sorry, I mean can you use an arrangement of smaller areas to find the total area?
#help-23
edgy breach
naive osprey
Yes
safe radishBOT
@naive osprey Has your question been resolved?
naive osprey
<@1288813551548628992> Has your question been resolved?
No
radiant canopy
@naive osprey do vu have to find the area of the whole shape
naive osprey
<@1288813551548628992> do vu have to find the area of the whole shape
Yes
naive osprey
7
naive osprey
okk
naive osprey
sos find the area of triangle and * by 7
√6^2 - 2^2
= 5,66
5,66•4•1/2
11,32•7
= 79,24
But ChatGPT says the answer is 84
naive osprey
why did u do sq root 6^2
Because of the Pythagorean
naive osprey
whats area of triangle
11,32 ig?
radiant canopy
pythagoras works on right angled triangle right
naive osprey
yes
radiant canopy
is the bigger triangle a right angle triangle
naive osprey
it isn’t the height
radiant canopy
the method chatgpt tried
was
0.5* perimeter * apothem
apothem is center to the side
this is only applicable for regular polygons
safe radishBOT
@naive osprey Has your question been resolved?
safe radishBOT
safe radishBOT
wild cape
tardy mango
"crypto casino"
vivid stream
Very sad
quasi timber
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Available help channel!
atomic river
My professor sent me this slide and the middle definition is confusing me, I'm not sure what it meant by bit-level and pattern-level, I would like to see some examples to clarify this.
- Does "NOT (x AND y)" has the pattern level of 2?
- Does "NOT (x OR y OR z)" has the pattern level of 2 or 3?
- Does "x NAND y" has the pattern level of 1 or 2 (since NAND could be said to be made up from NOT and AND)
-
- But since NAND is the universal logic operation, does that mean the opposite that "x AND y" is actually "NOT (x NAND y)" and therefore has pattern-level of 2?
- Does "1011 AND 1001" has the bit-level of 2, or 4?
- Does "(1011 OR 1110) AND 1011" has the bit level of 12, or 8, or 2 if the original statement is "(x OR y) AND x"?
safe radishBOT
My professor sent me this slide and the middle definition is confusing me, I'm n...
median vigil
the slide doesn't say there is a number associated with bit level or pattern level
it just means a logical operation at the bit level is an operation on a single bit, e.g. 0 AND 1 = 0, and on the pattern level is a bunch of bit level operations on corresponsing bits, e.g. 011 AND 101 = 001
strong scarab
a pattern-level operation here simply means an operation applied to one or two bitstrings, whereas a bit-level operation is an operstion on individual bits.
vagrant steppe
Mind me asking what kind of math that is
strong scarab
digital logic, mostly.
vagrant steppe
Ahhh okay thanks
safe radishBOT
@tidal haven Has your question been resolved?
tardy mango
Differentiate the Pythagorean theorem with respect to time
safe radishBOT
@tidal haven Has your question been resolved?
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@tidal haven Has your question been resolved?
onyx tiger
however this will only give for 1 time where the car is moving towards the intersection
fickle mantle
safe radishBOT
fickle mantle
My teacher got 81k
median vigil
you went from 3^-3 in line 2 to 3^-2 in line 3
prisma elk
ye that is fine
gritty sable
Idk how to make them look the same
Js take negative sign out from numerator
gritty sable
yea
fickle mantle
.close
gritty sable
Always
safe radishBOT
solar hazel
Wil j be able to do this
i love your handwriting
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serene locust
i need to use the iroc formula
@meager igloo
im sorry its 3 in the morning i have an exam tomorrow i really need this
safe radishBOT
i need to use the iroc formula
safe radishBOT
<@823462958079803432>
mighty mango
huh what's the bot doing
mighty mango
no, geography
serene locust
this is gr12 so it might be easy for u
serene locust
no, geography
damn mb
js pls
help
this is the formula i need to use @mighty mango
mighty mango
you surely are supposed to use differnetiation rules... right?
mighty mango
this is the formula i need to use <@858810915663511553>
I can help if you know the diuffernetiation rules
otherwise, I have quite hte trauma with that specific formula
serene locust
whats differnetiation rules
serene locust
☠️
mighty mango
okay... yeah I'm sorry, I cant differnetiate with that specific formula
serene locust
damn
astral glacier
,tex .diff trig
flat frigateBOT
Xavier 🌺
serene locust
i dont think this is what its about
astral glacier
This combined with chain rule should get you there
mighty mango
This combined with chain rule should get you there
they have to differnetiate using the limit defn
astral glacier
You're showing us the answers to 4
serene locust
the textbook has the question answers mixed up
question 4 is the answer to question 5 its confusing
but u just gota figure it out by looking at the answer
oh wait
nvm that is the right answer
astral glacier
The unit of the equation isn't years anywhere
astral glacier
nvm that is the right answer
Yes
serene locust
so how is the answer "answers may vary"
cus theres different methods correct?
i need to use this formula, and h=0.0001
astral glacier
I mean in that case it looks like you've got your work cut out for you
serene locust
is what youd think
but i got 1800 as my answer
which is pretty different than 4.19
astral glacier
Did you remember to set the calculator to degrees
(or to convert the stuff to radians)
serene locust
wel its an exam, and a bunch of units need it to be in radians
so my calc is in radians
astral glacier
Well then did you remember to convert 120° to radians
serene locust
oh
astral glacier
You either change your calculator to work with degrees or change the formula to be in radians
(don't do both)
serene locust
yeah so how would i edit the formula to be in radians
astral glacier
Do you know how to convert from degrees to radians
serene locust
we ac we were never told that
serene locust
So how many radians is 120°
pie minus 60 degrees?
wiat ik pie is 180 degrees
bro im confused as shit
astral glacier
When a question has degrees in it, it needs degrees
serene locust
but we always used radians for the degree questions like
theta and beta
quadrants
all that
this is our lesson if that helps
safe radishBOT
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dry forum
Help me
dry forum
,rccq
glass edge
,rccw
flat frigateBOT
glass edge
,rc
glass edge
np
proud tree
set up the integral then you use integration by parts i believe
dry forum
set up the integral then you use integration by parts i believe
i dont want to brute force it , i was thinking of some clever way around it
proud tree
i dont want to brute force it , i was thinking of some clever way around it
i haven't written it out but i don't think it would be that ugly
dry forum
i haven't written it out but i don't think it would be that ugly
i got the first result but the second one is something i cant get hold of
proud tree
i got the first result but the second one is something i cant get hold of
how far have you gone?
i think i got it, i may have made a mistake
dry forum
how far have you gone?
im just running loops at this point
dry forum
i think i got it, i may have made a mistake
ok and .....?]
proud tree
you start from the equation you get from the first part
dry forum
you start from the equation you get from the first part
yeah a(n) <1/n-1
proud tree
$A_n < \frac{1}{2n-2}$ is equivalent to showing $A_n<\frac{1}{2}\left(A_n+A_{n-2}\right)$
flat frigateBOT
Green
proud tree
after simplifying the inequality, consider the interval over which we are integrating
safe radishBOT
@dry forum Has your question been resolved?
frosty leaf
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frosty leaf
would the majority imply "in relation to the other content" or no?
in my mind 1ist statement is correct because it has the largest proportions relative to each other category
safe radishBOT
@frosty leaf Has your question been resolved?
sterile grove
for the question just want to make sure i'm doing this correctly.
to find out how far he is horizontally you do tan(35) = 125/a
sterile grove
and then for the direct distance you're trying to find the hyp so you take what you got for the horizontal^2 + 130^2 then take the root of it?
fading phoenix
for the question just want to make sure i'm doing this correctly.
to find out ...
it should be 120 bcz the sailor is seen at the light
sterile grove
it should be 120 bcz the sailor is seen at the light
lighthouse is 50m and the cliff is 80m but the light from the lighthouse is 5m from the top
so 50+80-5 right?
astral glacier
Would be helpful to everyone to draw a diagram
onyx tiger
Would be helpful to everyone to draw a diagram
🥀
onyx tiger
and then for the direct distance you're trying to find the hyp so you take what ...
right
sterile grove
does what i did look right scoob
onyx tiger
yh
sterile grove
right so that's why i used 125 in the first part
I have it drawn out on my paper but I can't send a pic lolol
onyx tiger
That's wrong no?
austere goblet
125 is correct, and scoob's diagram, while a bit awkward and off-scale (why is the 50 so much longer than the 80) also looks correct from the way he placed the 5
sterile grove
lmfaoooo ur awesome scoob
onyx tiger
ah it labelled wrong but you get the feel
vast lagoon
Consider set S={1,2,3....50}, where m,n belong to S, if P is number of ways such that 6 to power m + 9 to power n is divisible by 5 and Q is the number of ways in which (m+n) is the square of prime number, find(P+Q)
i couldnt find the question online and wanted to verify my answer as i have a different answer from where i got the question
safe radishBOT
Consider set S={1,2,3....50}, where m,n belong to S, if P is number of ways such...
naive dragon
First of all, are for example (1,3) and (3,1) counted as 1?
It does not seem like the first part and the second part of your solution agree on this
vast lagoon
First of all, are for example (1,3) and (3,1) counted as 1?
no i thought theyd be different
counting as 2
which part did i count them same as? first or second?
naive dragon
The second part
vast lagoon
for m+n to be 4 its either 1,3 or 3,1 and i did write 2 ways
naive dragon
9=
1+8
2+7
3+6
4+5
5+4
6+3
7+2
8+1
vast lagoon
n can only be odd right as we calculated in the first part
naive dragon
Or does it?
vast lagoon
whats the answer with your way?
naive dragon
It's the wording fault
vast lagoon
whats the answer with your way?
i think it was 1333 where i got the answer id have to recheck
naive dragon
whats the answer with your way?
Idk I haven't done it, I have just read your
vast lagoon
Consider set S={1,2,3....50}, where m,n belong to S, if P is number of ways such...
4 will have 3, 9 will have 8, 25 will have 24, and 49 will have 48
Q=83
so yeah 1333
thank you!
naive dragon
np
vast lagoon
.close
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glacial oyster
Let two circles of equal radii with centres A and B intersect at C and D. Let EDF || AB as shown. IDH is another line not parallel to AB.
I lies on the minor arc ED between E and D and H on the minor arc FJ between F and J.
Q.1
ID < ED and DH > DF.
Is this true?
Q.2 If yes, how can one prove this?
safe radishBOT
onyx tiger
Let two circles of equal radii with centres A and B intersect at C and D. Let ED...
!msgdel
safe radishBOT
Let two circles of equal radii with centres A and B intersect at C and D. Let ED...
The original post of this help channel has been deleted, and it will abruptly close and possibly lock. (This is irreversible.) Please claim a new channel, and don't delete the first message of any future channel you claim.
safe radishBOT
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faint glade
Does anyone know at which step I'm going wrong here?
safe radishBOT
Does anyone know at which step I'm going wrong here?
gray mulch
Does anyone know at which step I'm going wrong here?
You didn't multiply 3T by 5
faint glade
Ohhh
gray mulch
When you multiply both sides, you do it for the whole sum
faint glade
So wqhen you need to multiply something on one side, you multiply everything in the expression?
quasi bison
you multiply the ENTIRE left side and the ENTIRE right side by that
so really the fully 100% formally correct step would be $$5 \paren{3T + \frac{8T-8}{5}} = 5 \cdot 7$$ which then simplifies to $$5 \cdot 3T + 5 \cdot \frac{8T-8}{5} = 5 \cdot 7$$
flat frigateBOT
Ann
faint glade
This makes so much more sense
mighty mango
indeed! refer to the lovely distribution property you probably learned.
b-
okay 🤩
faint glade
should be 8t - 8
mighty mango
good that you noticed
faint glade
- -8
mighty mango
should be 8t - 8
indeed
safe radishBOT
@faint glade Has your question been resolved?
formal grail
i'm having trouble with this
safe radishBOT
i'm having trouble with this
formal grail
prove that for any x,y in Z
if x in Z+ and y not in Z+ then xy not in Z+
if xy = 1 then either x=y=1 or x=y=-1
using the equivalence class definition and properties of Z
safe radishBOT
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
I know what I need to do but I dont know how to make it fully work without assuming things that rent explicity proven
by def, x = (a,b) (with a stick on top) with a>b, and y = (c,d) (with a stick on top) with d≥c
so i can multiply those and get (ac+bd, ad+bc) with a stick on top
but idk how to prove that it's not in Z+ by using a>b and d≥c and N inequality properties
2
ok I found a way for the first one even if it's too long its the only one that satisfies em
safe radishBOT
@formal grail Has your question been resolved?
tardy mango
You may find page 2 here to be helpful: https://crawford.elmhurst.edu/classes/m301/2019Sp/wk4.4_Divisibility.pdf
formal grail
thank you! it might be honestly, i didnt consider that approach since we didnt really delve into divisors
they are defined in the material there just wasnt really any exercises around them
and i can use this, which isnt in the material, because its the logical conclusion of the first thign proposed
for the first one i did this, it's correct right
If i imagine all sets of parentheses have bars on top
x is in Z+ so x is (a,b) such that a>b
y is not in Z+ so y is (c,d) such that d≥c -> either d=c or d>c
its a known that for everything in Z always exactly 1 of in Z+ in Z- or =0 is true (the material calls this trichotomy)
And product in Z is such as (a,b)(c,d) = (ac+bd, ad+bc)
case 1: c=d
if c=d then (c,d) ~ (1,1) so it's 0 in Z
since for all Z, x*0 = 0, xy = 0 and 0 not in Z+ (the material says x*(1,1) = (1,1) which is the same thing but more convoluted)
case 2: d>c
the > in N is defined such that
if a>b, then there exists n in N such that a = b+n
same thing -> d = c+m
so ac + bd = (b+n)c + b(c+m)
= 2bc + nc + bm
and ad + bc = (b+n)(c+m) + bc
= 2bc + nc + bm + nm (only difference)
so using those two it can be seen that ac+bd = ad+bc +nm, and nm is in N (duh), so by def of > it implies that
ad+bc > ac+bd
so since the right side of the equivalence class that is the product > the right side, the product is in Z- and not in Z+ in case 2
so no matter what the product of a Z+ and a not in Z+ will not be in Z+
formal grail
You may find page 2 here to be helpful: https://crawford.elmhurst.edu/classes/m3...
idk if im allowed to use that (-m)(-k) = mk
so best to not mess w signs imo
9)b)
let x = (a,b) and y = (c,d), with a,b,c,d all in N ofc
1 = (2,1), so
(ac+bd, ad+bc) must be = (2,1), and by equivalence it means
ac + bd +2 = ad+bc + 1
ac + bd +1 = ad+bc (since 2=1+1) !!!!
if a=b, then bc+bd = bd+bc+1 not possible in N
same for if c=d, not possible
Case 1: a>b
there exists n in N such that a=b+n. substituting
(b+n)c + bd = (b+n)d + bc + 1
develop and cancel ->
nc = nd +1
so either c<d or c>d
case 1.a.: c<d so there would be k in N such that d=c+m so
nc = n(c+m) +1
nc = nc + nm + 1 not possible, so necessarily in case 1 c>d
so there exists k in N duch that c = d+k.
n(d+k) = nd +1
nd + nk = nd +1
nk = 1
since in N 1*a = a always, it means n=k=1
so a = b+1 and c = d+1
so a=suc(b) and c=suc(d)
so x = (suc(b),b) = 1 and y = (suc(d),d) = 1
Case 2 is the same by analogy but flipping a and b and c and d respectively results in
b = a+1 and d = c+1
so b=suc(a) and d=suc(c)
so x = (a,suc(a)) = -1 and y = (c,suc(c)) = -1
so if xy=1, either x=y=1 or x=y=-1
safe radishBOT
@formal grail Has your question been resolved?
west grail
GUYS TELL me what is this jacobimatrix good for?
safe radishBOT
GUYS TELL me what is this jacobimatrix good for?
plucky elk
do you know derivatives?
west grail
yes i know how to build the gradient as well
plucky elk
do you know what slope is in 1 dimension?
gradient is just the generalization to n dimensions
west grail
slope is steigung i guess yeah i will need to know what this matrix is good for
plucky elk
applications: https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant#Dyna...
yes then there are 3 applications here
west grail
yeah i guess dunno the dude in our exam preparation just showed us how to do it but not how it is used lol
guess the use is secondary in our case
safe radishBOT
@west grail Has your question been resolved?
formal grail
is the first one true or false? I know how to prove that it's true but also how to prove that it's false
safe radishBOT
is the first one true or false? I know how to prove that it's true but also how ...
glass carbon
give a counterexample (one is enough)
formal grail
nvm ugh
I know that the first one is true but some things I see keep attempting to give a counterexample even if there isnt because they wrongly interpret N as including 0
which would make the first impossible by saying they aren't the same kind of structure if (N,+) has neuter and (Z-,+) doesnt
But obviously (N,+) doesnt include 0 so this thing doesnt matter and it's easy to find a function that proves they are homomorphic
for the latter though it can be easily disproven by saying that (Z-, *) isnt closed so it cant be possible, right? @glass carbon
uneven ice
what is this operator ? same set? same cardinality?
glass carbon
if you define the set N as {1,2,3, ...} (without zero) then yes
formal grail
what is this operator ? same set? same cardinality?
wdym by this
formal grail
if you define the set N as {1,2,3, ...} (without zero) then yes
everything in the class is based on this definition yes
formal grail
no it means that they are algebraic isomorphisms
uneven ice
or that they of the same size?
formal grail
that the operation + in the set Z- is algebraically isomorphic to the operation + in the set N
and the same for * (although there I need to disprove since it's false)
formal grail
yeah I already knew how to prove it
serene locust
.
uneven ice
great-o
safe radishBOT
@formal grail Has your question been resolved?
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mortal sundial
This is from the answer key for an exam review package
safe radishBOT
This is from the answer key for an exam review package
glass carbon
like where does x/2 come from
If you plug x/2 + pi/6 into g(x) you'll obtain -cos(x) + 3
In other words, it is the undo of these transformations, the same with -y+3
glass carbon
How do I get the second table??
All you need to do is plug the values from the first table for x and calculate accordingly, e.g. for x = 0 we have x/2 + pi/6 = 0/2 + pi/6 = pi/6, y was 1, so now it will be -1+3=2 etc.
mortal sundial
but how do we get that x/2 + pi/6 from the original equation
plucky elk
but how do we get that x/2 + pi/6 from the original equation
"undoing the transformation" 2(x - pi/6)
plucky elk
where did (pi/6) / 2 come from
mortal sundial
if i look at 2(x - pi/6) i think (2x - (2pi)/6) OH
OHHHH
so if you divide it by 2 it's pi/6
i'm still struggling to pull it out of the original equatioon
safe radishBOT
@mortal sundial Has your question been resolved?
mortal sundial
I'll just hope
spark lynx
Is this correct? I believe it is I just want someone else to double check me.
It does not have to be fully simplified or even simplified at all, I just simplified it enough that people wont have an aneurysm reading it
glass carbon
(a+b)^2 isn't a^2 + b^2
spark lynx
(a+b)^2 isn't a^2 + b^2
Can you show me what you're refering to
glacial cairn
g²
spark lynx
Oh fair enough
glacial cairn
Wdym it doesn't get affected
glass carbon
these are not integrals
glacial cairn
(x^2+1)^2 is not x^4 + 1^2
spark lynx
tyty
sour folio
Idk if this question is too short to be asked here but is there a difference between the two sine laws or can I just always use one and I’ll get the same answers
safe radishBOT
Idk if this question is too short to be asked here but is there a difference bet...
glass carbon
one is enough (though it depends), you use it depending on your needs
glacial cairn
There is no difference, none of the denominators will ever be zero
safe radishBOT
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safe radishBOT
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
tired inlet
You just dumped like 20 problems there. pick one and try it
polar lynx
junior smelt
(also please don't spam your question across multiple channels, you have this one for yourself, so there's no need to disrupt other people with their questions 
)
tired inlet
You have to be trolling
hard crest
this is not appropriate and you know that.
sonic basalt
can someone tell me where to start number 7?
safe radishBOT
can someone tell me where to start number 7?
sonic basalt
and also if possible pls teach me how to find direction of force exerted on a hinge because they didnt teach it in the book yet many of the past paper questions uses it
wet maple
can someone tell me where to start number 7?
First, what are the forces that act on the rod?
sonic basalt
First, what are the forces that act on the rod?
hey sorry, so i found out how to do it
i just gotta resolve the forces vertically and horizontally, find moment on a, get y and x and find the magnitude, and use tantheta=y/x
wet maple
Ah ok gr8 :)
sonic basalt
thanks man
wet maple
Np
sonic basalt
.close
safe radishBOT
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safe radishBOT
is this wrong
formal schooner
where did x=-1 come from?
bruh......
you're trolling us right
you meant to use your alt
but you ended up using the same account
to reply to yourself
formal schooner
its the solution and im confused
that solution is clearly wrong
warm ocean
tardy mango
,w graph y=3x^2+6x, y=0
flat frigateBOT
tardy mango
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fickle mantle
safe radishBOT
fickle mantle
Could u help me
fickle mantle
this looks like a common expression
Factorize??
onyx tiger
Factorize??
yes
fickle mantle
onyx tiger
also denominator is under square root
flat frigateBOT
scoob
onyx tiger
now try to match it with RHS
onyx tiger
i would suggest split fraction
onyx tiger
,, \frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}
flat frigateBOT
scoob
onyx tiger
Does the cube root desperate?
what do you mean by separate?
safe radishBOT
@fickle mantle Has your question been resolved?
onyx tiger
,rccw
flat frigateBOT
onyx tiger
what have you tried
fickle mantle
onyx tiger
,, x = \sqrt{x}\cdot \sqrt{x}
flat frigateBOT
scoob
onyx tiger
or you could just cancel x in numerator and denominator here
onyx tiger
yh you cannot add numerator and denominator to add fractions
,, \frac{a}{b} + \frac{c}{d} \neq \frac{a+c}{b+d}
flat frigateBOT
scoob
onyx tiger
or you could just cancel x in numerator and denominator here
go with this cancel x in numerator and denominator
onyx tiger
👍
fickle mantle
.close
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vague rain
Hlw i can solve integral dx/((sqrt(6x+1) +2)
safe radishBOT
Hlw i can solve integral dx/((sqrt(6x+1) +2)
brave wolf
Hlw i can solve integral dx/((sqrt(6x+1) +2)
try rationalizing the denominator
by multiplying by the conjugate
or perhaps directly substituting could be quicker
quasi bison
i would think u := sqrt(6x+1) would be a better path tbh
quasi bison
Hlw i can solve integral dx/((sqrt(6x+1) +2)
!status
safe radishBOT
Hlw i can solve integral dx/((sqrt(6x+1) +2)
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
Where is my mistake?
quasi bison
you might wanna write the characters u, 4 and 6 in a way that doesn't make them all look similar
vague rain
u substituted t only to substitute x back in?
I dont like write but is same i got 6x -5
But i got a mistake
brave wolf
Hlw i can solve integral dx/((sqrt(6x+1) +2)
and is it sqrt(6x+1) or sqrt(6x-1)?
vague rain
Where?
6x-1
I am so dumb i cant see my mistake i dont know why syntethic division cant work but wether large division
brave wolf
I deleted it
hmm
thats not really common with a square root
and ur result is sqrt(u) - 4/(u-4)?
$u^{\frac{1}{2}}-\frac{4}{u-4}$
flat frigateBOT
MathIsAlwaysRight
brave wolf
i would think u := sqrt(6x+1) would be a better path tbh
Sure, I'd probably just start with this
either u := sqrt(6x - 1) or u := sqrt(6x - 1) + 2
vague rain
I can continue wirh u message i need 15 minutes me back
formal schooner
<@&268886789983436800>
vague rain
How I can solve thiw
safe radishBOT
How I can solve thiw
buoyant dragon
at very start of the question, Put
$u = \sqrt{6 x - 1}$
flat frigateBOT
Shikhar
vague rain
But i can multiply for conjugat3
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left folio
How I can solve thiw
dt = 6/sqrt(6x-1) dx
vague rain
dt = 6/sqrt(6x-1) dx
Wdym?
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south parcel
I stumbled across this question on a set of integral questions: A toilet roll has an inner radius r = 2 cm and an outer radius R = 7 cm. The thickness of the paper is 0.5 mm. What is the length of the paper when it is completely unrolled?
safe radishBOT
I stumbled across this question on a set of integral questions: A toilet roll ha...
slim lion
I stumbled across this question on a set of integral questions: A toilet roll ha...
i mean technically
the paper is in a spiral
so the outer radius of 7cm fluctuates depending on where you take the point
but let’s say we assume that the end of the spiral is 7 cm
south parcel
yeah ive come so far, and so for every layer the diameter increases by 2*whatever variable
is that right?
slim lion
the paper is in a spiral
im quite literally takin a shi scrolling math rn
so a bit ironic 😅
and i was about to solve it until i realised it was a spiral
south parcel
hahahaha
well I solved it without using integrals, however I really want to solve it using it as well
slim lion
yeah ive come so far, and so for every layer the diameter increases by 2*whateve...
not sure what this means tbh
slim lion
well I solved it without using integrals, however I really want to solve it usin...
i was thinking of a calculus solution too
because we want to take the arc length of the spiral
last belfry
not sure what this means tbh
I think he means cuz the paper laps around twice so its effectively adding 1mm each time it goes around
south parcel
the circumference is 2pir^2
slim lion
I think he means cuz the paper laps around twice so its effectively adding 1mm e...
to be completely honest, i dont really understand
why does it lap twice?
that’s the diameter, isn’t it?
last belfry
Yes
slim lion
we seem to only be concerned with the radius
south parcel
for the radius it increases by one thickness, however when its the diameter, it gets added to the other side as well
slim lion
for the radius it increases by one thickness, however when its the diameter, it...
right
last belfry
The integral is int(r>R) (2pix)/thickness I believe
south parcel
and so i used a sequence for the circumference Cn = pi*(d+2nt)
slim lion
but let’s say we assume that the end of the spiral is 7 cm
so can we agree that assuming this
we have 5/0.5 = 10 laps of toilet paper
slim lion
100 i can agree on
ok so we’ll stick with this
south parcel
yup
south parcel
not sure about that haha, its just 2nd semester economics maths
slim lion
not sure about that haha, its just 2nd semester economics maths
well we’re being exact here, aren’t we? 😅
last belfry
The integral is int(r>R) (2pix)/thickness I believe
I think you use this
For this level
But yea
slim lion
I think you use this
is that the surface area integral
last belfry
Yes
Then you have the thickness so area is just thickness x length
So you just divide the area by the thickness
I think
south parcel
i think thats where i fell off a bit
are we taking the integral in a way that sums up all the circumferences
at each "layer"
last belfry
at each "layer"
Yk you can just do this with basic level math?
south parcel
yeah I have done that
last belfry
Oh ok
south parcel
are we taking the integral in a way that sums up all the circumferences
but thats the idea of it?
.close
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tropic umbra
Call a nonnegative integer simple if its only nonzero digits are ones. Suppose S is simple, and R is the number obtained by reversing the order of its digits. If 901·S is simple, 901·R must also be simple. Why?
tropic umbra
i solved and the only simple integers works are repunit integers with more than 2 digits such as 111, 1111, ... also can end with 0 as 1110,11110,....
but i couldn't express in words so can someone help
quasi bison
what do you mean when you say "simple" integer
do you mean a number that's divisble by 1, itself and nothing else?
tropic umbra
what do you mean when you say "simple" integer
Call a nonnegative integer simple if its only nonzero digits are ones. such as 0, 1, 10 , 11, 100, 101
tropic umbra
do you mean a number that's divisble by 1, itself and nothing else?
no
quasi bison
oh nevermind
ok i thought you might've mistranslated from another language and meant prime
my bad
quasi bison
901S = (1000 - 100 + 1)S. this seems like it would be relevant.
tropic umbra
901S = (1000 - 100 + 1)S. this seems like it would be relevant.
iam confused can u explain it
quasi bison
try to write out some simple integers and their products with 901
see if anything pops out
tropic umbra
try to write out some simple integers and their products with 901
yes i did
tropic umbra
i solved and the only simple integers works are repunit integers with more than ...
.
quasi bison
are you sure that something like 111110000011111000 with the runs of 1's far enough apart wouldn't also work?
what exactly breaks down if you try it this way
tropic umbra
are you sure that something like `111110000011111000` with the runs of 1's far e...
i just tried it and it didd work
flat frigateBOT
tropic umbra
but it does,no?
yes i said it does
tropic umbra
ok clearly i need to go rest cause i keep misreading messages here
no worries thanks btw
safe radishBOT
@tropic umbra Has your question been resolved?
austere goblet
just react to the bot. the bot can't read text replies to that question
tropic umbra
oh my bad😭
naive dragon
Call a nonnegative integer simple if its only nonzero digits are ones. ...
so simple integers are just binary strings that don't start with 0?....
tropic umbra
so simple integers are just binary strings that don't start with 0?....
yes
ig
like 0,1,1011,100,101
austere goblet
so simple integers are just binary strings that don't start with 0?....
in base 10
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@tropic umbra Has your question been resolved?
onyx tiger
so what is left
flat frigateBOT
naive dragon
any simple number S with no single 1,0 or no consecutive pair 11 or 00 satisfy that 901*S is a simple integer
I think
S*901=900*S+S
so if S have a string abc111def we can well do addition there would be
...... 9 9 9 ....
........ 1 1 1 .....
there has to be at least 3 consecutive 1 or else when do addition
.....0 9 9 0 ....
.......0 1 1 0 .....
a 9 would appear
similarly for string ...1001...
...... 9 0 0 9 ....
........ 1 0 0 1.....
when do addition a 9 could appear, or
...... 9 0 0 9 9 9 ....
........ 1 0 0 1 1 9......
.............. 2 0 0 0....
a 2 would appear
ofc when we reverse the order there aren't anything changed with the number of consecutive 1's and 0's
So obviously its reversed in order multiply by 900 would also be simple integer
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naive dragon
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sudden crypt
Could someone please help me with this question?
safe radishBOT
Could someone please help me with this question?
lost lily
are you familiar with radians?
gleaming coral
Could someone please help me with this question?
Do you know the formula of angular speed?
sudden crypt
are you familiar with radians?
And ik that one revolution is 2pi
quasi bison
!noai
safe radishBOT
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
lost lily
if one revolution is 2 pi radians, then how many radians is 20 revolutions? and how many seconds pass in one minute? then you can find the number of radians per amount of seconds passed
proud bloom
10 pie /3 m/s
lost lily
are you familiar with the concept that the distance traversed on a circle is the product of the angle covered and radius?
sudden crypt
I am not
lost lily
I am not
when you go around a circle, you are going across a fraction of its perimeter (2 pi r)
when you travel a complete revolution of the circle you are travelling 2 pi radians multiplied by r resulting in 2 pi r
so when you travel any "T" radians across a circle, you are actually travelling T*r length
sudden crypt
Okkk
proud bloom
speed = distance /time = 40 . 5 pie /60 =10/3pie metre per second
lost lily
in your case you can find its rate by dividing with units of time to get linear speed = angular speed * radius
sudden crypt
So my radius is 5 so the perimeter would be 10pi
lost lily
you found the angular speed in step 1 of the problem in radians per second, this represents how fast the merry go round spins about its centre (how many radians it covers in one second)
sudden crypt
Ok...
lost lily
for any point on the edge of the merry go round, you would multiply that speed with how far you are from the centre (the radius) to get its linear speed
sudden crypt
So liner speed is angular velocity x 2?
lost lily
So my radius is 5 so the perimeter would be 10pi
this is correct but not the answer you are looking for for part 2
lost lily
So liner speed is angular velocity x 2?
not quite
sudden crypt
Linear speed is angular velocity x r
lost lily
Linear speed is angular velocity x r
yes...
lost lily
yes good job!
tropic umbra
So obviously its reversed in order multiply by 900 would also be simple integer
so u solved it ?
safe radishBOT
so u solved it ?
naive dragon
Not really, it's not a complete solution but you get the idea
safe radishBOT
@tropic umbra Has your question been resolved?
tropic umbra
Not really, it's not a complete solution but you get the idea
I feel stupid still trying to
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@tropic umbra Has your question been resolved?
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@tropic umbra Has your question been resolved?
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@tropic umbra Has your question been resolved?
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noble scaffold
I have a question. When confirming local extremes, is it correct to say that ‘function(point) is a local extremum’ or that ‘the point is a local extremum’? Or what would be the correct way to say it in an exam?
safe radishBOT
I have a question. When confirming local extremes, is it correct to say that ‘fu...
somber cape
I have a question. When confirming local extremes, is it correct to say that ‘fu...
function(point) is a local extremum
point is a critical point
glacial cairn
You can say extremum point for the x value and extremum value or just extremum for the y value
noble scaffold
Thank you! I have another related question. For this function, I had concluded that (0; 0) is a saddle point, but in an online solution, they stated that (0; 0; f(0; 0)) is the saddle point. Which one is correct, or are both wrong?
The exercise asks you to analyse whether f(0; 0) is a local extreme.
glacial cairn
Details really
(0,0) is the point in the 2D xy-plane which gives a saddle point in the 3D graph of the function
(0,0,f(0,0)) being that saddle point
Calling (0,0) a saddle point is perfectly fine
noble scaffold
That makes sense, thanks
In this case, would it be incorrect to say that f(0; 0) is a saddle point?
glacial cairn
f(0,0) is the value at that point, so I'd say it's technically incorrect
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earnest mirage
Hello, could someone check if this proof looks good please?
safe radishBOT
Hello, could someone check if this proof looks good please?
shadow glade
kind of confused by your argument here
the expression youre saying equals 6l doesn't seem to match the 5^2*k - 1 expression that youre substituting 6l for below
earnest mirage
kind of confused by your argument here
Typo, fixed 👌
shadow glade
but...in the top expression you have a k in the exponent
then below you have multiplication by k
ok
also need to fix the middle one
and i dunno just some thoughts for clarification, you are kind of changing n with k a lot
earnest mirage
Fixed 👌
\begin{Definition}[Natural numbers]
The set of the \emph{natural numbers} is the set $\bN = \{1,2,3,4,5,\dots\}$.
\end{Definition}
\begin{Theorem}
Suppose $n \in \bN$, then $6 \mid (5^{2n} - 1)$.
\end{Theorem}
\begin{proof}
Let $n \in \bN$. We proceed by induction.\\
\underline{Base Case.} The base case is when $n = 1$, and $6 \mid (5^2 - 1)$ as desired.\\
\underline{Inductive Hypothesis.} Let $k \in \bN$, and assume $6 \mid (5^{2k} - 1)$.\\
\underline{Induction step.} We aim to prove that the result holds for $k + 1$.
That is, we wish to show that $6 \mid (5^{2(k + 1)} - 1)$.
To do this, we begin with the expression $5^{2(k + 1)} - 1$:
\begin{align*}
5^{2(k + 1)} - 1 &= 5^2(5^{2k}) - 1 \\
&= 24(5^{2k}) + 5^2k - 1 \\
\end{align*}
By the inductive hypothesis, $6 \mid (5^{2k} - 1)$, and so, by definition of divisibility,
$5^{2k} - 1 = 6l$ for some integer $l$.
Then,
\begin{align*}
24(5^{2k}) + 5^{2k} - 1 &= 24(5^{2k}) + 6l \\
&= 6(4(5^{2k}) + l) \\
\end{align*}
Since $k$ and $l$ are integers, so is $4(5^{2k}) + l$.
Then, $5^{2(n+1)} - 1 = 6m$ where $m = 4(5^{2k}) + l$.
Thus, by the definition of divisibility, $6 \mid (5^{2(k+1)} - 1)$.
Therefore, by induction, $6 \mid (5^{2n} - 1)$ for all $n \in \bN$.
\end{proof}
in the hypothesis line, assume the statement is only true for n <= k because the way you phrased the induction hypothesis currently, it sounds like youre assuming the whole thing youre trying to prove
changing n to k there made it worse
flat frigateBOT
Mor Bras
shadow glade
Let me change that
my suggestion for hypothesis: assume $6 \mid (5^{2n} - 1)$ for $n\in\mathbb{N}, n\leq k$
flat frigateBOT
Soosh
safe radishBOT
@earnest mirage Has your question been resolved?
safe radishBOT
@earnest mirage Has your question been resolved?
earnest mirage
my suggestion for hypothesis: assume $6 \mid (5^{2n} - 1)$ for $n\in\mathbb{N}, ...
Thank you for your comment!
safe radishBOT
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sleek current
Why wouldn't
$$
t = 5(log25/log0.5)
$$
be correct?
safe radishBOT
Why wouldn't
$$
t = 5(log25/log0.5)
$$
be correct?
flat frigateBOT
Sep
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
median vigil
i suspect they want the "percent" to be given as a decimal between 0 and 1
median vigil
yes
dim rock
safe radishBOT
dim rock
I finally tried u-sub but I'm stuck trying to figure out the integral of 3^u
dim rock
idk
severe pond
learn derivatives before integrals
dim rock
I got a c in calc 1
dim rock
I'm thinking of withdrawling and learning calc 1 all over again
dim rock
first
severe pond
its before the deadline?
dim rock
idk about that
you think it's doable ?
dim rock
I'm good at math it's just last semster was hell
dim rock
you think it's doable ?
.
dim rock
3^x / ln(x) ?
dim rock
oh right
severe pond
derivative of b^x is b^x ln b
basically undoing that factor of ln b
so that it cancels
severe pond
you're welcome
btw you could've done 3^(ln x) = (e^ln 3)^(ln x) = (e^ln x)^(ln 3) = x^ln(3)
safe radishBOT
@dim rock Has your question been resolved?
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turbid crag
do you just want confirmation?
^ (sorry, forgot to reply)
yep
you always want to make it into an "if xxx, then yyy"
(well you don't always have to, but this always works)
lemme see
there are more ways to express this
do you know how to turn an implication into an OR statement and vice versa?
lilac crane
hard crest
ah pls don't delete modpings even if they've been handled, it gets super confusing when mods show up
as evidenced
hard crest
(you can edit them to say resolved or sth)
turbid crag
i just did not think of that — but off-topic
@drowsy vale sorry for everything that has happened in this channel lmao, you still here?
exotic anvil
A mod telling you off is never off topic 
turbid crag
A mod telling you off is never off topic <:sully:651816820122189834>
lol i wasnt clear, but im meaning that my set of excuses that i were about to dump out is off-topic
i got a ghost message lmao
safe radishBOT
@drowsy vale Has your question been resolved?
turbid crag
confirmation ||your answer is wrong, one of A / B / C / D is correct||
do you know how to express implication as OR
hard crest
confirmation ||your answer is wrong, one of A / B / C / D is correct||
wait are you sure
turbid crag
wait are you sure
||A?|| fuck.
clearly i'm not in the mental state of doing this rn
your answer is right marcel
hard crest
yeah. it turns out that p -> q is exactly equal to (not p) or q
twin fulcrum
Can you guys check this please
safe radishBOT
Can you guys check this please
quasi bison
you will benefit from making your z and 2 look less similar, this much i can tell you immediately
your final answer of (-1, 3, 5) satisfies the system, so you have made an even number of mistakes
twin fulcrum
you will benefit from making your **z** and **2** look less similar, this much i...
Gotcha, will do
naive dragon
you will benefit from making your **z** and **2** look less similar, this much i...
You can write z with a stroke "ƶ", I personally use it all the time when doing math problems
hard crest
one really nice thing about systems of eqns is that you can easily check your own work
by simply plugging the solution you get into your starting equations
quasi bison
You can write z with a stroke "ƶ", I personally use it all the time when doing m...
another option is to write your 2 with a bit of a loop to it
quasi bison
by simply plugging the solution you get into your starting equations
which is what i did and reported the result :P
safe radishBOT
@twin fulcrum Has your question been resolved?
twin fulcrum
New
<@&286206848099549185>
tried diff format still got same result, not sure what im doing wrong
clever gale
tried diff format still got same result, not sure what im doing wrong
Why do you believe your result is incorrect
,w solve 2x - y + z = 0, 3x - 2y + 4z = 11, 5x + y - 6z = -32
flat frigateBOT
twin fulcrum
Why do you believe your result is incorrect
oh, sorry someone said there was a mistake
quiet field
i need help with this one
safe radishBOT
i need help with this one
quasi bison
the goal is to find DE?
quiet field
yup
quasi bison
do you have progress so far?
quasi bison
,rccw
flat frigateBOT
quasi bison
hmm might be difficult this way
here's a better idea: drop a perpendicular from B into AC. call it BH for example. then consider triangles ADE and ABH
hollow trout
quasi bison
look at triangles ADE and ABH
there is something special about them
seeing as DE and BH are parallel
safe radishBOT
@quiet field Has your question been resolved?
safe radishBOT
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split fulcrum
I need help starting with this.
safe radishBOT
I need help starting with this.
quasi bison
do you know how spherical (R^3) coords work
split fulcrum
uh i think so
quasi bison
ok can you state the conversion from cartesian to polar in R^3
split fulcrum
ok can you state the conversion from cartesian to polar in R^3
r = sqrt( x^2 + y^2 + z^2)
theta = arccos(z/r)
phi = arctan(y/x)
quasi bison
misquoted and opposite to what i actually asked
split fulcrum
misquoted _and_ opposite to what i actually asked
what about now
did you mean cylindrical coordinates
quasi bison
no, i meant spherical
i expected:
x = r cos(θ)
y = r sin(θ) cos(φ)
z = r sin(θ) sin(φ)
or some permutation of this
ok i guess actually i am the fool here because i asked the question in the opposite way to my own intentions
split fulcrum
i expected:
x = r cos(θ)
y = r sin(θ) cos(φ)
z = r sin(θ) sin(φ)
or some permu...
okay yeah i was going to say this but you asked going from cartesian to polar and i was really confused lol
so what do we do with this
quasi bison
can you come up with a generalization to 4 coordinates in the same way i showed
use x_1, x_2, x_3, x_4 for the rectangular coords and r, theta_1, theta_2, theta_3 for the spherical coords
split fulcrum
(x1)^2 + (x2)^2 + (x3)^3 + (x4)^4 = r^2
x1 = rcos(theta1)
x2 = rsin(theta1)cos(theta2)
and
quasi bison
(x1)^2 + (x2)^2 + (x3)^3 + (x4)^4 = r^2
this one is unnecessary
split fulcrum
but didnt you say to use x1,x2,...
quasi bison
i did, but the equation i specifically replied to is not what im looking for.
quasi bison
ok great
thats good now
can you write down the generalization of this to n coordinates
you'll have one radial and n-1 angular coordinates on the polar side of things
also you will want to write down the ranges that these thetas go over
for integration purposes
split fulcrum
x_n = rsin(theta1)sin(theta2)...sin(theta_n-2)sin(theta_n-1)
x_n-1= rsin(theta1)sin(theta2)...sin(theta_n-2)cos(theta_n-1)
theta 1 and theta 2 from 0 to pi maybe
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@split fulcrum Has your question been resolved?
normal moss
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quaint marlin
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dull sequoia
What have you tried
edgy breach
why do you need integration?
dull sequoia
See it’s a little confusing what you’ve written
On the right side you have an integral with respect to t, and the integrand is a function of t, that’s perfect
But on the left side you have that v is a function of t
But there’s no dependency on t on the right side
Once you integrate the t will disappear and v(t) will always be a constant
It’s more like $v(t) = \int_0^t a(\mathcolor{green}{t}),d\mathcolor{green}{t}$
flat frigateBOT
frosst
edgy breach
i dont understand why you are using calculus at all when acceleration is constant
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@quaint marlin Has your question been resolved?
quaint marlin
No
I forgot that v(6)=45
quasi bison
$\int_0^2 a(t) \dd{t} = v(2) - v(0)$, and you don't know $v(0)$ (yet).
flat frigateBOT
Ann
dull sequoia
No
I forgot that v(6)=45
Did you understand anything I said?
quaint marlin
Yep
dull sequoia
**frosst**
So you understand this?
quaint marlin
So you understand this?
quaint marlin
I mean why i can do this directly
dull sequoia
Where did v(6) = 45 come from
quaint marlin
No
I forgot that v(6)=45
I forgot i'm sorry
dull sequoia
I mean why i can do this directly
Why can you or why can’t you
Where in the question does it say that