Un is the nth term
#help-0
cold zenith
vale wigeon
yeah, sure, but calling this "The Formula For All Sequences Ever™️" is... very sketchy
cold zenith
yeah i understand i just called it the formula for sequences cos its the only formula i was given for arithmetic sequences
i got 9 using that formula
i agree the question is badly worded it threw me off
.close
patent night
how do i find the length of PR?
lone heartBOT
how do i find the length of PR?
delicate jacinth
Pr = 2tu?
delicate jacinth
Yes, look at the image
jaunty pollen
jaunty pollen
How do I answer question e and f?
If you like I can send what I done for question a to diii
hollow sparrow
If you like I can send what I done for question a to diii
will be better
and send also the questions
jaunty pollen
and send also the questions
The questions are in the link provided
but I'll give you the answers
as well
wind cloak
jaunty pollen
nono just a set of questions in answering
jaunty pollen
so here's A
hold on could I get the others later because I done them on my personal computer
alpine sable
hi all i need help for assiments anyone can help ?
lone heartBOT
@jaunty pollen Has your question been resolved?
maiden sphinx
Q16
maiden sphinx
<@&286206848099549185>
alpine sable
!15m
lone heartBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
empty juniper
Q16
U probably should send a clearer pic of the diagram itself, can’t see a small portion of it
maiden sphinx
U probably should send a clearer pic of the diagram itself, can’t see a small po...
Ok , I'm sending
lone heartBOT
@maiden sphinx Has your question been resolved?
empty juniper
Ok so b4 we do anything we establish this,
Both triangles are isosceles
ADB = 90 = BDC and B bisects a 90 degree angle in half = 45 degrees for each triangle thus both are a 90-45-45 triangle since all angles of a triangle must add up to 180 degrees
Triangle ABC is EQUAL (similar in angles and also magnitude) to triangle BDC because of angle-side-angle similarity
BD is same for both triangles
angles ADB = BDC
angles ABD = DBC (B bisects the angle in equal halves)
Now since we have ASA similarity, both triangles are established to be same in dimensions and angles
Now we solve the problems
- Let us also assume that the side BD is some constant k since it is unnamed
x^2 = pz is simplified as
X^2 = p^2 + pq ( since z = p + q)
Here, p= q since both triangles are similar in size and p = k since it is an isosceles triangle
Therefore x^2 = p^2 + k^2 is proven by Pythagorean theorem and so the given equation is proved - by Pythagorean theorem
Y^2 = k^2 + q^2
Or Y = zq in the same way that we proved the last question, we just go in reverse - x^2 + y^2 = pz + qz
We get x^2 + y^2 = z(p+q)
Where p + q is geometrically equal to z so x^2 + y^2 = z^2 and Pythagorean theorem is proven
@maiden sphinx sorry for the late response it took a second to type it out lol
lone heartBOT
@maiden sphinx Has your question been resolved?
maiden sphinx
<@801316377432424459> sorry for the late response it took a second to type it ou...
Oh okay, i will see, thank you so much
vale tiger
Can someone help me answer these, I'm being skeptical but I think the first one is -2.
graceful sparrow
Can someone help me answer these, I'm being skeptical but I think the first one ...
alright
so what u do here
is u multiply -5 with the equation in the LHS
and -2 with the equation in the RHS
after that, u separate the variables and the constants
u take the variables to the left and the constants to the right
and if the variable has a coefficient, u divide both sides
this is how u do the first problem
gray isle
Can someone help me answer these, I'm being skeptical but I think the first one is -2.
show your work that lead to that answer
graceful sparrow
i assume once u get the hang of it, u can do the rest
vale tiger
.close
lone heartBOT
g(x+h)=(x-7)/(x+2), doesnt state a value for h
worn fox
Everytime you see x, replace it with x+h
south maple
<@&286206848099549185>
lone heartBOT
<@&286206848099549185>
last ether
!15m
lone heartBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
ocean sealBOT
Royal_love
spare plaza
<@&286206848099549185>
What does corresponding closure mean?
spare plaza
Yup
south maple
Do you know how to do it?
spare plaza
Do you know the answers?
Idk what it even asking
south maple
Even I don't get it 😭
lone heartBOT
@south maple Has your question been resolved?
nimble fern
<@&286206848099549185>
hello there! Do you still need help with your question?
nimble fern
okay
so to have closure w.r.t. to reflexive property means, add more items to the relation R so that it becomes reflexive
south maple
Wrt?
nimble fern
do you recall the reflexive prop. for relations?
south maple
Soo the answer is?
nimble fern
no answer giving.
nimble fern
good
nimble fern
2,2 and 3,3
that's all
lone heartBOT
@south maple Has your question been resolved?
hollow lark
hi can anyone help with this?
lone heartBOT
hi can anyone help with this?
royal plank
hi can anyone help with this?
at which point are you stuck
alas, I assume you have the formula for the geometric bodies
pseudo ice
Well first off, note that they give you a statement about the volume
,w millilitre volume
ocean sealBOT
pseudo ice
Find an expression for the volume and then set that equal to what they tell you it is
hollow lark
thank you thats what i was forgetting about
pseudo ice
That'll allow you to get the height h in terms of r
Thought so, I can't seem to remember the volumes myself tbh 
brazen berry
Can anyone verify my answer/work?
brazen berry
im trying to get rid of my other one 
ok done
if anyone is able to verify, i'd appreciate it
merry depot
cos(pi*b) does not go to infinity
brazen berry
heck
what does it go to? D:
pi *infinity
just infinity
is cos infinity something else?
merry depot
nothing. cos(x) is bounded between -1 and 1 and is periodic between those two values
brazen berry
oh
trig was my worst unit in precalc
so what would i even answer that with
since cos infinity doesnt exist
brazen berry
how so?
gritty talon
If the integral were convergent, that means the limit of whatever sequence you take of that integral converges to the same number
brazen berry
this one is divergent, no?
gritty talon
Yes
brazen berry
since cos infinity doesnt exist
gritty talon
No
brazen berry
oh
gritty talon
You can't really tell like that AFAIK
brazen berry
I havent learned about sequences in this context, i dont think
gritty talon
There is a sequential characterization of limits
lim when x->a of f(x)=l means that for all sequences xn such that xn goes to a when n goes to infinity, f(xn) goes to l when n goes to infinity
Sorry still haven't learned Late
Latex*
brazen berry
np np
gritty talon
Choose xn= n
And make the integral go from 0 to xn
and take the limit
You get (-1)^2 -1
which is already divergent
well, it comes back to the same thing I guess
(-1)^n I meant
You can then choose another sequence xn= n+ 1/2, and you get 0if I'm not mistaken
That clearly shows that it diverges
I hope I didn't complicate matters even more 😅
brazen berry
i uhhhh
😅
you might have, but only because I havent seen that stuff before
Idk if im allowed to use that in my solution
cursive nebula
lone heartBOT
cursive nebula
all of them except the last are the same right
rocky atlas
all of them except the last are the same right
Yes
cursive nebula
alright sweet
old mica
lone heartBOT
frigid stream
@old mica Hello, what did you try?
old mica
I assumed that the means are both zero but cannot think of a proof, For the Vars I got the following:
frigid stream
I assumed that the means are both zero but cannot think of a proof, For the Vars...
Well, the mean of Y is given, right?
old mica
Yes
frigid stream
For the mean of X, you know that epsilon_1 and epsilon_2 are independent, so what can you do with E(X) ?
frigid stream
What is the expectation of the product of two independent random variables?
No problem
old mica
The means multiplied?
old mica
0 no?
old mica
Gotcha
I guess I find the idea of expectation confusing
Like for the means I thought of it as multiplying two distributions by eachother then calculating the mean again
frigid stream
Multiplying two distributions does not really make sense here
You aren't given any distribution here anyway
frigid stream
No, watch out, do not confuse X,Y and epsilon_1, epsilon_2
old mica
Oh yes, i just meant as in the formula sorry
frigid stream
If X and Y are independent, yes
frigid stream
yes
old mica
Do you know how to get the covariance?
frigid stream
You have Cov(X,Y) = E(XY) - E(X)E(Y)
frigid stream
Yes
old mica
Could you explain what the top line means?
frigid stream
There is nothing to explain as it is the definition of the covariance
frigid stream
This is for a given sample
old mica
I see
frigid stream
A positive covariance tells you for example that if X tends to get bigger, then Y should tend to get bigger too
The opposite for a negative covariance
old mica
Understood
frigid stream
Back to the problem you already know what are E(X) and E(Y), so you only have to compute E(XY) in order to have the covariance
frigid stream
Are X and Y independent?
old mica
Oh, no I assume, as they both use epsilon2
frigid stream
You have a good intuition, X and Y are probably not independent
Sometimes, random variables can depend of the same one (here, epsilon_2), but are still going to be independent, surprisingly
But the key point here is you can never assume independence if you aren't being told
old mica
Understood
frigid stream
So unfortunately you cannot write E(XY) = E(X)E(Y), so we have to find another way
Your best shot is to replace X and Y by their given definition
Then maybe you can use independence 😉
frigid stream
Good, so give it a try
frigid stream
Yes
90% of the time the best way to compute a covariance is using the formula Cov(X,Y) = E(XY) - E(X)E(Y)
old mica
working out now
Is it just the epsilons subbed in, so zero?
E(ep1ep2^2)-E(ep1ep2)E(ep2)
frigid stream
E(ep1ep2) and E(ep2) are known as you already calculated the expectation of X and Y
old mica
And the two eps can be split given they are independent
frigid stream
And the two eps can be split given they are independent
Yes
ocean sealBOT
Fέliχ
old mica
Hmm
frigid stream
You rather have \
$E(\epsilon_1 \epsilon_2^2) = E(\epsilon_1)E(\epsilon_2^2)$
ocean sealBOT
Fέliχ
frigid stream
By independence
old mica
Is the expectation of the distribution squared different to the squared expectation of the distribution then?
or random variable
rather than distribution
frigid stream
It is different
E(X^2) is the mean of the random value X^2
(E(X))^2 is the mean of the random value X, but squared
old mica
Oh I understand
frigid stream
So it remains to compute $E(\epsilon_2^2)$
ocean sealBOT
Fέliχ
old mica
so E(ep1)E(ep2^2)-0*0
frigid stream
But hold on. E(epsilon_1) is 0
old mica
so we know it is 0 whatever
old mica
but can we find epsilon 2^2 anyway?
ocean sealBOT
Fέliχ
old mica
Could you explain this formula?
frigid stream
It is just the variance formula written differently:
Var(X) = E(X^2) - (E(X))^2
You used it above in your first screenshot
old mica
I see
old mica
here?
old mica
I see, so the answer is zero
then for the correlation u just use the formula
0/(1^0.5*1^0.5)
=0
frigid stream
Yes
old mica
Then as covariance=0
frigid stream
Exactly
old mica
They are in fact independent
So the result of the question is 'despite X and Y involving epsilon2, due to the means being zero they remain independent'
?
frigid stream
⚠️
If Cov(X,Y) =/= 0, then X and Y are not independent
But if Cov(X,Y) = 0, you cannot conclude anything
old mica
So how do i conclude whether they are independent or not?
old mica
Understood, what information would i need to conclude that?
Would I need to conclude that epsilon2 has no effect essentially?
I can review this later maybe
Could I do one further question?
tribal monolith
lone heartBOT
tribal monolith
i'm a little confused on how to find f(x)?
near garden
riemann sum is basically taking chunks of the integral and evaluating the integral as parts to estimate it
and the parts have the pattern of sqrt(8+(6n/n))*(6/n)
so the function would just be this
but be careful that its the RIGHT riemann sum
so the f(5) was taken as 6/n in the sqrt
and the 6n/n, which in this case is upper n = 1 was from the f(6) since we're taking the floor of the integral part
so itd be like sqrt(8+(6(n-5)/n))*(6/n)
im not sure about the usage of the n's in the summation formula tho
@tribal monolith
tribal monolith
inside? what do you mean
near garden
or just replace all the n's with x's
ocean sealBOT
Mehdi_Moulati
tribal monolith
**Mehdi\_Moulati**
how would i use the f(a+(b-a)k/n) part to find the function though?
hollow sparrow
,align
\sqrt{8 + \frac{6}{n}} * \frac{6}{n} + \cdots + \sqrt{8 + \frac{6n}{n}} *\frac{6}{n}
&= \sum_{k=1}^n \frac{6}{n} * \sqrt{8 + \frac{6k}{n}}\
&= \sum_{k=1}^n \frac{11-5}{n} * \sqrt{3 + 5 + \frac{(11 - 5)k}{n}}\
&= \sum_{k=1}^n \frac{11-5}{n} * \sqrt{3 + \qty(5 + \frac{(11 - 5)k}{n})}
lone heartBOT
Available help channel!
zealous oxide
I need help with 5 and 6.
cloud kiln
Im trying to disprove that the seq 1/n converges to 1
so anyways I did
cloud kiln
|1/n - 1| < eps
then
|1/n| - |1| < eps
but since both terms are positive
1/n - 1 < eps
1/n < eps + 1
1/(eps + 1) < n
but here I got a stage for n
tacit arch
wrong approach
cloud kiln
|1/n| - |1| < eps
triangular inequality
tacit arch
figure out the correct contrapositive first
cloud kiln
figure out the correct contrapositive first
if I don't have a stage n > N belonging to natural number then the sequence Sn does not converge to limit L for any eps > 0???
tacit arch
Yea that's not correct
negate this:
$a_n \to a$ if $\forall \eps > 0, \exists N \in \N s.t. |a_n - a| < \eps, \forall n > N$
ocean sealBOT
riemann
cloud kiln
$a_n \to a$ if $\forall \eps > 0, \exists N \in \N s.t. |a_n - a| < \eps, \foral...
an does not converge to a if there does not exist an epsilon greater than 0 and there exists N belonging to natural number such that |an - a| < eps for all n > N
tacit arch
oof
cloud kiln
😭
tacit arch
the very first part of the negation after saying a_n does not converge to a is
$\exists \eps > 0$
ocean sealBOT
riemann
tacit arch
|1/n - 1| < eps
so you just need to find one epsilon
cloud kiln
1/(eps + 1) < n
but here I got a stage for n
oh I just need to find 1 epsilon so that this does not hold?
tacit arch
for all N, yes
alternatively, you can just show 1/n converges to 0 and probably quote some theorem about uniqueness of limits and say that 0 is not equal to 1 and you're done
cloud kiln
hm alright
but I did the mathematical part correct right? Why did that guy sully triangular inequality part
tacit arch
|1/n| - |1| < eps
|1/n - 1| < |1/n| - |1| and |1/n - 1| < eps does not imply this
1 < 2 and 1 < 3 does not imply 3 < 2
cloud kiln
|1/n - 1| < |1/n| - |1| and |1/n - 1| < eps does not imply this
oh I thought |a| - |b| < |a-b|
oh u are correct
cloud kiln
yes I used |x-y| >= |x| - |y|
tacit arch
you sully the best reverse inequality
cloud kiln
whats going on over here???
tacit arch
some decent explanations here
https://www.physicsforums.com/threads/epsilon-n-proof-a-sequence-diverges.830426/
cloud kiln
whats going on over here???
you wrote it incorrectly
|1/n| - |1| <= |1/n - 1| < eps
therefore
|1/n| - |1| < eps
tacit arch
oh no i deserve the sully now
tacit arch
.close
meager pagoda
meager pagoda
How do I set up 7
ocean sealBOT
lone heartBOT
@meager pagoda Has your question been resolved?
merry depot
basically the same way you set up 6, but with a1 and a6 (or a12)
brisk ore
i need help with geometry
lone heartBOT
i need help with geometry
brisk ore
i have a few questions to ask. 1. A triangle has side lengths of 12, 35, and 36. What kind of triangle is it. how would i solve this?
slim spire
i have a few questions to ask. 1. A triangle has side lengths of 12, 35, and 36....
compute the angles using the cosine thm for instance
brisk ore
okay, theres another one that im going to send a picture of that im going to need help understanding
how would i solve for x and w?
brisk ore
okay, could you walk me through it? im so confused on wtf im supposed to be doin in this clss💀
gray isle
how much trig have you learned?
have you started right triangle trig yet?
brisk ore
im in geometry not trig so idk why im doing this but this is what my teacher assigned
brisk ore
im in geometry b right now
gray isle
go back to your teacher and go wtf
brisk ore
ik im so confused
gray isle
so you have no idea what sine,cos,tan are?
brisk ore
but it was due last week so if i dont finish the test today its considered an "absence"
i kinda do
ive been watching some videos on what they are and shi but i havent gotten too far into it
but this gotta be done tn so im trying to get as much help as possible
gray isle
an image of sohcahtoa
should be sufficient
assuming you're capable of basic algebra
brisk ore
let me look that up real quick
okay so with the image i posted up there^ would i use cosine?
for both or just for w or x?
what about this image
what type of sin should i use to solve this and how would i solve it?
lone heartBOT
@brisk ore Has your question been resolved?
brisk ore
no
hybrid stirrup
The host of a party wants to order 3 salads, 4 hot dishes, and 2 desserts from a catering company. The company offers 7 different salads, 6 hot dishes, and 5 desserts. How many ways can the host of the party select which items to order?
hybrid stirrup
Should the answer be 7C3 * 6C4 * 5C2 ?
hybrid stirrup
Let A and B be sets in U which satisfy n(A ∪ B) = 17, n(A) = 12, n(B) = 8, and
n(A′ ∪ B′) = 21. Calculate the size of the universe.
viral pagoda
wary stream
Let A and B be sets in U which satisfy n(A ∪ B) = 17, n(A) = 12, n(B) = 8, and
n...
Calculate the size of the universe.
Big
hybrid stirrup
.close
lunar lintel
lone heartBOT
waxen flame
$(i - \frac{1}{2})\cdot \Delta x = i\Delta x - \frac{1}{2} \Delta x$
ocean sealBOT
Kookiemon
waxen flame
This gives you the midpoints.
lunar lintel
This gives you the midpoints.
wdym
where did they get that
from
i was asking
it wasint in equation
waxen flame
Did you ever learn about sequences in Algebra?
That's just the formula for the sequence of the midpoints.
lunar lintel
Did you ever learn about sequences in Algebra?
i cant rmr
waxen flame
Well, it's the sequence for the midpoints.
lunar lintel
Well, it's the sequence for the midpoints.
ok well this was the formula i was given
for midpoint
left sum was
Xk-1
right sum = Xk
waxen flame
$x_{k-1} + x_{k} = x_{k-1} + \Delta x$
ocean sealBOT
Kookiemon
waxen flame
The former is used when the intervals are not all the same. The latter can be used when the intervals are equal.
eg.
Former -> {1,2, 5, 6, 7.5, 11, 12, 13}
Latter -> {1,2,3,4,5,6,7,8,9,10,11,12,13}
lunar lintel
The former is used when the intervals are not all the same. The latter can be u...
so my formula
used for when intervals are not same?
and i+1/2 is used for when they are same?
waxen flame
You can use the former regardless if the partitions are equal or not. The latter can only be used when the partitions are equal.
lunar lintel
so this would also be correct if they put this instead of i-1/2
waxen flame
Yes.
lone heartBOT
@lunar lintel Has your question been resolved?
lone heartBOT
@lunar lintel Has your question been resolved?
wide oxide
lone heartBOT
wide oxide
I’m currently doing matices and I’m wondering how to do these type of questions.
Where I have to find values of said variable which satisfy the question for which values of the varaibale does this matrix have a inverse?
If you want you can help me through question 12
lone heartBOT
@wide oxide Has your question been resolved?
wide oxide
<@&286206848099549185>
<@&286206848099549185>
Ok I solved Q.12 can someone help me with 14 and 15
I absolutely have no clue where to start
<@&286206848099549185>
lone heartBOT
@wide oxide Has your question been resolved?
lone heartBOT
@wide oxide Has your question been resolved?
alpine sable
Think about the formula for A^-1
alpine sable
<@&286206848099549185>
.
alpine sable
lone heartBOT
https://i.imgur.com/j41CKTJ.png
alpine sable
its pretty simple geometry, but im really bad in it and just want to make sure
i missed school today and my teacher sent this
ill get to the point
how do i prove the top triangle =~ to the bottom one
i got 2 angles
idk why she didnt mark the middle
?
what
can you elaborate ?
hard patio
idk why she didnt mark the middle
As in beta=beta?
alpine sable
ASA no?
hard patio
can you elaborate ?
Ohhh congruent
alpine sable
yes
hard patio
I thought similar
alpine sable
oh, no
alpine sable
can you say in words
i dont learn math in english
so i dont know angle something angle ?
hard patio
alpine sable
oh its called side
alright
so i get the two angles
lets add a letter for me to be more clear
how do i say DF = DB
hard patio
The diagonals of a parallelogram bisect each other
hard patio
how do i say DF = DB
FB no?
alpine sable
The diagonals of a parallelogram bisect each other
oh
but you still dont know its a parallelogram
you only know that when you prove
alpine sable
she just marked AB=DS because she proved its congruent
alpine sable
But I’m guessing that was a typo?
lemme open the question in the book real quick
hard patio
Where’s S?
alpine sable
i feel like im missing something
alpine sable
Where’s S?
bottom right
hard patio
That’s isn’t C?
alpine sable
haha
no
Oh wait it is
my bad
i opened the book,
its given that DF=FB
that makes it more clear
hard patio
Yes
alpine sable
so you just do congruence and then you know its a
parallelogram
complicated names man
well
thanks for the help
hard patio
complicated names man
What? Parallelogram?
hard patio
so you just do congruence and then you know its a
Not sure since you didn’t send in the full question
hard patio
What? Parallelogram?
Parallel- ogram. Idk what ogram means but a shape with 2 sets of parallel sides
hard patio
in hebrew its a lot more simple
What is it called in Hebrew?
alpine sable
Not sure since you didn’t send in the full question
i opened the book, they just give you 8 sections and you need to say if its certainly a Parallelogram or can be a Parallelogram and write what it needs more to be a Parallelogram
alpine sable
What is it called in Hebrew?
Parallelogram is מקבילית
rectangle is מלבן
a lot shorter
hard patio
Quadrilateral lol
hard patio
Quadrilateral lol
Remember our second grade teacher making us repeat that for the whole lesson
hard patio
That’s cool 😎
hard patio
i opened the book, they just give you 8 sections and you need to say if its cert...
Oh based on off different info they give, got it
alpine sable
thats so stupid honestly
hard patio
who thought of making 10 letter words shapes
For a 4sided shape, no less
alpine sable
Oh based on off different info they give, got it
yeah its certainly a para something
alpine sable
For a 4sided shape, no less
haha
alpine sable
well you could
and then you say its a parallelogram
Why not,
corresponding sides in congruent triangles
so AB=DC
Why not ?
Oh
its given
forgot to say that
i thought you meant equal
until i checked what parallel means in translator
hard patio
Also one more thing
alpine sable
yes?
hard patio
You assumed it was a parallelogram to prove that it is?
hard patio
Cause we used the fact that the diagonals of a parallelogram bisect each other?
Unless that was already given
hard patio
And you forget to mention
hard patio
You didn’t even give us that:((
hard patio
XD
alpine sable
idk why my teacher didnt write that on the board
i felt like we were missing something
and we did
hard patio
AB parallel DC, DF=FB
So ye
alpine sable
so yes we can prove its a parallelogram
also another question, when a question gives you info, how do you call it in english?
why not ?
hard patio
also another question, when a question gives you info, how do you call it in eng...
While writing proofs you just say:
Given,
AB||DC
DF=FB
Okay, It is a parallelogram
Cause the parallel sides are equal
@alpine sable
Do you get it?
lone heartBOT
@alpine sable Has your question been resolved?
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flint iron
@mental coyote
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<@532812686870708234>
echo socket
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flint iron
can i get help with geomitry
jaunty acorn
l.In a right triangle ABC with hypotenuse BC, the difference between the hypotenuse and the cathetus AB is equal to 9 cm. Knowing that the projection of AB onto the hypotenuse is 3.77 cm long, what's the area?
lone heartBOT
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acoustic mirage
Can someone pls explain the first step ?
lone heartBOT
Can someone pls explain the first step ?
acoustic mirage
PS: i already know the tan(a+b) property
I still couldn't get this thing as the book says
acoustic mirage
1 = (x+1) - x
So :
Tan((x+1) -x)
Where x+1 is a and x is b ??
gray isle
if you're referencing tan(a-b),
yeh
acoustic mirage
if you're referencing tan(a-b),
yeh
Yep i was referring to that
Thanks a lot
.close
inner path
Hello, I have just started the matrices and I would like to know if you know of any books or links to understand and practise because I still don't really understand what it is
lone heartBOT
@inner path Has your question been resolved?
worn fox
3blue1brown youtube series "essence of linear algebra"
lone heartBOT
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tepid prism
can someone explain me the 1st step
lone heartBOT
can someone explain me the 1st step
sharp peak
identities.
tepid prism
identities.
that's obvious but which one ?? I really think I am missing to understand one of them
Specially what happeened in the numerator
tribal oxide
Specially what happeened in the numerator
sin2x and cosC+cosD used
sharp peak
both in the numerator and denominator
tepid prism
sin2x and cosC+cosD used
ohhh got it ,thanks mate ,I was actually multipliying them and then trying to see which idetity fits in ,thanks again
sharp peak
btw instead of asking people you can always go have a look at an integral calc on the internet
@tepid prism https://www.integral-calculator.com/
tepid prism
btw instead of asking people you can always go have a look at an integral calc o...
thanks
that seems to be a helpful tool
sharp peak
DONT OVER USE IT
lone heartBOT
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acoustic mirage
How did pi/6 come ?
lone heartBOT
How did pi/6 come ?
acoustic mirage
Shouldn't pi/3 come instead ?
rich quiver
Cengage 🌚
acoustic mirage
I am way too dumb for it tho 💀
acoustic mirage
In step 2 ?
Yep
rich quiver
I am way too dumb for it tho 💀
Which grade?
acoustic mirage
12th
kindred anchor
,, \sin(A+B)=\sin(A)\cos(B)+\cos(A)\sin(B)
ocean sealBOT
acoustic mirage
Yes but shouldn't pi/3 come ?
kindred anchor
How much is pi/3 in degrees?
acoustic mirage
Sin pi/3 = root(3)/2
pulsar parcel
Please help with this problem for my 2D game development, pls, pls pls :)))
acoustic mirage
But it can be either cos or sin ?
acoustic mirage
So it can also fit in the formula of cos(a+b) ?
kindred anchor
So it can also fit in the formula of cos(a+b) ?
No
acoustic mirage
.close
lone heartBOT
acoustic mirage
Did you even understand?
Yea ig
It can be either sin(x+pi/6) or cos(x+pi/3) ....right ??
acoustic mirage
How's your jee prep
Really very bad 💀💀💀
I am sleep deprived
2 continuous board practicals
Which grade are u in ??
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rocky cloak
If I use superscript squared on a vector variable is it clear I mean the elementwise product with itself?
remote tulip
How do I solve this. Also how do I backwards in the other two pictures. My teacher only gave us formulas and nothing else. So I am super confused.
Specially I’m really confused about what to do when the variable is in the denominator
Currently in AP Calculus in highschool
rocky cloak
I've claimed this channel please read the rules
pseudo ice
Oh wait I see how you do the channel thing now
You were just a little bit too slow, you'll have to go back to the available channels and try and take one of those [ideally, copy and paste what you've written here so that you don't get it snatched from under you again!]
lone heartBOT
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rocky cloak
Just to post again
FargothUrIsOnline — Today at 2:59 PM
If I use superscript squared on a vector variable is it clear I mean the elementwise product with itself?
lone heartBOT
@rocky cloak Has your question been resolved?
alpine sable
20+8(x-7)=100 Can someone explain?
lone heartBOT
20+8(x-7)=100 Can someone explain?
quasi scarab
simplify the left side
alpine sable
simplify the left side
My guess was 17 but the answer turned out to be 3.
long axle
Show ur simplification of the left side
lone heartBOT
@alpine sable Has your question been resolved?
quasi scarab
a* (b+c)= a* b +a* c
quasi scarab
My guess was 17 but the answer turned out to be 3.
how u got 17
alpine sable
how u got 17
20 + 8x - 56 = 100
quasi scarab
put the numbers on the right side
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
put the numbers on the right side
I don't understand could you tell me how would you solve it with an equation or another way?
quasi scarab
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rocky night
"Students sit at their desks in three rows of eight. Felix, the class pet, must be passed to each student exactly once, starting with Alex in one corner and finishing with Bryn in the opposite corner. Each student can pass only to the immediate neighbour left, right, in front or behind. How many different paths can Felix take from Alex to Bryn?" from AMC 2022 Intermediate Q30
I've been struggling with this problem for quite a while. Unfortunately, I haven't been able to find an answer. I have tried a few common techniques such as back-tracking, starting with simple cases and looking for any recurrences but I've had no luck. I would appreciate if someone could provide an explanation for how one would solve the general case of an N by M grid under the same restrictions, thanks.
royal plank
"Students sit at their desks in three rows of eight. Felix, the class pet, must ...
do you know how do draw it as a graph?
if you do, looking at the amount of options to pass from back to front (3 students 'wide', or 2 edges) can help you take a good guess at the options
if you need more hints just ask, this is quite the annoying problem
rocky night
do you know how do draw it as a graph?
if you do, looking at the amount of opti...
I was thinking of that, and it seems that the number of passes from a back seat to a front seat for any given path is in the range {2,3,4...8}. To me, the only path from here seems to be case-work which doesn't sound appealing for this type of question.
prime badge
royal plank
I was thinking of that, and it seems that the number of passes from a back seat ...
well, there aren't many 'shapes' the path can take, since there are some restrictions:
a middle row student may only be passed to if either the back or front student had the pet
prime badge
there's no solution, literally no reason to click, but it's the same question so that's neat
lone heartBOT
Available help channel!
delicate yacht
some help solving this equation?
i noted 2 ^ x = a and 3 ^ x = b
I got to an quadratic equation with these 2 values, from there im stuck
delicate yacht
<@&286206848099549185>
lone heartBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
delicate jacinth
wait 15 mins before you ping
delicate jacinth
some help solving this equation?
i noted 2 ^ x = a and 3 ^ x = b
I got to an qua...
show what you got
delicate yacht
actually a = 3 ^ x and b = 2^×
got this by just bringing the left and right members to a common denominator and multiplicate diagonally
delicate jacinth
$a^2(b+1)(b-1)-ba+b^2+1=0$?
ocean sealBOT
sopinha
delicate jacinth
$a^2(b+1)(b-1)-4ba+b^2+1=0$
ocean sealBOT
sopinha
delicate yacht
idk, ive got delta = someting*something + 4, i ve broke down these somethings into 4's divisors, but it got me to ugly solutions which are not the right ones
considering that the equation has solutions (delta >= 0)
lone heartBOT
@delicate yacht Has your question been resolved?
alpine sable
@lone heart
lone heartBOT
@delicate yacht Has your question been resolved?
dawn sand
Hi, I have a question regarding this
what i do not understand is why is the mans velocity (u_m) in the other direction
i know it says with respect to the boat (relative velocity)
im just asking someone to explain to me why the velocity vector of the man is in the other direction
the question states the man is walking 2km/hr in a direction to the right and perpendicular, so its vector is 2(cos45ax + sin45ay)... but relative to the boat it is 2(-cos45ax -sin45ay)
why is its vector like that relative to the boat
uncut berry
Which of the options shows the bisector of angle XYZ?
lone heartBOT
Which of the options shows the bisector of angle XYZ?
keen mason
Which of the options shows the bisector of angle XYZ?
well a bisect is basically cutting in half
in what picture is the angle cut in half
so both of the angles on either side are equal
uncut berry
thank you
brazen berry
How is it getting (3t+1) i calculated it and got (3t-1)
lone heartBOT
How is it getting (3t+1) i calculated it and got (3t-1)
brazen berry
for the simplification
last ether
A common factor is e^(-3t)
brazen berry
pulling out e^-3t would give e^3t(3t-1)
OOOH
gotta multiply right side by -1/1
since its subtraction, not a negative
.close
ivory briar
lone heartBOT
ivory briar
need help with 4 and 6
i did synthetic division for the first two problems and got no remainder
i did it for 4, 6 and i got a remainder
what am i meant to do after
lone heartBOT
@ivory briar Has your question been resolved?
ivory briar
no one has even said anything
lone heartBOT
@ivory briar Has your question been resolved?
hallow moth
lone heartBOT
hallow moth
Shouldn't the shaded area be 605/12?
Integrating from 0 to 11 where my integrand is x - ((x^2)/44)
Since y=11 is my upper limit and y=x is the "top" line
integrating gives me ((x)^2/2) - (1/3)((x^3)/44)
which simplifies to ((x)^2/2)-((x)^3/132)
and when evaluated over 11 to 0, I get 605/12
what am I doing wrong here?
modern crown
Don't integrate from 0 to 11, integrate from 0 to 22, since the red curve starts at 0 and ends at 22.
hallow moth
Don't integrate from 0 to 11, integrate from 0 to 22, since the red curve starts...
Because the blue line intersecting at y=11 then becomes the new upper bound?
until x = 22?
modern crown
This gives you the area below the red curve. Then, the area of the shaded region is (area of rectangle + triangle) - (area under red curve).
hallow moth
This gives you the area below the red curve. Then, the area of the shaded region...
I'm sorry so, does my integrand remain the same or do I include an additional term?
modern crown
It's still $x^2/44$
ocean sealBOT
DavidL1450
hallow moth
I guess what I meant was, when I am setting up my integration, is it still S x - x^2/44
which then becomes x^2/2 - x^3/132
evaluated from 0 to 22?
<@&286206848099549185>
Should I consider integrating from 0 to 11 and then adding the results to integrating from 11 to 22 of 11x-x^3/132?
modern crown
There is a way to do that, but it would require two integrations : $\int_0^{11} (x - x^2/44) dx + \int_{11}^{22} (11 - x^2/44) dx$.
ocean sealBOT
DavidL1450
There is a way to do that, but it would require two integrations : $\int_0^{11} (x - x^2/44) dx + \int_{11}^{22} (11 - x^2/44) dx$.
hallow moth
What am I missing here? I originally got 605/12 but when I failed the question on MLM it told me the answer was 605/6
not really seeing what im doing wrong
modern crown
Right. what does that integral evaluate to? I get 605/6 as well.
I see now. You only did the first part, where you integrated from 0 to 11. There is also a second part from 11 to 22.
$\int_0^{11} (x - x^2/44) dx = 605/12$
hallow moth
So I do need to integrate from 0 to 11, and then again from 11 to 22
ocean sealBOT
DavidL1450
modern crown
yes, do two integrations and add them.
fair musk
lone heartBOT
fair musk
If we take integral of the top (red) and bottom (blue), why do we subtract them, not add?
To find the area that is within all 3*
waxen flame
Because you want the length from the upper bound to the lower bound.
fair musk
OHHH
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Available help channel!
knotty veldt
lone heartBOT
sullen vector
knotty veldt
Yo
knotty veldt
Stol my channel lmao
lone heartBOT
I'm new to this
Please read #❓how-to-get-help
knotty veldt
Idk wtf ur question is tho
Ok for my question: reviewing dif eq, solution was simple seperstion of variables, but i tried to work it out this way…v, is that a dead end? Also is there any intuition behind separation of variables besides it just makes the “integrals solvable”
waxen flame
,rotate
ocean sealBOT
knotty veldt
sry bout that
sullen vector
Hey
lone heartBOT
@knotty veldt Has your question been resolved?
lone heartBOT
@knotty veldt Has your question been resolved?
lone heartBOT
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knotty veldt
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timber basin
Hi, could somebody please explain me why -80+10=-70 and not -90
I know it's probably really simple, I've no idea how I graduated and don't wanna be stupid
timber basin
Yeah my bad
timber basin
because -80 - 10 is really just (-80) + (-10)
Why is 10 negative here
timber basin
Please
raven haven
80 + 10 = 90
-80 - 10 = -90
but -80 + 10 = -70
the negative sign is attached to the number
one way to think of it is whenever you see a negative
say n - m
you think of it as n + (-m)
if I have negative 80 and I add 10, I should get negative 70
trail cairn
At the football stadium, 35 000 people
attend a football match each week. What
is the order of magnitude of the number
of people who attend 8 weeks of games?
raven haven
firstly, how many people attend 8 weeks of games?
trail cairn
35,000
limpid turret
That's how many people attend a game in one week
trail cairn
do i times it
kindred anchor
Yes
trail cairn
so like 245000
kindred anchor
Do you understand why?
trail cairn
Do you understand why?
yes
kindred anchor
so like 245000
Ok, so what is the order of this magnitude?
trail cairn
i think i got the answer
kindred anchor
zealous moat
hey im new how am i suppose to get help from someonne
pseudo ice
hey im new how am i suppose to get help from someonne
Math Help Available
zealous moat
can you just help me lol
kindred anchor
Sure, just open your own channel
trail cairn
Explain your reasoning
because 35000x 8 =280000 then we put it in scientific notation it is 2.8x 10^5 so it equal 5
trail cairn
i check or you?
limpid turret
you
limpid turret
Ah you edited your answer
Yes
That looks good
And your reasoning is perfect
full marks
trail cairn
can you help me with this please