You know how we multiply probabilities together to see what the overall probability of them happening together is?
#help-0
fringe yoke
So we multiply successes together, but do I always have to multiply the failures as well?
glass lichen
You mean $P(A\cap B)=P(A)P(B)$?
ocean sealBOT
Mosh
glass lichen
that only holds for independent events
ionic crown
fringe yoke
When do I also multiply by the failures?
glass lichen
Not fully sure what you mean
naive valley
depends what you're trying to compute
fringe yoke
like getting 2 heads out of 11 throws is: $(11c2)\cdot (0.5)^2 \cdot (0.5)^9$
why do you also have the failure multiplied into it
Wait shit
glass lichen
that's just how the distribution is defined?
naive valley
yes because you're looking for a very specific sequence of successes and failures
ocean sealBOT
Tim O'Brien
naive valley
2 heads AND 9 failures
fringe yoke
Yeah
naive valley
versus say P(2 heads in the first two tosses) without caring about what happens in the other 9
fringe yoke
Ohhh
fringe yoke
versus say P(2 heads in the first two tosses) without caring about what happens ...
Yeah
We are looking specifically at 11 throws
So we consider everything that can happen
If that was unbounded the probability of getting 2 heads consecutively would be 1/4 right ?
glass lichen
If $X\sim \operatorname{Bin}(n,p)$, then $P(X=x)=\binom{n}{x}p^x(1-p)^{n-x}$
ocean sealBOT
Mosh
fringe yoke
Right
glass lichen
Binomial distributions are fundamentally a sequence of independent bernoulli trials, so each flip is either a success or a fail, so you need to account for every action in the sequence of n trials
fringe yoke
Yeah I drew it out on a tree and this makes sense
What happens if I send n to infinity?
glass lichen
to which the nCx is just accounting for the permutations of the x successes
fringe yoke
Yeah
So if we weren't looking at a specific n, then the probability of getting 2 heads after any consecutive coinflips would be 1/4 right?
glass lichen
yes
fringe yoke
Because then the distribution isn't binomial (we don't know n)
glass lichen
though n would be 2 there
glass lichen
cause you're asking "Out of 2 flips, P(both heads)"
glass lichen
If you wanted say "What's the probability I get my 3rd head on my 8th flip?", that wouldn't be binomial
fringe yoke
hmm
glass lichen
That'd be NegBin iirc
fringe yoke
rly?
glass lichen
Yeah
glass lichen
Binomial counts the number of successes in a given n-long string of indep. Bernoullis
NegBin will tell you P(xth head on the Nth flip)
lone heartBOT
@fringe yoke Has your question been resolved?
fringe yoke
NegBin will tell you P(xth head on the Nth flip)
Interesting
I will ask my teacher about that one tomorrow, thanks again for your help Mosh
cinder sundial
lone heartBOT
cinder sundial
Those two equation Are the same
severe sluice
keen mulch
lone heartBOT
wary stream
Looks like a job for the physics server, linked in #old-network
lone heartBOT
@keen mulch Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
spice lark
how do you find who
lone heartBOT
how do you find who
spice lark
h=90
w=43
o=47
t=20
wary stream
h=90
w=43
o=47
t=20
These values don't match the image you sent
wary stream
Apply supplementary angles concept to find WHO
You know what that symbol at MHO means, right?
spice lark
can you by chance use dummy terms
spice lark
You know what that symbol at MHO means, right?
no
wary stream
That symbol means it's perpendicular. Do you know what that means?
spice lark
I’m bad at math but I’m not like dumb dumb
wary stream
I mean, supplementary is a commonly used geometry term, and you stated that you didn't know what it meant, so I wanted to make sure if you knew what perpendicular meant
spice lark
I mean, supplementary is a commonly used geometry term, and you stated that you ...
supplementary is a type of line/angle
spice lark
yeah that one
can you just help me with it
i forgot how to get it
i know its something to do with subtracting 180 from numbers
spice lark
You know what that symbol at MHO means, right?
I THOUGHT YOU MEANT A MATH TERM
i feel dumb
wary stream
Not exactly
spice lark
alright lets see
wary stream
Remember when I asked what that symbol at MHO was?
spice lark
90+43+47
spice lark
Remember when I asked what that symbol at MHO was?
yeah its a right angle
90 degrees
its not 4 is it
spice lark
90+43+47
= 176 180-176 = 4
am i right
for mho
h = 90
and o = 47
180-137
what does mho have to do with anything
you got me confused
wary stream
You were asking how to find WHO
wary stream
And I was saying WHO + MHO = 180 because supplementary angles
You know the angle at MHO because it's perpendicular
spice lark
133 is my final guess
wary stream
If MHO is perpendicular, what is that angle?
spice lark
which angle
wary stream
So you are asking how to find the angle for WHO, which I drew in orange. That black line, which I'm calling MHO, is given because of that perpendicular symbol. That blue line I drew is supplementary, meaning two angles added equals 180. If that is supplementary, then WHO + MHO = 180
spice lark
dang your dedicated
if your meaning to tell me its been 90 this whole time
i feel dumb
it is 90 right
wary stream
Yes, the value for WHO is 90
lone heartBOT
wary stream
Now you have WHO, you can find t
lone heartBOT
Available help channel!
lone heartBOT
90+10=100/5 = 20
spice lark
.close
lone heartBOT
lone heartBOT
Available help channel!
pale arch
okay where do i even begin with this
lone heartBOT
okay where do i even begin with this
pale arch
i know how to divide a polynomial but
is it asking me to divide the one top by the long ass one on the bottom??? ive just gotten started with dividing by stuff like x + 2 or whatever
small horizon
is it asking me to divide the one top by the long ass one on the bottom??? ive j...
Yes; It’s just a trinomial now
The idea of added integer carries over pretty much the same now that you have a squared term and a linear term
pale arch
shit
im just gonna write out the long division
ill be back if i cant figure out wtf im doing
small horizon
shit
im just gonna write out the long division
ill be back if i cant figure out ...
Yes. Not that fortunately the coefficient of the x^2 term in the denominator divides the coefficient in the numerator, so you will have a -4, it’s just a question of what the remainder is
If I’m interpreting what the question is asking for correctly
pale arch
dumb question but if you divide a number w x squared by a number w x squared do the sqaured x's cancel out
small horizon
dumb question but if you divide a number w x squared by a number w x squared do ...
Yes
You mean like this right:
$ \frac{wx^2}{wx^2}$
ack my latex is shoddy
pale arch
like uh
20x^2 divided by 4x^2 is just 5
small horizon
Yes
What you might consider an extension of that is polynomial long division in algebra 2
pale arch
i feel like i have done something wrong o_o
the assignment im doing usually has like. pre-laid out boxes for the long division questions but for this question it didnt have those.....
urgh
my professor frustrates me sometimes
hes a nice guy but the homework will sometimes have questions on stuff we havent covered yet
small horizon
Don’t forget it’s -4 at the end but yes you have the right idea
I think what they then want is the binomial remainder in the second box
pale arch
oh shoot u right
lemme just. send a pic of the question rq
small horizon
Does your software let you try answers multiple times
pale arch
yup
how in the world do i divide -27x by 5x^2
i dunno if its gonna allow decimals or fractions
negative 5.4 times the square root of x...?
small horizon
how in the world do i divide -27x by 5x^2
i dunno if its gonna allow decimals or...
This is the point of the remainder r(x) expression
small horizon
I think what they then want is the binomial remainder in the second box
See this
pale arch
ohhh! lemme try that then!
small horizon
ohhh! lemme try that then!
When polynomials don’t divide perfectly, we can put the result of an integer (the ideal quotient based on the highest degree terms’ coefficients) and a remainder polynomial divided by the same divisor polynomial
small horizon
i typed in -27x + 3 and it said wrong
ouch
Did you put -4 in too
pale arch
wrong again :-(
small horizon
Can you send pic again?
small horizon
LOL
You have to put the remainder polynomial in the second box!
You can’t leave it blank
only the -4 goes in the first box
And you need to specify the power of x on 27
pale arch
ok the -4 was right
but i put -27x + 3 in the second one and it says wrong
also im still strugglingg a little to understand where u got the -4
small horizon
also im still strugglingg a little to understand where u got the -4
You divided the polynomials and got -4
Because 5 goes into -20 -4 times
pale arch
ah right!
small horizon
You can’t divide the remaining terms properly which is why we need to partition this remainder polynomial fraction off
Can you send a picture of what you put in the box?
Software could be finicky with formatting
pale arch
small horizon
OH
Mb lol
Here’s the formal way to get the right remainder:
Take your OG polynomial dividend
And subtract off -4 times the divisor
pale arch
kk
small horizon
$-20x^2 -11x -1 - , -4(5x^2 + 4x - 1)$
ocean sealBOT
giratinalawyer
small horizon
= 5x - 5
pale arch
omg yay! u got it right, tysm!
its probably gonna be a while til i really get it, but still ty
.close
lone heartBOT
lone heartBOT
✅
pale arch
lets see here
small horizon
It was just a signs issue, which is usually the easiest hurdle conceptually to figure out
It boils down to finding the largest integer multiple of the largest degree in the divisor that goes into the dividend, then subtracting out that multiple of the divisor from the dividend and getting the remainder polynomial
pale arch
i see!
xcubed divided by xsquared is uhhh just x right
small horizon
i see!
xcubed divided by xsquared is uhhh just x right
Yes
Consider factoring out the x’s separately then cancelling
$\frac{x x x}{xx} = x$
ocean sealBOT
giratinalawyer
ocean sealBOT
selkiesHiraeth
pale arch
my dog keeps trying to play with me. noo sorry go away!
hmm. where do i go from here...?
do i add the -6x to -13x?
small horizon
hmm. where do i go from here...?
do i add the -6x to -13x?
Zoom out
There shouldn’t be an X on that in the first place
pale arch
umbral citrus
i think that the -6x is supposed to be positive
and ur also saying that 2x x 4x^2 is 8x^2
and thats how u get
that second -6x
pale arch
oh shoot youre right
whoops. gotta go fix that
hold on rq
umbral citrus
that second -6x
which us also supposed to be postivie
pale arch
okay i fixed it
but now im left with this
do i just bring down the 6x - 9?
pale arch
hm. isnt 8x^2 divided by 4x^2 equal 2x? thats what the little umm. program thing i typed here told me
umbral citrus
when ur dividing w exponents u subtract
umbral citrus
when u did 8x^3/4x^2 u got 2x(^1) bc 3-2=1
umbral citrus
thank you!
yw
pale arch
.close
hollow axle
Find the Jacobian matrix of the function f : R3→ R2 defined as f(x,y,z) = (x+y+z, xyz) and evaluate it at (2,1,3).
hollow axle
Suppose a computer program has an error in it. To detect the error, the programmer conducts a series of independent tests. The probability of a random test detecting an error is 0.10. Find the expected number of tests required to detect the error.
lone heartBOT
@hollow axle Has your question been resolved?
sly mantle
@hollow axle pls use 1 channel, and post what u tried
lone heartBOT
@hollow axle Has your question been resolved?
raw fractal
What angle are you referring to?
Uh, can you draw a brief sketch?
Because I don't understand which angle you mean, but it should be findable.
Angle between the parabola and the horizontal?
Ah, OK, you can use calculus to find this.
Lemme draw a sketch real quick. One sec.
sudden hinge
slope triangle seems like a good idea @alpine sable
you can make it really small ;)
infinitesimally small, so to speak
raw fractal
So, let f(x) be the equation of the parabola. Then, the slope of the parabola at a is its derivative at a, f'(a).
sudden hinge
and then think about what the derivative means again with respect to the slope triangle
raw fractal
Yeah, so $\tan \theta = f'(a)/1$, so $\theta = \arctan f'(a)$.
ocean sealBOT
PhenomPlasma
alpine sable
what did i do wrong
lone heartBOT
what did i do wrong
rigid smelt
for the first ibp, which did you pick for u and which did you pick for dv?
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
Trying to differentiate* the following:
f(x) = x^3 -3x +1
I got x = sqrt(1)
But after looking online, people seem to have different answers. Am I doing something wrong?
silver adder
Trying to differentiate* the following:
f(x) = x^3 -3x +1
I got x = sqrt(1)
Bu...
you mean differentiate?
alpine sable
you mean differentiate?
yea sorry
silver adder
use power rule
silver adder
x^2 - 1 = 0 has 2 roots
alpine sable
sqrt1
alpine sable
x^2 - 1 = 0 has 2 roots
could you expand on that
silver adder
x^2 = 1
alpine sable
-> sqrt(1)?
silver adder
,w plot x^2 - 1 = 0
ocean sealBOT
cold arch
A triangular prism is 37 inches long and has a triangular face with a base of 42 inches and a height of 28 inches. The other two sides of the triangle are each 35 inches. What is the surface area of the triangular prism?
lone heartBOT
A triangular prism is 37 inches long and has a triangular face with a base of 42...
@cold arch Has your question been resolved?
white ferry
Discrete Math Proof. Is anyone able to help me work through this example?
white ferry
For instance a list of all the things I need to prove to prove the whole proof?
spark creek
For instance a list of all the things I need to prove to prove the whole proof?
I'm not sure what your question is, you want a explanation of the solution or something else?
white ferry
Like I can follow the question and example. But lets say I just got given the question. whats the first thing I should be doing. I need to prove left side is a subset of right side and right side is a subset of left side for them to be =, is there anything else I need to be thinking?
spark creek
For questions like these you can either prove the left side to the right side or you can solve both sides up till the point they are equal
white ferry
which have they done in the example? This is quite confusing for me sorry, this is the second example of a proof they have shown me.
spark creek
Discrete Math Proof. Is anyone able to help me work through this example?
This question specifically is an identity so you might not be asked to prove this but instead more convoluted questions will be asked and you'll need to reduce them to this identity or something else
white ferry
im actually being asked in the work book to write this proof
obviously the answer is there but struggling to put the steps together without seeing the answer I guess
spark creek
So AU(BUC) is a set
and assuming x belongs to this set
So x can either belong to Set A or the union of Set B and C
So the first case they take is to assume x to be in A
And solve ahead
Second case they take is to assume x to be in the union
The second case has 2 sub cases:
x can belong to B
x can belong to C
And they solve from there
Sorry if I'm not clear, I'm finding it a bit tough to concisely explain the working here
white ferry
im reading through now thanks
ok so what am I solving in each step? that x can be in A then B and then C?
the last line here. How can we know its a subset of the right hand side
I mean I know it is, its all joined by unions, so if x is in any of them it has to be in the right hand side.
are we assuming that is true?
spark creek
I mean I know it is, its all joined by unions, so if x is in any of them it has ...
Yup
A basic overview of the solution is proving lhs is a subset of rhs and then proving RHS is a subset of LHS
This is only possible if both sides are exactly equal
white ferry
yep I understand that much. I dont know why I need to show x in A B and C
if x in A then its also in RHS
spark creek
if x in A then its also in RHS
You're right but it is what it is lol, if it's asked in your assignment then you gotta go through the whole proof even it's extremely straight forward
white ferry
Yeh I just dont know how to figure out the steps
like trigger in my head ok for this I need to prove X in A B and C for LHS for example
What is the give away that thats what i need to do here?
am I always trying to do stuff to the LHS to make it written the same as the RHS?
spark creek
So you usually for set questions you can start with assuming an element to be in a set and then going ahead from there
Frankly speaking it depends from question to question
spark creek
am I always trying to do stuff to the LHS to make it written the same as the RHS...
Yup, either this or solving both sides independently up to the point they're equal to each other
white ferry
ok thanks ill keep working on it.
spark creek
Lmk if you have any other doubts
white ferry
thanks
cold depot
I don't like how that solution just jumped to (A∪B)∪C. A more detailed proof should say that if an element's a member of a set, it's also a member of any set that's a superset of that set, and that the union of set X and set Y is a superset of set X.
spark creek
Since they already proved LHS to be a subset of RHS, they went on to RHS to prove the same thing
I get what you're saying but I guess some things are implied here so that the solution doesn't become unnecessarily complex
lone heartBOT
Available help channel!
normal night
How am I supposed to notice this?
lone heartBOT
How am I supposed to notice this?
alpine sable
How am I supposed to notice this?
Could you provide more context ?
normal night
Could you provide more context ?
Wait that's the wrong image.
This is better.
My problem is not with a specific case scenario.
I just cannot see these things.
I don't notice them. I don't get how I am supposed to notice them. I keep making mistakes because I derail and try to solve questions other ways.
alpine sable
What would the question be ?
normal night
In that last image the question was.
silver adder
its noticeable that both 24 and 8 are divisible by 8
normal night
I don't notice it.
silver adder
I don't notice it.
do you know the multiplication table?
normal night
The question was that if (24y-8)=29 what is 3y-1.
normal night
do you know the multiplication table?
I had issues learning it as a child. I did go through it with Anki and am much better at it now.
I know that 8*3 is 24. I used that in the question before this one. So I know that to heart.
I still couldn't see it.
alpine sable
If 3y-1 is 8 times less than 24y-8 what would 29 be in the 3y-1 case?
normal night
I don't know.
normal night
Yes you divide it.
silver adder
we also know that 24y-8 = 8 * (3y-1)
he doesn't know that immediately
normal night
I don't know that 24y-8 = 8*(3y-1)
alpine sable
The text mentions that 24y-8 is 8 times 3y -1, so they are the same
normal night
Cause I didn't notice it.
normal night
The text mentions that 24y-8 is 8 times 3y -1, so they are the same
No the text I sent is the explanation for the question.
It is step one.
And I failed at it.
I got 21/75 as an answer instead.
normal night
I don't have problems with the actual solving part.
I just cannot see or notice that 24y-8 is 8 times 3y-1
I just don't get it.
I never notice these and fail on every question that relies on me noticing it.
alpine sable
Oke so do you know how prime numbers work ?
normal night
I do know how prime numbers work.
alpine sable
oke so which numbers are involved in creating 24 ?
normal night
What does that have to do with anything?
normal night
oke so which numbers are involved in creating 24 ?
8 and 3
If you multiply them.
20+4
Infinite amount of answers to that question.
alpine sable
8 is not prime tho
normal night
What does that have to do with 24.
alpine sable
you want to simply 24y-8 to 3y-1
normal night
What
alpine sable
Seeing that 24 can be divided by 8 to create 3 is a big part
normal night
I cannot see it
I just don't
I want to know how to.
From what I can get it is magic.
silver adder
you know that 8*3 = 24 and 8*1 = 8
normal night
Yes.
But I cannot notice it in a question.
I do not understand how I would even notice that
silver adder
do you know that 8*3 = 24 also means 24 = 8*3
silver adder
what are the factors of 24?
normal night
8 and 3
silver adder
theres more factors than that
normal night
But i can only say that
normal night
theres more factors than that
Yeah
I don't get how I am supposed to work back
my brain cannot do it
Is it natural to you?
Cause I cannot.
I'd have to run through the whole table to get the factors
silver adder
yeah cus i know all the factors
normal night
Am i supposed to memorize the factors of 24?
An all numbers
thats an impossible task
I have an exam in 2 months
silver adder
i recall that 24 = 1*24 = 2*12 = 3*8 = 4*6
normal night
I cannot recall that
On the spot
at all
how am i supposed to do that
I know 2 times 12 is 24
but i cannot tell you that 24's factors are 2 and 12
or 4 or 6
but if you asked me the other way around i would say 24
i don't get how this is supposed to work
alpine sable
Can you tell how many times you can divide 24 by 2 untill its not longer possible ?
normal night
Can you tell how many times you can divide 24 by 2 untill its not longer possibl...
24
infinitly
alpine sable
by 2
alpine sable
how many times can you divide it by 2 and not create a decimal number
alpine sable
i am asking how many times you can divide it by 2 and create a number that does not have a decimal
normal night
oh
normal night
3
alpine sable
exactly and what is left ?
normal night
3 is left
normal night
i do not see it
normal night
how is that helpful
normal night
thats cool
normal night
this doesn't help my problem
this has nothing to do with the problem i have
you want me to do this everytime i see a number?
alpine sable
You cant solve your problem if you dont see this
normal night
run through all the possible factors
one by one
to see if it is that way
i have a minute per question
this is impossible to do
i have only one brain
alpine sable
how many seconds did it take you to see the building block for 24
normal night
i don't know
i don't see it
to begin with
i didn't see it
i did not see that 24 is 8 times 3
i just dont see it
when i look at 24
i don't think
"that is 8 times 3"
it never comes to my mind
if i do it methodically it never works cause it takes too long
and i still have all the other stuff in the question to solve
i think you are missing the point here
i do not see the factors of 24 when i look at it
i just don't
i cannot do it
it never comes to my mind to check the factors
so i'd need to check it everywhere to make sure i wasn't missing them
from how no one seems to understand the problem i am having to begin with
i guess i am just disbled
well there goes my dreams then
i like math
but i cannot do anything with it appeantly
becusae of magic
.close
alpine sable
lone heartBOT
alpine sable
this is the answer for the question: the price of a shirt increased by 17.8 percent. the original price is 49.9
but why is it not just 49.9*0.178
lone heartBOT
@alpine sable Has your question been resolved?
ocean sealBOT
Osi
alpine sable
no clue why this is the answser
lone heartBOT
lone heartBOT
Available help channel!
cosmic oasis
Huh
cosmic oasis
Bot glitched I guess
pale kestrel
.
lone heartBOT
@cosmic oasis Has your question been resolved?
lone heartBOT
@cosmic oasis Has your question been resolved?
errant dagger
how do you
lone heartBOT
how do you
stoic barn
what type of techniques are used to find meromorphic extensions of functions?
I have some type of zetaish looking holomorphic function on Re(s) > 1 that also sums reciprocals to the power of s. except instead of reciprocals of natural numbers I have reciprocals of a certain sequence of complex numbers whose absolute value grows with roughly Kn + O(log(n)) (absolute value of the nth term). There are apart from that some other information about the argument of the terms but I won't go into much detail for now.
I've tried using the argument principle to get an integral representation of the sum, but didn't really get anywhere.
I've also tried to somehow adapt the approach they presented on wikipedia of the functional equation for the riemann zeta functions, but I didn't find a way to generalise it as the behaviour of my sequence isn't as clean as the sequence of natural numbers. They're all transcendental numbers in general and I can only give asymptotic approximations of where the terms of the sequence actually are.
lone heartBOT
what type of techniques are used to find meromorphic extensions of functions?
I...
@stoic barn Has your question been resolved?
lone heartBOT
@stoic barn Has your question been resolved?
stoic barn
<@&286206848099549185>
brittle sequoia
<@&286206848099549185> someone should help this guy
untold pier
lone heartBOT
@stoic barn Has your question been resolved?
gleaming terrace
help pls
alpine sable
do you know how to complete the square?
gleaming terrace
yes
lone heartBOT
@gleaming terrace Has your question been resolved?
gleaming terrace
<@&286206848099549185>
tacit arch
<@&286206848099549185>
jelly already told you a hint. complete the square
gleaming terrace
what do i do next
tacit arch
jelly already told you a hint. complete the square
complete. the. square
gleaming terrace
i did
tacit arch
what help do you need with next
gleaming terrace
idk what to do after completing the square
gleaming terrace
tacit arch
,rotate
ocean sealBOT
tacit arch
did you find a and b here?
gleaming terrace
no
tacit arch
where did this come from then
gleaming terrace
i completed the square of 7-2x²-12x
gleaming terrace
the link doesnt work
tacit arch
put into your search engine: khan Parabola focus directrix review
gleaming terrace
i read it idk what it means
kindred talon
I'm a bit confused on how to solve this problem on my hw, can I get some guidance please?
I know for a it's x[f'(x)]+x'f(x), but do I just plug in the values like x[3]+x'(5) so maybe 8?
lone heartBOT
I'm a bit confused on how to solve this problem on my hw, can I get some guidanc...
@kindred talon Has your question been resolved?
kindred talon
<@&286206848099549185> 🙂
lone heartBOT
@kindred talon Has your question been resolved?
tacit arch
I'm a bit confused on how to solve this problem on my hw, can I get some guidanc...
Yes
edgy sand
lone heartBOT
edgy sand
I have the formulas for these but not sure on how to use them
knotty spire
Well what are they
knotty spire
Alright, so what do we know from the task
knotty spire
well what are the bounds of our integration
knotty spire
for equal width, yes
knotty spire
Well, Delta_x isn't really the change in variable here, rather it is the width of an interval we take
but yes
edgy sand
okay so lets start with the left sumn then
I would have LN= 1/2 3sigma j=0(2+j(1/2)) ?
knotty spire
I would have LN= 1/2 3sigma j=0(2+j(1/2)) ?
why 2
for your a
As you have written it right now, your bounds would be from 2 to 4
edgy sand
oh our a is 0?
ocean sealBOT
Remavas
knotty spire
Now you can evaluate this. This is a simple finite sum.
edgy sand
can i punch this into my calculator?
edgy sand
wait you substituted f(0+j/2) ?
knotty spire
what I mean by that is insert the actual formula for the function f
instead of writing f(...)
$L_N = \frac{1}{2} \sum_{j=0}^{3} \frac{j^3}{2^3}$
ocean sealBOT
Remavas
edgy sand
you got x^3 from the original problem right?
knotty spire
mhm
I will use my wolfram superpowers instead
,w \frac{1}{2} \sum{j=0}^{3} \frac{j^3}{2^3}
edgy sand
i got 9/4
ocean sealBOT
Requested by Remavas#3737
knotty spire
,w 1/2 * the sum from j=0 to 3 of j^3 / 2^3
ocean sealBOT
edgy sand
ez asf
knotty spire
correct
edgy sand
okay so right side is same process except the different values above and below the sigma right
knotty spire
yes
edgy sand
okay and lastly, how would I find the integral of this ?
knotty spire
$\int_0^2 x^3 \dd x$
edgy sand
I know with impropers where there is a inf at top or bottom i can do limit
ocean sealBOT
Remavas
knotty spire
well
how much do you know about definite integrals
I presume you already encountered the fundamental theorem of calculus
edgy sand
yes
knotty spire
$\int_0^2 x^3 \dd x = \frac{x^4}{4} \rvert_0^2 = 4 - 0 = 4$
ocean sealBOT
Remavas
knotty spire
Just apply the power rule to find the antiderivative
then apply the fundamental theorem of calculus
knotty spire
Once you have the theoretical groundwork, yes, it is pretty easy
edgy sand
.close
gray heart
How am i supposed to know if my angle should be larger than 90 when using arcsin?
tacit arch
How am i supposed to know if my angle should be larger than 90 when using arcsin...
what problem are you trying to solve?
gray heart
gray heart
what problem are you trying to solve?
i already know the answer
but for angle b i got 83.5
then i learned i had to subtract it from 180 because the real answer was larger than 90
but if i never knew the real answer, how am i supposed to know if i should subtract from 180 or not?
tacit arch
but for angle b i got 83.5
how did you get 83.5
gray heart
how did you get 83.5
tacit arch
,calc sin(33 deg) * 27
ocean sealBOT
Result:
14.705253945406
,calc sin(33 deg) * 27 / 14.8
ocean sealBOT
Result:
0.99359823955444
help plz
tacit arch
help plz
this channel's occupied. read #❓how-to-get-help
,calc asin(sin(33 deg) * 27 / 14.8) * 180 / pi
ocean sealBOT
Result:
83.513367413633
uh im confused
tacit arch
then i learned i had to subtract it from 180 because the real answer was larger ...
So your confusion arises because $\sin(x) = \sin(180 - x)$. I think in this case, you're supposed to be able to tell from the diagram that angle $B$ is larger than 90 degrees.
ocean sealBOT
riemann
gray heart
So your confusion arises because $\sin(x) = \sin(180 - x)$. I think in this case...
i guess that makes sense
but the teacher always tells us we can’t assume angle measurements relative to other angles
i’ll have to ask her again
.close
fallen rain
can someone give me some tips about this question?
lone heartBOT
can someone give me some tips about this question?
@fallen rain Has your question been resolved?
fallen rain
@tacit arch
tacit arch
<@!261933205387477002>
don't ping me
fallen rain
don't ping me
...can you help me with this question please?
tacit arch
don't ping me
.
alpine sable
lone heartBOT
pine kettle
what math class are you in
tacit arch
draw a sign chart
alpine sable
a sign chart?
tacit arch
alpine sable
i look that up and only thing I see is zodiac signs
tacit arch
prime badge
alpine sable
so all the real number in X?
tacit arch
and
https://math.libretexts.org/Courses/Monroe_Community_College/MTH_165_Colleg...
do Example 3.8.1
alpine sable
was there a reason for the test numbers?
tacit arch
was there a reason for the test numbers?
For each test value, 𝑣 , determine if 𝑓(𝑣) is positive or negative and record the result on the sign chart for each region.
tacit arch
this asks for values where the left side is negative or zero
tacit arch
maybe watch a video
https://www.youtube.com/watch?v=Fd5ys4PQ-aM
wet tusk
lone heartBOT
wet tusk
did i do this right?
tacit arch
Yes
tacit arch
shouldnt it be 9x^3 - x^2
No
tacit arch
You invented a 2 when substituting the definition of V(3x)
tacit arch
You lost a 9 being multiplied by x^2
So either the formula is wrong or your algebra is wrong
lone heartBOT
Available help channel!
tribal geyser
Can anyone help with 24)b pls
cinder sundial
lone heartBOT
open folio
The answer should be -1 tho
Negative/Negative = Positive
cinder sundial
Negative/Negative = Positive
Yes but the correct answer is -1
open folio
Yes but the correct answer is -1
Then I would assume you made an error?
open folio
Book might be wrong, unless that original equation is different than the one you solved
cinder sundial
Could you put it into sth like wolfram
Cuz I don’t know how to put trig on calculator
lone heartBOT
@cinder sundial Has your question been resolved?
silver adder
,calc cos(270 degrees)tan(180 degrees)cot(180 degrees)/(sin(90 degrees)tan(540 degrees))
ocean sealBOT
Result:
0.5
wack
daring kindle
lone heartBOT
daring kindle
What does $(g \circ f)(X)$ denote and how is it different from $g(f(X))$?
ocean sealBOT
Bread
glass lichen
they're the same thing
daring kindle
I am confused why wouldn't they just write it as the same thing?
distant granite
I have a question on how to solve this problem
lone heartBOT
I have a question on how to solve this problem
distant granite
trim plinth
distant granite
👌
distant granite
Alr
undone chasm
ok
lone heartBOT
distant granite
.close
lone heartBOT
Available help channel!
teal frigate
Hey guys does the order of a cross produtter ? aka a X b vs b X a? if so, why?
lone heartBOT
Hey guys does the order of a cross produtter ? aka a X b vs b X a? if so, why?
@teal frigate Has your question been resolved?
tacit arch
produtter
huh?
lone heartBOT
@teal frigate Has your question been resolved?
tight locust
yes
the cross product is special though.
it's sort of like subtraction
(a-b) = -(b-a)
(a x b) = -(b x a)
we call this property "anticommutativity"
it is "anticommutative"
stone scroll
lone heartBOT
tacit arch
My answer is -3/5 but my calculator says it's 0
Are you inputting it into your calculator correctly
lone heartBOT
@stone scroll Has your question been resolved?
stone scroll
Are you inputting it into your calculator correctly
Nice, I found the problem HAHAHA thanks
steel turret
hello
bright hedge
is 216 a power of 6? if so, what is that power? that is your answer
lone heartBOT
@steel turret Has your question been resolved?
steel turret
6^3
glass vale
lone heartBOT
glass vale
Trying to use structural induction to prove part a.
This is what I have so far, but not too sure where to go from here.
Any thoughts?
tight locust
Make a "tree"
After applying the recursion the first time you have 2 new elements of S
glass vale
Make a "tree"
Like this?
tight locust
Yes!
tight locust
You tell me!
We are trying to prove that all members of S are even
Tbh i don't see why you need induction
glass vale
And we start at 2 because 2 is the only number in the set initially right?
tight locust
It is as simple as saying that the square of an even number is even and that twice an even number is even
And because the only number we start with is even then all members of the set must be even
autumn lantern
hi! what's meant by the set of integers $\mathbb{Z}_7^2$?
lone heartBOT
hi! what's meant by the set of integers $\mathbb{Z}_7^2$?
ocean sealBOT
richard
autumn lantern
what elements does the set have? sorry i am not familiar with the notation
autumn lantern
same that's what I'm having problems with haha
merry depot
it means $\bZ_7\times \bZ_7$
ocean sealBOT
Zybikron
merry depot
the same way $\bR^2 = \bR\times \bR$
ocean sealBOT
Zybikron
split vector
lone heartBOT
split vector
how do u find c
merry depot
are you given some kind of initial condition or anything?
merry depot
I don't know if you're supposed to find a number for C or just state what it represents
without some numbers to work with, I don't know if you can find an actual quantity for C
split vector
yeah thats why im a bit confused
merry depot
i think they mean to just state what C represents in the equation
in a horribly worded sort of way
lone heartBOT
@split vector Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
visual plinth
$$\int_{\large sin^2(t)cos(t)dt}^{}$$
lone heartBOT
$$\int_{\large sin^2(t)cos(t)dt}^{}$$
ocean sealBOT
kenzo
visual plinth
What is method should I use to integrate this
spark creek
Substitution
visual plinth
is there a clear substitution here ?
lone heartBOT
@visual plinth Has your question been resolved?
distant kestrel
lone heartBOT
distant kestrel
Hi can someone help me please with number one
All the extra information i know is that BPO is 90 degrees
spark creek
Use the fact that OA and OP are the radii of the circle
strange fractal
0
strange fractal
Can someone help? why is it 1,1?
feral sluice
definition of x intercept is the x value of where the value "intercepts" the x axis, which is when y = 0
and vice versa for the y intercept
so check the table for what x is equal to at y= 0
lone heartBOT
@strange fractal Has your question been resolved?
Available help channel!
Available help channel!
stone scroll
lone heartBOT
winged rock
Looks like it
split cloud
lone heartBOT
rigid smelt
have you heard of conjugates?
rigid smelt
actually nvm, that's just going to make it look worse
anyway, in order to get rid of that square root, what do you think we can do?
split cloud
what i did first was
add sqrt x-1 to the 1
moved it
then i sqaured both
leaving 2x-5=x+2 sqroot x-1
x-5=2sqrtx-1
rigid smelt
yeah looks good
split cloud
it does?
rigid smelt
yep
split cloud
but how do i get that answer
split cloud
square root?
rigid smelt
so what can you do to get rid of that square root?
rigid smelt
show me what you got after squaring both side
rigid smelt
yep, thats great
split cloud
make =0?