X= 4 and y= 0 aren’t right?
#help-10
round island
sly elm
,rccw
round island
17
warm shaleBOT
sly elm
it is kinda difficult to read, you seem to have written x = 16 in somewhere, for x^2 = 16
you willl have two values +-4
also you have another root
round island
I send you the original equation
warm shaleBOT
round island
Is y ok?
round island
I have to find x and y intercepts
Which I’m doing both of
Which is written on the page
sly elm
yes x intercept is alright
sly elm
,rccw
warm shaleBOT
hazy idol
How do you solve 2x2 systems? For example 5x=6y+40 2y=8-3x
obtuse pebbleBOT
How do you solve 2x2 systems? For example 5x=6y+40 2y=8-3x
quick nova
there's usually two different ways of doing
one way is that you rearrnage to make one of the variables the subject
hazy idol
quick nova
and then substiute it to the other
for example from $5x = 6y + 40$ you get $x = \frac{6y+40}{5}$
warm shaleBOT
MxRgd
quick nova
which you can subsitiute to the other equation 2y = 8 - 3x to find the value of x
once you've done that, you can plug the x value into either of the two equations to get your y value
obtuse pebbleBOT
hazy idol
/.close
tardy epoch
the bot takes time to close. you can just leave it alone
obtuse pebbleBOT
Available help channel!
simple nova
Hello, im not sure how to answer question 6. Its to do with ratios.
obtuse pebbleBOT
Hello, im not sure how to answer question 6. Its to do with ratios.
obtuse pebbleBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
I don’t know where to begin, im mostly just trying subbing in values to see if that gets better anywhere
obtuse pebbleBOT
@simple nova Has your question been resolved?
gloomy pelican
Hello, im not sure how to answer question 6. Its to do with ratios.
you could do a/b = c/d = e/f = k
and now a = bk c = dk e = fk substitute some things and maybe you can simplify the left side
simple nova
you could do a/b = c/d = e/f = k
and now a = bk c = dk e = fk substitute some th...
ive done that to get k^4(2b^6 + 3b^2 -5f^5)
then im assuming I cancel out the like term and then resub a=kb in
to get a^4/b^4
gloomy pelican
yeah
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
hidden apex
obtuse pebbleBOT
restive gorge
<@587715738484211754> the pics didnt send mb
Just use an integral again
\hzl [ int limits_{2}^{N} frac{ln(x+1)}{(x+1)^2} dd{x} \le sum_{r=1}^{N} frac{ln(r)}{r^2} ] maybe
warm shaleBOT
hidden apex
Just use an integral again
So i js flip
restive gorge
wdym
obtuse pebbleBOT
undone stirrup
Use Sum of Darboux
$\Delta x \sum_{i=1}^{n} f(a + i\Delta x)
;\le;$$\int_a^b f(x),dx
;\le;$$\Delta x \sum_{i=0}^{n-1} f(a + i\Delta x)$
warm shaleBOT
William James Moriarty
restive gorge
undone stirrup
With $\Delta x = \frac{b-a}{n}$
warm shaleBOT
William James Moriarty
obtuse pebbleBOT
Available help channel!
safe glade
How do I do this?
obtuse pebbleBOT
How do I do this?
sand roost
,rcw
warm shaleBOT
safe glade
.close
obtuse pebbleBOT
obtuse pebbleBOT
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ebon shoal
hello, I am working on this problem. I understand that all you have to do is realize 1 over 1-x = 1+x+x^2 .... and whatever and I got there. However I am a little iffy on how convergence and differentiability acts when i do this process, maybe someone can explain it to me?
obtuse pebbleBOT
hello, I am working on this problem. I understand that all you have to do is rea...
gentle smelt
hello, I am working on this problem. I understand that all you have to do is rea...
power series are differentiable on their interval of convergence
ebon shoal
Can i jsut say $\sum 1 + x+x^2+\ldots$ is continuous on |x|<1 and then is infinitly differentialble and thats it?
warm shaleBOT
hummingbirdpostnerf
gentle smelt
I recommend starting with finding the series of 1/(1-x)³ and then multiplying by x
gentle smelt
Can i jsut say $\sum 1 + x+x^2+\ldots$ is continuous on |x|<1 and then is infini...
but you need to finf the series of the function in the exercise
ebon shoal
but you need to finf the series of the function in the exercise
sorry, I guess I am just confused if I am able to do this, from a calc2 POV i know i just differentiate 1 over 1-x and its power series twice and multiply by x on both sides i am just wondering if i have to
argue it in some way or something
gentle smelt
yes, you do argue it by saying that
ebon shoal
i see
gentle smelt
power series are differentiable on their interval of convergence, and the differentiation is termwise
ebon shoal
i see and this is for all power series?
gentle smelt
ya
ebon shoal
and is it always infinitly differntialbe
gentle smelt
and is it always infinitly differntialbe
know what induction is?
ebon shoal
oh it is only if f is
ebon shoal
know what induction is?
i would hope so...
gentle smelt
well, if the derivative of a power series is a power series
then it follows inductively that they are infinitely differentiable
gentle smelt
now, you have to prove in the first place that
the geometric series is convergent to 1/(1-x)
but you probably did that already in an earlier exercise or in class
gentle smelt
np
obtuse pebbleBOT
gentle smelt
infinity is counterintuitive
ebon shoal
yea...
obtuse pebbleBOT
Available help channel!
hollow cradle
What is the difference in process between finding the tangent line of a parametric curve WITH vs. WITHOUT eliminating the parameter?
(currently doing problem 13)
obtuse pebbleBOT
What is the difference in process between finding the tangent line of a parametr...
crude coral
What is the difference in process between finding the tangent line of a parametr...
without eliminating the parameter would make u use chain rule
$$ \frac{\dd y}{\dd x} = \frac {\dd y}{\dd t} \cdot \frac{\dd t}{\dd x}$$
and eliminating the parameter means that u remove the parameter (which is t here) , so u get a equation only based on "x" and "y"
warm shaleBOT
JustToPro
obtuse pebbleBOT
@hollow cradle Has your question been resolved?
hollow cradle
Got it! Would it look something like this?
crude coral
Got it! Would it look something like this?
u should check the thingy
so the channel dont close
obtuse pebbleBOT
crude coral
.reopen
obtuse pebbleBOT
✅ Original question: #help-10 message
crude coral
i dont know how u did part b btw
ornate sable
Got it! Would it look something like this?
U didn’t eliminate the parameter u just plugged it in
crude coral
i would count that entire procedure as , finding without eliminating the parameter
ornate sable
By eliminating I thought you meant t=e^(x-1), so y=e^2(x-1)+2, and now just dy/dx
crude coral
By eliminating I thought you meant t=e^(x-1), so y=e^2(x-1)+2, and now just dy/d...
yeah that is whats meant by eliminating the parameter
ornate sable
yeah that is whats meant by eliminating the parameter
And he did sth else
Bro just found t and substituted
That’s a continuation of method 1
crude coral
Bro just found t and substituted
tbh , thats fine cuz we were trying to find without eliminating
ye
ornate sable
tbh , thats fine cuz we were trying to find without eliminating
Yeah but he’s written it under “eliminating the parameter” so I think OP is getting confused here with its meaning
crude coral
most likely
obtuse pebbleBOT
@hollow cradle Has your question been resolved?
undone plume
can someone explain what I am supposed to do, i am unsure of what this question is even asking
obtuse pebbleBOT
can someone explain what I am supposed to do, i am unsure of what this question ...
proud geyser
but to do that you will first need to prove the base case, so that's your current goal.
ornate sable
but to do that you will first need to prove the base case, so that's your curren...
Yeah, she already said she plugged in one
You might need to plug in two later I’m not sure
proud geyser
she seemed to be questioning whether she needed to or not, so I'm just making it clear that she should.
obtuse pebbleBOT
@undone plume Has your question been resolved?
tired quest
i am having trouble deciding on when to use disc method or shell methjod
tired quest
how do i pick which method to use
bitter terrace
how do i pick which method to use
the washer method always (mostly) work, but the shell method sometimes can make it a bit easier, you want to use the shell method when your rotating perpendicular to the axis your integrating on
say your rotating a curve around the y axis and your integrating with respect to the x axis then you would want to use shell method
tired quest
i see
one more question
how would i do these types of problems
without a having a picture of the graph
number 9 revoling around the y axis
high lily
make your own graph
bitter terrace
Which method do you think you should approach this one with (shell or washer/disk)?
cobalt laurel
^
tired quest
well you want the representative recatngle to be perpindicular to the axis of revolution
and its not
its paralell
so
i think
shell?
bitter terrace
yeah
tired quest
i dont understand how i would do these types of problem without the graph though.
my test is no graphing calculator
bitter terrace
to do it without a graph
you want set the equations equal to each other and find where they intersect
to give you your bounds of integration
tired quest
ok
bitter terrace
so for example you want to find x when 4x -x^2 = 4
to find where the curve intersect the line y = 4
tired quest
its at 2
bitter terrace
ok and now we also want the other bound
bitter terrace
the other bound would just be x = 0
bitter terrace
sometimes you only have to set one equation equal because in this case they say x = 0 as a bound
so they give you that bound
tired quest
how do you know what is a bound and what is a equaation
bitter terrace
its a bound and an equation, you can imagine it like this the line x = 0 is a vertical line at 0
so our region is bounded by this verticle line
bitter terrace
if we had a linear function like x, we would have a triangle, but we have a parabola so it wouldnt be triangle more like a curved triangle or something
tired quest
if we had a linear function like x, we would have a triangle, but we have a para...
my drawing kinda sucks it looks like a liknear func oops
bitter terrace
even if you draw it wrong as long as you get the bounds right and integrate the right equation youll get the right answer
tired quest
so once we have the bounds what do i do
tired quest
even if you draw it wrong as long as you get the bounds right and integrate the ...
ok
bitter terrace
now we want to use the shell method
and so you can just apply that formula with the correct bounds and function
tired quest
is shell method the one with 2pi
bitter terrace
yeah
tired quest
how do i find out like the things inside the integral
like the 2 radiuses
theirs like a height
and radius
how do i do it
bitter terrace
Does your forumla look like this
$$ 2\pi \int_a^b r(x)h(x)dx$$
warm shaleBOT
Branshi (Hints only plz)
bitter terrace
so r(x) is going be the distance to the line your revolving around
we are revolving around the y axis
another way to say that is we are revolving around the line x = 0
bitter terrace
it would be x + 1
bitter terrace
hmm explaining that might have make me go deeper in the math and I have to go soon, but maybe this image will help
so when were integrating remeber that we are really adding up infintely thin rectangles
and we are integrating from 0 to 2 so think of x as traveling from 0 to 2
now here in the image imagine we rotate along the y axis
that rectangle becomes a cylinder (thats the shell method)
the r(x) in the formula is the length from this arbtrary cylinder at position x to the axis of rotation
bitter terrace
yeah
obtuse pebbleBOT
tired quest
.reopen
obtuse pebbleBOT
✅ Original question: #help-10 message
tired quest
wait
one kmore quesiton
since i wont be able to draw a represenative rectangle
how do i know which one to choose again?
cobalt laurel
if they ask you know, if they dont ask you generally go for the bounds that are easier to solve for
maybe one is f(x) and one is f(y) which ever is easier to make f(x) or f(y) is the one to pick
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
naive ingot
PLEH
proud geyser
naive ingot
i looked at the worked solutions and they always think of some way of writing the vectors which always gets to my head because how-am-i-meant-to-know-that
this is the worked solution
eh
imma give this the sack
-close
hate this
vector proofs 🙄
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
weary pebble
For 5 we are just being asked to ovulate the log without a calculator an I don’t know how to contuine
obtuse pebbleBOT
For 5 we are just being asked to ovulate the log without a calculator an I don’t...
quick nova
For 5 we are just being asked to ovulate the log without a calculator an I don’t...
what would log_5 (25) be
craggy valley
For 5 we are just being asked to ovulate the log without a calculator an I don’t...
(Asked to what the log?)
quick nova
it's log_5
quick nova
Would k just multiple it by 1/3?
what k?
weary pebble
(Asked to what the log?)
It just says evaluate the log expression without using a calc
weary pebble
So it would be 0.67
craggy valley
Best to use exact form.
weary pebble
So just the faction
proud geyser
unless required to do so, you should avoid decimals.
weary pebble
Now I have Lne^-4 and I don’t really know where to start I don’t see anything I can do
proud geyser
is this a separate question?
weary pebble
Yea but same overall if that makes
proud geyser
so you're asked to evaluate $\ln(e^{-4})$.
warm shaleBOT
non-Euclidean cat (Yukari)
proud geyser
this should be straightforward, yes?
proud geyser
just the 4?
weary pebble
But I I guess I don’t really know what it is asking me to do like I don’t know how my final answer should look like
proud geyser
your final answer is one number.
weary pebble
Am I finding the value of e?
quick nova
remeber that $\log_a (a^b) = b$
proud geyser
Am I finding the value of e?
no.
warm shaleBOT
MxRgd
proud geyser
e is a constant anyway.
weary pebble
I’m so confused
weary pebble
If this was a log not an ln I could do it
quick nova
ln is the same as log_e
proud geyser
...did you forget that $\ln = \log_e$?
warm shaleBOT
non-Euclidean cat (Yukari)
proud geyser
so $\log_e(e^{-4})$.
warm shaleBOT
non-Euclidean cat (Yukari)
latent quiver
If this was a log not an ln I could do it
you can turn any logarithm to your logarithm of your choice, if that was your concern
weary pebble
how can a number equal a negative expoinet
proud geyser
huh?
pallid willow
**non-Euclidean cat (Yukari)**
if you insist on a missing value, let x = this log and solve for x.
but it makes no difference, and you should not rely on this method.
weary pebble
Wait so it would be -4?
proud geyser
exactly.
weary pebble
I thought this rule only applies when you have a log in the exponent
proud geyser
huh?
weary pebble
How do I know when this rule applies and does not apply?
proud geyser
this rule always applies within the domain of logs.
weary pebble
Huh
proud geyser
I'll redirect that "huh" back to you.
weary pebble
proud geyser
,rccw
warm shaleBOT
weary pebble
Oh
pallid willow
you're conflating $\log_a(a^b) = b$ with $b^{\log_b(a)} = a$.
warm shaleBOT
differential Towametry (Towa)
weary pebble
Does the first one apply when the base is equal to like the gf that’s what I call the thing inside the ()
proud geyser
it's called the argument, and yes.
pallid willow
if by equal you mean that red and green have to be the same then yes
craggy valley
All the logarithm does is give you the exponent to raise the base to so you get the argument.
weary pebble
When I say gf I meant like growth factor which I use in like word problems but it’s so ingrained in my memory I can’t change it
pallid willow
honestly, it may be time to revisit the definition of a logarithm and the four basic log rules you can derive from it directly.
weary pebble
My test is tomorrow 😅
I get a reference sheet but idk what’s on it so I guess I’ll pray it’s smth actually useful
craggy valley
That's like, plenty of time to revisit the basics for this one thing.
pallid willow
esp. when it's just one definition and four laws
craggy valley
It just helps you find exponents when you know the base and the result.
With careful algebra you can invent the log rules yourself just from knowing $\log_a(b) = c$ means $a^c = b$.
warm shaleBOT
velverette
weary pebble
I feel like I know the other ones pretty well
pallid willow
ideally there are seven rules, but two of them follow from exponent laws, and one of them is base change, so it remains for you to master the four basic ones
weary pebble
I mainly get tripped up on the natural logs
craggy valley
Whenever you see $\ln$ just replace it with $\log_e$.
warm shaleBOT
velverette
pallid willow
$\ln = \log_e$, just keep that in mind.
warm shaleBOT
differential Towametry (Towa)
craggy valley
Great minds.
pallid willow
but all rules of logs apply to lns just as much as they apply to regular logs
yes, including base change
weary pebble
but then for something like this do I put two Es or one E
pallid willow
wdym two e's
weary pebble
Like if ln is always log tiny e where do we put the e in the orginal equation
Cus it’s the b value
urban trench
weary pebble
Typo again sorry I need to get sleep lol
pallid willow
two of us literally just told you that
weary pebble
Yea I know I’m just questionifn myself on how to write it
craggy valley
Think about it like $\log_e$. $\ln$ is just shorthand.
pallid willow
never ln_e
warm shaleBOT
velverette
pallid willow
if that's what you're asking
weary pebble
Like I know that to be true but then I just get confused when actually doing it
pallid willow
need more practice then I suppose
my way for students in this situation is this
write down ln = log_e in front of you
then, while this statement is always in your sight, do a bunch of problems with lns
weary pebble
Is this writing by it correct
pallid willow
yes
weary pebble
write down ln = log_e in front of you
I have that memorized well I just have trouble converting between the log and ln
pallid willow
that's why I said to write it down in front of you.
because it seems that you're unable to recall or use the fact on demand, presumably because either you don't believe it somehow or you can't connect lns to log_e, even though the statement itself is in your mind
craggy valley
Practice is key!
weary pebble
I think I get confused on where to put the e’s
pallid willow
that's why my advice is to write it down (1)
so that if you get confused, you need only look back
of course, you should do it now so that it sticks in your mind for the exam and not wait till during the exam (but if you recall it at the start of the exam, write it down ASAP and refer to it if necessary)
craggy valley
With enough exposure to problems it'll be like you have it written down in your head.
pallid willow
also as miss Yukari said earlier, learn to step back when you feel like you've hit a dead end. often the best course of action is to pivot to another question first, then come back later after your mind has reset
weary pebble
I’m confused why the ^2 just got moved around on the right side
pallid willow
what?
weary pebble
wait I’ll send the question sorry my bad
“ Each statement below is false. Determine the error and write an equation using the log rule correctly.”
weary pebble
I don’t really know why they are not equal I thought 2 would be put in front for both of them
pallid willow
I will say I kinda hate the arrangement of this answer
$\log(a^2) \neq (\log(a))^2$
warm shaleBOT
differential Towametry (Towa)
pallid willow
to illustrate, let's use a very simple example in base 10.
$\log(100) = \log(10^2) = 2 \log(10) = 2$, BUT $(\log(10))^2 = 1^2 = 1$
warm shaleBOT
differential Towametry (Towa)
craggy valley
I’m confused why the ^2 just got moved around on the right side
(I mean this is kind of a silly question because you can just evaluate them and see that they're not equal lol.)
(Also you can just divide both sides by log(5) and they're clearly not equal.)
weary pebble
It was one of the earlier homework’s so maybe my mt teacher was trying to ingrain the rules in our head
But I was not here for one lesson and she was out for the next so that’s why I’m so lost 😅 and that is why I legit never miss math unless I’m forced to
craggy valley
“ Each statement below is false. Determine the error and write an equation usin...
I mean given this [what's written] should be fine.
All you might have missed was a little more time establishing the log rules. Logarithms are not very deep.
weary pebble
Yea the main thing is I missed a block we call iblock at our school the same day I missed math so like 3 lessons worth of quesifon got piled up
craggy valley
Oh that sucks. ^_^;
weary pebble
I was able to understand and do up u til the final step where it was equal to 3/2 I thought it was mane the rule we talked about earlier but there’s no expoinet
craggy valley
This is correct.
You can also do this pretty directly. log(10) is 1 and log(sqrt(10)) is 1/2.
craggy valley
Oh lmao sorry. I should have been more vigilant.
weary pebble
I just don’t understand how we got 3/2
I tried setting it up as like 10 to what equals equals blah blah blah but could not
random panther
I just don’t understand how we got 3/2
1+1/2, from the powers of 10
craggy valley
I was able to understand and do up u til the final step where it was equal to 3/...
$10 \cdot 10^{1/2} = 10^1 \cdot 10^{1/2} = 10^{1 + 1/2} = 10^{3/2}$.
warm shaleBOT
velverette
craggy valley
And of course log(10) = 1 as always.
pallid willow
$10 \cdot \sqrt{10} = 10 \cdot 10^{\frac12} = 10^1 \cdot 10^{\frac12} = 10^{1 + \frac12} = 10^{\frac32}$
warm shaleBOT
differential Towametry (Towa)
pallid willow
oh bruh
craggy valley
Lmao. Think alike.
weary pebble
Yea I undedtahd that but then the whole thing is equal to 3/2 which I don’t understand
pallid willow
product rule of exponents!
craggy valley
Yea I undedtahd that but then the whole thing is equal to 3/2 which I don’t unde...
I mean the working is there . . .
weary pebble
OHh
Bro I need to stop overthinking it
Like all my problems have been either natural logs or overthinking it
quiet pike
I was able to understand and do up u til the final step where it was equal to 3/...
this is a bad way to do it, just pull out the exponent from the second term and then it becomes 1 + 1/2
pallid willow
OP, I'm afraid overthinking is probably just part of the issue here...
pallid willow
this is a bad way to do it, just pull out the exponent from the second term and ...
that's the answer key
weary pebble
OP, I'm afraid overthinking is probably just part of the issue here...
Yea that’s what I said. That sounds rude sorry I suck at conveying tone over text
pallid willow
Yea that’s what I said. That sounds rude sorry I suck at conveying tone over tex...
being rude to me is the least of your concerns atm
craggy valley
Perhaps it was a good thing you missed your teacher if they're going to be so convoluted haha.
pallid willow
Idm if you cussed me in the face if that helps you improve your math
weary pebble
Maybe she is trying to do all the problems in the most consistent similar way idk 😅
random panther
this is a bad way to do it, just pull out the exponent from the second term and ...
but this is good for learning the rules isn't it?
quiet pike
no
weary pebble
Idm if you cussed me in the face if that helps you improve your math
I suck at math but I get good grades in it so whatever
craggy valley
The most consistent way would be the simplest.
weary pebble
I’m a senior I got like 30 days left
pallid willow
well, sure Ig
quiet pike
literally no reason to do it that way and teaching it that way is bad for learning since it makes you do extra steps for no reason
they should just give problems that actually require the rules
craggy valley
I’m a senior I got like 30 days left
Damn that's like 30log(10) days.
quiet pike
instead of trying to show a convoluted way to arrive at the same answer
weary pebble
Damn that's like 30log(10) days.
😀
random panther
they should just give problems that actually require the rules
yes i agree
weary pebble
hopefully
I got a good grade on my last test so like maybe it will balance out and I’m still doing practice problems
craggy valley
You're set to ace the next exam.
quiet pike
logs, like most topics in introductory algebra, are something you just have to do lots of practice problems on and then eventually it'll click
weary pebble
Although I got no idea where to start with this one like I know it will become division because of the subtraction I know I could make the 3 and 4 into exponents
weary pebble
logs, like most topics in introductory algebra, are something you just have to d...
Ugh I suck at algebra
craggy valley
Although I got no idea where to start with this one like I know it will become d...
What are they asking you to do?
pallid willow
Although I got no idea where to start with this one like I know it will become d...
I mean you basically have the right idea.
execute it.
weary pebble
Simplify to a single number or expression using log properties
pallid willow
wait
didn't Ramonov do it with you like... three days ago?
this exact question even
weary pebble
probably
I do all the homework over again
Cus I have a sucky memory so it’s basically a new question
quiet pike
pull those coefficients inside the logarithm argument as exponents (make sure to distribute them to each variable), then use the subtraction/divison property to write it as the log of a fraction and cancel the terms in the fraction
craggy valley
Combine the logs then. This isn't too bad.
weary pebble
and also it allows me to see if I actually remember the stuff I learned
craggy valley
pull those coefficients inside the logarithm argument as exponents (make sure to...
Give them time to guess lmao.
weary pebble
quiet pike
you have to distribute the exponent to both terms
it becomes log_5 ((xy)^4)
= log_5 (x^4 y^4)
the exponent applies to the whole argument
weary pebble
Oh ok but what would I do after adding those cus I’m basically in the same place
craggy valley
(Also a good idea to write $\log_5\left(\frac{x^4y^4}{y^3z^3}\right)$ instead.)
warm shaleBOT
velverette
quiet pike
yea and those y's cancel
craggy valley
Give them time to guess lmao.
quiet pike
mb
weary pebble
You can’t do anything after that right and u are still left with one y up top
craggy valley
Yeah.
quiet pike
yes that's the final expression
weary pebble
Ok well I’m going to head out cus I think this is the best it’s going to get with just repeating old stuff and k got a free tomorrow before my test so 🤷♀️
weary pebble
PFT
pallid willow
restrict the custom tip to exponentials so that the tip will always be nonzero positive
pallid willow
Ok well I’m going to head out cus I think this is the best it’s going to get wit...
!done then
obtuse pebbleBOT
Ok well I’m going to head out cus I think this is the best it’s going to get wit...
If you are done with this channel, please mark your problem as solved by typing .close
@weary pebble Has your question been resolved?
mighty light
could someone please explain to me what part c)d)e) all mean
i understand that for it to be a real vector space, it needs to be closed under addition, and closed under scalar multiplication and also contain the zero vector, which is true for part a). part b) isnt closed under scalar multiplication but i dont know if i am understanding wha tthe question even means?
obtuse pebbleBOT
could someone please explain to me what part c)d)e) all mean
i understand that ...
mighty light
or just how i can understand this question and this topic better 😭
restive gorge
-# sniped
mighty light
are you not sure what those sets are?
yeah what the sets are
kind hawk
well I can write them in set notation but I doubt that is gonna help
what exactly is confusing about those sentences
mighty light
what exactly is confusing about those sentences
oops im not making it clear
what is the difference between like 'at most' in part b with ' exactly' in part c, how do those words impact my answer?
and also kind of same with the words integer and real but ik thats a silly question
ik what real numbers are
kind hawk
at most 5 means deg(p) <= 5
exactly 5 means deg(p)=5
so the set in b has polynomials like x^2+3, 15x^5-3x^4+7 and x^5+x^4+x^3
and the set in c has polynomials like 15x^5-3x^4+7, pix^5-3 and x^5+ln(2)x^3+130.3071
but not for example x^2+3
mighty light
AHHH okay thank u so only set in c will have polynomials to deg 5
so it would work for addition
but not scalar multiplication?
kind hawk
would it?
kind hawk
what about -15x^5
jolly raptor
The zero polynomial is also not in (C) so you can immediately dismiss it as a vector space
mighty light
anyway, gtg. gl
thank u !!!
mighty light
The zero polynomial is also not in (C) so you can immediately dismiss it as a ve...
how do you show this
oh no
nvm
bcs
if i had a polynomial like 15x^5 - 7
restive gorge
The zero polynomial is also not in (C) so you can immediately dismiss it as a ve...
wdym
restive gorge
just set all coefficients to 0
jolly raptor
zero vector isnt in it
Yes
mighty light
just set all coefficients to 0
oh
jolly raptor
just set all coefficients to 0
No, it requires it to be exactly degree 5
Well is p(x) = 0 a degree 5 polynomial
🤔
restive gorge
Well is p(x) = 0 a degree 5 polynomial
I thought it would be a trivial one since you can choose the coefficients
jolly raptor
mighty light
oh
jolly raptor
With (d) you could use the fact that the kernel of a linear map is a subspace and that all subspaces are vector spaces
mighty light
With (d) you could use the fact that the kernel of a linear map is a subspace an...
im so sorry wdym by this
restive gorge
Do do you know what the kernel is
mighty light
no :(
restive gorge
Its the null space, all solutions that x s.t. T(p(x))=0
mighty light
OH
mighty light
Its the null space, all solutions that x s.t. T(p(x))=0
but how do i apply this to part d
hm
restive gorge
sorry i lied
mighty light
oh
restive gorge
We have T(p)=0 where T is a linear transformation
We can say T(p)=p(0)-p(1) is this map where its preimage of 0 would represent the kernel
timid silo
<@&268886789983436800>
autumn edge
so I got this task from ratial equations
lemme translate it
train was supposed to go between 2 cities in a time dictated by the timetable, due to a malfunction it was stopped for 30 minutes on a in-between station. the rest 120km it drove with a velocity 20km/h higher than the first part, thanks to this it wasn't late, calculate what should be the average velocity of the train according to the timetable
so, what can I see
-1 - referring to first part of the road
-2 - referring to the second
s length
v velocity
t time
v1 = v2 - 20km/h
v2 = v1 + 20km/h
s1 = ?
s2 = 120km
t1/2 = ?
and I'm lost what to do next with the given values
I know that v * t = s and due to that s / v = t but don't know how to apply it
I even found a solution to it which I'm attaching, but don't really understand the reasoning behind it (sorry for 4k full hd)
obtuse pebbleBOT
so I got this task from ratial equations
lemme translate it
train was supposed t...
@autumn edge Has your question been resolved?
mystic folio
First line is the time it took the train to go from the in-between station to the next city ( in hours)
The rest is just solve for v
(v obviously cant be negative)
obtuse pebbleBOT
@autumn edge Has your question been resolved?
autumn edge
First line is the time it took the train to go from the in-between station to th...
Thanks, I will try with that in mind
fathom basin
Help
fathom basin
2pi
latent quiver
what can you say about your unknown angle in relation to a full rotation, 2pi
fathom basin
Idk
timid silo
Wow
nova sentinel
can you kindly observe that it is one sixth pi short of a full rotation of two pi?
obtuse pebbleBOT
@fathom basin Has your question been resolved?
nimble rock
obtuse pebbleBOT
@fathom basin Has your question been resolved?
solar stump
can you kindly observe that it is one sixth pi short of a full rotation of two p...
Careful - it's closer to two full rotations
pallid willow
Careful - it's closer to _two_ full rotations
actually now that I see this
OP said the answer is... D?
eh wait bruh I am actually a dumbass
vital pollen
Can someone check my work here?
obtuse pebbleBOT
Can someone check my work here?
restive gorge
yes
formal island
Using desmos kinda beats the purpose of doing a rough sketch
zenith raft
what work
deep kraken
Bro drew after using Desmos 
short crescent
the point of this exercise is to try and draw it without using a graphing calculator 😭
deep kraken
Peak btw, bro got Desmos help
vital pollen
the point of this exercise is to try and draw it without using a graphing calcul...
I am allowed to use a graphing calculator
deep kraken
Not Desmos
quick nova
I am allowed to use a graphing calculator
cg50 i'm guessing?
vital pollen
cg50 i'm guessing?
maybe
brave burrow
try to find the horizontal vertical and oblique asymptotes
short crescent
no need if desmos can do it for you 
vital pollen
try to find the horizontal vertical and oblique asymptotes
is it +-2?
wait
Thats Vertical
vital pollen
try to find the horizontal vertical and oblique asymptotes
y=3
For full cred, all I need to do is draw whhat I wrote
- Vertical: (x = -2,; x = 2)
- Horizontal: (y = 3)
- Oblique: None
and this
quick nova
btw I'd be careful drawing it like this since it's not meant to be L-shaped
hidden compass
* **Vertical:** **(x = -2,; x = 2)**
* **Horizontal:** **(y = 3)**
* **Oblique:*...
Correct
But I guess you need to show the calculations as well.
Hence limits, domain and sign of the function, and its intersections with x and y axis
vital pollen
btw I'd be careful drawing it like this since it's not meant to be L-shaped
wdym?
supposed to be curved?
vital pollen
btw I'd be careful drawing it like this since it's not meant to be L-shaped
like this?
quick nova
like this?
Yeah like that
hidden compass
supposed to be curved?
Of course, otherwise it would be a first degree polynomial (a.k.a. a line)
vital pollen
Correct
But I guess you need to show the calculations as well.
Hence limits, do...
y=\frac{3x^2-8}{x^2-4}
Vertical asymptotes:
(x^2-4=0 \Rightarrow (x-2)(x+2)=0 \Rightarrow \mathbf{x=-2,,2})
Horizontal asymptote:
Same degree → ratio of leading coefficients
(\frac{3}{1}= \mathbf{3} \Rightarrow \mathbf{y=3})
Oblique asymptote:
Degrees equal (not top = bottom + 1) → (\mathbf{\text{none}})
hidden compass
Can someone check my work here?
Desmos does help you in this
hidden compass
y=\frac{3x^2-8}{x^2-4}
**Vertical asymptotes:**
(x^2-4=0 \Rightarrow (x-2)(x+2...
!nogpt
obtuse pebbleBOT
y=\frac{3x^2-8}{x^2-4}
**Vertical asymptotes:**
(x^2-4=0 \Rightarrow (x-2)(x+2...
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
hidden compass
Oh alright
vital pollen
Vertical: (x = -2,; x = 2)
Horizontal: (y = 3)
Oblique: None
Vertical asymptotes:
(x^2-4=0 \Rightarrow (x-2)(x+2)=0 \Rightarrow \mathbf{x=-2,,2})
Horizontal asymptote:
Same degree → ratio of leading coefficients
(\frac{3}{1}= \mathbf{3} \Rightarrow \mathbf{y=3})
Oblique asymptote:
Degrees equal (not top = bottom + 1) → (\mathbf{\text{none}})
This is alll I need for full cred?
It's a practice exam, but my prof uses the same questions on the test
not even joking
He uses the same questions
hidden compass
This is alll I need for full cred?
Seems so, yeah
vital pollen
Seems so, yeah
100 percentaroonie?
hidden compass
Well, I'm not your teacher so I don't know 🤷♂️
But I'd say that this is the bare minimum required
quick nova
np
obtuse pebbleBOT
@vital pollen Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
plush dew
can someone summarize step by step on how to do square roots?
ex.
square root of 1600
obtuse pebbleBOT
can someone summarize step by step on how to do square roots?
ex.
square root o...
urban trench
can someone summarize step by step on how to do square roots?
ex.
square root o...
write them as product of prime factors
plush dew
write them as product of prime factors
im kind of slow.. can u explain
inner sierra
notice that 1600 = 16 * 100
so you can take square roots of those 2 numbers instead and multiply back together
urban trench
im kind of slow.. can u explain
you could write 40 as 2×2×2×5
notice that all the number that I used, to express 40 as multiple of other numbers, are Prime ( only 2 and 5 )
plush dew
So like just chopping them down?
latent quiver
So like just chopping them down?
yeah
urban trench
So like just chopping them down?
bingo
inner sierra
Bro my teacher was on my dick
wtf
inner sierra
nuh uh
obtuse pebbleBOT
old lily
nuh uh
is your username supposed to be funny?
it's not really
it could very well be -infty
lim 1/x is undefined
ah wait you probably don't know what limits are
restive gorge
this blud
obtuse pebbleBOT
Available help channel!
magic mortar
How does this become this?
I don't think im supposed to multiply (1-i) 7 times to find out but i don't see how else could i conclude that
obtuse pebbleBOT
How does this become this?
I don't think im supposed to multiply (1-i) 7 times t...
restive gorge
How does this become this?
I don't think im supposed to multiply (1-i) 7 times t...
maybe convert into exponential form
indigo niche
(1-i)^7 you can use z^n = |z|^n (cos(ntheta)+isin(ntheta))
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
warped holly
hi can a kind soul explain to me why the second limit diverges? how does p affect the limit here exactly
obtuse pebbleBOT
hi can a kind soul explain to me why the second limit diverges? how does p affec...
restive gorge
hi can a kind soul explain to me why the second limit diverges? how does p affec...
-p+1=-(p-1) so if p>1 then 1/(x-a) goes to inf
obtuse pebbleBOT
restive gorge
I am not a kind soul tho
quick nova
I am not a kind soul tho
but you are a star that someone looks up to 
warped holly
you were kind enough to help
obtuse pebbleBOT
Available help channel!
autumn belfry
hi, with my online teacher i'm doing "calculus". derivative.
and we're using the "principle" of "rate of change" (sorry i'm not english native, so maybe our vocabulary may vary, it's basically saying that f(x + h) -f(x) on h)
and he assigned me the exercice of trying to find the derivative of f(x) = x^1/2.
but i'm kinda stuck. so obviously i asked chatgpt and he told me to use something called "Conjugate (square roots)"
obtuse pebbleBOT
hi, with my online teacher i'm doing "calculus". derivative.
and we're using the...
quick nova
do you know the power rule?
autumn belfry
yes?
quick nova
apply that then
autumn belfry
by power do you mean a^n
quick nova
also chatgpt telling you to use conjugate is funny 
quick nova
by power do you mean a^n
yeah that one
quick nova
but yeah another thing, using Ai for maths tends to be false/unhelpful info
as you've seen
quick nova
oh
autumn belfry
so i don't know what to do
quick nova
you're doing it by first principles?
quick nova
bro i have no idea what you talm bt
$f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$
warm shaleBOT
MxRgd
quick nova
this
quick nova
you don't include the lim part?
autumn belfry
boi
quick nova
or else what you're working with isn't a derivative
autumn belfry
i'm solving it but without include f'(x) = limh->0
quick nova
i'm solving it but without include f'(x) = limh->0
How can you though
autumn belfry
i'll show you
quick nova
anyways yeah since you're doing it by first principles. Using conjugate would give you $$f'(x) = \lim_{h \to 0} \left( \frac{\sqrt{x+h} - \sqrt{x}}{h} \cdot \frac{\sqrt{x+h} + \sqrt{x}}{\sqrt{x+h} + \sqrt{x}} \right)$$
warm shaleBOT
MxRgd
quick nova
Okay but you need to include the lim part ;-;
autumn belfry
bro
autumn belfry
just forget about that part i'm strictly talking about the solving part
autumn belfry
Okay what is h then
it's the infinitly small between 2 points. (i think)
quick nova
this part here basically doesn't make sense without it
autumn belfry
it's not relevent to purely solving
quick nova
it is relevant because it doesn't make sense if you didn't include it
restive gorge
this part here basically doesn't make sense without it
-# well technically adding a "as x->0" would solve it
autumn belfry
i'm not actually here to argue about syntax
i'm here to solve the problem i came with...
quick nova
Okay suit yourself then, but you might get deducted marks for it if you didn't
autumn belfry
finding the derivative of f(x)= x^1/2
autumn belfry
Okay suit yourself then, but you might get deducted marks for it if you didn't
bro i'm learning for myself
it's just for fun
autumn belfry
yes. anyway
quick nova
what's conjugate
It's basically a pair of binomials with the same terms but opposite signs in the middle, like a+b and a−b
quick nova
**MxRgd**
so basically from here the conjugate of $\sqrt{x+h} - \sqrt{x}$ is $\sqrt{x+h} + \sqrt{x}$
warm shaleBOT
MxRgd
autumn belfry
ok boi
autumn belfry
ye but why can we do that
quick nova
that's how a conjugate is defined
quick nova
It's basically a pair of binomials with the same terms but opposite signs in the...
from here
autumn belfry
so it's an axiome?
quick nova
Not really? it's just useful sometimes to consider the conjugate of something
for example complex numbers
autumn belfry
bro, i don't think you understand what i'm asking
quick nova
for example complex numbers
If you have the root of a polynomial that is a complex number, then it's conjugate is also a root too
this is an example where it can be used
quick nova
bro, i don't think you understand what i'm asking
No I do, though your question doesn't really make sense
autumn belfry
ok. thanks then
restive gorge
ye but why can we do that
it's just algebra
if we have an expression a+b then a-b is called conjugate that's all, a definition
autumn belfry
so is it something we accept as true.
like for exemple a(b+c) = ab + ac
restive gorge
so is it something we accept as true.
like for exemple a(b+c) = ab + ac
You don't treat a definition the same way as a theorem
A definition can be useful or not useful
autumn belfry
what's the objective of conjugate?
eliminating square roots in the denominator ?
lone echo
so is it something we accept as true.
like for exemple a(b+c) = ab + ac
that's not an axiom nor definition, that's a property that can be derived from the definition of sum and definition of product
autumn belfry
that's not an axiom nor definition, that's a property that can be derived from t...
that's what i wanted (to "hear")
lone echo
what's the objective of conjugate?
eliminating square roots in the denominator ?
multiplying and dividing by the same number is the same as multiplying by 1, so the same as doing nothing.
However, it can help obtain an equivalent thing that you can compute instead of one you cant
autumn belfry
that's not an axiom nor definition, that's a property that can be derived from t...
like why can we create out of thin air (a+b^1/2) x (a - b^1/2)
is there are rule or somethingh
lone echo
we dont create anything out of thin air
quick nova
what's the objective of conjugate?
eliminating square roots in the denominator ?
it's useful for rationalizing denominators, simplifying complex number, etc
quick nova
It depends
lone echo
you cant remove things just because either
let's say you have x
you can multiply x by y/y
since y/y=1, that product is still x
so you'd get xy/y
but it might be more useful to have xy/y
you do that all the time when adding fractions, for example
you might have 4, but it might be more useful to have 12/3 instead
obtuse pebbleBOT
drowsy cliff
you removed this from <#578008840193310740> only to post it here bruh
lol
quiet fog
brazen viper
.close
obtuse pebbleBOT
brazen viper
I'm not really in the mood to play games. Use #chill attempting to repost in a help channel will result in a mute.
olive yew
Again, these channels are for asking questions, not for tomfoolery
brazen viper
Is this an actual question you need help with, or is this just a pointless question
ok pointless question got it.
only use these channels for actual questions you need help with.
drowsy cliff
trying to learn values of x and y
thorny ginkgo
o fr?
olive yew
@thorny ginkgo don't fuel the trolls, and just leave
thorny ginkgo
mb
thorny ginkgo
<@911627710802038894> don't fuel the trolls, and just leave
yo please ban this troll
brazen viper
they're new, so I'm giving them the benefit of the doubt.
olive yew
Thank you, I think we can handle moderation concerns on our own
thorny ginkgo
Thank you, I think we can handle moderation concerns on our own
ill leave it to the orzed ones
cya
thorny ginkgo
they're new, so I'm giving them the benefit of the doubt.
this server is blessed with considerate mods
brazen viper
@drowsy cliff this channel has been locked and might close abruptly, see #❓how-to-get-help for how this all works.
drowsy cliff
this is serious question 90+x=120 i dont know fr
brazen viper
I think though, that my doubt has been exhausted. Your solution is 30 minutes.
thorny ginkgo
this is serious question 90+x=120 i dont know fr
rearrange to isolate for x
obtuse pebbleBOT
Available help channel!
drowsy cliff
🙁
brazen viper
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
bitter terrace
obtuse pebbleBOT
bitter terrace
The max, min equality makes complete sense but I am having trouble writing down its proof
like if x is in S, then x is in S1 or S2
if x is not in S1 then it is in S2 and f_S(x) = f_S2(x), f_S1(x) = 0
Oh right let me give you the notation for f_S
how do you logically discuss max
probably through contradicition
but hm let me see if I can approach it directly
if x is not in S1 then it is in S2 and f_S(x) = f_S2(x), f_S1(x) = 0
if x is not in S2 then it is in S1 and f_S(x) = f_S1(x), f_S2(x) = 0,
S1 and S2 completes S and so f_S(x) for x in S, (not sure how to transition this to max equality)
mm I see
I need to parition over Q and show in every case f_S(x) = max{f_S1(X), f_S2(X)}
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
valid sierra
I know it's plus or minus 4 but why is option 3 wrong
obtuse pebbleBOT
I know it's plus or minus 4 but why is option 3 wrong
shut lagoon
valid sierra
Oh im stupid
old zinc
I know it's plus or minus 4 but why is option 3 wrong
if you think about a parabola
valid sierra
Thanks
old zinc
like both ends go up
in the middle its smaller, less than 16. so its the option with the edges
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
loud zodiac
obtuse pebbleBOT
loud zodiac
What do you not understand
I dont understand how to solve it
Maybe the one that has the same distance from top to bottom is the f’ because it has no C
dark coyote
what do you know about f'(x) from f(x)
arctic scaffold
i trick i use is i just know this \
there's a horizontal tan line right
honestly just look at the horizontal tangent line, look at regions or decreasing, then look at regions of increasing. then just see what lines up
because you should know if a function is decreasing, then its derivative MUST be negative...
if a function is increasing, its derivative MUST be positive...
and if a function has no change or a horizontal tangent line at a point, then its derivative MUST be 0...
do you remeber learning stuff like this in class?
obtuse pebbleBOT
@loud zodiac Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
obtuse geode
could this be written as
obtuse pebbleBOT
could this be written as
obtuse geode
?
restive gorge
yes
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
fresh relic
How does this work?
obtuse pebbleBOT
How does this work?
fresh relic
thick oracle
fresh relic
No but it is above the other one
obtuse pebbleBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
fresh relic
As a helper, please do not give out answers that could be copied as a homework s...
huh
warm shaleBOT
Master Larp
fresh relic
$\frac{ \frac{3}{2a}}{4b}$
warm shaleBOT
Kaasplank3333
thick oracle
now you need to flip the denominator
fresh relic
yes
surreal plover
(Move the 3/2a out of the numerator)
thick oracle
like they did in the website
fresh relic
4b/1 * 2a/3?
thick oracle
$\frac{ \frac{3}{2a}}{ \frac{4b}{1}}$
warm shaleBOT
Master Larp
fresh relic
**Master Larp**
How does the LateX work?
thick oracle
lets focus on the question
then you can go to #latex-help if you want to learn latex
warm shaleBOT
Kaasplank3333
$(\frac{\frac{2}{2a}}{4b}\$
```Compilation error:```! Missing $ inserted.
<inserted text>
$
l.50 \end{document}
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.```
fresh relic
Whoops
thick oracle
fresh relic
$\frac{\frac{2}{2a}}{4b}$
warm shaleBOT
Kaasplank3333
