sure makes sense lol
#help-13
lunar lynx
Basically, Sum is less than 1/3 -> works.
Sum is greater than 1/2 -> works.
Both would have worked too but that's not possible in this case.
minor crystal
Okay makes sense, that was probably a stupid question
For this one
I had Quantity B is bigger
i used hypergeometric on both
,, \frac{3C_2 \cdot 2C_1 + 3C_1 \cdot 2C_2}{5C3} = \frac{9}{10}
Is that quantity A?
wraith daggerBOT
kanna22
minor crystal
Quantity B looks like 1 because there's no way he doesn't pick a red even in the worst case scenario where he picks BBB and then R
lunar lynx
What if BBRB ?
lunar lynx
It's certainly not 1.
minor crystal
,, \frac{3C_3 \cdot 2C_1 + 3C_2 \cdot 2C_2}{5C_4}= 1
I guess order doesn't matter in hypergeometric
wraith daggerBOT
kanna22
lunar lynx
First one also seems a bit wrong to me. You are assuming that you are taking out 2 Blue and 1 red, or 1 blue and 2 red, but they consider all orders so you are adding extra cases.
Like RBB is also included in 3c2 * 2c1.
minor crystal
Yes I'm aware now that i've written it out
How do i do it with permutations then
Or whatever
lunar lynx
I think you do it this way - Instead of doing it for 3 balls out of bag, do it for 2 and then ensure that third ball being taken out is blue. For part A.
Denominator would change accordingly i.e. 5c2.
Edited.
cedar kilnBOT
@minor crystal Has your question been resolved?
cedar kilnBOT
minor crystal
.reopen
cedar kilnBOT
✅
minor crystal
Denominator would change accordingly i.e. 5c2.
BBR and BRR?
BBR = 3/6 * 2/5 * 2/4 = 1/10
BRR = 1/10 as well
1/10 + 1/10 = 1/5
lunar lynx
BBR and BRR?
RBR as well.
minor crystal
RBR as well.
sure yeah
wraith daggerBOT
Result:
0.2
Result:
0.2
so 2/5 for quantity A
Quantity B: BBBR, BBRR, and other permutations?
BBBR = 4!/3! = 4
BBRR = 4!/(2! * 2!) = 6
so
,calc 4* (3/5 * 2/4 * 1/3 * 2/2)
wraith daggerBOT
Result:
0.4
,calc 6* (3/5 * 2/4 * 2/3 * 1/2)
wraith daggerBOT
Result:
0.6
what
lunar lynx
RBR = 2/5 * 3/4 * 1/3
BRR = 3/5 * 2/4 * 1/3
minor crystal
same thing
lunar lynx
Both are 0.1 so total is 0.4.
lunar lynx
0.4
minor crystal
yes i already did that though
minor crystal
so 2/5 for quantity A
.
lunar lynx
Ah. I misread.
minor crystal
How to do Quantity B?
oh i see
"BBBR = 4!/3! = 4
BBRR = 4!/(2! * 2!) = 6" this is a bit wrong
BBBR = 3!/3! = 1 because we're only permuting BBB's
BBRR would be 3!/2! so 3
,calc 3/5 * 2/4 * 1/3 * 2/2
wraith daggerBOT
Result:
0.1
,calc (3/5 * 2/4 * 2/3 * 1/3)*3
wraith daggerBOT
Result:
0.2
Yeah. That seems correct.
lunar lynx
Why do you need 0.4?
lunar lynx
,calc (3/5 * 2/4 * 2/3 * 1/3)*3
1/2 not 1/3
wraith daggerBOT
Result:
0.3
okay 0.3 + 0.1 = 0.4
so they're equal
but this was way too long to do tbh
I have 1 minute to do the question lmao
without a calculator too
and also there's the fact that i could make silly mistakes on top of that
I guess there's a more optimal way to do this
Oh wait
Aren't they equal because they're independent events?
Probability of me getting head on the 100th flip and on the 1st flip is the same
Wait
THey're dependent events
Lol because "without replacement"
thorn spindle
does anyone know how to prove a rotated shape are the same or any resources I can look at
solid juniper
plush thistle
What do you mean the same?
solid juniper
what?
thorn spindle
an example would 2 be triangles are rotated , what is the minimum information i need to know they are the same
green thorn
rotation preserves angle measure and dimension
in other words, a shape is congruent to its image after rotation
green thorn
(also for a polygon of N sides)
shouldnt matter
rotations are a rigid transformation no matter what youre rotating
rose flax
cedar kilnBOT
green thorn
!status
cedar kilnBOT
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
between 1-2 i have got a answer for sin301 but i dont know how to approach the rest or if it is right
green thorn
between 1-2 i have got a answer for sin301 but i dont know how to approach the r...
alright lets start with sin301
waht did you get
rose flax
waht did you get
-sin59
rose flax
is cos75 correct for the next?
green thorn
tan70? im not too sure
well
not quite
lets take a look at the unit circle
does it make intuitive sense that tan(90+x)=-tan(90-x)
rose flax
yea
rose flax
so what is x in this case
110?
green thorn
does it make intuitive sense that tan(90+x)=-tan(90-x)
so if we know this
then 110=90+x
and x=?
rose flax
(using the equation above)
-tan(70) ?😭
green thorn
-tan(70) ?😭
mhm
rose flax
cos(2pi/3)
hmm
rose flax
what quadrant is it in
second?
rose flax
what cosine in the first quadrant is this going to look like
120 maybe
rose flax
300'
green thorn
cos 60 is
right
but cos(120) and cos(60) arent exactly the same
what do we have to do
rose flax
what do we have to do
perhaps -cos60?
rose flax
cot(-2pi/3
green thorn
i know cot x = cosx/sinx
right
so what value in the first quadrant has the same tangent as -2pi/3
rose flax
60?
green thorn
60?
right
so if tan(60)=tan(-2pi/3)
then 1/tan(60)=1/tan(-2pi/3)
and cot(60)=cot(-2pi/3)
rose flax
so 1/cot(60)=1/cot(-2pi/3)?
green thorn
so 1/cot(60)=1/cot(-2pi/3)?
cot is 1/tan right
and we know the tangents are equal
so the cotangents must also be equal
rose flax
so the cotangents must also be equal
sorry i havent done this bit before
rose flax
yes
green thorn
which means you understand cot=1/tan
rose flax
yes
rose flax
yep is cot60= 1/tan(-2pi/3)?
green thorn
ah okay and does that fall within the range given
well
ah
they want it in [0,40]
well
we can just invert it i suppose
cot(60)=tan(30)
rose flax
ah i see haha do the rest of fall into the range?
rose flax
hmm does cos75 work
green thorn
hmm does cos75 work
for which
green thorn
well
for specifically angles in the first quadrant
sin(x)=cos(90-x)
and cos(x)=sin(90-x)
rose flax
so sin 15?
green thorn
right
rose flax
oki thank you!! just one last thing haha when it says in terms of trig function of a single argument
green thorn
what does that mean ?
?
green thorn
oki thank you!! just one last thing haha when it says in terms of trig function ...
oh
uh
a single argument just means theres only one things in the parentheses
like sin(1234)
green thorn
np
rose flax
.close
inner solar
The matrix A ∈ C^(n×n) is called antihermitian if A = -Ā^T, where Ā = (Āij) is the matrix obtained from A by taking the complex conjugate of all its elements. Show that the set of all antihermitian matrices of type 2 × 2 forms a vector space over R (the set of real numbers). Find a basis for this vector space and determine its dimension. Explain why it is not a vector space over C (the set of complex numbers).
inner solar
to show that it is closed under addition i just need to do this? $A+B={-}{\overline{A}}^T{-}{\overline{B}}^T={-}({\overline{A+B}})^T$
wraith daggerBOT
Slowaq
crimson delta
yes
inner solar
alrigh and with that logic to show Closure under scalar multiplicationis is this satisfactory? $Ac={-}{\overline{A}}^Tc$
wraith daggerBOT
Slowaq
cedar kilnBOT
@inner solar Has your question been resolved?
inner solar
scalar multiplication is usually from the left
ah yes you are right
inner solar
where have you used that c is real
i dont understand what you mean with this
$cA=c{-}{\overline{A}}^T$
wraith daggerBOT
Slowaq
crimson delta
later on they ask you to show that its not a vector space over C
so if you allow c to be a complex number then something has to fail
you have to show that $cA = -\overline{cA}^T$
wraith daggerBOT
Denascite
inner solar
ah yes i understand now
inner solar
**Denascite**
so how shoould i show that
be patient with me please bacause i am kind of lost xd
crimson delta
well you have shown so far that $cA = -c\overline A ^T$
wraith daggerBOT
Denascite
crimson delta
so thats quite close
inner solar
now i just take complex conjugate of c?
inner solar
hm c is real number since i am trying to show closure under scalar multiplicationi then it shoulnd change
crimson delta
yes
inner solar
so i can just write $cA = -c\overline A ^T= -\overline {cA}^T?$
wraith daggerBOT
Slowaq
inner solar
and thats it?
crimson delta
if you specifically write down that the second equality holds because c is real
cedar kilnBOT
@inner solar Has your question been resolved?
inner solar
if you specifically write down that the second equality holds because c is real
andd how should i show this? (A + B) + C = A + (B + C)
crimson delta
well this holds for all matrices
which you hopefully have shown before
so in particular it holds if you only consider special matrices
inner solar
which you hopefully have shown before
yes of course
i got it
and now how do i find its basis?
@crimson delta
inner solar
$A = \begin{pmatrix} ip_1 & a \ -\overline{a} & ip_2 \end{pmatrix}$, $p_1, p_2 \in \mathbb{R}$, $i \in \mathbb{C}$
wraith daggerBOT
Slowaq
inner solar
something like this?
i found this on polish wiki xd and it is general form of antihermitian matrix
crimson delta
ok so we can choose p1, p2 and if we write a=c+d then we can also choose c and d freely
now make easy choices (aka all of them zero except for one) and you get your basis
inner solar
write out the elements as (a,b ; c,d)
a is from this not general form i wrote?
inner solar
ah alright
inner solar
sry I meant a=c+di
so for example i put p1,p2,c=0 and d=1?
crimson delta
for example, yes
inner solar
$\langle \begin{pmatrix} 0 & i \ -i & 0 \end{pmatrix},\begin{pmatrix} 0 & 1 \ 1 & 0 \end{pmatrix}, \begin{pmatrix} 1 & 0 \ 0 & 0 \end{pmatrix}, \begin{pmatrix} 0 & 0 \ 0 & 1 \end{pmatrix}\rangle$
co can this be my basis?
inner solar
for example, yes
hm but i dont think it generates R
inner solar
ah true ture sory ymy bad
wraith daggerBOT
Slowaq
inner solar
4 basis elements
is this better?
inner solar
oh 😦
well in first matrix ive put all zero except d, then all 0 except c, then p1=1 and lastly p2=1
isnt it that what youve meant?
crimson delta
exactly what I meant, yes
inner solar
**Slowaq**
and so that is what i have done here
inner solar
ah true treu
$\langle \begin{pmatrix} 0 & i \ i & 0 \end{pmatrix},\begin{pmatrix} 0 & 1 \ -1 & 0 \end{pmatrix}, \begin{pmatrix} i & 0 \ 0 & 0 \end{pmatrix}, \begin{pmatrix} 0 & 0 \ 0 & i \end{pmatrix}\rangle$
now correct?
crimson delta
check the first one again
wraith daggerBOT
Slowaq
inner solar
now?
crimson delta
yes
inner solar
noice
inner solar
yes
and the reason why it isnt vector space over the set of complex numbers is that all coeficients could be zero except for matrix $\begin{pmatrix} 0 & 1 \ -1 & 0 \end{pmatrix}$ and since it does not have any complexx component it can not create complex number?
wraith daggerBOT
Slowaq
crimson delta
no
inner solar
😦
crimson delta
**Slowaq**
this doesnt work if c is allowed to be complex
find a matrix A and a complex number c such that A is in the set but cA is not
one of your basis elements will do
inner solar
so if my complex number will be $-i$ then if i multiply it with for example $\begin{pmatrix} i & 0 \ 0 & 0 \end{pmatrix}$ i will get $\begin{pmatrix} 1 & 0 \ 0 & 0 \end{pmatrix}$ and this matrix is not in yout space?
wraith daggerBOT
Slowaq
crimson delta
yes
inner solar
alright thank you so much
cedar kilnBOT
@inner solar Has your question been resolved?
paper vortex
with which series can i compare 1/(2(n+1)) to prove convergence or divergence?
dire geode
with which series can i compare 1/(2(n+1)) to prove convergence or divergence?
Is your series
$\frac{1}{2(n+1)}$?
wraith daggerBOT
riemann
paper vortex
yes
dire geode
Why do you think that converges
paper vortex
if i compare with the harmonic series it doesnt prove me anything since 1/n is bigger than 1/2(n+1)
dire geode
Factor out 1/2 from your series
dire geode
Factor out 1/2 from your series
Did you do this hint
floral arrow
$\sum_{n=1}^{\infty} \frac{1}{2(n+1)}$
wraith daggerBOT
Nel
floral arrow
You want to know whether this converges, right?
paper vortex
yeah
paper vortex
It's a sum, you can factor thing out
maybe im not getting the comparison test right, because i suppose you mean i should compare 1/n+1 with 1/n ( 1/n+1 < 1/n), since 1/n is known to diverge, but isnt this pointless since 1/n+1 is smaller than 1/n? if it was the opposite i would know for certain that 1/n+1 explodes
like 1/n-1
floral arrow
You can just add 1/(2*1) to that sum
floral arrow
maybe im not getting the comparison test right, because i suppose you mean i sho...
$\sum_{n=1}^{\infty} \frac{1}{2(n+1)} = \left(\sum_{n=0}^{\infty} \frac{1}{2(n+1)} \right) - 1/2$
wraith daggerBOT
Nel
floral arrow
Note the change to n=0
vague nebula
cedar kilnBOT
vague nebula
Need help with this one
meager jungle
n/(n²+kn+k²) = (1/n)/(1+(k/n)+(k/n)²)
vague nebula
mhm
meager jungle
you could change this to an integral form
vague nebula
doesnt it become undefined
no no
im wrong
it becomes
integral 1 to 0 dx/(1+x+x^2)
lemme calculute that
@meager jungle
meager jungle
yes
meager jungle
yes
meager jungle
use the fact that T_n = S_n - 1/(3n) + 1/n
vague nebula
mhm
yeh i got the answer
the idea i suppose
i will take on from here
thx man
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
lean glade
Given that car A is 500 m behind car B at t = 0, at what value of t does car A
catch up with car B?
lean glade
Can I use a suvat equation to work it out?
sharp lotus
another way you can think about it...the area under the graph of the velocity equals the distance the car is traveling
for example since distance = time x velocity, look at car B's left part of the graph, the part where its velocity is 15 and it's traveling for 30 minutes at that velocity
distance for that part = 15 x 30, which is the area of that rectangle
you can convince yourself it works for a triangular part of the graph too by thinking of average velocity for that part
lean glade
distance for that part = 15 x 30, which is the area of that rectangle
but then how would you get the exact time
sharp lotus
so you would have to figure one at which part of the graph, the area under the graph of A is 500 more than the graph of B
that means it would be catching up at that moment
lean glade
at t=40
b is 100 ahead of a
so
20 seconds more#
cuz b is 25ms-1 and a is 30ms-1
thus 5 difference
and
100/5 = 20
so at t=60
sharp lotus
b is 100 ahead of a
how did you get this? im getting different numbers
oh wait no youre right, my bad
lean glade
np
cedar kilnBOT
@lean glade Has your question been resolved?
winged hull
sssuuup
dull oxide
echo estuary
Hi I have a problem but I don’t really know how to explain it since I’m not a native English speaker so I’ll try my best to translate it and let me know if you don’t understand a thing
Basically it’s about « divisibility in Z »
Let a and b be two natural integers with 1<= a <=9 and 0<= b <= 9
We consider the number abab….ab written in the decimal system
This number is therefore composed only of the digits ab repeated n times, where n desginates a non-zero natural number
- We consider the number ababab. Write this number in terms of a, b and powers of 10. (I did this one)
- Deduce that ababab is a multiple of ab (I need help for this one)
Here’s what I did for the first one :
a10^5 + b10^4 + a10^3 + b10^2 + a10 + b1
For the second one my teacher told me to obtain something like a(…..) + b(…..) = ab
I started by doing a(10^5 + 10^3 + 10) + b(10^4 + 10^2 + 1) = 0
After this I’m completely lost
echo estuary
You mean I have to do a(10^5 …..)/10 ?
dire geode
You mean I have to do a(10^5 …..)/10 ?
Why are you dividing
eager jasper
If ababab is multiple of ab then ababab = 10^5(10a+b) + 10^3(10a+b)+ 10(10a+b) now take 10a+b common hence done
echo estuary
Why are you dividing
I just realized what you meant, factor mean dividing in my language but sorry
Misunderstood it
dire geode
I just realized what you meant, factor mean dividing in my language but sorry
Oh I see
eager jasper
You can do it for arbitrary terms
dire geode
Yea dx gave you the solution
echo estuary
If ababab is multiple of ab then ababab = 10^5(10a+b) + 10^3(10a+b)+ 10(10a+b) ...
Alright thank you I’ll try this !!
echo estuary
If ababab is multiple of ab then ababab = 10^5(10a+b) + 10^3(10a+b)+ 10(10a+b) ...
If I do this and I develop I get a whole other thing that does not match my first answer is this normal ?
Maybe you meant 10^4(10a+b) + 10^2(10a + b) + (10a+b) ?
Because it matches better my first answer
eager jasper
Yup thats work fine
echo estuary
And so after doing that what am I supposed to do I don’t really understand
eager jasper
Okay so when we talk about multiple
Like multiple of ab
Whats ab actually in its 10a + b
Like 34 = 3*10 + 4
So now the number which you are given
ababab
Has to be a multiple of ab
I.e of type m(10a+b)
Where m is some number
That's what we are doing
First writing ababab in decimal notation
eager jasper
a×10^4 + b×10^3....
echo estuary
Thank you sooooo much really
eager jasper
Omg thanks it’s been like 3days I’m stuck on it
Its confusing because u might be thinking of ababab as a number
But ababab is just numeric notation
Like 123
Actually they are 100×1 + 10×2 + 3
echo estuary
Alright I see thank you so much
eager jasper
Np
echo estuary
I appreciate
eager jasper
faint crescent
so x3+y3+z3=k
cedar kilnBOT
so x3+y3+z3=k
faint crescent
E=mc2
neon kindle
hello?
cedar kilnBOT
@faint crescent Has your question been resolved?
novel topaz
huh
primal lake
a loan of £5000 with an APR of 14%. in two equal instalments
primal lake
and £700 to be paid back in 3 equal monthly payments at an APR of 744%
cedar kilnBOT
@primal lake Has your question been resolved?
primal lake
<@&286206848099549185>
rare wadi
i think you didn't state what you want to do with it
primal lake
?
primal lake
i think you didn't state what you want to do with it
i want to find the value of each instalment
<@&286206848099549185>
cedar kilnBOT
@primal lake Has your question been resolved?
primal lake
<@&286206848099549185>
cedar kilnBOT
@primal lake Has your question been resolved?
cedar kilnBOT
@primal lake Has your question been resolved?
crimson sedge
cedar kilnBOT
crimson sedge
<@&286206848099549185>
wind elbow
When 10 cubic meters of water are placed in a volume of 20 cm³, the volume of the water is 50 cm³. If the density of the bold ball is 9.0 g/cm3, find the mass of one ball.
crimson sedge
When 10 cubic meters of water are placed in a volume of 20 cm³, the volume of th...
?
the question has nothing to do with density
!close
/close
crimson sedge
When 10 cubic meters of water are placed in a volume of 20 cm³, the volume of th...
how do i close help channel
c!close
royal loom
.close
cedar kilnBOT
crimson sedge
<@456226577798135808> that is how
also can u help me with a math question in #help-31
cedar kilnBOT
Available help channel!
weary plaza
hi
weary plaza
ive got this problem wrong
however since i dont rlly have a teacher
i just wanna know, what the actual answer was so i can learn off this mistakes
thanks
<@&286206848099549185>
cedar kilnBOT
@weary plaza Has your question been resolved?
gusty forum
the problem is that t is supposed to represent hours but clearly sin(0) ≠ sin(24)
mental quail
can someone show me how to solve for the exact value of this log?
I was shown one method but it seemed very convoluted and i'm just looking to see another way thats simpler
crimson sedge
can someone show me how to solve for the exact value of this log?
I was shown o...
what's your method?
tbh, i'd just write everything in powers of 3
and simplify further
mental quail
not mine but the log rule someone showed me was something i hadnt seen before. where they turned log_9 into log_3^2 then turned that into 1/2 log_3
crimson sedge
not mine but the log rule someone showed me was something i hadnt seen before. w...
yep, that's what you'll do
write everything in powers of 3
and use log properties
$\log_{3^2} (3^7 \cdot 3^{\frac{4}{5}})$
mental quail
can you show me the rule for turning log_3^2 into 1/2 log_3? like an image from the web or something
wraith daggerBOT
notamy
crimson sedge
can you show me the rule for turning log_3^2 into 1/2 log_3? like an image from ...
you want proof for that?
mental quail
**notamy**
what you wrote this part i know is equal to the original
and further simply the things in the backet to 3^39/5
but i just dont really get the moving the ^2 to be 1/2
so i want to see the log rule for that explained somewhere
for example
i see all this but i never see how they rearrange the b infront of log
and as a fraction
crimson sedge
$\log_{a^2} b = \frac{\log b}{\log a^2} = \frac{1}{2} \frac{\log b}{\log a} = \frac{1}{2} \log_{a} b$
wraith daggerBOT
notamy
mental quail
ahhhh......tysm
that clears it up
is there anything else i should know or is that it?
crimson sedge
**notamy**
that's it, you can use the other log properties to simplify this ^^
mental quail
ty again
crimson sedge
you're welcome
mental quail
.close
verbal pawn
cedar kilnBOT
verbal pawn
Problem A and B I don’t know how to start it
For 77
Here’s the notes
I think it’s y=k/x but what to go from here?
dire thorn
I think it’s y=k/x but what to go from here?
Yeah. In your problem its x+6 instead of just x though, so how would you modify it to fit this
verbal pawn
Replace “k” with x+6
crimson sedge
replace x with x+6
y = k/(x + 6)
dire thorn
Because in the sentence, x is replaced with x+6. So it should make more sense that we place the x in the formula with x+6 rather than the k
crimson sedge
ye and plug in value of k as well
verbal pawn
K is also 0?
crimson sedge
y = k/(x + 6)
you'll need to find value of k before proceeding to B part
the question has given the information via which value of k can be found - "y = 1 when x = 1"
so put y = 1 and x = 1 then what would be value of k?
crimson sedge
oof, happens sometimes
crimson sedge
okay now what do I do after that
do you still need help or you've figured it out?
cedar kilnBOT
do you still need help or you've figured it out?
verbal pawn
do you still need help or you've figured it out?
ya I need help
crimson sedge
okie, you've found that value of k right? it's 7
verbal pawn
yes
verbal pawn
that’s it or nope
crimson sedge
that's it
verbal pawn
DONT LEAVE ME
crimson sedge
that'd be the answer for b
verbal pawn
I have one more question
crimson sedge
alright alright
verbal pawn
so if I’m writing it as a sin wave
ok wait
first question is
what would the period be ?
if I’m making sin wave
I have to write sin equation
crimson sedge
is it possible to find where the graph intercepts the x-axis?
verbal pawn
Idek
crimson sedge
cause there's a slight shift to right
and idts we can find it by just seeing the graph
verbal pawn
what if we were writing a cosine equation then?
crimson sedge
cause there's a slight shift to right
solid juniper
is it possible to find where the graph intercepts the x-axis?
don’t think you need that
crimson sedge
the equation would be of the form 4sin(x - a)
solid juniper
you can just look at the peaks to determine a
crimson sedge
what would the period be ?
wait, you need period. it'll just be 2π
minor crystal
model it as acos(b(x + c)) + d
a = (max-min)/2
d = (max + min)/2
c is just the phase shift so compare it to how cos(x) would normally be at x = 0
@verbal pawn
verbal pawn
<@1149290949961334884>
Thx kanna that’s what I got too
minor crystal
Thx kanna that’s what I got too
np
converting to a sin(x) counterpart is trivial using cos(pi/2 - x) = sin(x)
,w graph 3sin(pi/2 - (x + pi/2)) +1
wraith daggerBOT
oak parrot
cedar kilnBOT
oak parrot
Using brute force, I was able to prove that this sequence has a lower bound of 0 and no upper bound
However, I'm unable to understand how to use the theorems on limits to prove this problem
Like is it alright if I just say if n =1, then xn equal to 0. As n is not bound above, so is xn thus it is divergence when n approaching inf?
<@&286206848099549185>
cedar kilnBOT
@oak parrot Has your question been resolved?
oak parrot
<@&286206848099549185>
oak parrot
i am once again, looking for help.
cedar kilnBOT
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cursive valve
Hello
cursive valve
I found a pattern in number line that is new to me.
If i want to find if something is divisible by 7 -> I find the one's place of that number so let's say the number is 245, one's place is 5. So in each 10th iteration there is always one number that is multiple of 7 that yields a number with 5 as it's one's place. For instance 7 * 5 is 35, 7 * 15 is 105. So I can check if 245 is divisible by 35 or 105 to reduce the number of steps of division I do. If it is divisible, then it is also divisible by 7 else not.
What's the term for this technique in mathematics ?
crimson sedge
if some number is divisible by say 35 then it is also divisible by its factors (like 7)
Its kind of obvious, since the last digit of a product of 2 numbers is defined by the last digits of the 2 numbers you multiply
You can prove it with modular arithmetic
cursive valve
if some number is divisible by say 35 then it is also divisible by its factors (...
So basically try to find the highest number that is a multiple of the number that I want to find.
idle tusk
I found a pattern in number line that is new to me.
If i want to find if somethi...
some terms you might want to look up:
- modular arithmetic (specifically mod 10)
- general divisibility rules
cursive valve
That will yield the lowest number of steps the division takes.
cursive valve
some terms you might want to look up:
- modular arithmetic (specifically mod 10)...
I will look into those.
crimson sedge
Its HCF(Highest common factor)
cursive valve
I don't know if these are basics or not. But I feel as if I discovered this pattern by myself instead of reading in some book.
Also I am new to maths.
crimson sedge
U discovered HCF which is pretty useful
idle tusk
I don't know if these are basics or not. But I feel as if I discovered this patt...
i wouldn't say it's basics per se (at least none of the school's i've been in studied modular arithmetic in high school) but it's nothing super advanced either. these topics have been studied thoroughly before so you have plenty of resources to study
cursive valve
I think I have read about modular arithmetic when I learned about the RSA algorithm.
I've just read it though, i don't fully understand it.
Anyone have anything to say more about this can reach me out in my DM. I am closing this.
.close
orchid linden
how would you solve this? I don't know how to start
cedar kilnBOT
how would you solve this? I don't know how to start
nimble mountain
you could start by drawing what they said in a diagran
cedar kilnBOT
@orchid linden Has your question been resolved?
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muted mica
heyy inverse function again
cedar kilnBOT
heyy inverse function again
prisma gull
im confused, how do i get the domain and range without x in the denominator
You want the find the domain and range of this function?
muted mica
yea
but the example that my friend sent, it has an x in the denominator but if theres no x, what am i gonna do
nova snow
if theres no x then its better for you
muted mica
how soo
nova snow
if theres x on the bottom you have to worry about what values will make the function undefined and have asymptotes and stuff
but this is just a straight line
muted mica
so its simply { 2, to infinity}?
nova snow
so its simply { 2, to infinity}?
are you saying x values dont exist below 2?
because they do
little junco
Help
cedar kilnBOT
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little junco
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lean nest
how would you solve this? I don't know how to start
EFGH forms a parallelogram and the length of side equal to the half of respective diagonal length using midpoint theorem you had read in your class 10th. it will not work for pentagon.
cedar kilnBOT
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green jungle
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jaunty plume
Is -inf squared inf?
cedar kilnBOT
Is -inf squared inf?
crystal raptor
How are you defining squaring for something that is not a number?
jaunty plume
I don’t understand how to solve this
Well -inf^2 that’s where I got it from the a is squared
hollow minnow
show your work cause it looks to me like -inf
wraith daggerBOT
jaunty plume
It’s the e)
jaunty plume
show your work cause it looks to me like -inf
Can you tell me how do I proceed with sqrt (-inf^2+1)
hollow minnow
sqrt((large negative number)^2) = large positive number
large negative number - large positive number = large negative number
jaunty plume
Huh
hollow minnow
think of it as a gets bigger rather than a = infinity
jaunty plume
Nvm ln(0)=-inf and because of F(b)-F(a) it becomes inf
vocal nexus
is my solution okay to find the radius of convergence?
cedar kilnBOT
is my solution okay to find the radius of convergence?
@vocal nexus Has your question been resolved?
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@vocal nexus Has your question been resolved?
cedar kilnBOT
@vocal nexus Has your question been resolved?
junior bluff
is my solution okay to find the radius of convergence?
Looks good to me
errant wasp
whenever performing algorithms on vector spaces, do you want to put them in their basis
errant wasp
so then you only perform these operations on all the unique vectors than are in the span of a subspace
crimson delta
that is such a general question, impossible to answer
most useful algorithms are probably written just in terms of a basis, not in terms of the vector space
cause well usually vector spaces have infinitely many elements so doing stuff to them is kinda impractical
errant wasp
a basis theoretically is just all the unique vectors that belong in some dimension right
errant wasp
i just said that because the vectors are like linearly independent
crimson delta
they are, yes
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signal nymph
can $e^arcsinx$ be simplified
cedar kilnBOT
can $e^arcsinx$ be simplified
wraith daggerBOT
tim
signal nymph
had a howler with latex
can $e^(arcsinx)$ be simplified
can $e^(arcsin)x$ be simplifie
can $e^{arcsinx}$ be simplified
wraith daggerBOT
tim
misty pier
no
cedar kilnBOT
misty pier
I was patiently waiting for you to get it right
signal nymph
😂
quaint quiver
👀 see you question again🤣
cedar kilnBOT
Available help channel!
grave sky
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paper vigil
you could just do substitution
paper vigil
grave sky
how can i tell when i ned to do integration by parts and when to do u sub
paper vigil
if you can do u sub then do it
if you can't then go to other methods i guess lol
rugged cape
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rugged cape
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austere hull
!status
cedar kilnBOT
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
@rugged cape
austere hull
I think you need formula for that iirc
rugged cape
error for volume of tank=1000/2=500 and error for volume of a full cup=10/2=5. We have to take the upper bound of the water tank to have as much water as possible and take the lower bound of the full cup volume to reduce it and thus get more (but smaller) full cups. Upper bound of tank volume=6500 cm^3 and lower bound of full cup volume=295 cm^3
6500/295=22
wait it gives 22
sorry I took 255 instead of 295 in my calculator and got 25
Thanks
.close
sly abyss
cedar kilnBOT
sly abyss
<@&286206848099549185>
Ye I’m cooked
If it helps I’m a law of sines and cosines unit
.close
sick dew
Question: Consider a simple coin game where you can bet any amount of money. If it lands on Heads, you double your bet; if it lands on Tails, you lose your bet. Consider a strategy where you start by betting $1. If you lose, you will bet $2. If you lose again, you will bet $4, and so on in this way until you finally win a toss. Once you have won a toss, your strategy has been implemented, and you stop. If you have a total bankroll of $63 available to implement this strategy, what is your expected profit?
rain drift
hi channel is occupied. Please wait for another channel to open
sick dew
Question: Consider a simple coin game where you can bet any amount of money. If ...
So I thought it would be lke this: you have 1/2 chance of winning on the first try so 1/2 * 2 + the chance you loss on the first try and then bet 2 and then win which is 1/4 * 4
then repeating this for all possible bets gives: 1/2 * 2 + 1/4 * 4 + 1/8 * 8 + 1/16 * 16 + 1/32 * 32 + 1/64 * 64
which equals 6 dollars
solid juniper
6 dollars can't be right
half the time you'll end up with $64, right?
oh
wait
expected profit being like
you end with $69
slate lintel
half the time you'll profit $1 yeah
solid juniper
6 dollars still sounds wrong
sick dew
Yeah 6 seems wrong
slate lintel
it is wrong
slate lintel
So I thought it would be lke this: you have 1/2 chance of winning on the first t...
this doesn't consider the costs
solid juniper
you can't expect profit
slate lintel
ie the bets that you lost
sick dew
half the time you'll profit $1 yeah
ah ok so then half the time you'll proft +$1 and half the time you'll lose -$63
wraith daggerBOT
Sam525
slate lintel
ah ok so then half the time you'll proft +$1 and half the time you'll lose -$63
i don't think that's true, you have to lose a lot of times in a row to lose $63
sick dew
Then I thinkk to lose all 63 dollars you need to lose 6 times in a row so 1/2^6 chance of losing 63?
sick dew
So then if the expected gain is $1 and expectd lss s 63/64 iis the expected prof 1-63/64=1/64 dollar?
sick dew
you add it like (−63)(1/64) + 1(63/64)
isnt this 0?
fair geyser
it is
i know you said 0 along time ago
i just don't think your calculation made sense but i could be wrong
sorry for tht
sick dew
Ah ok no thank you for explaning it properly I was saying 0 based on vibes lol
Thank you for your help!
.close
sinful falcon
can someone check this for me
digital cliff
cedar kilnBOT
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.
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viscid frigate
cedar kilnBOT
viscid frigate
a little confused on how to approach this question
broken mist
If it asked you to find h(4), what would you do?
white latch
What makes you think that?
white latch
a little confused on how to approach this question
What does 4n mean to you?
viscid frigate
What does 4n mean to you?
4 x a number representing n = ur solution
white latch
4 x a number representing n = ur solution
Right, so an x value correct?
viscid frigate
yes
white latch
Knowing that is true why would you set it up so its 4h then? What do you mean by that.
Looks like your saying a vertical expansion of 4 almost which is ambiguous and would be changing the function which we cannot do.
viscid frigate
ohh
white latch
so x = 4n
is an input.
We have to INPUT that into the function.
The original input is the x, all we did was apply operations on it and transform it where we have 2x^2 - 3
viscid frigate
gotcha
white latch
Do you understand how inputs and outputs work?
Its alright if you don't, I just need to see where your gaps are coming from.
viscid frigate
input is what goes into the function and output is what comes out of it
white latch
Right, so lets say I inputted 1 into the function
what would that come out to be?
h(1)?
viscid frigate
-1 ?
white latch
Of course its negative 1 what else would it be?
Do you just want the answer?
I can then guide yah through step by step or I can keep hinting yah and make yah think analytically till u understand why.
viscid frigate
no keep going
white latch
Ight, so make u think abt it critically right?
viscid frigate
yes
white latch
Kk. Thats what I like to see.
viscid frigate
it will help me understand this better 😭
white latch
Ofc.
viscid frigate
not sure what else it would be except for -1
viscid frigate
1
white latch
Ima teach u abt inputs and outputs
u seem to be lacking in that.
Which is where the confusion is coming from.
Are you doing compositions as of rn?
viscid frigate
yes
white latch
Ight I'm gonna help for 10-15 more mins but then gotta dip.
viscid frigate
nwss
viscid frigate
mhm
white latch
Think of a function as a machine
we plug something into it.
We get something out of it.
viscid frigate
gotcha
white latch
Now here is a confusing part
Many people believe that any operation we perform on our initial x value is a considered a functions operation.
Here hold up this may take a while to explain ima just eplain it simpler terms for yah.
h(x) = 2x^2 - 3
I think where your confusion is stemming from is that your thinking if x = 4n, but 4n can equal anything then how can we have that as an input and thats causing you all these problems?
viscid frigate
ohh
white latch
Is that whats confusing you?
Because if I say something like find h(8)
You are able to compute that just fine as you did with h(1)
viscid frigate
yeah i think thats the root of the problem
white latch
Mk, so compositions are a "function of a function." Its not a definite number as such that we plug in since its a function.
familiar with this notation?
viscid frigate
yes
white latch
mk, so f just denotes f(x) and g denotes g(x)
What would this come out to be its okay if your unsure.
I don't expect you to know this as its your primary root confusion.
viscid frigate
not sure
white latch
Alright, no worries.
Now the notation here represents "f of g" or in others the function f defined in terms of g.
initially what was our input for the function f?
f(g(x)) what would that come out to be?
we are updating the initial variable for f(x) with g(x).
Well star I wish I could stay longer and help, but am unfortunately busy.
viscid frigate
its ok 😭
white latch
I'm going to post the answer, but am going to keep the message hidden.
Unblur it once you have come to an answer or have done the best you could.
viscid frigate
ok thank u sm!
white latch
|| h(x) = 2x^2 -3 --> x = 4n (AN INPUT) --> h(4n), we need to update the initial varialbe x with our new input. Therefore h(4n) = 2(4n)^2 - 3 --> 2(4n)(4n) - 3 --> 32n^2 -3 ||
white latch
ok thank u sm!
I strongly urge you watch some videos on Khan Academy. Its going to help you resolve this question of yours.
A deadly sin is doing problems before understanding the concept. DO NOT do that.
formal pasture
cedar kilnBOT
cedar kilnBOT
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