#help-13
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..
x^2
How about AB?
1+x+x^2
Do you know how to assume two terms that one is greater than the other( a>b)?
nope
Assume a-b>0
If the case is not valid, then the answer will be on the other side
Different
alr
Try it out first
I guess yk what to do next, right?
factorise
yessss
Valid, the assumption was true
could it also be x is larger than or equal to 1
Any questions left?
for now nope
oh wella cttually
Type
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ye?
i have one mroe
Sure
the things not sending gimme a sec
Okay
so with this question, i’ve proved the 4 triangles, how can i prove it’s a rhombus now
First, prove that the four sides of the "unknown" graph are the same
so ps, pr, sr and rq?
Second, prove that the diagonals of the "unknown" graph are vertical to each other
yes
I just realized that you don’t need second part lol
The first part is just enough
gl, ping me when you’re done
@wicked mantle does it hjave something to do with pythag?
pythagoras theorem
so (so)^2 + (po)^2 = (sp)^2
and if we replicate that in all four triangles
each side of the rhombus is the same
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When writing a sequence, do u need to write it by order or by most to least? If there is a repeat term, do u write it twice?
sequence of what
and for what purpose
We have an assignment which asks us to find the first 5 terms of a sequence whose general term is insert formula
depends on the formula
I believe I posted the exact assignment yesterday
I'm just confused as to how I should write the sequence
See the terms are supposed to be -2, 1, 0, 1, 32 do I write it that way or does it have to be least to most? So, -2, 0, 1, 32 no repeated terms?
@dire geode
.
Oh its an=(n - 3)^n
for what n
Depends on which number of a sub so 1, 2, 3, 4, 5
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Please help I don’t understand how to get these two answers I’m grade 10
I’m stuck on where to even start I k no w these will be on test and forget. Everything else was easy with conjugated but I think this is similar where u multiple by both denominator and numerator but after that I don’t know
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Help me understand a.)
,rotate
which equation doesn't make sense first
The first one below a
its just poor working out. f(x) = cos, f' = -sin
They should have wrote f(x) = cos on that line, OR f'(x) = d(cosx)/dx
there's a mistake in the notes on that line
Where?
f'(x) = cos x is wrong
Why?
that's the wrong notation
$f'(x) = (cos(x))' = -sin(x)$
riemann
what about it
m = slope
slope at a point = derivative at a point
the function 'm' is not defined.
When you write f(input) that is the function named f, and an input you are passing to it.
You seem to not understand function notation fully. Scratching up on that should help you
You should write f'(pi/2) instead and calculate. Then say let the tangent be y, g(x) or another name and define it as y=mx+c. Then say that the gradient of the tangent, m, is equal to f'(pi/2).
Where did -1 came from?
@gray oasis Has your question been resolved?
do you know special values for sin function
in particular that one
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Help
@old ridge
@open mauve Has your question been resolved?
<@&286206848099549185>
<@&286206848099549185>
why?
hello are you braindead
their question still hasnt been answered
@open mauve Has your question been resolved?
<@&286206848099549185>
I know but what is your problem?
that is different person
I mean he refers to my question, and this is kinda my slot too XD
@open mauve Has your question been resolved?
@open mauve Has your question been resolved?
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$g^{(n)}(x)=p_n(1/x)e^{-1/x}$ for $x>0$ and some degree $2n$ polynomial $p_n$
Austin
I am trying to prove this by induction but I keep getting stuck on the degree part at the end
the base case I've done
suppose it is true that g^(m)(x)=p_m(1/x)e^(-1/x) where that polynomial is degree 2m
then
g^(m+1)(x)= (p_m(1/x))' * -1/x^2 + 1/x^2 e^(-1/x)
are you going to make us guess what g might be 
well what are you trying to prove then
"g doesn't matter"
and then from this, like p_m(1/x)' will be degree 2m+1
and then multiply by the 1/x^2 and it will give 2m+3
which I don't want
it should be 2m+2
but I don't see a mistake 
$$g(x)=e^{\frac{-1}{x}} \quad x>0$$
Austin
$$g'(x)=\frac{1}{x^2}e^{\frac{-1}{x}}$$
Austin
Suppose $g^{m}(x)=p_m\left(\frac{1}{x}\right)e^{\frac{-1}{x}}$ where $p_m$ is degree $2m$
Austin
Then $$g^{m+1}(x)=\left(p_m\left(\frac{1}{x}\right)\right)'\cdot \frac{-1}{x^2} + \frac{1}{x^2}e^{\frac{-1}{x}}$$
Austin
and I have no idea how this new thing is supposed to match up with the degree we want
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"A woman’s necklace of pearls broke while (rule 2).
A third of the pearls rolled onto the floor,
one-fifth was scattered on the bed,
she herself retrieved one-sixth,
and her lover picked up one-tenth.
If only six pearls remained on the string,
how many pearls did the necklace have?"
Found this in my book
Seems like algebra, but im not sure where to start
The name of the poem is elementary arithmetic
So... 💀
So for this question, you will be adding fractions. Start off by taking all of your fractions and adding them. From there, you can obtain the lowest common denominator. From there, solving this is a matter of adding the numerators, then simplifying your final fraction (if possible, which it should be due to the context of the question involving whole objects).
I apologise for not answering for a while. So you understand that this is a fractions problem, right?
Well yes, it is a necklace problem involving fractions.
necklace problem but sure
Sure
go on please
You have your set of fractions. To get the total number of beads, you must add the fractions, and in order to add fractions with different denominators, as shown in the problem, you want to make all the fractions have the same denominator.
The denominators of all of your fractions. You want to make the denominators of all fractions the same denominator.
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what's a factor theroem
factor theorem states that if (x-a) is a factor of f(x), f(a) = 0
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hello
there was a test question i wasn't able to solve, i cant remember all the components but it goes like this:
the equation of asymptotes of a hyperbola are y=± (4/3)x
However, the focal points are (0,10), (0, -10)
The part that confused me was the focal points
because i thought the focal points would be: a^2 +b^2 = c^2 ---> ±√(a^2 +b^2) = c
but it doesnt work in this case
Please and help and thank you!
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Whats 1+1?
Whats up?
consult Whitehead and Russell
nah i do t need that i need 1+1?
<@&268886789983436800>
No actually
1+1 = 2 day timeout, please do not troll in help channels
I dint
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oh
ohh
wait chain rule
idk hwy i did product rule
wait
wait yeah then how do i get g'
ohhh
yep
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I'm working on this discrete math problem
and I know I have to find the least common multiple of the two numbers, but I'm not really sure why that works
it might help you to write down the times that each of them return to the start
like the first one returns at 2:04, 2:08, ...
some numbers are common multiples of 4 and 6
for example 300 is 75×4 and also 50×6
the first number like that is the least common multiple
Like this
2:04 -> 2:08 -> 2:12
2:06 -> 2:12
and then i would notice that they both meet at 2:12
and 12 is the LCM of 6 and 4
and if you keep listing them out
you'll see that they meet at every common multiple of 6 and 4
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could anyone help me with this question? ive got no idea where i go from here💀thanks in advancee :)
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for question 2, is there anything that i’ve done wrong so far? i’m not sure what to do after the last step i did
how did u write angle DEA =150?
co interior angles
that's for parallel
180 - angle edc
ohhh
are those parallel
yes
but we cant find angle dea
what I'd suggest is start from the Left most of the diagram
assume angle HBG to be x
then by using properties of triangles, try to label each angle in terms of x until you get to angle GDE
would angle hbg + angle hgb = angle hgf
well you don't need to ask "if that is equal to that"
Just keep in mind that sum of all angles in a triangle is 180 degrees and sum of angles of a linear pair is 180
i got angle bed = 8x
are you sure?
i can't solve it
well 180= angle HGB+ angle FGH+ angle FGD
6x - 180
@vernal kite Has your question been resolved?
X is 4.2 something
no
X is 6
yes
U got it?
nope
Should I explain?
yes please
Just a sec
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✅
So now in EBD 4x + x + 150= 180
5x = 30
So x = 6
Ask me if I don't understand anything
how is angle fgd = 3x
isn't the sum of two opposite interior angles = one exterior angle
Yes but here the angle is not the complete ext angle
Got it?
Yeah...
yea i get it
Ohh
in aus?
In India
We love maths for some reason
year 12 here
all asians do
How old are u btw?
cant tell u
True
K np its just that the year system is confusing
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in the derivation of $\ds\vj T = \dv[\vj r]s$
we can say the following:
\begin{align*}
\vj T &= \4{\dv*[\vj r]t}{\3{\8{\dv*[x]t}^2+\8{\dv*[y]t}^2+\8{\dv*[z]t}^2}} \qq \0r{\8[\bigg]{s = \int_\alpha^\beta\3{\8{\dv[x]t}^2+\8{\dv[y]t}^2+\8{\dv[z]t}^2}\dd t}} \\
&= \4{\dv*[\vj r]t}{\dv*[s]t}
\end{align*}
but the problem is that u have to makea beta vary right? 
usually you would define it as s = integral from alpha to t of some dummy variable
right
and i guess u have to place some conditions
like the curve has to be simple and smooth
(smooth: continuous and not 0. simple: does not cross itself)
i don't think it necessarily needs to be simple
wouldnt it just go on an infinite loop if it was non-simple?
since the integral is like directed
@sacred grail you said something about this like 2 years ago to me
can u tell me again
idk what the question is 
like, can we define the arc length of a non-simple curve
@crimson sedge Has your question been resolved?
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integral represent area
yes
what did you get
so 1/2 + 1/3 +1/4 +.......... 1/k is the sum of the rectangles
after that no idea how to simplify it
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help how do i solve for this?
yes find the slope and see if it meet the requirement
alright
is letter b right for no.7? @spice kraken
I don't think so
im confused
what are the slopes you calculated
x - 2y = 2
-> y = 1/2x - 1
a. y = 1/2x - 5/2
b. y = x + 1
c. y = -2x + 3
d. y = -2/3x + 3
the slope is 1/2
oops
b has slope of 1
what
y = 1/2x - 1 has slope of 1/2
well which option has slope of -2
c
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2x + y = 1000
how do I find the highest possible value of xy?
ping me if you respond, I am not having this chat open
solve for one in terms of hte other
what does f(z,y) mean? I have only worked with equations with 3 unknowns on paper
x should be was writign very fast
that is function, not the equation, write it in yoru exercise book and find its maximum, that is all
I dont fully understand whats being done here, can you explain it step by step?
oh wait
your new function gj is a quadratic function, its expression is a parabola opens down, so it reaches its maximum at the vertex
find coordinates its vertex
then you get where x is reched and value fo max that is all
I came to the answer x = 250 and y = 500, is that correct?
right, i was not calculatin the est in my mind, so if yo wroe correct then all is ok
maximum si reached at x = 250 and its max value = 500
\thsi way , it shud be written in an exercise book
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hey I needed some help with this question
so
avery
the tank has a 1cm thick wall
to find the volume of the material
u need 2 radii
one is 1m
ummm
other is 1m + 1cm
👀
now you apply the regular formula for the volume of cylinder but replace r square
with r1 square - r2 square
r1 being 1m
okie tyy
i cant see the third part :((
I assume cuz ur finding the volume only of the outer wall of the tank
ohh
thanks
i suck at following along but
yh
ur subtracting the empty inside
from the full volume
to js find the iron leftover
u get it?
loool its fine :))
ofc
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Hi, is reverse matrix the same thing with inverse matrix?
And what does this phrase mean?
infinite reverse right-handed perspective projection matrix
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Is this correct?
swerriee
how did you get 6^x
you can take 2^x common
swerriee
nooo that was just an example
correct
And what do I do next
simplify further
How do I get 32 to exponential form
take lcm of 32
its like this
Yeah I got it
is it 7^x or 7x?
.
You will get the answer in terms of log then
and root smh
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this may seem like a silly question but
if u had a convergent sequence with limit L s. t. for all epsilon > 0, |an - L| < epislon for all n => N
why does it also follow that |an - L| < epsillon/2 for all n => N
or is there a way to prove it
it's true that |a_n - L| < e
so if you want |a_n - L| < f/2
then you can let e = f/2
and then that just works
but then wouldnt e just be restricted to the values of f/2
yes
like does it follow that for all e > 0, there exists N st. n > N => |a_n - L| < e
ok so: for all f > 0, there exists N st. n > N => |a_n - L| < f
so if f = 2e
there exists N st. n > N => |a_n - L| < 2e
wait i perhaps asked the wrong qu
i want the converse of that statement
eg if < 2e then does it follow for all < e
yes
ok so: for all f > 0, there exists N st. n > N => |a_n - L| < 2f
you want |a_n - L| < e
so let e = f/2
then for all e > 0, there exists N st. n > N => |a_n - L| < 2f = e
like
the point is that if you can make this thing as small as you like
then you can just make it twice as small
sorta??
oh icic
one more qu
when u say for every e > 0, |a_n - L| < e for all n => N, it doesnt imply |an - L| = 0 for all n => N right?
absolutely not
for example just take like
then why do they do they do it in this proof
1, 1/2, 1/3, 1/4, 1/5
they're talking about the limits there
the limits are not the same as the sequence
ok so
take 1, 1/2, 1/3, 1/4, 1/5
yes
as one sequence
and then take -1, -1/2, -1/3, -1/4, -1/5 as another
basic
then the differences are
2, 1, 2/3, 2/4, 2/5,
none of these are ever 0
but the limits
the limit of the first one is 0
and the limit of the second one is 0
yes
and 0-0 = 0
the differences go to 0 but aren't 0
the limit of the differences is 0
waza
or something like that
but if the differences go to 0 isnt that the same thing as saying an becomes L...
ohh
no
wait but then why do they conclude |M - L| = 0 tho
ok so
let the limit of the differences in my example be like D
so D is the limit of 2, 1, 2/3, 2/4, 2/5, ...
yes
then we can say
D < 2
D < 1
D < 2/3
D < 2/4
in fact
D < 2/n for all n
but a number that isn't negative that's smaller than 2/n for every n
has to be 0
because if D was positive then you could find 2/n smaller than D
but D < 2/n for all n
i am followin somewhat
i think this the type of thing which i need to let sit for a before it clicks
lol
yeah basically
oh wait i think im understanding
the reason we say |an - L| is because if an tends to L, a_n will always get arbitrarily close to L but never actually approach it
hence the for all epsilon > 0, |a_n - L| < epsilon bla bla
however since L and M are fixed real numbers, if we say for all epsilon > 0, |L - M| < epsilon for all n => N, then this implies that |L - M| = 0 because unlike a_n which tends to the limit L, these are fixed real numbers
therefore the only way for them to be < epsilon for all epsilon > 0, is for |L - M| = 0
is that right @azure horizon ?
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hello , i have a question in my book that should be similar to this : but its a triangle that should be solved to find X
who can help?
didnt u just get the vallue of x
no i meant its similar to this
question is :Question : find x that makes the triangle larger or equal to 20
u mean area of triangle or perimeter of tiangle?
i dont get it please help
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shoudn't it be
$8(3-2x)^-4/7$
Daddy Goat
how is it positive
yup that's a typo
he continued on solving it as it is lmao
typo
can you share the video
This calculus video tutorial explains how to find the derivative of radical functions using the power rule and chain rule for derivatives. It explains how to find the derivative of square root functions and cube root functions.
Derivatives - Fast Review:
https://www.youtube.com/watch?v=5yfh5cf4-0w&t=1s
Equation of the Tangent Li...
thanks
i put the time stamp read just play it
rare organic chem L
real
bro wants me to fail my math test 😂
good thing i noticed immediately tho!
most of his videos are good
yep he is my favorite, very chill guy
so wait is the answer
$d/dx 52/7 ^7sqrt{3-2x ^11}$
Daddy Goat
,rotate
try not to say d/dx = the original function
u wanna do
$\frac d{dx} [8(3-2x)^{-\frac 47}]$
anyways
oh you mean the {}?
this
ok so look at ur application of the chain rule
when u took the derivative of the inner function
3-2x
whats the derivative of that
ye
give me a sec
Stephen
also howd u get 52?
I multiplied 2 with -4/7 and then
56/7 - 8/7
Oh yeh that should have been done first
ur final answer looks good now, just make sure u have parentheses around (3-2x) otherwise it looks like 3-2x^11
Aight, I will try to rationalise it rn and send the simplified form
idk what if my teacher asks me that during the exam
then do it, but u wont be able to rationalize this
ok well thank you for the help man 💪🏽
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part b, i worked out part a using cosine rule and have length ac but have no idea how to work out length dc
Ig you can equate the power of the point(X) along AX and DX
what do you mean equating the power of the point
From the external point X, if a line is drawn to a circle intersecting at one or more points then product (BX)(AX) is a constant
Have you ever come across anything like that?
im 14 bro 😭
no
it sounds more intimidating than it actually is
is this not calculus stuff
makes sense
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could someone please help me? // check for convergence/divergence of series
@hasty warren Has your question been resolved?
expand the denominator then compare the highest powers of the numerator and denominator
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can u please write it out for me rq?
no do it yourself
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hello can someone explain this
like how are they doing that
pretty sure that's just direct application of power rule
Yeah
it is but im not sure whats going on
d/dx(x^n) = nx^(n-1)
Do you know why the power rule is true
So what do you not understand completely
what is happening in the first step
they found the derivitive of x^4
which is 3x^4
4x^3 but yes
so what's confusing
then whats happening in the second step
Thats the other rule that i forgot the name of where you can take constants on a temporary vacation outside the derivative
So it can see the world
do you have a textbook...reading it would probably help
#constantslivesmatter
he is not actually useless
Yes
(what is the next step)
@uncut roost
https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/03%3A_Derivatives/3.03%3A_Differentiation_Rules
Just read this. This clears up everything you're asking. From there, it's plug and chug with the power rule
He comes home from the vacation after the student finishes the derivative with a new sense of self worth and freedom
I'm just going to leave cause I'm cringing at this conversation
LMAO
no wait
DONT LEAVE!
@lost gyro how do you know if the constant has to go out
Generally you want to get the multiplication constants out of the derivative
Sadly the fate of the addition constants in this case is death from overworking
But multiplication constants can go outside the derivatice
And it becomes easier to solve
Yep
wait where is the vacation place
He gets reduced to zero
where is he even going
Outside the derivative sign, symbolizing his dream of escaping work and going to the places of his dreams
Whether it be hawaii, or maybe a nice cruise ship in mexico
Whatever it desires
Its implied
They just skipped a step
it's not implied... it's indicated by the f'(x)
does he have to leave?
Yes but moving it out of the derivative and back in is implied
Yes he does
always?
Yea
Same thing again basically
cant they do that for the second step too
yes
They do 6*2/3
no
multiply it from the top
the little top part multiplied by the first number
the exponent
no they didnt
they f ' (x) it
only the x^4
🤬
WHY DID THEY MAKE THIS TECHNIQUE
okay
i understand now
Wym
x^4 = 4x^3
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hello i need help
You can expand it
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Can someone explain this to me?
I dont understand any of it
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I have to factor by completing the square and I swear I did everything right but apparently the answer key says I’m wrong (second pic)
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1)Apply herons
2) BC let be base
Write equation of BC and drop a perpendicular from A and find its length and 1/2 b * h
Kinda like this
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notice that n choose k is the number of subsets of S with k elements
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If a quadrilateral has 2 pairs of parallel sides then the opposite sides are congruent
