#help-42
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m x n 
e.g. something like $\pmqty{ 1 & 0 & 0 \ 0 & 1 & 0}$ meets the first condition but not the second
@upper sparrow
wow
my mind is eluminated
but if it said if ALL columns are pivots???
then thats c

.solved
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i found RREF
the only vector in Nul A is (a), the zero vector is also included since thats that definition of a subspace
so only b and d are left
i know a basis can only consist of linearly independent vectors
,w rref [[3, 1, 4, 0], [1, 2, 3, 5], [2, 0, 2, -2]]
These ones can be painful can’t they 
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guys would it be the same if i just did the product rule for tan x and 3x2-9 and then did it again for that result and x3
@verbal lintel
f = x, g = x, h = x
derivative of fg then h method
(x + x)’x + (x+x)x’
2x + 2x = 4x
Now fgh method
x^2 + x^2 + x^2 = 3x^2
Thus they’re unequal, so u can’t do that
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School puzzle related somehow to permutations
I think it’s not solvable because of lack of information
@fresh crag Has your question been resolved?
How?
if u follow the 5 steps its pretty straight forward
Can u elaborate?
I just followed the 5 steps
that are in the assignment
and it fits together from there
Yh but explain idk
if u set up a table and go through them one by one it sorts itself out
theres not really anything to explain
but do u have to do permutations or is it just sort it in a table?
Teacher just said solve it
ah ok
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just asking if im wrong or right
$$\int^3 _{-1} |x|$$
JustToPro
JustToPro
abs(x) = sqrt(x^2)
JustToPro
cant use u sub , no x present and if i cancel sqrt with 2 then thats wrong
ik its related to piecewise functions and splitting the integral
but im kinda bad at it , so wanted to ask if i split the integral correctly or not
This seems right…
Honestly, I would do something like this
No, I was just wondering why u did the sqrt(x^2) stuff
Its my dumb idea
....
Abs(x) isn’t x from -1 to 0
x is negative from 0 to -1
Oh right....
U don’t really need that third case lol
Just define one of the previous conditions to be >=
hm
But this is good
btw another question if u dont mind
whats the difference between
mclaurin series
taylor series
arent they both used to just expand stuff? like ln or cos or sin or smthing
Isnt mclaurin series is just taylor series but modified so that the expansion center is not at 0 but other point a
i dont understand
Let say u want to convert sin(x) to a series of polynomial using Taylor series
But the number of polynomial is limited, so u can only expand to 3 terms
Okay...
taylor series goes f(a) + f'(a)(x-a)/2! so on
and maclaurin goes f(0) + f'0)
so on
so are they same thing? just a = 0?
@polar frost ?
If a = 0 then they're just the same thing yes
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how do i solve this question and set up the limits for the integrals
ive tried that, but still a bit confused,
Confused after drawing it or during drawing it
after, on how to set up the integral
and what about x
After the y
In a classroom, 1/3 of the students are 10 years old, 1/6 are 11 years old and 15 students are 9 years old. What is the number of students in the room?
Actually you'd need to do x first sorry
I'd write the bounds of x in terms of y
And then integrate wrt y
So x would go from y to y√3
And y would go from 0 to 2
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The number of values of $c$ for which $y=4x+c$ is a tangent to $\frac{x^2}{4}+y^2=1$ is
ƒ(Why am. I here)=misery
the number of values where $f'(c) = 4$?
b
Yeah, was about to type my thoughts
mb carry on
ƒ(Why am. I here)=misery
I think I'm missing what the C is doing though
Have to figure that out
I know. it's the y intercept
but have to figure out why that matters
maybe too strong of a hint: ||number of intersections||
don't comment on my art but
these two lines have the same slope but different c values
Hmm
so just drew a diagram
so basically I have to find the distance between the origin and the line
and equate it to some parameter of the ellipse?
you are overthinking
keep in mind they don't actually care what the c value is
just the number of solutions
in that case just 2, I think
slope is fixed
the c value can be. changed to translate the line parallel to itself
am I missing something
that sounds right
what's y'?
dy/dx
$\frac{x}{2}+2yy'=0$
ƒ(Why am. I here)=misery
$\frac{x}{-4y}=-y'$
ƒ(Why am. I here)=misery
You can use some sort of parametric co-ordinates rather than working with x and y
(doesnt really matter)
b
ie two cases
just plug y=4x+c into the other equation
you mean $\frac{x}{-4y}=-4$?
ƒ(Why am. I here)=misery
oh wow we are overthinking it
solve x^2/4 + (4x+c)^2=1
oh
that gives you the intersections of the line and the ellipse
if you only have one intersection that means you have a tangent
determinat
do you mean discriminant?
quadratic in x, set discriminant equal to zero, get quadratic in c
ƒ(Why am. I here)=misery
if you multiply this out, you get a quadratic in x
you are interested when this has one solution
so you look at the discriminant of this equation
so that would be when the discriminant is zero
yes
and the discriminant is some expression involving c
turns out, that expression is again a quadratic
I get
$\frac{x^2}{4}+16x^2+c^2+8cx-1=0$
so how I take the det of this as a function of c and set that to 0?
still not det
well what is the discriminant
bring it into the form ax^2+bc+c
oh btw, -1 at the end
ƒ(Why am. I here)=misery
$c^2+8cx+\frac{x^2}{4}+16x^2-1=0$
ƒ(Why am. I here)=misery
for now its still an equation in x
ƒ(Why am. I here)=misery
so now a=33/4, b=8c and c=c^2-1
with awful naming on my part
now the discriminant is what?
$64c^2-33(c^2-1)=0$
- not =
ƒ(Why am. I here)=misery
this?
hmm
ok 16+1/4 is not 33/4
,w (x^2/4)+(4x+c)^2=1
ah
this is very nasty IMO
I def don't want to find the tangent if the equations are like this
but the idea is the same, right?
this isnt that nasty
I mean as soon as you have c you have the tangent
the tangent will be exactly 4x+c
wait, what
of course computing that would be bad but I mean why should you want to do that
this should actually be 64c^2-65(c^2-1)=0
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Im not sure why any of this was done. The curve is an ellipse and it is quite obvious by a diagram that two tangents of any slope will occur.
thats why
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being $a_n = \frac{\left(n+1\right)^{n}}{k^n \cdot n!}$ for which $k \in \mathbb{N}$ does $\lim_{n \to \infty} a_n = 0$?
milanesa de pollo
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how do I get it started¡
for example, I think its known that n! grows faster than n^n
or is it not?
How is that?
I said n! can be treated as a polynomial of degree n, it doesn't grow faster :P
i have a way but probably not the intended way: ||sterling’s approximation for the factorial||
no clue how to do it the conventional way tho
I dont think he wants to do this
yeah
<@&286206848099549185>
@snow hare Has your question been resolved?
@snow hare Has your question been resolved?
@snow hare Has your question been resolved?
@snow hare Has your question been resolved?
Because n! = n * (n-1) * ... * 2 * 1 and n^n = n * n * ... * n * n and these two expressions have the same number of terms, we can easily see, because each term in the product of n^n is greater than or equal to the corresponding term in n!, that n^n > n!
As for a method to approach this problem, I can only see using the Sterling approximation. I have no idea how to approach this otherwise.
,align \log a_n & = -\sum_{j = 1}^n \map[\bigg]\log {\f {kj} {n + 1}} \
& = -(n + 1)\sum_{j = 1}^n \f 1 {n + 1} \map[\bigg]\log {\f {kj} {n + 1}} \
& \overset{\mathclap{n\to\infty}}\sim -(n + 1) \int_0^1 \log(kx) \dd x
= -(n + 1)(\log(k) - 1)
@snow hare Has your question been resolved?
try using the squeeze theorem maybe?
find two simpler upper and lower functions which bound it
and then try and find values of k
how doyou propose to find them in this case
is K supposed to be a fixed value?
hmm
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i need help
i am unable to answer any part of it
i think we use sin cos and tan?
<@&286206848099549185>
using the cosine formula,
$cos x = (|AB|^2 + |AC|^2 - |BC|^2) / 2|AB||AC|$
ar1tr0
yea but do you know what the steps after that are?
im not really good with these types of formulas
me neither, it comes from the addition rule of vectors which is pretty intuitive.
hm alright thanks tho
plug in the values of the side lengths then it's easy
ah okay
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is this correct ? im pretty confident about it all until the last 2 steps
@solid talon Has your question been resolved?
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The central angle of the circular sector is 120° and the radius is 15 cm. The circular sector is bent into the shell of a straight circular cone. Determine the angle between the side line and the base of the cone.
Idk how to do this............... i need help
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I don't know how to proceed
what is G, what is z real complex please detail a little
its written
G is a region?
@hexed ginkgo Has your question been resolved?
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If f0 = 1 f1 = -1, find f9 for a fibonocci series
I solved it -13 but the answer was -8
am I wrong or the answer?
I also ran it with chatgpt and it got -13
@plain umbra Has your question been resolved?
.close
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how do I derive 5.4 from 5.1, 5.2, 5.3? i got 5.5 and 5.6 on my own
I got 5.5 and 5.6 on my own
some outline is here
either sin(theta) = 0 or sin(90-phi) = sin(theta) (making the second factor 0)
from this just few cases follow
you can verify for which of these cases the 2nd and 3rd condition holds
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@empty marlin Has your question been resolved?
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where is the 1/21 coming from?
what's the integral of y^6/3?
i don't know where the 1/3 y^6 came from either
x^3/3
but do you not add indices so y^5
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how do i do this?
i know how you're supposed to do it
but i keep getting something wrong with the algebra
show us
so first
i took the derivative of sqrtx
wait let me write it out
that would be better
wait, do i have to differentiate both sides
when try to find dy/dx?
of course
ah ok then that was the issue
i didnt take the derivative of the 2
ok so the answer matches up, thanks

do you know how to do this one instead?
i do
i only got to the integral of this
and i dont know where to go from there
how do you evaluate the infinity
the integral i got was
-12(x+3)^-1/2
$\int_a^\infty f(x) \dd x = \lim_{t\to \infty} \int_a^t f(x) \dd x$
Steakanator
some dummy variable
so i think i did this and
a is 1
and then
if the equation is -12(x+3)^-1/2
doesnt it go to 0?
seems like it
but i checked the answer
and its 6
oh wait
it's 0 for the first only only
when you plug in 1 it gives 6
indeed
are all improper integrals solved that way? with a limit
cause i remember our lesson with improper integrals had some nasty formulas that i didnt bother remembering
but i probably have to for the ap test smh
it's slightly more formal than "plugging in infinity"
so if infinity was on the bottom what do i do there
do i flip it and make it negative?
infinity on the bottom would be weird
and if the bottom was negative infinity and the top is positive
if negative infinity on the bottom then you would want another limit yes
ok
ok last one
how do you do seperation of variables with this one
is the integral of dy/dx = y/x?
it isn't
hmmm... so how can i split off the dx from the dy/dx
same way as usual, just "multiply" by dx
wdym
and then is the integral of dy = y?
where's that coming from?
im trying to integrate both sides but idk
i think you need to look at the steps for separation of variables again
well you need to get everything involving y on the same side
hmm ok
so
dy + ydx = 2dx
but then how do you get rid of the dx on the left side
okay so i integrate it now?
Steakanator
uhh
i dont know what you're getting at here
do i take the derivative of both sides?
you asked if you could integrate. I integrated and am asking you what that even is
well
this is why I asked you to re-consult whatever notes you have on separation, because hopefully it contains the proper way to separate them
i do know
that's not a super well defined question
im trying to take the derivative of both sides
why?
of the equation dy + ydx = 2dx
you're solving a differential equation
uhhh
ok no, cease
I've told you that adding ydx to both sides isn't the way forward
you have dy = (2-y)dx
what's another way, aside from adding, that you can move everything with a y to the same side?
by?
2-y?
$\int \dd x = \int 1 \dd x$
Steakanator
surely you can integrate 1 by yourself
oh wait
ok
umm
so i got 1-e^(x-1)
but thats not one of the answer options
.close
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assuming we're trying to find m and n for the same function and we're given two different x x-cords, f(3) = 0 and f(2) = 85
Can someone check if my substitution is correct, and confirm if this is the correct answer. I got varying results on my other attempts(not shown here), but I feel confident this is correct
as far as I can tell it looks ok
the way to check this
is to now plug in 3 in the function
and see if you get 0
ahh yeah and see if I get the correct remainder
and plug in 2 and see if you get 85
man, all that for me to not think of doing that.. holy I'm so cooked
🤣
ty tho
.close
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hello
SAS they are both right angle with 2 sides of the same value
But the included angle isn’t in between them
The SAS theorem states that the angle needs to be inside the two corresponding sides
no?
if u use arccos for both triangles
u will get the same angle between them
arccos(8/17) for both trialges
for find the angle between the two
@cedar sinew
someone told me it’s HL
@iron cliff Has your question been resolved?
idk what HL is so theycould be right
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MCQ on absolute inequalities
!status
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I've done it and my ans is B, but obiviously the correct one is going to be D)
Don't get how
Can you send your work
Yes
Oh shit I forgot to check critical points
Yeah makes sense, sorry
Also messed up the second case sign, doing stuff mentally when you're a beginner is not good
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i dont get 2,3,4
angle sum to deteremine the third angle
then do whatever you didn in Q 1
i got 38 degrees
for number 2
and number 3
135 degrees
and for 4
i got 84
could you check if its correct
how are you getting 135°
won't get you 135
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These 2
Hi i fell asleep by mistake
Lolll
I still need help never got it
what are u even stuck at
Wait no it’s
“Is the cylander 2181370.319 grams?”
Those 2 questions
Please help? @shut sierra
the first question is not hard, it's just tedious
Please i never learned this deadass i didnt
the second is more straight forward than the first
My tescher never tought it please help
My teacher never taught the lesson @shut sierra
cylinder is 2182485 grams
are you taking pi = 3.14 instead or some approximate value?
Idk tbh 😭
Like i said teacher never taught this
so what did you use to calculate the volume of the cylinder
Idk
Sorry if i sound dumb
so how did u get this value?
Ai app
Im just being completely honest
But idk if its correct
@shut sierra
how about you look at the question again and think and tell me how you would attempt to solve it
Idk
How am i supposed to somve something i didnt lesrn
Sorry ok ill try
misha
Volume of cylinder then multiply by density
correct
do we know any of those values?
do we know either the volume or density of the cylinder?
Using a calculator i got 133183.422319224
Mass
show your working
how is this your working
first of all that answer is horribly wrong because you used the wrong units of measurements
Oh ok
I understand y
and i'm not going to help you if you keep searching for the easy way out
Sorry
ask someone else to help you then
No ill acually try
I didnt mean to sorry
@shut sierra
I apologize for that and ill acually try now im sorry
Ok whats the step mam @shut sierra
Ill listen to you please 😭
Im sorry bro @shut sierra
Please bro im acually crying irl
I dont wanna fail!!!
@shut sierra im so sorry i wont do it again
Bro 😭
Did u figure out one
Cause i tried doing things easy way and i apologize for that
Ah
I acually will listen and do the work!!!
Well then why don’t u just google it or is this study material for a test
I csnt google it it gives me wrong answers i triedd
Bro please im sorry for what i did
@fallen linden idk what imma do
No one can help on any server
They left already
Theirs no point they won’t come back
Anyone else?
Hmm
Please help
Hi @trail valley
That guy there
I put in ur question straight into google and the answer came up
Bro wrong answer bro
So idk how you didn’t find it?
Wait how do u know it’s wrong
It doesn’t sound wrong
There’s even an explanation
You checked?
But doesn’t the check have the answer
I press it again it goes your teacher limit check button
No
Just tells me if answer correct or wrong
So it isn’t 12745987.2 grams?
No
Nope
I think it is
Wait so it’s just ur final grade????
Bro can someone helonme please
I still havnt done my chemistry homework
Im deadass crying rn irl
Does she not do that
No!!!
What grade
Look anyone help?
<@&286206848099549185>
@harsh siren sorry maybe u can help kinda emergency
@deft grove
@vast trellis
Can y’all help maybe
Is it high school
@trail valley grab a piece of paper
10th grade I think
What's up
and a pencil or pen
Ok mam
Sonic ur teachers are here
W pfp
Im sorry for earlier btw
Don’t screw it up this time
Which is ohh mvm
the question asks us to find the mass of the cylinder
Yep
can you tell me again, how do we find the mass?
One seccond
calculate the cylinder volume, then multiply the volume by the density
^^
Yep
which do we know
Volume
Da volume lol
misha
Yep thats what i said
r is the radius and h is the height
calculate that
the question told us the radius and the height
With what numbers?
Ohh nvm
Got it
the question gave us
V≈57905.84
yes
look at the question again
the values for the radius and height were given in inches
Kk
Yep
but the density is given in grams per cubic centimeter
Mhmm
so we must convert from inches to cm
So convert this to cm?
not quite
this value is 57905.84 cubic inches
Oh ok
This tomes 16.387?
yes
948903.00008
Idk i multiplied like u said?
Idk
Using the calculator
now that we have the volume, we can find this
Is this correct?
do you not have a calculator
I do but dont wanna get it
you can see if it's correct or wrong?
oh
I already used it once
did you use the check button on the first question yet
Its omly 5 questions
Yep
Wait so u only are on question 1?
No i skipped it
So how many u have to do
5 questions 1 is my last 1
So onky 1?
I think #5 is wrong but im tryna get 3 and 1 correct so i can ger 1 wrong to get 80% B
K keep going then.
Ok number 1 please
Kk
What grade r u in
10
So geometry 1?
Mhmm
Bruh
How’d you go?
He still needs to do one more
I think
Why don’t u ask ur teacher for an extension
You usually can’t for quizzes
This doesn’t seem like a quiz
I’ve never had homework on a website so I wouldn’t know lol
Never???
No
I have it so much
We’d get pdfs with questions
Do they print it out for the class
Or textbook chapters
And give it to u
We don’t use our textbook the teacher just gives us worksheets or we can choose the online ver
Ah I see
U use ur textbook to get the questions?
No no it’s either the questions are found in a long pdf that’s posted
Or questions from a textbook
I’m not in hs anymore lol
University
Ah
I don’t do math
But-
What does this mean then
Or this???
That was my experience when I was in school
Ahhhh hs?
All of highschool math was like that
Yepp
Ok forget #1 please help me with rhis it seems easier
Lol ty
U might have to find people urself this time sorry
I have to go to bed
I am
K
Bye noob god
Bye 😦
Wait do u have. A test or is it just hw
Its 2:05 am for me rn
Ah the good old topic tests
Hw
English write during class period
Okay everyone good night bye.
Bye
let me see hm
Also i wanna check if this is correct
I did this with someone else but checking my answer
Yep ^^
and its density
Yep
remember what density is?
What the formula?
Kk
but we can find it!
Kk
with the radius and the hight we can find the volume of the cylinder
before operating, lets check the units
for this one
Soo V=πr2h
yep
Ok
So hao i plug the # in?
Kk
Plug what #?
Ok
you should get
V≈3769.91
My bad
dsjkfh np
yeah, 40^2 is a huge number...
