alright, i'll give that a try, thanks :D
#help-10
deft bramble
ahhhhhh icic tysm for the help i tried to go from one side only :)
will close for now (may be back later as i'm tryna get through a lot of inequalities) lmao
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
floral hound
Anyone?
timid silo
draw out the region
thats a good start
also any specifications on the range of possible a values?
floral hound
also any specifications on the range of possible a values?
Yeah need help with this
timid silo
wot
obtuse pebbleBOT
@floral hound Has your question been resolved?
cerulean tartan
Your integrating on bounds y = [x2,2a-x] and x = [0,a]
Aka y = x2 and y = 2a-x
Now switch these bounds and evaluate x in terms of y
timid silo
obtuse pebbleBOT
timid silo
I’m not sure where to start
I wrote a sequence which I think is wrong: n, n+1….
Then I did: (n) + (n+1)…
Reversed it then summed it up
cerulean tartan
Then just divide it by 2 ur done
cunning burrow
So either they want you replicate the proof using algebra. Another way is mathematical induction. Fairly easy to understand just YouTube if need be.
bitter laurel
and they will repeat n/2 times
timid silo
Then just divide it by 2 ur done
I got 3n + 3
bitter laurel
So either they want you replicate the proof using algebra. Another way is mathem...
induction is also a good idea
timid silo
What’s that
bitter laurel
if you dont know induction then you probably not supposed to use i t
timid silo
I’ll just search it up@on youtube
timid silo
So since they are natural numbers, the nth term is n/2 ?
timid silo
Why is that how many times it is repeated?
bitter laurel
Because we over lap them
Let’s say we have 1 to 10
1 2 3 4 5
10 9 8 7 6
now add them vertically
11 11 11 11 11
timid silo
Yes
timid silo
Ohhhh ok
timid silo
So n + 1
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
vital pilot
hello could someone please verify that my answer and workings are correct?
obtuse pebbleBOT
@vital pilot Has your question been resolved?
obtuse pebbleBOT
@vital pilot Has your question been resolved?
timid silo
well is this simply saying If you have a bunch of whole numbers (like 1, 2, 3, not fractions or decimals), and when you add them all up, you get an odd number, then at least one of those numbers has to be odd. technically If you add up a bunch of whole numbers and get an odd number, then at least one of those numbers has to be odd. There's no way around it.
obtuse pebbleBOT
@vital pilot Has your question been resolved?
vital pilot
well is this simply saying If you have a bunch of whole numbers (like 1, 2, 3, n...
I proved it by contradiction, is it correct?
timid silo
well i see it seems to be correct but i have some advices You could improve the clarity of your proof by explicitly stating the justification for each step. like show every step rverything matters in proofs
and you could directly show that 3 can be written as a multiple of 4 plus 0. but good work in overall
obtuse pebbleBOT
@vital pilot Has your question been resolved?
vital pilot
well i see it seems to be correct but i have some advices You could improve the ...
Noted. Thank you
vital pilot
im not entirely sure if im solving for the right thing in b and c
How about this one
timid silo
.
sorry but it's not clear to me can u take a clearer screenshot?
sorry for replying late ,i was busy.
obtuse pebbleBOT
@vital pilot Has your question been resolved?
timid silo
well you've correctly found that the system has no solutions, for b and c it seems right but i feel like there's a missed context or sth but it seems right
obtuse pebbleBOT
@vital pilot Has your question been resolved?
vital pilot
well you've correctly found that the system has no solutions, for b and c it see...
Okay thank you
.close
brisk arrow
Does anyone here famillar with probability and combination
obtuse pebbleBOT
Does anyone here famillar with probability and combination
brisk arrow
and want to have fun doing some high school questions related to these subjects
then you are in luck
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
queen flax
obtuse pebbleBOT
timid silo
obtuse pebbleBOT
timid silo
For the first question, I said
- translation by column vector (2 0)
- followed by vertical stretch scale factor 5
The answer says the opposite tho
Won’t we evaluate what’s inside the bracket and then what’s outside?
<@&286206848099549185>
timid silo
.reopen
obtuse pebbleBOT
✅
obtuse pebbleBOT
@timid silo Has your question been resolved?
timid silo
<@&286206848099549185>
slim lake
Won’t we evaluate what’s inside the bracket and then what’s outside?
The order doesn't matter when the directions are different.
Hence yours and theirs is correct
warm shaleBOT
Max
obtuse pebbleBOT
@timid silo Has your question been resolved?
timber island
$\int_{}^{} e^\frac{1}{t}t^n dt$
obtuse pebbleBOT
$\int_{}^{} e^\frac{1}{t}t^n dt$
warm shaleBOT
Felicienne Babun
timber island
If I do IBP n times
wait actually i wanna know
do I do IBP n times, n-1 times or n+1 times
tardy epoch
Try it for n=2
timid silo
The order doesn't matter when the directions are different.
aha I see
obtuse pebbleBOT
timid silo
The order doesn't matter when the directions are different.
say for instance
if an equation is given s
*as
$$af(2b - c) + d$$
warm shaleBOT
Al-Mardhikwar
timid silo
What order would the transformations be applied in
should it be:
- horizontal stretch by scale factor 1/b
obtuse pebbleBOT
Available help channel!
obtuse pebbleBOT
1. horizontal stretch by scale factor 1/b
@timid silo Has your question been resolved?
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
dapper abyss
What is the approach to solve this?
obtuse pebbleBOT
What is the approach to solve this?
timid silo
basically like
set up an identity matrix
3x3 identity matrix
and whatever transformations that get you from the first matrix to the second
do them in the identity matrix as well
and you recover your elementary matrix
dapper abyss
So I try to transform the first matrix into the output matrix, and apply all transformations to the identity matrix?
did i get it right
timid silo
yes
languid zephyr
I have a very simple question
(a+b)^2 the same as (a+b)(a+b) or it's not?
timid silo
it is indeed
winged ibex
how do i solve this equations with 4 uknowns easier
obtuse pebbleBOT
how do i solve this equations with 4 uknowns easier
light raft
obtuse pebbleBOT
@winged ibex Has your question been resolved?
winged ibex
.close
timid silo
obtuse pebbleBOT
timid silo
idk how to go about dilation with respect to a point
royal basin
"wrt a point" means that point stays where it is
and everything else moves towards or away from it
timid silo
yes
i got that part
so im imagining a point P near Q
if i dilate P it may go towards the Q or away
royal basin
yeah depending on whether r is less or greater than 1
timid silo
with respect to Q prolly mean if we dilate Q by same amount
the path of P should be
it?
to dilate it with respect to q
royal basin
with respect to Q prolly mean if we dilate Q by same amount
i told you that isn't what that means
timid silo
ahhh
i think its like
the way we have O as for usual dilation
everything else moves
around it
royal basin
towards/away from it
timid silo
i have to somehow make the
Q the center
so i have to think
relative to that
if a point away from O then its just |A|
for Q its gonna be
|A-Q|
so A-Q is the position of A relative to Q
now i dilate it
r(A-Q)
but thats off by Q for the whole R^{2}
r(A-Q)+Q
will be the final dilation?
obtuse pebbleBOT
@timid silo Has your question been resolved?
timid silo
@royal basin can u check pls if im correct
lucid drift
domain of this funtion is?
obtuse pebbleBOT
domain of this funtion is?
true summit
status?
lucid drift
what
true summit
!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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
oh
i know how to solve it
but i always check in mathway
and im getting a different answer
and want to know why
true summit
what did you try
lucid drift
well
first its x equal or greater than 5 then x is equal or greater to negative 2
now we go to the denoninator
x cant be -1 or +1
and now we plot the domain
however mathway didnt check the denominator
it included 1 and -1
how?
lucid drift
oh shit
true summit
so you dont need to subtract that set again ({1,-1})
true summit
no?
lucid drift
why not
true summit
0 gives unreal soln
true summit
check
the numerator
the numerator has domain -infinity to -2 , 5 to infinity
0 lies in the no no reagion
true summit
bet np
lucid drift
@true summit one more question if you dont mind
in the numerator
its (x-5) (x+2) >= 0
right
so then isnt supposed to be x>= -2 and x>= 5
timid silo
domain of this funtion is?
get the possible values for numerator and denominator then u do intersection of them
thats gonna be domain of
whole function
solar raven
so then isnt supposed to be x>= -2 and x>= 5
no x>=-2 cause one value will be positive and other wil be negative
oblique kelp
signs should have been reversed, ye?
solar raven
not greater or equal*
timid silo
so then isnt supposed to be x>= -2 and x>= 5
isn't thats more like
x<=-2
its not greater
-1 and 1
are already excluded
if u notice
grand thunder
obtuse pebbleBOT
grand thunder
why does the model solution not multiply the e^(-x) part of the ansatz by x to prevent an overlap with the general sol for the homogeneous equation
grand thunder
.reopen
obtuse pebbleBOT
✅
snow dawn
Q: Spherical Integration (Triple Integrals)
obtuse pebbleBOT
Q: Spherical Integration (Triple Integrals)
snow dawn
Consider the volume of revolution modelling an ``Ice cream cone'' shown in the attached figure.
Where the density of the object is modelled as:
[
\rho(x,y,z) = \sqrt{x^2 + y^2} ]
[R=1]
[\Phi=\frac{\pi}{4}]
warm shaleBOT
median dome
the attached figure?
snow dawn
Using spherical polar co-ordinates calculate: The mass of the object given by the volume integral:
snow dawn
Using spherical polar co-ordinates calculate: The mass of the object given by th...
[
M=\iiint_V \rho(x,y,z);dV
]
warm shaleBOT
snow dawn
So far what I've written down:
snow dawn
I've also worked out that the integrand:
[
\rho = \sqrt{x^2 + y^2}=r\sin(\theta)
]
warm shaleBOT
snow dawn
All together:
$$
\begin{aligned}
M &= \iiint \rho\; dV = \int^{2\pi}_0\int^{\frac{\pi}{4}}_0\int^{1}_0=
\left[r\;\sin(\theta)\right]r^2\;\sin(\theta)\;dr\;d\theta\;d\phi\\
&=
\left(\int^{2\pi}_0 \;d\phi\right)
\left(\int^{\frac{\pi}{4}}_{0} \sin(\theta)^2\; d\theta\right)\left(\int^{1}_0 r^3\;dr\right)
\end{aligned}
$$
I'm struggling with the evaluation of sin^2(\theta)
(plus, would be nice to see if my method for this so far is correct 
)
warm shaleBOT
obtuse pebbleBOT
@snow dawn Has your question been resolved?
obtuse pebbleBOT
@snow dawn Has your question been resolved?
grand thunder
obtuse pebbleBOT
grand thunder
how do you get that?
flat geyser
$\cos\left(x\right)=\frac{e^{ix}+e^{-ix}}{2}$
warm shaleBOT
Combustion
grand thunder
ty
obtuse pebbleBOT
@grand thunder Has your question been resolved?
winged estuary
obtuse pebbleBOT
obtuse pebbleBOT
@winged estuary Has your question been resolved?
winged estuary
whats this
This is occupied bro
I'm here
Alr so then I factor
One sec
Imma write and show u
This right?
Before finding lcd?
Aren't u supposed to find lcd before factoring tho?
Can u factor (y-4)^2?
Oh
I forgot
Is this correct?
So far
y?
Y-4 & y+4?
Yes
But that'd add up to (y+4)^2
Oh ok
Ok
So the common is only y+4 @timid silo
Huh
Oh ye mb
Alr so the common
Is y-4
Then what
Distribute?
Do I put the y-4 in the numerators
No
I don't get this
I don't know it well
Can u explain
So I multiply 6 by y and -4 and by y and 4?
14
I missed almost a month of school so I missed all of this
Ok so the y over y-4 is the common
And u canceled the denominators y-4?
So if u take common u take from both sides?
One sec
So what do u do after u get here
Lcm or lcd?
Do I include the common that's outside
Alr 1 sec
6(y+4)(y-4)
Then add the y-4 to the denom and numerator of the first fraction
And then add y+4 in the denom and numerator of second
Right?
@timid silo
@timid silo
Wdym
How do I make them the same? Multiply by 3?
@timid silo
Timezone moment
Rq tho
Wdym multiply and divide
Then?
So 22?
My teacher is monstrous she'd kill me
obtuse pebbleBOT
@winged estuary Has your question been resolved?
lunar spade
obtuse pebbleBOT
lunar spade
I've already shown the first part
but I can't seem to get anything that can show the second part
been on this for like two hours now lol
first part
this is what I have for the second part
I started with what I showed in the first part
the logic was that since the line is now a tangent, there is only one solution to the equation
meaning the discriminant is equal to zero
but that's not really getting me anywhere
is it just a problem with the algebra or the logic
i have no clue this is driving me insane
astral ivy
Wdym the line is a tangent
What if it hits the circle twice
Then it’s not a tangent
lunar spade
Wdym the line is a tangent
in the question
it says that given that l is a tangent to C show that:
astral ivy
Right
That’s a weird problem
Why would anyone glean any meaning from that random equation
lunar spade
What if it hits the circle twice
i think we solved that in the first one right?
lunar spade
Why would anyone glean any meaning from that random equation
idk
there's even more in the question
this is the full one lol
astral ivy
Oh you’re doing part (b)
lunar spade
but i just want help with b i think
yeah
idk i thought my logic was sound but the result you get from it seems unreasonable to rearrange
given that these are exam practice questions i doubt anyone would set that for a time pressured exam
so there might be something im missing idk
astral ivy
I would personally set (a,b) = (0,0) and r = 1, to make things easier
Then figure that out
Then generalize
Now you’re showing
c = +- sqrt(m^2 + 1)
or in other words, c^2 = m^2 + 1
Maybe this leads somewhere
lunar spade
mhm
true
without a and b it just makes the algebra a lot nicer tbh
i guess im looking for a 'b - ma' from all the extra terms you get from introducing the a and b
messing around with the original equation, looking to keep m(c-b) in that form kinda gets me closer?
native dune
hi
obtuse pebbleBOT
@native dune Has your question been resolved?
mighty jacinth
I'm having a hard time understanding the topological definition of openness
mighty jacinth
like, I get that a set is open if it's contained in a topology
but what's stopping any closed interval of the real line from being an "open set"
because the null set is closed (clopen), as is the entire real line.
so it contains both the null set and the real line
and the arbitrary unions and finite intersections of closed intervals are all closed as well aren't they?
civic zealot
but what's stopping any closed interval of the real line from being an "open set...
not much, as long as you have a valid topology. but you're probably using the analytic definition of open/closed there and not the topological definition.
mighty jacinth
so closed intervals are open sets?
mighty jacinth
ok
civic zealot
take the power set of the real numbers. every subset of R is in the set.
That's a topology
civic zealot
every closed interval is in the set, so every closed interval is an open set
civic zealot
yep
mighty jacinth
but for example, i saw in my topology textbook that a set is closed if and only if it contains all its limit points?
is that still referring to the same definition?
i would think not, because it doesn't apply to open intervals, which are closed under the topology of all closed intervals
unless i'm missing something?
mighty jacinth
i would think not, because it doesn't apply to open intervals, which are closed ...
when i say this, i mean that open intervals don't contain all their limit points
civic zealot
it's a related definition, yes
mighty jacinth
in this case is it referring specifically to the standard topology on $\mathbb{R}$?
warm shaleBOT
friendlyneigborhoodtopologydonut
civic zealot
I'd have to see the text to be sure, it's been a while since I really studied topo
civic zealot
,rcw
warm shaleBOT
mighty jacinth
ok thanks
civic zealot
ah, yeah. that's true.
mighty jacinth
how so?
oh wait
i see it now
i'm sorry
i've been misunderstanding what a closure is
thank you for your help
.close
bright mica
How would you solve this problem? Do you need to make the paths from each point represent their speed, like does the first point's path's distance have to be 3/4 of the second path's distance?
Image
obtuse pebbleBOT
How would you solve this problem? Do you need to make the paths from each point ...
bright mica
Answer is that the minimum time is 4.388 seconds, and here's the picture of the scenario
Closest I got was the x on the line being 1.18
worn yoke
pick some point T (x1, y1), then you can find the distance from each given point to T using the distance function (pythagorean)
for a constant velocity the time it takes to travel a given distance is distance/velocity
bright mica
yes this is true
worn yoke
so you can find a function for the total amount of time it takes for the particle to travel these distances, then find the minimum of that function given the constraint that T is on the line (i.e., x1 and y1 satisfy the equation for the line)
obtuse pebbleBOT
@bright mica Has your question been resolved?
bright mica
so you can find a function for the total amount of time it takes for the particl...
ok
grim sparrow
Hi I need help with this problem, I’m unsure how I’m supposed to solve it using that 51’
obtuse pebbleBOT
Hi I need help with this problem, I’m unsure how I’m supposed to solve it using ...
grim sparrow
tardy epoch
51 minutes = 51/60 degrees
tardy epoch
$a^\circ b^'$ is read as $a$ degrees and b minutes
warm shaleBOT
riemann
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
tardy epoch
and in this case means addition
grim sparrow
Thank you!
obtuse pebbleBOT
@grim sparrow Has your question been resolved?
fading herald
obtuse pebbleBOT
fading herald
Can I have a starting point on how to solve this? I don't want the answer though, trying to remember all my log and epxonent rules
shut lagoon
Hum I feel like you can just apply the definition of the logarithm on the left side to get the right side.
ln(1+x) is the exponent you give to e to get 1+x
coral nest
there are some restrictions on the domain tho
shut lagoon
Hum I feel like you can just apply the definition of the logarithm on the left s...
(let alone some domain issues)
fading herald
ln(1+x) is the exponent you give to e to get 1+x
sorry not quite sure if i understand
shut lagoon
In particular, exponentials cancel logarithms of the same base
We say ln(a) = b exactly because e^b = a
fading herald
yes i understand that
shut lagoon
So ln(x+1) = b means that ….
fading herald
e^b=x+1
chrome crypt
Can I have a starting point on how to solve this? I don't want the answer though...
Mk, so we know ln(1+x) is what when using logarithim
Express that using logaritihim
log_e(x+1) = y
we know that
e^y = x + 1
thus we can rewrite the top as e^y = (1+x)
b^log_b(a^x) = a^x
lilac pebble
obtuse pebbleBOT
lilac pebble
Need help wiith problem 11,14, and 15
wait for problem 11
i listed out all the possiblities
1+2+8 , 1+3+7 , 1 + 4 + 6,
is it 3?
is Problem 14 B? i have no idea how to do problem 14 other than trial and error (By grouping the even numbers together and odd numbers together in the fractions bc answe rhas to be a whole number
lilac pebble
1+2+8
1+3+7
1+4+6
2+3+6
2+4+5
oh yeah u can change the hundred digit
thans
do u have a idea on how to do 14 and 15
for 15
i drew it out on a number line
which means the difference between their ages is 12?
but then that menas D=39 which isnt a option
bc i got a=3 by doing a+b=18 and a+12=b
hybrid swan
do u have a idea on how to do 14 and 15
i have no idea for 14, but i'm trying to solve 15
lilac pebble
ok thanks
hybrid swan
i apologize as it's quite complicated for me to help you with the others... but i hope i helped you on 11 
hollow dove
since their ages are equally spaced apart, you can write the age of B as (A+d), the age of C as (A+2d), and the age of D as (A+3d), where d is the common difference
which should simplify the equations
so now we have A + (A+d) = 18, and (A+2d) + (A+3d) = 34
which are 2 simultaneous equations in 2 variables, so you can solve for A and d
lilac pebble
which are 2 simultaneous equations in 2 variables, so you can solve for A and d
so D=19 right
hollow dove
what did you get for A and d?
lilac pebble
ok thanks
Guys can i also get help on 17,18, and 19
I have no idea for 18 and 19
for 17 the yellow triangle has height of 15cm ik
the base would be like 15-x
something to do with ratios? i thikn
surreal forge
something to do with ratios? i thikn
not needed
you can use the given information to directly calculate the area of the yellow region
hollow dove
considering this triangle might also help
lilac pebble
considering this triangle might also help
i dont see
still only know one side is 15
hollow dove
the yellow and white triangles are the same, just reflected
so they have the same area
and yellow and blue have the same area
so the three regions trisect the area
so area of yellow = 15 * 15 / 3
lilac pebble
wait how does yellow and blue have same area
hollow dove
given in the question
lilac pebble
so area of yellow = 15 * 15 / 3
dont understand how u got this
hollow dove
15 * 15 is the area of the entire square
and white = yellow = blue
so each part is 1/3 of the square
so area of yellow is 15 * 15 / 3
lilac pebble
OHH
lilac pebble
so area of yellow is 15 * 15 / 3
x is 5 right
hollow dove
yes
lilac pebble
thanks
lilac pebble
help on 18 pls
hollow dove
the new parts of the perimeter are just the two side bits of the square
so 1.1 * 4s = 4s + 2p where s is the side of the big square and p is the side of the little square
lilac pebble
so 1.1 * 4s = 4s + 2p where s is the side of the big square and p is the side of...
yeah i already solved that one
its 4% right
hollow dove
yes
lilac pebble
i just dk 18
lilac pebble
its fine lol
hollow dove
not great with diophantine equations
you can narrow it down a little bit since you know the coefficient has to be odd (and less than 25, since we're working with positive x,y)
but not sure what else you can do yet
ah wait, positive so non-zero
lilac pebble
yeah
hollow dove
I mean I think all the odd numbers up to 23 just work
since you can just do y=1 to get 2x + (odd number) = 25
subtract (odd number) from both sides and you get a positive integer solution for x
obtuse pebbleBOT
@lilac pebble Has your question been resolved?
lilac pebble
oops forgot i already pinged once
obtuse pebbleBOT
@lilac pebble Has your question been resolved?
obtuse pebbleBOT
@lilac pebble Has your question been resolved?
obtuse pebbleBOT
@lilac pebble Has your question been resolved?
obtuse pebbleBOT
@lilac pebble Has your question been resolved?
timid silo
This one is quite simple
Have you done any working yet?
@lilac pebble
Could you shre your working?
obtuse pebbleBOT
@lilac pebble Has your question been resolved?
lilac pebble
Have you done any working yet?
idk its so confusing
river idol
Let me take a look at this
ok so it we know the dog is 0 dog years when ruby is 9
The question says "in 4 years, Ruby will be 4x older than me"
So you want to find her age when Ruby is 4x older and then minus 4
lilac pebble
So you want to find her age when Ruby is 4x older and then minus 4
is it 14
i mean 17
i just wrote 0 and 9 in different columns and listed the difference every year
probably a better method but i really cant think of how to make a equation with that
river idol
i mean 17
Yeah, to me it seems to be 17. When she is 21 the dog will be 12*7 years old
which is 84
river idol
probably a better method but i really cant think of how to make a equation with ...
Me neither, I was trying to think of an equation but it's 1am and I had a headache
surreal mason
@lilac pebble still need help?
lilac pebble
<@748281210538819704> still need help?
yes
timid silo
hey
surreal mason
@lilac pebble for 28, you are removing 2,4,6,8,... until you remove number 1000, so the question is how many numbers are left?
lilac pebble
<@748281210538819704> for 28, you are removing 2,4,6,8,... until you remove numb...
Im up to there being 1, 5, 9, 13, 17, ..., 997 left
now 1, 9, 17, 25, ..., 993
i dont see it ever stopping
its just keeps removing
oh wait
sorry i made a mistake
so when u have 1,5 , 9, ...997
999 got removed
wait no i didnt make a mistake
cuz when 999 gets removed
1 is still kept
im up to 1, 17, 33, 49, ...993 and 993 gets kept
that menas 1 gets removed
so how do i find how many numbers are left now'
lilac pebble
you can probably just recurse
i've never done this type of problem before can you help me start?
hollow island
hi, is this from the amc?
recursion may work, but you could just do it by combinations
just see the distinct tilings for a 3 by n grid, and combine them together
river wagon
I need help
old yarrow
hi
obtuse pebbleBOT
@lilac pebble Has your question been resolved?
timber island
Try finding the number for 3x3 and 4x3 and see if u notice a pattern
lilac pebble
.close
queen ruin
help i can't see the solution
versed stratus
Hint:- cos^2 (A)-cos^2(B)=Sin(A+B)sin(B-A)
rough python
obtuse pebbleBOT
wooden cipher
show it then
wooden cipher
the partial wrt to x looks good
word of warning that the notation doesnt use the '
wooden cipher
seems fine to me
rough python
Okay thank you so much
wooden cipher
youre welcome
queen ruin
Hint:- cos^2 (A)-cos^2(B)=Sin(A+B)sin(B-A)
thanks dude helped me to solve
obtuse pebbleBOT
thanks dude helped me to solve
queen ruin
.close
jolly hinge
Hi i need help with a real numbers question
obtuse pebbleBOT
Hi i need help with a real numbers question
jolly hinge
I think it should be B but i am not sure
inner scaffold
1 is not prime
median dome
1 is not prime
? why does it have to be?
median dome
I think it should be B but i am not sure
why don you think the reason doesn't explain the assertion
inner scaffold
Can we write 1 in prime factorisation i am not sure
median dome
Can we write 1 in prime factorisation i am not sure
well, the prime factorisation of 5 is 1x5
i guess?
it is kinda ambiguous i'm not sure
jolly hinge
why don you think the reason doesn't explain the assertion
Because while it is true that the prime factors of 5 are 1 and 5 it doesn't explain that why the 5^n can't end with zero
median dome
Because while it is true that the prime factors of 5 are 1 and 5 it doesn't expl...
does it not?
what factors does a number need for there to be a 0 at the end
inner scaffold
well, the prime factorisation of 5 is 1x5
Okay
jolly hinge
what factors does a number need for there to be a 0 at the end
It needs 2 as a power
No no
Not power
It need 2 as a factor
To be a zero
median dome
yes
and, since 5 does not have a factor of 2, 5^n also doesn't have a factor of 2
I would say the reason does explain the assertion
the only point of question is where "the prime factorisation of 5 has only two factors, 1 and 5" is a factually correct statement
jolly hinge
the only point of question is where "the prime factorisation of 5 has only two f...
Thats what i am saying it is factually Correct but it doesn't justify the assertion, it does not explain why the number 5^n cannot end with zero
obtuse pebbleBOT
@jolly hinge Has your question been resolved?
copper dust
A coupon bond is listed on the market with 9 months of residual life, half-yearly coupons at 6% per year, redemption value 105, market value 103,967. Calculate h(0;9/12)
I was already given h(0;3/12)= 0,0235
h(0;6/12)= 0,0254
h(0;1)= 0,0288
Can someone help me?
obtuse pebbleBOT
A coupon bond is listed on the market with 9 months of residual life, half-yearl...
@copper dust Has your question been resolved?
copper dust
No
lone fulcrum
how am i supposed to do this?
obtuse pebbleBOT
@lone fulcrum Has your question been resolved?
timid silo
Could someone guide me through 7-8? (Ignore the work shown)
obtuse pebbleBOT
Could someone guide me through 7-8? (Ignore the work shown)
timid silo
,rotate
warm shaleBOT
stone radish
do you know the formula for area of sector and arc length?
timid silo
do you know the formula for area of sector and arc length?
Yes
Central angle /360 * circumference
Is this right
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
silver torrent
in the image below, CB and AM are of length 1, and you have to find out how large α is.
obtuse pebbleBOT
in the image below, CB and AM are of length 1, and you have to find out how larg...
silver torrent
I already have some equations that are using the sine and cosine laws
I already got an answer that I think is correct but im trying to simplify it
can anyone tell me if what I have is correct and how to continue from here
<@&286206848099549185>
surreal forge
this approach is a bit overcomplicated...
silver torrent
might be
surreal forge
(on an unrelated note i am glad to see you have still worked on this problem since you last posted it 🙂 )
silver torrent
yes I have
silver torrent
this approach is a bit overcomplicated...
its literally the one you suggested
<@&286206848099549185> anyone?
surreal forge
its literally the one you suggested
it would be a bit easier to simply work ith 40 and 20 instead of epsilon and delta
i will read what i sent that day though
silver torrent
yeah but since you cant simplify it with the values I put the variables instead
surreal forge
you'd have to use trig identities
i specifically chose 40 and 20 instead of 50 and 70 (or like any alternate) because 40 and 20 relate better to each other
silver torrent
wdym chose
surreal forge
like because sin(40) = cos(50)
silver torrent
also its 140 and 20
surreal forge
we can write these expressions and equations however we want, but 20 and 40 are best numbers to use
i will look over your work
silver torrent
*confusion*
surreal forge
what is CU at the start?
silver torrent
thats supposed to be CM
surreal forge
ah ok
surreal forge
i will read what i sent that day though
i did not suggest law of sines or law of cosines
in this problem, i would have specifically avoided that approach
surreal forge
can anyone tell me if what I have is correct and how to continue from here
using your approach, it looks like you've done everything correctly
surreal forge
i will spend a min or two and see if i can do anything
obtuse pebbleBOT
@silver torrent Has your question been resolved?
silver torrent
i will spend a min or two and see if i can do anything
u done?
surreal forge
this is a very unfortunate expression to simplify
it's a combination of trig identities i have not yet discovered
the method i first used to solve this problem was relatively straightforward but i'll still spend a bit more time to see if i can get your expression to simplify
surreal forge
alright it's done
silver torrent
grand reveal?
silver torrent
@surreal forge
surreal forge
in the image below, CB and AM are of length 1, and you have to find out how larg...
Steps
Cleaning the expression
- Multiply numerator and denominator by sin(40)
- In all instances of sin(40), Apply double angle identity sin(40) --> 2sin(20)cos(20)
- Divide numerator and denominator by sin(20)
- Distribute cos(20) inside the denominator square root
Work in the numerator
- In numerator, Apply sum to product identity 2cos(20) - cos(40) --> cos(20) + 2sin(30)sin(10) = cos(20) + sin(10)
- In numerator, Apply cofunction identity sin(10) --> cos(80)
- In numerator, Apply sum to product identity cos(20) + cos(80) --> 2cos(50)cos(30) = sqrt3 * cos(50)
- In numerator, Apply cofunction identity sqrt3 * cos(50) = sqrt3 * sin(40)
Work in the denominator
- In denominator, Apply product to sum identity 4cos(20)cos(40) --> 2cos(20) + 1
- In denominator, Apply power reduction identity 4cos(20)^2 --> 2 + 2cos(40)
- In denominator, Apply sum to product identity 2cos(40) - 2cos(20) --> -4sin(30)sin(10) = -2sin(10)
- In denominator, Apply cofunction identity -2sin(10) --> -2cos(80)
- In denominator, Apply double angle identity -2cos(80) --> 2 - 4cos(40)^2
- In denominator, Apply Pythagorean identity 4 - 4cos(40)^2 --> 4sin(40)^2
- In denominator, Evaluate square root sqrt(4sin(40)^2) = 2sin(40)
...extremely stupid expression to simplify
silver torrent
ima just put it here again for reference
ima have to look into trig identities to understand all that
surreal forge
yeah it's impossible to do this problem without trig identities i believe
even the "simpler" solution i found makes use of sum to product at least once
obtuse pebbleBOT
surreal forge
ok thank you
welcome
i would look into the other one though
CB = 2CMcos(20)
AM = CMsin(40) + CMsin(40)cot(a)
in this system, a is the answer
obtuse pebbleBOT
Available help channel!
indigo thistle
what will the discriminant be for a non linear equation where the quadraric functuon and linear function only intersect once
obtuse pebbleBOT
what will the discriminant be for a non linear equation where the quadraric func...
indigo thistle
I kinda need to know 🙂
ruby path
if a straight line and quadratic intersect at one point only, then the composite equation in either y or x will have a discriminant of 0
this is true for a straight line and any degree 2 equation
keen ingot
I did 1/8 of the area of a sphere which is 1/2 * pi * r^2
obtuse pebbleBOT
I did 1/8 of the area of a sphere which is `1/2 * pi * r^2`
keen ingot
But that isn't correct
smoky vigil
you need to account for the flat sides
keen ingot
ahh
smoky vigil
which are just quarter circles
royal basin
^
keen ingot
Okay new answer
5/4 * pi * r^2
for the total surface area of this 4 sided solid
hmm, still wrong
where did I go wrong?
@smoky vigil
smoky vigil
well you were given specficially r=2
smoky vigil
np
keen ingot
.close
timid silo
"A manufacturing operations consists of 10 operations. However, five of the 10 machining operations must be completed before any of the remaining operations can begin. Within each of these two sets, operations can be completed in any order. How many different production sequences are possible?"
obtuse pebbleBOT
"A manufacturing operations consists of 10 operations. However, five of the 10 m...
timid silo
The answer is:
1st step: 5!
2nd step: 5!
Multiplication rule, 5! * 5! = 14,400 different sequences
Why did they use permutation? In permutation, order matters, but the problem clearly states that the order doesn't matter. This is a combination problem, no? So why did they use permutation??
How many different production sequences are possible? They are looking for ALL possible arrangements
timid silo
**How many different production sequences are possible?** They are looking for A...
Isnt that combination?
no
How. Order doesnt matter in combinations so shouldnt it give more outcomes
I think this is permutation because you have to do the sets in order.
firstly, the amount of ways you can choose from a list of items is bound to be lesser or equal than the amount of ways u can permute them
secondly, they are looking for all the different production sequences. A production sequence could occur with a certain item going first and the other second and so on. The fact that it says the operations can be completed in any order is just specifying that there are no particular restrictions on how you can arrange your items. NOT that the arrangement is inconsequential
I see. Ty
.close
obtuse pebbleBOT
slate grotto
Hello, I would like to know how exactly does the value of 1/(1+x^2) came to be.
slate grotto
Thank you, perfect. Didn't realize that tan^-1 is just arctan, thanks.
tardy epoch
yea common misunderstanding
fallen inlet
Ok 2 questions. For the dancing one it’s 9 right because it’s asking for people who like ballet and modern. Apparently it’s wrong idk why.. and for the second one I thought it’s X + 3 because 3x -2x is x and 2 +1 is 3 but that’s wrong too
obtuse pebbleBOT
Ok 2 questions. For the dancing one it’s 9 right because it’s asking for people ...
fallen inlet
For the dance should I have done 13 + 14?
hybrid swan
For the dance should I have done 13 + 14?
i think it's asking in general, so all the people who like ballet, modern or both
try 13+9+14
i think the second picture cut out some numbers, correct me if i'm mistaken
fallen inlet
If you click on it it shows the whole pic
hybrid swan
is it g(x)=-2x?
fallen inlet
Let F(x) = 3x + 2 and g(x) = -2x + 1
Find f(x) - g(x)
That’s what it says
I’m not sure what I should do
hybrid swan
negative with negative becomes positive
-(-2x + 1) = +2x - 1
i believe that's what went wrong
fallen inlet
Should I multiply something
hybrid swan
almost there, you have to flip the +1 as well, as it's part of the brackets
fallen inlet
Ohh
hybrid swan
so 3x + 2 + 2x - 1
fallen inlet
5x + 1 then
hybrid swan
yes! 
fallen inlet
Yay Tysm
hybrid swan
no problem
i'm here if you need further help, but if you don't have any more questions, you can close the channel by typing ".close"
obtuse pebbleBOT
@fallen inlet Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
minor furnace
"Consider the function $y(t,x) = e^{-kt^{2}}(cos(\omega t + \Phi x) + sin(\omega t + \Phi x))$, find a first order Taylor series expansion about the point t(0), x(0)"
in this case would it be possible to apply angle sum formulae to the trig terms then individually expand each series?
obtuse pebbleBOT
"Consider the function $y(t,x) = e^{-kt^{2}}(cos(\omega t + \Phi x) + sin(\omega...
warm shaleBOT
Triaxyz
obtuse pebbleBOT
@minor furnace Has your question been resolved?
fossil crag
I think all approaches are valid, you only want the first order so there's really only 3 terms to find
Another straightforward approach is to compute $\frac{\partial y}{\partial t}(0,0)$ and $\frac{\partial y}{\partial x}(0,0)$
warm shaleBOT
rafilou2003
fossil crag
Very easy with standard rules of differentiation
minor furnace
$(1+(-kt^2)[1\cdot 1 - (\omega t)(\Phi x) + (\omega t)(1) + (1)(\Phi x)]$
warm shaleBOT
Triaxyz
minor furnace
@fossil cragis this valid for first order
first parentheses is e^.., the subsequent terms are the result of me using angle sum
minor furnace
**rafilou2003**
also, yes, but I haven't really covered multivar taylor series that much to understand why you only need these terms
like if I dig up my computation class notebook I can probably find it somewhere
minor furnace
first parentheses is e^.., the subsequent terms are the result of me using angle...
(the cos terms are just 1 because the following term is of order 2 and we only want 1st order)
fossil crag
<@246787399991033858>is this valid for first order
It isn't unfortunately
You can quickly check that for first order, you can only have a constant term, a term in t¹ and a term in x¹
In your result you have a term in t² which is impossible at this order
But you're not far off
minor furnace
right but the order of the series itself is 1, just with -kt^2 substituted in
is that not how order is measured?
fossil crag
No, -kt² is the first order for t²
-kt² is second order in t
The order is measured in the max power of t and x combined term by term
minor furnace
can you elaborate on "max power of t and x combined"
eg does this mean that the coupled term is 2nd order?
fossil crag
can you elaborate on "max power of t and x combined"
Well for example
I'll elaborate
t^m is of order m
in general, when we have two variables like x and t
$t^mx^n$ is a term of order $m+n$
warm shaleBOT
rafilou2003
fossil crag
When we want the taylor polynomial of order 1, we get rid of all terms of superior order
fossil crag
Oh you used cos
Yes this term is of second order
Needs to be gotten rid of
Here's one last thing to remember
If you write something as $(1+t)(1+x)$
warm shaleBOT
rafilou2003
fossil crag
Is this already in 1st order form?
minor furnace
no because it includes a term t*x which is of order 1+1
fossil crag
Ok great you got everything
minor furnace
nice, let me work out the 2nd order now because it's a part of the assignment too and I'll check with you if you don't mind
fossil crag
The final answer should be $1+\omega t + \Phi x$
warm shaleBOT
rafilou2003
fossil crag
Now when we work with second order, a lot of terms will not be removed this time
fossil crag
**Triaxyz**
This was a very nice approach to start with
Except now we need just a little more terms
minor furnace
would you argue that it's a good idea to first expand everything to 2nd order, then wait until the end to distribute everything to check which terms are of superior order
fossil crag
Yes it's a very valid idea
It's easier to drop useless terms than to pop useful terms into existence
minor furnace
okay so far I have $(1-kt^2)[1+\frac{\Phi^2 x^2}{2} + \frac{\omega ^2 t^2}{2} - \Phi \omega tx + \omega t + \Phi x]$
warm shaleBOT
Triaxyz
minor furnace
all other terms that were previously in the brackets were discarded because they were of order 3 or higher
fossil crag
Now you can expand the product
And in order to instantly know which terms will vanish
minor furnace
what I'm seeing is that any term past the 1 when multiplied by -kt^2 is of higher order