Eh
#help-0
tall topaz
,calc 3^6 -81*3-486
ocean sealBOT
Result:
0
(this means (x-3) is a factor of the numerator)
summer quarry
(this means (x-3) is a factor of the numerator)
Eh
(x-3) still equals 0
0/0 still doesn't make sense
tall topaz
?
x-3 is a factor of the numerator so factor out x-3
do horner scheme or whatever
in fact
,tex \polylongdiv{x^6 -81x-486}{x-3}
ocean sealBOT
Pure
tall topaz
,tex \polyhornerscheme[x=3]{x^6 -81x-486}
ocean sealBOT
Pure
ocean sealBOT
summer quarry
Something like this???
summer quarry
And I can get rid of that (x-3)
white fulcrum
where do i get help
tall topaz
white fulcrum
thankss
neat totem
hi
neat totem
ye
rancid radish
what is quartile 3 of 10,19,21,28,34,37,40,42,43,43,45,50,54,56,61,65,70,88
neat totem
we struggling to know if quartile 3 is equal to 56 or 58.5
10,19,21,28,34,37,40,42, 43,43 ,45,50,54,56,61,65,70,88
Quartile 1 quartile 2 quartile 3
or
10,19,21,28,34,37,40,42,43 43 43,45,50,54,56,61,65,70,88
Quartile 1 quartile 2(median) quartile 3
we search online and results vary on each site
ox ajas
this is box and whisker plot
lone heartBOT
@neat totem Has your question been resolved?
rancid radish
<@&286206848099549185>
lone heartBOT
@neat totem Has your question been resolved?
neat totem
NO
lone heartBOT
@neat totem Has your question been resolved?
buoyant summit
help
lone heartBOT
@neat totem Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
river badge
how do u make an equation out of this
One of the zeros at -2, y-axis is the axis of symmetry and the value of a is 2.
barren portal
What's the standard form of a parabola you have?
storm ridge
What's a?
river badge
2
river badge
What's the standard form of a parabola you have?
you can use any of the form?
standard
Vertex Form
roots of x
lone heartBOT
@river badge Has your question been resolved?
storm ridge
(Sorry for the ping)
twin jewel
lone heartBOT
twin jewel
I don't know what to do
lone heartBOT
@twin jewel Has your question been resolved?
lavish cave
where do the lines on the diagram intersect?
like, what's the x-value
and what's the y-value
lavish cave
7 is correct (wait, your x and y are switched)
but try again, 2 is not correct
you might need to click on the image to make it bigger
twin jewel
yes i just realised that too lol
twin jewel
ok
twin jewel
7 and -8
lavish cave
shit sorry for the typo
lavish cave
yes
twin jewel
so thats the anwser?
twin jewel
ok#
lavish cave
and as we found before, x = 1 and y = 7
lavish cave
it's the same as
alpine sable
Help
lavish cave
Help
the cuboid surface area is 6 rectangles
and circular sector is 60/360 * area of circle
still ibex
but the cuboid is asking for surface area, not volume
you could just calculate the area of each side of the cuboid and add them up
lavish cave
shit
alpine sable
but the cuboid is asking for surface area, not volume
Is it cm² or cm³ for surface area
stark crater
Is it cm² or cm³ for surface area
Surface area is squared (just like area is)
alpine sable
Oh thanks
Idk the area of the sector one tho
Idk how to do it
I havnt done that in ages
stark crater
If it was a full circle could u find it
alpine sable
Probably
stark crater
That is step 1 so start by finding that
alpine sable
Alr
turbid sigil
Think that a full circle has radian 2π, and area of a full circle is πr^2, so what is the area of part a circle
turbid sigil
You have to use the Google keyboard
Download it
Or latex if you know what that is
$\pi$
ocean sealBOT
cali5nia
stark crater
if ur on pc u can hold alt then press 2 2 7
turbid sigil
2π•1/2•r^2 is area of a full circle
turbid sigil
Where the angle is 2π radians
alpine sable
So how do u find a sector
turbid sigil
I don't want to spoil it😭
alpine sable
Dw
stark crater
So how do u find a sector
How many degrees are in a circle
turbid sigil
You can Google it if you really care to
alpine sable
How many degrees are in a circle
360
turbid sigil
But it makes sense if you think about it
stark crater
you are given a slice with 60 degrees
How many slices do you need to form a full circle
alpine sable
You can Google it if you really care to
I have but its giving me a weird symbol like a 0 with a line in the middle of it
alpine sable
How many slices do you need to form a full circle
Ohhhh so u do 360÷60
stark crater
yeah
thats how many slices would form a full circle
you only have 1 slice though, when a full circle is 6. So the area is going to be 1/6 of if it was a full circle
stark crater
When you have something that looks complex, see if you can relate it to a more simple shape (squares,triangles,circles) and find a relationship between them
autumn juniper
Sorry for sneaking in , just wondering if any of you are free to help , thanks.
alpine sable
When you have something that looks complex, see if you can relate it to a more s...
Is the answer 42.416 recurring
stark crater
yeah but to be precise its not recurring if you use the true value of pi, it will be more random
alpine sable
So should I put it in terms of pie?
stark crater
Yeah you usually put the exact value unless they ask otherwise. In this case that means putting in terms of pi
alpine sable
Ok thanks for all the help!
My calculator says in terms of pi it's 27/2 pi
Do I do 27÷2 or do I just leave it at 27/2 pi
stark crater
both are fine. I believe most people would leave it in fraction form though so 27/2pi
lone heartBOT
@alpine sable Has your question been resolved?
calm helm
lone heartBOT
fervent timber
just plug stuff into the scenario
calm helm
just plug stuff into the scenario
what goes where
echo geode
You have h, all you need is to evalute y0 y1 y2 by inserting the values of points
calm helm
looking at the example provided and i dont understand where they get 6 from
echo geode
consider each point coordinates as (x,f(x)) it would help
alpine sable
How do you get one of these bots to help you? I did the tutorial it’s not working😭
lone heartBOT
@calm helm Has your question been resolved?
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@calm helm Has your question been resolved?
sacred plume
I've been struggling with #5 and idk how, please someone tell me what I'm doing wrong or misunderstanding
sacred plume
Here's my work and if you need anything else I'll be more than willing to give it
I thought I did everything I was supposed to am I missing smth or
alpine nacelle
the problem comes from P and P^-1 (more precisely, first column of P seems very dubious, 2nd seems ok)
you should read your lesson about how to find P again
idk your method but something here is wrong
you should get
0
1 instead to have a valid column
lone heartBOT
@sacred plume Has your question been resolved?
sacred plume
you should get
0
1 instead to have a valid column
Ohhh okay i see, lemme look through my textbook again sorry
alpine nacelle
the columns of P have to be a basis of eigenvectors for the space
you first column (1, 0) is not an eigenvector for the eigenvalue -1 (2nd column is eigen for 1 so it's ok)
A*(1, 0)^t = (1, 6) not (-1, 0)
which is why your P doesn't work
but with (0, 1) instead it works bc A maps it to (0, -1)
the part I screenshot is where a problem occurs
sacred plume
Okay I got it now tysm T_T
lone heartBOT
lone heartBOT
Available help channel!
dusk umbra
ok new question
lone heartBOT
ok new question
dusk umbra
can you have a commutator between a vector and a scalar?
mortal trellis
well how should that look like
lone heartBOT
@dusk umbra Has your question been resolved?
tranquil cipher
hello 🥲 im sorry if its not exactly math related (more on physics) but im really desperate rn and maybe someone here understands how this works.. does anyone know how he got the latter equation from the first equation (conservation of momentum equation)? like how he manipulated it to be like that, thank you vm!!
tranquil cipher
KE is 1/2mv^2 and PE is mgy
outer lark
is this part of a bigger problem?
tranquil cipher
yes it is
outer lark
can u post that please ? :D
tranquil cipher
should i send the entire problem
thank you so much!!! sure sure
here is the problem
and the questions are: A. Write the equation for the conservation of momentum in the inelastic collision of the bullet and the woodblock
B. Suppose that a very massive bullet (where m>>M) is fired at the wooden block pendulum and still resulted to an inelastic collision. Determine the speed of the wooden block immediately after collision.
C. At what height y will the wood block pendulum rise after the collision? Express your answer in terms of the object masses and the velocity of the bullet.
D. Suppose that we fire a bullet with mass m=10g at a speed of Vb= 400 m/s into a wooden block with mass M=5.85kg and suspended by a taut string of length L= 75.0cm. By how much height y will the wood block rise? Express your answer in cm units
E. If we carry out the ballistic pendulum test described in D. On the surface of the moon where the acceleration due to gravity is 1.63m/s^2, how many times would the measured height differ from what is obtained on the surface of the earth?
i already have answers for A and B (though im not sure if theyre correct) and currently working on C
outer lark
yeah so
this is combined mass
and initially we have maximum kinetic energy
and no potential
and we transfer all of that kinetic into potential
giving it new height y
outer lark
hello 🥲 im sorry if its not exactly math related (more on physics) but im reall...
that is where the reasoning behind this comes from I believe
tranquil cipher
so its just kinetic energy of both masses in the left hand side of the equation?
combined kinetic energy of the wooden block and bullet?
then on the right hand side its just potential? combined potential energy ?
outer lark
then on the right hand side its just potential? combined potential energy ?
combined mass yes , combined potential doesnt word right imo
the bullets kinetic energy is responsible for moving (m+M)
and yes it transitions all kinetic energy to potential
at a maximum y
tranquil cipher
but i kinda dont understand why it will be merged on the initial states since only the bullet is moving and the wooden block is stationary still the collission didnt happen yet
outer lark
well it starts moving the instant they collide
aka when they combine
that is your initial moment
final is at the peak y
tranquil cipher
ohh wait the question is what height will be wood pendulum rise after collission i see
so the initial is the very moment they collide
and the final is the heighest it will go
highest*
Okok i seee
for question D, it has a given value of 75 cm for the length a taught string, where will i plug that value in?
do i need to use trigonometry for this
lone heartBOT
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gusty ocean
lone heartBOT
gusty ocean
I need help to understand and get better at doing these questions
harsh crypt
but is coted off on the right
harsh crypt
if every mile have expence of 2.25, and 20 per hour
in 1 day it haved 50 mile per hour and the gas and truck maintence is 147.50
first we make the 2.25 per mile and add 20 per hour
harsh crypt
wich 2.25*5 is 10.25
harsh crypt
so h =hour
yes
now we add the 0 we removed giving 102.50
then add 20 with become 122.50
gusty ocean
do u know wt the equations would be
harsh crypt
wait
need make a system to dertime number of hours droved and the mile the truck drived
gusty ocean
but 1457.50 is only for that one day he drives 50$ per hour I thought
?
and dont u mean g instead of m
harsh crypt
harsh crypt
ended?
gusty ocean
yeah
harsh crypt
use .close
gusty ocean
.close
late token
can u put variable after a metric unit
lone heartBOT
can u put variable after a metric unit
tacit arch
can u put variable after a metric unit
!original
lone heartBOT
can u put variable after a metric unit
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
late token
35cmx for example
tacit arch
35cmx for example
What do you want this to mean
tacit arch
35cm multiplied x
And what's x
late token
a variable
ionic jewel
no you can't
well you can but you shouldnt
you shouldn't have the cm be in your problems at all tbh
but if you do you need some indication of multiplication that's not concat
late token
but if you do you need some indication of multiplication that's not concat
concat?
ionic jewel
concatenation
late token
.close
granite jetty
How exactly do I figure out what to use for the starting guesses?
granite jetty
do I use a positive and negative number?
like 2 random numbers such as -100 and 100
I also set it to 0 first so i'm using
x^8 - x - 3
lone heartBOT
@granite jetty Has your question been resolved?
steady tiger
Optimization Problem
"A cylindrical tank with a given volume V is to be made without a lid. The material for the bottom costs five times as much per unit area as that for the sides. What should be the ratio of the height to the radius for minimum cost?"
How do I solve this optimization problem? I have formulated an equation for its total cost:
C = 2πrhx + 5πr^{2}x
mighty sinew
Have you tried defining some variable a = h/r and somehow differentiating w.r.t it?
steady tiger
No i haven't tried that but am I right for getting the cost function???
I've tried deriving h from the volume of the cylinder:
V = πr^{2}h
h = V / πr^{2}
Then substituting h into the cost function
and arriving at:
C = 2Vx/r + 5πr^{2}x
<@&286206848099549185>
dense wigeon
i found a b and d but i need help with finding c and e
steady tiger
<@&286206848099549185>
simple grotto
yes
lone heartBOT
@steady tiger Has your question been resolved?
wide onyx
lone heartBOT
wide onyx
,rotate 270
ocean sealBOT
steady tiger
how do i find trig ratios
Most common angles are multiples of 0, 30, 45, 60, 90
u can refer to the unit circle to get their values in radians
wide onyx
Most common angles are multiples of 0, 30, 45, 60, 90
u can refer to the **unit...
but i dont have the common angles
steady tiger
in this case u can substitute the angle in radians 2π / 9
into the trig functions like sin(x), cos(x), or tan(x)
wide onyx
just do sin(2pie/9)
steady tiger
just do sin(2pie/9)
yepp
lone heartBOT
@wide onyx Has your question been resolved?
little turret
hello
static kelp
hi
just replace dt with x
and try to make a graph
it comes out to be something like this
little turret
is there anyway to do it without just plugging in smaller and smaller numbers for dt?
static kelp
yeah that is what we call getting a limit of a function right
you plug in closer and closer values to 0
and see how the function behaves
little turret
hmmm okay
static kelp
but this is a standard limit right
so its better to remember it rather than deriving it from time to time
samjha bhai?
naive sorrel
how do we know that this limit approaches 1?
u can also do it algebraically with lopitals I tjink
little turret
u can also do it algebraically with lopitals I tjink
yeah but i'm tryna use it prove that the derivitave of e^x=e^x
so to take the derivatave of the top function i would have to know that already
static kelp
oh yeah okay
hasty creek
$\frac{e^{dt}-1}{dt} \\$ $x=e^{dt}-1 \\$ $\ln\left(x+1\right)=dt\\$ $lim_{x\to0}\frac{x}{\ln\left(x+1\right)}\\$ $lim_{x\to0}\frac{1}{\ln\left(\left(x+1\right)^{\frac{1}{x}}\right)} =\frac{1}{\ln\left(e\right)}=1$
ocean sealBOT
Combustion
static kelp
for that you need to know the first derivative rule for limits
@hasty creek yo how did you do that?
hasty creek
the steps are there lol
wintry mango
I have three methods:
1.pinch theorem:1/(1-x)>e^x>1+x
2.Lhopital:0/0
3.taylor expansion
hasty creek
the last step depends on $lim_{x\to0}\left(\left(x+1\right)^{\frac{1}{x}}\right)=e$
ocean sealBOT
Combustion
little turret
**Combustion**
how did you do the third step?
primal warren
how can i show this limit doesnt exist? lim x->0, y->0 of sin(xy)/(x^2+y^2)
static kelp
as this type of limit is in the form of f(x)/g(x) where lim of g(x) tends to zero but not the same for f(x)
hence we can say that limit of the given function in totality does not exist for x,y tending to 0
left isle
,rotate
ocean sealBOT
wintry mango
by calculating the limit from two directions,and the results not same,we can prove that
for example:from y=x and y=2x
and the results is
0.5 not equal with 0.4
lone heartBOT
@primal warren Has your question been resolved?
dire gale
An equipment consists of nine components, each of which will independently fail with a probability of p. If the equipment is able to function properly when at least six of the components are operational, what is the probability that it is functioning properly?
dire gale
is p = 0.5 and q = 0.5?
lone heartBOT
@dire gale Has your question been resolved?
dire gale
.close
static panther
hi my question is find arctan(tan(3))
lone heartBOT
hi my question is find arctan(tan(3))
static panther
is the answer 3 - pi?
3 > pi/2
so if we subtract pi it is between [-pi/2, pi/2]
tacit arch
,calc atan(tan(3))
ocean sealBOT
Result:
-0.14159265358979
oh so it is 3-pi
novel lake
is the 3 degrees?
static panther
the question doesnt specify
novel lake
oh okay then 🙂
static panther
.close
blazing skiff
Hey gang, so we're doing some trig and I got this question correct except for tan, I'm not sure why you can turn "1 over radical 3" into "radical 3 over 3".
hearty quartz
It is just equivalient fraction. Multiplication by sqrt(3). Basically it gives an idea of the value of 1/sqrt(3). E.g. take 1/sqrt(2). Multiply top/bottom by sqrt(2) => sqrt(2)/2. We know that sqrt(2) = 1.4 approx. Therefore we can say that 1/sqrt(2) = 0.7 approx
blazing skiff
Ohhhhhh yeah because you can't have radicals on the bottom of a fraction, so you have to multiply the top and bottom by the radical to get rid of it.
I forgot lol. Thank you!
.close
red patio
How do I do this
lone heartBOT
How do I do this
gray jewel
i've been trying to figure this out for hours
Do you know the formula for linear approximation?
gray jewel
What have you got?
red patio
its 1-3/4(x-3)
but idk what to do from there
I cant find any resources on this either
gray jewel
I cant find any resources on this either
Check the hint
(3.01)^2 is given as 9.06
So what happens if you normally plug 3.01 into the f(x) function?
red patio
oh shit
gray jewel
👀
red patio
you get sqrt(4.06)
gray jewel
Yup
gray jewel
you get sqrt(4.06)
Which means?
red patio
so I just plug 3.01 into x now in my linearized formula?
gray jewel
Alright
gray jewel
I get 0.925
I think that's not correct
zinc haven
which is the correct notation, $x = \varnothing$ or $x \in \varnothing$
ocean sealBOT
FungusDesu
zinc haven
likewise, which is the correct notation, $x = \mathbb{R}$ or $x \in \mathbb{R}$
ocean sealBOT
FungusDesu
zinc haven
an explanation would be helpful
frail grove
What is x?
zinc haven
a variable
zinc haven
It doesn't make any sense to write a variable equal to a set
what about the empty set? it doesnt make any sense either to say something belongs to an empty set, since there isnt anything in there in the first place
frail grove
Yeah are u trying to write solutions to an equation?
ocean sealBOT
FungusDesu
zinc haven
what is S^R
ocean sealBOT
Adam Chebil
frail grove
It means the set of solutions in R is equal to empty set
Or simply write: no solutions in R
ocean sealBOT
Adam Chebil
lone heartBOT
@zinc haven Has your question been resolved?
untold cloud
well, you raise it to the nth power so, the value in the parenthesis is just a bit greater that 1, and since n is so large, it approaches e^a
don't think about this one as plugging in infinity, because you cant do that and the value is going to be just a bit greater than zero for large values of n, and when you add 1 to that and exponetiate n times you get e^a
shii.... thats when my knowledge ends lol
jagged sigil
Well, there is a flaw in your argument.
The difference is in your expression, you are applying the limit both at the denominator n and the exponent n at once.
vivid minnow
1^infinity is indeterminate
jagged sigil
While, in the images, you are doing it separately.
So, you can not use association on it.
It is right that $\lim_{n\to\infty}{1^{n}}=1$
ocean sealBOT
Anbit
jagged sigil
1^infinity is indeterminate
But, as this user has stated 1^inf has no meaning. So, that argument does not work.
After applying the power rule, you are getting 1^inf right?
It is indeterminate.
You can use this rule when n is finite
not when n is infinite
tropic obsidian
lone heartBOT
alpine sable
x + 1/4 (1/x) = 1?
limpid turret
Let the fraction be $x$, the reciprocal is $\frac{1}{x}$. One quarter of the reciprocal is $\frac{1}{4}\times\frac{1}{x}$. The sum must be one. So to determine the fraction, just solve for $x$ in $x+\left(\frac{1}{4}\times\frac{1}{x}\right)=1$.
ocean sealBOT
SWR
lone heartBOT
@tropic obsidian Has your question been resolved?
limpid turret
@tropic obsidian do you still need help?
jovial cedar
lone heartBOT
jovial cedar
how do i do part c?
limpid turret
Looks like your net forces are gravity, and drag (going in opposite direction). So $F_{\text{net}}=mg-\alpha v$
ocean sealBOT
SWR
limpid turret
Use Newton's second law to get $ma=mg-\alpha v$
ocean sealBOT
SWR
limpid turret
Then you have the differential equation $\ddot{x}=g-\alpha \dot{x}$
ocean sealBOT
SWR
limpid turret
Have fun with your differential equation.
storm ridge
Have fun with your differential equation.
Is that dog yours
storm ridge
Lol
limpid turret
lone heartBOT
@jovial cedar Has your question been resolved?
lone heartBOT
@jovial cedar Has your question been resolved?
prime seal
$\int e^{-|x|} ,dx$
lone heartBOT
$\int e^{-|x|} \,dx$
ocean sealBOT
Slowaq
lone heartBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
@prime seal Has your question been resolved?
prime seal
<@&286206848099549185>
alpine sable
hi
prime seal
hi
prime seal
.close
old sinew
lone heartBOT
old sinew
Can you explain me the idea of branch cut in argz?
If i choose (0,2pi]
i can see that, value of argz little above positive real axis is close to 0
and below positive real axis is close to 2pi
<@&286206848099549185>
lone heartBOT
@old sinew Has your question been resolved?
rigid sphinx
lone heartBOT
snow cobalt
didn't you ask this a while back and someone answered it too?
fervent timber
use chain rule
rigid sphinx
.close
lone heartBOT
lone heartBOT
Available help channel!
unique pendant
Hi,
If i have a biased coin with 60 percent chance of head and 40 percent chance of tail and flipped 100 times, what would be the range of heads I would get?
lament wyvern
Hi,
If i have a biased coin with 60 percent chance of head and 40 percent chance...
...0-100?
you could get 0 heads or all 100 heads
unique pendant
on averge though
last walrus
Youd "expect" to see 60 heads but that doesnt mean you necessarily have to get 60 heads when you flip 100 times
unique pendant
like you said i can get any no of heads but I want to know the range of average in which 60 percent of heads will get me.
last walrus
Oh so maybe you mean to build a confidence interval?
unique pendant
ye thats it like i could get 40 heads or maybe 70 heads, and i want to know how to find that interval
last walrus
ok give me a sec to think about it
Do you know about the binomial distribution?
Flipping a coin 100 times is a binomial distribution with $n=100$
ocean sealBOT
last walrus
and if treat flipping heads as a success, we have $p=0.6$ and $q=0.4$
ocean sealBOT
last walrus
Most of our possibilities should land "roughly" within two standard deviations of the expected value
So we could create an interval where we are most likely to see the number of heads this way
unique pendant
okay
last walrus
The expected value of binomial is $np$ and the standard deviation is defined to be $\sqrt{npq}$.
ocean sealBOT
last walrus
so we should be able to use the formula $np \pm 2\times \sqrt{npq}$ and sub in numbers to get a reasonable upper and lower bound
ocean sealBOT
last walrus
I'm not sure if that makes sense to you or not 🙂
unique pendant
it does im just takimg some time
60 plus 2X 4.9
60 minus 2 X 4.9
is that correct?
last walrus
yes
unique pendant
tysm i get it now
last walrus
I get about $50$ as a lower bound and $70$ as an upper bound
ocean sealBOT
last walrus
and this should be valid "roughly" 98% of the time
unique pendant
so 2 sd is 98 percent?
last walrus
Correct, I am loosely using the 2SD ~ 98% rule
unique pendant
okay got it👍
lone heartBOT
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Available help channel!
civic barn
lone heartBOT
<#488120190538743810>
jade sierra
Bruh
civic barn
bruh
jade sierra
Idk how to do this shit don't ping me for it 😭
jade sierra
High school algebra with a bit of trig on the side
alpine sable
I can help but I gtg
civic barn
bruhh
civic barn
I can help but I gtg
the why mesg
coarse marlin
you can simplify the expression in the () using the sum to inf GP formula
civic barn
what is the formula
coarse marlin
if a, ar, ar^2, ar^3, ...... inf are in gp.
the sum of all those terms is a/(1-r)
in the (cos^2 + cos^4 + cos^6 + .... inf)
a is cos^2 and r is also cos^2
coarse marlin
anything the uni teaches me
civic barn
oh
exotic canopy
anything the uni teaches me
gender studies?
coarse marlin
gender studies?
bro, they do offer that course. 😂
i never would want to know wut they teach in that though
lone heartBOT
@civic barn Has your question been resolved?
slim chasm
Hi. Just wanna check that these equations are equal
lone heartBOT
Hi. Just wanna check that these equations are equal
exotic canopy
Hi. Just wanna check that these equations are equal
only if v2=v and v1=0
slim chasm
should it be
slim chasm
Ek = 1/2m(v2-v1)^2 ?
exotic canopy
i've never seen the second form
slim chasm
i've never seen the second form
hmm
lone heartBOT
@slim chasm Has your question been resolved?
kindred jacinth
did i do this correctly ?
lone heartBOT
did i do this correctly ?
lone heartBOT
@kindred jacinth Has your question been resolved?
lean forge
How is Fourier transform defined for a matrix in M_n(R) (n.n matrix)?
lone heartBOT
How is Fourier transform defined for a matrix in M_n(R) (n.n matrix)?
@lean forge Has your question been resolved?
lone heartBOT
@lean forge Has your question been resolved?
devout egret
What is the standard form of the polynomial p(x)= 4x^2+2?
vale crag
How is Fourier transform defined for a matrix in M_n(R) (n.n matrix)?
idk, is it even a thing ?
do you have an example where ppl are talking about that or are you just wondering ?
lean forge
do you have an example where ppl are talking about that or are you just wonderin...
just wondering
lone heartBOT
@lean forge Has your question been resolved?
sharp harness
hi guys i should check if this is a linear mapping
sharp harness
jagged cobalt
is it?
sharp harness
oh ok
another question
generally
when i have a linear mapping
f(0) = 0
is this always true?
prisma current
Yes, this it a requirement from linearity
jagged cobalt
has to be
prisma current
What does linearity say about f(0+0)?
prisma current
Yep
So we have that f(0)=f(0+0)=f(0)+f(0)
And so f(0)=f(0)+f(0)
Can you use this to determine what f(0) must be?
sharp harness
hm lemme check
prisma current
Yep 
sharp harness
noice
can i send you the scalar property too?
Hmm
i really thought from first view that this would be a linear mapping
but it isnt
does someone has an intuitive explanation
g(x+y) = 2(x+y) + 5 /= g(x) + g(y) = 2x + 5 + 2y +5 = 2x +2y + 10
foggy pecan
you have to prove this:
$g\left( \alpha\cdot x+\beta\cdot y \right)=\alpha\cdot g\left( x \right)+\beta\cdot g\left( y \right)$
ocean sealBOT
Joanna Angel
foggy pecan
start from left side and reach right side
sharp harness
but it fails on the first condition
g(x+y) = 2(x+y) + 5
is not the same as
g(x) + g(y) = 2x + 5 + 2y +5 = 2x +2y + 10
therefore it cant be linear?
vale crag
it's just that the "linear algebra" linear mapping has a stricter meaning than the usual way ppl use linear
foggy pecan
yes
sharp harness
oh
vale crag
you need y(0) = 0 in a "lin alg" linear mapping in particular
@sharp harness you have other questions or no?
lone heartBOT
@sharp harness Has your question been resolved?
rocky juniper
lone heartBOT
rocky juniper
would $S: \mathbb{R} \rightarrow \mathbb{R}, S(x) = x^{2}$ be fine as it is surjective every value is mapped in the co-domain but it is not injective i.e $S(-2) = 4 \land S(2) = 4$
ocean sealBOT
luke1
rocky juniper
so the inverse would be
many to one
i mean
one to many
since the original function is many to one
golden canyon
Yeah, codomain shouldn't be R
rocky juniper
R+ ?
golden canyon
$\mathbb{R}_{\geq 0}$?
rocky juniper
ye
golden canyon
not that R though
ocean sealBOT
Jelle
rocky juniper
yes
edgy merlin
Or any set at least 2 elements into a set with one element
S: {1,2,3} $\rightarrow$ {1}
ocean sealBOT
Gapi
edgy merlin
S(x) = 1
rocky juniper
oh i guess thats easier
edgy merlin
Its simpler
rocky juniper
but $\mathbb{R}_\geq 0$ is fine right
ocean sealBOT
luke1
edgy merlin
Yeah
tall shuttle
I have f(g(x)) = h(g(x)) for all x.
f,h are bijective functions from X to X.
g is a bijective function from Y to X
tall shuttle
Can i say that f = h?
limpid turret
If $f : Y\to X$ and $h:Y\to X$ are two functions, you can say that $f=h$ when $f(y)=h(y)$ for all $y\in Y$.
ocean sealBOT
SWR
tall shuttle
So I just need to say that g is surjective?
limpid turret
seems like it, yup
lone heartBOT
@tall shuttle Has your question been resolved?
limpid urchin
lone heartBOT
limpid urchin
heu guys,i got stuck here while solving i just don't know ehat happens with x-pi/3->0
pallid glen
heu guys,i got stuck here while solving i just don't know ehat happens with x-pi...
HI
limpid urchin
do i move the -pi/3 so it would be x->pi/3 and then it would be 0/0 and do lhopitals rule?
pallid glen
ill help
limpid urchin
please
young parrot
Discrete math:
could someone tell me how one would solve this (with steps?)
the answer is n=3 with witnesses k=1 and C=4; but with the method i'm using i get n=4
young parrot
my current method:
$3x^3 + (log x)^4 <= 3x^3 + x^4 <= 3x^4 + x^4 = 4x^4$
so n = 4 with witnesses k=1 and C = 4
ocean sealBOT
Jody
young parrot
right, should be noted that we're using log 2,
im not all too familiar with logarithm (my previous highschool never taught it) so there may be some simple logarithm inequality that will allow me to show that (logx^4) <= x^3; but i dont know nor do i know if its true or provable?
fickle heath
log(x)^n is polylogarithmic, which is below linear
For any n > 1 (n = 1 makes it just logarithmic)
young parrot
ah, so log(x)^n <= nx?
ocean sealBOT
Nel
fickle heath
log(log(x)) grows more slowly than log(x), obviously
So there exists x_0 such that x > x_0 => log(x)^n < x
young parrot
oh im following now
does that apply for a function f(x) as well?
log(f(x))^n < x for large enough x?
fickle heath
Of course not, just take f(x) = 2^x
fickle heath
log(f(x))^n < f(x) though, if f is increasing (I think that's a sufficient condition)
(for large enough x, again)
log(x^n) ?
young parrot
yea
fickle heath
That's just nlog(x), so O(log(x))
young parrot
i definitely have to go back and properly learn logarithm
but this makes sense
thanks a bunch
.close
summer hemlock
How do I graph this?
lone heartBOT
How do I graph this?
summer hemlock
I'm supposed to pick some x's and replace them with x
I'm not sure how to find which x's though
The x's I have currently are - 2.5 and -3.5
hot bluff
f(-3.5) = 2
summer hemlock
f(-3.5) = 2
How do I find what x's to pick other than -2.5 and -3.5
hot bluff
absolute value is just a V shaped graph. you know where the function = 0, so now you just need the slope, you make the V shape pointing at the 0 and use the slope to draw the rest.
lone heartBOT
@summer hemlock Has your question been resolved?
summer hemlock
absolute value is just a V shaped graph. you know where the function = 0, so now...
My teacher wants me to find the x's though
hot bluff
what x's? there are technically infinite x's to find.
lone heartBOT
@summer hemlock Has your question been resolved?
spare fern
Could someone help me out with this?
lone heartBOT
Could someone help me out with this?
spare fern
ocean whale
If the bases are the same, you can just equate the exponents and solve for x from there
ocean sealBOT
Lex1729
spare fern
$$6x\log \left(7\right)=20\log \left(7\right)+4x\log \left(7\right)$$
ocean sealBOT
Lex1729
spare fern
$$x\left(6\log \left(7\right)-4\log \left(7\right)\right)=20\log \left(7\right)$$
ocean sealBOT
Lex1729
ocean sealBOT
alphaGengar
spare fern
**alphaGengar**
Why?
untold cloud
because you want to cancel the 7
so you have just the exponent stuff
recall that
log_x(x) = 1
so log_7(7) = 1
ocean whale
Yes
lone heartBOT
@spare fern Has your question been resolved?
wicked tree
lone heartBOT
placid zinc
Check your endpoints. That is, what is the function doing along the lines?
The first line is y = x - 4
wicked tree
mhm
so if I plug that into 11x-5y
then I get 6x+20
if I plug in -x-4 then I get 16x+20
if I just plug in 4 then I have 11x-20
but then what do I do with that? @placid zinc
lone heartBOT
@wicked tree Has your question been resolved?
wicked tree
<@&286206848099549185>
hasty umbra
wicked tree
.close
drifting seal
is the question correct?
lone heartBOT
is the question correct?
drifting seal
cuz when k 1 or even 2, it’s not divisible by 19
lone heartBOT
@drifting seal Has your question been resolved?
drifting seal
<@&286206848099549185>
silver flare
is the question correct?
yup
lone heartBOT
@drifting seal Has your question been resolved?
velvet nacelle
is that true
lone heartBOT
@velvet nacelle Has your question been resolved?
acoustic wave
Hi there, I am having a hard time wrapping my head around applying Richardson extrapolation in my homework assignment. I don't even know where to begin....
acoustic wave
Okay well, maybe I do know where to start: I need to compute Q0, however I need a small n and a large N for that, and I'm not sure what they are in this case
I’ve gotten to this point
However, I'm not 100% sure that I even need it in sum form...
<@&286206848099549185>
Perchance 0 is an unlucky number....
deep basin
Yeahs
acoustic wave
Yeahs?
deep basin
Wqcuzbi?
acoustic wave
Uh ohhh
deep basin
Uh ohhh
acoustic wave
Well, at least I have someone to talk to
deep basin
Wefechu
acoustic wave
However, I imagine taking up a help channel is not ideal, so Ima close it
Good luck, random person
acoustic wave
.close
lone heartBOT
deep basin
Bbh I am not sure if I will be in a relationship or not but if you can
lone heartBOT
Available help channel!
inner haven
find cos(x) and tan(x) if csc(x) = -sqrt(6)/2 and cot(x) > 0
echo socket
csc(x) isn't the same as 1/cos(x) though
inner haven
csc(x) isn't the same as 1/cos(x) though
how would i appraoch this problem
echo socket
Can you recall what csc(x) is?
inner haven
1/sin
echo socket
Right, so you have sin(x) = -2/sqrt(6)
inner haven
yes
echo socket
Are you solving for x in [0, 2pi) or are you looking for the general solutions?
inner haven
general
echo socket
Just use (-1)^k arcsin(-2/sqrt(6)) + pik where k is an integer then
inner haven
oh wait actually
what is the difference between general and solving for x
This was all the problem said
Oh wait would cos be sqrt2/sqrt6
echo socket
Yes
lone heartBOT
@inner haven Has your question been resolved?
scenic wing
lone heartBOT
ocean sealBOT
putridplanet
scenic wing
$-cos(x)+cos(-x)$
ocean sealBOT
putridplanet
scenic wing
now what
echo socket
Recall that cosine is an even function
scenic wing
wdym
echo socket
cos(-x) = cos(x)
scenic wing
why
echo socket
Changing the sign of the angle on the unit circle is equivalent to reflecting your point around the x-axis
That, however, does not change its x-coordinate
scenic wing
ok
echo socket
Hence cos(-alpha) = cos(alpha) for all angles alpha (I named it alpha here not to confuse it with the x coordinate)