pike
wait, you just came into 11th?
yeah
lilac jackal
so lets agree on a rewording
brisk pike
so lets agree on a rewording
why would anyone disagree lol
lilac jackal
f(x)=.. with domain being the set where bottom!=0
brisk pike
f(x)=.. with domain being the set where bottom!=0
yeah then its easy
thanks
If the roots of $x^2+x+a=0$ exceed $a$, then which of the below is true: \
A) $2<a<3 \$
B) $a>3 \$
C) $-3<a<3 \$
D) $a<-2 \$.
my problem:
$D = 1-4a>0 \implies a < \frac{-1}{4}$
jolly parrotBOT
rak³en
inland ivy
yes, that's one condition
brisk pike
yes, that's one condition
why would you apply the other conditions here
OH
i am stupid
inland ivy
you haven't considered the roots being > a
inland ivy
classic mistake
brisk pike
and also that should be 1/4 not -1/4
inland ivy
yes
pearl pondBOT
@brisk pike Has your question been resolved?
pulsar stump
why he didnt add C?
pearl pondBOT
why he didnt add C?
compact harness
you dont have to add c when the numbers are specified
there are 2 types of integration
definite and indefinite
in definite integration, the number is specified from where to where the integration is possible
the number 1 and infinity in the integration show that it is definite
so you dont have to add c
dusty flame
The C cancels anyway
pulsar stump
the number 1 and infinity in the integration show that it is definite
i dont see why
this is still a riemann integral is it not?
dusty flame
So basically
pulsar stump
i mean it's improper integral i guess
dusty flame
U don’t add c because it cancels anyway
pulsar stump
but +C is for the former function
dusty flame
+c to specify that it is a group of function
But u only want a number for definite integrals
pulsar stump
+c to specify that it is a group of function
but then it's not equality
dusty flame
?
dusty flame
So it’s definite integral, yes
dusty flame
Like we add +c if u want to show in the final result that it is a group of function
compact harness
so he's wrong
the integral given has a start and end point
it goes from 1 to infinity
pearl pondBOT
@pulsar stump Has your question been resolved?
lucid prism
Hello, I am computing the flux of the vector field
F=(x^2 + xy)i + (z - xy)j + ((x^2)y - xz - yz)k
out of the surface of the solid S which lies inside the cylinder x^2 + y^2 = 1
and the sphere
x^2 + y^2 + z^2 = 5.
But musnt it be 0 if the divergence of F is 0?
pearl pondBOT
@lucid prism Has your question been resolved?
lucid prism
<@&286206848099549185>
dusty flame
i think ur reasoning is sound?
it is a closed orientable surface and triple integral over 0 is 0.
lucid prism
thats what im thinking, im just used to all the problems im assigned having page long answers so i was quite sure i was missing something
but thank you!
🙏 🙏 🙏
.close
pearl pondBOT
pearl pondBOT
Available help channel!
modest dragon
Show that this number is a perfect square for every n>=1
pearl pondBOT
Show that this number is a perfect square for every n>=1
buoyant tide
dam, you even got the harry potter symbol there
pearl pondBOT
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
Sorry that s a 4
modest dragon
```
What step are you on?
1. I don't know where to begin.
2. I have begun but go...
1 ?
buoyant tide
I guess to start, rather than showing that its a perfect square. Try to expand it to see if it becomes easier to work with
modest dragon
Expanding will make it worse
buoyant tide
$(a+\sqrt{b})^2 + (a-sqrt{b})^2 = a^2 +2a\sqrt{b} + b +a^2 -2a\sqrt{b} + b = 2a^2 +2b$
jolly parrotBOT
Yeatte
modest dragon
Yeah but it s n
buoyant tide
do you know the binomial formula?
modest dragon
Not really
buoyant tide
hm
when you say not really, Is it because they didn't go over it well?
or did they not teach it?
buoyant tide
it would make this problem a lot easier, but it would mean you have to be comfortable working with summatino
$\sum$
jolly parrotBOT
Yeatte
buoyant tide
did they teach you about these?
pearl pondBOT
@modest dragon Has your question been resolved?
modest dragon
did they teach you about these?
Yes
buoyant tide
I see, then what about factorials?
buoyant tide
$(a+b)^k = \sum_{n=0}^{k}{a^n b^{k-n}\frac{k!}{(k-n)!n!}}$
jolly parrotBOT
Yeatte
buoyant tide
we can just substitute (-b)^(k-n) insteaf of b^(k-n)
the reason why I use this is because for odd powers of k-n, then (-sqrt(p))^(k-n) ends up having a negative sign and a square root. but for even powers of (k-n), then (-sqrt(p))^(k-n) ends up being positive and the square root is squared
ex:
(-sqrt(2))^1 = -sqrt(2)
(-sqrt(2))^2 = 2
(-sqrt(2))^3 = -2sqrt(2)
(-sqrt(2))^4 = 4
lowkey im not sure how to go from here
<@&286206848099549185> I'm not sure how one would solve the problem rieman posted
pearl pondBOT
@modest dragon Has your question been resolved?
vital crescent
Show that this number is a perfect square for every n>=1
one way is to try induction
Hint: $(3+2\sqrt 2)(3-2\sqrt 2)=1$
jolly parrotBOT
qwertytrewq
pearl pondBOT
pearl pondBOT
Available help channel!
cobalt hinge
Dear lord save me from this hell
pearl pondBOT
Dear lord save me from this hell
cobalt hinge
I managed to fluke the last one but I forgot how to set this up
pearl pondBOT
@cobalt hinge Has your question been resolved?
acoustic path
I managed to fluke the last one but I forgot how to set this up
notice that region R is enclosed between a red curve and a blue curve
Recalling that the polar area integral is 1/2 int_a^b r(theta)^2, your goal is to find an integral 1/2 int_a^b (blue(theta)^2 - red(theta)^2) that will give you the area between the blue and red curves over a specified range as shown in the image
cobalt hinge
Recalling that the polar area integral is 1/2 int_a^b r(theta)^2, your goal is t...
Wait really?
I thought I had to take the whole blue region and subtract it from the little parts
acoustic path
idk what that means
cobalt hinge
Like the empty parts
cobalt hinge
The white enclosed by blue
acoustic path
Recalling that the polar area integral is 1/2 int_a^b r(theta)^2, your goal is t...
this is what this is doing
notice this is saying: take the area of blue over some interval and subtract the area of red over the same interval
cobalt hinge
Will it be just 2 or 1 integrals?
acoustic path
there’s only one integral written, so one
you get this from: 1/2 \int_a^b blue(theta)^2 - 1/2 int_a^b red(theta)^2 but you combine the integrals into one because they have the same interval of integration
cobalt hinge
Alright
$\frac12\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}(5+5\sin(\theta))^2-(2-2\cos(\theta))^2d\theta$?
jolly parrotBOT
;(
cobalt hinge
Nah wait, not really
I don't know the theta-value of that intersection points
Okay wtf is that
These bounds are disgusting
$\frac{1}{2}\int_{\theta_{1}}^{\theta_{2}}\left(\left(5+5\sin\theta\right)^{2}-\left(2-2\cos\theta\right)^{2}\right)d\theta$, $\theta_{2}=\pi-\arcsin\left(-\frac{3}{\sqrt{29}}\right)-\arctan\left(\frac{2}{5}\right)$, $\theta_{1}=\arcsin\left(-\frac{3}{\sqrt{29}}\right)-\arctan\left(\frac{2}{5}\right)$
jolly parrotBOT
;(
acoustic path
<@392866251149410305> Correct?
yes
brittle marsh
pearl pondBOT
brittle marsh
1-(4C2/10C2)is this correct?
frozen lantern
brackets
peak lark
is this lebron?
pearl pondBOT
@brittle marsh Has your question been resolved?
clear trout
Help
eager jewel
for which question
celest cedar
I also don’t know what bedmas is
$a^2 \times a^3 = a^{2+3}$
jolly parrotBOT
╰ 𝕃 𝕌 ℂ 𝕀 𝔽 𝔼 ℝ ╮
celest cedar
For example
celest cedar
Wrong expression for b, because -5⁴ = -625
It must be (-5)⁴ = 625
clear trout
Wrong expression for b, because -5⁴ = -625
It must be (-5)⁴ = 625
Ok I thought it was -625 someone told me it was not
celest cedar
Ok I thought it was -625 someone told me it was not
Yes, it was not
U have (-5) × (-5) × (-5) × (-5)
But: -5⁴ = -1 × (5 × 5 × 5 × 5) = -1 × 625 = -625
So it's wrong, and it should be (-5)⁴ = 625
celest cedar
I’m confused where is the -1 coming from
-5⁴ is different than (-5)⁴
That's what I'm trying to say.
@clear trout
Do you have any additional questions?
pearl pondBOT
@clear trout Has your question been resolved?
clear trout
Do you have any additional questions?
How do I do bed mas
And you still didn’t answer how I can do the questions I have not done yet
celest cedar
How do I do bed mas
Means Priorities in calculating
Example: we multiply and then add.
$(2^3 + 3^2) - (2^2 + 1^3)$
jolly parrotBOT
╰ 𝕃 𝕌 ℂ 𝕀 𝔽 𝔼 ℝ ╮
clear trout
Calcul numbers inside brackets, then Do the minus operation
Can you do it for me so I can understand I do g know what minis operation is
celest cedar
Can you do it for me so I can understand I do g know what minis operation is
What is 2³ + 3² = ?
clear trout
What is 2³ + 3² = ?
17
clear trout
What is 2² + 1³ = ?
5
pearl pondBOT
@clear trout Has your question been resolved?
broken fossil
What is 2³ + 3² = ?
(2−3i)(2+3i)
celest cedar
(2−3i)(2+3i)
Wrong, we have 2³
broken fossil
Wrong, we have 2³
aw man i misread it
naive plume
i need to find the area of the shape. second image uh im hoping thats related
dusk horizon
Are you trying to find r?
The area of the shape is easy to find and doesn't care about r
next forum
i ould genuinelysplit it into atriangle up top andtrapezoid donbelo and then make thetrapezoid a triangleandrectange
if you could
pearl pondBOT
@naive plume Has your question been resolved?
naive plume
The area of the shape is easy to find and doesn't care about r
i need the area of the shape
<@&286206848099549185>
void sandal
i need the area of the shape
I'm assuming "the shape" is the circle
what values are you given at the start?
pearl pondBOT
@naive plume Has your question been resolved?
dusk horizon
i need the area of the shape
Then just use the coordinates to find the area of triangles
kindred acorn
How do you integrate this? I have to use trig substitution but idk what to do
unkempt yacht
u = x^2 comes first to mind
kindred acorn
from the x^3 or the sqrt(x^2+10)
last summit
midnight haven
How do you integrate this? I have to use trig substitution but idk what to do
take u = x^2 + 10
kindred acorn
It work when did strictly u subs but it says to use trig funtcions
midnight haven
du = 2x dx
kindred acorn
yupp
midnight haven
It work when did strictly u subs but it says to use trig funtcions
oh
kindred acorn
you can take x = sqrt(10)*tanu
yeah i tried that but eventually i got stuck
midnight haven
yeah i tried that but eventually i got stuck
how so
midnight haven
dx = sqrt(10)*sec^2u
here sec^u can be written as 1+tan^u then you can split it ig but yea I get it
kindred acorn
hold up i'll send where i got stuck
midnight haven
I have a better idea
kindred acorn
midnight haven
take x^2 = 10-sin^x
midnight haven
you forgot to sub in x^3
kindred acorn
you forgot to sub in x^3
u sub x^3?
kindred acorn
Ohhhhh shit you’re right
midnight haven
kindred acorn
god damn it one sec
midnight haven
Happens more often than you'd think
kindred acorn
Good thing I’m early with the problems left or I’d be cooooooked
My exam is Thursday
kindred acorn
Happens more often than you'd think
alr im stuck again
maybe i transform sqrt(10 sec^2 theta) into sqrt(10) sec theta
ouuhhhh
wait idk
midnight haven
maybe i transform sqrt(10 sec^2 theta) into sqrt(10) sec theta
no just write down 1000* tan^3 theta * sec^3 theta * d theta
kindred acorn
no just write down 1000* tan^3 theta * sec^3 theta * d theta
wait whattttt
that works?
midnight haven
wait whattttt
no you'd need to simplify further
kindred acorn
i was thinking of writing 100tan^3 theta sqrt(10)sec^3 theta d theta
midnight haven
i was thinking of writing 100tan^3 theta sqrt(10)sec^3 theta d theta
you're missing a sqrt(10) multiplier there
midnight haven
i just put them together yk
Yeah see there's 2 sqrts
kindred acorn
Yeah see there's 2 sqrts
im sorry but idk i dont get what you mean
can you write it down ?
kindred acorn
100\*sqrt(10)\*sqrt(10)
well yeah that gets you the 1000 you said earlier
then i can take out a tand theta and sec theta
i think
nah it doesnt work
midnight haven
nah it doesnt work
just take u = cos theta
tan^3 theta* sec^3 theta will be sin^3 theta /cos^6 theta
du = -sin theta d theta
the remaining sin^2 theta is (1-u^2)
Simplifies nicely, split and integrate, then reverse substitute twice to get answer
pearl pondBOT
@kindred acorn Has your question been resolved?
whole idol
need help plugging in a equation into a calc (trigonometric notation)
whole idol
whole idol
how do I plug the 0=tan-1(5/5\3) in a calc
whole idol
Like how did my teacher get 30