It's -x2
#help-36
atomic mural
stiff harness
then idk
atomic mural
When an equation is represented in the form of y=mx+c
It's a straight line
Where m is the slope
And c is the y intersept
So for example if you had the equation
y=4x+5
What would it's slope be?
stiff harness
4
atomic mural
Amazing
Now whenever the maximum power of x and y is 1, the eqaution will always represent a straight line
stiff harness
so x^2 is curved?
atomic mural
Do you understand this part?
atomic mural
so x^2 is curved?
Yes exactly!
grim badger
You should know what vertex form is, like this
atomic mural
That is also a curve but different to x² and x
atomic mural
double curve?
Not exactly a double curve
If the maximum power of y is 1 then the power of x represent how many time it intersects the y axis (I'm sorry I meant to write x axis)
So when we discussed about y=mx+c
The power of x is 1 so it will intersect the x axis once
stiff harness
so x^3 is a doulbe curve
atomic mural
So how many times would the graph of x³ intersect the x axis?
atomic mural
Yes correct
grim badger
So how many times would the graph of x³ intersect the x axis?
Talking about roots is unnecessary for this question
As mentioned @stiff harness, you need to understand vertex and this image
stiff harness
As mentioned <@1036291904138129498>, you need to understand vertex and this imag...
yes
atomic mural
Talking about roots is unnecessary for this question
He needs to understand how graph works, so a similar question won't trouble him, giving the straight answer will just get them by this question not the actual thing
grim badger
yes
Do you understand that h relates to horizontal translation and k relates to vertical?
stiff harness
Do you understand that h relates to horizontal translation and k relates to vert...
so h is x and k is y?
grim badger
He needs to understand how graph works, so a similar question won't trouble him,...
Yes, but you don't need to explain first order or third order equations
grim badger
so h is x and k is y?
Yes
So if h is positive and k is positive, as the question states, what are the signs of the x and y coord?
stiff harness
positive
grim badger
For both or just x or just y?
stiff harness
both because it said h and k
atomic mural
Yes, but you don't need to explain first order or third order equations
That was my way helping him out, there was no need to overtake the convo. Anyways it'll be good either way as long as he understands it
grim badger
both because it said h and k
So if the x and y coords are positive, what quadrant does that represent?
granite oracle
K
grim badger
And there you go
stiff harness
but the answer sheet say its 2
grim badger
I forgot what the equation looked liked, and had to scroll up again, there was a negative sign outside
So -(x + h)^2 + k
Wait
stiff harness
but h and k are still pos
the - is just which direction the things points up or down
grim badger
You need to focus on that part
Because the sign was positive in your equation , and in the general equation, it's always negative
stiff harness
(-)(-)=+?
stiff harness
so h has to be - to have -h be pos
grim badger
Yes
gritty sable
Quick question: Can I use L'hopital if I had the indeterminate form "∞/0"?
gritty sable
Its inf*0, but you can change it
Yes, but does that mean I cant use l hopital if I had a case where I cannot rewrite it and it had infinity/0
gritty sable
Try rewriting it
I took the derivative without rewriting it, is it okay?
robust mulch
You did rewrite it lol
gritty sable
oh lol
wintry urchin
How do you find the area of the overlap of the semicircles?
final saddleBOT
How do you find the area of the overlap of the semicircles?
vital crag
How do you find the area of the overlap of the semicircles?
not that it matters, but is the hypotenuse really 12
one of your sides is incorrect
vital crag
i guess you write the equation of each circle and then find the point of intersection then integrate
wintry urchin
How would you find the point of intersection though?
vital crag
i guess you write the equation of each circle and then find the point of interse...
you do the first part first
then set them equal
and find the points of intersection in the first quadrant
wintry urchin
The first part?
vital crag
you write the equation of each circle
wintry urchin
Oh
final saddleBOT
@wintry urchin Has your question been resolved?
bold hearth
you wont solve it even if you tried
final saddleBOT
you wont solve it even if you tried
bold hearth
.close
final saddleBOT
bold hearth
.reopen
final saddleBOT
✅
bold hearth
you will not solve the problem.
robust mulch
ok, i wont then
bold hearth
ok, i wont then
ok, you wont then
hybrid heath
Did you have a question of any kind?
bold hearth
Did you have a question of any kind?
yes, how to solve/process?
hybrid heath
There's one primary error I spot right away
Your probability space does not factor in her the incorrect answers that she eliminated from the first two questions
bold hearth
yeah, the answers i plugged in were from the previous question from a different randomization of the red numbers
the original question ( 7 questions, two possible answers, three questions)
same answers i plugged in
hybrid heath
So let's reduce it. What's the probability she gets the first question right?
hybrid heath
is it 1/78125 ?
Nah I'm asking for just getting the first problem right. What is the probability?
hybrid heath
is it 1/78125 ?
this is the probability of getting all 7 right with purely random guessing and no ability to eliminate any wrong answers
bold hearth
Nah I'm asking for just getting the first problem right. What is the probability...
1/5 chance to answer 1 question correctly
hybrid heath
1/5 chance to answer 1 question correctly
In a purely random guess, yes
bold hearth
In a purely random guess, yes
do we do this 7 times
hybrid heath
Put the question states she can eliminate one wrong choice from the first (and second) question(s).
So if you can eliminate one wrong answer from the first question, what is the probability of getting it right?
bold hearth
So if you can eliminate one wrong answer from the first question, what is the pr...
1/4
bold hearth
oh so she does this to 2nd question aswell
1/4 * 1/4 * 1/5 * 1/5 * 1/5 * 1/5 * 1/5
😄
hybrid heath
is there some reverse thing we do for (b) ?
What's the probability of getting the first problem wrong now?
hybrid heath
Remember, we eliminated one guess
hybrid heath
ah im stuck on (c)
Ah yes
The old complements (not to be confused with compliments)
So ask yourself this: What happens if she does not answer every question incorrectly?
bold hearth
So ask yourself this: What happens if she does not answer every question _incorr...
then she passes with 100% lol
hybrid heath
then she passes with 100% lol
Not quite
If you don't answer every question incorrectly, that does NOT mean you answered them all correctly
The opposite of answering every question incorrectly is answering at least one correctly
bold hearth
The opposite of answering every question incorrectly is answering at least one c...
in that case, here are my final answers
bold hearth
yeah i have noticed that
hybrid heath
3/4 * 3/4 * 4/5 * 4/5 * 4/5 * 4/5 * 4/5 = 576/3125
Yeah. Check here
bold hearth
hybrid heath
bold hearth
i-
hybrid heath
hm?
bold hearth
how did i type 4 isntead of a 5 man like wtf
hybrid heath
I have dyslexia
I miss mistakes like that all the time
You gotta take a lot of time and always double check
But the core is that you understand that problem now
That's what matters
bold hearth
Yeah
I was rushing because I have an exam on this tomorrow
So I guess I need to take with finalizing the answer
bold hearth
That's what matters
The pretest is essentially the exam, and it is a 9 question exam. Want to take a look?
hybrid heath
100%
Believe in yourself
You worked out this problem.
Take each bit of information, sort it out, ask yourself the questions to help carve out your path to a solution
,rcw
soft zealotBOT
final saddleBOT
@bold hearth Has your question been resolved?
bold hearth
.
light brook
final saddleBOT
light brook
needing help on where to start
light brook
it’s a practice final exam that doesn’t count towards my grade 😂
sweet summit
looks like Practice
light brook
i made sure to include that in the screenshot 😘
sweet summit
haha good call
light brook
dry light
Gosh darn I can't get someone banned today 
Anyways youre fine
Your x intercepts and zeroes are right
For distance
Use distance formula
light brook
Gosh darn I can't get someone banned today <:sad:532803514892812288>
y’all tried !!😔
ik the rules thankfully 😆
light brook
Use distance formula
let me try
bold hearth
light brook
so i pick a random y point
muted prairie
Pythagorean theorem with the grid lines
bold hearth
(7, -4) and (-3,4)
light brook
thank y’all
bold hearth
(x1, y1) and (x2, y2) is how i like to see it
severe kraken
Hi I need help with it’s this I have no idea what is happening with the radicals and stuff
final saddleBOT
Hi I need help with it’s this I have no idea what is happening with the radicals...
@severe kraken Has your question been resolved?
severe kraken
<@&286206848099549185> 
(sorry for the ping)
muted prairie
They used Pythagorean theorem to find the diagonal of the square
That's where the square roots came from
Then they used that to find the radius of the cylinder
Oh wait no they did the opposite
muted prairie
They use Pythagorean theorem to find the side length of the square
severe kraken
how though
muted prairie
My bad
severe kraken
3 radical 2??
severe kraken
the one to the right is the example problem
the one on the left is the one i am trying to do
muted prairie
In your problem you wouldn't have square roots
muted prairie
the one on the left is the one i am trying to do
Do you mean the top one?
muted prairie
You posted two images
severe kraken
problem i am trying to do
muted prairie
Yes that is the one on top
severe kraken
yeah then that would be the problem I am trying to do 
muted prairie
Ah, it displays differently on computers
i was on mobile
but you're looking for the volume that's in the cylinder that isn't in the prism
so you do the volume of the cylinder minus the volume of the prism
severe kraken
that seems easier
but why does it make a whole complicated mess on the example one?
muted prairie
ohhhhh surface area
not volume
im dumb
ngl looks like they screwed this up tho
i have no idea what they're doing
soft zealotBOT
muted prairie
anyways
split it up into smaller areas
start with the outer rounded edge of the cylinder
then the inner walls made by the prism cutout
muted prairie
then do the top and bottom by subtracting the area of the square from the area of the circle
tranquil pine
tranquil pine
The other guy wasn’t helping
spice portal
ill close the other channel just to avoid confusion
tranquil pine
The latter three
Lmao
If you could just help me with the third one for now, that would be greatly appreciated
tranquil pine
which one do u need help on
Am I bad luck or something?💀
spice portal
Am I bad luck or something?💀
sorry its just like 1 am and my brain isnt processing much. 5 AP exams can really fuck up your brain ong
spice portal
If you could just help me with the third one for now, that would be greatly appr...
alright lemme look 1 sec
by 3rd one, u mean 25??
tranquil pine
sorry its just like 1 am and my brain isnt processing much. 5 AP exams can reall...
I feel you
tranquil pine
by 3rd one, u mean 25??
I do, yes
spice portal
I do, yes
okay, so if you need explaination please consult someone else
i got the answer bc i just did it all in my head
actually nvm screw it
ill just do some work and send u
gimme a few mins
spice portal
I feel you
someone who understands lol 🥹
tranquil pine
Thank you so very much
spice portal
just so you know the answer is C
unless i messed up a step which is totally possible cuz i did half of it in my head. im just doing work to confirm
btw is this calc 2 or calc 1?
tranquil pine
Calc 2
spice portal
ah thats why
i have calc 1 but my bitch ass teacher made us learn eulers method
cuz this is a little more advanced than we practiced
tranquil pine
Yeah?
final saddleBOT
@tranquil pine Has your question been resolved?
tranquil pine
You do?
spice portal
Ik, its messy af
Please bear with me, its almost 2 am lol
if something doesnt make sense, please lemme know
@tranquil pine
im going to sleep now @tranquil pine, hope it makes sense, if not. please dm me
fresh patio
final saddleBOT
fresh patio
I don't know where to start
I know the definition of a power series
and I've only seen functions being represented as power series by rewriting in the form 1/1-x
I've also seen power series representations using integrals and derivatives of functions
<@&286206848099549185>
native geyser
find the n-th derivative of sqrt x then use the maclaurin series
desert mantle
dont use the maclaurin series for a function that is not differentiable at x=0
fresh patio
are power series the same as taylor/maclaurin series?
desert mantle
essentially
if you have a series that equals a function in some neighborhood of a point and I think some slight extra conditions, then that series is the taylor series at that point
fresh patio
how do I know that such a series will exist for this function (or any function)?
craggy plume
as long as you can differentiate the function infinitely
desert mantle
not exactly
for real-valued functions analytic and infinitely differentiable are not the same thing
all elementary functions are analytic (on open sets in their domain)
fresh patio
why do we need a function to be analytic for its taylor series to exist?
and what does being analytic mean?
desert mantle
analytic means taylor series exists and equals the function in some neighborhood
just taylor series existing is kind of useless
without that extra guarantee of actually equaling the function
fresh patio
essentially
so we're studying taylor series so we can write more complicated functions as a power series/polynomial-like function of x?
desert mantle
there is a very classic example (which I always forget) of a nonzero function that is infinitely differentiable but whose taylor series is constant zero
we are studying taylor series to write stuff as series, yes
desert mantle
yeah I think that's the one
final saddleBOT
@fresh patio Has your question been resolved?
fresh patio
dont use the maclaurin series for a function that is not differentiable at x=0
so is this how I should proceed?
fresh patio
umm why can I choose any c just like that?
can't I just leave a generic c in the final expression?
desert mantle
then you might aswell have not calculated the derivatives
cause the formula like this is unusable anyway
cause to use it you first would have to pick some c and then calculate all the values and simplify etc
fresh patio
hmm what do you call a nice c?
can I pick like 1?
are there any restrictions on the value of c I can pick?
it seems weird to me that I can pick from multiple possible values of c, plug in for x, and get an approximation for x^1/2
final saddleBOT
@fresh patio Has your question been resolved?
desert mantle
the approximation will converge quicker near c
and in general the radius of convergence will depend on c
if you pick c=1 then it will converge in (0,2), if you pick c=15 it will converge in (0, 30)
(and maybe at the endpoints, dont wanna think about those)
vivid musk
I was wondering, if one sees a function defined like this e.g., does one usually assume that $(-1,1)$ is equipped with the order topology or the subspace topology?
final saddleBOT
I was wondering, if one sees a function defined like this e.g., does one usually...
soft zealotBOT
CoffeeMan
tranquil pine
@vivid musk what do you mean by this
there is no subspace cohomology
neither homomorphic meromorphic group
vivid musk
Ehh, sorry, I don't understand those terms.
tranquil pine
the natural topology on the domain $(-1,1)$ is the subspace topology induced by the standard topology on the real line. Well this is because $(-1,1)$ is a subset of the real line as you see the example gave you, and the standard topology on the real line is the one induced by the usual order relation on the real numbers. hence Real space if you are asking the field?
soft zealotBOT
Nimajneb
vivid musk
I just mean that $(-1,1)$ could be understood both as a subspace of $\mathbb{R}$ with order topology and just as itself with order topology here.
soft zealotBOT
CoffeeMan
vivid musk
Ah, ok
tranquil pine
well that is up to the author tbh
vivid musk
I see.
tranquil pine
it doesnt matter here
vivid musk
Ye
tranquil pine
since , the function is continuous with respect to both the subspace topology and the order topology
tranquil pine
If the function involves convergence or like continuity or somehting, then the choice of topology can affect the properties of the function. In such cases, the author should be clear about the topology being used and its properties. this should be explicit
no
there usually isnt
tranquil pine
search up monotonicity
vivid musk
I see in this book it is assumed the subspace - found the passage
vivid musk
Ok, thank you
tranquil pine
Lets say, if we are interested in studying the behavior of a function on $(-1,1)$ that is monotonic with respect to the order on $(-1,1)$, then it may be more appropriate to use the order topology induced by the usual order relation on $(-1,1)$. Similarly, if we are working with a metric space that is homeomorphic to $(-1,1)$, then we may use the metric topology induced by the corresponding metric. This is quite high level stuff though, so make sure you get grasp of set theory first
soft zealotBOT
Nimajneb
final saddleBOT
final saddleBOT
Available help channel!
mortal basin
Write the system
x − 2y + z = 7
2x − y + 4z = 17
3x − 2y + 2z = 14
in the matrix form by using matrix multiplication then solve the equation system by using Cramer’s method
final saddleBOT
Write the system
x − 2y + z = 7
2x − y + 4z = 17
3x − 2y + 2z = 14
in the matrix...
final saddleBOT
@mortal basin Has your question been resolved?
oblique portal
hard cave
final saddleBOT
@mortal basin Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
carmine plaza
final saddleBOT
iron breach
!status
final saddleBOT
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
@carmine plaza Has your question been resolved?
carmine plaza
I'll be back
final saddleBOT
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stuck field
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@stuck field Has your question been resolved?
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@stuck field Has your question been resolved?
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@stuck field Has your question been resolved?
lament mirage
Hi
lament mirage
determine all points, if any,
in which the tangent planes to it are parallel to the coordinate planes
I started with the gradient(a,b,c) * (x-a,y-b,z-b) = 0
I don't know how to continue
final saddleBOT
@lament mirage Has your question been resolved?
lament mirage
<@&286206848099549185>
ornate hollow
wat
final saddleBOT
@lament mirage Has your question been resolved?
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@lament mirage Has your question been resolved?
tawny bluff
I started with the gradient(a,b,c) * (x-a,y-b,z-b) = 0
pardon?
how exactly did you get that
gradient f is <6x-6, 32/3y, -4z>
the coordinate planes are those vectors with at least one component zero, so you can solve each component for zero separately, then work backwards from working locations to find valid points
pearl wraith
why substituting the angle gives me the point of tangency?
final saddleBOT
why substituting the angle gives me the point of tangency?
pearl wraith
they substituted pi/3 to r = f(theta)
then that gave point of tangency
why?
who can tell me why
🙏
marsh temple
one of the requirements for a tangent line at a point is that both the line and the graph have to pass through that point
pearl wraith
one of the requirements for a tangent line at a point is that both the line and ...
yeah
marsh temple
so at theta = pi/3, r = 2 and thus that's the point of interest
pearl wraith
hmm okay
final saddleBOT
@pearl wraith Has your question been resolved?
tranquil pine
Using , the dot product and cross product formulas of vectors, show that the dot product and cross product are distributive,
- when the three vectors are coplanar
- in general case
final saddleBOT
Using , the dot product and cross product formulas of vectors, show that the dot...
fickle crater
question is pretty straight forward
what exactly do you not understand @tranquil pine
tranquil pine
what exactly do you not understand <@456226577798135808>
Using A . B = AB Cos Theta and A X B = AB Sin Theta, We have to show that the dot and cross product are distributive, if the three vectors are coplanar, so in coplanar means they lie in the same plane, so the angle will be zero i guess?
fickle crater
right what is the distributive property, take any vectors with xyz coordinates or even n coordinates and write it down
magic sparrow
$\vec{u} \cdot (\vec{v} + \vec{w})= \vec{u} \cdot \vec{v} + \vec{u} \cdot \vec{w}$
for dot product
you'd have to show that that is true
1st for coplanar vectors
fickle crater
yes
magic sparrow
2nd in the general case
and then rewrite that property above, using the cross product instead of dot product
and do the same thing
fickle crater
you just write down both sides, expand them and at the end you prove that they are both equal
proving the property
the arrow missing on that v tho 🗿
soft zealotBOT
AustinU
fickle crater
👍
yeah it's nice, it really gives a stronger intuition behind both products and vectors overall
@tranquil pine check 3blue1brown linear algebra if you have free time, he gives the intuition behind some of this stuff
elfin hemlock
so i have multiple points that i know are exponential and i want to find an approximate equation for them
(30, 15)
(15, 30)
(7.5, 60)
(3.75, 120)
(8 1/3, 54)
the points' x and y can be flipped and it'll still be a valid point, so you can add a point like (60, 7.5) as it will just be the opposite instead (halving vs doubling kind of stuff)
i already tried some calculators out but nothing seemed to really work. idk if this is just impossible to fully solve? you can find exact points by using multipliers, so i figured you could make an equation for whatever point you want to find
final saddleBOT
so i have multiple points that i know are exponential and i want to find an appr...
elfin hemlock
it doesn't need to be solved btw, just trying something out for something
earnest temple
that's not exponential
earnest temple
...well what do you think it is then?
earnest temple
the actual pattern is that the product of the x and y coordinates is 450
earnest temple
well it goes through all the points
i don't have any more information on this than you do but it looks pretty reasonable
scenic tree
final saddleBOT
final saddleBOT
final saddleBOT
Available help channel!
granite siren
surely if A1 = {Heads, Tails, Tails, Tails, Tails, Tails, Tails} and A2 = { Heads, Heads, Tails, Tails, Tails, Tails, Tails} the intersection wouldn't be the empty set
final saddleBOT
surely if A1 = {Heads, Tails, Tails, Tails, Tails, Tails, Tails} and A2 = { Head...
sturdy cypress
{Heads, Tails, Tails, Tails, Tails, Tails, Tails} is not A1 but one elements of A1
sturdy cypress
but it's not like this explains it, i just don;t understand why you;re confused
granite siren
i thought A1 represented like any possible set with heads
sturdy cypress
okay
you could notice that a set can't even look like that
they wouldn't dare call it a set
A1 is a set of "sequences" not sets
granite siren
.close
gilded schooner
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gilded schooner
<@&286206848099549185>
final saddleBOT
@gilded schooner Has your question been resolved?
neat sable
@gilded schooner what q
gilded schooner
<@869395681683587133> what q
5
final saddleBOT
@gilded schooner Has your question been resolved?
gilded schooner
<@&286206848099549185>
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@gilded schooner Has your question been resolved?
flat flame
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rich tide
one dimension is doubled i.e. for example the height is doubled
so what is the new volume assuming length is l and breadth is b
final saddleBOT
@flat flame Has your question been resolved?
final saddleBOT
flat flame
.reopen
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flat flame
so what is the new volume assuming length is l and breadth is b
hmm
but how would I write that in the question
woeful atlas
if you double a dimension of a rectangular prism the volume of the shape is affected
given the volume is length x width x height
doubling any of the dimensions would double the volume
and with the same logic, doubling two dimensions would quadruple the volume of the rectangular prism
and three would multiply the volume by 6, so on
and for the cylinder you'd be quadroupolign the volume
quadrupling
as $hπr^2$ would turn into $hπ(2r)^2$ which would be $hπ4r^2$
soft zealotBOT
Zouni
indigo plover
Hello i belive i got the hang of this questiilon thanks to someone in this server
final saddleBOT
Hello i belive i got the hang of this questiilon thanks to someone in this serve...
indigo plover
So if possible can anyone make me a question similar to this one to see if i can get it right
To prove to myself i understsnd this concept fully
hybrid heath
Solve for $x$ in $\frac{2z+y}{3x+4}=\frac{y-z}{x-1}$
soft zealotBOT
SWR
indigo plover
Wow
I definitely still dont undertsnad this
would the first step be getting rid of that x-1?
hybrid heath
First step would be cross-multiply
indigo plover
Ok illdo
OK so
2zx-2z+xy-y = 3xy-6x+4y-8
Not sure i wouldve thought to combine like terms but that = sign
hybrid heath
2zx-2z+xy-y = 3xy-6x+4y-8
you get the left side correct, but not the right side
indigo plover
Ah
i do again
Ah ok i got mixxed i thought a 2 was a z or something
Ok so now
2zx-2z+yx-y=3xy-6x+4y-8
final saddleBOT
Please read #❓how-to-get-help
hybrid heath
Ok so now
2zx-2z+yx-y=3xy-6x+4y-8
You wrote the same thing
indigo plover
ah im writing the qeustion wrorng its messing me up twice in a row sry
again 2 mins
Ok surely
2zx-2z+yx-y=3xy-3xz+4y-4z
So the goal to solve for x
i wanna make it alone
Is good ?
-2z i mean
hybrid heath
Yeah, you need to subtract 2z, not 2
You're not done, you still have an x on both sides
final saddleBOT
@indigo plover Has your question been resolved?
indigo plover
Ohh
gritty solar
$\log_{16}^2 x - \log_{16} x + \log_{16} k = 0$
final saddleBOT
$\log_{16}^2 x - \log_{16} x + \log_{16} k = 0$
gritty solar
I need to find the number of values of k such that this equation has one solution
soft zealotBOT
NEONPerseus
gritty solar
I was able to find only one value
For k = 2
But apparently there's another one?
Am I missing an absolute value somewhere
versed crater
Let log16x = z
ocean lintel
Clearly a quadratic in z
gritty solar
I just completed the square directly
versed crater
z² - z + c = 0
ocean lintel
Just let the discriminant be zero and solve for k
versed crater
Let’s see
versed crater
1 - 4(1)(c) = 0
gritty solar
looks like everyone is missing an absolute value
vital crag
,w solve z^2 - z + c = 0
soft zealotBOT
gritty solar
It needs to have only one solution
Note that x must have one value not z
I don't think that matters tbh
vital crag
,w solve z^2 - z + 1/4 = 0
soft zealotBOT
magic sparrow
is it log_16(x) or log_16(|x|)
gritty solar
No absolute value inside
I think something's up with the question tbh
k cannot be negative
And there's only one positive value
magic sparrow
if k=2, then there is only one solution x to the equation
versed crater
Is your log defined for negative values
vital crag
k=2 is the only positive value of k where there is one solution for z
gritty solar
No its not
versed crater
It could be extended though
magic sparrow
k=2 is the only positive value of k where there is one solution for z
W I beat riemann I said it first make me honorable quick
versed crater
The slider just moves this thing up and down
gritty solar
The slider just moves this thing up and down
Lol
gritty solar
why though
versed crater
Then you can see if it has 1 and only 1 solution then there is only 1 k value for it
dry light
Let's see
gritty solar
Hmm true
versed crater
If that’s allowed
dry light
,w Reduce[Log[16,x]^2 + Log[16,x] + Log[16,k] == 0, k, Reals]
gritty solar
Maybe that's what it's referring to
dry light
You suck
versed crater
Possibly
dry light
Wolfram will die
versed crater
Thank you
gritty solar
Perchance
I'll just ask my teacher
But can you really
Replace a parameter with a variable
dry light
Hold on lemme see
gritty solar
Astagfirullah
soft zealotBOT
gritty solar
Stage 4 cancer
dry light
Literally
gritty solar
Hey it says k = 1
AND log x = 0
Isn't that fun
@versed crater if you were to let x = k
versed crater
You can’t assign values to x
gritty solar
k = x
versed crater
Yeah
versed crater
Pov you loop through i and midway in you change what i is
gritty solar
So that can't be it
gritty solar
k = 2
versed crater
No no no
gritty solar
versed crater
k = 1 and k = x is different
versed crater
If k = x, the 2nd term cancels
dry light
I'm just seeing which values of k changes the function.
gritty solar
But if x is any positive real value
versed crater
That’s how you get x = 1 being a single root
dry light
gritty solar
(was hoping for Umbra commentary)
versed crater
And we want all k’s that satisfy that condition
gritty solar
I'll just ask my teacher
I think frosst's explaination made the most sense
But it's sort of finding an answer because you know it's there
:/
In any case, thank you to y'all
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versed crater
I doubt letting a constant turn into a variable makes much sense
But here you can see both curves are 0 at x= 1 so when you sum them you get that as a root
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rigid inlet
I’m stuck on finding the height, length and area of the equilateral triangular prism. It needs to be able hold 12 golf balls, with each having a diameter of 4.267 cm. The equilateral prism also needs to be two layers in height, which i think is the distance between bases (correct me if I’m wrong).
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I’m stuck on finding the height, length and area of the equilateral triangular p...
@rigid inlet Has your question been resolved?
rigid inlet
<@&286206848099549185>
rigid inlet
I think the distance between bases is 8.534
O O O
O O
O
I think it should look like this
For the setup
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rigid inlet
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verbal sonnet
hi
lilac stratus
If in matrix multiplication, AB=AC, does this imply B=C?
final saddleBOT
If in matrix multiplication, AB=AC, does this imply B=C?
lost ginkgo
If A is inversible then it does imply B=C, because you can multiply both sides by A^{-1} in the front
lilac stratus
If A is inversible then it does imply B=C, because you can multiply both sides b...
What if |A|=0
In matrix you can't divide but you multiply by inverse
lilac stratus
If A is inversible then it does imply B=C, because you can multiply both sides b...
If |A|=0 then that means A is not invertible
Also in this question I asked, I didn't mention A is invertible or not. So can you directly imply B=C here?
lost ginkgo
No, it is not directly implied then
lilac stratus
Ok then
lost ginkgo
imagine if A was a matrix of zeros, then any B or C would work
lilac stratus
imagine if A was a matrix of zeros, then any B or C would work
Oh that's true
That's a perfect counter example
Thank you
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lilac stratus
imagine if A was a matrix of zeros, then any B or C would work
Wait, isn't that the same in case of scalars like ab=ac then b=c but if a=0 then b and c can be any scalar and so not necessarily b=c
lost ginkgo
yeah 0 is non invertible since 1/0 isnt defined
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spice lintel
Considering this Venn Diagram,
I calculated;
P(A|B) = 0.315
P(C|A) = 0.364
and still need to calculate;
P(B|C) = The formula of P(B|C) = P(B∩C) / P(C) does not make sense to me as of now because how can I find the probability of C and B happening at the same time?
Note: This is all the information I have
tiny gorge
Considering this Venn Diagram,
I calculated;
P(A|B) = 0.315
P(C|A) = 0.364
an...
B and C are disjoint, no?
spice lintel
B and C are disjoint, no?
yes B and C are disjoint thats why I don't understand how to find P(B|C)
tiny gorge
yes B and C are disjoint thats why I don't understand how to find P(B|C)
well if B and C are disjoint, what does that imply about P(B∩C) ?
B∩C = empty set
tight ravine
@tiny gorge can you help me next please?
spice lintel
B∩C = empty set
That it would = 0 ?
I asked my professor about it too and he said
I can't tell you what the answer to 5(f) is, but the same formula works in all cases.
thats why I was hesitant to think it was 0
tiny gorge
P(empty set) is always zero yes
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hot oracle
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hot oracle
I’m confused
Wouldn’t that mean that there’s only two solutions between 0<x<2pi ?
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fathom walrus
enlightenment is real
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stoic obsidian
How would you know where to place the decimal in binary division
In the final answer
final saddleBOT
How would you know where to place the decimal in binary division
In the final a...
stoic obsidian
you've done it correctly
This is a solution
But I was wondering if I have to move to the right by two steps
tranquil pine
both numbers were multiplied by 100
which is why the decimal moves to the right for both
multiplying both numbers by the same thing does not affect the division
stoic obsidian
both numbers were multiplied by 100
But if you multiply by 100 in the calculator it doesn't display the decimal or is that normal
tranquil pine
101010101.101
the decimal of this moves 2 to the right
tranquil pine
But am referring about the 0001101
the decimal in this goes directly above the decimal of the 101010...
(as in your solution)
stoic obsidian
the decimal of this moves 2 to the right
So if it was 1010.101010
It moves 5 times to the right
tranquil pine
np
stoic obsidian
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dapper goblet
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dapper goblet
help idk which part i got it wrong
the answer is 2x + 2/x²
almost got it but still not righy
<@&286206848099549185> \
minor mist
question?
manic anchor
im trying not to do it by direct method
minor mist
yeah yeah
minor mist
direct method is that easy but cant use that 😭
yeah i know
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@dapper goblet Has your question been resolved?
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@dapper goblet Has your question been resolved?
dapper goblet
<@&286206848099549185>
lyric oxide
<@&286206848099549185>
simplify and you will get
lim 2x + h + 2/(xh+x^2)
h->0
f’ = 2x + 2/x^2
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hot sedge
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hot sedge
I don't understand how you're supposed to be able to find the c-matrix of T
if you aren't given what the transformation of vector w maps to
forest nova
i need help
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@hot sedge Has your question been resolved?
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carmine plaza
i have ap calc bc test monday i desperately need help reviewing ;-;
final saddleBOT
i have ap calc bc test monday i desperately need help reviewing ;-;
carmine plaza
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pseudo dock
i have ap calc bc test monday i desperately need help reviewing ;-;
send any question related with that, and im willing to help :)
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tranquil pine
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tranquil pine
I’m doing test corrections and was absent for the entire unit pls help me
#5 period b and phase shift
@strange shore
Are you available right now?
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@tranquil pine Has your question been resolved?
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@tranquil pine Has your question been resolved?
tranquil pine
i have a question about some steps
final saddleBOT
i have a question about some steps
tranquil pine
oh wait im so dumb
sec(x) has its own intergral which is the ln(|secx + tanx|) right
tulip coyote
sec(x) has its own intergral which is the ln(|secx + tanx|) right
Yep!
final saddleBOT
@tranquil pine Has your question been resolved?
tranquil pine
Yep!
okay cool
also
is there a way to do this w out the partial frac decomp
idk im having trouble with this expansion
formal trail
you do need partial fractions for this yeah
tulip coyote
is there a way to do this w out the partial frac decomp
Not that I can think of atm at least
tulip coyote
idk im having trouble with this expansion
The partial fractions one?
tulip coyote
Not that I can think of atm at least
(In particular it almost certainly isn’t of the form f’(x)/f(x) as the denom has degree 4 and numerator is degree 2)
tulip coyote
the partial fractions is messy unless im going very wrong
It does look like it’ll be quite painful tbh
tranquil pine
can i show my work
tulip coyote
can i show my work
Yea please do 
tulip coyote
Hmmm 
not that I've spotted 
I mean you could do the whole "substitute values in" thing too which might be less painful but only slightly
So from this point, choose x=1, x=3 and then two other x values to get equations
tranquil pine
okay tysm can i ask one more question
tulip coyote
Yea of course! 
tranquil pine
okay tysm
i had this intergral on an exam
it was improper righ
and i got -1/9 but thats not fully correct
the feedback says use l hospitals or introduct t-> 0 and i went wrong but i dont understand the correct solution
tulip coyote
Yea it's improper because of the 0
tranquil pine
why
tulip coyote
e.g. ln(0) isn't defined
tulip coyote
That's why they do the limit thing, so like $-\int_{t}^{1} x^{2} \ln(x) \dd x$ then let $t\to 0$
tranquil pine
let me see
soft zealotBOT
@tulip coyote
tranquil pine
wait i dont understand where lhospitals could come into place
tulip coyote
<@788085606483361802>
Guessing on working out this integral in terms of t
tranquil pine
then this is clearly divergent right
also why did you flip the bounds of integration
is that for readability
ik its a proper of intergrals but yeah
tulip coyote
is that for readability
Just cause it annoyed me tbh 
You don't have to flip them at all but for me it just gets me any time I see integrals "the wrong way round" 
tranquil pine
i gotcha
i tried checking the answer w online calculator and it kept saying 1/9 but it should be divergent right
tulip coyote
then this is clearly divergent right
And not quite either no
tulip coyote
Work out the integral in terms of t
tranquil pine
i see my mistake
its positive 1/9
ln(0) (0)/ 3 - 0^3/9 = 0
uhhh
ln(0) dne right
0 times inf is 0???
tranquil pine
for the ln(t)t^3/3
tulip coyote
for the ln(t)t^3/3
As per the other question you posted, because $t^{3} = \frac{1}{1/t^{3}}$, you can then write that as
[
\frac{1}{3} \frac{\ln(t)}{1/t^{3}}
]
which is a form you can use lopital's on
soft zealotBOT
@tulip coyote
tranquil pine
ln(t)t^3/ 3 is indeterminite, use lhopitals there first
do i rlly need to rewrite it
tulip coyote
Well if you rewrite it like that, it becomes easier to justify why you can lopital it and what happens when you do
Once you apply lopital's, it becomes something much nicer to work with (remember that lopital's only applies for things of the form 0/0 and ±♾️/♾️, but 0 * ♾️ can be converted into that form as per above)
tranquil pine
i gotcha
can i ask about this too
is it just 2pi from bounds 0 to 2 x sqrt(1 + 4x^2)
tulip coyote
Hmmm I don't think it is? 
At least not with me trying it out I get something a little different
tulip coyote
can i ask about this too
Do you like have formulas for surface areas of revolution?
tulip coyote
It's kinda like that yea
We're rotating about the y axis here of course but want our integral in terms of x
tranquil pine
wait whats the diff in rotating amoung the y axis if its not expressed in terms of y
tulip coyote
Well in this case we have that $y = x^{2}$ so then you get that $x = \sqrt{y}$ (in this case because we're between $(0, 0)$ and $(2,4)$, then we take the positive square root)
soft zealotBOT
@tulip coyote
tulip coyote
anyways, from that, you can basically substitute to then get that integral back in terms of x
tulip coyote
We're rotating about the y axis so we would be taking g(y) = sqrt{y}
tulip coyote
It's kinda like that yea
and using the second form here
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@tranquil pine Has your question been resolved?
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past bluff
final saddleBOT
past bluff
I need assistance w this