Denascite
#help-10
warm shaleBOT
loud tangle
if you really want you can do ln x and get 0.25 × ln x
then have (ln x)/4
glad stag
Hmmm okay
obtuse pebbleBOT
@glad stag Has your question been resolved?
glad stag
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
fervent girder
Need some help on 2 permutation and combination questions with explanation,
-
There are 3 trays of sushi. The first has 3 pieces of A, the 2nd has 2 pieces and the last has 4 pieces. Find the number of ways to choose at least 1 sushi from any of the trays
-
In a class, students form groups which consist of 4 or 5 students each. In how many ways can the project work groups be formed if the class size of a particular class is 17?
obtuse pebbleBOT
Need some help on 2 permutation and combination questions with explanation,
1. ...
fervent girder
answer to the qn 1 is 59, answer to qn 2 is 35735700
sweet cobalt
Ok so looking at Q1, the very simplified example to start with is how many ways are there to pick a piece of sushi from the first tray?
fervent girder
3?
sweet cobalt
Yeah, and then how many ways are there to pick 2 pieces of sushi from the first tray?
fervent girder
Need some help on 2 permutation and combination questions with explanation,
1. ...
the sushi's are identical in each tray
my bad for not mentioning that
fervent girder
I know the way to solve it is (number of ways without restrictions) - (number of ways where no sushi is chosen) = (number of ways at least 1 sushi is chosen)
sweet cobalt
Yep
fervent girder
but I'm not sure how to go about from there
sweet cobalt
So number of ways to pick 0 is 1 right?
fervent girder
yep
sweet cobalt
I'm not sure if I quite understand the question then
Oh wait I see it I think
Ok so now we need to find the number of ways without restriction
fervent girder
yeah
sweet cobalt
Looking at tray 1
What are your differetn options for amount of sushi picked?
(0 is allowed as we are ignoring that for now)
fervent girder
so 4?
sweet cobalt
Yep, and then tray 3 is 5
Ok, so does it make sense that the total number of ways to pick from all 3 is 4 x 3 x 5?
fervent girder
ohh ok
fervent girder
Yeah I did that at first, its always a pain to remember 0 lol
yeah...
sweet cobalt
Ok first lets look at the group composition
Which combinations of groups of 4 and 5, will sum such that every student is in a group?
fervent girder
3 groups of 4, 1 group of 5
sweet cobalt
Yep exactly
So we only need to worry about one combination
Ok let me do some calculations
fervent girder
im guessing either the answer is wrong or I've been trying to solve the question wrongly the past few hours
timid silo
which one u still need help with
fervent girder
qn 2
timid silo
okay
fervent girder
answer is apparently 35735700 but I can't seem to get that number
timid silo
well it has to be 3 groups of 4 and 1 group of 5
fervent girder
yep
fervent girder
what I tried was 17C4 x 13C4 x 9C4 x 5C5, but I didn't get the answer
^^ tried this way
timid silo
so first you choose group of 5 with 17c5
timid silo
what I tried was 17C4 x 13C4 x 9C4 x 5C5, but I didn't get the answer
wait if im correct this answer should be 6x too much
timid silo
yeah
you have to divide by 3! for the order of the groups of 4
since it doesnt matter which group of 4 you are in
fervent girder
but in questions that give a certain number with a specific number of people in a group, why is it unecessary to divide as well?
timid silo
wdym
fervent girder
eg. in how many ways can 6 different articles be subdivided into groups of 2 articles each?
this answer is just 6c2 x 4c2 x 2c2
timid silo
👍
ancient lantern
obtuse pebbleBOT
ancient lantern
Anyone help w these?
twin lotus
all of them
?
well in 3 i) u just have to prove that at least any two angles are the same using angle facts e.g alternate angles are the same or opposite angels on a intersection are the same
@ancient lantern
ancient lantern
Here
ancient lantern
all of them
Ye
twin lotus
well in 3 i) u just have to prove that at least any two angles are the same usin...
do u understand this
ancient lantern
I'm trying
ancient lantern
Similar
twin lotus
ok then yh, just prove any two angles are equal
ancient lantern
And for 3 ii?
twin lotus
is ND = DA?
ancient lantern
It doesn't say
twin lotus
well i think its only true if so, but idk how to word it
if its been awhile just @ the helpers roll
obtuse pebbleBOT
@ancient lantern Has your question been resolved?
timid silo
i am from germany so sry if my english on the paper is weird. But well i am cs student and we are learning proofs and i am hardstuck on this ... they didn't even show it properly in a lecture and the book also doesn't really show how to proof something, i don't even know if i got the notations right in my "try". I learned about logic but this one just feels a bit different
obtuse pebbleBOT
i am from germany so sry if my english on the paper is weird. But well i am cs s...
timid silo
proving this is the task
keen tiger
as you've written down, 2 sets A and B are equivalent if and only if A is a subset of B and B is a subset of A
kind hawk
what is the overline? complement or something?
timid silo
complement yeah
kind hawk
ok. lets take $x\in\overline{M\cup N}$. Then we know that $x$ is not in $M\cup N$
warm shaleBOT
Denascite
kind hawk
we want to show that $x$ is in $\overline M \cap \overline N$. That means we want to show that $x\in\overline M$ and $x\in\overline N$
warm shaleBOT
Denascite
timid silo
yeah i can follow 🤔
kind hawk
when is x in overline M
timid silo
when it's not in M
kind hawk
ok. so that's where we want to get
we know that x is not in MuN
how do we get to where we want
timid silo
when we show that x is not in M and not in N at the same time
kind hawk
lets just show one of them for now, the other is then essentially the same
we know: x is not in MuN
we want: x is not in M
kind hawk
what does it mean if x is not in MuN
timid silo
it's part of everything else but MuN
kind hawk
and what is MuN?
timid silo
not x?
kind hawk
what is the set MuN
timid silo
M combined with N
kind hawk
which elements are in that set
timid silo
everything in M + everything in N
kind hawk
if an element is in MuN, then it is in M or in N
timid silo
ahh i oversaw that little detail
it's like the logical or and the other one is like the logical and
for x
kind hawk
yes essentially
timid silo
so i can convert it to the logical one, proof it and then convert it back?
kind hawk
if you do the conversion correctly, yes
timid silo
x is in -(M v N)
then i do de morgans of the bracket
x is in -M and -N
i wanted the screenshot to be posted first
kind hawk
well lets not do MvN. "set or set" is nonsense
the logical or is for statements, not sets
timid silo
well if we know that x is not in M u N
then we already know (MuN)\x
i get the set operators but i just can't figure out of to work with them
the logic operators are so much easier to work with
kind hawk
$M\cup N$ is a set. $x\in M\cup N$ is a statement
warm shaleBOT
Denascite
kind hawk
try to write everything in terms of "x in ..." and "not(x in ...)"
timid silo
ah ok so earlier my mistake was not using the correct terms?
kind hawk
well lets not do MvN. "set or set" is nonsense
this one, yes
kind hawk
that's what you want to show
x is in compl(MuN)
not(x in MuN)
not(x in M or x in N)
not(x in M) and not(x in N)
x in comp(M) and x in comp(N)
x in comp(M) n comp(N)
timid silo
the transition from or to and seems a bit odd to me
kind hawk
that is de morgan
timid silo
i get the rest but how does or become and once it splits
kind hawk
not(A or B) = not(A) and not(B)
timid silo
what how did they not teach us that
kind hawk
what do you think de morgan is
timid silo
ohhh
wait you used the same de morgan from logic
i am just not allowed to write it like that
with v
timid silo
ok i kinda get it, now i just need to try the right side myself
timid silo
v is not defined for sets
ah ok i see, but i can just write the or with normal language and it works
timid silo
but stuff like "M or N" or "x in M or N" are false
oh like in programming i have to write it twice like x in M or x in N
kind hawk
yes
(of course informally this stuff is fine. just you know, gotta stay correct for proofs)
timid silo
yeah that's important, the professors told us to be very precise in this subject
x is in comp(M) and x is in comp(N)
not(x is in M) and not(x is in M)
not (x is in M or x is in N)
not ( x is in MuN)
x is in not(M u N)
x is in comp (M u N)
that should be the right side
kind hawk
(which are the same steps as I did, just other direction)
timid silo
is this the case for most proofs?
kind hawk
no
kind hawk
dont worry about not seeing it. its also very good that you correctly produced the correct steps
timid silo
it was because of this
kind hawk
yes
usually to show that sets are the same we need to show that each is a subset of the other and the directions are usually different
kind hawk
sure I just didn't have that symbol ready to write
timid silo
ah ok thx a lot dude, you explained it very clearly
kind hawk
youre welcome
marble hamlet
obtuse pebbleBOT
marble hamlet
Why does the way they factored out the bottom here not make sense? they have -2sin^2 theta
I only see cos^2theta and -sin^2theta which I made to cos(2theta)
Is it just a different identity?
timid silo
just using cos^2=1-sin^2
marble hamlet
Ahh ok - I see that. is it wrong/better to use one or the other? I got the same answer using double angle
marble hamlet
Yeah that's what I'm wondering as far as finding my tangents now - is that denominator easier to find the zeros for my dx/dtheta tangent ? gonna try with my equation too
timid silo
i mean just try and see which one seems like less algebra
bleak eagle
Ann if you are still out there, my battery died but I could still really use some help with the p-adics
obtuse pebbleBOT
Ann if you are still out there, my battery died but I could still really use som...
timid silo
bleak eagle
oh thanks! i'm still not certain exactly how i would go about this problem with the geometric series
let me grab a picture from the book real quick
timid silo
$\sum_n p^{2n} =\frac{1}{1-p^2}$
bleak eagle
$\sum_n p^{2n} =\frac{1}{1-p^2}$
timid silo
multiply the whole sum by 2
bleak eagle
i'm so lost, im so sorry! we were introduced to p-adics a week ago in my intro to math experimentation class and I have forgot everything about sums and series from calc 2
how can i pull a 2 out of the whole sum if there are terms in the sum with a coefficient of 1?
timid silo
$\sum 2p^{2n}=2\sum p^{2n}$
warm shaleBOT
Toby
timid silo
how can i pull a 2 out of the whole sum if there are terms in the sum with a coe...
split the sum as in dena's message
obtuse pebbleBOT
@timid silo Has your question been resolved?
daring rock
What was the original problem?
@timid silo
You just need to multiply the remainder by 2
Since the division you did was technically by (x-0.5), your remainder term is -2.5/(x-0.5) which is equivalent to -5/(2x-1)
Yeah, everything you did is right except the remainder should be -5
$$\frac{8x^3-20x^+2x-2}{2x-1}$$
$$=\frac{4x^3-10x+x-1}{x-\frac{1}{2}}$$
warm shaleBOT
tatpoj
daring rock
This is what you did before you did the division, right?
And then you end up with
$4x^2-8x-3-\frac{2.5}{x+\frac{1}{2}}$
warm shaleBOT
tatpoj
daring rock
But, really you weren't dividing by x+1/2. You were dividing by 2x+1
So if we multiply the last term by 2/2 we get
$4x^2-8x-3-\frac{5}{2x+1}$
warm shaleBOT
tatpoj
daring rock
okay
You can continue factoring 8x^3-12x^2+6x-1
How do you know what you can use?
Like, why did you use 1 last time?
Do you know the rational root theorem? Or sometimes it's called the rational zero test, or something like that
So use that. What are the possible rational zeroes of 8x^3-12x^2+6x-1 ?
That's not all
No, the numerator has to be a factor of 1, and the denominator has to be a factor of 8
So you could have 1, -1, 1/2, -1/2, 1/4, -1/4, 1/8, or -1/8
No, but like, if 1/4 is the zero, it would correspond to a factor of (4x-1), for example, not (x-1/4)
So you'd have to do the multiplying and dividing thing we did up here
Yeah, synthetic division only works with things of the form (x-a)
So you have to "cheat" it a little to make it work
Or just use long division. But your directions say to use Horner so 🤷
8x^2-8x-2 ?
Should be 4x^2-4x+1
Yes
Because $\frac{8x^3-12x^2+6x-1}{2x-1} = \frac{4x^3-6x^2+3x-\frac{1}{2}}{x-\frac{1}{2}}$
warm shaleBOT
tatpoj
daring rock
This only works because you divided the numerator and denominator each by 2
You can't just divide the denominator by 2, that changes the result
Yeah, looks good
So then so far you have (x-1)(2x-1)(4x^2-4x+1)
Oh, okay yeah
daring rock
**tatpoj**
It's because we did this
We really wanted to divide by 2x-1, but synthetic division only works with something of the form (x+-a)
But really the factor was 2x-1 all along
carmine widget
Hi
obtuse pebbleBOT
@carmine widget Has your question been resolved?
young atlas
obtuse pebbleBOT
young atlas
fierce lagoon
So it is synthesis of ammonia
fierce lagoon
How many moles of ammonia are there is 10.63 g ammonia
fierce lagoon
Hydrogen has a molar mass of 1.01 g/mol
Lemme check
,calc 10.63/(14.01 + 3(1.01))
warm shaleBOT
Result:
0.62382629107981
0.9362
fierce lagoon
Sure
And then multiply that by 2.02
I wonder if intermediate rounding screwed you over
Maybe you need to put it all into one equation
fierce lagoon
Turn it into moles first
Because the equation uses moles
And then stoich
And then convert back to grams
young atlas
i got this
6.05⋅1019
molecules
@fierce lagoon whats the coeffiencent of h2o
is it 1
fierce lagoon
You dont need H2O
young atlas
ik but i want to knoiw what it is
fierce lagoon
There's no H2O in the synthesis of NH3
You don't need H2O at all
It's utterly useless
fierce lagoon
Okay I feel like that's cut off
Because no water should be produced in the synthesis of ammonia
fierce lagoon
Well that's hella important
young atlas
not sure how to find this
fierce lagoon
I'm missing information
fierce lagoon
Since O2 is the Limiting, you use stoich with the moles of oxygen
young atlas
so my clacualtion is wrong
limpid hill
HELP QUADRATIC FUNCTIONS ON A GRAPH
obtuse pebbleBOT
HELP QUADRATIC FUNCTIONS ON A GRAPH
visual epoch
YES QUADRATIC FUNCTIONS ON A GRAPH WHAT?
limpid hill
VERTEX FORM STANDARD FORM AND CONVERTING STANDARD TO VERTEX AND VICE VERSA
nocturne minnow
WATCH VIDEOS
nocturne minnow
If you don't have a specific problem you are stuck on, you are wasting people's time
So you should close this and watch videos
limpid hill
i do have a specfici problem
visual epoch
yeah, show us
nocturne minnow
And the goal is?
limpid hill
y=(x+2)^2 - 1
visual epoch
my phone died
lol
limpid hill
y=x^2 +2x -3
(this one is being converted to vertex form
y= -2x^2 +12x -10
this one is being converted to vertex as well
y=1 (x-1)^2 -5 (this one being converted to standard
idle thunder
do you know how to find the vertex of that quadratic?
limpid hill
do you know how to find the vertex of that quadratic?
which one
idle thunder
of x^2 +2x -3
limpid hill
ok thats a quadratic equation correct
idle thunder
ok thats a quadratic equation correct
yeah
limpid hill
first
idk but that one they plug y as 0 first
then found two numbers when mutliply give -3 but added give 2
then the factorize thing
i would send a picture but my phone is dead
young atlas
anyone know chem ?
idle thunder
you can factor the quadratic to find the roots, then find the axis of symmetry, then find the vertex
young atlas
rlly need some help
limpid hill
you can factor the quadratic to find the roots, then find the axis of symmetry, ...
the aos is always the x coordinate right
idle thunder
the aos is always the x coordinate right
yes
I would use this equation
vertex x-coordinate is -b/2a
limpid hill
idle thunder
then use that x coordinate to find the y value
limpid hill
here it is
limpid hill
vertex x-coordinate is -b/2a
so x cordinate is -b/2a got it
and plug that into x to find y
and you got the vertex
limpid hill
but how would u find the intercepts for both x and y
idle thunder
idle thunder
so in the space would be 1^2 right
yes, correct
limpid hill
oh you're doing it by completing the square
well that was what was in the video
idk it any other way
idle thunder
think of it like this
y + ____= (x^2 +2x + ____ ) - 3
y + 1 = (x^2 +2x + 1)-3
y = (x^2+2x+1) - 4
we added something to the RHS so we needed to add it to the LHS
nocturne minnow
we added something to the RHS so we needed to add it to the LHS
Something in response to this, it's an equation so it needs to be balance. Just imagine like scales, whatever you do to one side, you need to apply to the other to keep the sides balance. So when you added 1 in the parentheses, you need to add 1 on the other side to balance the sides
limpid hill
Something in response to this, it's an equation so it needs to be balance. Just ...
and when you add the 1 to both sides it cancels out from the left
idle thunder
what do you mean cancels out?
y + 1 = (x^2 +2x + 1)-3
-1 ...................... ...........-1
y = (x^2+2x+1) - 4
limpid hill
but in the second line the one isnt on the left side but it was on the right
-3 + 1 to -4
idle thunder
but in the second line the one isnt on the left side but it was on the right
the +1 in the parenthesis needs to stay because we need to turn the (x^2 +2x + 1) into (x+1)^2
limpid hill
the +1 in the parenthesis needs to stay because we need to turn the (x^2 +2x + 1...
well where does the one from y+1 go
idle thunder
we subtracted 1 from both sides
y + 1 - 1 = (x^2 +2x + 1)-3 - 1
y = (x^2+2x+1) - 4
limpid hill
OHHH
a
a is 1
ok
also im confused about this one too the 2 is positive but how did it become negative
obtuse pebbleBOT
@limpid hill Has your question been resolved?
timid silo
someone pls help
whas the question
limpid hill
also im confused about this one too the 2 is positive but how did it become nega...
this is it
and also why do we go down 8 units instead of 4 here
brooo
someone respond
<@&286206848099549185>
timid silo
this is it
oh sorry
i was
looking elsewhere
bsaically
vertex of a parabola is when
the (x+h)^2 term
is 0
so x=-h
what?
limpid hill
<@&286206848099549185>
timid silo
idk how to explain sory
sleek sinew
Would I prove this using AAS for the triangles to show XD = XE = XF?
And using CPCTC?
And I do not know how to prove Ray n contains point X
obtuse pebbleBOT
Available help channel!
brazen agate
How do you factorise x^2+4x−12?
obtuse pebbleBOT
How do you factorise x^2+4x−12?
sleek sinew
<@&286206848099549185>
timid silo
what
sleek sinew
Need help with showing ray n contains point X
timid silo
How do you factorise x^2+4x−12?
(x+6)(x-2)
fierce lagoon
(x+6)(x-2)
Don't give out answers
fierce lagoon
How do you factorise x^2+4x−12?
(x+a)(x+b)
a + b = 4
ab = -12
timid silo
Don't give out answers
oh
i didnt know how to give a hint for that tho
also i kinda felt like it was a joke
question
fierce lagoon
(x+a)(x+b)
a + b = 4
ab = -12
_ _
brazen agate
(x+a)(x+b)
a + b = 4
ab = -12
ight
fierce lagoon
People can struggle with conceptualization
brazen agate
thanks
brazen agate
also i kinda felt like it was a joke
I'm in seventh so like
this would be too easy for you tbh
fierce lagoon
Lol literally people in my Calc 3 class struggle with factorization 💀
timid silo
fr
fierce lagoon
Dw
brazen agate
Lol literally people in my Calc 3 class struggle with factorization 💀
Ah okay
fierce lagoon
Factorization for whatever reason seems hard for even high school seniors
brazen agate
Factorization for whatever reason seems hard for even high school seniors
thanks for the help
fierce lagoon
Np
obtuse pebbleBOT
Available help channel!
meager bison
timid silo
why did you do the same thing twice
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
meager bison
can some one help me please?
teal birch
Hey guys! I was wondering about the warnsdorff's heuristic, notably in regards to it's use in the knight's tour. I have an understanding of the general idea (starting from any initial position on the board, move the knight to the square with the lowest possible moves) but I don't understand at all the mathematics behind it and I was hoping someone could guide me onto a good direction to research for myself or to give me an overview of the mathematics.
(I've used the warnsdorff path for myself on multiple knight's tours and i'm sure it works but i don't know WHY it works and that irks me quite a bit because I have no clue where to go to find out why).
Thank you in advance! :D
obtuse pebbleBOT
Hey guys! I was wondering about the warnsdorff's heuristic, notably in regards t...
teal birch
Btw please ping me if you're going to respond, would be highly appreciated :D
obtuse pebbleBOT
@teal birch Has your question been resolved?
teal birch
.close
grizzled bay
obtuse pebbleBOT
grizzled bay
I would like help as soon as possible, this is a timed homework assignment and only got 20 minutes left
olive swan
Wait
grizzled bay
I just need to know the inequalities to graph
pale maple
obtuse pebbleBOT
pale maple
Hey I’m having trouble solving number 23!
<@&286206848099549185>
It's the setting up thats getting me. I understand that if we were to only look at it in the x y axis, we can get a figure and use that to find the bounds
obtuse pebbleBOT
@pale maple Has your question been resolved?
pale maple
.close
stoic condor
Wouldn't Option D also be correct?
obtuse pebbleBOT
Wouldn't Option D also be correct?
daring rock
Depends on the question, I guess
But yeah option D would be equivalent to B for whatever function f is
stable rain
lol ye
obtuse pebbleBOT
@stoic condor Has your question been resolved?
undone ember
obtuse pebbleBOT
undone ember
could someone explain to me how the equation above was changed to the equation below
mental plaza
common denom
spice citrus
add 6 to both sides and factor out the y', then divide by the stuff that doesn't contain a y' on the left
sacred totem
obtuse pebbleBOT
next reef
sacred totem
I simply couldn't prove it
I tryed some stuff
1 sec
Excuse my writing
I don't think antg is useful here
obtuse pebbleBOT
@sacred totem Has your question been resolved?
sacred totem
. reopen
obtuse pebbleBOT
Available help channel!
mental plaza
hey
spice citrus
where do the curves intersect?
spice citrus
the bounds are where they intersect: x^3 = x
mental plaza
how do I find that
spice citrus
subtract x and factor
spice citrus
yeah, there are 2 areas
mental plaza
x=0 or x= 1 or -1
spice citrus
Maybe the mean the combined area?
yes
let's just consider the area between 0 and 1, if you want the area of both areas just multiply the answer by 2
so, which function is bigger on the interval 0 to 1?
spice citrus
a function f is odd if f(-x) = -f(x) for all x
mental plaza
ohhh
spice citrus
in other words: you can rotate a point on the graph by 180 degrees around the origin and the point will still be on the graph
but which function is bigger on the interval?
mental plaza
but which function is bigger on the interval?
hi I’m back
spice citrus
well want to find the area, which is always positive
so you need to integrate over 1 function minus the other
,w graph y = x, y = x^3
warm shaleBOT
spice citrus
what function is bigger for 0 <= x <= 1
obtuse pebbleBOT
@mental plaza Has your question been resolved?
warm shaleBOT
Jelle
maiden pollen
so what we need is $\int_{0}^{1}\left(x-x^{3}\right)dx$
that's not what you need
obtuse pebbleBOT
that's not what you need
maiden pollen
what yall need is jesus
obtuse pebbleBOT
@maiden pollen Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
elfin lagoon
What does -> mean in first order logic and can someone give me an example of a real world activities -> can be used in
obtuse pebbleBOT
What does -> mean in first order logic and can someone give me an example of a r...
elfin lagoon
Like q->p
drifting wraith
"if the kettle is boiling it has water"
elfin lagoon
Can -(r^p) be translated to something cannot be both the colour red and purple?
scarlet gale
What does -> mean in first order logic and can someone give me an example of a r...
It means the first part is false or the second part is true.
A → B means that if A is true, then B has to be true as well.
So, if A is false, it doesn't have to do anything extra.
elfin lagoon
It means the first part is false or the second part is true.
Wouldn’t it mean everything in the brackets is false?
scarlet gale
If B is true, well, A is fine either way.
I'm talking about the → part you started with, not the ¬(r ∧ p).
elfin lagoon
Oh ok
scarlet gale
It's like a promise.
If A happens, B will happen too.
If A happens, B has to happen.
If A doesn't happen, it doesn't matter.
elfin lagoon
Ok thanks
scarlet gale
¬ means everything but this.
So, ¬(r ∧ p) means it can be anything except red and purple at the same time.
So, it could be red but not purple.
It could be green.
With DeMorgan's, ¬(r ∧ p) ≡ ¬r ∨ ¬p.
So, it's either not red or it's not purple or neither one.
elfin lagoon
K thanks
scarlet gale
No problem.
timid silo
obtuse pebbleBOT
timid silo
the one above
obtuse pebbleBOT
@timid silo Has your question been resolved?
clever vigil
What is your question @timid silo
timid silo
the one above in the photo
clever vigil
What did you not understand ?
obtuse pebbleBOT
@timid silo Has your question been resolved?
solemn osprey
by substitution with infinity its indeterminate
I think I have the answer, but I only have reasoning, not necessarily a proof
timid silo
say
solemn osprey
When taking limits to infinity, it’s important to consider the rate of increase
Of all the term, n, n^2, 2^n, 3^n, and 5^n, 5^n will always come out on top as the fastest grower
Eventually 5^n overtakes all of the other terms
Here’s a rule of thumb: a quadratic function (like n^2) eventually overtake a linear function (n)
And exponential functions( like 2, 3, and 5^n) eventually overtake quadratic functions
You with me so far?
solemn osprey
You understand everything and agree with everything?
timid silo
im quite confused honestly
solemn osprey
Okok that’s good u told me
timid silo
we havent been thought that many things on limits so far
i was thinking about the limit being 0
by trying to show concrete examples of n and seeing that there are decreasing fractions
solemn osprey
I think it’s actually 3/6
Because those are the coefficient of the biggest, fastest growing functions
Coefficients of 5^n
solemn osprey
OHHHHHHH
solemn osprey
My bad my bad
timid silo
thats why i couldnt understand where 5^n appeared
solemn osprey
Lol
Actually, kind of the same reasoning there
(1/2)^n is a kind of exponential that goes to zero
And it grows smaller way faster than a linear function grows bigger
timid silo
yes
timid silo
yes
solemn osprey
This problem I can actually use a proof, but idk if u guys learn lhopital’s rule or not
solemn osprey
Lhopital’s rule basically compares the growth of functions, and finds the net growth so to speak, but let’s just stick with reasons not proofs
timid silo
thats the only thing i can think about regarding this exercise
solemn osprey
Yes result is zero
solemn osprey
Point is. Exponential growth, either smaller ir bigger, are faster than a lot of things
So they usually overtake them and, in the end, determine the “net growth” either being growing bigger or growing smaller
R u helping or getting help? Plz claim ur own help channel
clever vigil
$0 \leq \frac{1}{2} \leq 1$
warm shaleBOT
Surv
clever vigil
Thats why lim 1/2^n = 0
solemn osprey
Facts ^^
timid silo
yes but i was confused by the multiplication by n which by substituion will lead to an indeterminate
solemn osprey
But also (1/2)^n goes to zero faster than n goes to infinity. (1/2)^n wins
solemn osprey
YUSSS
timid silo
lets go
solemn osprey
SUCESSSSSS
timid silo
finally
solemn osprey
timid silo
thanks bro
solemn osprey
Np bro
timid silo
.close
lofty wraith
I dont understand this problem (its 2^N not 2N)
obtuse pebbleBOT
I dont understand this problem (its 2^N not 2N)
@lofty wraith Has your question been resolved?
unique anchor
halp me
unique anchor
I don't understand this picture
what is x + h=
how do they conclude that is the length of h?
etc
rotund rune
x+h is basically an arbitrary point picked
the distance from x+h to x is, logically, x+h-x = h
unique anchor
x+h is basically an arbitrary point picked
I don't get it
rotund rune
say you have a graph y with a point (x, f(x))
unique anchor
say with a,b instead, f(x) confusing
rotund rune
then, you pick an arbitrary point with distance h from x, which would mean that point is (x+h, f(x+h))
rotund rune
say with a,b instead, f(x) confusing
what...
unique anchor
then, you pick an arbitrary point with distance h from x, which would mean that ...
What does f(x+h) - f(x) mean?
isn't it just supposed to say f(x+h)?
why the -f(x)
rotund rune
f(x+h)-f(x) means the distance between f(x+h) and f(x)
unique anchor
oh
true
What does it mean "derivative of f at x" is it same as derivative of f(x)?
rotund rune
derivative of f at x means we're deriving f wrt to x
rotund rune
what...
obtuse pebbleBOT
@unique anchor Has your question been resolved?
silver plover
dont understand how they got to the answers tbh
spice citrus
if it's a field there needs to be an additive identity, in the case of R\Q that should be 0, but 0 is an element of Q, thus not an element of R\Q
for iii: the multiplicative identity is 1, the multiplicative inverse of a is the number b, such that for b in Z, a * b is the multiplicative identity, but 2 * 0.5 = 1 and 0.5 isn't an element of Z
for iv: the additive inverse of a is b, if a + b = 0, because 0 is the additive identity, but if a = 1 for example then 1 + b = 0 => b = -1, which is not on the interval
sacred verge
obtuse pebbleBOT
sacred verge
I don’t get what is the question looking for?
royal basin
sort the values from smallest to largest
sacred verge
In option a
Are they already sorted so
What about c option, how can we make all the ratios the same?
Such as only, cos or only sin
@royal basin
royal basin
yes, in a they are already sorted
for b you might want to know that sin(x) = cos(90°-x)
obtuse pebbleBOT
@sacred verge Has your question been resolved?
slim leaf
You can try putting some values of n to observe if its increasing/decreasing
Then use induction
Okay so assume a_(n+1) >= a_(n) for some n
You have to show a_(n+2) >= a_(n+1)
Oh decreasing
Yes
Mb
sacred verge
for b you might want to know that sin(x) = cos(90°-x)
What about c
obtuse pebbleBOT
@timid silo Has your question been resolved?
slim leaf
@timid silo Sorry for the late reply but it seems induction is long.
slim leaf
You can try rationalizing and then you'll come to $\frac{1}{(n) \sqrt{n+1} + (n+1) \sqrt{n}}$
@timid silo Well I hope you see what Im trying to say
And then it should follow easily without induction that the sequence is decreasing
.close
fickle niche
Hello, i have a question about when calculing delta
obtuse pebbleBOT
Hello, i have a question about when calculing delta
fickle niche
i have x - 1, how to calculate delta ?
untold flax
why'd your denominato rchange from x + x to x + 1
fickle niche
no its x + 1
untold flax
ok
fickle niche
i wrote bad in the first line
untold flax
also I still don't see a delta here
fickle niche
but i need to solve the inequation
and for that i need to find delta
to calculate x
untold flax
this is a delta
fickle niche
yeah
untold flax
and for that i need to find delta
? there's no delta there though
you don't need delta to calculate x
fickle niche
b2 - 4 . ac
untold flax
oh discriminant
fickle niche
yeah
untold flax
you still don't need that
fickle niche
so how
untold flax
ok so we have 2 cases, when x = -1 and when x is not equal to -1
when x is not equal to negative 1 we can just mutliply by x + 1
wait sorry what I mean to say is
it's not defined at x = -1
after you multiply by x + 1 what do you get
fickle niche
i understand the x cant be equal to + 1 but what do i need to do
untold flax
get it in the form of ax^2 + bx + c
because we can solve those
to do that we need to remove denominator though
fickle niche
but we dont have a b c
untold flax
so how do we do that
untold flax
but we dont have a b c
no not literally, they just repeesent the coefficents
we need to get it in the form ax^2 + bx + c where a, b and c are real numbers
fickle niche
ok and what is b
untold flax
b is the coefficient of x
fickle niche
so 1
untold flax
you're skipping a step though
fickle niche
and to find a coefficent that we dont have
untold flax
ye just to get rid of denominator
untold flax
ye
sturdy meteor
Ummm wait do u guys allow middle schoolers in here
fickle niche
on the x2 + x i need to multiply by x + 1 ?
untold flax
Ummm wait do u guys allow middle schoolers in here
if you're above 13 then yeah
untold flax
on the x2 + x i need to multiply by x + 1 ?
no why
just need to get rid of denominator
untold flax
0 * (x + 1) = x+1 ? 🤔
sturdy meteor
ok i guess it's fine
untold flax
yes well I am almost 14 years old.
yes it's fine then
fickle niche
0 * (x + 1) = x+1 ? 🤔
i got rid of the denominator
fickle niche
why does it not
fickle niche
oh you mean i could do that from the beginning ?
untold flax
no
well you could've
I'm saying that what you wrote is wrong
you multiplied the left side corectly, not the right side
fickle niche
so its 0? on the right
untold flax
factor the left hand side
untold flax
yes
fickle niche
now i need to do that tab
the sign tab
but i need to put the impossible (from factor x)
untold flax
it's irrelevant in this case
since it's less than or equal to
what's x less than or equal to
fickle niche
0
untold flax
there you go
sour jungle
Could anyone help me solve this integral?
obtuse pebbleBOT
Could anyone help me solve this integral?
kindred bear
sage geode
Post your question in an available help channel
stray yew
how do i graph y=-4x^2
sage geode
Post your question in an available help channel
stray yew
how do i know whoch one is available
sage geode
You see the #❓how-to-get-help and the help-forum?
There are 3 available channels below them
24, 25 and 32
last crow
hi