but whatever
#help-19
low locust
so the question is why is F[x] a PID for a field F
frosty plover
i dont really know
frosty plover
they're commutative rings
low locust
well that depends on your definition of ring
(in particular including a 1)
but they are more than that
frosty plover
ik their characteristics. 0 is in I, they have additive inverse, theyre associative and you check the ideal condition where ir is in I for all r in ring R
low locust
ok. aka additive subgroup + ideal condition
frosty plover
ah ok
frosty plover
if I doesn't equal R?
low locust
well R is also an ideal that contains them but thats kinda boring
if thats what you mean
frosty plover
ik that ideals dont include multiplicative id, which seperates them from fields
low locust
well they sometimes do
but if they do then they are the whole ring
sry I have to go
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@frosty plover Has your question been resolved?
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ionic cargo
I have been working on this problem for over an hour and can’t find the answer. Help!
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@ionic cargo Has your question been resolved?
vague bobcat
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vague bobcat
i dont understand multiplying fractions good
i usually just make them into decimals
cold sage
$\frac{a}{b} \cdot \frac{c}{d}=\frac{ac}{bd}$
clever fjordBOT
AℤØ
vague bobcat
what about multiplying whole numbers with them?
cold sage
you can write any whole number as itself/1
vague bobcat
would i make a denominator for the whole number?
cold sage
same logic applies
sharp oak
2 is the same as 2/1, for example
odd edgeBOT
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low imp
i'm correcting my work, i feel like my work is wrong but idk where it went wrong (pic taken on laptop 💀)
low imp
how can i prove that options c and d are the largest and smallest values?
fresh ruin
I'd try turning them all into something easy to compare between, like log_3(x)
looks like you did something similar trying to get things in 27^x=... form
low imp
yeah, i'll try that this time
thx, i'll get back
for the first option, is this the right work?
@fresh ruin
fresh ruin
it's actually just fine as the top part, as long as you see that sqrt(45) is between 6 and 7
low imp
wait between 6 and 7? can you elaborate pls 😭
fresh ruin
like the goal is to have them all turned into something like
log3(6.7)
log3(5)
log3(7.6)
log3(5.2)
log3(8)
and it'll be easy to see
remember that sqrt(49)=7 is close by
so sqrt(45) would be a little less, that's all you have to get for that part
low imp
i forgot to mention, this was a no calculator test :(
we had to leave everything in log form
thx tho 💪
fresh ruin
yea you just have to get a feeling for what sqrt(45) is approximately and move on
low imp
i think i got it now, thank you so much! have a great rest of your day/night/whatever :)
ur method of referring to logs with good numbers rlly helped
@fresh ruin
fresh ruin
great!
low imp
.close
odd edgeBOT
limpid turret
question 29
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limpid turret
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jade cloud
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open knot
is this an alt acc?
astral nymph
no lmfao
jade cloud
no
jade cloud
i’m tryna get an answer for hee
open knot
k :D
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wintry viper
Can someone tell me what I did wrong when intergrating?
wintry viper
Sorry that it’s messy in advanced
minor crypt
Can someone tell me what I did wrong when intergrating?
what r u integrating?
wintry viper
(8cos - 6sin)^2
I did the actually integration on the last line
But I had to simplify it first
wintry viper
I basically turned the cos^2
Into
1+ cos 2(theta)
And for sin
^2
Into
1-cos(theta)
wintry viper
yea i did
odd edgeBOT
@wintry viper Has your question been resolved?
rough ginkgo
can somebody explain to me the relationship between parametric vector form and the top formula?
rough ginkgo
what is a, v1,v2
stark elbow
So the "equation" way of representing a plane, is just describing all of the points on the plane.
So all points (x_1, x_2, x_3) that satisfy that equation, are on the plane.
For the parametric way, think of a as any point on the plane.
And think of v_1, v_2 as vectors on the plane, meaning they describe the direction of the plane.
Any point on the plane can now be expressed by taking a, and adding to it some multiple of v_1 and some multiple of v_2.
So if you consider all points of the form:
$a + \lambda_1v_1 + \lambda_2v_2$
clever fjordBOT
RedstonePlayz09
stark elbow
Those points will form your plane.
Here is a picture I found on google:
So for example to get to point B, you first get to A, which is some point on the plane.
And then you have b_1, b_2 as direction vectors on the plane, so you add some multiple of them to get to B.
In this picture, A is your a, and b_1, b_2 are your v_1, v_2
This also shows that you can represent a plane in multiple ways using a parametric equation.
We can choose a to be ANY point on the plane, and choose v_1, v_2 to be ANY direction vectors (as long as they aren't multiples of eachother).
odd edgeBOT
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icy nest
What's the domain for this? I think my professor might've just input the wrong text on the automatic correction app.
icy nest
I have exactly this done.
odd edgeBOT
@icy nest Has your question been resolved?
icy nest
<@&286206848099549185>
I kinda need an answer lmao, I'm not confident enough yet to ask my professor directly
gentle crypt
Also check the other square root
icy nest
Also check the other square root
The other square root is a smaller ellipse, anything that's larger than or equal to 1 suffices.
So I just need to analyse the larger ellipse, which will cut out the part inside it for the domain.
Or at least it should be such.
gentle crypt
Oh, I hadn't seen you did both in the screenshot, my bad
Yes, correct, one is fully contained in the other, so just the larger one matters for the domain
icy nest
Damn, that's all then.
I was weirded out when the correction thing said it was wrong.
I'll ask my professor later today what's the matter.
Thanks, mate.
.close
odd edgeBOT
gentle crypt
What does the correction say, then?
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wary plinth
<@&286206848099549185> In this conversion of a DFA to an NFA, why are states {p0,p1}, {p0,p2}, and {p0,p1,p2} not final states?
odd edgeBOT
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wary plinth
here are my transition tables for reference:
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wary plinth
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modern bane
How did they go from the first step to the second? I asked ChatGPT, but it really didn't help
dense sonnet
tall veldt
You have a cubic equation, you can use the rational root theorem to find a root (provided it has a rational root) and from the root you get a factor
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modern bane
You have a cubic equation, you can use the rational root theorem to find a root ...
I feel like this is too complicated for what the scope of the question is... surely there must be a shorter way, because the video I'm watching on what you're suggesting is kinda... lengthy
odd edgeBOT
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tall veldt
Its pretty much your only option for factoring cubics fairly quickly
Alternatives are the cubic formula which is hideous or spotting some clever complicated manipulated enabling you to factor by grouping
odd edgeBOT
@modern bane Has your question been resolved?
modern bane
Alternatives are the cubic formula which is hideous or spotting some clever comp...
That is likely what the question wants
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glass horizon
could anyone help me figure out where i went wrong for this problem?
fresh ruin
that +1/2at^2 formula doesn't apply because the acceleration changes over the 8 seconds
you can split it up into the 3 parts with different w0 and a's or you could find the signed area under the w-t graph, same thing
glass horizon
ohh acceleration has to be constant? @fresh ruin
fresh ruin
yea all the displacement-velocity-acceleration equations require constant acceleration
for these graph problems I'd just try finding the area instead
glass horizon
ah i forgot about that
if i got 52 as the total area under the graph, that would be the theta after 8 seconds?
or do i just need to find t he area from 7-8
fresh ruin
it's asking for the whole thing yea
and remember the graph is in radians and 2pi radians = 1 revolution
fresh ruin
right that's the final answer
odd edgeBOT
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stiff kettle
it says, determine the equation of the parabola with... vertex (0, - 10), and x intercepts 5 and -5
stiff kettle
how should i start
bc the answer key says y=0.4x^2-10
but i dont get why they did that
because i got y= 2/5 ( x-5) (x+5)
is that the same LOL
oh it is rhe same
stiff kettle
because i got y= 2/5 ( x-5) (x+5)
BUT ISNT THIS RIGHT
LIKE WHY DID THE ANSWER KEY EXPAND IT...
cold sage
what did it specifically ask
stiff kettle
it says, determine the equation of the parabola with... vertex (0, - 10), and x ...
THIS
word for word :')
odd edgeBOT
@stiff kettle Has your question been resolved?
dim matrix
Did it give you the focus or directrix
stiff kettle
it says, determine the equation of the parabola with... vertex (0, - 10), and x ...
it told me this
dim matrix
That's it
indigo reef
For each of the following three graphs, consider a Markov chain defined by a random walk over the nodes of the graph:
- The cycle graph with n=13.
- The cycle graph with n=12.
- The cycle graph with n=13 and an extra edge connecting nodes 1 and 6.
Q: For each Markov chain, explain whether it is aperiodic or irreducible.
indigo reef
Is it
irreducible, periodic
irreducible, periodic
irreducible, aperiodic
?
supple cloak
can the walk go both directions around the graph or just in one direction?
odd edgeBOT
@indigo reef Has your question been resolved?
indigo reef
can the walk go both directions around the graph or just in one direction?
Yes, they're (undirected) cycles
supple cloak
Yes, they're (undirected) cycles
well in that case I think that if n = 13 then the graph might not be periodic because you can return to any point in 2 or 13 moves (or a bunch of other numbers as well)
you said that the cycle graph with n =13 is periodic
indigo reef
you said that the cycle graph with n =13 is periodic
oh, right. The one without the extra edge
indigo reef
well in that case I think that if n = 13 then the graph might not be periodic be...
if this is the case, then isn't the n=12 graph also aperiodic?
supple cloak
if this is the case, then isn't the n=12 graph also aperiodic?
I think that one would be periodic because there isn't a way to get back to any point in an odd number of steps
so the period would be 2
indigo reef
I guess that's true by definition. a-b-a is a len 2 cycle, and gcd(2,13) = 1 so n=13 graph is aperiodic
I'm convinced
indigo reef
so the period would be 2
do you have any idea about irreducibility?
supple cloak
do you have any idea about irreducibility?
they're all definitely irreducible because you can always just go around the circle normally to reach every state
indigo reef
they're all definitely irreducible because you can always just go around the cir...
🙏
thank you
.close
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limber comet
odd edgeBOT
limber comet
how is this a homogeneous equation
odd edgeBOT
@limber comet Has your question been resolved?
limber comet
helpplease
static sable
odd edgeBOT
static sable
how i solve
timid cairn
gcd has to divide x right
so as a lower bound we can say x is at least 490
thats honestly as much as i can say without giving it away i think
odd edgeBOT
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static sable
thats honestly as much as i can say without giving it away i think
give it away as much as you possibly can
ik the answer is 980 i just don't know how to get there
timid cairn
well its at least 490
and its not 490 just cause the problem tells us
it needs to be a multiple of 490 because 490 is a divisor
so the least multiple of 490 is 490x2
also works with lcm
if lcm only had 2 and not 2^2 we would have needed to multiply by 3 instaed
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mystic saffron
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mystic saffron
This is the question. Its a bit archaic so i find it tough
help
I understand that for the case where sweets of 3 distinct flavours are selected, the no. of permutations is 6C3
potent folio
I understand that for the case where sweets of 3 distinct flavours are selected,...
yep, what about the other case(s)?
potent folio
yes, so any ideas? or are you stuck there?
mystic saffron
i was thinking
if i selected two out of 6 sweets
id have 15 possible combinations
and for the other one im not sure what to do
potent folio
okay so if there are 2 sweets of the same flavor, there are only 6 ways to choose that specific flavor. then how many choices are there for the last flavor?
mystic saffron
5 ig
wait
ah i added 6 and 5
instead of multiplying
forgot they were the same case
the final answer is 50 right?
.close
odd edgeBOT
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fair bridge
Hey
fair bridge
Can someone help me with roaller coaster assignment in desmos?
cold sage
im curious now
cold sage
you havent actually asked anything
odd edgeBOT
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fair bridge
?
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@fair bridge Has your question been resolved?
visual hazel
Hello, help me to finish simplifying this trigonometric expression pls.
green elm
working with this:
you need alpha - pi/4 here, so use the fact that sin(x+pi/2) = cos(x) and similarly for cos(x+pi/2)
to convert this into a form involving alpha - pi/4
then you can use this:
@visual hazel
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@visual hazel Has your question been resolved?
visual hazel
you need alpha - pi/4 here, so use the fact that sin(x+pi/2) = cos(x) and simila...
I'm sorry but I didn't understand very well, why do I need to have alpha - pi/4?
green elm
because you are trying to reach tan(alpha/2 - pi/8)
alpha/2 - pi/8 = (1/2)(alpha - pi/4)
you want to use the half angle formulas
so you need a formula involving alpha - pi/4
visual hazel
alpha/2 - pi/8 = (1/2)(alpha - pi/4)
and how can I get this?
green elm
^ you want to use this (specifically tan(A/2) = the expression at the far right hand side)
with A = alpha - pi/4
visual hazel
I still can't see your track :/
visual hazel
^ you want to use this (specifically tan(A/2) = the expression at the far right ...
the question is how do I get that "A"?
visual hazel
but in the exercise there is alpha + pi/4
green elm
you have sin(alpha + pi/4), which you can rewrite as cos(alpha - pi/4)
and similarly you can rewrite cos(alpha + pi/4) as -sin(alpha - pi/4)
visual hazel
you have sin(alpha + pi/4), which you can rewrite as cos(alpha - pi/4)
waitt, why?
green elm
use the general fact that sin(x) = cos(x-pi/2)
and cos(x) = -sin(x-pi/2)
here, x = alpha + pi/4
visual hazel
and cos(x) = -sin(x-pi/2)
Do these identities have a name? Because I don't know them and I need to look them up
green elm
hopefully it's obvious from the graphs
you can get them using the sum formulas, for example:
cos(x - pi/2) = cos(x)cos(pi/2) + sin(x)sin(pi/2) = cos(1)(0) = sin(x)(1) = sin(x)
visual hazel
and similarly you can rewrite cos(alpha + pi/4) as -sin(alpha - pi/4)
I'm not really understanding most of it, but I'd like to finish it and understand it later
green elm
yea you're basically there
use this:
you have (1 - cosA) / sinA
where A = alpha - pi/4
so your answer is tan(A/2)
which is what you want
cloud wedge
could someone explain this proof? i don't understand how they go from the third line to the fourth. https://www.forgottenbooks.com/en/download/TheModernGeometryoftheTriangle_10001164.pdf
page 96, section 133
odd edgeBOT
could someone explain this proof? i don't understand how they go from the third ...
@cloud wedge Has your question been resolved?
jagged idol
I feel like I did something wrong. Can I get help identifying what.
zinc glacier
odd edgeBOT
@jagged idol Has your question been resolved?
jagged idol
Oh.
I'm currently on the bus home, can't take it out again. I'll be back in about 15-20 minutes.
odd edgeBOT
@jagged idol Has your question been resolved?
jagged idol
You know, it's fine.
odd edgeBOT
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magic hedge
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tidal marsh
What's the question?
magic hedge
What's the question?
you need to point out if Assertion is true or false
If Reason is true or false
and
if Reason is the correct explanation for the Assertion
tidal marsh
Did you get any of those parts yet
magic hedge
Did you get any of those parts yet
I think reason is correct
but I didn't understand the maning
of 'surd roots'
tidal marsh
Surd is just an irrational square root
So surd roots have square roots like sqrt7, sqrt 10
tidal marsh
Yes
magic hedge
so reason is true
tidal marsh
Yes
magic hedge
which would make assertion true as well
tidal marsh
Yep
magic hedge
and it does explain it
tidal marsh
Yeah
magic hedge
alright thank you
tidal marsh
Yw!
magic hedge
.close
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orchid thunder
I solve integral of 1/sin(x) by using trig sub, but I get different answer than it should be. Graphically it looks almost identical, so I assume there is some minor issue. Could anyone help?
fresh ruin
yea since graphically they line up your answer is correct, but the tan(x/2) form is a little more simplified using a trig identity, you sort of just have to check your trig fractions to see if they line up with a double/half angle identity
here your (1+cos(x))/(1-cos(x)) turns into 1/tan(x/2)^2
tight nova
love your handwriting
orchid thunder
here your (1+cos(x))/(1-cos(x)) turns into 1/tan(x/2)^2
where do you see it am I blind
orchid thunder
love your handwriting
lol I know its terrible
fresh ruin
the bottom right one is your fraction upside down in a square root
tight nova
lol I know its terrible
bro no im dead serious
orchid thunder
the bottom right one is your fraction upside down in a square root
ohh now I see
thank you sm
.close
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vale root
can I please get help on this
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Available help channel!
vale root
vale root
@reef sandal
reef sandal
loud bough
g(x) = 8log (2(x))
= 8[log 2 + log ×]
= 8log_10 (2) + 8log_10 (x)
= 2.408 + log_10^1/8 (x)
= 2.408 + log_1.3335 (x)
= log_1.3335 (x) + 2.408
vale root
yes
loud bough
my name is parvati too.
vale root
is it the value of x?
LMFAO WHAT
my name isn’t Parvati I just love the goddess <33 you have a pretty name
vale root
so how does it relate to a)
oh I have that written down but how does 8log_x become log ^ 1/8(x)
loud bough
so how does it relate to a)
g(x) = 8log[2(x)] = log_1.3335(x) + 2.408
the equivalent function is log_1.3335(x) + 2.408
where b is 1.3335, x is x and c is 2.408
vale root
okay
loud bough
oh I have that written down but how does 8log_x become log ^ 1/8(x)
it is a property of log
vale root
vale root
The third property I have written?
vale root
from the 8?
loud bough
so it goes to 10^(1/8)
loud bough
from the 8?
yes
loud bough
8log_10 (x) => 1/1/8log_10(x) => log_10^(1/8)(x)
loud bough
and put log _ ^ 1/8
yes
vale root
I get that part now
loud bough
are you in college?
vale root
no
loud bough
what grade?
vale root
12 but taking a gap
loud bough
same
vale root
running a business
loud bough
nah nah it's ok
vale root
I thought you were in college lol
loud bough
i just get lucky some times
vale root
😂
loud bough
I thought you were in college lol
i took AP classes so i know a lot of college stuff
vale root
you should accept my fr and we can talk more
vale root
.close
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raw dome
this was in my last exercise sheet , didnt get answer sheet just yet, is there anyone who can solve it:?
odd edgeBOT
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raw dome
<@&286206848099549185>
green elm
the functions are defined piecewise, and each piece is a polynomial, so the only possible discontinuities will at the boundaries between the pieces
did you check those points?
next prawn
did you check those points?
I don't think that's their issue
This is asking for an epsilon-delta proof
green elm
oh ugh, you get to do epsilon/delta on the "obviously continuous" parts too? 😁
fortunately they're easy
raw dome
fortunately they're easy
any chance you could show me what i should have wrote?🤞
green elm
what you have is pretty good
you just need to be careful to make sure your delta is small enough that both x and c are in the same "section"
(for case 1 and the trivial case)
setting delta = epsilon may not guarantee this
something like delta = min(epsilon, |c|) should do it though
odd edgeBOT
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mystic saffron
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mystic saffron
options:
<@&286206848099549185>
need it done asap im gonna get a detention 😭
aaa
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tall spruce
- Plane P consist of points A, B, C, D, and E. The points A and C are collinear to point D. Line BE intersects line AC at point D. where point E is non collinear with points A and C. Such that, line m intersects line AC and parallel to line BE.
planene w contains lines AB and XY, which intersects at Point P. Line JG intersects wat point H that is not collinear with line AB.
odd edgeBOT
@tall spruce Has your question been resolved?
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@tall spruce Has your question been resolved?
tall spruce
<@969829352516759552> Has your question been resolved?
Help
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@tall spruce Has your question been resolved?
tall spruce
Ok ill help
please
tall spruce
is my answer right??
tiny karma
is my answer right??
Kinda…
tiny karma
Oh shit is this 8th grade math
tiny karma
Tell him “Point A and C show no points of collinearality” but in this case your answer is right
@tall spruce
tall spruce
Tell him “Point A and C show no points of collinearality” but in this case your ...
alr
thanks
so 1 and 2 are right??
tall spruce
plane w contains lines AB and XY, which intersects at Point P. Line JG intersects plane w at point H that is not collinear with line AB.
thats the 2nd pic says
tiny karma
so 1 and 2 are right??
Yep
paper moth
Hi this is my assesment task i have no idea how to do it
vernal yacht
Hi this is my assesment task i have no idea how to do it
Can you show your "timesheet" ?
sharp oak
Hi this is my assesment task i have no idea how to do it
This is not a question, this is a summary of the assignment. Did you post the right picture?
paper moth
something like this ig
paper moth
This is not a question, this is a summary of the assignment. Did you post the ri...
yes but idk how to do anything in the assignment
you have to calculate the income and tax paid
vernal yacht
...
odd edgeBOT
@paper moth Has your question been resolved?
paper moth
yay
open onyx
you filled in nothing, so you can do nothing with it
paper moth
someone finally came
paper moth
you filled in nothing, so you can do nothing with it
no but how would i find the income if it was filled?
<@&286206848099549185>
omd
someone help me
open onyx
rate tells you how much you get paid per hour
and you fill in how many hours worked
given that information find the income
open onyx
it should be given to you
it's like working a job then ask your boss "hey how much do i get paid again"?
paper moth
but isn't their like a formula
like
ok
but what do i do with the overtime
don't i multiply it?
open onyx
different rate same thing
open onyx
then you can do nothing
open onyx
the whole idea of your task is they give you every number you need
open onyx
as far as i read your assignment they give you everything filled in the time sheet
and you figure out income and then tax
(which is never a part of timesheets anyway)
paper moth
ig but idk
paper moth
(which is never a part of timesheets anyway)
k thx
open onyx
if there's a number you need other than income and tax and you can't find complain to your instructor
tidal barn
odd edgeBOT
tidal barn
I need to prove this but modifiee, we assume A is symmetrical matrice 2x2
And I have to show equivalance between: given equation represent scalar product <=> a11>0 and det(A)>0
And I know(can use) that given equation is scalar product if and only if A is positive definite
So I can skip tranverse and linearity
for any u non zero <u,u> > 0
Thats what I have to prove
So how to start
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mystic saffron
Hi I'm a bit stuck, I've drawn this up, is this correct?
wispy birch
Yeah..ig so what was the qn
odd edgeBOT
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silk coyote
<@&286206848099549185>
silk coyote
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tidal temple
could someone help with geometry proofs
odd edgeBOT
could someone help with geometry proofs
tidal temple
bro
gray hawk
could someone help with geometry proofs
Sure
tidal temple
ok
tidal temple
i hate proofs
been sailing through this stuff
then this deltamath came
at this point im spamming it
also thanks btw
tidal temple
uh
gray hawk
Etc
tidal temple
well
i cant solve the proof
and i cant figure out where i went wrong
or what im missing
obviously not wrong
gray hawk
Lemme look at it for a hot minute
tidal temple
that problem tells me whats wrong and what not
i just cant figure out where to go
i also prob have more lines then i need
gray hawk
Alright im gonna try to solve this on my whiteboard
tidal temple
aight
gray hawk
To be honest I'm not entirely sure how to solve it either
tidal temple
lol
gray hawk
I was really good with proofs when I took the class but this stumped me
tidal temple
i hate this guy with deltamaths
never gave us proofs with multiple shapes in class
but randomly had problems with it on deltamath
tidal temple
imean usually i like the delta math
because it helps me actually understadnt the math
because i have to do it until i get it right and has videos n example
but when its this stuff im cooked
gray hawk
Hold on for a second I'll be back I need to ping help in my thing rq
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ashen ether
Hello
ashen ether
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ashen ether
\||c||^2 means <c,c>
yes but there is a 2 at the bottom and a 2 at the top
what does bottom 2 mean?
fresh ruin
oh it's a very technically descriptor for what the || . || metric is
here it's || . ||_2 for the 2-norm, which is the usual norm everyone uses and means ||c||^2 means <c,c>
ashen ether
but it does not affect the calculations in any way?
and after they say that
you know why ?
A^T Ax , x
fresh ruin
I mean it matters but it's the usual version of the norm so I wouldn't worry about it
2 the comes from the exponents here, if it was a 3 norm you'd do x^3 and cube root
that's a matrix property for dot products, to move a matrix across <x,Ax> you do <A^tx,x>
ashen ether
ok thank you very much for your help !
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mystic saffron
how does it turn into 4???
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how does it turn into 4???
lean willow
What have you tried
mystic saffron
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fervent hawk
the last part, the numerator should be √(x+5) +2
mystic saffron
.close
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mystic saffron
thank you
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jagged sable
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nocturne ridge
Any questions.
jagged sable
Any questions.
like do i distribute the square
or do i cancel out cuz it's under the radical
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jagged sable
.close
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sacred gale
Can anyone who is dutch help me with this problem? I can translate if u want.
sacred gale
I dont know whats wrong with the graph.
glossy summit
I think it would help the dutch helpers if we could see the graph and questions. Just like zoom-in.
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spring tendon
x^2+ax+2a+5=0 In order to get 2 reel solutions what numbers can a be? Is the question im stuck on the part where a^2-8a-20=delta but delta is higher than 1 since there needs to be 2 different reel solutions
spring tendon
Ah tru but still dont understand how to do it also this is a problem from languages what is quadratic inequalities
I might have leaned it might not have
glossy perch
so intuitively the way to solve a²-8a-20≥0 is to graph a²-8a-20, and see where the graph is above the x axis
spring tendon
Ah yeah didnt learn that
glossy perch
it seems overly complicated but you'll get used to it
glossy perch
so the graph would be a parabola facing upwards, intersecting the x-axis at -2 and 10
does that make sense
spring tendon
Yeah
glossy perch
so if you imagine, on the right of 10 the parabola keeps going up, and on the left of -2 the parabola also keeps going up
so that means the quadratic in a is greater than 0 when a≥10 or a≤-2
glossy perch
the middle part is when a²-8a-20≤0, which is not what you wanted
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young oyster
One person is going at 5km/h while after 1h 40min another person starts going from the same point. They meet after another 50min, at what speed what the second person going at?
dusty wyvern
what have you got so far?
young oyster
dont really know where to start
long tinsel
relative velocity?
young oyster
yea i think so
dusty wyvern
that’s a nice way to think about it
to unpack it a bit
say the second person is going x km/h faster than person one
then this speed is exactly the speed at which their distance decreases
so we have a speed of x, 50 minutes and the distance travelled in 1h 40min at 5mph
to calculate the distance in the 1h40min, firstly translate that into hours, so 1+40/60 = 1+2/3
then times by speed, so 5+10/3 = 8+1/3 km
so we want to find x where x is the speed that goes 8+1/3km in 50 min
so divide 8+1/3 by 5/6, aka (6/5)*(25/3) = 10km/h
so the relative speed is 10km/h
ie person 2 is going 10km/h faster than person 1, so overall they’re going at 10+5 = 15km h
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dreamy olive
There's another way to do it just like shifting math graphs
If you were starting at 20 minutes, then you have t-20 everywhere instead of t
so t-20 is defined when t≥20, and see that matches cuz that would evaluate to 20-20=0 relative for the guy that started later
young oyster
so we want to find x where x is the speed that goes 8+1/3km in 50 min
i know the answer is right but i still dont get why you would try finding how long it would take them to get to the point at which the other person is already moved away from
ok i finally figured it out
.close
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chrome nimbus
approximating
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approximating
chrome nimbus
2(9+3)-5(21+12)=0
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lavish jackal
2(9+3)-5(21+12)=0
use a calculator
chrome nimbus
why
lavish jackal
wdym why?
chrome nimbus
i cant
chrome nimbus
Vieta's formulas
lavish jackal
go for it
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spiral jetty
can anyone help me understand why this works? I know from the definition provided in class that this is how you compute these sorts of problems but im not understanding why this actually works
spiral jetty
in my mind, my intuition is telling me the answer should be 0 since as n goes to infinity, 1/n approaches 0
and then if that goes to 0, then you just times the whole thing by 0. this is not the case however
long tinsel
that only works for a finite number of terms
in this case the number of terms are not finite
spiral jetty
but surely as n goes to infinity there are an infinite amount of terms?
low locust
do you also think that as n goes to infty, 1/n*n goes to 0?
it also has 1/n in it
the number of terms isnt necessarily the problem. but the point is that the value of those grows with n. which counteracts that 1/n goes to zero
spiral jetty
when you say 1/n* n do you mean 1/(n^2) or (1/n) * n ?
low locust
(1/n)*n
spiral jetty
the *number* of terms isnt necessarily the problem. but the point is that the va...
the value of the terms grows with n?
spiral jetty
but why are you saying that we are looking at (1/n) * n, sorry im a bit confused hahaha
low locust
your problem has 1/n*some sum
you are trying to argue that because 1/n goes to zero, the whole thing should go to zero
in my example, we still have 1/n* something
and by that same argument, it should also go to zero
but it clearly doesnt
spiral jetty
i am confused as to why it doesn't go to 0, i know it shouldnt because of how i've been taught "if you have a problem looking like this, use this method to solve"
i think what is confusing me as well is the fact that we have the sum starting from k=1 to n but n is going to infinity
intuitively this is not making sense to me hahaha
low locust
well first you compute the whole expression. and then you send n to infinity
you dont actually have infinitely many terms
your best bet will be to actually calculate the expression
grab a pen or a calculator and calculate the value of the expression
for example for n=3,4,5,6
spiral jetty
i have a pen, give me sec
so for n=3, im computing 1/9 + 2/9 + 3/9 ?
total, this equal to 2/3
no wait i forgot to square the numerator sorry
14/9 = 1/9 + 4/9 + 9/9
then multiply this by 1/3 to get 9/27 = 1/3 ??
spiral jetty
ah yes, my bad sorry
14/27, my mistake
so if i repeat this for n=4, 1/16 + 4/16 + 9/16 + 4/16 = 30/16, multiply by 4 to get 30/64 ?
low locust
keep going
spiral jetty
ah wait, i can sort of feel how this wont be going to 0
like i cant articulate my thoughts but I can feel it if you get me
ill try for n=5
low locust
like i cant articulate my thoughts but I can feel it if you get me
yes. thats what I want
spiral jetty
1+4+9+16+25 / 25
55/25 ?
it cant go to 0 if we have the end term of our sum being n from k to n
ah no wait, i can feel it but i cant say it sorry haha
we have been learning about intergration and step functions this week so I will try to relate to that
low locust
the sum keeps growing
sure, you divide it by 1/n which gets smaller. but because the sum keeps getting bigger, it balances out
spiral jetty
the sum is growing, we are finding areas of the rectangles and the widths are decreasing sort of?
like it feels like we are approximating but it only gets better as n is going to infinity
i think
low locust
we are exactly approximating the area under the curve
smaller rectangles -> better approximation
spiral jetty
no matter the value of n, the last term in our sequence will always be equal to n
yes exactly what I wanted to say
this is making so much more sense
for a greater value of n the better the approximation of n, as n is going to infinity, the appoximation is becoming exact
we are getting closer to the "true" value
am i correct in my thinking?
low locust
yes
spiral jetty
i think im starting to understand it now
omg, you know when you learn a new concept and youre unsure
and then you breakthrough and have a eureka moment
im just thinking back to how we defined step functions and the integrals of them, this makes so much more sense
so as we are increasing the value of n the width of the rectnangles decreasing, leading to a better approximation, thus leading to the definition of the integral
i love mathematics sometimes holy
spiral jetty
yes
youre a legend man !
thank you for taking me through the process of working out what the sum is for each n value
low locust
you're welcome
spiral jetty
as n is increasing, each term will be getting smaller BUT it will be getting more accurate
so n increasing is decreasing the width
AH
spiral jetty
you're welcome
thank you so much omg
spiral jetty
you're welcome
without the 1/n outside the summation, our series would diverge or can we not say?
wait no, let me think about it a second sorry. i have a bad habit of making statements without proof
without the 1/n the series will always have the final term equaling to 1
rocky juniper
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rocky juniper
Hello, I'm having trouble with finding an efficient algorithm for this. The tip says that I should use the gcd, do you have an idea or another tip?
1 <= k <= 10
south plume
Hello, I'm having trouble with finding an efficient algorithm for this. The tip ...
is gcd slow?
rocky juniper
no it isn't
but i can't see the relation for that
I drew a hasse diagram for k = {2,4,5} and range [1,20]
where the number of non divisible numbers is 8
but e.g. 20 / 5 + 20 / 4 = 9
do you maybe have an idea?
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errant notch
need help, the teacher didn't even teach us the formula too
odd edgeBOT
need help, the teacher didn't even teach us the formula too
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mellow vigil
How do i do the square part
odd edgeBOT
How do i do the square part
tiny hazel
mellow vigil
5
clever fjordBOT
flurry
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stone leaf
hi, ive been struggling so much with part b, i dont know where to begin?
stone leaf
the first part was just fine, im just unclear now
slender rampart
hi, ive been struggling so much with part b, i dont know where to begin?
log(a^k)=kloga
stone leaf
yes i know that, i just don't really understand what im supposed to do with the expression and substituting
weary pelican
slender rampart
hi, ive been struggling so much with part b, i dont know where to begin?
well
once u factor out ln3
it becomes a series of r(r+1)
stone leaf
oh i see, thank you very much!
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obsidian loom
Need help with part b all the work is done here I just forgot how I did it
obsidian loom
In part b, in the third line I don't understand where that came from and same with the 6th line
How did we get the values of EQ and EP
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sinful bison
how do I solve this by parts without going into a loop? I tried the problem using both possible values of u and dv and either way I end up in a loop
amber schooner
you use the loop
sinful bison
my issue is I keep reaching a point where the u and du values are back to what they were at the start though
if I integrated again here I would just end up with the first step again right?
shy sundial
amber schooner
ok but notice that you have an integral of e^xsinx
which is what you had originally
yes look here
odd edgeBOT
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silent zephyr
hello i don’t really understand how to do this because my teacher’s example was a whole completely different equation/word problem than this
silent zephyr
and i wasnt given a formula
I tried just doing it the normal trig way but the answer wasnt correct (i have the answer sheet at the end of my hw)
but i need to show my work and i wanna know how to do this
hushed island
Do you know law of cosines