by an amazing coincidence, i watched a tv show last night with an actress who had a face like a komodo dragon
#help-33
marsh citrusBOT
@drifting swallow Has your question been resolved?
static quarry
<@&268886789983436800>
quaint hill
.close
placid quarry
2 0 2 3 4 5 6 7
3 0 3 4 5 6 7 8
3 0 4 5 6 7 8 9
5 0 5 6 7 8 9 10
i have this in an array of vectors such that they are sorted based on first element
now see
I am given a number n
I want to choose indices in each array so that the sum of all the values at those indices is n.
there can be multiple ways to do it,
so my restriction is that the lowest array should have the maximum index and first array should have the minimum
In each array, the first two indices are not permitted in the summation
what do you think would be an optimum way to do this?
is there some tricky theorem I have no idea about?
marsh citrusBOT
2 0 2 3 4 5 6 7
3 0 3 4 5 6 7 8
3 0 4 5 6 7 8 9
5 0 5 6 7 8 9 10
i have this in...
placid quarry
@quiet anvil
have a look if possible 
thank you anyhow
quiet anvil
^ I asked him to ping me.
for clarity, your array of vectors is first vector (2, 3, 3, 5), second vector is (0, 0, 0, 0) and so on?
and the idea is you choose an index into all of these vectors simultaneously?
so if I choose index 0 that gives me 2 + 0 + 2 + 3 + 4 + 5 + 6 + 7?
oh, you can choose the indicies independently
and the restriction is that your sequence of indices must be monotonically decreasing.
placid quarry
for clarity, your array of vectors is first vector (2, 3, 3, 5), second vector i...
no no
its (2 0 2 3 4 5 6 7)
second one is (3 0 3 4 5 6 7 8)
and so on
in this case, I already wrote them in sorted order based on first element
So the sorting is done between arrays and not array elements
placid quarry
yeah
but somehow the question has assured you that there is atleast one possibility
if so, find that, otherwise, optimize and make it so that the lowest array has the highest index possible
quiet anvil
so is the following a valid matrix?
1 2 5 3 9 2
1 3 4 6 1 3
2 0 3 4 3 2
i.e. the entries in each row are not necessarily increasing after the first two.
placid quarry
so if I choose index 0 that gives me 2 + 0 + 2 + 3 + 4 + 5 + 6 + 7?
the summation is done between different arrays
in another way, its done column wise
2 0 2 3 4 5 6 7
3 0 3 4 5 6 7 8
3 0 4 5 6 7 8 9
5 0 5 6 7 8 9 10
so the first and 2nd element of each array are not permitted
so first combination would be 2+3+4+5=14
say the target value is 15, then this is not a possibility
so we go on from the bottom
we choose 2+3+4+6=15 as the best combination becase 6 has the highest index and is in the lowest array, while the other elements are in the minimum index positions possible
basically at no point, would there exist a selection such that it has a higher index than another selection below it.
quiet anvil
the reason I ask is because your matrix from column 3 to the end has a very special structure.
and if we can leverage that structure then the problem is easy
but if this structure is not guaranteed then the problem is probably np-hard
placid quarry
i.e. the entries in each row are not necessarily increasing after the first two.
no no, its a given that they will increase
that's a helping hand to help increase the possibilities
in any row, after the first two elements, the values at subsequent indices must increase.
quiet anvil
and the goal is the lowest maximum?
so you can pretty rapidly figure out the range of the final index by just summing each column. If the sum undershoots the last index must be higher, if it overshoots then it can be that index or smaller.
placid quarry
yeah
the lowest array should have the selection with the maximum index
and all the other selections above this array, would have their respective selected indices in decreasing order
here take a look at this
2 0 2 3 4 5 6 7
3 0 3 4 5 6 7 8
3 0 4 5 6 7 8 9
5 0 5 6 7 8 9 10
a valid selection for a given target value of 15
quiet anvil
and because these are sorted, you can use a binary search to do so, so you don't have to sum each column.
placid quarry
2 0 2 3 4 5 6 7
3 0 3 4 5 6 7 8
3 0 4 5 6 7 8 9
5 0 5 6 7 8 9 10
this is also a valid selection for a given target value of 18
quiet anvil
So this step, determining the range of the final index is O(log n) where n is the number of columns.
placid quarry
and because these are sorted, you can use a binary search to do so, so you don't...
binary search in each array?
placid quarry
i think that won't work, probably
because i don't know how n will be split among the column values, i don't know what I must search for
its not necessary that they must be of a same column
otherwise all selections will have the same index
quiet anvil
So you can do better for 18 because 4 + 5 + 6 + 7 = 22, so we can drop 4 worth to get 2 + 4 + 5 + 7 = 18
this just is to give you bounds on the final value.
3 + 4 + 5 + 6 = 18 directly though
oh, you're trying to do the opposite of what I am assuming?
huh
placid quarry
hm this has gotten interesting
so even now its possible to have more than one correct answer 
placid quarry
oh, you're trying to do the opposite of what I am assuming?
no no
ur doing it right
quiet anvil
well 2 + 3 + 4 + 9 = 18 as well
oh
well, ok
in that case, here's how I would approach it. Find the column where the sum is the first to go over the target.
then adjust the indices above it to try to make the sum
if no combination works, you will have to move on to the next one.
let's try 21 as an example.
placid quarry
well, how about I impose one more instruction
but before, because if there are multiple answers, then its no good
even an optimized algorithm would still fundamentally be checking more possibilities than required, the question says it will have only 1 answer
and if i am getting multiple answers, then this means that I might as well have used recursive backtracking or two pointer approach to do it, but its a very tedious job to optimize based on that
would you like to hear the other condition, which will certainly assure only one unique solution?
quiet anvil
2 0 2 3 4 5 6 7
3 0 3 4 5 6 7 8
3 0 4 5 6 7 8 9
5 0 5 6 7 8 9 10
These sum to 18, too low.
2 0 2 3 4 5 6 7
3 0 3 4 5 6 7 8
3 0 4 5 6 7 8 9
5 0 5 6 7 8 9 10
These sum to 22. So we have overshot. Now we need to figure out how to adjust an index to reduce the sum by 1. Here it is easy. We can change the 4 to 3 in the first row.
would you like to hear the other condition, which will certainly assure only one unique solution?
I would obviously want to know the entire problem before attempting to solve it...
placid quarry
dw thinking in this direction will definitely help with the final solution
but its not quite done yet
the final instruction tells me to use the first index of each column, which we earlier ignored
basically, now we have more constraints
each row will have only 8 elements
and then, all the way from the last element, we set a initial value x to 10 , then subsequently on moving left, we decrease x by 1 until we encounter the 2nd index, at which point we stop
we do not include the 2nd index
2 0 2 3 4 5 6 7
3 0 3 4 5 6 7 8
3 0 4 5 6 7 8 9
5 0 5 6 7 8 9 10
-
- 5 6 7 8 9 10
quiet anvil
the problem seems ridiculously convoluted.
placid quarry
:') it is
well, let's finish it while we're at it
i didn't tell you this at the start because i thought there'd be a unique solution
but you showed me there could be still be more than one correct answer
the whole problem is kinda complicated, but here it is anyway
quiet anvil
I don't understand this final instruction
placid quarry
wait wait, its not complete
2 0 2 3 4 5 6 7
3 0 3 4 5 6 7 8
3 0 4 5 6 7 8 9
5 0 5 6 7 8 9 10
_ _ 5 6 7 8 9 10
now that we have assigned a value to each index other than the first two, we describe some basic math
basically, instead of the lowest array having the maximum index (that instruction you can scrap)
now you have to calculate points
each point is allocated based on a very specific method
suppose you make a selection like this
2 0 2 3 4 5 6 7
then as written earlier, the value allocated to this position is 8 as in
_ _ 5 6 7 8 9 10
so its the 3rd one from the end
now we have 8/10, 10 is a fixed number, 8 is determined by position
and we get 0.8, we multiply 0.8 by the first element, that is 2, to get 1.6
now we store this 1.6 in another value called sum
our goal is to maximize the overall sum
for that, we need to select the appropriate index at each row
Earlier on,I said that the array was sorted based on first element, that was done to help get the highest value at the lowest position, so that we could directly find the required position
@quiet anvil
marsh citrusBOT
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.
placid quarry
i tried to optimize it 😭
the original problem is this
earlier on i believed it could be simplified
otherwise this is one heck of a long question
quiet anvil
please post the original question verbatim
placid quarry
uh
idk how to post that
its not written in eng
quiet anvil
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.
placid quarry
and it even has links attacted to it to explain the whole math that I described to you
alright
have a read
i asked this in this server cuz I thought there's gotta be some algorithm for it
maybe discrete math ppl would know 
i translated it to eng
google translator
ugh, i feel guilty for some reason
quiet anvil
can you give a translation of how to calculate CGPA?
I'm not sure how each letter grade is weighted
my assumption is A = 4, AB = 3.5, B = 3 and so on?
placid quarry
a grade A means 10 points
AB means 9 points and so on till D
D is 0 points and its not allowed to fail
suppose someone gets 6 points
then since all points are out of 10, its converted to 0.6
then its multiplied by the credits awarded to that subject
finally all credits you scored, vs total credits is evaluated against 10 points
so if you have 8/12, its converted to 2/3 *10 = 6.6
that's your final cgpa
quiet anvil
ok
that doesn't work out though
if A = 10, AB = 9, B = 8, BC = 7, C = 6, CD = 5, D = 0?
big drop?
placid quarry
if A = 10, AB = 9, B = 8, BC = 7, C = 6, CD = 5, D = 0?
yeah
quiet anvil
ok
placid quarry
alright
I am gonna have lunch, take your time
i hope that's ok?
quiet anvil
and D being the minimal passing grade
placid quarry
typically I'm used to F being the failing grade
uh yea,
its just different here
quiet anvil
ok
so here's my thoughts so far, if you're not allowed to fail any course, then automatically you need to invest hours equal to the sum of the third column
from there you now have a budget.
and that budget is your remaining hours.
placid quarry
have a read
i asked this in this server cuz I thought there's gotta be some algo...
ummm
uh wait
let me think a bit
is this speaking realistically or...?
oh
sh**
yeah you're right
D is minimum passing
yeah, it has 4 points then
although realisitcally in my uni, D and F are essentially the same since you have to repeat course anyway
sorry...
ik ur patience is being tested with me and this question 😓
quiet anvil
You can have a rather stupid algorithm which might be sufficient which just looks at the next column for each subject and chooses the one that maximizes the net benefit, but this greedy algorithm might be suboptimal. For instance, if you have one column that has a required investment of 6 days, but is a 5 hour course to go from a D to a CD, but then only 1 hour to go from a CD to a C, it might be preferable to choose that over 1 day each to 7 other courses to bring them all from a D to a CD
but the greedy algorithm will only "see" the lower courses.
hmm... I would need to sit down and do the math to figure it out.
placid quarry
I'll sit together with you once I finish meal
Middle of having it
quiet anvil
well, I do need to go do work, so I can't stick around.
placid quarry
oh ok
In that case I'll leave it open and do some figuring out on my own which you can cross check when you get back
quiet anvil
unfortunately, I have run out of free time. Had you sent the original question immediately instead of 30 minutes into the work, I might have had time to solve it.
😦
placid quarry
I am very sorry :(
marsh citrusBOT
@placid quarry Has your question been resolved?
marsh citrusBOT
@placid quarry Has your question been resolved?
marsh citrusBOT
@placid quarry Has your question been resolved?
marsh citrusBOT
@placid quarry Has your question been resolved?
marsh citrusBOT
@placid quarry Has your question been resolved?
steep ruin
marsh citrusBOT
steep ruin
Im using cosine rule as given in the answer, but im getting different answer..
late geode
show your work
late geode
is your cacluator in degrees or radians mode
steep ruin
is your cacluator in degrees or radians mode
radian
I tried both radian and degree, but both does not work
worn plank
why -2x(x+2)^2 and not -2x(x+2)
errant hull
marsh citrusBOT
errant hull
There are four integers between a and b.
Which of the following cannot be the product of a and b?
A) 24 B) 30 C) 36 D) 50
marsh citrusBOT
@errant hull Has your question been resolved?
lilac siren
There are four integers between a and b.
Which of the following cannot be the pr...
let's consider the restrictions of a & b
since there are four integers between them
a & b can at max deviate from the smallest/largest of those integers by a value less than 1
since otherwise we'd include five integers
so for instance, if we took the first negative integers:
-1, -2, -3, -4
then -5 < b < -4 and -1 < a < 0
(alth it depends on how they define between, because it could still allowed -5 <= b < -4 and -1 < a < 0)
meaning the largest possible product we can achieve is arbitarily close to -5 * -1 = 5
and the smallest possible is arbitarily close to -4 * (a getting arbitarily close to 0) = 0
meaning all values of (0, 5) would be valid answers
lets regard the next interval:
-2, -3, -4, -5
-6 < b < -5
-2 < a < -1
product is bounded by 12 and 5
so (5, 12) are valid
-3, -4, -5, -6
-7 < b < -6
-3 < a < -2
product is bounded by 21 and 12
(12, 21) are valid
-4, -5, -6, -7
-8 < b < -7
-4 < a < -3
product is bounded by 32 and 21
(21, 32) are valid
-5, -6, -7, -8
-9 < b < -8
-5 < a < -4
product is bounded by 45 and 32
hm that's odd, all of the answers are valid
is there some restriction you haven't shown us?
@errant hull
e.g. if a,b would have to be integers as well
in that case:
a = -3 b = -8 to get 24
and have 4 in between
30 can't be constructed with 4 in between, since we only have the options 1 * 30, 2 * 15, 3 * 10, 5 * 6
a = -4 b = -9 for 36
a = -5 b = -10 for 50
next time maybe come back to your channel and post the full question .-.
errant hull
by
marsh citrusBOT
@errant hull Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
scarlet wing
marsh citrusBOT
scarlet wing
0/4 marks given, I'm pretty sure that I'm right tho
marsh citrusBOT
@scarlet wing Has your question been resolved?
scarlet wing
I'm right, the website just didn't like my work so i found a working out online which literally gave me the same answer and it was right and mine was wrong
/close
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
barren abyss
marsh citrusBOT
barren abyss
i need someone to help me find the solution
what i have done so far is plug the intervals into the equation 1 at a time and see if it increases
cyan parcel
It's really easy
barren abyss
ya
barren abyss
ya
cyan parcel
So x = k * pi/2 the graph reaches special points
barren abyss
i dont get that
cyan parcel
When the graph goes up, which mean the bear population increase
barren abyss
ya
barren abyss
i dont understand what the equation represents
cyan parcel
Oh, its a way to remember special value of x where the graph reaches certain special point
barren abyss
is that the graph
cyan parcel
See that after 2pi, the graph repeat itself?
barren abyss
so whats the next step
barren abyss
is it from pi to 2pi
cyan parcel
barren abyss
they are both right
and thats my problem
idk which one to put
should i do b because techinicly c is in b
barren abyss
i have a diff question i also need help with
i completely forgot how to calculate instantaneous rate of change
novel juniper
find the derivative
cyan parcel
Do u know anything abt Calculus?
cyan parcel
Yeah
The rate of change looks like this
Instant mean the distance between 2 points approach 0
For instant rate of change = 0
U want to find this
barren abyss
so the turning points
cyan parcel
YEP
barren abyss
should i answer the turning points for the base functions
cyan parcel
should i answer the turning points for the base functions
Nope
Hmm
Idk actually, in ur textbook is there anything relates to instant rate of change?
Cause instant rate of change is usually abt derivative AKA calculus
barren abyss
this is the only thing i have screen shotted from the leasons
but this is a genuine iroc question
<@&286206848099549185>
tranquil ice
whats iroc
cyan parcel
Oh
cyan parcel
this is the only thing i have screen shotted from the leasons
Yeah this is just derivative
barren abyss
ok what is it with derivatives
cyan parcel
Well, seem like in your course, they didnt teach specifically abt derivative but this formula is just a way to calculate the derivative
Its like, they want u to know abt it, yet not reveal to u what it is?
Basically
cyan parcel
For this question
cyan parcel
Just find these point
cyan parcel
this is the only thing i have screen shotted from the leasons
Then simply apply this formula
To "prove" thats its 0
cyan parcel
Just find these point
But u know from this step, it will be 0
barren abyss
i dont know the formula
barren abyss
bro i cant understand that
cyan parcel
u want the general formula?
Well
@barren abyss
Listen carefully
When it asks u abt IROC (instant rate of change) the give u y = somthing
IROC = ( y(x) - y(x+0.01) ) / 0.01
So
So the rate of change y= sinx at point x=2 is:
[sin(2) - sin(2 +0.01)] / 0.01
cyan parcel
[sin(2) - sin(2 +0.01)] / 0.01
If the value close to 0; like 0.005 or something like that, just set it to 0
sturdy jackal
how i get this to 11?
marsh citrusBOT
how i get this to 11?
vocal leaf
winter smelt
how i get this to 11?
this just doesn't equal to 11 wdym?
sturdy jackal
it say it does in my answer
winter smelt
bro don't occupy every channel for you question, go back to your channel pls
winter smelt
no worries
sturdy jackal
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
tame swift
it's a simple question
marsh citrusBOT
it's a simple question
tame swift
I've never done trigonometry but my friend is asking me and I'm definitely confused
clever slate
it's a simple question
so we want reflex bca?
tame swift
I don't think it supposed to be this complicated? it's a grade 8 question so...
clever slate
oh lol
tame swift
but it's 63 instead of 67
clever slate
is that specifically specified?
hollow sparrow
bearing is from north
tame swift
is that specifically specified?
well umm according to the pic yes
hollow sparrow
so took the north
tame swift
I suppose that also helps find 63+bac, yea, ok and then?
tame swift
well the final point is to find what is 63+bac
tame swift
yea
hollow sparrow
wait if you are pre university math why do you need help in this
tame swift
I don't learn trigonometry
hollow sparrow
alright
tame swift
it's a friend from grade 8
hollow sparrow
alright
tame swift
and isn't pre university maths about high school maths 
anyways
it's fine it's just a maths question after all 
hollow sparrow
my bad
i was calculating the wrong bearing the whole time
thought it was a from c
i have to redo it again
tame swift
oh ok it's fine 
tame swift
yes
tame swift
x+y=90 (?)
hollow sparrow
so now we will use simultaneous equations
hollow sparrow
x+y=90 (?)
yes
hollow sparrow
so now we will use simultaneous equations
idk whats its called in american english
so now x+y=90
and 63+x = 180-(27+y)
which is 63+x=153-y
which is equal to x=90-y
so its equal to x+y=90
wait
tame swift
?
tame swift
this is exactly what I was similarly going over and over again 
and that's why I came, I suspect that there's actually not enough info? even though it looks like it does?
tame swift
it's supposed to be a longgggggg one and I just conclude it up
one sec
it's very messy though
hollow sparrow
yes
marsh citrusBOT
hollow sparrow
use the time speed formula to calculate distance
if you know further maths such as sin cos tan you can use it to find bac and then find the bearing of it
marsh citrusBOT
Available help channel!
velvet barn
so if i had a problem of x^2+x+1 = 0
marsh citrusBOT
so if i had a problem of x^2+x+1 = 0
velvet barn
that means id have to use the -b +- sq(b^2 +4ac)/2a
since there are multiple of the same variable?
sage pelican
since there are multiple of the same variable?
Not really
You use this formula because it is for a quadratic equation
amber birch
so if i had a problem of x^2+x+1 = 0
You can use the quadratic formula for any quadratic
Yes
sage pelican
Ie. $x^2$
elfin berryBOT
mlysikowski
amber birch
You should use the quadratic formula here because your quadratic is not factorisable
E.g another quadratic is 3x^2 - 5x + 2 = 0
Or 4x^2 - 1 = 0
Or -3x^2 + 4x = 0
The term in front of the x^2 just can't be 0
And it can't have any x^3 or x^4 or higher, or have like sin(x) or ln(x) etc
sage pelican
You should use the quadratic formula here because your quadratic is not factoris...
She could factor it... but I am not sure whether the question is about complex numbers
velvet barn
basically
it gave us the equation for h
and we wanted to find when it would hit the ground
the projectile
so i set it equal to 0
sage pelican
so i set it equal to 0
The equation is wrong then, I think
amber birch
The equation is wrong then, I think
Yes
velvet barn
how
amber birch
Your equation is wrong
It doesn't have any real solutions
They're all complex numbers
velvet barn
so then how would i find when it hits the ground
burnt abyss
velvet barn
2+24.5t-4.9t^2
then i set that equal to 0 and solved for it
using the quadratic thing
amber birch
2+24.5t-4.9t^2
Yeah okay that's more realistic
sage pelican
2+24.5t-4.9t^2
Yeah, whetever you have something to the second power in this form, then this formula is the way to go
velvet barn
Yeah, whetever you have something to the second power in this form, then this fo...
so this is what makes it qualify to use the quadratic eq
velvet barn
like what would be the thing that makes me recognize that i have to use it
velvet barn
It is still strange. The object does not start from the ground level?
let me find the problem give me a sec
sage pelican
like what would be the thing that makes me recognize that i have to use it
Anything like $a^2$
elfin berryBOT
mlysikowski
amber birch
It is still strange. The object does not start from the ground level?
Nope, it doesn't have to start from the ground
Projectile motion is like that
velvet barn
and i was doing d)
amber birch
Yeah ok
sage pelican
Projectile motion is like that
seems ok
sage pelican
so whenever theres a x^2 x and a constant i can use quadratic
Yes
amber birch
so whenever theres a x^2 x and a constant i can use quadratic
Yes
sage pelican
And no other elements
sage pelican
Whenever the equation is of the form $a x^2 + b x + c$
marsh citrusBOT
elfin berryBOT
mlysikowski
marsh citrusBOT
Available help channel!
signal wyvern
marsh citrusBOT
signal wyvern
These r my last two questions and then I’m done w the assignment
high pine
Well, first part is good, but the second... is not
Do you know what's the antiderivative of sqrt(x)?
amber birch
Yeah you need the power rule for integrals
elfin berryBOT
south
signal wyvern
Haha
amber birch
Like you'll have $\frac{x^{3/2}}{3/2}$
elfin berryBOT
south
amber birch
1/2 + 1 = 3/2
signal wyvern
You know what
amber birch
Also do you know what 1/(a/b) is?
signal wyvern
I got the 2 jumbled in there
amber birch
You know what
Oh wait yeah?
signal wyvern
I didn’t need it
amber birch
I got the 2 jumbled in there
Yeah, very important you write x^(1/2)
Cause it stops you from confusing yourself
signal wyvern
Also do you know what 1/(a/b) is?
Where would this come into play?
amber birch
Where would this come into play?
You have $x^{3/2} \cdot \frac{1}{3/2}$
elfin berryBOT
south
amber birch
Yeah so just times that by 2 actually, cause you have 2 sqrt(x) in the original question
Then sub in x = 1, y = -1 again to find C
Yeah okay I guess you just need a bit more time going over the steps
But you seem to understand the process of integration, like finding C given an initial condition
signal wyvern
**south**
Where is our 2 at this point, ik you said multiply but is it 2(x^3/2/(3/2)
?
elfin berryBOT
south
amber birch
Cause 2/2 * 2 = 2 ofc
signal wyvern
2/1 times 3/2 is 3
amber birch
2/1 times 3/2 is 3
Yes....
amber birch
2/1 times 3/2 is 3
But that's not what I mean
signal wyvern
amber birch
Okay yeah that's true
You should know why 1/(a/b) = b/a, you 'flip' the fraction
It comes from 1/(a/b) * 1 = 1/(a/b) * b/b
amber birch
Okay so it's $\frac{4}{3}x^{3/2}$
elfin berryBOT
south
elfin berryBOT
south
signal wyvern
Ok?
I have two attempts left
Is that the final answer? Looks like it
(But mathwork is still wrong) @amber birch south
amber birch
Is that the final answer? Looks like it
No
You stilll need to find C
Given F(1) = -1
signal wyvern
C + 9/4
= -1
-1 - 9/4
C = -13/4 @amber birch
Just tryna finish this up b4 work soon
amber birch
Yeah so -1 = 1/4 + 4/3 + C
amber birch
<@1151031274413228043> Final?
Yes
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low egret
marsh citrusBOT
low egret
Is this correct?
lone hare
I think its 1/2 sin²x but looks right
low egret
I think its 1/2 sin²x but looks right
Yeah I just realized
How about this
I think this is solid
low egret
the - became a + when you split the integral into 2
Right
coral cloak
theres an easier way with u-sub i think
low egret
Yeah I messed it up
coral cloak
cos^3 2x = cos^2 2x * cos2x
= (1-sin^2 2x)(cos2x)
so if you let sin 2x=u
=> du = 2cos2x
=> du/2=cos2x
so the integral becomes (1-u^2)*du/2 which u can integrate easily
you get the same answer u-sub just gets u there easier comparatively
low egret
so the integral becomes (1-u^2)*du/2 which u can integrate easily
I don’t think this way is allowed in the finals but I will ask my tutor
This is way easier
coral cloak
I don’t think this way is allowed in the finals but I will ask my tutor
well its the same thing
in the last step
u cancel the integral sign and cos x dx
low egret
Integrate then put “u” value after integration
It is the same thing and it’s very easy you’re right
coral cloak
if you want to do it the way in ur notebook just write it as
1/2 int (1-sin^2 2x) 2cos2x dx
low egret
I will text my tutor
low egret
the same way u did
Interesting
You learn a new thing every day huh
Thanks man I’ll definitely look into it
Ok I know I messed up but I don’t know exactly where
So, help?
lone hare
you forgot to actually integrate
wait no
ok so basically integrating 1-u^2 is just same as how you would for x or any other variable
you would get u-u^3/3
low egret
you would get u-u^3/3
But isn’t what I did the rule of integrating parentheses to the power of n?
lone hare
power rule is only for something like u^n
you cant use it for something more complicated
low egret
you cant use it for something more complicated
I don’t understand, isn’t this was supposed to be easier?
low egret
how would you integrate 1-x^2
X-x^3/3
But didn’t he say that I can cancel int with du?
lone hare
But didn’t he say that I can cancel int with du?
they meant cancelling as in du/2 = cos(2x) dx
low egret
they meant cancelling as in du/2 = cos(2x) dx
Can you do this on paper please
low egret
What I can’t seem to wrap m head around is when he said cancel int with du
Is there to integrations now?
One with int and du and one with int and dx?
lone hare
i dont think they literally meant cancelling the integral
no everything should be in u after you substitute
its just integral (1-u^2)/2 du
low egret
its just integral (1-u^2)/2 du
But where did dx go
lone hare
cos(2x) dx is just du/2
low egret
Wait I think I got an idea
lone hare
so you can replace that with du/2
low egret
Because du is du/dx
lone hare
du is du
low egret
When we get the derivative of u we put it with respect to x
U= sin2x
Du/dx = 2cos2x
Right?
low egret
but yeah ask your teacher if youre unsure
Thanks for the help
still temple
i have a problem with some simple question
marsh citrusBOT
i have a problem with some simple question
still temple
i found the x^2 coefficient to be -1/8a^2
equated it to 24 and i can't get -+8 which is the possible values of a which they got
marsh citrusBOT
@still temple Has your question been resolved?
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@still temple Has your question been resolved?
still temple
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wise karma
i need some physics help if anybody can
i feel like its simple but maybe its a trick question i just need somebody to check my work, the physics discord is very inactive
marsh citrusBOT
i need some physics help if anybody can
i feel like its simple but maybe its a t...
wise karma
for 3 i thought it was just mg because the tension is equal to the weight of the child
then for 4 it was the centripetal force added with the weight because fc = ft - mg, ft = fc + mg
and for 5 its ft = fc-mg
and for 6 its fc-mg = ft = 0 ???????
i got 4.85 m/s could somebody please help me check that
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vestal mist
how would i prove if $\sum^{\infty}_{n=2}{\frac{n*2^n}{4n^3+1}$ converges or not
elfin berryBOT
talk_less
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vestal mist
im a bit unsure about which test to use
cunning fiber
red nimbus
diveregnce test would be the best i guess
vestal mist
diveregnce test would be the best i guess
will it diverge?
i mean, ill find out sooner or later
red nimbus
I mean 2^n is a very big indicator that it's not a null sequence in the first place, which is a necessary criterion for convergence of a series.
vestal mist
interesting
i will have to use lhopitals for the limit i believe
then its (2^n*ln(2))/12n^2
does that also give an indeterminate form?
red nimbus
inf/inf
storm dagger
yep
red nimbus
you could technically argue that 2^n is dominant
storm dagger
2 more LHR and you should notice it diverges
red nimbus
or this ^
vestal mist
yup
vestal mist
you could technically argue that 2^n is dominant
what does that mean?
red nimbus
so that eventually it diverges
short canopy
How do I solve the Riemann hypothesis?
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long wigeon
marsh citrusBOT
proper isle
radius isnt 6 😑
long wigeon
can u explain how to find it then
im sorry. our teacher gave us this packet over break and didnt teach us how to do this so im very confused
proper isle
the 12'' can fit 2 spheres diameters
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slim spire
a bad function to check your intuition with is the function that sends everything to 1
amber rock
okay ill try it out using f(x)=1 for all x e A
i think i get what you're putting down
one second friend
lemme try this out
marsh citrusBOT
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slim spire
there's no nice way of making them factorials, there's weird things like 10!!! = 10*7*4*1 but it doesn't help or anything
you just need to write a formula for the next term in each sum, here it's (5k-2)/(4k+3)
(so in a sense it's like the terms scale by 5/4 each time)
slim spire
yea by the ratio test
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tawny vapor
What exactly do i have to do here?
Solve cot(2θ) = 7/24, Find sinθ and cosθ
tawny vapor
i dont know if i should apply the double angle formula or use pythagoras formula to find sin and cos
amber birch
i dont know if i should apply the double angle formula or use pythagoras formula...
Pythagoras is a good approach along with the double angle formula later
Cause 7, 24, 25 is a right triangle
So you can work out sin(2 theta) and cos(2 theta) from this
And then start with cos(2 theta) = 2 cos^2 theta - 1 to figure out cos theta
tawny vapor
So you can work out sin(2 theta) and cos(2 theta) from this
there are no degrees even tho
amber birch
there are no degrees even tho
What do you mean?
tawny vapor
for the value in 2sinA
wait i have to put the value of A from the triangle right?
or find a degree for the value of sinA
amber birch
wait i have to put the value of A from the triangle right?
What is A?
tawny vapor
24
amber birch
You're not finding 2 sin 24
tawny vapor
A 24 B 7 C 25
amber birch
Okay yeah the sides
amber birch
or find a degree for the value of sinA
You don't know sin theta yet
This right angle triangle is for the angle 2 theta
Not theta
amber birch
Yeah so can you tell me what cot is in terms of opp, adj, hyp?
amber birch
so just the value of A right cuz there is no B and C
I don't get what you're saying
tawny vapor
Cot is Adj/Opp
amber birch
Yes
tawny vapor
I don't get what you're saying
amber birch
I know
Yeah okay just use theta then, cause you said A was the side of the triangle earlier
amber birch
Yeah like you can replace A with theta or x in all of these
I'm just saying not to use A, cause you're using A here for something else already
amber birch
Cot is Adj/Opp
Yeah so your adjacent side is 7
Your opposite side is 24
tawny vapor
yeah
amber birch
And that means your hypotenuse is 25
Yeah so what's cos(2 theta) from this information?
tawny vapor
7/25
amber birch
Yep
tawny vapor
sin is 24/25
amber birch
So we have $\cos(2 \theta) = 2 \cos^2 \theta - 1 = \frac{7}{25}$
elfin berryBOT
south
tawny vapor
yeah
amber birch
Yeah so what must cos theta be?
tawny vapor
ummmmm
tawny vapor
2x^2 = 32/25
amber birch
Yep
tawny vapor
oh right
amber birch
What exactly do i have to do here?
Solve cot(2θ) = 7/24, Find sinθ and cosθ
We have to go back to the original problem
cot(2 theta) has the same period as tan(2 theta) as cot(2 theta) = 1/tan(2 theta)
But tan theta has a period of pi radians
So tan(2 theta), which is going twice as fast, has a period of pi/2 radians
This means there's a solution in every quadrant
4 solutions in the interval 0 < theta < 2pi
tawny vapor
do we have to find all of them?
amber birch
So that means that both sin and cos can be negative or positive
tawny vapor
nvm
amber birch
Negative or positive for each = 2 choices
2 * 2 = 4 choices
tawny vapor
right
amber birch
nvm
Yeah so basically both of the signs are possible
For sin and cos
For other questions where the angle is in a certain quadrant, only one sign is possible
tawny vapor
so i just need to find sin now
tawny vapor
2sinAcosA = 7/24
amber birch
Fair enough, that's one way
amber birch
it gets multiplied by 24?
You already know cos theta so you can sub that in
amber birch
2sinAcosA = 7/24
Wait this should be 2 sin A cos A = 24/25
tawny vapor
oh true
amber birch
Yeah so your adjacent side is 7
Your opposite side is 24
Your opposite side is 24 and the hypotenuse is 25
tawny vapor
i put in the value of cot instead
amber birch
Yeah
amber birch
2sinA = 24/25 - 7/24
Wait no
It's just 2 sin A (4/5) = 24/25
Well we'll put the plus minus signs in at the end
amber birch
2 sinA = 20/125
Man you're tripping
2 sin A is just being multiplied by 4/5
You keep subtracting for some reason
amber birch
can i subtract now
Why do you keep subtracting
amber birch
It's just 2 sin A (4/5) = 24/25
Okay so we can multiply both sides by 5/4
2 sin A * 4/5 * 5/4 = 24/25 * 5/4
2 sin A * 1 = 6/5
tawny vapor
there is nothing left to do
amber birch
Cause 5/25 = 1/5 and 24/4 = 6
amber birch
then sinA(8/10) = 24/25
This means (sin A) * (8/10) = 24/25
There's always a multiplication in there when you have brackets like that
tawny vapor
then ig sin A is +-3/5?
tawny vapor
then sinA = -3/5, +3/5 and cosA = -4/5, +4/5
amber birch
Yep
tawny vapor
Okay so we can multiply both sides by 5/4
2 sin A * 4/5 * 5/4 = 24/25 * 5/4
2 si...
can this method be used anywhere to get 1?
because i dont use it that much
amber birch
can this method be used anywhere to get 1?
Yes, a/b * b/a = (a * b) / (b * a) = 1 for any a, b
If a, b aren't zero that is
(to avoid dividing by 0)
amber birch
No worries
fervent blade
how do i start this
marsh citrusBOT
how do i start this
runic temple
what does angle bisector mean?
fervent blade
the line in the middle i think
runic temple
yes, it splits the angle into two equal angles
fervent blade
do you know what the formula is to find x
fervent blade
2x-2=x+6
runic temple
so x is?
fervent blade
8
runic temple
good job
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valid hinge
marsh citrusBOT
valid hinge
of cos-1cosx
Actually No
valid hinge
T-1T?
fallow fossil
trig function^-1(trig fuction(x))
marsh citrusBOT
fossil grail
did I solve this problem correctly?
marsh citrusBOT
did I solve this problem correctly?
@fossil grail Has your question been resolved?
fossil grail
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dense jacinth
He wants to know the meaning of life I think
fossil grail
He wants to know the meaning of life I think
<@&268886789983436800> I think spam is unnecessary
anyway
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viscid dirge
He wants to know the meaning of life I think
please dont post in a help channel if you dont want to contribute
@fossil grail you might have more luck asking this in #multivariable-calculus instead maybe
or actually just #prealg-and-algebra maybe
fossil grail
<@923268887909384202> you might have more luck asking this in <#4967849965104660...
Ohh I didn't notice
thank you so much
viscid dirge
i mean this is fine too, seems to be a slow day
fossil grail
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upper blade
hi i think this is available server
smthn is wrong with the other channels
gonna ask it here
<@&268886789983436800> channels are broken btw
quaint hill
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vocal leaf
I need help
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strong dagger
Where am I going wrong?
marsh citrusBOT
Where am I going wrong?
strong dagger
problem is in top right, induction problem
supposed to create a formula for the sequence and prove it works for all numbers but I am confused
glass silo
6 is not 3 * 3 
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errant finch
hi! Is this integral evaluation right? I've got slightly different answers out there, but i need someone more experienced to look at my calculations.
marsh citrusBOT
hi! Is this integral evaluation right? I've got slightly different answers out t...
winter smelt
hi! Is this integral evaluation right? I've got slightly different answers out t...
that looks fine, however don't forget your constant at the end after an integration. Also, what can you notice about the value of $1+e^{2x}$ for all x
elfin berryBOT
lgkoo
winter smelt
actually expression is positive for every x
yup, more specifically since e^(2x) > 0, 1+e^(2x) > 1 right?
errant finch
yeah exactly
winter smelt
right, since 1+e^(2x) > 1, what can we say about
$\sqrt{1+e^{2x}}-1$?
elfin berryBOT
lgkoo
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errant finch
That is still $\sqrt{1+e^{2x}} > 1$, so $\sqrt{1+e^{2x}}-1 > 0$
elfin berryBOT
spdie
winter smelt
yup, therefore you can drop the modulus sign inside log (and just write normal () brackets)
errant finch
oh i see, i didnt even look at the expression inside logs
anyway, thanks for help
.close
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radiant herald
Two circles of equal size, both radius r = 5, are next to each other.
One circle covers 1 inch of radius across the other circle.
What is the new unexposed area of the circle?
The blue is the unexposed area
marsh citrusBOT
Two circles of equal size, both radius **r = 5**, are next to each other.
One c...
primal sierra
The way I would do this is algebraicly, do you know the equation of a circle ?
primal sierra
ah ok
sand fable
Two circles of equal size, both radius **r = 5**, are next to each other.
One c...
when u have area problems involving circles intersecting other shapes
always split circles into sectors such as in this image here (and continue using trigonometry or something)
primal sierra
Personally, I would find points of intersection, apply area of segment formula and then double that area
marsh citrusBOT
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proper isle
use formula quick solution
true bluff
marsh citrusBOT
true bluff
does it matter where the ^2 is? can it be 3cosx^2?
sand fable
cosx^2 usually means cos(x^2)
true bluff
so it can be?
lilac siren
so it can be?
It does matter whether you write cos²(x) or cos(x²) ofc :]
They'd be different functions
marsh citrusBOT
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radiant herald
when u have area problems involving circles intersecting other shapes
always sp...
O ok. Uh so we have like two crescents?
marsh citrusBOT
radiant herald
cosx^2 usually means cos(x^2)
Always*
cos x^2 implies cos(x^2) bcz x^2 is one term