but like I said the point of taylor series is to avoid using annoying functions such as e^x
#help-0
celest anvil
oh i wasnt told to
ocean sealBOT
ScapeProf
celest anvil
wait so what is M?
noble sinew
like obv the error is what you get when you evaluate the two functions at 1.5, however that isn't normally what you do
here
celest anvil
and what is t?
noble sinew
max value of f^(n+1)(t) in an interval, but since they ask for at x_0=1.5 it is just 1.5 here
but probably check what you are meant to do
celest anvil
so that equation gives me the max?
noble sinew
if you are just meant to use a calculator you just evaluate the two functions and there difference at 1.5
celest anvil
i don't think im supposed to use one
noble sinew
however the whole reason for using taylor is to avoid that, hence there exists theorems like the one I said above
celest anvil
but even if i did evaluate the difference the answer wrong
celest anvil
like this right?
celest anvil
no kept it the same
celest anvil
nope
noble sinew
there you go
in feedback they even said what to use
which is the same as what I typed
you should always round if you leave it as x number of digits? what
noble sinew
first step is finding K, which I called M_n
celest anvil
it says |f^4(t)|<=Mn
noble sinew
okay so seems like we need the 4th derivative does it not
celest anvil
e^x
noble sinew
and plug in x=1.5
celest anvil
e^1.5(t) what is t
celest anvil
|e^1.5(1.5)|
noble sinew
no
celest anvil
nvm
celest anvil
e^1.5
noble sinew
now you have K and just calculate now
celest anvil
noble sinew
,calc e^1.5
ocean sealBOT
Result:
4.4816890703381
si
jagged jetty
someone can help me cuz im dumb
noble sinew
just some misunderstanding ig. Like obv the error is the two functions evaluated at 1.5, but then we have to use our original function which we don't want (why we even using Taylor in the first place then?). Instead we use the theorem and give an upper bound on the error (which as we see is like 4x greater than the actual error) (when finding max on an interval for n+1th derivative you often just use very extreme inequalities to make calculations easier which can make our bound on maximum error a lot bigger than it actually is).
weary lance
celest anvil
just some misunderstanding ig. Like obv the error is the two functions evaluated...
i noticed that for max, the x value you plug into the n+1 derivative is the larger one
so in this case 1.5
noble sinew
no its for when its asking for the maximum error of |f(x)-T_n(x)| on an interval [a,b], so for example maximum error of |f(x)-T_3(x)| on [-1,1]
you then have to maximize the n+1th derivative on that interval and evaluate at that point
here our interval was just [1.5 , 1.5], which only contains the point 1.5 so nothing to maximize
maximising a big complicated polynomial on an interval can be very annoying hence you often just apply extreme inequalities like I said to give an obvious upper bound
celest anvil
Oof
I thought it was 0 to 1.5
Ok
It’s because some functions get bigger when the value gets smaller nvm
weak plaza
Im confused on the proper order to do this problem
weak plaza
So 1/4 correct?
topaz scaffold
Addition last
topaz scaffold
So 1/4 correct?
No
alpine sable
Yes
topaz scaffold
I meant just for the square
Oh yes
alpine sable
Yes
weak plaza
Cool thanks guys!
alpine sable
2 * (1 / 2) * (1 / 2) + 6 + 8
topaz scaffold
Is logarithmic differentiation just take the log of both sides and do implicit differentiation basically?
alpine sable
2 * (1 / 2) * (1 / 2) + 6 + 8
2 * 0.25 + 14
0.5 + 14
14,5
oak chasm
@topaz scaffold You can do it without that. f' = f (ln(f))'.
topaz scaffold
I'm not understanding the notation, sorry
oak chasm
The derivative of f is f times the derivative of ln(f).
reef dust
oak chasm
,rccw
ocean sealBOT
pseudo bramble
Can someone please help me with this and 3 more?
alpine sable
what have you tried so far?
peak gorge
Me or TTV?
alpine sable
TTV, but you were before so they should delete theirs or you can repost yours.
peak gorge
I actually don't expect people to know how to do IFDTs
alpine sable
would also recommend that you post yours in an adv channel
yeah, that's why i said it.
you are more likely to get help there
peak gorge
Ok, so just help me in some other topic
When doing an operation on a function defined by parts, does the operation apply to parts as a sum?
I mean, like if one would apply the Laplace transform on a function defined by parts, would the transform be the transforms of each individual part summed?
pliant oracle
what do you mean by 'by parts' here, do you mean a function defined as a sum/series of other functions?
peak gorge
I mean this
pliant oracle
oh, piecewise functions, sure
i can't really say a general thing as there's no real difference between these functions and 'normal' functions other than the way you define it
tall marten
alpine sable
Please don’t multipost
topaz scaffold
They are different questions I think
alpine sable
They obviously havent made any effort at all
tall marten
never mind ill jsut fail then
alpine sable
We’re here to help you learn not give you answers
tall marten
i know i just need help how to understand it
alpine sable
So from the questions you posted I gather you don’t understand ratios
If so that’s fine, i’m happy to explain
alpine sable
No, we can do it here
That’s what the channels are for
so ratios are about relative quantities
alpine sable
If you have some ratio 1:2 between two things A and B, it means that for every A you have, you have 2 Bs
for example, please post your first question real quick
tall marten
alpine sable
Right, you have 6 cups of flour for every 2 cups of milk
What do you think the ratio of flour to milk is going to be?
alpine sable
If you have some ratio 1:2 between two things A and B, it means that for every A...
No, following what I said here
eager plume
Ñ
tall marten
so it would be 12 cups of flour and 2 cups?
or
2 cups and 12 cups
4 cups or 6 cups
alpine sable
Not quite, no
I want a ratio x:y of two numbers
I don’t know if you’ve understood what a ratio is yet
tall marten
No i do i just forgot the whole process
alpine sable
Well the process in this case is very simple
If you have 6 cups of flour for every 2 cups of milk, you have a ratio from cups of flour to cups of milk of 6:2
alpine sable
I literally told you
tall marten
why im i so dumb
alpine sable
12:4 is equivalent, but I don’t know why you’re multiplying by 2
tall marten
what i supposed to be multiplying by?
alpine sable
Yes
alpine sable
Yes
tall marten
oh so it actually says what is it
alpine sable
In this question yes
It is telling you the ratio and you just have to recognize that
zenith spruce
someone help
alpine sable
Ok now that you seem to understand ratios i’m going to sleep
tall marten
...
zenith spruce
?
alpine sable
,calc 817*918/9
ocean sealBOT
Result:
83334
yea.
alpine sable
Although if you have (x*y)/z
Then you can divide either x or y by z
And multiply the result
For example, in your question
alpine sable
You can do 918/9 and then multiply by 817
zenith spruce
You can do 918/9 and then multiply by 817
ok
alpine sable
Nah go find exercises online, I can’t be bothered to test you sorry
alpine sable
Oh lol
tall marten
@alpine sable do you have a degree?
tall marten
Nice
alpine sable
Thx
gaunt magnet
ho ho
hi
. Find the horizontal asymptote. Find all critical
points (i.e. find both (x , y) values). State the intervals of increase and decrease and intervals of concavity. Find the points of inflection (i.e. find both (x , y) values). Find all local maximums and local minimums. Show all of your work! Find all points to 3 decimal places.
Having alot of trouble with this question
calm hearth
I would take the value of the function as x approaches infinity to find the horizontal asymptote, and differentiate with the quotient rule to find the critical points by solving the derivative for zero
Then repeat the differentiation for the point of inflections.Then apply the first derivative test to find the local maximums and minimums, and do similar for the inflection points
Then test the intervals in between to find the intervals of increase and decrease and intervals of concavity
alpine sable
can anyone help me with this question: jane bought two new skirts for school. one cost 15 less than twice the cost of the total cost for both skirts was 75, what was the cost of each skirt?
sly mantle
@atomic lodge don't multipost
atomic lodge
sly mantle
pls stay in the first channel you posted in
undone scroll
can someone explain this pls
how do u use chain rule with this and why is it du/dx
placid zinc
Without getting into the "why", do you understand why the line after "using chain rule" is true?
undone scroll
not really
placid zinc
Note the left could be written as dF(x)/dx
sly mantle
we have $F(x)=g(u(x))$ with $g(x)=\int_1^x\sin$
ocean sealBOT
Fateful Clash Among the Cosmos
sly mantle
the use of chain rule is clear when writing F as a composition
sly mantle
by chain rule, F’(x)=g’(u(x))u’(x)
sly mantle
you understand the use of chain rule to write F’(x)=..?
undone scroll
so why isnt the answer just sin(u) using ftc
sly mantle
g’(x)=sin(x) by ftc
undone scroll
you understand the use of chain rule to write F’(x)=..?
yeah i understand on the format
undone scroll
oh ok
placid zinc
Note that ftc works when the upper bound is just x.
In this case, it's a function of x. So, ftc isn't directly applied. But, we can fix that with the chain rule
undone scroll
oh ok
wait so why isnt the left term d/dx[F(u)]
or why is the bottom one u(x) but the top one is x
tall marten
Is this right
ionic jewel
celest anvil
but you should be looking at the ratio of paint to birdhouses
undone scroll
Note that ftc works when the upper bound is just x.
In this case, it's a functi...
could i ask why you would substitute u instead of the actual numbers? is it easier that way to solve and then plug in the end or is it always required
celest anvil
can someone explain to me
proportionality is the ratio. 2 cups of milk to 3 tablespoons becomes 8 to 12
what value did 2 to 3 multiply to become 8 to 12?
celest anvil
correct
judging from the other problem, the theme of your work is ratios and proportions
in case you didnt know
tall marten
oh
placid zinc
@undone scroll
What would "the actual numbers" be here?
undone scroll
<@448700868649418753>
What would "the actual numbers" be here?
it was u(x) = sqrt(x)
i sort of get it now though
tall marten
vapid smelt
hey, how would I do this $2^{y+3} - 9 \cdot 2^y + 1 = 0$
ocean sealBOT
Inheritanc-e ♦
vapid smelt
I am confused in the part to turn this into quadratic
alpine sable
U do a^2 + b^2 = xyz^41
vapid smelt
huh?
sharp sigil
2^y as x
gaunt magnet
<@&268886789983436800> i was ghost pinged 5 times
sly mantle
for future reference, report by dm’ing @fierce herald
alpine sable
lmao
supple prairie
How do you solve
x^2 -36=0
alpine sable
ill show you
but you understand what i did up there?
how i moved th3 36 to the other side
supple prairie
yes
alpine sable
okay cool
alpine sable
pretty much, we added 36 to the left, and added 36 to the right
supple prairie
ah,ok
supple prairie
(x ) (x ) ??
alpine sable
so far weve got x^2 equal to 36 right?
alpine sable
now we wanna find x
supple prairie
yes
supple prairie
yes
supple prairie
ohh
alpine sable
weve rooted x^2 on the left hand side
but we have to root the right handed side as well
because whatever we do to the left, we have to do to the right
simliarly to how we added 36 on both sides
alpine sable
aight you tell me whats next
remeber x^2 is now x since weve rooted it
we have also rooted 36
supple prairie
so x=6?
alpine sable
sweet!
aight got one more question for you, just to make sure youve got it
x^2 = 49
solve for x
supple prairie
ah thanks
alpine sable
well to turn degrees into radians
you multiply by pi/180
we can see that angle is close to 180
so 180 x pi/180
ancient dragon
Could someone help explain this. The teacher didn’t go over problems like this and I have no idea how that’s the right answer.
ocean sealBOT
RipeOrange
somber osprey
this is math
topaz scaffold
this is math
Yeah
ancient dragon
Gotcha, I though dividing by 0 was undefined.
topaz scaffold
For limits, something over 0 means that there's an asymptote there
Which means that it goes to plus or minus infinity at the limit
placid zinc
You get 2 / (w + 1)
Where w is a number slightly larger than -1
topaz scaffold
0/0 means that there's either asymptote or a hole
placid zinc
That's why you get +inf and can disregard the possibility of -inf
topaz scaffold
^^
ancient dragon
Ok thank you
deep scroll
candid thistle
no
topaz scaffold
Isn't that like a roblox game?
jolly stone
<@&268886789983436800> please delete this, i joined by accident and somehow got backlogged by bot in that server
sly mantle
b&
jolly stone
hopefully no nigerian princes will chat at me
alpine sable
Hey can sm plz calculate the hours I’ve got
topaz scaffold
I think you can do it, mate
lapis jacinth
Hey folks, I am currently trying to program a voronoi diagram problematically, and really confused about what the endpoints of this parallel bisector would be. Anyone got any ideas?
Edge parallelbisector(Point a, Point b){
Point midpoint = midpoint(a,b);
float rise = (a.y - b.y);
float run = (a.x - b.x);
//todo work this section of math out
Point endPointA = new Point(endpointAX,endpointAY);
Point endPointB = new Point(endpointBX,endpointBY);
return new Edge(endPointA,endPointB);
}
Trying to solve the endpoints at new Point(Math,Here)
Be gentle, am self taught mostly with math and its not my strongest point
I know I need the negative reciprocal which is run/-rise (I think)
crystal tapir
Can I get help with this question
Ben is driving his train slowly. He realises he’s left an important package in the last car of the train. He needs to hop out of the train, walk all the way to the back to retrieve it, and then walk to the front of the train again.
The train is 3 kilometres (km) long and it’s going at 1 km per hour. Ben can walk at 2 km per hour.
Ben stops the train to retrieve the package, as he knows it’s the safest option. But he wonders if it would have been faster to let the train keep rolling. Or, perhaps it would take the same time either way.
Can you work out the fastest option?
topaz scaffold
Occupied channel, Beluga
jolly stone
Hey folks, I am currently trying to program a voronoi diagram problematically, a...
when does the point end? i'm a bit confused here
so there's a point A and B on the plane (assuming 2D), and you want to find parallel bisector?
lapis jacinth
Correct
jolly stone
if you're doing Voronoi diagram shouldn't it be perpendicular bisector?
lapis jacinth
Attempting to make a voronoi diagram for a map creator I am making
jolly stone
you want to find a line that is perpendicular to AB and bisects AB, right?
lapis jacinth
yes
jolly stone
yep that's a perpendicular bisector
lapis jacinth
this function is taking the two sites, working out the midpoint betwwen them and is then supposed to create an Edge
jolly stone
and since it's a line, there's no end unless you know where else the points are
so basically it's like this
lapis jacinth
Can I share the whole class? I don't know if you know java?
jolly stone
i can read them, forgot how to code but i can google
lapis jacinth
I have borders partially set up (4 sites that act as a border so its not going to infinity)
This is the third/forth time I have rewritten it this week
jolly stone
because you don't know when lines end with only two points, you need to determine when it should end with more points
for example in this case
if you have only A and B, it can extend to infinity
you have to know point C and its intersection E
lapis jacinth
Oh, its a triangulation
jolly stone
but you can see E is the circumcenter of the triangle ABC
because 3 perpendicular bisectors all intersect at the same point
now given so many points, how do you know you find the closest point C, that's another problem
my idea is to scan all n points in plane, and detect if triangle with vertex A,B, and that point contains another points inside in it or not
tbh, it is very very very slow compared to coloring individual pixels
lapis jacinth
Thats vaguely the idea, I am currently solving each point against all points then reducing it down (In theory)
Its for a fantsasy map generator I am creating
jolly stone
if you also want to know all the cells' vertices and edge endpoints, there's a lot of computation involved, and probably takes a lot of time to run
jolly stone
i would actually find other libraries to do this, cuz it's pretty hard to program tbh
lapis jacinth
Nah, the point is to learn and be able to write difficult stuff myself ❤️
jolly stone
library scipy in python has this function https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.Voronoi.html
lapis jacinth
Literally self taught and doing so by setting difficult challenges, its been really helpful
Makes me study hard
jolly stone
i see, i wish i could do that ;w;
lapis jacinth
watched about 5 hours of algebra videos today already
jolly stone
but for me i don't think it's an easy algorithm to grasp in a few hours
you could do that, but i definitely can't do that in a few minutes lol
jolly stone
i would try read the source code of this and grasp the concept behind voronoi diagrams
it's also part of the learning
lapis jacinth
Oh I spelunk the crap outta github lol
jolly stone
trying to code this algo by myself is like discovering calculus lol
jolly stone
sorry that i cant help with this ;w;
lapis jacinth
no worries ❤️
jolly stone
and sadly scipy library just hid the source code for voronoi algorithm ;-;
you might try ask #numerical-analysis for help from more advanced gods there too
small cypress
crystal tapir
Can I get help with this question
Ben is driving his train slowly. He realises he’s left an important package in the last car of the train. He needs to hop out of the train, walk all the way to the back to retrieve it, and then walk to the front of the train again.
The train is 3 kilometres (km) long and it’s going at 1 km per hour. Ben can walk at 2 km per hour.
Ben stops the train to retrieve the package, as he knows it’s the safest option. But he wonders if it would have been faster to let the train keep rolling. Or, perhaps it would take the same time either way.
Can you work out the fastest option? if u can help pls ping greatly appreciated
karmic jungle
do you know what's bigger than
1056x720
but smaller than
1920x1080
does anyone know how to figure this out
topaz scaffold
Any number in between those numbers
karmic jungle
no just the same proportions
if i could double it it'd be easy
but i ant go higher than 1920x1080
crystal tapir
he just spams his question everywhere
sorry man i just wanted some help
topaz scaffold
no just the same proportions
You still can choose any number for one of the sides, then scale the other side accordingly
karmic jungle
what do you mean how do you know what the other nunmber will be
wicked breach
watched about 5 hours of algebra videos today already
i cant even watch a 2 minute video about addition 💀
karmic jungle
if i put in 1920 the other number won't match
thin urchin
so i tried using python and a graph and a data table
no luck finding the limit approaching zero for the function
hope its not cuz of rounding error
karmic jungle
it's slightlhy too big is there a way to reduce 1920 by 10%
or will that screw up the entire ratio
wary stream
no luck finding the limit approaching zero for the function
Approach zero from both sides
karmic jungle
is that still a 1056x720 ratio
topaz scaffold
Should be
karmic jungle
because if 1056 jumps up to 1920 how does 720 jump up only by 300
thin urchin
Approach zero from both sides
yea but its not seeming to approach anything and the answer is not 'does not exist'
topaz scaffold
yea but its not seeming to approach anything and the answer is not 'does not exi...
So you got your answer
topaz scaffold
because if 1056 jumps up to 1920 how does 720 jump up only by 300
Because that's kinda how it works
thin urchin
no
because the answer is not DNE
maybe my python program is giving me a rounding error
topaz scaffold
,w differentiate √(x+16)-4
ocean sealBOT
wary stream
Instead of 16
woeful pulsar
is this a graded test
wintry vortex
Wait, did it just want me to show the problem expanded?
celest anvil
remember (3y-8)^2 is just (3y-8)(3y-8)
woeful pulsar
wait, special product?
maybe it's special because it's a square
thought it's some weird definition for a sec
wintry vortex
So is it just wanting me to foil it out and show the porblem expanded and simplified?
celest anvil
you didn't follow the example
wintry vortex
Cause that would be so much easier
gaunt magnet
😮
celest anvil
plug in a=3y and b=-8 for a^2-2ab+b^2
wintry vortex
wouldnt A=3y?
manic glade
how would you go about calculating the number of possible combinations of 7 letters in all lengths where letters cannot repeat and the order doesnt matter ?
wintry vortex
got it ty
manic glade
i thought it would be something like 7 choose x for 1 to 7 and add them up but the result doesnt make sense
ah probably need to subtract the unions
prime badge
same as 2^7 − 1
manic glade
127 doesnt make sense though
manic glade
because it takes maybe a minute to go by the equivalent scenario by hand of just matching items 127 seems too high
by hand as in with physical items
maybe im translating the scenario incorrectly
prime badge
127 is too high because it takes a minute to count manually?
That doesn't make sense
you expect to take a whole second to count one thing?
prime badge
yeah
you should be able to build 2 combinations per second
list combinations for ABC
if you get 7, you're translating correctly
drowsy field
anyone can help with these?
i am bad at curves tips to get better on it would be nice as well
celest anvil
you can always graph them in desmos
jolly stone
you mean the arc length of y away from black point?
yeah you can find arc length between point A and point B of parabola using arc length formula integral sqrt(1+f'(x)) dx from A to B
modern iron
8th grade math class is really hard
jolly stone
it is a bit hard to solve i think, searched wolframalpha and got 1/4 (2 * t * sqrt(1 + 4 * t^2 + arcsinh(2 * t)) for arclength from (0,0) to (t,t^2)
if you want the reverse, aka y distance away from x you gotta solve the equation to find location t
1/4 (2 * x * sqrt(1 + 4 * x^2 + arcsinh(2 * x)) - 1/4 (2 * t * sqrt(1 + 4 * t^2 + arcsinh(2 * t)) = y
definitely not an easy equation to solve
well except if you code and solve for numerical value instead that might be possible, you might get 2 solutions (left/right from point x)
just to clarify, the curved arclength right?
t is the point (t,t^2) in parabola x^2 such that the arclength from point (t,t^2) and (x,x^2) is y
the input is x and y, you just gonna solve for t
junior beacon
jolly stone
it's an arclength so it's definitely not simple
junior beacon
😐
jolly stone
there's a closed formula already there, so there's no way to make it any simpler
if you accept some tolerance for error, you might try approximating some functions
junior beacon
:l
jolly stone
but even so, it will have errors for large values of x
did some python
>>> from scipy.optimize import fsolve
>>> import math
>>> def solve(x,y):
... equation = lambda t : -1/4*(2*x*math.sqrt(1+4*x**2+math.asinh(2*x)))-y+1/4*(2*t*math.sqrt(1+4*t**2+math.asinh(2*t)))
... return fsolve(equation,x+y)
...
>>> solve(0.5,1)
array([1.0701783])
>>> solve(0.5,0)
array([0.5])
>>> solve(0.5,0.1)
array([0.57617289])
>>> solve(50,0.1)
array([50.00099996])
>>>
not sure what your programming language is but you can find other libraries to solve optimization
this one is only for finding right side, if you want left side just change equation to 1/4*(2*x*math.sqrt(1+4*x**2+math.asinh(2*x)))-y-1/4*(2*t*math.sqrt(1+4*t**2+math.asinh(2*t))) (switching sign for the x term and t term)
jolly stone
it's much faster than 100 times per second actually
depending on initial conditions, so i'm not sure
sadly about 0.2-0.5 ms
yeah if it's in C then should be much much faster
reef dust
Use integrals to solve this
dim cloud
Use integrals to solve this
No, but what limit is it?
reef dust
I think there is no certain type to it
alpine sable
jolly stone
Hi there, can anybody tell me what kind of limit this is?
you can manipulate the terms like this:
1/(n+1) + 1/(n+2) + ... + 1/(2n)
= 1/1 + 1/2 + ... + 1/(2n) - 2 * (1/2 + 1/4 + ... + 1/(2n)
= 1/1 - 1/2 + 1/3 - ... + 1/(2n-1) - 1/(2n)
and this should be a well known series
dim cloud
you can manipulate the terms like this:
1/(n+1) + 1/(n+2) + ... + 1/(2n)
= 1/1 +...
So its a limit of series?
sage bronze
$$\frac {4 \sin {\theta} - \cos {\theta}}{4 \sin {\theta} +\cos {\theta}} = \frac {1}{2}$$
$$(4 \sin {\theta} - \cos {\theta}) \times 2 = 4 \sin {\theta} +\cos {\theta}$$
$$8 \sin {\theta} - 2\cos {\theta} = 4 \sin {\theta} +\cos {\theta}$$
$$8 \sin {\theta} - 4 \sin {\theta} = 2\cos {\theta}+ \cos {\theta}$$
ocean sealBOT
HELLOBELLO
sage bronze
express sin in terms of cos and you should be able to calculate cot @alpine sable
jolly stone
So its a limit of series?
yep you can find the limit of that series
alpine sable
haha
echo wadi
K is the set of all three-digit numbers that do not contain 0 but have at least two digits in common. If x is the median and y is the range of all elements of K, then the value of y-x is?
So I was helping a friend with his assignment and they had this question, I am kinda confused with two digits in common part like wouldn't there be a different set for each value of those two digits
vale sapphire
first of all, don't spam questions
it doesn't make them look urgent, just annoying
second, calculate the determinant and see when it's equal to 0, boom
if you just wanna see if a small (< 4x4) matrix is invertible, the determinant works
it's what the determinant is : a scalar quantity that describes the invertibility of a matrix
for things higher than that, use row reduction
vale sapphire
please don't ping people individually
reef dust
Calculate ratio of sides of the two triangles
And you know that ratio of areas is square of ratio of sides
reef dust
👍
jovial breach
its 0
reef dust
It's right
reef dust
No such value exists
jovial breach
^
reef dust
At least in this timeline 🙃
vale wigeon
you're stuck where?
at the beginning, not knowing how to start?
or somewhere further down the line?
round crown
not knowing how to start....
vale wigeon
okay
could've said so outright.
alright.
would you mind if i presented you with a simpler but similarly-structured equation?
round crown
sure
vale wigeon
here it is: $10 - \frac{z}{8} = 4z$
ocean sealBOT
Ann
vale wigeon
can you solve this equation for z?
round crown
yeah i can
vale wigeon
okay, solve it for z and share all of your steps.
ideally, post a picture of your work, or type it up in LaTeX if you're able.
the work will be important in explaining how to solve the equation you came here with.
ping me once you're done or stuck.
alpine sable
**Ann**
do you only multiply the numerator with 8 since a * b/c = ab/c or do you multiply the whole equation with 8?
hollow swift
Can anyone help me how to find absolute value of 3+4i
reef dust
Can anyone help me how to find absolute value of 3+4i
Absolute value of complex means it's modulus
hollow swift
Absolute value of complex means it's modulus
How to solve it?
reef dust
Isn't it (real^2+ imag coeff^2)^1/2
hollow swift
Oh thank you
teal garnet
can I use the power law to take the derivative of sqrt(x^2+1)?
teal garnet
why is that?
vale wigeon
sqrt(x^2 + 1) isn't a pure power of x nor a sum of pure powers of x
teal garnet
what do you mean by sum of pure powers of x, could you give me an example?
vale sapphire
a polynomial
vale wigeon
not quite
vale sapphire
right, you can have non-integer powers mb
vale wigeon
when i say ``pure power of $x$'', i mean a function of the form $ax^p$ where $a$ and $p$ are real constants (and i allow $p$ to be a non-integer to that end)
ocean sealBOT
Ann
vale wigeon
for example, $\sqrt{x}$ would fall under that definition (as it is $1x^{1/2}$)
ocean sealBOT
Ann
teal garnet
you mean $1/2x^{1/2}$?
ocean sealBOT
Kono
vale wigeon
no, i'm talking about the function itself, not its derivative.
even so, you forgot the parentheses.
teal garnet
ohh im sorry now i get it
teal garnet
**Ann**
but let's say if x= u^2 +1 , would it be still pure?
or x must strictly always be just x
vale wigeon
i said what i said. x must strictly be x.
teal garnet
okay roger
vale wigeon
if it's anything else, you will require the chain rule.
teal garnet
I think now I understand since if it's something else it fits the chain rule definition and not the power rule definition. Did I get that right?
vale wigeon
well
you are mostly right, yes
to say you aren't would be to invoke a technical caveat bordering on the pointlessly bureaucratic
teal garnet
please point out what I said was wrong, since the details may make a difference
vale wigeon
they won't
but if you insist: the chain rule can always be applied in a trivial fashion by means of a trivial substitution that entails only renaming one variable and nothing else,
or by letting one of the functions composed be the identity
brittle nimbus
can anyone help with what each of these is?
jagged imp
what's giving you trouble with this?
brittle nimbus
im not sure whether I'm right
jagged imp
then... post what you've tried so far and say why you're not sure
brittle nimbus
i.) not injective or surjective
ii.) injective but not surjective
iii.) bijective
vale wigeon
you're wrong for all of them
reef dust
I think first is injective
brittle nimbus
you're wrong for all of them
Fundamental misunderstanding haha.
vale wigeon
(i) is injective only
(ii) is surjective only
(iii) is injective only
it should be somewhat clear that $ix = iy$ implies $x = y$ even without assuming $x, y \in \bR$ simply by dividing both sides by $i$
reef dust
I think first is injective
It covers only purely imaginary and not all complex no.s
ocean sealBOT
Ann
vale wigeon
and as arya22 just said the range of the function in (i) is only the imaginary axis, rather than all of C as would be required for surjectivity
brittle nimbus
Right. That makes more sense. I didn't think about it enough for i.). Thanks guys.
vale wigeon
are you going to retry ii and iii or should i explain these too
buoyant willow
Hey ho, I'm trying to teach myself something and I'm unsure as to how to do this.
So if anyone can help, that'd be nice.
vale wigeon
@buoyant willow channel busy please move
buoyant willow
Alright.
brittle nimbus
true true false true, bet that's wrong as well.
vale wigeon
let's see
brittle nimbus
need to look at my notes for this for sure.
vale wigeon
(i) is correct
(ii) is wrong
(iii) is wrong
(iv) is correct
jade peak
Hey, How do i check percentage between a value X and 0? .. Percentage can be positive or negative
gray isle
do you have a specific question where this is coming up?
what you asked is unclear and vague
jade peak
i have histogram , value x can go above or below zero line of histogram , thought maybe to display percentage of x from histogram 0... not sure it's possible since no range
remote seal
U=R, Solve the inequality, Can someone help me?, im stuck in this question
reef dust
anyway, try to divide it into two cases so you can cross multiply
x-7 might be negative so we cannot directly cross multiply
reef dust
> try to divide it into two cases...
Instead of two cases we can directly subtract 2 from both side.....I think it might be more convenient
rigid smelt
either way you still have to divide the inequality into two cases
the way you are doing it is you are manipulating it into a product so that you can check the sign, which is viable and no different because you still are considering cases of x
reef dust
👍
reef dust
i got a bit stuck
Square on both sides as both sides are positive
reef dust
👍
errant dagger
ty
I couldn’t do 13a either
i’m a tad confused on tension and which way it acts
reef dust
Break AC into 2 components.....one parallel to 50N force and other parallel to AB
Now balance them as the particle is in equilibrium
errant dagger
whaty does tension 50n mean
cus the diagram shows
just like a force downwards of 50n
@reef dust yah i dunno how to balance them cus idk the tension of AB
waiut
its 2x
crude zephyr
Can someone help me?
reef dust
cus the diagram shows
It's not any tension......it's just an external force
reef dust
but im still confused on directions acting
Away from object
errant dagger
the tension is fighting against the downwards force right
reef dust
the tension is fighting against the downwards force right
Rather a component of tension
reef dust
wait so does AB have no tension???
Other component of AC as I mentioned balances it
errant dagger
ahh okay right i gotcha
crude zephyr
Knowing that the products of the roots of the - (photo) equation, calculate the value of M
errant dagger
bro
crude zephyr
i need help pls
reef dust
Lol
reef dust
Knowing that the products of the roots of the - (photo) equation, calculate the ...
Product of roots is 5.....so (m-3)=5
errant dagger
hmm
yeah im still cnfused @reef dust
I dont seem to have enough info from what Im doing
reef dust
I dont seem to have enough info from what Im doing
Let AB=T.....then AC=2T
Then use Pythagoras
errant dagger
can I do
AB + AC = 50
AC/2 + AC = 50
3/2 * AC = 50
AC = 100/3?
well
it gives me a maths error
so I guess not
I dont rlly understand :/ @reef dust cus I dont have AB
reef dust
Use Pythagoras theorem
errant dagger
How
reef dust
For right angled triangle
errant dagger
I only have one value
reef dust
I assumed the unamed point in your diagram as B
crude zephyr
Calculates the sum and product of the equations without solving them
reef dust
reef dust
Calculates the sum and product of the equations without solving them
For a quadratic equation ax^2+bx+c
Sum=-b/a
Product=c/a
reef dust
You got it ?
errant dagger
no
hold one one second sorry
I do now, sorry @reef dust
I got pi/3, or 60 degrees?
reef dust
Wait I will solve it too
reef dust
I got pi/3, or 60 degrees?
👍
errant dagger
i will try ii thank you very
late moss
errant dagger
sorry bruh 
tight basin
Seemingly simple question but apparently I keep getting it wrong and I don't know what I am missing. Suppose z = y / x. If z = 0.6 x 10^7 and y = 3.5 x 10^-3, what is the value of x?
errant dagger
Seemingly simple question but apparently I keep getting it wrong and I don't kno...
sub values for z and y in
multiply x to LHS
then divide z to RHS
and solve for x
errant dagger
what did u get
tight basin
2.1x10^4
tight basin
(3.5x10^-3) x (0.6x10^7)?
split oriole
(3.5x10^-3) x (0.6x10^7)?
Base are same so add -3+7 =4 ,and multiply 3.5 with 0.6
Answer will be
3.5*0.6 x 10^{4}
split oriole
2.1*10000=21000
split oriole
Write it like 2.1*10^4
alpine sable
i got x=10 and y=5 but 10+5 is 15 not 16, what is wrong?
reef dust
i got x=10 and y=5 but 10+5 is 15 not 16, what is wrong?
Is x+y=16?
alpine sable
yeah
gray isle
what are you doing?
alpine sable
yes i think
alpine sable
You’re more likely to get an answer there, this question seems a bit too advanced for questions channels
sinful glacier
rightt ill move all this to there then, thank you
alpine sable
Only thing i can help you with is that https://en.wikipedia.org/wiki/Fibonorial might be helpful if you havent looked at it
alpine sable
Don't worry about it
dark basin
is this channel available?
wispy olive
I am afraid I will take the opportunity earlier.
dark basin
what?
nocturne saddle
CR/AP+CR/BQ=1
nocturne saddle
Ann are you free?
divide 2 sides for CR
alpine sable
i need help with c and d
golden arch
thorn kindle
solve for y' and integrate
alpine sable
did you try anything to try to tackle it?
hot wedge
thing is, i don't know how to do functions a ton because I didn't focus in class 💀
alpine sable
or which ideas/attempts you tried?
ocean sealBOT
reef dust
i got this wrong on a test
Best way to solve is directly checking the options
hot wedge
alr
alpine sable
once you've watched it, we can continue
alpine sable
once you've watched it, we can continue
can u help me meanwhile?
you can post yours in a free channel, and you might get help then
alpine sable
that's okay, step by step
hot wedge
alr
alpine sable
so i'm guessing you are also new to function composition
but essentially, let's take f(x)=x-2.
hot wedge
ok
alpine sable
$f({\color{green}{x}})={\color{green}{x}}-2$ can you find what $f({\color{green}{2}})$ will be?
ocean sealBOT
Al𝟛dium
alpine sable
right, good job
now similar idea but with another function.
$f({\color{green}{x}})={\color{green}{x}}-2$ can you find what $f({\color{green}{x-4}})$ will be?
ocean sealBOT
Al𝟛dium
alpine sable
i'll ask again
$f({\color{green}{x}})={\color{green}{x}}-2$ can you find what $f({\color{green}{x-4}})$ will be?
ocean sealBOT
Al𝟛dium
alpine sable
try not to overthink this, it's the same exact idea
alpine sable
great job
alpine sable
okay so now back to our problem
hot wedge
alr
alpine sable
we are given $f({\color{green}{\gamma}})=2f(\delta)$ and ${\color{green}{\gamma}}=2\delta$, can you try to substitute the right equation with what we know into the first one?
ocean sealBOT
Al𝟛dium
alpine sable
this first step doesn't have anything to do with functions, just simple substitution
alpine sable
it's not an 8, it's delta but yes
alpine sable
$f(2\delta)=2f(\delta)$
ocean sealBOT
Al𝟛dium
alpine sable
yeah, it's a greek letter.
alpine sable
okay, so here comes the part, you can and i'm guessing you are meant to go with each option and check if it checks out or not
so let's try so
hot wedge
this is a bit confusing because I can't insert the Y value anywhere in the right equation
alpine sable
yeah i know don't worry about it just yet, this is a functional equation and since i'm assuming you are in precalc, you aren't meant to know how to solve them
hot wedge
im not in precalc
alpine sable
which class are you in?
hot wedge
i actually finished alg 1 in june and im taking alg 2 when high school starts
alpine sable
but my point doesn't change anyways
hot wedge
alr
hot wedge
mhm
alpine sable
we will try now with the first option x, and see if it checks out.
hot wedge
alr
alpine sable
let's try with f(x)=x, what would f(2x) be if f(x)=x?
hot wedge
2x
alpine sable
great, so now let's look at our eqn that we are supposed to check
hot wedge
alr
alpine sable
do you mind if i instead of delta, i write x?
alpine sable
**Al𝟛dium**
for this equation
hot wedge
ok
alpine sable
we have tried with $f(x)=x$ and we've figured out that $\{\color{green}{f(2x)}}=2x$. Now let's check if it's true or not: $$f(2x)=2f(x)$$ you've figured out ${\color{green}{f(2x)}}={\color{green}{2x}}$ and ${\color{blue}{f(x)}}={\color{blue}{x}}$ so we'll plug what we know in: $${\color{green}{f(2x)}}=2{\color{blue}{f(x)}}$$ $$\overbrace{{\color{green}{f(2x)}}}^{\color{green}{2x}}=2{\color{blue}{f(x)}}$$ $$2x=2\underbrace{\color{blue}{f(x)}}_{\color{blue}{x}}$$ $$2x=2x$$
ocean sealBOT
Al𝟛dium
prisma dove
Hi im very bad at math. anybody who can tell me what the median, the average and how many observations there?
reef dust
we have tried with $f(x)=x$ and we've figured out that $\\{\color{green}{f(2x)}}...
Man I think at this level they just needed to check the options
alpine sable
Man I think at this level they just needed to check the options
that is.. precisely what i'm doing?
@prisma dove please read #❓how-to-get-help , this channel is occupied.
prisma dove
ok
alpine sable
**Al𝟛dium**
@hot wedge does what i did there make sense?
hot wedge
so the first answer choice is right bcuz 2x = 2x?