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#help-17
vast shale
vocal sleetBOT
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flat heart
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flat heart
Need help understanding how h is solved here
In this question h is the height when the triangular trough is volumetrically half full
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merry hemlock
Hii, working on a polynomial division here and i need to find the spots where the graph hits fhe X axis. I know how to do that but when doing the division, as in the example provided does the first thingie, in this case -x^3 have to be positive or is negative fine? Im confused bc we once had one where we had to make it into a positive and it only worked then. So yea basically does the first x thingie have to be positive or is negative fine too?
vocal sleetBOT
Hii, working on a polynomial division here and i need to find the spots where th...
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merry hemlock
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merry hemlock
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still anvil
where does the -15 come from? I undertsand the 8x being the derivative at the point * x
vocal sleetBOT
where does the -15 come from? I undertsand the 8x being the derivative at the po...
still anvil
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weak sail
hi, the instructions for the question are in the screenshot, can someone help me please? this is a (geometric) series question, i belive, thank you.
vocal sleetBOT
hi, the instructions for the question are in the screenshot, can someone help me...
plain aurora
hi, the instructions for the question are in the screenshot, can someone help me...
you need to control for the alternating signs
right now, see what happens if you write out the first few terms explicitly
will you actually get -3+0-27+...
weak sail
you need to control for the alternating signs
how would i be able to do that then
plain aurora
yea i see that
have an extra sign term
(-1)^k
which is -1 if k is an odd integer
and 1 if even
so adjust your starting k to make your first few terms agree with -3+9-26+...
weak sail
lemme try that out for a sec
plain aurora
are you familiar with coding?
weak sail
are you familiar with coding?
lmao yes a bit
languid berry
another issue is that you're doing 3k, which would give you 3, 6, 9, 12, not 3, 9, 27, 81
weak sail
another issue is that you're doing 3k, which would give you 3, 6, 9, 12, not 3, ...
yes lol that clicked after i posted my question, so then i would be raising to a power right?
weak sail
for k≤[range]: do ...
oh yeah!!!
plain aurora
yes lol that clicked after i posted my question, so then i would be raising to a...
yes
plain aurora
oh yeah!!!
yep
each k is an iteration
in each iteration, what do you want to add to your cumulative sum?
weak sail
this part of the sigma is correct though, it's just the expression on the right that isn't, correct?
plain aurora
this part of the sigma is correct though, it's just the expression on the right ...
depends how you are deinfing your summand
weak sail
depends how you are deinfing your summand
ughh wait i have no clue what it'd be though😭
plain aurora
$\sum\limits_{k=1}^6(-1)^k\cdot 3^k$
twin meteorBOT
Kakaka
plain aurora
that is one potential sol
but if you reindex, you could also have something like
$\sum\limits_{k=0}^5 (-1)^{k+1}\cdot 3^{k+1}$
twin meteorBOT
Kakaka
weak sail
ohh
oh my gosh i didn't even get the index right😭 i wrote 9 instead of 6 lmfaooo
let me work this through and see if it clicks in my brain, thank u for ur help!!
plain aurora
oh my gosh i didn't even get the index right😭 i wrote 9 instead of 6 lmfaooo
in general, you want to do a sanity check
plug in your last term and see what you get
just like how you would check first/last iterations when programming a loop
weak sail
plug in your last term and see what you get
will do!!
languid berry
$\sum\limits_{k=1}^{12}\frac{ (-1)^{\left\lceil{\frac{k}{2}}\right \rceil}\cdot 3^{\left\lceil{\frac{k}{2}}\right \rceil}}{2}$
lol
weak sail
hold on its saying this is incorrect as well
twin meteorBOT
aurelianus
weak sail
its not parenthesis sensitive either
languid berry
hold on its saying this is incorrect as well
you have to wrap the (-1) in brackets
plain aurora
maybe it wants you to start at k=0 then?
weak sail
you have to wrap the (-1) in brackets
still didn't go through😭
vast shale
Symbols too maybe
languid berry
maybe it wants you to start at k=0 then?
maybe this^
weak sail
maybe it wants you to start at k=0 then?
possiblyy
vast shale
Maybe it doesn't understand the ×
plain aurora
^^
languid berry
what platform is this
weak sail
what platform is this
mathspace
plain aurora
try * or nothing
weak sail
Maybe it doesn't understand the ×
lol nah the program takes in any form of multiplication symbols as x on the screen even if i do *
vast shale
It's (-1)^k
languid berry
they tried that
weak sail
yeah
languid berry
maybe it has to be $((-1)^k3^k)$ all wrapped in parentheses?
twin meteorBOT
aurelianus
weak sail
lemme try that
vast shale
Nice
weak sail
really appreciate the help guys!!
languid berry
nice
vocal sleetBOT
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ebon patio
marble harbor
vocal sleetBOT
marble harbor
absolutely no idea how 2 do this
languid berry
i swear u were doing like cross products 10 minutes ago how did you get to this
marble harbor
😭
vocal sleetBOT
@marble harbor Has your question been resolved?
marble harbor
SOMEONE HELP ME
bronze osprey
SOMEONE HELP ME
I'm working on it
bronze osprey
o shit frl?
Wait but you don't know how to use calculus to do it right
bronze osprey
There's this formula where tan(2 theta) = B/(A - C)
= -sqrt(3)/(5 - 4) = -sqrt(3)
So theta = -pi/6, well that's one of the values
marble harbor
ur clutch
bronze osprey
So you need the top left entry which is cos theta to be cos(-pi/6) and the bottom left entry needs to be sin(-pi/6)
Let me check
Yeah the answer should be C I think
bronze osprey
There's this formula where tan(2 theta) = B/(A - C)
theta is not the angle of rotation: it's the reflection axis
So the ellipse is being reflected across the line theta = -pi/6
We need to theta cause if we have a point on the x-axis and we want to reflect it across theta = k
Then the reflection will make our point go to theta = 2k (rotate k to get to the line of reflection, and rotate k again for the reflection)
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ebon parrot
Hello people, very quick question, why is the second one a non-linear differential equation? Can you not divide y from both sides (if y is not 0) to make it linear?
vocal sleetBOT
Hello people, very quick question, why is the second one a non-linear differenti...
molten crypt
hello how to get start evaluate this??
\int \frac{cot:\sqrt[3]{x}:csc^2\sqrt[3]{x}}{\sqrt[3]{x^2}:\left(4:+:cot^2:\sqrt[3]{x}\right)}:dx
vocal sleetBOT
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ebon parrot
yeah i saw that but i was thinking can you not divide y from both sides
so this simplifies to dy/dt = ty +t
arctic mantle
you'll lose solutions then
ebon parrot
i'll ask my professor ty anyway
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molten jasper
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vast shale
factor
molten jasper
factor ?
vast shale
ye
molten jasper
factorize what ?
ruby grove
xy = x+y from equ 1 subsitute that in 2
vast shale
you do realize they are 2 separate questions right
molten jasper
lmao
ruby grove
those are conditions
leaden hedge
if they are separate would there not be infinite solutions?
ruby grove
not 2 diff equations
vast shale
no theres a condition that x,y are natural numbers
leaden hedge
still
ruby grove
🤦♂️
vast shale
which makes it solvable
leaden hedge
i dont think so
ruby grove
do u how big the set of natural numbers is
vast shale
why would the question ask you to find all pairs of (x,y)
molten jasper
do u how big the set of natural numbers is
how do i find that tho ?
ruby grove
how do i find that tho ?
dude its infinite u cant
vast shale
do u how big the set of natural numbers is
ok for example (x-1)(y-1) = 1
molten jasper
why would the question ask you to find all pairs of (x,y)
😭
candid salmon
.
obtuse sierra
its not infinite
molten jasper
there are only 2 cases
the solution is x,y is 2,2
obtuse sierra
and i think they want you to solve this by hit and trial 🤷♂️
molten jasper
but I dont get it how
ruby grove
and i think they want you to solve this by hit and trial 🤷♂️
he cld plot the graphs if he wanted and then get the intersection
vast shale
hell no
ruby grove
yup
obtuse sierra
he cld plot the graphs if he wanted and then get the intersection
but again, he cant just find those points by plotting the graph himself
vast shale
no its not
ruby grove
-_-
vast shale
0 is not a natural number
leaden hedge
0 is a whole snumber
vast shale
also the question asked you to find all pairs of (x,y)
obtuse sierra
even if they asked whole numbers, (0,0) still wouldnt be one of the pairs
vast shale
no
leaden hedge
even if they asked whole numbers, (0,0) still wouldnt be one of the pairs
cuz 1/x would be undefined in the first eqn?
ruby grove
u will get them
ruby grove
even if they asked whole numbers, (0,0) still wouldnt be one of the pairs
I did say that
obtuse sierra
6x=3y+38 :x =1/6(3y+38)
they are separate questions 🤦♂️
obtuse sierra
cuz 1/x would be undefined in the first eqn?
yes
molten jasper
and i think they want you to solve this by hit and trial 🤷♂️
ig I have to do something like this
obtuse sierra
ig I have to do something like this
yeah
hit and trial
i think only (2,2) satisfies the first question
you can confirm by subbing in more values
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unique path
Hi, here are two of my methods for answering the question. The second one gives the correct result but the first one doesn't. Where have I gone wrong?
vocal sleetBOT
Hi, here are two of my methods for answering the question. The second one gives ...
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uncut crypt
Does anybody know how to measure the data from the instrument EQ-5D questionnaire regarding health?
vocal sleetBOT
Does anybody know how to measure the data from the instrument EQ-5D questionnair...
crystal gazelle
https://www.ncbi.nlm.nih.gov/books/NBK565677/ This might help you if you are wanting to statistically analyse
Casting my mind back to my little time spent training as a doctor (before realising I could have a better life as a pilot lmao), it was a little more qualitative
If you look up the defn of that questionnaire you get a number 1-5 for each Q
Then you just write it as a 5 digit number
uncut crypt
are any of you aware of an instrument to measure work performance? ;-; badly need it for our research
crystal gazelle
And it would be interpreted as effectively a snapshot of that person's health
crystal gazelle
are any of you aware of an instrument to measure work performance? ;-; badly nee...
Probably need to answer the question of a) what kind of work and b) how would you like to quantify performance before you pick/create one
uncut crypt
what happens when our respondents work in different fields?? We're just using working students as our respondents , can we still make one regarding their work performance??
crystal gazelle
One person might say performing well in work is simply a function of productivity, but then in more complex jobs productivity is a bit abstract; and another person might say performing well is how liked you are as part of a team since team coherence correlates to overall productivity
Well, part of research is deciding what best encompasses what you're investigating
No individual metric is perfect but that's why you generally assess multiple things to get a number of datapoints, and weight accordingly
uncut crypt
we're getting rushed by our professor to have tables and interpretations already ;-; without teaching us properly how to gather data ;-;
crystal gazelle
Not ideal
Were you only given the word 'performance' or did they want to hone in on some specific aspect of their work
uncut crypt
they only gave us work performance
could we focus on work attitude?? like going to work on time? filing for leaves?
crystal gazelle
Not a bad idea, could easily look at total number of hours lost to lateness/absence
uncut crypt
The title of our research is 'Correlation of Physical Health, and Work to the Academic Performance of Grade 12 Working Students' could we possibly just focus on work attitude than just work in general?
since work attitude could also reflect their academic performance no?
if we formulate our own instrument to measure their work performance, do we analyze it like we would a normal likert scale??
crystal gazelle
Oh, I wouldn't interpret that as work performance tbh unless you've been told you have to
I'd just look at number of hours worked
uncut crypt
could that work? just the number of hours they work?
crystal gazelle
I think so, you have a score for physical health, number of hours worked, and academic performance
Assuming you keep all your data continuous you can do multiple regression
If you categorise the data, it's probably an anova (but statistics is something I avoid at all cost and use prism when I have to do them as it tells me what I need lmao)
Either way I think hours worked is certainly much easier than trying to come up with a metric for work performance
i also think you're more likely to generate statistically significant results with a simpler metric lol
uncut crypt
does these things u mentioned still work even though there's just a small number of respondent's?????
we only have 13 working students in our school ;-;
uncut crypt
we only have 13 working students in our school ;-;
for grade 12 at least
crystal gazelle
Well whether you look at hours worked or work performance, n is still small it doesn't really affect the outcome
Just something to talk about when your critique your stats
Not a bad thing unless you want this published in the lancet lmao
uncut crypt
could I still use number of hours if I plan to use pearson's?
because our teacher recommended to use pearsons and just pair the three variables with each other
so x to y, y to z, x to z
Could I ask for the average hours worked in a week? or should I ask the hours daily?
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still nymph
this is probably a stupid question but can someone tell me what this curly horiztonal brace/bracket means?
vocal sleetBOT
this is probably a stupid question but can someone tell me what this curly horiz...
cyan talon
prolly saying that the thing above it equals a or something
but you better show a bigger screenshot to be sure
lime kraken
this is probably a stupid question but can someone tell me what this curly horiz...
can you zoom out lol
arctic mantle
are you studying quantum mechanics or smth?
still nymph
lmao no this is a part of an algorithm for ambient occlusion.
arctic mantle
no idea what that is and i won't ask
still nymph
im studying a reserch paper
still nymph
no idea what that is and i won't ask
fair lol
subtle helm
there's usually context when that curly brace show up
still nymph
hmmm do you think its safe to assume that (weird a hat ^ symbol) is just equal to all of that
subtle helm
in here, i assume they're calling $\hat{a} = \int_{\theta_1} ^ {\theta_2} \cos(\theta -\gamma)^+ |\sin(\theta)| d\theta$
twin meteorBOT
chebyshev's infinite pee norm
still nymph
right makes sense
yeh alright i think i understand now as later they say this so i assume that a^ is equal to the above
i tried
anyways i think i got everything i need to understand now so
thank you all!
.close
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abstract vapor
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vast shale
any ideas ?
vocal sleetBOT
any ideas ?
lone linden
b. Square both sides and use $1+\tan^2 x=\sec^2 x$ \ \ c. $$\tan x+\cot x=\frac{2}{\sin x \cos x}$$
twin meteorBOT
Civil Service Pigeon
lone linden
As a further hint for c, ||you can find (sin x + cos x)^2 from sin x cos x||
vocal sleetBOT
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vast shale
As a further hint for c, ||you can find (sin x + cos x)^2 from sin x cos x||
ill try
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vast shale
**Civil Service Pigeon**
btw tanx+cotx = 1/sincos
ebon saddle
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outer flicker
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viscid sable
so we can think of this as a geometric sequence right?
it starts of with 11 people
and they tell 2 other new people about the rumor
be careful of that
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hazy hound
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hazy hound
not really sure what to do because of the absolute value
my intuition is to handle it case by case ...
suppose $X - Y > 0$, then $$f_Z(z) = \int_{0}^{1}f_{X}\left(x\right)f_{Y}\left(z-x\right)dx$$
twin meteorBOT
o.O
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sage dew
think back to the criteria for the ratio test and what it means for a subsequent term a_(n+1) to be larger than a_ n
does it show the criteria for ratio test convergence/divergence?
it doesn't tell you what happens if the limit is less than 1, equal to 1, and greater than 1?
that's what I meant by criteria
and that's sufficient to explain this
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solar jungle
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solar jungle
are the answers correct
rugged orchid
Looks good
solar jungle
Looks good
thanks!!
desert plume
You can do this faster with a calculator
desert plume
I do
desert plume
You can do this faster with a calculator
Not sure if mine is the same as yours, but a CASIO calculator just go to Mode > EQN > ax^2+bx+c=0
vocal sleetBOT
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tall swallow
ß = 23°; б = 107°
How much is y - a
vocal sleetBOT
ß = 23°; б = 107°
How much is y - a
main scaffold
You can calculate Alpha by subtracting delta from 180 as they form a linear pair
arctic mantle
@tall swallow like karshi said; calculate alpha. after that, use the fact that a triangle's angles will add up to 180 degrees to calculate gamma (the y)
tall swallow
<@608907165117448212> like karshi said; calculate alpha. after that, use the fac...
It’s 12?
tall swallow
?
tall swallow
Where did a come from?
This one
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hollow raft
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hollow raft
i dont understand why they wrote this in the answer:
the so x = root 1+x
why can it be written that way?
spark storm
using a property of infinity
hollow raft
ah okay so its just itself inside itself over and over again
copper crypt
yea cause its infinite like that
hollow raft
awesome ty very much!!
copper crypt
np
hollow raft
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vocal sleetBOT
peak matrix
(side note: sometimes this trick doesnt work, because putting x = sqrt(1+sqrt(1+....)) already assumes that it has some solution, which might not always be the case)
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urban laurel
is this correct :
$\ \text{if }f(x) \sim h(x) \ \text{then } \lim_{x\to a}f(x) g(x) = \lim_{x\to a} h(x)g(x)$
twin meteorBOT
Adam Chebil
urban laurel
if f(x) approximates h(x)?
it means f(x) is equivalent to h(x)
graceful canopy
then yea obviously
urban laurel
$\lim_{x\to a} \frac{f(x)}{h(x)} = 1$
twin meteorBOT
Adam Chebil
graceful canopy
r u saying f(x) is equal to h(x) or is their ratio of the limit equal to 1
urban laurel
r u saying f(x) is equal to h(x) or is their ratio of the limit equal to 1
ratio of the limit equal, that's the definition of eqiuvalence
graceful canopy
thats asymptotic equivalence
which means
a must be infinity
the limit is approaching to infinity
urban laurel
the limit is approaching to infinity
it's true when the limit is approaching a real number also
urban laurel
asymptotes are the behaviour at infinity
they are also defined at a point
how do u think series expansion work then
graceful canopy
bro im saying
their ratio may not be 1
at said point
and those series expansions are taylor series to some order around x=0
graceful canopy
$\lim_{x\to a} \frac{f(x)}{h(x)} = 1$
this statement may not hold if a=3 for example
consider the function 3x^2/(3x^2+2)
f(x)=3x^2, g(x)=3x^2+2
at a=3, the limit is not 1
but as a tends to infinity
the limit becomes 1
urban laurel
but as a tends to infinity
yeah they're equivalent at infinity but not at x = 3
graceful canopy
and thats asymptotic equivalence
urban laurel
but there are fcts that are equivalent at x = a
urban laurel
sin x and x at x = 0
graceful canopy
oh true
subtle helm
You can define ~ to be the limit at a finite point a, but generally it's implied that you're examining asymptotic behavior toward infinity
Unless otherwise specified
urban laurel
**Adam Chebil**
ok but i must verify that the limit of h(x) exists before replacing f(x) with h(x) here right ?
subtle helm
If they all individually exist, I believe it holds, the only counter example you would get is if at least one of those limits don't exist
urban laurel
can u even replace the functinos?
that's my question 🙃
graceful canopy
i think u can prove it using
the distributive property of the limit when multiplied
urban laurel
If they all individually exist, I believe it holds, the only counter example you...
i mean if the limit of h(x) exists then the limit of f(x) also exists since the limit of their ratioj = 1 (they're equivalent))
subtle helm
no
graceful canopy
since the lim of f(x) = lim of g(x), u could prolly replace the functions when multiplied with h(x) right?
urban laurel
no
can you give an example where lim f/g = 1 but only one of the limits don't exist ? 🙂
subtle helm
i mean if the limit of h(x) exists then the limit of f(x) also exists since the ...
ah sorry I saw the picture above your msg and mixed up the g and h between the two of you
subtle helm
i mean if the limit of h(x) exists then the limit of f(x) also exists since the ...
Yes this is fine
if any two of the three limits exist you can always get the third by a product of limits = limit of product argument
subtle helm
If they all individually exist, I believe it holds, the only counter example you...
Which is why I said a counterexample would only exist under this circumstance
I suppose to be more specific I should have said at least two
urban laurel
I suppose to be more specific I should have said at least two
yeah it's clear now, ty 💗
brazen sluice
$x^{x-1} = (x-1)^x + 1$ how to find x
vocal sleetBOT
$x^{x-1} = (x-1)^x + 1$ how to find x
twin meteorBOT
General_Jacob
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vast shale
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vast shale
Part c
I have literally no idea how I am interpreting wrong
Integrating *
I’m pretty sure I’ve put the values in my calculator correctly so are my limits wrong ?
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vast shale
.reopen
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@vast shale Has your question been resolved?
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crystal gazelle
@vast shale
Unless I'm missing the obvious, you've already integrated the function
So you're getting it wrong because you're sticking the result of the indefinite integral into your calculator and it's integrating again
You should be putting g(x) into the integral i.e. $$\int_{-2}^{5} 2x^3 + x^2 - 41x - 70 dx$$
twin meteorBOT
TayBee
crystal gazelle
Or -2 to 0 and 0 to 5 if you feel more comfortable doing that (no need though as the sign of the function doesn't change in the interval)
vocal sleetBOT
crystal gazelle
With what you're putting in at the moment your calculator is going to sub the limits into $\frac{\frac{1}{2}x^5}{5} \dots$ and so on
twin meteorBOT
TayBee
vast shale
You should be putting g(x) into the integral i.e. $$\int_{-2}^{5} 2x^3 + x^2 - 4...
OOOOH I SEE THE CALCULATOR INTEGRATES THE FUNCTION FOR YOU
vocal sleetBOT
OOOOH I SEE THE CALCULATOR INTEGRATES THE FUNCTION FOR YOU
vast shale
THANKS SO MUCH FOR YOUR REPLY THAT HELPS ALOT
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umbral monolith
ive completly forgotten how to solve this and these are gonna be on my final someone help pls
vocal sleetBOT
ive completly forgotten how to solve this and these are gonna be on my final som...
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umbral monolith
<@&286206848099549185>
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umbral monolith
<@&286206848099549185>
sage path
hi
vast shale
<@&286206848099549185>
still need help?
umbral monolith
yes please
vast shale
ok so first we need to use the formula deltaQ=mc deltaT
vast shale
wait do you want the answer for the question or the WHOLE explanation?
umbral monolith
whole thing please
so i can write it all down
in my notes
i was absent the day they taught this
vast shale
okay sure. give me a few mins :))
umbral monolith
alrighty
vast shale
the kinetic energy of the spheres, as they are moved through a distance L during each inversion, is converted into heat energy. the gravitational potential energy for each sphere each time it is inverted is mgL. With n spheres inverted s times, the total mechanical (gravitational) energy is nsmgL. As each of the n spheres experiences a temperature increase of Delta T, let c be the specific heat capacity of lead. hence the total heat energy required to raise the temperature by Delta T is nmcDelta T
vast shale
ive completly forgotten how to solve this and these are gonna be on my final som...
answer = B
vast shale
is that all you need or do you want me to explain further?
umbral monolith
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potent stirrup
can we find two strict rationals numbers such that both their sum and product is an integer?
vocal sleetBOT
can we find two strict rationals numbers such that both their sum and product is...
potent stirrup
I’m getting something like
b is ak multiple of b
and a^2 is a multiple of b^2
idk if that’s helpful
@hybrid flicker I’m effectively expressing integers as rationals
Like 6= 12/2
not getting strict rationals as i mentioned
is that correct?
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potent stirrup
<@&286206848099549185>
edgy arch
Hello here it is
[ xy = \frac{a}{b} \cdot (k - \frac{a}{b}) ]
The next step shows the distribution of the (\frac{a}{b}) term across the terms inside the parentheses, giving:
[ xy = \frac{ak}{b} - \frac{a^2}{b^2} ]
This is the final simplified form of the expression as shown in the image. The first term (\frac{ak}{b}) comes from multiplying (a/b) by (k), and the second term (\frac{a^2}{b^2}) comes from multiplying (a/b) by (a/b). The expression is now fully simplified.
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tori
\[ xy = \frac{a}{b} \cdot (k - \frac{a}{b}) \]
The next step shows the distribution of the \(\frac{a}{b}\) term across the terms inside the parentheses, giving:
\[ xy = \frac{ak}{b} - \frac{a^2}{b^2} \]
This is the final simplified form of the expression as shown in the image. The first term \(\frac{ak}{b}\) comes from multiplying \(a/b\) by \(k\), and the second term \(\frac{a^2}{b^2}\) comes from multiplying \(a/b\) by \(a/b\). The expression is now fully simplified.
edgy arch
Thx bot
potent stirrup
<@246787399991033858> I’m effectively expressing integers as rationals
please check if this correct
if not i’ll proceed further
edgy arch
It’s partially correct
The variable 'k' in the original expression should remain consistent throughout the simplification process. However, in the image, 'k' is mistakenly replaced with '1' in the first step of simplification. The correct simplification should maintain the variable 'k', not '1'.
edgy arch
please check if this correct
Here's the correct simplification:
[ xy = \frac{a}{b} \cdot \left(k - \frac{a}{b}\right) ]
[ xy = \frac{a}{b} \cdot k - \frac{a}{b} \cdot \frac{a}{b} ]
[ xy = \frac{ak}{b} - \frac{a^2}{b^2} ]
potent stirrup
pls don’t help me
edgy arch
pls don’t help me
Ok
hybrid flicker
**tori**
```latex
\[ xy = \frac{a}{b} \cdot (k - \frac{a}{b}) \]
The next step s...
I would have kept the a as factor
hybrid flicker
and so would have written it as $a\left(\frac{kb-a}{b^2}\right)$
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rafilou2003
hybrid flicker
if this is an integer, then $b^2|(kb - a)$
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rafilou2003
potent stirrup
is it correct to say if b^2 divides then b divides?
if b divides then certainly b^2 divides
idk the converse
hybrid flicker
if b divides then certainly b^2 divides
what, absolutely not
2|6
yet does 4|6 ?
you got it the other way around
potent stirrup
makes sense
hybrid flicker
then b|(kb-a)...
so if we have this...
potent stirrup
then b|(kb-a)...
ie b divides a
hybrid flicker
yep
edgy arch
Hmmn I see
hybrid flicker
**rafilou2003**
also this part has to be justified with Gauss' theorem
potent stirrup
y is a difference of intgers
potent stirrup
then b|(kb-a)...
i got b divides a from here
gauss lemma applies if b is a prime ig
so x= a/b is an integer, so y= -a/b + l must be also an integer
hybrid flicker
gauss lemma applies if b is a prime ig
no that's not it
originally we have b^2|(a(kb-a))
since you can't forget the a that we factored
Gauss' lemma applies because b and a are coprime
potent stirrup
originally we have b^2|(a(kb-a))
doesn’t this imply b| akb-a?
hybrid flicker
doesn’t this imply b| akb-a?
b|(akb-a^2)
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cunning saddle
Help
candid nymph
What do you have to calculate ?
cunning saddle
how i can apply rieman sum
this
cunning saddle
What do you have to calculate ?
whith rieman sum
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potent stirrup
The definition I have says a prime is a non zero, non unit element ‘a’ in an integral domain such that a|bc implies a|b or a|c
vocal sleetBOT
The definition I have says a prime is a non zero, non unit element ‘a’ in an int...
potent stirrup
Isn’t it sloppy when talking about ring of integers?
because -3 can also be a prime I suppose
-3 isn’t a unit, and -3|bc implies -3 divides one of them
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solar field
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solar field
can someone pls explain how this works?
cause when i try x^5 = f(x)
i end up with F(x) = (x^6)/6 + C
and F'(x) = 12x^5/36??
hazy nebula
and F'(x) = 12x^5/36??
check this again
how are you deriving x^6/6
what's the formula
solar field
(vdu/dx - udv/dx )/ v^2
hazy nebula
ah i see where the mistake is happening
that's the quotient rule
x^6/6 doesn't use quotient rule
solar field
oh?
hazy nebula
do you remember what we can say about coefficient when deriving
solar field
its the exponent?
hazy nebula
a coefficient would be like d/dx (ax^n) where a is the coefficient
solar field
x^n = dydx nx^n-1
hazy nebula
x^n = dydx nx^n-1
that's the power rule (which is needed for this problem)
$\frac{x^6}{6} = \frac{1}{6}*x^6$
twin meteorBOT
RS
solar field
so i apply the product rule here?
hazy nebula
so i apply the product rule here?
you don't need to do that because 1/6 is a coefficient
solar field
interesting
hazy nebula
you might learn it as some other name but the formula works like this
where c is a constant
solar field
how do i know when to use the quotient rule then?
when there isnt just a constant on denominator?
when theres a variable on denominator?
hazy nebula
quotient rule is used when you are dividing variables
hazy nebula
when theres a variable on denominator?
not always but most of the time yes
for example if you have a problem like (x^2+x)/x it would be easier to split it into 2 fractions and simplify, then derive
but it the case of something like (x^2+x)/(x-2) you need to use quotient rule
so try using the power rule on x^6/6+C
also a good way to think about integrating and deriving is that they have a similar relationship to adding and subtraction or multiplication and division
where one undoes the other (just remember that for integrating you get a +C at the end)
the screenshot you sent is what is the called the first fundamental theorem of calculus
the derivative of an integral of f(x) dx is just f(x)
solar field
0
hazy nebula
ok good so you dont need to write x^6*0
and then using the multiple constant rule you can rewrite d/dx (x^6/6) as 1/6* d/dx (x^6)
and using power rule we get 1/6 * 6x^5
just remember
to simplify 1/6 * 6
to 1
leaving just x^5
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desert glen
as a general rule here, if theres a square root in the denominator, should i multily both sides by the reciprocal of that
vocal sleetBOT
as a general rule here, if theres a square root in the denominator, should i mul...
desert glen
and if theres one in the numerator, multiple both sides by the reciprocal of the numerator?
pale perch
what do you mean by the reciprocal
desert glen
2+sqrt(x)
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hazy nebula
as a general rule here, if theres a square root in the denominator, should i mul...
conjugate works in a general case but another thing that's just good to know is that 4-x can be rewritten as a difference of squares and simplify for this question (only works for specific cases like here but imo smth good to know)
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mossy belfry
I get this proof until the last line where it says C^(n-1)(1/1-C)|x2-x1|--->0, is this because lim (n-->inf) C^(n-1)(1/1-C)=0 and |x2-x1| is just some random number so everything converges to 0? and how does this imply x_n is cauchy since cauchy requires that for epsilon>0 there exists N in N st |xm-xn| (m,n >N) <epsilon?
vocal sleetBOT
I get this proof until the last line where it says C^(n-1)(1/1-C)|x2-x1|--->0, i...
sly sierra
"smuggling"
mossy belfry
ok?
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ancient patio
Solve A , how do you multiply sqr 3 with 4sqrt2 ?
vocal sleetBOT
Solve A , how do you multiply sqr 3 with 4sqrt2 ?
vast shale
,, \3a\2\3b=\3{a\2b}
twin meteorBOT
vast shale
you can use this
vast shale
yeah
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pale wagon
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vagrant halo
pretty sure its just a property of values between 0 and 1, you cant cube a number greater than 1 to get something less than 1, and if you cube root a positive number less than 1 you also get a number less than 1
upbeat patrol
Break the absolute value into two separate inequalities
Then take cube root
See what happens
upbeat patrol
Z is complex???
pale wagon
yes
but can we say that taking the cubic root of both sides you arrive to this conclusion?
upbeat patrol
Where does it say its complex?
pale wagon
i am doing coplex analysis 😛
pale wagon
can we say that |z^3| = |z|^3
edgy gulch
Where does it say its complex?
well the series itself has an i^k so
pale wagon
so we take the cubic root of both sides
pale wagon
Inequalities do not work with complex numbers
it is the absolute value
so it should be a real part
pale wagon
can we say that |z^3| = |z|^3
but is it correct to say this and then take the cubic root
upbeat patrol
No
upbeat patrol
can we say that |z^3| = |z|^3
If z is complex then no
Try this : |z| = sqrt(x^2 + y^2)
Wait a second
Maybe it is true
upbeat patrol
Try to let z = x + yi and cube it
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broken rover
Examine the discontinuity of the function given below. If the discontinuity is removable, redefine the function to make it continuous.
f(x)= 2x²-x-3/x+1
I get everything I just need clarification on the piecewise function if I did it right this time:
Here's my piecewise
f(x)={2x-3, if x≠ -1
-4, if x= -1
Feel free to correct me though
vocal sleetBOT
Examine the discontinuity of the function given below. If the discontinuity is r...
broken rover
.close
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livid horizon
Does f(r,s) actually mean something or is it just made up as per the question?
livid horizon
I thought it was like you take 2 elements and pair them up from S to that you have n(n-1)/2 + n elements
livid horizon
I thought it was like you take 2 elements and pair them up from S to that you ha...
So is this what (r,s) is then?
livid horizon
I thought it was like you take 2 elements and pair them up from S to that you ha...
Btw I just took the combination here
vast shale
So is this what (r,s) is then?
I thought it was like you take 2 elements and pair them up from S
yes, any two elements within S, applied by f, satisfy the two conditions
livid horizon
Ah
vast shale
what you want to show is that ${f(r, r) : r \in S} \subset S$ and $S \subset {f(r, r) : r \in S}$
twin meteorBOT
45
vast shale
that's how you usually show that two sets are equal
livid horizon
Here, I took the case when n=3
I have taken only the combinations coz f(r,s)=f(s,r) anyway
It seems to satisfy the given conditions and still I can't find anything
Ik there's smth wrong
But idk what
@vast shale Sorry for the ping but you there?
<@&286206848099549185>
kindred stratus
<@&286206848099549185>
it didn't satisfy condition(ii)
livid horizon
it didn't satisfy condition(ii)
How so?
kindred stratus
${f(1,1),f(1,2),f(1,3)}={1,2}, condition (ii) says it must be {1,2,3}$
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democracy_landing
livid horizon
Condition 3 just says that the set of f(r,s) is S for all r,s in S right?
kindred stratus
Condition 3 just says that the set of f(r,s) is S for all r,s in S right?
nope, it means $f(r,s)$ is S for any given $r$ and $s\in S$. which meas ${f(1,s),s\in S}=S$, so as f(2,s) and f(3,s).
twin meteorBOT
democracy_landing
livid horizon
Oh
kindred stratus
tell the differences between ${f(r,s),r,s \inS} $ and ${f(r,s), s \in S}$
twin meteorBOT
democracy_landing
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
kindred stratus
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slate shadow
$\int{(x+2)\sqrt{x-2} \dd x}$
vocal sleetBOT
$\int{(x+2)\sqrt{x-2} \dd x}$
twin meteorBOT
la garce
slate shadow
i need help solving this integral
snow dune
use substitution
slate shadow
we just learnt u-substitution, but only when the derivative of the inner function is in the integrand
flint idol
what would you substitute as u?
slate shadow
i would guess x-2?
flint idol
alright so we can replace that x-2 with u
slate shadow
$\int{(x+2)\sqrt{u} \dd u}$
twin meteorBOT
la garce
slate shadow
hmmm
flint idol
if u=x-2, x+2=?
slate shadow
the only word that comes to mind is conjugate
flint idol
yep exactly
slate shadow
bruh
flint idol
so u+4=x+2
slate shadow
$\int{(u+4)\sqrt{u} \dd u}$
twin meteorBOT
la garce
flint idol
use {}
slate shadow
well you know what i mean
twin meteorBOT
la garce
slate shadow
so i can split that up into two integrals
flint idol
and be careful on the second term there
slate shadow
then just evaluate
flint idol
it’s sqrt u not just u
flint idol
yw!
slate shadow
i cant believe i didnt see that, ive done way too much maths today
flint idol
haha yeah all good
slate shadow
alright
so final answer is
$\frac{2}{5} u^{{\frac{5}{2}}} + \frac{8}{3}u^{\frac{3}{2}} + c$
river kettle
Rip tex
slate shadow
yep
river kettle
Also you still need to sub in u back
slate shadow
oh yes of course
im so dead from all this work 😭
but other than that, should all be good
river kettle
Hold on
twin meteorBOT
la garce
river kettle
Wait nvm I was just seeing things
river kettle
glad vessel
stuck halfway in this
vocal sleetBOT
stuck halfway in this
peak shard
show what you have done so far
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glad vessel
<@&286206848099549185>
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@glad vessel Has your question been resolved?
distant fiber
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cold temple
what are you trying to achieve?
dawn dune
its right
distant fiber
what are you trying to achieve?
to convert exponential form into logarithmic form
bright parcel
how do i solve this
vocal sleetBOT
how do i solve this
subtle helm
!status
vocal sleetBOT
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
1
subtle helm
split it up first
bright parcel
split up the 2j+5?
subtle helm
$\sum_{j = 7} ^ {95} 2j + 5 = 2\sum_{j = 7}^{95} j + \sum_{7}^{95} 5$
twin meteorBOT
chebyshev's infinite pee norm
subtle helm
do you know how to compute each of those individual sums?
bright parcel
not really
subtle helm
are you familiar with triangluar numbers
bright parcel
not sure
bright parcel
yeah i know that
subtle helm
the left sum looks like that
except shifted
cause its
7 + 8 + 9 +... + 95
so manipulate it however you want to look like a triangle number
the right sum is just adding 5 over and over
bright parcel
7 + 8 + 9 +... + 95
ok i know that
bright parcel
the right sum is just adding 5 over and over
so that means
7 + 12 + 17 + ... + 95?
subtle helm
no
bright parcel
5 + 10 + 15 + 20?
subtle helm
$\sum_{j=7}^ {95} 5 = 5 +5+5+5+\cdots + 5$
twin meteorBOT
chebyshev's infinite pee norm
subtle helm
that's just the answer
bright parcel
19?
subtle helm
no
subtle helm
the left sum isn't 7, and the right sum isn't 5
bright parcel
the left sum isn't 7, and the right sum isn't 5
what do you mean
subtle helm
$\sum_{j = 7}^{95} j\neq 7,$ and $\sum_{j=7}^{95} 5 \neq 5$
bright parcel
well the left sum is 7 + 8 + 9 ....
twin meteorBOT
chebyshev's infinite pee norm
vocal sleetBOT
@bright parcel Has your question been resolved?
fair vault
(x-2)/4 - (y-4)/2 = z. What are the coordinates of the point where this line intersects with the yz-plane?
vocal sleetBOT
(x-2)/4 - (y-4)/2 = z. What are the coordinates of the point where this line int...
fair vault
Well the vector equation of the line is (2, 4, 0) + t(4, 2, 1). But idk how to go ahead from there
unborn coral
(x-2)/4 - (y-4)/2 = z. What are the coordinates of the point where this line int...
should there be an equals to instead of a minus between the x and y terms?
fair vault
Yeh yeh
fair vault
in the yz plane you have x = 0
Ok this helps, but do I just put it into parametric form and solve from there
unborn coral
not really
unless you want to make it harder lol
if you have $(0-2)/4 = (y-4)/2 = z$
twin meteorBOT
OssihLikesBlue
unborn coral
can you not solve for $y$ and $z$?
twin meteorBOT
OssihLikesBlue
unborn coral
Ok this helps, but do I just put it into parametric form and solve from there
you can still do it in parametric but its making it a bit trickier for no reason!
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vague vessel
vocal sleetBOT
vague vessel
??
pale perch
whats the problemo
vague vessel
Idk how to do this
pale perch
heard of implicit differentiation?
vague vessel
Yeah
pale perch
realise you need to apply that here?
steel snow
Idk how to do this
What part are you stuck on
vocal sleetBOT
@vague vessel Has your question been resolved?
vague vessel
realise you need to apply that here?
Ok so I deriv it once and then plug in those points for x and y?
steel snow
yes
vague vessel
👍
steel snow
very cool
eternal glacier
eternal glacier
