what partial differential equation
#help-0
crisp cargo
lone heartBOT
@shadow oxide Has your question been resolved?
shadow oxide
Not yet
swift bridge
lone heartBOT
gray isle
!status
lone heartBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
have you ever factored stuff before
swift bridge
yes
gray isle
so what's your issue with factoring this
swift bridge
so what's your issue with factoring this
am I supposed to just factory the formula? not includ any numbers from the question?
im a little bit confused by all the text
gray isle
ignore all the text
swift bridge
and if I should include something I haven't noticed
gray isle
yes
gritty verge
Multiple integral Qn
lone heartBOT
Multiple integral Qn
gritty verge
im not so sure how to do this! Appreciate help ^^
crisp cargo
imagine that x were replaced by some constant and integrate with respect to y
crisp cargo
have you computed a double integral before this?
gritty verge
like u substituition?
im not sure how i can perform u substituiton hehe...
gritty verge
have you computed a double integral before this?
mhm
crisp cargo
just consider the part in the middle and pretend that x were replaced with a for example
would you know how to integrate e^y/a dy
crisp cargo
yes
now if you apply the bounds, you should get a single integral in terms of x
from 0 to 1
crisp cargo
yes
gritty verge
wait i feel like my brain is on halt, but how is the e^(x^2) integrated
gritty verge
wait so like i let uhh x^2 be u or smth?
crisp cargo
yea
gritty verge
wait how wld the whole thing look written out?
crisp cargo
you can factor it so that it is x(e^x^2 - 1)
then you should be able to replace x^2 by u and dx by du/2x, as you already discovered
ocean sealBOT
gritty verge
i think i missed smth smwhere
cus it shld be -2 not -1 oml
oh nvm
found it
tysm!
.close
alpine sable
lone heartBOT
alpine sable
I know how to do this type of problem it's just expanding it is the problem.
This is what I have to the expanding process
swift shore
lone heartBOT
alpine sable
.reopen
lone heartBOT
✅
alpine sable
I am having the most trouble with this problem.
From here, do I multiply each term by 9?
and simplify them?
.close
native venture
lone heartBOT
native venture
is 6 true or false?
crisp cargo
im assuming the first big N refers to the natural numbers and the second statement is a quantification over sets
it would be false then
native venture
can you tell why?
crisp cargo
what does it mean for the cardinality of a set to be less than another cardinality
and what does the powerset operator do
native venture
powerset operator gives subsets
native venture
what does it mean for the cardinality of a set to be less than another cardinali...
Small n is not a set , it is a number right?
native venture
it would mean that there is a natural number which is greater than the cardinality of all subsets of natural numbers
native venture
u can think of it as an ordinal i guess
what is that
crisp cargo
transitive and well ordered set
|X| = the least ordinal such that there is a bijection between X and the ordinal
thats not important tho
crisp cargo
it would mean that there is a natural number which is greater than the cardinali...
is the natural numbers a subset of its powerset?
crisp cargo
wait my bad 😅 thats what i meant to ask
crisp cargo
|X| < n if after putting every element from each in one to one correspondence, there is still something left over in n
native venture
n is one number
crisp cargo
yes but you can think of it as the set of natural numbers up to n for example
if you want to compare cardinalities
native venture
oh alright so it is basically saying cardinality of natural numbers is less than the cardinality of natural numbers
?
crisp cargo
for it to be true, that would have to be the case
native venture
Yea which is why false is the answer?
crisp cargo
does it make sense to you?
crisp cargo
yes
mystic dune
These two correct?
carmine reef
,w 612/36
ocean sealBOT
carmine reef
yes
mystic dune
both?
carmine reef
yes
carmine reef
np
mystic dune
carmine reef
u gotta be ok with getting a hw problem wrong by mistake every now and then lol
mystic dune
since both sides are the same is it b for number one
carmine reef
indeed
mystic dune
okay appreciate u
carmine reef
np
carmine reef
u gotta be ok with getting a hw problem wrong by mistake every now and then lol
ig it's checking understanding of the concepts makes sense nvm
carmine reef
yeah
mystic dune
perfect
lone heartBOT
lone heartBOT
Available help channel!
native nebula
help
subtle birch
yes
subtle birch
find the base using cosine rule and then use 1/2*a*bsinx to find the area
let me see if there's a trick
subtle birch
105
native nebula
that is not the angle between the known sides
subtle birch
I mean use
12^2=(12*(sqrt(3)-1)/sqrt(2))^2-x^2+2*x*12*((sqrt(3)-1)/sqrt(2))cos(105)
subtle birch
we know the value of y which is (12/sqrt(2))(sqrt(3)-1)
native nebula
x is known or y is known?
subtle birch
take angle between x and y
native nebula
not x and y
subtle birch
it's result will be 12
native nebula
take angle between x and y
why
subtle birch
a^2=b^2+c^2-2bccosA
Here a is known
c is known
A is known
b is unknown
So you can find b
native nebula
a^2=b^2+c^2-2bccosA
Here a is known
c is known
A is known
b is unknown
but this is not the correct formula
gray isle
how is it not correct
gray isle
what exactly don't you understand here
you have the cos rule/law
and know 3 of the 4 variables
native nebula
what exactly don't you understand here
.
gray isle
your diagram is wrong
native nebula
how
gray isle
the side with 12 should be opposite that 105° angle
native nebula
ok
native nebula
the side with 12 should be opposite that 105° angle
but I should be knowing angle C in order to use the cosine rule
gray isle
you have angle A
you have the cos rule/law
and know 3 of the 4 variables
a^2=b^2+c^2-2bccosA
Here a is known
c is known
A is known
b is unknown
So you can find b
alpine sable
where does the x^-2 come from?
lone heartBOT
where does the x^-2 come from?
alpine sable
agh wait I thought the ^-1/x was -11x, Im all good now
worn fox
I also thought the same
gray isle
context matters
alpine sable
.close
lone heartBOT
lone heartBOT
Available help channel!
lucid ferry
how to find x
lone heartBOT
how to find x
gray isle
you've already most of the work
you have a right triangle with 2 known sides with 2x being the angle in between
2x can be determined with trig
and x can be determine from that
lucid ferry
i dont really get it
ik that i have 3 sides of the the triangle
alpine sable
i dont really get it
ik that i have 3 sides of the the triangle
you have three sides and an angle
lucid ferry
you have three sides and an angle
yes the sides 13,12,5 and the angle 90 but how do i find x
alpine sable
law of sines
law of cosine
inverse tangent
inverse sin
inverse cosine
Probably other ways as well but idk
brisk heath
isn't that wrong?
lone heartBOT
isn't that wrong?
foggy copper
nope
brisk heath
x <= -3 so ]-infty , -3]
x <= 2 so ]-infty , 2]
x C ]-infty , -3]
foggy copper
huh
brisk heath
isn't that how you solve it
lone heartBOT
inner hinge
I need help with the bottom question
lament forge
,rccw
ocean sealBOT
glacial rover
As in all parts from i to iv?
inner hinge
I need help with the bottom question
glacial rover
Wait yeah my bad
inner hinge
I get the +4 to the first part and the second part is equal to 0 but idk how they got that
fringe idol
integral of f' is just f(x)?
inner hinge
But wouldn’t that make the answer equal to -75
glacial rover
The question should be worded as fine the area
Then given you the integral
Basically because the integral of a differentiated function is the function itself the net area it is adding is 0
opal pendant
integral of f'(x) is f(x)
so then it would be f(5)-f(0)
by looking at the graph you can tell the y values at x=5 and x=0
so f(5)=0, f(0)=0
0-0=0
wintry igloo
dT/dx = aT + ac*sinx + bcosx
lone heartBOT
dT/dx = aT + ac*sinx + bcosx
glacial rover
I’m assuming it can be left in terms of other terms
So start with trying to integrate the function
lone heartBOT
@wintry igloo Has your question been resolved?
wintry igloo
i tried @glacial rover
wintry igloo
some one suggested T'-aT = 0
wintry igloo
@glacial rover
T' - aT = ac sinx + bcosx
solving T'-aT=0 gives T=k exp(ax)
then find any single solution to T'-aT=acsinx+bcosx (hint T will be trig) and add kexp(ax) equals solved
i didnt get it tho why we did this
glacial rover
Is that the method they used to find the correct answer?
lone heartBOT
@wintry igloo Has your question been resolved?
alpine sable
I want a solution to This: $\int \dv[2]{x}{t} \dd x$
lone heartBOT
I want a solution to This: $\int \dv[2]{x}{t} \dd x$
ocean sealBOT
cat-anoia😺
alpine sable
Book mentions how the second equation follows from integrating the first one with respect to x
worn fox
Well then your answer is right there
alpine sable
Yes but how
worn fox
1/2 * (dx/dt)^2
wind cloak
Isn't this the equation to a simple harmonic oscillator
alpine sable
How is it true
wind cloak
And the energy
alpine sable
Isn't this the equation to a simple harmonic oscillator
Yes
worn fox
Differentiate it
alpine sable
Differentiate it
Uhh sure but I want to know how it works in the inverse way
I can see it's true
But I want a solution to This: $\int \dv[2]{x}{t} \dd x$ that's it
ocean sealBOT
cat-anoia😺
alpine sable
How is that somehow equal to 1/2 * (dx/dt)^2
wind cloak
$\dv[2]{x}{t} = \dv{v}{t} = \dv{v}{x} \cdot \dv{x}{t} = v\dv{v}{x}$
ocean sealBOT
NEONPerseus
alpine sable
Ohhhh
wind cloak
$\int \dv[2]{x}{t} \dd x = \int v \dd v$
ocean sealBOT
NEONPerseus
alpine sable
Ahhh
Thanks so much
Wait but I have a
Doubt again
Wait lemme formulare
Ut
Basically
What if we
Integrate
The second equation wrt x again?
alpine sable
We will get another constant right
Just like u got total energy as a constant of integration
alpine sable
If you differentiate energy you get force*
Yeah
alpine sable
Maybe we will get some constant with no physical meaning
alpine sable
You should have limits whenever integrating in phsyics
Hmm
Ok anyway thanks
I guess I just forgot the old d2x/dt2 = v dv/dx
wind cloak
You basically want to integrate the first equation to get to the second right?
alpine sable
You basically want to integrate the first equation to get to the second right?
That I got
median dirge
**NEONPerseus**
This is correct 
alpine sable
Now I want to see what will happen if
We integrate the second equation
With respect to x
median dirge
I guess I just forgot the old d2x/dt2 = v dv/dx
Back from your JEE days, clattanoid
ocean sealBOT
NEONPerseus
wind cloak
Like this?
alpine sable
Yea
wind cloak
This would be weird
alpine sable
That shud be something undefined right
wind cloak
Not undefined
wind cloak
It wouldn't be beneficial
alpine sable
?
wind cloak
Did you multiply it on both sides
alpine sable
Integrated both sides wrt x
alpine sable
dx
wind cloak
Why is kx^2 outside the integral
alpine sable
I integrated it already
Forgot to write the constant of integration tho
But i wrote it in next line
wind cloak
You should get 1/6kx^3
alpine sable
I integrate 1/2 kx
wind cloak
1/2kx doesn't have significance
wind cloak
I mean you know that $\dv{x}{t} = v$
ocean sealBOT
NEONPerseus
alpine sable
wind cloak
And you presumably have an expression for it
alpine sable
And you presumably have an expression for it
What expression?
Whats integration of v^2 dx
wind cloak
$\int_0^v v \dd v = \int_A^x \frac{-k}{m}x \dd x$
alpine sable
How to integrate first term in this
wind cloak
At the amplitude, i.e. the extreme position, the velocity is 0
alpine sable
Yes
wind cloak
And at displacement x the velocity is v
alpine sable
Yes
wind cloak
How to integrate first term in this
You find the value of v^2 from the above integral
ocean sealBOT
NEONPerseus
wind cloak
Why does indefinite integral work for the rest
Where did you use an indefinite integral
alpine sable
Where did you use an indefinite integral
In finding the energy equation from the shm equation
wind cloak
We don't derive that equation from the equation of SHM
wind cloak
Instead we write the total energy of the oscillator, kinetic + spring potential
alpine sable
By integrating with respect to x?
alpine sable
Instead we write the total energy of the oscillator, kinetic + spring potential
We get this wehn we integrate the shm equation wrt x
wind cloak
You won't get anything wrong
alpine sable
Yes
wind cloak
But you need to plug in the initial conditions to get your constants right
Or get rid of them entirely
alpine sable
But we got the energy constant right with indefinite integral
I mean
I agree that
When we use definite integration
It will be a more solid
Thing
wind cloak
Energy will be constant yes
alpine sable
Yes so
wind cloak
That's a property of a simple harmonic oscillator
alpine sable
Why can't we further integrate
alpine sable
That's a property of a simple harmonic oscillator
Property of an simple harmonic oscillator which is represented in the shm equation
alpine sable
Does Edx or xdE give you anything useful
I just want to see the new constant it produces
I was intrigued by the fact that the total energy comes out of integrating the shm equation
So I thought what if
We integrate further
We will yield another constant right
What is that constant
I'm interested
In that
wind cloak
I was intrigued by the fact that the total energy comes out of integrating the s...
Because conservative force can be defined as an energy gradient
alpine sable
Yes
wind cloak
$-\vec{F} = \pdv{U}{x} \hat i + \pdv{U}{y} \hat j + \pdv{U}{z} \hat k$
ocean sealBOT
NEONPerseus
wind cloak
The "constant" that you would get upon integrating again would just be the initial value of the new physical quantity defined by Ex
... which is meaningless
alpine sable
The "constant" that you would get upon integrating again would just be the initi...
Oh
Hmmm
Yes
That quantity is just worthless I gues
Yea
I understand where I'm wrong
Thanks
alpine sable
You're not wrong
Wrong in assuming something fun will comes out of it
alpine sable
Or any at all
Yea exactly
I thought we will keep getting some fun constants as many times we integrate
Silly me
Unfortunately the world is not that beautiful
.close
alpine sable
hey guys, how would i go and solve
ln(x^2-1) = 0?
what is the inverse of ln
idk actually
do you know what logarithms are?
yeah
what are they
just started with em tho
wdym
what are logarithms
you should know right?
vale wigeon
You deleted your original post. The channel will abruptly close and possibly lock. (This is irreversible).
Please claim a new channel and do NOT delete the first message of any future channel you claim.
do you know what logarithms are?
vale wigeon
please open a new channel. this one will lock in less than 10 minutes.
alpine sable
please open a new channel. this one will lock in less than 10 minutes.
umm its still open so who cares
anyways its to find how many times a number should multiply by itself to reaches a certain number
its hard to explain i dont study it in english
alpine sable
anyways its to find how many times a number should multiply by itself to reaches...
its hard to explain i dont study it in english
oh i see
alpine sable
hey guys, how would i go and solve
ln(x^2-1) = 0?
do you know how to solve this?
next brook
As Ann said, open a new help channel instead of posting in the closed one.
alpine sable
do you know how to solve this?
You're probably better off relearning what logarithms are instead of trying to solve the problem
next brook
You're probably better off relearning what logarithms are instead of trying to s...
Stop replying in the closed channel, please.
tired fox
lone heartBOT
median oar
Vertical strips
You can tell because of the integral you’re estimating
It says dx
warm turtle
How to find formula of tan(A/3)? How do you find value of tan50?
median oar
How to find formula of tan(A/3)? How do you find value of tan50?
Open your own channel
median oar
do not memorise formula
warm turtle
Open your own channel
What do you mean?
median oar
Every formula you use you should know how to derive them
median oar
What do you mean?
Then first learn how they got this formula
It’s not about watching videos that do derivation
It’s about can you derive them from scratch
If you can, you’ll understand exactly where each part of the formula comes from and which variable is what
Then what are the y0, y1, y2, … yn-1’s, yn?
And what are those values
What is y0 and yn specifically
Yes
What about y1 to yn-1?
So we want to find what n is, right?
Let’s see
y0 = first value
yn = last value
How many values do we have in total
Well, in general it’ll be n+1 values
That formulation is not particularly good
The last y value
Like yn is at x=b
There’s 2 different n’s here
It’s pretty yucky
The n in yn refers to how many points (-1) you have, in this question you have 5 points
Because x=1, x=1.5, x=2, x=2.5, x=3
That’s your 5 points
Oh wait that’s why they start with 0
Yuck
5 points give you 4 intervals
ocean sealBOT
-Znar
median oar
Because x=1, x=1.5, x=2, x=2.5, x=3
As is obvious from this
I don’t know
Show your work
You’re missing a set of brackets
(y0 + yn) + 2(y1 + y2 + … + yn-1) is bracketed
.
Looks kinda right
misty bison
got a proof question here got no idea where to start
lone heartBOT
got a proof question here got no idea where to start
tacit arch
Square both sides
thick lynx
That's the AM-GM inequality
misty bison
do i not need to do anything with the denominator of 2 before that
misty bison
That's the AM-GM inequality
am gm?
thick lynx
Arithmetic Mean Geometric Mean inequality
misty bison
never heard of it
thick lynx
It's useful, I used it yesterday for determining a minimum value of a function, without having to derive twice, set the first derivative to 0, ... for example
misty bison
oh
im doing first year of a level maths atm we've literally only done integration and differentiation
trynna prep for my end of year AS exam but these questions for revision have me fumbling
thick lynx
got a proof question here got no idea where to start
There is a variation of this for three variables and generally n variables too
Here is a Math StackExchange post that asks for a proof of the two variable version that you have:
misty bison
alr lemme have a look
thick lynx
This answer, upside-down, is probably what @tacit arch wanted to do:
https://math.stackexchange.com/a/1689315
misty bison
i got a point of 4xy <= x^2 + 2xy + y
but now im just lost even after looking at that
thick lynx
but now im just lost even after looking at that
At which one?
misty bison
howd he go from here to here
thick lynx
howd he go from here to here
It's maybe clearer if you start from the bottom:
(I was writing it up and I clicked away from it accidentally, now it disappeared, I will write it up in a second)
misty bison
It's maybe clearer if you start from the bottom:
(I was writing it up and I clic...
💀 oh ive been looking at it the wrong way
thick lynx
\begin{align*} \sqrt{xy} &\leq \frac{x+y}{2} \ xy &\leq \frac{x^2 + 2xy + y^2}{4} \ 4xy &\leq x^2 + 2xy + y^2 \ 2xy &\leq x^2 + y^2 \ 0 &\leq x^2 - 2xy + y^2 \ 0 &\leq (x-y)^2\end{align*} which is true, since anything squared is atleast $0$.
misty bison
but then
for b
what would i sub in to get a number that isnt greater or equal to 0
thick lynx
Well, you can just try any negative x and y, say x = -1 and y = -1, that would give you 1 <= -1, which is false.
x = -1 and y = -1 is the counter example
misty bison
is that not equal to 0?
thick lynx
\begin{align*} \sqrt{(-1)(-1)} &\leq \frac{-1 + (-1)}{2} \ 1 &\leq \frac{-2}{2} \ 1 &\leq -1 \end{align*}
misty bison
ohh id have to sub it back into that inequality
and not the one we rearranged for
so -5 and -3 also work
thick lynx
ohh id have to sub it back into that inequality
Well, we did all the rearranging just to prove the original equality
The question asks you to give a counter example when the original inequality is not true for neg x and y
thick lynx
so -5 and -3 also work
Yeah
thick lynx
u dev on roblox?
Not anymore
misty bison
ah
thick lynx
Now I'm doing maths all day :D
misty bison
what you trynna achieve
thick lynx
Well, I want to study mathematics, I'm in high school currently
I want to become a mathematician
misty bison
wait.. how old r u
thick lynx
16
thick lynx
u must score 100% on all ur papers
On math exams? Yes.
In physics too, but in everything else not, haha
misty bison
On math exams? Yes.
In physics too, but in everything else not, haha
thas what i meant
cause im 17
😭
stone gulch
😂
misty bison
@thick lynx where what and when did u start learning from
thick lynx
<@332561465405865985> where what and when did u start learning from
Uh, I self-studied some competition math, now I'm self-studying analysis and linear algebra from german books (Königsberger and Fischer), I'm participating in "math student seminars", our local university's math department offers them, they cover concepts from the first semesters, and I'm allowed to study mathematics at uni beginning from 11th grade, so in a few months.
I still do some competition math to prepare, since my high school will send out a team to participate in a competition, including me, but I think self-studying ahead uni math is more useful (Terence Tao, a maths field medalist, wrote an article in his blog about this, by the way)
misty bison
fair
i mean i got a month to go over my specification which isnt much time but link me that article, if that isnt a big ask
lone heartBOT
@misty bison Has your question been resolved?
misty bison
alr
thx
lowkey stuck again
i went in a full circle and got to 4a/b + b/a >= 4 (the original inequality )
but dont know where to go from there
wild trail
lowkey stuck again
use the previously proved identity
use this form: $2 \sqrt{xy} \le (x+y)$
ocean sealBOT
numbpy (anti glomed)
wild trail
think what would be an appropriate vale for x and y
wild trail
yes, you're supposed to use the previous question to solve this one
This is pretty common tactic question setters use
wild trail
it wasn't necessary but it should simplify
I think you can now see what x and y should be
compare both the equations
misty bison
uhm
misty bison
I think you can now see what x and y should be
i can see the similarities but not sure what to do
wild trail
what similarities do you see
misty bison
ab in common
thick lynx
ab in common
Both are an inequality with a factor of two on the RHS, we know that the second is true since we proved it
We need to prove the first
Both have two terms on the LHS too
Hint: we should substitute something
thick lynx
How can we make $x + y$ be equal to $\frac{4a}{b} + \frac b a$? What do we need to plug in for $x$ and $y$?
misty bison
as in what we need to sub in for a and b?
thick lynx
as in what we need to sub in for a and b?
We should rather sub in for x and y, because with x and y, we already established an inequality that we know is true
misty bison
but what does the x+y have to do with this question
_>
is that supposed to be the original form its in
thick lynx
If we sub in some values for x and y and we get the left hand side of the inequality in question, then our established inequality will give us a lower bound on it.
[x + y \geq 2\sqrt{xy}] is true for all positive $x$ and $y$, we proved that earlier. Now, we need to prove that [\frac{4a}{b} + \frac b a \geq 4.] If we could transform our true inequality, [x + y \geq 2\sqrt{xy}] into [\frac{4a}{b} + \frac{b}{a} \geq something] and $something$ happens to be $4$, then that would be great.
fossil latch
On a much more special case, what happens if y= 1/x?
misty bison
2rt4a/b.b/a?
thick lynx
as in what we need to sub in for a and b?
If we sub in $x = \frac{4a}{b}$ and $y = \frac{b}{a}$ into [x + y \geq 2\sqrt{xy},] then we would certainly have [\frac{4a}{b} + \frac{b}{a} \geq 2\sqrt{\frac{4a}{b}\cdot \frac{b}{a}},] now the LHS of our true inequality matches that of what we want to prove. We know that [\frac{4a}{b} + \frac{b}{a} \geq 2\sqrt{\frac{4a}{b}\cdot \frac{b}{a}}] is true because we established that $x + y \geq 2\sqrt{xy}$ earlier, for all positive values of $x$ and $y$, and $\frac{4a}{b}$ and $\frac{b}{a}$ are also positive values, since $a$ and $b$ are positive.
This proves the inequality. We started with our inequality that we know is true and transformed it into that in the question by transforming the left hand side into that of the one in question, and the right hand side happened to be 4.
misty bison
how did u go from here to here
thick lynx
how did u go from here to here
The a and b's cancel
wild trail
If we sub in $x = \frac{4a}{b}$ and $y = \frac{b}{a}$ into \[x + y \geq 2\sqrt{x...
I wanted to nosols this but this is honestly beyond just giving an answer
misty bison
just gonna check the mark scheme for this rq
to see what it wanted
cause i think thats a lot for 4 marks
wild trail
a lot? this is like 3 lines
misty bison
well its a little more than what you need to do for a 4 mark proof question
at A level
thick lynx
cause i think thats a lot for 4 marks
The explanation makes it look long, maybe. It's just \ [x + y \geq 2\sqrt{xy}] sub $x = \frac{4a}{b}$, $y = \frac b a$, then [x + y \geq 2\sqrt{xy} \implies \frac{4a}{b} + \frac b a \geq 4]
misty bison
oh makes more sense
thick lynx
If you include all the steps and thought processes, that x and y will still be positive if a, b > 0, ... then it will look longer, of course
misty bison
i dont get what the mark scheme did differently tho
thick lynx
Perhaps they did it like this: [(2a-b)^2 \geq 0] since anything squared is atleast $0$. [4a^2 -4ab + b^2 \geq 0] and so [4a^2 + b^2 \geq 4ab,] now divide both sides by $ab$: \begin{align*} \frac{4a}{b} + \frac b a &\geq 4 \ &\hspace{3cm} \square \end{align*}
lone heartBOT
@misty bison Has your question been resolved?
misty bison
still processing
alr i somewhat get it now just need to practise more of these
actually
why do they do this step
actually nvm i get it i think
thx for ur help
thick lynx
np
thick lynx
why do they do this step
Since on the RHS, they have 4ab, and they want 4 instead, as in the problem, so they divide by ab.
lone heartBOT
@misty bison Has your question been resolved?
plain bone
I'm stuck in trying to figure out how to solve BE. It seems like I could use the ratios to solve the next one but pls help me solve this problem.
plain bone
<@&286206848099549185> pls help 🙏🏼
kindred crescent
Cause FC and and BE share the same fight
plain bone
fight..?
kindred crescent
height
remote herald
@plain boneyou know similarity of triangles right?
remote herald
I can't confirm right now. I'm travellin hope someone comes to check that.
exotic belfry
remote herald
$$AE/EB = AG/GC$$
$$CG/GA = CF/FD$$
$$AE/EB = FD/CF$$
GIven, $FD = EB$ .
$AE = 9$ and $CF = 4$
plain bone
ok thanks to both of you!
ocean sealBOT
Quasar
alpine sable
``8. A firm selling CDs finds that the number sold(N thousand) is related to the price (P) by the formula 6p + N = 90.
a. Draw the graph of N against P for 0 <= N <= 90 (the vertical axis should be the P axis, and the horizontal axis should be the N axis)
b. Use your graph to find the price when 30 000 CDs are sold.
c. Use your graph to find the number sold if the price of a CD is set at 8 euros
d. Use your graph to find the price if 90 000 CDs are sold. Is this a sensible value?``
heady pollen
!status
lone heartBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
@alpine sable Has your question been resolved?
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
so for a. it wants you to graph the equation 6p+N=90, basically with p as y and N as x
what part do you not understand?
lone heartBOT
@alpine sable Has your question been resolved?
winter ivy
What’s wrong here?
lone heartBOT
What’s wrong here?
mystic nebula
lone heartBOT
mystic nebula
no thats just what the denominator is factored into
the only thing in the way of me solving the equation is this
hushed locust
try multiplying it out
versed lily
^
hushed locust
the 2y changes the way it factors
versed lily
^^
sonic ridge
what doesnt make sense about it?
mystic nebula
because you look for what multiplies into -27 and adds into +3
9 and -3 dont and neither does -9 and + 3
hushed locust
we're looking for something that multiplies into -27 and adds into +3 when one of them is multiplied by 2
mystic nebula
im lost
sonic ridge
because you look for what multiplies into -27 and adds into +3
only when the coefficient in front of the squared term = 1
when the coefficient isnt 1, that strategy really doesnt apply
mystic nebula
what do i do then
sonic ridge
youre right that the constant terms of factored form needs to multiply into -27
that remains true
you need to figure out 2 values that multiply to -27
and add to +3 when one of the two values is multiplied by the value in front of coefficient
sonic ridge
yes sorry
mystic nebula
so 2(-9) + b = 3 or
9 + 2(-3) = 3
so how does that affect the way i express the equation
sonic ridge
well when you factor it, you should have something that looks like (2y+a)(y+b) right
and a*b=-27
2a + b = +3 OR a + 2b = +3
find the values of a and b that satisify the conditions
sonic ridge
well when you factor it, you should have something that looks like `(2y+a)(y+b)`...
and just plug them back into this
lone heartBOT
@mystic nebula Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
summer ermine
Is this a function?
lone heartBOT
Is this a function?
slender quiver
wdym
summer ermine
Does the graph represents two different functions?
slender quiver
it can
summer ermine
The question is use the vertical line test to determine which graphs show relations that are functions.
slender quiver
ok..
summer ermine
{... (-1,1), (-1,-1), (0,0), (1,1), (1,-1) ...} or {... (-1,1), (0,0), (1,-1)... } and {...(-1,-1), (0,0), (1,1)...}?
If it is the first one, it isn't a function. If it is the second one, it represents two different functions, y=x and y=-x.
.close
lone heartBOT
lone heartBOT
Available help channel!
wide mango
is it an applicable method to any similar problem?
lone heartBOT
is it an applicable method to any similar problem?
slender quiver
yeah but what about the +3 at the end
wide mango
yeah but what about the +3 at the end
i cant resolve it after doing that method?
5h^2 * 3
slender quiver
yes
wide mango
so is it safe to do that method?
wide mango
ok it was just a doubt
wide mango
is it an applicable method to any similar problem?
because i was stuck at this
i had no idea on how to proceed
and i was afraid that i wouldnt be able to do similar problems
slender quiver
oh
wide mango
.close
crisp kindle
Can someone help me w. understanding this?
lone heartBOT
Can someone help me w. understanding this?
crisp kindle
I thought there was 100 combinations of icecream since it was 10x10
so 800/100 = 8
but the answers did this
upbeat hornet
I thought there was 100 combinations of icecream since it was 10x10
you can’t have vanilla and vanilla, for example
and vanilla and chocolate is the same as chocolate and vanilla
vale wigeon
Buy two different flavored scoops
swift bridge
lone heartBOT
swift bridge
I feel like im doing something wrong
alpine sable
I feel like im doing something wrong
how tall are the walls of the box
swift bridge
how tall are the walls of the box
5?
alpine sable
I feel like im doing something wrong
where is the 5 in your volume formula?
swift bridge
where is the 5 in your volume formula?
oh my bad, ok I replaced it now its x= 2.5, x=17.5
so is one of these answers is the answer for the question? because I feel like im supposed to use something else
alpine sable
i asked about the volume formula
not what the x value was
before cutting out the four corners of the paper
what are the dimensions of the paper?
what is the length after you cut out two corners?
what is the width after you cut out two corners?
swift bridge
x * 35 and the length is 5
swift bridge
I am confused man
alpine sable
x or 35 can be the length
lets just say x is the length
x is the length
35 is the width
you are cutting 5 inches from the length and width
what is the length when you cut out two lengths of 5?
what is the width when you cut out two lengths of 5?
swift bridge
what is the length when you cut out two lengths of 5?
what is the width when you...
(x-5) * 30 right?
alpine sable
2 * 5 = 5?
swift bridge
2 * 5 = 5?
why multiply 2 and 5?
alpine sable
why multiply 2 and 5?
swift bridge
oh okay........so (x-10) * 25?
alpine sable
oh okay........so (x-10) * 25?
yes
alpine sable
oh okay........so (x-10) * 25?
That would be the shape highlighted in red right?
swift bridge
That would be the shape highlighted in red right?
yeah
swift bridge
5 right?
alpine sable
yeah
what is the length, width and height after you cut out the squares and fold the flaps up?
swift bridge
what is the length, width and height after you cut out the squares and fold the ...
im not very sure
how to write it? like (x-10) * 25 +_ 20?
im so sorry man, I am just very confused. these questions weren't in my lesson.
bear with me 😂
<@&286206848099549185>
kindred crescent
yo
swift bridge
alguien habla español?
ah, english?
swift bridge
no
swift bridge
If you need help go to #❓how-to-get-help
or go to one of the channels under it and send your problem, people will help you
alpine sable
as which
alpine sable
ok thanks
swift bridge
.close
spice cape
!claim
spice cape
for question b, would the quadratic formula work for determining the number of x intercepts? Or can it not be applied to cubic functions
pearl hamlet
for question b, would the quadratic formula work for determining the number of x...
quadratic formula is only for quadratic equations
and cubics are not quadratic
spice cape
so do you know a potential way to determine the number of x intercepts other than the quadratic formula?
coral cosmos
what does CAS refer to btw ?
pearl hamlet
computer algebra system
spice cape
what does CAS refer to btw ?
its a type of calculator
pearl hamlet
so do you know a potential way to determine the number of x intercepts other tha...
well actually, you can kind of use the quadratic formula if you factor it into a quadratic times a linear
fossil latch
But is that any different from factorizing though
spice cape
isnt that factorization tho for the first step?
pearl hamlet
actually yea nvm lol
you can prolly use fundamental theorem of algebra
to check existence of roots
spice cape
my teacher pretty much hinted that the quadratic formula is an answer but I wasnt too sure
can the discriminant be used?
pearl hamlet
hmm, i can't think of a nice way using the quadratic formula other than factoring it first
spice cape
would the discriminant work?
pearl hamlet
cubics have their own discriminant thats different from the quadratic
spice cape
could i just use the cubic discriminant?
lone heartBOT
spice cape
.reopen
lone heartBOT
✅
spice cape
.close
hollow thicket
how come it isn't -5/4loge**|2-4x|**+ c instead
lone heartBOT
how come it isn't -5/4loge**|2-4x|**+ c instead
median oar
,w d/dx -5/4 ln|2x-1|
ocean sealBOT
median oar
5/(2-4x) = -5/2 * 1/(2x-1) = -5/4 * 2/(2x-1)
lone heartBOT
@hollow thicket Has your question been resolved?
hollow thicket
wait so are tehse the same thing?
devout yew
why the bottom x does not eliminate or reduce the top x?
lone heartBOT
why the bottom x does not eliminate or reduce the top x?
gray isle
x isn't a common factor
that isn't how fraction simplification works
there's no justification for erasure of expressions that happen to appear in the numerator and denominator
devout yew
how do i know when to rest/add them to the top?
gray isle
$\frac{ab}{ac}$ simplifies to $\frac bc$ as
$$\frac{ab}{ac} = \underbrace{\frac aa}_{1} \times \frac bc = \frac bc$$
ocean sealBOT
ℝamonov
barren portal
If you have $\frac{5^2-5+6}{5+2}$
ocean sealBOT
.doc
barren portal
can you just cancel of 5 ?
devout yew
mm no because one is positive and the other negative?
lament forge
if you have $\frac{3+1}{2+1}$ (so, $\frac{4}{3}$), \ can you cancel out the $1$s and turn it into $\frac{3}{2}$?
ocean sealBOT
bee [it/its]
