3a+b =12 doesn't lead to a+b =4
#help-13
livid hound
native shuttle
why not?
livid hound
how are you getting from
3a+b = 12 to a+b=4
native shuttle
divided 3a/3 and 12/3
livid hound
remember, same operations to both sides,
if you're going to divide, you're supposed to divide both sides by the same amount and not just a single term on each side, whatever terms appear first and/or whatever you feel like
native shuttle
so b should also be divided by 3?
livid hound
if you intended to divide both sides by 3, yes
you're better off just leaving
3a+b = 12 as is for now
and using
f'(x) = 3a * x^2 + b (only)
what do you get from f'(0) = 6
native shuttle
b=6
livid hound
yes, and using that,
it should be relatively easy to find a now; using
3a + b = 12
native shuttle
ah i was right originally but for a i put -2 instead of 2
ty for the help!
.close
balmy current
cedar kilnBOT
balmy current
can i get help on this?
native shuttle
if the square brackets are cordinates as in its supposed to be
4(-1, 2) and 4(0, -4)
then itd be e
gentle remnant
Is this even possible?
Give examples of sets A, B, and C and f : A -> B and g : B -> C satisfying that g is not surjective but g o f is surjective.
gentle remnant
I get this from google:
The composition of surjective functions is always surjective: If f and g are both surjective, and the codomain of g is equal to the domain of f, then f o g is surjective. Conversely, if f o g is surjective, then f is surjective (but g, the function applied first, need not be).
cedar kilnBOT
@gentle remnant Has your question been resolved?
gentle remnant
I'm still very confused how if g is not surjective, how can g o f be surjective?
cedar kilnBOT
@gentle remnant Has your question been resolved?
lethal jackal
yeah I don't think that can happen
g circ f surjective basically implies that g has to be surjective
hard belfry
People I hope y’all having a nice day and fun and enjoyment learning math! 😃
cedar kilnBOT
@gentle remnant Has your question been resolved?
woeful igloo
How do you solve these types of questions?
cedar kilnBOT
How do you solve these types of questions?
woeful igloo
So...
f'(x^3) --> 3x^2 3*3^2 --> 0?
woeful blade
So...
``f'(x^3) --> 3x^2
3*3^2 --> 0``?
why would 3 . 3^2 = 0?
woeful igloo
great question, I plugged it in wrong into my calculator
that does not make sense though lol. So 27 then. Thanks!
.close
quartz dome
how do i simplify a^-2+b^-1 over b+a^2
cedar kilnBOT
how do i simplify a^-2+b^-1 over b+a^2
narrow fiber
how do i simplify a^-2+b^-1 over b+a^2
have you tried anything?
quartz dome
have you tried anything?
i dont kow where to start sorry
livid hound
you could start by expressing those negative exponents as fractions
quartz dome
oh alr imma try
quartz dome
you could start by expressing those negative exponents as fractions
ok what do i do next
livid hound
what do you have atm
cedar kilnBOT
@quartz dome Has your question been resolved?
quartz dome
no
potent dragon
a^1/2+b^1/2 over b +a^2
i do not think that's the right simplification.
a^-n = 1/a^n
you wrote: a^-n=a^1/n
try this and you should get your answer
quartz dome
alright lemme try
quartz dome
try this and you should get your answer
1/a^2+ 1/b over b+a^2?
where do i take that
or is that it
potent dragon
1/a^2+ 1/b over b+a^2?
take the lcm and you should get your answer in a few steps
quartz dome
take the lcm and you should get your answer in a few steps
omg ur genius
kk ty
.close
austere bolt
complete the square : y2+6y+2
cedar kilnBOT
complete the square : y2+6y+2
jaunty pumice
complete the square : y2+6y+2
What is yiur question
jaunty pumice
What we need to do?
jaunty pumice
Yes
jaunty pumice
is that the answer?
.
jaunty pumice
See if you want to make a perfect square you have to divide the coefficient of y by 2 and make it like $(y+3)²-9 +2$ and then simplify it
wraith daggerBOT
Anagh
jaunty pumice
@austere bolt
austere bolt
<@853432087611834379>
how bout for
2x^2 -5x +3
how can i make it into like a perfect square
jaunty pumice
how can i make it into like a perfect square
So first take 2 common of all terms
And then apply same which i told above
$2(x²-\frac{5}{2}x+\frac{3}{2})$
wraith daggerBOT
Anagh
crimson sedge
complete the square : y2+6y+2
[
y^2 +6y + 2 {\c o {}+{} 9 - 9}
]
wraith daggerBOT
austere bolt
And then apply same which i told above
Oh okay thank you
austere bolt
\[
y^2 +6y + 2 {\c o {}+{} 9 - 9}
\]
whats this?
jaunty pumice
Same thing
austere bolt
alright
jaunty pumice
Another way of explaining
cedar kilnBOT
@austere bolt Has your question been resolved?
marble trout
How do I use separation of variables on this (assuming x_inf(v) and tau_x(v) are constants)?
marble trout
I know the answer is supposed to look like this
And I keep getting everything except for the -x_inf * e^(-t/tau_x)
dire geode
Show the original problem
marble trout
Using separation of variables, derive (3.7) from (3.6). Assume that x∞ and τx are constant.
3.7 is second pic, 3.6 is first pic
I've done Diif Eq, and I should remember how to do this, but for the life of me I can't figure this out
dire geode
How do I use separation of variables on this (assuming x_inf(v) and tau_x(v) are...
So it's just a first order linear differential equation then?
marble trout
Yes
dire geode
y' = a + by
marble trout
Sure
dire geode
marble trout
That's integrating factor method, I need seperation of variables
wraith daggerBOT
AustinU
wraith daggerBOT
GeekyGecko18
marble trout
$x_{inf}(v) -x = e^{\frac{t}{\tau_x(v)}+c}$
royal loom
-ln(x-xinf)?
wraith daggerBOT
GeekyGecko18
marble trout
Yes, I think that should work
royal loom
Isn't that what it is though
not what you put
just wondering if they are equivalent
also, it seems like you have it solved, so what is your question?
marble trout
I mean basically I am gettting $x = x(0)e^{-\frac{t}{\tau_x}}+x_{inf}$ which is missing a factor of $-x_{inf}e^{-\frac{t}{\tau_x}$
wraith daggerBOT
GeekyGecko18
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
royal loom
okay
so
Is this an initial value problem? I am not sure where the x(0) is coming from
but would you agree that this is a valid answer?
marble trout
$e^{t+c} = e^t*e^c = x(0)e^t$
wraith daggerBOT
GeekyGecko18
royal loom
,, x=c_1e^{\frac{-t}{t_{x}(v)}}+x_{inf}(v)
wraith daggerBOT
AustinU
royal loom
ah
it is using x(0) as a new constant[
you have that constant as well
see how you can split the e^ whatever+c
into e^whatever * e^c
marble trout
Yeah, and yes, that is what i keep getting, but I know the answer has to be
royal loom
okay so the issue is the last term on there, the (1-e^(-t/T_x))
marble trout
Just the -e^(-t/T_x)
royal loom
yah
marble trout
The one is just my x_inf
royal loom
agreed
okay, how do you know that has to be the answer? because we both have came to the exact same answer * that isn't that one * Is there any more information for this question? Or where did that answer come from?
marble trout
The first picture is from a book, and the second picture is my homework
And you can ignore the part about "for x = m, h, n"
royal loom
sorry, I honestly do not know where that answer is coming from
try deriving it backwards, if you use that x(t) as a solution
and take the derivative
you will find it does not equal to what they say dx/dt
is
so.. idk
Is it for a course you are taking?
marble trout
Yes, computational neuroscience lol
royal loom
interesting! Well do you have time to talk to the professor about this question then? I believe that that answer is incorrect
,, x(0)e^{\frac{-t}{x}}+x_{inf}*(1-e^{\frac{-t}{T_x}})
wraith daggerBOT
AustinU
wraith daggerBOT
AustinU
wraith daggerBOT
AustinU
royal loom
so that cannot be the solution?
marble trout
LOL, idk I feel so stupid. I'm literally about to graduate with a degree in math and I can't even do basic diff eq
I feel like I should def be able to get this right, but it's not happening
royal loom
well if it makes you feel any better, this doesn't seem like basic diff eq to me, but I feel like I could be struggling just as hard as you
what degree are you getting? I am interested in studying math
marble trout
Computational and Applied Mathematics
royal loom
bachelors?
marble trout
Yeah, though I'm technically a partial masters student right now
royal loom
nice, I don't want to take you off the path of this question too much though so I will digress lol
marble trout
I mean if you want to talk about it we can talk about it, I'll probably just try and ask a classmate for help lol
royal loom
might be for the best lol. Did you ever think about studying pure math, or like what career are you thinking about that your specific degree path is taking you towards?
marble trout
Well, I can't say I was super deliberate when getting into this. Basically I ended up going to an engineering college not really knowing what I wanted to do, but knowing I wanted to do STEM. It turns out diff eq was the last required math class that all majors had to take at my school, and ironically I liked it so much that I decided I couldn't just be done with math, so I decided to become a math major.
I'm in applied math because it was either that or stats as far as math majors my college offered and I much prefer computational and applied to stats. However, this worked out well for me because I really don't like analysis very much, and really prefer applied math.
As for career plans, I kind of want to do mathematical biology (hence the computational neuroscience class) but it seems like most of the work in that field is remaining in academia and I feel like I might need a bit of a break before jumping into grad school. I have a minor in data science, so since this is my last semester of undergrad I might try to get someone to hire me for that so that someone will pay me LOL
But like I said I am currently in a combined bachelor/masters program so if I can't find a job I want I'll just spend another year getting my masters
royal loom
That's pretty awesome, honestly I am not sure what mathematical biology would entail but it must be pretty interesting. Diffeq was the last math course offered at my 2 year school and actually the only math course I wasn't able to take (maybe why I am unable to help you lol), but I've done I feel like a bit of all the math except really anything applied like you are doing, I'm not sure how I would like it. Congrats on all your hardwork already though, you seem pretty smart.
sorry I can't help with your question
marble trout
LOL, no worries. IS there a specific degree you are thinking you want to persue in math?
royal loom
Well initially a B.S / B.A in pure mathematics, but I am considering possibly being a professor in the future, so I may end up wanting to pursue a PhD in pure mathm although that seems pretty far in the future from where I am now.
marble trout
Where are you now?
royal loom
I am in the middle of my gap year right now and fairly bored with my life, I graduated Highschool and earned an A.S last july
I finished through mutlivariable calc, linear alg, and basically all the 2yr math except diffeq like I said
I did a lot of stats to but wasnt the biggest fan, I got a certificate of completion in data analysis too
marble trout
Is there anything else that piqued your interest besides math?
royal loom
I did a lot of sciences because I was on the pre-physical therapy track, and I am pretty interested in that aswell although not as much as math, I definitely can't see myself being a PT or doctor or anything like that, and I think I am chiefly interested just because I really like training
I have never got the chance to take physics, but it does seem like something I could be somewhat interested in
marble trout
Yeah, you should definitely try physics it's like applied applied math
I would have done it, but I wasn't very good at it
royal loom
my highschool didn't have any physics and then I basically had to choose at my running-start program between biology or physics :/ I wish I could have taken some by now though
It comes up so much in the MIT OCW and the professors expect their students to already know the models and such and I just get stuck for so long learning random physics models in the middle of their lectures
marble trout
Yikes, that really sucks
I took algebra based physics in highschool and calc based is very different. Harder, but more interesting
royal loom
yeah, I mean physics questions came up occasionally in my calculus classes- especially as more like application questions and they always were so much more difficult than the usual questions. It was always the physics things too that were omitted or just had to be accepted without proof when they were introduced lol
marble trout
LOL yeah
royal loom
anyways though, good luck with your question and thanks for the chat, I will be heading off now. Goodnight
marble trout
Good night, and good luck :)
royal loom
thank you!
marble trout
.close
vernal basin
is khan academy a good site for learning math?
cedar kilnBOT
is khan academy a good site for learning math?
marble trout
I've found it pretty useful in answering questions
vernal basin
does it fully teach the units
marble trout
It's certainly trustworthy, but IDK if you mean like as a self guided thing, then IDK
zenith sail
Khan academy is very thorough in my opinion
vernal basin
alr
marble trout
Like if you looked up how do derivatives work and Kahn Academy came up and had a video series on it, they would cover what you would need to know
marble trout
What is AOPS
vernal basin
art of problem solving @marble trout
marble trout
Huh, I've never heard of them
But don't take that as a bad thing or anything, I just don't know them
royal dock
cedar kilnBOT
royal dock
I need help to find the domain
i already have an idea but idlk how to countinue and solve
crimson obsidian
i already have an idea but idlk how to countinue and solve
for each number inside log it has to be greater than 0
So x+1>0 and x-4>0
The term inside root has to be greater than or equal to 0
And log is non negative number only when the number is greater than or equal to 1
So x+1 >=1 and 0<x-4<=1
Wait
crimson obsidian
i try to do it, now i send to you a photo, check if is correct
Ok
royal dock
crimson obsidian
If base is greater than 1 then for log to be greater than or equal to 0 the number has to be greater than or equal to 1
Not greater than 0
royal dock
so the first bacame x+1>1?
crimson obsidian
It can be 0
And when log is 0 the number is always 1
Isn't it?
You forgot equal to sign
royal dock
where i should put the equal sign?
crimson obsidian
x+1>=1
This equal to sign
Do you know greater than or equal to sign
I don't have it in keyboard
royal dock
one question, why is x+1>=1 and now x+1>=0??
crimson obsidian
one question, why is x+1>=1 and now x+1>=0??
X+1 can never equal 0
It is Against the domain
I never told x+1>=0 I told x+1>0 but not "now", I told before
royal dock
sorry i wrong to type i mean x+1>0
crimson obsidian
one question, why is x+1>=1 and now x+1>=0??
Also because log is under sq root so the rule says it has to 0 or positive so for that log can't be between 0 and between 0 and 1 if base is greater than 1 as then the answer will be negative
So x+1>=1 is the correct one, not x+1>0
Its unrelated question, but do you know graph of log function?
royal dock
ok
crimson obsidian
But you can draw graph and check what I said
Did you learn graph for log when base is between 0 and 1 and when base is greater than 1 ?
They will be 2 different graphs for log, I learnt them but I'm not sure if you have learnt them as well.
crimson obsidian
i shoould draw?
Yes you should draw. I suggest solving these questions with help of graph
royal dock
More or less this is the first
crimson obsidian
Where is the function
royal dock
this is log2 (x+1)
crimson obsidian
Are you drawing the graph of y= log x to the base a? For when a>1?
So as you can see, for log to be positive and 0 the x+1 has to be greater than 1 and equal to 1
Does this confirm what I said?
Which is just x has to be greater than or equal to 0
Which is shown by the graph
You can similarly solve the inequality of second log
crimson obsidian
one question x+1>1 so x>2?
I had told before it's >=
royal dock
right x>=o
crimson obsidian
Yes
This is concluded by watching the graph
You have to know that what is range of the number for which range of log is greater than or equal to 0
Because any number inside sq root has to be greater than or equal to 0
Otherwise it's complex number
royal dock
ok, about the second instead in my notes is correct or i should change somethings?
crimson obsidian
ok, about the second instead in my notes is correct or i should change something...
I thought I was clear before, both are wrong
Wait let me see again
crimson obsidian
ok, about the second instead in my notes is correct or i should change something...
Why did you say x>0 in the second one
It is log(1/2)(x-4)?
I was confused of that sorry
royal dock
I set the argument to be greater than 0
crimson obsidian
Yes you're right
royal dock
is only x, 4 is outside
royal dock
ok
crimson obsidian
Only the first one you have to improvise
Second one is good
After finding in inequality from first one, intersect the two inequality to find final answer
cedar kilnBOT
crimson obsidian
good thanks for ur help
Your welcome
cedar kilnBOT
Available help channel!
crimson sedge
Construct the graph of the function and determine the range of values of this function if you know its domain. Write in words what it is
graph (line, half-line, line).
crimson sedge
gilded elm
!status
cedar kilnBOT
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
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
<@&286206848099549185>
nimble veldt
take 2 numbers of your choice (for a fixed a, e.g. a = 3), use them as x, calculate y, draw the points (x_1,y_1) and (x_2,y_2) in your sketch, draw a line through the 2 points.
make this again for another a.
crimson sedge
take 2 numbers of your choice (for a fixed a, e.g. a = 3), use them as x, calcul...
Wait
@nimble veldt Is that right?
nimble veldt
looks good.
cedar kilnBOT
@crimson sedge Has your question been resolved?
primal olive
how would I solve cube root(x) = 2? I've tried searching google but it just keeps telling me how to get the cube root of 2
crimson sedge
i mean you can solve this quite instinctively, bc you can try to think of what number cube-rooted would equal to 2
but the more standard approach would be to cube both sides of the equation
primal olive
alright thanks
cedar kilnBOT
Available help channel!
patent lake
this youtube video did the hamming code completly different from this boook, and im so confused
patent lake
so in the video they check if the parity bit is even or odd based on how many ones, and then when every parity bit is calculated they check to see if they are corrected, and then all the parity bits that are false theirs positions are added together and you will find the position to change the biit
BUT the textbook did different
cedar kilnBOT
@patent lake Has your question been resolved?
crimson sedge
cedar kilnBOT
crimson sedge
Could anyone please help
I solved part c
Ax=b
And got xp as
-2
1
0
-3
0
But they go
1
2
0
1
-1
I'm pretty sure I did it right. Used online calculator to verify too
Is their answer for x_p incorrect?
cedar kilnBOT
@crimson sedge Has your question been resolved?
stiff cradle
cedar kilnBOT
prisma gull
hey
chilly trench
hi
prisma gull
just prepare a table for values close to 1/2
prisma gull
$f(x)=\frac{x^3-x}{1-2x}$
stiff cradle
wraith daggerBOT
.doc
prisma gull
The whole notion of limits to check what happens to the functions as you get closer and closer to a particular vale
prisma gull
If the limit of a value is say L, then that's where the neighborhood of the values goes to
so if approaching 1/2, check f(1/2+0.000001), f(1/2+0.000001)
super close to 1/2 but right side
similarly analyse the left side
and make a conjecture about the behavior
prisma gull
super close to 1/2 is a fraction right?
stiff cradle
yess
prisma gull
basically we want to know what's value of the function as you get super close to 1/2
where the neighborhood of the values goes to, not what the exact value is
stiff cradle
ohhhh
stiff cradle
are 2/5, 9/20, 47/100, 49/100 valid values
icic so these values are valid?
since
they are approaching to 1/2
prisma gull
if you write limit is equal to 2, by definition it means the neighborhood is equal to 2 or the limit is 2
so try not to confuse with equality sign along with a limit
prisma gull
are 2/5, 9/20, 47/100, 49/100 valid values
you can choose any number close to 1/2
prisma gull
you can't because they aren't extremely close to 1/2
prisma gull
even if you have them in table
your conjecture is based on values verry close to 1/2
stiff cradle
your conjecture is based on values verry close to 1/2
yupp
prisma gull
so that's the whole notion, check what the neighborhood goes
stiff cradle
thanks for helping really appreciate itt
prisma gull
have a good one
cedar kilnBOT
@stiff cradle Has your question been resolved?
regal wadi
i believe that this may be right? but would someone mind seeing if it is rigt or wrong and help me understand why?
regal wadi
it's asking which step was solved incorrectly
cosmic steppe
Why do you think it's step 1
regal wadi
because wouldn't step one hve to start by distributing the properties wouldnt that make it -4x-(3x+3x2)>3x+4?
cosmic steppe
3x2 as in 3 • 2?
regal wadi
yes
regal wadi
oh
cosmic steppe
Imma say Hannah seems to forgot how to do addition/subtraction
crimson sedge
whos hannah?
cosmic steppe
i believe that this may be right? but would someone mind seeing if it is rigt or...
The girl in the problem lol
regal wadi
then perhaps step 2 may be wrong becasue we have to get rid of the parenthesis so we can continue the problem?
wouldn't step 2 be technically step 3?
cosmic steppe
She got rid of the parenthesis in step 1
regal wadi
oh
cosmic steppe
Go through her process
regal wadi
so she gets rid of the parenthesis in order to continue the equation, and then she distributes the properties (aka step 2) and then for step 3 im not too sure what she did
cosmic steppe
What happened to the 3x
cosmic steppe
No
She subtracted 3x from both sides
It's just like solving an equality
If I said to do:
5x + 7 = 2x + 8
What would you do to isolate x
regal wadi
well if i -5 from both sides i'd get -3 would i for the 2?
cosmic steppe
Wdym by that
regal wadi
so lets say i -5 from both sides right? 5x would be cancelled out isolating that x but 2-5 is -3
sorry i probably sound really stupid
regal wadi
yes
cosmic steppe
You're gathering the x terms onto one side
That's what's Hannah's also doing
She subtracts 3x from both sides
-7x - 3x = -10x
So step 2 and step 3 are correct
regal wadi
subtracted 4 from 6?
wait no
-4 from both sides right?
wait a minute that would mean step 5 is wrong
cosmic steppe
-4 from both sides right?
No
Look
She gathered the constants
Notice something?
Imma ask you again
What did she do to get from step 3 to step 4?
regal wadi
added 6 to both sides
cosmic steppe
What is 4 + 6
regal wadi
10
regal wadi
right but for step 5 isnt it x<-1??
regal wadi
oh right step 4 made the outcome on step 5
cosmic steppe
She made a mistake going from step 3 to step 4
ornate dagger
Could someone guide me through the steps, and NOT give me the answers.
Colin invests £4000 into his bank acount
He recieves 5% per year simple interest
How much will Colin have after 3 years?
timber violet
u know the formula for simple interest?
ornate dagger
No
timber violet
simple interest formula = PRT/100 where P = principle,R = rate of interest, T = years
use this and find SI for 3 years
then u add it to ur principle
timber violet
umm,ya
timber violet
is it £4000?
yup
ornate dagger
simple interest formula = PRT/100 where P = principle,R = rate of interest, T = ...
So it would be P+R+T then?
timber violet
PRT = P x R x T
ornate dagger
oh ok
dusk finch
ah okay, sorry
candid pelican
cedar kilnBOT
candid pelican
Is this correct? I'm assumign my homework is just asking me to find an example
I made it such that the dot product of the direction vectors was 0
scarlet garnet
sure, you could even shorten the second direction vector to just (1,0,1), but this is correct
scarlet garnet
Is this correct? I'm assumign my homework is just asking me to find an example
yes, an example means you just have to provide one case where the rule applies
candid pelican
yes, an example means you just have to provide one case where the rule applies
appreciate it! is it cool if i ask another vector question
scarlet garnet
appreciate it! is it cool if i ask another vector question
yes
candid pelican
For this question
basically I set up the vector <1,2,1> and <a,b,c> (aka v) in a matrix
I set up each of them and solved to find the determinant
this led to a system of 3 equations
the issue is I tried to solve this system and what happened was 2 of the 3 equations ended up being the same
cedar kilnBOT
@candid pelican Has your question been resolved?
cedar kilnBOT
@candid pelican Has your question been resolved?
cedar kilnBOT
candid pelican
.reopen
cedar kilnBOT
✅
candid pelican
@scarlet garnet sorry for ping just wanted to follow up
scarlet garnet
the x here is cross product right?
candid pelican
the x here is cross product right?
Yes
scarlet garnet
so you got something like (2c-b,c-a,b-2a)=(3,1,-5)?
scarlet garnet
did you maybe make a mistake solving the system>
candid pelican
did you maybe make a mistake solving the system>
I’ll check and get back to u
Thanks!
cedar kilnBOT
@candid pelican Has your question been resolved?
candid pelican
@scarlet garnet for part b, would we just basically do the same kinda process as a but just show no solution to system
wraith daggerBOT
scarlet garnet
do that formally, with steps, and thats it
candid pelican
do that formally, with steps, and thats it
Ur the best!
candid pelican
@scarlet garnet I keep getting infinite solutions
Oh that might be on purpose bc the question says solutionS
cedar kilnBOT
@candid pelican Has your question been resolved?
candid pelican
,w solve 2c-b=3 and a-c=1 and b-2a=-5
wraith daggerBOT
cedar kilnBOT
@candid pelican Has your question been resolved?
covert robin
how did this turn 13?
cedar kilnBOT
how did this turn 13?
winter trench
Yep
vale flax
i need help on math homework
covert robin
y = -10 + x
wait i dont get it
vale flax
i need help on math homework
covert robin
how did 3 came
vale flax
i need help on math homework
covert robin
y = 3
covert robin
😭
vale flax
i need help on math homework
covert robin
get your own channel
covert robin
yeah you click help
vale flax
on homework
covert robin
then type there
vale flax
i did
covert robin
idk
elder slate
so y = x - 10 and x = 13
covert robin
so y = x - 10 and x = 13
yes
elder slate
yup
cedar kilnBOT
cedar kilnBOT
Available help channel!
ivory grove
Is this type of answer okay or should I be using variables? How do I find the basis of this as well?
ivory grove
.close
tired inlet
how would I do this problem?
cedar kilnBOT
how would I do this problem?
tired inlet
basically I started with finding the derivative of u
du/dx = 1/x
then I got dx = xdu
in the integral the x cancels out and I'm left with u/2 du
but how do I integrate this
obsidian coral
in the integral the x cancels out and I'm left with u/2 du
Recall that $\frac{u}{2} = \frac{1}{2} \cdot u$
wraith daggerBOT
dldh06
tired inlet
oh I see so I can do 1/2 mutliplied by the integral u du
obsidian coral
Yes
obsidian coral
so the final answer would be 1/4(lnx)^2 + C
Yes
obsidian coral
Yes
obsidian coral
The sqrt(u) is still in the denominator, right? All you did was cancel x^2
tired inlet
oh, right.
so my final answer would be 2u^1/2 + C
then I substitute x^3 - 1
@obsidian coral
obsidian coral
I know dx = du/3x^2
What about the 3 from here? You never canceled that out
obsidian coral
Yes
obsidian coral
alright so I got 2/3 sqrt(x^3-1) + C
Yes
tired inlet
alright thanks
outer moon
cedar kilnBOT
outer moon
I keep getting b as the answer
but answer booklet says a
not sure what im doing wrong
royal loom
@outer moon could you give me some explanation as for the notation? What does a parenthesis mean instead of the bracket in regards to these sets?
royal loom
No worries
outer moon
.close
outer moon
cedar kilnBOT
outer moon
why is A not a valid function?
cerulean sail
Is ln(x^2 - 1) defined for all possible values of x that are greater than or equal to 1?
coral valley
tes
coral valley
how do you find out eigen values with these kind of variables?
is it even possible?
cedar kilnBOT
@coral valley Has your question been resolved?
humble cipher
matrix A has eigenvalues 10, -1,- 1
how do i find the eigenvectors?
humble cipher
my thingy only has an example with a 2x2 matrix
cedar kilnBOT
@humble cipher Has your question been resolved?
humble cipher
<@&286206848099549185>
what
thats not at all what i asked
i know how to find the eigenvectors of a 2x2 matrix using its eigenvalues
in this case i know the eigenvalues of a matrix and want to find its eigenvectors
ok and what if 2 of the eigenvalues are the same
we would start by doing that and then what
and this is for the eigenvectors whose eigenvalues are the same?
alright thanks
.close
stone vortex
What am I doing wrong here?
cedar kilnBOT
What am I doing wrong here?
stone vortex
It felt like I was doing it correctly but the final answer seems wrong
Wait might it be the radius since it’s y less than or equal to zero??
royal loom
your work is very neat and organized, I like the diagram aswell. That's awesome
couldn't you just find the volume without using integration though?
stone vortex
thank you 🫡
stone vortex
using the shell method
royal loom
It would probably be for the best I just link you this https://youtu.be/ydyXf01WNYA
if you want someone else to try to help you in the chat though, feel free
stone vortex
oh i watched this a day ago
royal loom
I don't have the shell method on the top of my mind at the moment, so I don't see anything glaringly wrong with your math, but I am sure an example from that could help you out
good luck
cedar kilnBOT
graceful perch
so this is what you were talking about
glad to help
first of all @arctic stump
which decade has the most amount of pennies?
that would be the 2000s with 7517 pennies.
the 2nd? 2010s with 5710
oops
sorry
wrong ping
@arctic stump
u listening?
digital cliff
cedar kilnBOT
@arctic stump Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
broken knoll
yo
lusty grotto
if the function is defined at x = 2, the limit exists as x approaches to 2, and the function at x = 2 equals to the limit as x approaches to 2
it is continuous
broken knoll
but
2 is greater then 1
so the possive of the limit approaching to x will be 5
and the negative of the limit approaching to the x will be 2
wouldn't it suppose to be like that
lusty grotto
when x > 1, the function is 5 everywhere
lusty grotto
draw a graph maybe
when u approach 2 starting from a point slightly to the left of 2, the function stays at 5
coz this point slightly to the left of 2 is still greater than 1
real quail
A photograph is 18cm by 12cm. It is to be surrounded by a frame of uniform width whose area is
equal to that of the photograph. Find the width of the frame
real quail
How would you do this, I have no idea how to approach
lusty grotto
draw a picture
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
cedar kilnBOT
warm bone
Look at (2.3) closely
crimson sedge
Look at (2.3) closely
But why 1/i?
warm bone
$$i \cdot \frac{1}{i} = 1$$
wraith daggerBOT
草w
warm bone
If you'd like you can specify $i \neq 0$
wraith daggerBOT
草w
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
.close
crimson sedge
What do you think is the right answer?
cedar kilnBOT
What do you think is the right answer?
@crimson sedge Has your question been resolved?
frigid musk
arctan(pi/2 t²) ~ pi/2 t² at 0 then you can integrate this comparison relation (because of positivity) check the lecture notes, so the integral equivalent to pi/2 x³/3
so the limit is 0
tepid spruce
yo
vagrant elbow
Do you need a decimal value or?
tepid spruce
it just says simplify
tepid spruce
4x
vagrant elbow
Yup
frosty ocean
Similarly factor out things here
tepid spruce
yeah but you can subtract surds with different roots
vagrant elbow
So 5√2 + √2?
tepid spruce
cant
vagrant elbow
yeah but you can subtract surds with different roots
So just let em be then
gilded elm
wow the pre edit message is so cursed
vagrant elbow
💀
tepid spruce
ah thanks man
frosty ocean
wow the pre edit message is so cursed
Neon reached a new level of ascendancy in math, he can transform into surds
gilded elm
can you be sqrt(2) real quick
tepid spruce
what about d
vagrant elbow
You can factor √2 out and simplify the fraction
frosty ocean
That makes him irrational
gilded elm
That makes him irrational
proof? 
vagrant elbow
Atleast I'm still real alright
tepid spruce
You can factor √2 out and simplify the fraction
how to do that
frosty ocean
Assume Neon is rational and put him on a trial, I'm sure he wouldn't be.
vagrant elbow
$\sqrt2 (\frac13 + \frac12)$
wraith daggerBOT
NEONPerseus
tepid spruce
**NEONPerseus**
huh
gilded elm
Assume Neon is rational and put him on a trial, I'm sure he wouldn't be.
proof by "im sure"
brb lemme replace all my analysis proofs with
"im sure"
vagrant elbow
Multiply it like normal?
tepid spruce
can you multiply surds with different roots?
tepid spruce
isnt it 6 root 21
vagrant elbow
Yes it is
vagrant elbow
Yes
cedar kilnBOT
@tepid spruce Has your question been resolved?
crimson sedge
Can anyone solve this?
cedar kilnBOT
Can anyone solve this?
crimson sedge
I don't know where to begin lol
latent bloom
Okay what part of the question feels hard?
crimson sedge
I tried to do it w direct proportion so yea idk what method to use
latent bloom
Okay first of all, the question says that you have an initial population of 1,000,000. It starts declining over the span of 40 years. It became 50,000. The question mentions that the decline is linear. The question asks when will the population fully get wiped out (ie. population = 0)?
Linear means you look for the straight line equation.
latent bloom
$m = \frac{y_2 - y_1}{x_2-x_1}$
wraith daggerBOT
VulcanOne
latent bloom
Yep
Then you find the time required for the population to reach 0 after it reached 50,000
crimson sedge
Can u show it? I can't get the answer lol
crimson sedge
Hey sorry n yea I did that for ohhh no wait i kinda swapped the values lmao
Lemme do it again
Wait
So I find the value of y this way?
What do i do next?
latent bloom
What did you get for the slope?
crimson sedge
1250
latent bloom
Uhm
Whatever happened, you didn't get to the right slope
So
When you find the slope, you go ahead and take 2 points
Or if you have 2 y values and the distance between them, that works too
So
$m = \frac{50,000-1,000,000 \text{ parrots}}{40 \text{ years}} = -23,750 \frac{\text{parrots}}{\text{year}}$
crimson sedge
Wouldn't m be 1000,000-50000/40?
wraith daggerBOT
VulcanOne
latent bloom
Wouldn't m be 1000,000-50000/40?
Yep
vagrant elbow
define a new unit for parrots per year
crimson sedge
Oh I think I forgot a zero
vagrant elbow
Dimensions $[M^0 L^0 T^{-1}]$
wraith daggerBOT
NEONPerseus
latent bloom
crimson sedge
What do I do after finding the slope😭
latent bloom
You have 50,000 parrots remaining
And they leave their homes at a rate of 23,750 parrots per year
How many years will it take for them to leave completely?
crimson sedge
2 to 3?
latent bloom
Yep
crimson sedge
Thanks!
latent bloom
crimson sedge
Can I ask u another question?
crimson sedge
Sure lmao Imma eat till then
crimson sedge
30 mins?
latent bloom
Yep it's better to open another channel
wild elbow
P(A+B) = P(A) + P(B)
Probability of EITHER A or B, but NOT both
P(A+B) = P(A) + P(B) - P(AB)
Probability of STRICTLY BOTH happening
Is this correct?
Here's a question:
We have batch A of glasses, 200 total. 190 of which are standardized.
We have batch B of glasses, 300 total. 280 of which are standardized.
Picking one randomly, what's the probability of the selected glass being standardized?
To me, the answer seems like a simple 470/500 = 0.94, right?
MY PROFESSOR DOESN'T THINK SO
P1 = 190/200 = 0.95
P2 = 280/300 = 0.93
P(A+B) = 0.95+0.93-(0.93×0.95) ≈ 1
Fucking 100%. How did she come up with this answer?
wild elbow
The notation we use differs from the standard, I know. Don't ask why it's like this, I have no clue either.
sage forge
P(A+B) = P(A) + P(B)
Probability of EITHER A or B, but NOT both
P(A+B) = P(A) +...
The first formula is for P(A+B) if the union of A and B is empty
The second one is the more general one
The reason why you have to subtract P(A and B) is that it "is included twice". Once in P(A) and once in P(B)
wild elbow
This is how the first formula is defined in the book she uses:
"The probability sum of incompatible events is equal to the sum of the probability of these two events"
The second is defined in the book as follows:
"The probability sum of compatible events is equal to the sum of the probability of these two events, minus the probability of the two events happening together"
wild elbow
The first formula is for P(A+B) if the union of A and B is empty
Empty union?
sage forge
Like no element is in A and B at the same time
wild elbow
So, the probability of exclusively A or B being true/happening?
sage forge
The second one is A or B happening. Note that or means both can happen
wild elbow
The way you define it is very technical and abstract (To me) . Professor defines them more practically. "If A or B can happen at the same time, use the 2nd formula. If only one can happen, use the first formula."
sage forge
Yeah, that's right
wild elbow
Okay, so multiplying two probabilities gives us the probability of both occuring/being true (and only this)
P(AB)
sage forge
There are some rules for culculating the probability of both of them being true. But since the experiments are identependent you're right
wild elbow
Okay I'm thinking in like a venn diagram structure.
The first formula, P(A) + P(B) is used for finding the probability of exclusively one event happening (given that the union, I.e both being true, is empty and just inapplicable)
If both can happen, that means we need to remove the union by adding in that little "- P(AB)", right?
sage forge
The first one is the probability of either A and B happening. If you drew it as two circles they wouldn't intersect. Therefore, their area just adds up
sage forge
Okay I'm thinking in like a venn diagram structure.
The first formula, P(A) + P...
For the second one they are interesecting. So by adding the area of A and B you add the area they have in common twice. So you have to subtract it from the area of A and B
So you're explanation was right 🙂
wild elbow
Okay, I got the hang of the formulas now. Now, can I know why the fuck did she say 100% is the answer in that question?
There's another question she showed that I'm confused on, but let's just get this one out of the way first
Okay ANOTHER question
We throw a six-sided dice. What's the probability of the thrown dice being either an even number, or a factor of 3?
Do we treat this as 2 events or one? My teacher treated it as two, and got:
P1 = 3/6 = 1/2
P2 = 2/6 = 1/3
P(A+B) = 1/2 + 1/3 ≈ 0.83
Why can't we just do 4/6 = 0.66?
If we use the second formula, we get
1/2 + 1/3 - (1/2 × 1/3) ≈ 0.66, which is more in line with what I think is true?
tawny niche
What numbers from 1 to 6 are either even or a factor of 3? ("Either" meaning "Exactly one of those properties")
cedar kilnBOT
@wild elbow Has your question been resolved?
jade sandal
cedar kilnBOT
dusk finch
jade sandal
Then?
dusk finch
Now try to simplify the last expression as most as you can. Once you are done, you will have something in the form a+b*log(x)
Then just remind yourself that f(x)=log(x) and you can substitute to get a+b*f(x)
tall saffron
cedar kilnBOT
half forge
,rotate
wraith daggerBOT
half forge
what did you do?
tall saffron
Oh god I can show u my work but its really messy
half forge
is that the original question?
tall saffron
tall saffron
is that the original question?
Yea and my answer
half forge
what even is the question asking for
tall saffron
Just to get the answer to the linear equation
half forge
you need to multiply the LCM of the denominators
half forge
Just to get the answer to the linear equation
it's not a linear equation tho