i was just typing in it, #help-8
#help-10
warm siren
high lily
you deleted your original message
warm siren
no the channel closed after i did that
high lily
which irreversibly sets the channel to abruptly close after a minute or so
which either locks it or resets it to available
warm siren
it just closed, and I put another question in which moved it to occupied
rigid pine
no the channel closed after i did that
It would be weird if it closed it before you deleted it.
warm siren
ill just post again
high lily
it isn't immediate you can still send stuff for a certain amount of time until the lock triggers
warm siren
that must be it then
this is wherre i left off, do I plug in bnounds now or is there more i gotta do
rigid pine
You expanded the brackets wrong.
idle thunder
(a-b)^2 isnt a^2-b^2 😉
rigid pine
(e^t - 1)^2 = e^(2t) - 2e^t + 1.
rigid pine
Looks right.
warm siren
wait the +1 is in exponent?
rigid pine
No. That would be e^(t + 1) if it were.
rigid pine
I think the only interpretation is the correct one, sadly.
Simplify the result and I suspect you get to be able to factorise.
warm siren
i got sqrt (e^2t -2e^t+1+4e^2t/2)
rigid pine
i got sqrt (e^2t -2e^t+1+4e^2t/2)
This is not the correct way to write it.
4e^2t/2 = 2t e^2.
Just simplify it and write 4 e^t.
Note. You should have wrote 4e^(2t/2).
warm siren
idle thunder
2t/2 = t
idle thunder
-2e^t + 4e^t = 2e^t
idle thunder
DONT FORGET dt
warm siren
rigid pine
DONT FORGET dt
Instructions unclear. Now it’s in the square root.
rigid pine
Try and factorise. I’ll start you off e^(2t) + 2e^t + 1 = (e^t + …)(e^t + …).
warm siren
(e^t +1 )^2 ?
rigid pine
Yes.
warm siren
so that gets rid of the sqrt
rigid pine
When you take the square root you get |e^t + 1| = e^t + 1.
rigid pine
Yes.
warm siren
now do I plug in bounds and integrate?
idle thunder
beautiful
rigid pine
Yes.
warm siren
what happens to the 1
rigid pine
Studying arc length when you can’t integrate. 🧐
warm siren
im just burnt out tbh
rigid pine
That’s more then burnt out. That’s the most basic integral possible. 1 integrates to t.
rigid pine
Yes.
warm siren
i got e^2 +1
rigid pine
Seems right.
warm siren
is that my length?
rigid pine
It is.
hallow kettle
Can somebody help me with this problem?
obtuse pebbleBOT
Can somebody help me with this problem?
hallow kettle
Or this whole worksheet
I'm not trying to look forward for answers, I just need to learn how to solve the problems.
This is just a practice on what I'd cover on the benchmark
I already finished it
Number 2 is what I need assitance on at the moment
forest sinew
hallow kettle
This one, yes
kindred storm
assuming the two marked angles are equal the top and bottom line segments are parallel because it's a transversal through two lines
hallow kettle
Yeah I got that down
for 2a I said "We know these two triangles are similar due to it's shape and similar theorem which would be SAS"
I'm having a hard time with 2b though
I solved for x and got 10 but I don't know how to solve for y
kindred storm
similar triangles aren't congruent
hallow kettle
I did x/15=8/12 but I forgot how I got it I just asked my teacher for helped and I forgot how we solved it, cross multiplied, did 12x/12=120/12 and got 10 as my x
kindred storm
sas means they are the same triangle, similar just means all the angles are the same
kindred storm
I did x/15=8/12 but I forgot how I got it I just asked my teacher for helped and...
so in a similar triangles corresponding line segments are all scaled scaled by the same value.
so the part where the x/15 = 8/12 is essentially stating that the ratio of the top and bottom segments is the same as the ratio between x and the segment of length 15 units
you can apply the same logic and use the equation 5/y = 8/12 to find y
hallow kettle
My answer won't be a number though
It's gonna have a decimal point
Will that be fine?
I got y=7.5 as my answer
kindred storm
I believe that's correct
hallow kettle
I'm still confused
hallow kettle
sas means they are the same triangle, similar just means all the angles are the ...
So since you'd seem that this explanation is wrong, do you know how to put it in a better explanation?
kindred storm
So since you'd seem that this explanation is wrong, do you know how to put it in...
since both triangles have 3 each corresponding angles that are congruent, the triangles are similar
do you know the difference between similar triangles and congruent triangles?
hallow kettle
Let me look at my notebook rq
kindred storm
SAS is a way to prove two triangles are congruent, including proving that corresponding side lengths are congruent
essentially congruent triangles are identical just rotated or mirrored or something
hallow kettle
Congruent means same shape and size while similar also means same shape but could be different sizes
Is that correct or not?
kindred storm
that's correct
All you need to prove for similarity is angle congruence, you shouldn't involve side length at all
hallow kettle
Thank you
Can we move on to 3?
I attached a document that you can see if you go to the previous messages
I have a hard time solving problems involving probability so if possible, I would like if you can point out some methods on how to solve for probability
Umm...
Hello?
You alright there pal?
zinc falcon
In question 3a he is asking to find the percentage probability of left handed males
hallow kettle
I know that
I just need help to solve the complete probability
So you'd like divide the number of male left handed to the total amount of males both left and right handed?
Is that how it goes or no...?
zinc falcon
Exactly 💯
And then multiply the answer with 100 to find percentage chance/probability
hallow kettle
I got 7.35%
But this problem relates to probability right? Sorry I know it's sounds like an obvious question, I just want to be sure
zinc falcon
Yeah it's related to probability
hallow kettle
Same applies to female too?
zinc falcon
Yeah
zinc falcon
It's better to round it
hallow kettle
Oh ok
and as for c, you'd divide the number of left handed males and females with left handed females right?
zinc falcon
Correct
hallow kettle
Yeah you're right
Lol
I got 53.33%
I rounded all of them so here they are rounded:
a. 7.45%
b. 86.8%
c. 58.3%
just showing you my answers so i'm sure if i'm correct or not
hallow kettle
Alright thanks!
I see that you sent me a friend request
I accepted it but it's for educational use right?
Pls tell me that I don't have to pay 😭
Uh hello?
zinc falcon
Yeah
hallow kettle
Oh sorry you were remaining idle
granite robin
I have a problem in Lebesgue out measure: \sigma(S) represent the volume of S. I don't have any idea to the part(b), can any body give me some clues?
obtuse pebbleBOT
I have a problem in Lebesgue out measure: \sigma(S) represent the volume of S. I...
elfin burrow
I have a problem in Lebesgue out measure: \sigma(S) represent the volume of S. I...
can you send your definition of sigma maybe? is this working in R?
elfin burrow
oh okay, so intervals actually mean rectangles
granite robin
Yes
elfin burrow
I have a problem in Lebesgue out measure: \sigma(S) represent the volume of S. I...
do you see what happens if all of the intervals in the S are disjoint from all of the intervals in T?
obtuse pebbleBOT
@granite robin Has your question been resolved?
granite robin
<@&286206848099549185>
obtuse pebbleBOT
@granite robin Has your question been resolved?
obtuse pebbleBOT
@granite robin Has your question been resolved?
devout warren
obtuse pebbleBOT
devout warren
Could someone please explain how they went from the left to the right in the blue circle
Doing so i believe assumes Xp = e^at / p(a)
But I don't know why that would be true if it is
rigid pine
x_p can be shown to be equal to 1/P(a)[e^(at)].
If u = 1 then 1/P(D + a)(a) = 1/P(a).
You might have to look up how the resource proves the exponential shift theorem. It might require a particular starting form to apply it or something.
devout warren
where would the p(D + a) part come from
im very new to these proofs so i apologise im not very knowledgeable at all
rigid pine
I'm not sure how best to approach guiding you is the problem.
devout warren
well im just wondering because the expression doesnt seem to have changed at all, the ue^ax still remains but now theres a (+a) in the polynomial operator
rigid pine
This result can be proven by induction. Set u(x) = 1,
Then it can be shown that P(D)(e^(ax)) = e^(ax) P(a).
You can show from here e^(ax) = P(D)/P(a)e^(ax).
If x_p is a particular solution of the D.E. P(D)x = e^(ax) then it follows that P(D) x_p = e^(ax).
We arrive at P(D) x_p = P(D)/P(a) e^(ax).
obtuse pebbleBOT
@devout warren Has your question been resolved?
devout warren
Thank you!!
I'll read through it now
That makes a lot of sense, thank you!
I really appreciate your help
.close
latent jasper
$\lim_{(x, y) \to (0, 0)} \frac{x^3 + y^4}{x^2 + y^2}$
obtuse pebbleBOT
$\lim_{(x, y) \to (0, 0)} \frac{x^3 + y^4}{x^2 + y^2}$
warm shaleBOT
afeAlway
latent jasper
I need help here, cuz I can't simplify or directly put in x&y, I can't substitute. So my last method was to show this doesn't have a limit and I did show that but when I checked the answer they said that the limit is 0.
This is what I did, when you get close to (0,0) from (1,0), I get that the limit is 0. When we get close to (0,0) from (0,1) I get that the limit is 0. When I get close to the origin from y=x I get that the limit is 1/2. Since it is not zero here too, the limit doesn't exist!
pine sail
How do you get limit = 1/2 from y = x?
latent jasper
so if y=x then the fraction will be (x^3 + x^4)/2x^2
nevermind it is zero I made a mistake
pine sail
Yeah.
latent jasper
but that still won't prove it has a limit tho so what do I do?
pine sail
I think it does.
latent jasper
but there are many other ways you can near the origin tho?
infinite ways, maybe not infinite but many ways lol
pine sail
Because both x and y approach zero, you definitely can approach this limit from y = x
besides you can just notice how the Exponents of the numerator are larger in comparison to the denominator. And that will make the numerator closer to 0 as (x,y) -> 0
You should have done limits like this in the past.
Where you'd have rational function and x would approach infinity or something.
You'd just check the term with highest Exponent of x.
latent jasper
wait I am confused wouldn't the numerator having larger term contribute to infinity, like 0.01/0.00001= infinity?
latent jasper
Because both x and y approach zero, you definitely can approach this limit from ...
isn't that right?
pine sail
when |x| < 1 then x > x^2 > x^3
Numerator might have the larger exponent but in this case larger exponent ensures the smaller term.
Because of the fact stated above.
And it'd not be what you said, rather
0.0000000001/0.001
Or something like that
pine sail
when |x| < 1 then x > x^2 > x^3
You can try this.
1/2 > 1/4 > 1/8
latent jasper
And it'd not be what you said, rather
0.0000000001/0.001
Or something like that
yeah you're right sorry I got confused. But would that suffice as a proof?
latent jasper
I was thinking of squeeze thorem but have no clue how to go at it?
What should my bounds be?
royal basin
**afeAlway**
is this the problem y'all are solving?
pine sail
Yes.
royal basin
why not go polar
then the denom will be r^2 and the num will be what
r^3 cos^3(θ) + r^4 sin^4(θ)
so dividing that out you have r (cos^3(θ)+r sin^4(θ)), in which the former factor approaches zero and the latter is bounded
pine sail
Nice, now after this I do realise that approaching origin from y = x would infact not be contempt haha.
latent jasper
wait so you mean as in rewrite both the denom and num?
royal basin
of course
i am switching from rectangular to polar coords
or suggesting you do the same
latent jasper
I see that you did something already but let me try it myself and get back
yeah I also got r(cos^3(θ) + r sin^2(θ))
@royal basin what is the equivalence of lim (x,y)->(0,0) here?
x= r cos(θ) so when x=0, then r=0 or cos(θ)=0 which will make θ=0, π? And y = r sin(θ), when y=0 then r=0 but θ=π/2, 3π/2
royal basin
you got the values of theta at which sine and cosine are 0 switched around
anyway, (0,0) is the only point whose radial coordinate is 0, so r approaches 0
while theta does not approach anything
latent jasper
while theta does not approach anything
so I function is then dependent on r right?
as in like T(r)
so Ig what I am trying to ask is if this is the reason we are not taking lim θ -> t, where t is some random number. Or do we always focus on r even if θ also approaches a specific value?
royal basin
theta can go wild
latent jasper
is it because like no matter which direction we take to the origin it should be 0
royal basin
for a general function it may be that all limits along straight paths toward zero exist, but the bivariate limit doesn't
latent jasper
but if it is dependent on θ the angle it will not
royal basin
so just looking at all straight line limits is not enough
latent jasper
so just looking at all straight line limits is not enough
wait wdym here?
royal basin
if you fix theta and let r approach zero,
or, in rectangular coordinates, if you focus only on points on the line y=kx for some constant k and let x approach zero,
you are considering a straight-line limit
it is kind of like a one sided limit for single variable functions, in that you approach the origin from a fixed direction
except that in the case of two variables there are now a continuum of directions
and what i am saying is that even verifying that the function approaches the same limit from all directions like this isn't enough
obtuse pebbleBOT
@latent jasper Has your question been resolved?
latent jasper
and what i am saying is that even verifying that the function approaches the sam...
How is proving that the limit when you approach a point from all directions is not enough? In single variable proving that the limit as x appraoches a point from both sides (all sides) is equal will prove that there is a limit. Why is not true here?
In any case I did continue with the question and used squeeze theorem 0<= r(cos^3(θ) + r sin^2(θ))
<= r+r^2. When r approaches 0 then the function will squeezed in 0 to 0, meaning it will also be 0.
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
brave oxide
Is this correct and if it is, why did they get infinity as an answer to this exercise?
obtuse pebbleBOT
Is this correct and if it is, why did they get infinity as an answer to this exe...
obtuse pebbleBOT
@brave oxide Has your question been resolved?
obtuse pebbleBOT
@brave oxide Has your question been resolved?
trail musk
you forgot the x in the denom
brave oxide
.close
fluid sinew
obtuse pebbleBOT
fluid sinew
can someone help me with this question?
obtuse pebbleBOT
@fluid sinew Has your question been resolved?
kind hawk
what do you know about the number of solutions to a system of linear equations
quartz raft
please help me with this
obtuse pebbleBOT
please help me with this
quartz raft
for letter a, I drew a venn diagram w 2 circles and then I putted 27 in the middle
and the rest is 52 and 59
am I correct?
how am I gonna answer letter b and c
proven zephyr
why 2 circles?
there are 3 transportation vehicle,
bus
jeepney
train
why not make 3 circles
proven zephyr
nooo
quartz raft
I'm lost sorry
proven zephyr
number of people that likes bus + number of people that likes jeepney
but keep in mind there are some that likes both
and also some that likes bus and train & jeepney and train
quartz raft
u could use an online whiteboard :>
quartz raft
is it addition?
proven zephyr
yes
quartz raft
ohh
proven zephyr
it's not just 52 + 59 + 27 + 32 + 29 btw
quartz raft
ohhh
proven zephyr
52 people that likes bus is including the people that likes bus and jeepney, bus and train, and likes all of them
proven zephyr
basically this whole thing is 52
quartz raft
199-52?
quartz raft
ohhh
proven zephyr
nooo
proven zephyr
it's the same for. the jeepney
you do a + b + c + d = 59
and find each
well.. you've found b and d already
labeled everythinggg
basically you're trying to find a + b + c + d + e +f
quartz raft
well.. you've found b and d already
ohhhh
quartz raft
so 52+59?
proven zephyr
nooooooo
quartz raft
OMG TvT
proven zephyr
you're double counting the b and d
you're counting the people who like bus and jeepney twice
quartz raft
ohh
proven zephyr
ok lets just do this step by step
a + b + c + d = 52
b + d = 27
c + d = 29
d = 12
first of all, do you understand where i got this from?
proven zephyr
ok
so d is the people that prefer all of em
and c + d is the people that prefer trains and bus
the people that prefer all of em also prefers trains and bus so they're also counted as people that prefers trains and bus thus c + d
c + d = 29
d = 12
try to find c (people who only prefers bus and trains)
proven zephyr
is it 29-12?
this one
proven zephyr
i meant you're still finding each of em
proven zephyr
you found this
quartz raft
so for letter b
proven zephyr
yes?
proven zephyr
it is correct
29 for the b
well, it's technically correct
hmm... how do i say this
proven zephyr
maybe erase everything except 12 first
quartz raft
ohh wiat
proven zephyr
wait
you mixed up 27 and 29
you switched
but yeah remove everything first
except 12
proven zephyr
this is 27 right?
quartz raft
yesss
quartz raft
27-12?
proven zephyr
yes
quartz raft
15
proven zephyr
yes
quartz raft
do I need to add them all to find a?
proven zephyr
you're welcome
quartz raft
I'm gon send my answersss
proven zephyr
what's your answer for a?
quartz raft
still figuring it out lol
proven zephyr
oh okayy 🙂
quartz raft
f = 5
e = 27
is it correct?
my answer for letter a is 15
b. 21
c. how 😭
is the answer for letter c is 32? since I added 21 +27 + 8 + 12 then subtracted it from 100
so these are my answers so far
a. 15
b. 21
c. 32
btw thank u for your patience and help, I really appreciated your help 
💗
obtuse pebbleBOT
@quartz raft Has your question been resolved?
untold garnet
if the answer is this is it still correct if i put f-1(x) = 1/30x -500?
obtuse pebbleBOT
if the answer is this is it still correct if i put f-1(x) = 1/30x -500?
knotty crow
yes
idle thunder
yea
weary ember
Hi guys. Please help me choose the right option for this statement: The uniform step method always/never
gives a filled magic square when n is odd/even
obtuse pebbleBOT
Hi guys. Please help me choose the right option for this statement: The uniform...
untold gate
Can someone please explain to me what I highlighted in yellow? I understand everything but what I highlighted.
obtuse pebbleBOT
Can someone please explain to me what I highlighted in yellow? I understand ever...
untold gate
For the first one we have 7 - 7 + f = 2 which equals 2 faces. But I see 3 faces? (because we always count the infinite face)
For the second one. First of all. The vertex count is wrong it should be 8. And the edge count should be 12. So 8 - 12 + f = 2 which equals 6 faces. Okay nvm I understand this one. It's just the first one.
So my assumption is the formula only works for connected graphs?
.close
fossil current
do i have to find the value of c first
obtuse pebbleBOT
do i have to find the value of c first
knotty crow
it might help
fossil current
for number 27
knotty crow
but it isn't necessary to know c value in order to find 2nd root
fossil current
how do i find the other root
knotty crow
the simplest and the most obvious way is to find 'c' plugging x = 2 into the function and then use quadratic I'd say, but Vieta's formulas seem to be more efficient
in this case
u know them?
knotty crow
rather 6
fossil current
why is it positive
knotty crow
substitute x = 2 into the function:
(2)^2 - 5(2) + c = 0
4 - 10 + c = 0
-6 + c = 0
c = 6
knotty crow
yes
fossil current
ohh i know this
I never knew the name
learned something new 👍
Thank you
.close
humble maple
Hey, how would i solve this using logarithms
obtuse pebbleBOT
Hey, how would i solve this using logarithms
fierce lagoon
Take the natural log of both sides
humble maple
Like this? @fierce lagoon
humble maple
What does that do? @fierce lagoon
dark stirrup
If $2^{x-1}=3^{x-2}$, then you can take the natural log of both sides and get $\ln(2^{x-1})=\ln(3^{x-2})$.
warm shaleBOT
SWR
dark stirrup
Then use your log rules to get where to what umbrella showed you
fierce lagoon
What does that do? <@349354952961032192>
Distribute, collect like terms, isolate the x term
Literally makes algebra easier
humble maple
So should I rearrange it to (x-1)(x-2) = ln(2)ln(3), expand the left and right side, bring the right side to the left, make it equal to 0 and solve for x? @fierce lagoon
fierce lagoon
You didn't distribute
fierce lagoon
Just do (x-1)ln(2) = (x-2)ln(3)
Expand/distribute
humble maple
@fierce lagoon
fierce lagoon
You didn't do what I said to do
humble maple
I think i am missing something from what you asked
fierce lagoon
So would I want ln(2x3)?
No
How are you getting that
ln(2) and ln(3$ is a number in itself
timid silo
<#488120190538743810>
sorry my bad
obtuse pebbleBOT
@humble maple Has your question been resolved?
ornate radish
obtuse pebbleBOT
ornate radish
so it's a simple sequences of positive terms induction question
the left picture is a solution the teacher gave
in hypothesis 3 I saw another way to do it, on the right
which solution is better?
ornate radish
basically the same
do you prefer one over the other?
civic zealot
nope
idle moth
how would I find how many timeslots there are using graph colouring?
obtuse pebbleBOT
how would I find how many timeslots there are using graph colouring?
idle moth
do i find the combination of subjects that students study and put that in a graph then graph colour? or do I use the combination of subjects they give and put that into a graph
obtuse pebbleBOT
@idle moth Has your question been resolved?
timid silo
The question is somewhat ambiguous. I believe what they are asking for is:
"No students at the school study the following combination: [blah blah]. In the worst case, assuming that all other combinations are taken by some student, find the number of exam slots needed
So now, you can imagine a graph with 8 vertices. One vertex for each subject
And an edge between vertex (u, v) means that no student takes u and v together
So now, you need to find a coloring of the vertices, such that all vertices with the same color are on the same time slot. That means that all vertices with the same color form a clique. Find the minimum number of colors needed
Does it make sense so far?
For eg.
A, B, C, E form a clique
Similarly A, B, C, H also form a clique. But A, B, C, E, H doesn't form a clique since (E, H) isn't an edge.
A, B, E, F is also a clique
D, E, F is also a clique
I think the answer is:
A, B, C, H in one time slot
D, E, F in another slot
G in another slot.
So 3 time slots in total are needed.
Pretty sure that you can;t do it with just 2 slots.
obtuse pebbleBOT
@idle moth Has your question been resolved?
sand agate
obtuse pebbleBOT
warm canopy
those are vieta's formulas
the sum of the roots of a quadratic is always minus the coefficient of the linear term
and the product is always the constant term
sand agate
those are vieta's formulas
yeah i know that but
for part ii it just says whats z1 + conjugate of z1
so
a+bi + a-bi
no?
sand agate
yes
warm canopy
so vietas formulas hold
sand agate
how did they get 3
warm canopy
the sum of the roots is minus the coefficient of z
sand agate
a+bi+a-bi-3
that it?
warm canopy
the sum of the roots is equal to minus the coefficient of z
sand agate
u use it to create the equation
the green bit
oh my god
@warm canopy i realise it now
nvm and thanks
.stop
.clos
.close
rustic glacier
Can someone explain this to me?
obtuse pebbleBOT
Can someone explain this to me?
idle thunder
Can someone explain this to me?
do u know the x coordinates of the critical points
rustic glacier
yeahh its -5/2
rustic glacier
we plug in -5/2 to see if it is a min or max
rustic glacier
thats the thing the second derivitave is a constant of -2
idle thunder
so does that mean there is a minimum or maximum at that point
rustic glacier
I have no clue; its a max but why?
idle thunder
maximum
think the derivative is going from positive to negative
(negative second derivative)
the function increases then decreseases reaching its maximum value
does that make sense?
rustic glacier
ohh okay I see that now, where was it positive?
idle thunder
ohh okay I see that now, where was it positive?
what do you mean
rustic glacier
like the derivite goes from posiotive to negative?
OHH I see now
because it is a negative and it once was a quadratic there would be a parabola there and since their both decreasing its a max
thanks
.close
true talon
I have no idea what the function below the prompt means. I know how to find taylor series with given functions like ln(x) c=1 or something like that but this is different
obtuse pebbleBOT
I have no idea what the function below the prompt means. I know how to find tayl...
vast linden
I have no idea what the function below the prompt means. I know how to find tayl...
if you are determining the Taylor series yourself, then you need to find all the derivatives and express them depending on the order of the derivative
here you are already given all the necessary derivatives
true talon
I don't see what you mean there about the derivatives
vast linden
$f^{(n)}(7)$ is the derivative of the $n$-order at the point $7$
warm shaleBOT
rkky
true talon
so to my understanding you use derivatives in taylor series to find the terms of the taylor series
I'm not sure how that connects with the above
does that mean I have to find the integral of the above function?
obtuse pebbleBOT
@true talon Has your question been resolved?
vast linden
I am kinda confused rn, so to make everything clear – are we talking about the summation text field with the red X?
vast linden
so to my understanding you use derivatives in taylor series to find the terms of...
yes
true talon
I am kinda confused rn, so to make everything clear – are we talking about the s...
yes
it has a red x because i put an incorrect answer
vast linden
how would you write a Taylor series as such a sum maybe?
for a generic function $f(x)$?
warm shaleBOT
rkky
vast linden
so you haven’t used the $\sum$ notation before at all, correct?
warm shaleBOT
rkky
true talon
no I have
vast linden
so how does the Taylor series look like with the $\sum$ notation? how would you write it out?
warm shaleBOT
rkky
true talon
I have
vast linden
so how does the Taylor series look like with the $\sum$ notation? how would you ...
then how does it look like?
vast linden
n! is correct, (x-c) should be instead of (x-1) and instead of $(-1)^n$ you’ll have $f^{(n)}(x)$
warm shaleBOT
rkky
vast linden
here you wrote n-th order derivative for the $(x-c)^n$ term, so we kinda hide it under the umbrella which I described above
warm shaleBOT
rkky
vast linden
$f^{(n)}(7)$ is the derivative of the $n$-order at the point $7$
here
vast linden
you can interpret it as the $n$-th derivative simply
warm shaleBOT
rkky
vast linden
like the 2nd derivative is f’’ etc.
vast linden
exactly
true talon
I can't help but think "now what?"
The nth order derivative for c=7 is the right side of the function
vast linden
yes
vast linden
n! is correct, (x-c) should be instead of (x-1) and instead of $(-1)^n$ you’ll h...
so now according to this you can try to write down the Taylor series
true talon
so instead of f^(n) (x) I replace it with the right side of the given function?
vast linden
awesome
uncut jacinth
give just this part of a derivative, what is the steepest point on the original graph?
obtuse pebbleBOT
give just this part of a derivative, what is the steepest point on the original ...
uncut jacinth
the answer is showing
the vertex of the derivative but thats its minimum
how can that be true?
its restricted to be between 0 and 22
wouldn't 22 be the steepest?
idle thunder
is this f' or f
uncut jacinth
the answer took the second derivative and found the inflection point at 10 and said that is the steepest point
vestal thorn
well the steepest point would be the extreme value of the derivative
steep doesn't just mean positive
a slope of -10000 is steeper than a slope of 4
vestal thorn
are always the extreme values?
of the derivative, sure more or less. it's the exact same thing as when you're trying to find the extreme values of a regular function by examining when the sign of the derivative changes, but you're trying to find the extreme values of a derivative by examining when the sign of the second derivative changes
you're just moving up the derivative ladder one
obtuse pebbleBOT
@uncut jacinth Has your question been resolved?
timid silo
how
flint ivy
what translations take the graph of y=\sqrt{-2x+2}-1 to y=sqrt x
obtuse pebbleBOT
what translations take the graph of y=\sqrt{-2x+2}-1 to y=sqrt x
flint ivy
transformations
i got
a dilation by a factor of 2 from the y axis , a reflection in teh y axis, and a translation of 2 units to the right
is this correct
apparently my friend says y=\sqrt{-2x+2}-1 should be y=\sqrt{2(-x+1}-1 and hence it will only need to be translated by 1 unit in the right
<@&286206848099549185>
obtuse pebbleBOT
@flint ivy Has your question been resolved?
timid silo
Consider the line y= - 7x + 3.
Find the equation of the line that is parallel to this line and passes through the point (5, -5).
Find the equation of the line that is perpendicular to this line and passes through the point (5, -5).
obtuse pebbleBOT
Consider the line y= - 7x + 3.
Find the equation of the line that is parallel to...
pine sail
!status
obtuse pebbleBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
@timid silo Has your question been resolved?
timid silo
<@&286206848099549185>
fathom flicker
respond to the status prompt
fathom flicker
what have you tried? do you have any work you can show?
timid silo
its on aleks
its online
so all the work i done it was wrong
and it goes away after that
fathom flicker
you should try graphing it on paper and trying some work on paper, if you find that you get stuck then send your work here
obtuse pebbleBOT
@rocky sierra Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
still flower
when you derive ax+b what do you get
obtuse pebbleBOT
when you derive ax+b what do you get
fathom flicker
Do you mean differentiate?
fathom flicker
what do you mean by derive then?
fathom flicker
you mean taking the derivative?
still flower
yes
still flower
Ok
still flower
yes
fathom flicker
with respect to x, I assume?
still flower
Exact
fathom flicker
Okay, what is the derivative of a constant?
still flower
0
still flower
well 1
fathom flicker
so ax would go to a*1 = a
still flower
thx
still flower
.close
hot dawn
halppp
warm shaleBOT
normalAtmosphericPa=101,325
unreal musk
I mean, think about how, for example, $\dim_{\bR}(\bR) = 1$
warm shaleBOT
@unreal musk
unreal musk
You can span $\mathbb{F}{17}$ as a $\mathbb{F}{17}$-vector space by $1_{\mathbb{F}_{17}}$
warm shaleBOT
@unreal musk
warm shaleBOT
normalAtmosphericPa=101,325
unreal musk
I mean you can, but note that Z is not a vector space (but you can consider it as a module over itself)
obtuse pebbleBOT
@hot dawn Has your question been resolved?
digital pond
can someone explain to me how to do these max/min type problems for part c step by step
obtuse pebbleBOT
can someone explain to me how to do these max/min type problems for part c step ...
@digital pond Has your question been resolved?
digital pond
@ruby fulcrum
obtuse pebbleBOT
@digital pond Has your question been resolved?
obtuse pebbleBOT
@digital pond Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
opaque galleon
is this correct?
opaque galleon
is the solution and answer correct?
timid silo
a/(1-r)
Well not exactly...
Since the series you have is infinite and starts at 1, you can just use 1/(1-r) though
Well actually I guess I also have to mention that you can use that simpler formula because r^n goes to 0 as n goes to infinity
opaque galleon
what if it doesn't start at 1
timid silo
Oh right that's how you got a/(1-r)
Somehow I missed that
Yes, a/(1-r) is correct after all...
opaque galleon
Yes, a/(1-r) is correct after all...
I wish there was a site like integralcalculator and derivativecalculator but for series
timid silo
I wish there was a site like integralcalculator and derivativecalculator but for...
You can use WolframAlpha or Desmos and replace infinity with some decently big number
,w sum from n=0 to 1000 of 1/2^n+1/3^3
warm shaleBOT
warm shaleBOT
timid silo
Even better
opaque galleon
,w sum from n=0 to infinity of 1/2^n+1/3^3
warm shaleBOT
timid silo
You used the one that was written incorrectly
opaque galleon
,w sum from n=0 to infinity of 1/2^n+1/3^n
warm shaleBOT
timid silo
Uh-oh
opaque galleon
what did I do wrong
timid silo
,w sum from n=0 to infinity of 1/2^n
warm shaleBOT
timid silo
,w sum from n=0 to infinity of 1/3^n
warm shaleBOT
warm shaleBOT
opaque galleon
nice
timid silo
is it a good idea to do divergence test first?
Yes
timid silo
Don't even ask me
Actually I think I can prove it diverges using the comparison test but I'd rather not bother and I don't have time
Good luck with that monstrosity
opaque galleon
Good luck with that monstrosity
repeated L'hopitals 😦
lost quartz
need help in help-0
timid silo
Where do I start?
timid silo
.close
gilded depot
obtuse pebbleBOT
sage geode
That is impossible though
timid silo
is that enough info to solve? i think something is missing
obtuse pebbleBOT
@gilded depot Has your question been resolved?
robust sleet
Strat?
patent jetty
Spicy lmaoo
I had a teacher who used to refer to hard questions as 'spicy questions' lol
obtuse pebbleBOT
@timid silo Has your question been resolved?
prisma moat
how do we solve part B
obtuse pebbleBOT
how do we solve part B
prisma moat
need a hint
i dont think its simply intgeral from 3 to infinity of the pdf simply because its conditional
mighty geyser
need a hint
P(a | b) = P(a and b) / P(b)
prisma moat
hmm i tried that but got the wrong answer
so here are my events
i probably did something wrong
B : Exceeds 2 hrs
A: Exceeds 3 Hrs
p(A and B)
here is where im suspecting i did something wrong
we just multiply A and B because theyre independent?
mighty geyser
no, they are not independent
prisma moat
a repair takes at least 2 hours and takes at least 3 hours
it takes at least 3 hours?
mighty geyser
yeah
prisma moat
right will try to solve it and get back to u
okay so its 1/e^3
B is 1/e^2
leaves us with e^2/e^3
1/e
but this is the answer on the book
pdf is e^-x
,rotate
warm shaleBOT
prisma moat
am i doing something wrong in terms of using the pdf to get the probability of P (X > 2 ) ?
obtuse pebbleBOT
@prisma moat Has your question been resolved?
obtuse pebbleBOT
@prisma moat Has your question been resolved?
prisma moat
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
serene fiber
The line of intersection between pi1 and pi2 is [x,y,z]=[2,4,-6] +t[1,-5,-1]. The point A(3,-4,1) lies on plane pi1, while the point B(4,-2,5) lies on plane pi2, determine the scalar equations of pi1 and pi2
obtuse pebbleBOT
The line of intersection between pi1 and pi2 is [x,y,z]=[2,4,-6] +t[1,-5,-1]. Th...
serene fiber
I just answered a question like this with different values and was wondering if my process was correct
I first used the position vector in the line with point A and B to get 2 direction vectors for pi1 and pi2
Then from I made vector equations of both planes by using their respective points (A and B) the direction vector I just made, and the direction vector from the lines vector equation
From there I used cross product to get a normal for each plane which I then used to makethe scalar equation for both
Then I simply solved for the missing D value by plugging in points A and B respectively
Does that sounds like the correct process?
<@&286206848099549185>
obtuse pebbleBOT
@serene fiber Has your question been resolved?
obtuse pebbleBOT
@serene fiber Has your question been resolved?
serene fiber
.close
timid silo
How is i going?
obtuse pebbleBOT
How is i going?
still wind
??
timid silo
I can help with stuf up to 6-t class and under
still wind
🙃ok
verbal kettle
Any conditions about the lines mentioned?
royal basin
@timid silo you're supposed to open one of these channels if you're the one who NEEDS help
if you can provide help then just do it. don't advertise.
timid silo
I am going to assume that that is a rectangle w/ diagonals and that we can make a statement like:
4(18) = 2m(7m + 13)
obtuse pebbleBOT
@timid silo Has your question been resolved?
craggy parcel
Hey I have a quick question. If I have the equation of the line r:x=y=1 how can I change it to parametric equation?
obtuse pebbleBOT
Hey I have a quick question. If I have the equation of the line r:x=y=1 how can ...
craggy parcel
yes to both
trim portal
well so for any t, what will y and x be?
craggy parcel
1?
trim portal
yep, so x=1, y=1, and z will depend on the parameter t somehow
and it really doesnt matter how (almost)
craggy parcel
can I use this λ? this is what I see on some exercises
trim portal
yeah you can
so z will depend on parameter lambda
you can just say z=lambda for -inf<lambda<inf
and thats the line
actually saying z=2*lambda would result in the same line
I just chose z=lambda for simplicity
obtuse pebbleBOT
obtuse pebbleBOT
@timid silo Has your question been resolved?
grave halo
I'm stuck on this problem
obtuse pebbleBOT
I'm stuck on this problem
grave halo
I tried change of variables with $u = xy$ and $v = y/x$ but I don't get the right answer
warm shaleBOT
Yann
grave halo
I was told you can do this by using a horizontally simple domain with 1<y<4 but I can't imagine the map to get there
Oh and this is how I visualised the domain
with the two relevant parts between the 4 points
rigid pine
Doesn’t look like you have to do a transformation.
The double integral has symmetry so equals twice the double integral of the region in the first quadrant. This can be split up using y = 2.
grave halo
im sorry i don't understand how i can set up the bounds of my x to work with this
^ integral of x
grave halo
so like $\int^4_1 \int^{4x}_{x }f(x,y)$
warm shaleBOT
Yann
grave halo
oh ok so the top region is from y=2 to 4 bounded by the curve and the line and similar for bottom but y=1 to y=2
rigid pine
$\int_{1}^{2} \int_{\frac{1}{y}}^{y} f(x, y) \dd{x} \dd{y}$.