#help-49
1 messages · Page 88 of 1
f(why am i here )= I don't know
lol
I mean it's technically correct.
I would suggest to call a function g(y)
But yk.
sqrt(x)+x, sqrt(x), 1/x
I think that's more likely resonable
Oh ye, this is much more better
np
But my example would be wrong, right?
no that's fine
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The radius is squareroot 34 how do I write it in gen equation
I know I have to cancel the squareroot but idk how to input it
@faint loom Has your question been resolved?
Idon’t understand that help
I have to write in general equation
Nvm
Is my gen equation right
Nvm I got it
.close
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we get homology groups by taking the boundary maps between n skeletons and taking ker n/im n+1 right. and it kinda means n holes in a space?
cohomology is similar but instead we look at boundary maps between maps from a n skeleton to a graded ring? not sure what it means help please
I guess it keeps on going
yeah I get it
to the advanced section with you
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u arent coming with me? 😭
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if i was given y = x(x+1) how do i get back x from y ?
im thinking like x = y / sqrt(y-1) or something but that doesnt work
y=x^2+x
Now, notice that this can be rearranged as a quadratic in x
Btw, it would be better to say “isolate x/solve for x in terms of y”
or completing the square (which is the same thing)
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what does it mean by from parameters to points?
its probably asking what is the hole of the function
ie what makes the numerator and denominator 0
no cause that doesnt explain the whole "what point is missing"
unless its just dumb grammar
ur gud LUL
im failing to understand why proving its monotonic increasing helps u on whethers it one to one or not
all that tells you is the curvature of the function
yeyeye
I see, so ur basically finding the acceleration of both functions
yea
ye that should work
if i do that and say theyre both pos, then its one to one right?
yep
you kinda saved me
i dont think you gotta find the concavity tho
nah jus differentiate the parameterized functions individually
you only need to differentiate once not twice
thanks for the help
ofc
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if the 6th term of an a.p. is equal to four times its first team, and the sum of its first 6 terms is 75 , find the first term and the common difference
i got my answer as first term as 5
and common difference as 3
can someone cross check it
it is correct
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idk how to start
@manic bison Has your question been resolved?
use the trignometric relations
Cos(3sinx ) = cos(90-4cosx)
Use cosa = cosb
Then a = 2npi +- b
Here in this case n = 2
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How should I approach this problem?
any hint is fine...
Use identity that sin2x = 2tanx/(1+tan^2)
Did u try converting the whole into terms of cos and sine
ah got it thank you so much
Ohh ryt 
And tan2x = 2tanx/1-tan²x
it's a mess that way
It surely is lol
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Can someone talk in french here?
non
Oui mais parcontre ouvre un nouveau canal d'aide
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B is in 1st quadrant, so -B has to be in 3rd Q
you seem to be calculating with -80deg, which makes it in 4th Q
@blissful drum Has your question been resolved?
yeyeye i just noticed
i was supposed to do 80+180
260
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You should be able to solve it by proving that ASO and ATP are similar triangles and then finding the similarity constant
@feral barn Has your question been resolved?
OK ty
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sounds like a circle
@manic bison Has your question been resolved?
<@&286206848099549185>
Wait a min solving someone else's question rn
alr
it is a circle
VincentBH
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Sorry but I don't really understand your handwriting
Could you explain what you're doing?
Its integral u substitution
What was your original integral, what was your u choice and what did you end up with?
My u is (1-e^t)^1/2 and i end up with 2(√1-e^t)^1/2
Alright, with that u, du=(-e^t)/2^-1/2
That should be where the - comes from?
And btw, if you want some advice: I'd recommend choosing what's inside the root as u instead of the entire root
It's much easier to differentiate and will make things cancel out pretty neatly in this case
Can i try to write it?
Sure
And the resulting integral is just u^-1/2 du
can i ask a question how did we get 1/2?
You wrote it on the du
I mean, it shouldn't be there as I told you
That 1/2 is a mistake you made differentiating
The derivative of (1-e^x) is -e^x
Go on from there, integrating with respect to u
And you should get to the right answer without too much difficulty
du is negative right?
Yeah
Integral of -1/sqrt(u) du
The square root is still there
And it's still dividing
Write the integral sign, and write the u already
Else it'll get too confusing
thanks bro i believe this is the final asnwer
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hey i need help
in middle school cant understand this
i try something and my teacher says its wrong
im confused
please help
i would use logarithms to solve that
what is that
Show your work, and if possible, explain where you are stuck.
dont have the work with me atm its at my school
you can write 9^y as 3^{2y). right?
yes
so compare the powers
as in?
If the bases are the same, then you can set the exponents equal to each other
oh
yes
so what would y equal?
and how would i find that
i just want to understand the working of this atm
Apply what was stated
ok
Make 9^y have the same base as 3^12
yes
Then set the exponents equal to each other
Yes
and then i reverse calculate?
.
Yes
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guys help
18 times 3 is 54
o yea
and the language of this question is really strange imo
that "basketballs" thing
this is what concerning me
is it the complete question?
yes
basketball means 1 ball right?
ys
and basketballs means more than 1
what grade are you in
LOL"
Probably question setters did a mistake there i suppose
yeah
full question
ohh lol
yeah that table doesn’t make sense
Help for 18 x 3?
i think they expect you to do it via addition
column for number of bballs, and cost
Long day for u
bballls
n cost
1 18
2 36
etc

or just be malicious and write
$18 x 3 = $54
over all the lines in the "table"
yes
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just say
first statement implies B is a subset of A
second statement implies A is a subset of B
therefore A = B
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how do you know whether the number of primes between 0 to 1000 is more than the number of primes between 10^8 and 10^8 + 1000?
My first thought is to use the prime no theorem no of primes between 1 and n is app n/log(n)
tbh idk if that works well
and that was my first thought too
but consider something like
primes between 7001 and 8000 and primes between 9000 - 10000
But that's just an asymptotic approximation, it doesn't prove it is the case for the particular bounds given
if u use your approximation
you get the wrong answer in this case
btw if you were curious, yesterday's geometry problem used our trig insights but without trig
💀 at least that's what i found out
u easily show x < 45 and y < 45 from geometry with no construction except with the fact that larger angle -> larger side

if 90 - x = a and x well = x
then a > x because one side was 3s and the other one was s? and so a > 45 and x < 45 💀
same idea but smth like that
Why find the no of primes before 10^8
And find no of primes before 10^8 + 1000 subtract the no so you will get the no of primes between them

The prime number theorem is only an approximation
cuz of the counterexample i provided
isn't he suggesting to use an approximation to count the number of primes between 10^8 and 10^8 +1000
acknowledging that it is indeed an approximation
so what else
The only way I can think of doing it would be using a computer program
Otherwise I wouldn't be surprised if this question fits #advanced-number-theory
it was on my test lol
😭
Really?
Maybe I'm missing something obvious then
i think tbh their argument was probably
primes get sparser the further you go
but like that argument doesn't hold for a finite length interval
maybe?
That's not a correct argument
cuz of my counterexample above
yeah exactly (byut i'm guessing they're oging for that)
or well smth else idk tbh
i have no ideas other than using the approximation just like display said (that was my hunch too)
There could be stronger more concrete approximations that gives you some bounds on the error
Something like that could maybe be used to prove this
But idk
do you suppose i should go to the adv number theory channel or something then?
i don't want them to think i'm trolling lol
Yes, I think that channel fits this question
If I'm mistaken and this is somehow trivial, blame me
alright thanks
i'm a pending postgraduate for a bit now
💀
You don't have access to that channel?
not with my initial roles yeah
You don't need postgraduate role for it
Undergraduate is enough
it's an undergrad+ channel
Btw is the answer 0 - 1000
Actually proving this seems infeasible?
,w number of primes between 0 to 1000
,w number of primes between 10^8 and 10^8 + 1000

You know it's basically certain that it's true by the prime number theorem
what's this "prime number theorem"
hold on
pi(n) ~ n/log(n)
but.... the approximation fails for the case where you count the number of primes between 7001 to 8000
and number of primes between 9k - 10k
Not sure what you mean by "fails"
It's an approximation
That as n goes to infinity gets closer to the actual value
yeah but it gives me a wrong conclusion, i need a definitive conclusion on which closed interval with fixed length has a higher prime number count
i don't have to count them
I don't think such a thing exists
Then maybe ur going to revolutionize the feild of number theory
well that was the question, i'm dubious whether we're missing something trivial or this question is just pretty hard for the average elem number theory student

💀
Go to advanced number theory or analytic number theory channel maybe they can help you
I do have a person in mind but he's just to rude on answering easy ques 
who?
@ruby pivot
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??
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No of primes ko count karne ka koi exact method hai
Ya fir distribution dekhne ka koi method?
waise sooya nahi tu ab tak
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Can someone coach me normal precalc?
plz
Normally you ask specific questions and we help you with those
It's against server rules to ask for money in exchange for tutoring, I believe
i know .. but he talked about coaching
it's another thing
I ain't paying shit
!vol
Helpers are just people volunteering their time to help you. Be polite and patient.
Just ask a question and if someone finds an interest in it they’ll help you
i ain't teaching shit
Why you that desperate for money
I will offer something
i am not despare ... i was only curious ...usually coaching is payed
I will offer something
I pay you 100
i am not interested anymore...additionally we are not supposed to speak about that here
In veitamese currency
How 100 of it cant even be represented in euros, even with cents
👍
Don't convert it to usd currency.
It is more valuable in USD than in euros 💀
Its like 0.004 usd
<@&268886789983436800>
I said in veitanmese currency, so I ain't paying sherlock
Anyway, try to have a look into khan academy and online stuff, many are free and well construct courses
ok tysm
Here are questions answering/ exercices checking, its not learning about full topic
I'm about to get ban to offer less than a cent.
.close
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.reopen
✅
@novel nexus since you are claiming that your offer was only a cent I'm gonna assume you were kidding. In general please don't use the server to arrange paid tutoring. We can't deal with the complications that come with that. Please only use these help channels for asking actual math questions. You can ask whatever precalc qs you like in them. There is also #precalculus as well.
Precalc level stuff also tends to have a broad range of people ready/able to address too.
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✅
The same goes for you. If you suspect somebody is breaking a rule or toeing the line please try to just point out the rule conflict and ping mods if you feel it needs addressed by mods.
Sorry dezpa I know you're trying to close this.
.close
Closed by @formal blade
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wtf happened here
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How is this 1/5
sin (0) / (0)
should be undefined right
$\lim_{x\to0}\frac{sin(x)}{x}=1$
Skill_Issue
the logic goes as follows
instead of looking at the value at that location
like sin(x)/x
at x = 0
because that becomes 0/0 and that is undefined
we look at a value close to x = 0
for example x = 0.1
and then x = 0.01
and so on and so forth
and you look at the limit of that as x goes closer and closer to 0 without ever getting to 0
and it results in 1
you can calculate it yourself
you can use our favourite calculus trick, lhopital's rule if you forget
the important message here is
$\lim_{x \rightarrow 0} \frac{\sin(x)}{x} \neq \frac{\sin(0)}{0}$
Katharine
and so we say that sin(x)/x is not continuous at x = 0
well it's not even defined there so it can't possibly be continuous
yes but even if it was defined
if the limit isn't equal to the value then it is not continuous
but $f(x)=\begin{cases}\frac{\sin(x)}{x} & x\neq 0 \ 1 & x = 0\end{cases}$ is continuous everywhere
this is all unrelated to the question though just some info on what that inequality says
frosst
in that case the limit of f(x) x -> 0 = f(0)
and in general $f(a) = \lim_{x\to a}f(x)$ need not hold
frosst
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Please don't occupy multiple help channels.
@gritty badger Has your question been resolved?
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yeah but C contains every element of D
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Let A and B be two different points from the plane. what are the set of points M from the plane that satisfy AM + MB = AB
do you know what AM, MB, and AB mean?
lengthes
so AB is the length from point A to point B?
now suppose instead of going right from A to B, we stop at point M somewhere between. So it's like saying we went from A to M, stopped at M then went from M to B
i js want an instant answer i dont want explanations
welp
yeah
so then M lies somewhere between A and B
do i just throw you the answer?
am i allowed to do sothx for those dislikes brothers
go for it
?
pajamamamallama is helping
!noans
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
so what is it a test
well no i would understand how to think as well
understand the method
the way of thinking
not learn it by heart
alright here's a diagram of what I mean. Notice how we could've just traveled AB, but instead we took a stop at M right?
There's not mathematical notation for this that I'm aware of
unless knief knows of some
may i write one now 😭
😭
Barycentric?
?
js send it
kinda paralyzed to do anything after ive received 3 dislikes
from unknown people 😦
so idk
bruh
help as you please
alr thanks
notation for this is [AB] / {A,B}
so segment AB privated from A and B?
yep
why is A and B removed
A and B are two different points from the plane
so they cant be on top of each other
and if u sub A and B in ur equation
AA + BB = AB
thats wrong
np
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no not at all, you're free to help all you like :)
just don't give answers to people
oki
u heard that donia
even tho
i wanted the answer
alr
did so
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i completely forgot how to do this someone help
@twin anvil Has your question been resolved?
Find the derivative
Then plug thr x value in it
I'm telling u how because u forgot how to do it, and it's not ur first time learning
@twin anvil Has your question been resolved?
are you familiar with definition of derivative
Can u help me
?
is that an insult or
idk what thats supposed to mean
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My Question is: Let $a_{n}$ be a sequence of positive integers and define $U_n$ and $V_n$ by the recursion $$f_{n + 2} = a_{n + 2}f_{n + 1} + f_{n}, ~~ f = U, V$$, with initial conditions $U_{0} = a_{0}$, $U_{1} = a_{0}a_{1} + 1$, and $V_{0} = 1$, $V_{1} = a_{1}$. Prove that $\gcd(U_n, V_n) = 1$ using Bezout's Identity.
What I've Tried:
So, firstly I know that it's trivial to say that $\gcd(U_0, V_0) = 1$, since I can write $0 \cdot U_{0} + 1 \cdot V_{0} = 1$. Then I tried to work out a general pattern, noticing that $V_{0} U_{1} - U_{0}V_{1} = 1$, which would imply that $\gcd(U_1, V_1) = 1$. However a problem immediately arose when I found that, upon indexing all of terms in $V_{0} U_{1} - U_{0}V_{1}$ by 1, I came across an issue:
$V_{1}U_{2} - U_{1}V_{2} = a_{1}(a_{0}a_{1}a_{2} + a_{2} + a_{0}) - (a_{0}a_{1} + 1)(a_{1}a_{2} + 1) = -1$.
Now I'm almost certain that this pattern is too similar for it to not be a coincidence, and I'm wondering that if I have perhaps structured my steps in such a way that my choice of Bezout Coeffiecents doesn't work for the case where $n = 2$. Or if I've just completely misunderstood the problem entirely. Any help at all would be very appreciated
Ammardian
@obtuse pivot Has your question been resolved?
<@&286206848099549185>
yes
sh
dhani (Vorqid)
have you tried a proof by induction?
The plan has been proof by induction, the trouble is that I get $V_{n}U_{n + 1} - U_{n}V_{n + 1} = -1$ for $n = 1, 3, ..., 2k + 1$. It feels like it goes in circles, with it working for $n = 0, 2, 4, ..., 2k$ and then being so close to working with the odd cases
Ammardian
I'm not sure if there is some case to be made where I use strong induction, with two base cases of $n = 0$ and $n = 1$, then I get to specify two different sets of bezout coefficients in my inductive hypothesis.
Ammardian
Wdym by it not working for the odd cases
well I need to find coefficients x and y so that $xU_{n + 1} + yV_{n + 1} = 1$, but it gives me -1 in the odd cases
Ammardian
If my choice of coefficients is such that $xU_{n + 1} + yV_{n + 1} = -1$ idk if that still implies that $\gcd(U_n, V_n) = 1$
Ammardian
switch the signs of x and y.
Can’t you just multiply by -1
so I can switch the signs for evey second case and that will work?
and then have my inductive hypothesis specify two different sets of coefficients for odd and even cases?
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hey, how do i approach number 7? (i dont think i have to translate anything since all the information is given)
i know that |z| is 1
also the question wants theta in degress for some reason
<@&286206848099549185>
hey
are you looking for some fancy solution?
without plugging those values directly in the equation
?
there must be right?
this is an olympiad problem n most questions do that
ah okok
lemme see
maybe 1 - az could be manipulated
manipulated in terms of what?
I can't think of any other than Trig identities
i think i found it
factorize |z| you get |z||z^-1 - [conjugate of a]|
|z| is 1 and 1/z is conjugate of z
then the two things are equal to eachother no?
so cos x = 0
x = pi/2 + 2(pi)n
(2n + 1)90 in degrees
am i right?
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How do I show this is true? $$2abcd\leq (ad)^2+(bc)^2$$
Good
I derived it from $$
|z+w|\leq|z|+|w|
$$
Good
Assuming z = a +bi, w = c+di
if you derived it then that seems pretty good to me
as hayley said, if you derived something from a formula that is true, then the derived formula will also be true.
But how could I be sure that 2abcd is less or equal than (ad)^2 + (bc)^2?
Or how do I show it?
use AM-GM
np:)
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i dont know where to start
are you supposed to use any formulas?
or without them?
i have no restriction
you can always convert some sin into cos
observe 1 and 89
oh
similarly 2 and 88 and so on
sin(x) =cos(pi/2-x)?

you can also convert it to linear cosines and use formula too
but that will be inefficient
Someone once told me that method is not efficient
Express the first half of the series as cos
you mean cos2x = 1 - 2 sin^2(2x) ? Thats gonna be hard to solve
Then do (1st+last)+(2nd+penultimate) and use the trig identity sin²x+cos²x=1
yeah that thing
ohhhhhhhhhh
okay yeah that was smart
i didnt thought of that
😁
ok so answer is 45
what did you do with sin^2(45)?
ohh
that's 1/2
mb
but wait
i dont understand this
so sin^2(1) => cos^2(89)
right?
yes
Yes
no its not
Wait let me try again
personally id convert 89 to 1 so its easier to count
Ok yes that's it
its okay i got it
Not times though
45 * 1/2 = 22.5
$45\frac12$ is a mixed fraction representing the value $45 + \frac12$ \
it is not the product of $45$ and $\frac12$
ℝαμΩℕωⅤ
ohh
i understand
thank you
Yes I mean 45½
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anyone can help me with (b)?
@dim crane Has your question been resolved?
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13 is just a buch of horizontal line segments, right?
How
Those 2 sets look mighty finite
The Cartesian product will also still be finite
[1,2] is an interval IMO
Cool. Thanks!
Well I mean just draw them
The x are fixed at whatever the first set has
Then slide it around with the 1, 2 interval
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Thanks
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Nah
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okay now i do need help with these two😭
the first one i got stuck after getting to them over 6
Send your work
Fr
at this point what does anything come from
Do u know how to add fractions?
bro inventing his own methods
fr
Fr
he s so cooked that he started inventing his own formulas
i don't get fractions-
Then learn how to do that before doing questions
i did get the common denominator-
okay
do this
actually step by step
don’t do anything in ur head
and send that
How u got 6x
you kinda skipped a step in showing ur work
Yes
when you combined the denomintors on the left
oh
i think that tripped you up
cuz you have the right idea
like this, then you can add them together
oh right
its the same as i first send it-
okay not the same
only the 8 changed to 3
so,,
And that makes a difference doesn't it
well, yeah
Get x terms on LHS and non x on RHS for easier calculations
shouldnt i need to eliminate the 6s first?
Just do this and you'll know it's easier
the movement should be the first step
ah
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If a,b,c and d are four distinct numbers chosen from the set {1, 2, 3, 4, ... ,9}, then the minimum value of (a/b) + (c/d) is:-
A) 3/8
B) 1/3
C) 13/36
D) 25/72
the numerators must be as small as possible, the denominators as large as possible
so it's obvious which 4 numbers to choose, although it might not be yet obvious in which order
oh i get now
I was lacking the thought of order
thank you so much
np
.close
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help no 3
It simply says you to
How many possible combinations are possible out of 9 numbers
It's simply 9c3
,calc 987/(6)
Result:
84
@lyric dust Has your question been resolved?
so the order doesnt matter?
wait can it be solved using fcp?
They r asking for combinations
The answer possibly would be 9³
Or if numbers are distinct it will be 9×8×7
It's better you check the answer key , it's not clear what actually they want
true
my teacher doesnt really teach that well
ill go with 9C3
assuming that numbers could repeat
right?
No repetition here
When we take 9c3 it's all distinct numbers and order doesn't matter
ohhh
If it's 9p3 numbers are distinct but order matters
i think order doesnt matter for a lock code
Yeah maybe they asking for combinations
So just go with it
wait last
how about 9
am confused also by that
combination right?
because when u order food u dont really have it in order?
It's 7c5
Yeahh
,calc 7c2
The following error occured while calculating:
Error: Undefined symbol c2
thank u so much xor
ur the first one who like helped me right away
hey
can u help with one question in science?
its about physics
what determines the accuracy with which you can make measurements using the vernier caliper and micrometer
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help with factoring out lowest power factors
would i be able to make x = x-6
and factor out ^3/2
i don't know im im on the right track or completely off
im pretty sure it wants you to factor the ^3/2 out yeah
looks good?
i forgot a line
x^3/2(x) -36(x)
and then i plug the x for x?
well x-6
and simplify
?
doesnt look right
it cant be x+/- 0 can it?
i was thinking i could js make the parenthesis x
instead of havign the whole thing of (x-6)7^7/2
which explains the x=x-6
it wasnt given in the example so to speak
whar
FOR EXAMPLE
you have to replug x=x-6 for the x^3/2 aswell
that works yea, but in the paper you still had 36x (but you treated it as 36, so its fine for end result
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I don't understand how to derive rev and profit from the formulae above
@sudden harbor Has your question been resolved?