Omega =2πf
#help-26
rough mesa
A tank contains 40.0 L of a mixture of plant fertilizer and water, in which 20.0% of the mixture is fertilizer. How much of the mixture should be drained and replaced with an equal amount of water to dilute the mixture to 15.0% fertilizer?
civic nymph
valid ice
Rad/s
topaz sinewBOT
@civic nymph Has your question been resolved?
covert current
Do you know what a proportional relationship is
A proportion is a ratio basically
Do you know what a ratio is
Ok so if I have 100 apples and 25 bananas
Is it a test?
ummmm
You can’t do that
You can get banned
thorn briar
.close
topaz sinewBOT
covert current
Bro
topaz sinewBOT
Available help channel!
burnt crown
how do i calculate these?
topaz sinewBOT
how do i calculate these?
burnt crown
could somebody maybe send a path on how to solve them
topaz sinewBOT
@burnt crown Has your question been resolved?
whole zephyr
topaz sinewBOT
whole zephyr
I've been stuck on this problem for like 20-30 min. The answer is not .76% please help <@&286206848099549185>
jade meadow
i have an approximate guess on how this should work
(im not 100% sure, but reasonably sure)
try finding the final growth
like the total change in those years
and then put that as a decimal, and raise it to the power of 1/5
whole zephyr
the total change is 3.8%
jade meadow
no, like
growing by 5.5% and then 1.1%
isnt growing by 6.6%
because growing by 5.5% means multiply by 1.055
jade meadow
did u do like 1.055x1.011x.965x.989x1.018
for each growth, you multiply by (1+percentage/100)
jade meadow
so we have 1.03627495 times our original value
now assume we have n% growth rate for all five years
what would n be to make the total growth be 3.6...%
whole zephyr
but it wants the mean growth
but just dividing that by 5 doesnt get me the right anwer
jade meadow
because it's exponential
growth is exponential
so you would need (1+n/100)^5=1.03627495
||i got 0.7152 from this||
whole zephyr
.close
topaz sinewBOT
jade meadow
i do but this isnt the right place to ask because this channel is occupied @agile ruin
prob move to #math-discussion or sm
agile ruin
Where should i ask ?
topaz sinewBOT
Available help channel!
formal sentinel
which rule did they apply to take out the i
topaz sinewBOT
which rule did they apply to take out the i
rigid ivy
which rule did they apply to take out the i
$\frac{1}{i}=-i$
thorny flameBOT
SWR
formal sentinel
.close
kind bridge
How do I integrate from 0 to 3 √(x^2+9)? I think I have a general idea on the steps, but I'm not sure.
topaz sinewBOT
How do I integrate from 0 to 3 √(x^2+9)? I think I have a general idea on the st...
kind bridge
I got x/(2√(9-x^2)) - (1/2) [ ln |(9+x√(9-x^2))/3√(9-x^2)| ] 0 to 3, but I don't think this is right.
topaz sinewBOT
@kind bridge Has your question been resolved?
kind bridge
.close
cyan creek
How many arrangements of UNIFORM such that U is to the right of M
cyan creek
It would be half of the total, but my teacher wrote made the M and U into variable X so XXNIFOR and did the permutations of this. I don’t really understand how it works
topaz sinewBOT
@cyan creek Has your question been resolved?
willow helm
topaz sinewBOT
willow helm
idk where to start
tbh
it doesn't have an upper limit so i'm just confused
and the graph for secx just goes up forever
silver wasp
were you able to at least draw the region?
willow helm
no
silver wasp
can you try?
willow helm
ik what it looks like but it just doesn't make sense to me
cus secx is a upward parabola
and they don't give an upper limit
so im confused
silver wasp
yeah but you know the range of x yeag?
silver wasp
yeah
silver wasp
sure
willow helm
yes
willow helm
can you set up the integral?
silver wasp
correct
silver wasp
yes
silver wasp
yup
willow helm
.close
fresh wyvern
this doesnt look right 🙄
topaz sinewBOT
this doesnt look right 🙄
tough nest
the cos 2x?
opal vault
Aye you might need parentheses
Cos(2x)
I can only assume your calculator intrepreted it as cos(2)x because of the lack thereof
fresh wyvern
i was doing (cos(2(.1))
opal vault
Yep always parentheses
topaz sinewBOT
topaz sinewBOT
Available help channel!
chrome kernel
topaz sinewBOT
chrome kernel
for parts c,d, how does one find the requested n for the desired margin of error?
doubtful that $\frac{s_n}{\sqrt{n}}t_{n-1,\alpha/2}=0.05$ is analytically solvable
thorny flameBOT
elrichardo1337
chrome kernel
and im not sure if im supposed to use the fact that t converges to the normal for very large n here
topaz sinewBOT
@chrome kernel Has your question been resolved?
chrome kernel
<@&286206848099549185> can anyone help clarify the above 😭 should i just use z score instead
topaz sinewBOT
@chrome kernel Has your question been resolved?
topaz sinewBOT
@chrome kernel Has your question been resolved?
chrome kernel
.close
topaz sinewBOT
fair thorn
tbh idk much about chem
more of the bio/physics guy
BUT
okay-
that works too
damn @shell forum
fair thorn
LOL
topaz sinewBOT
shell forum
and disallowed by the rules of the server
😭
fair thorn
ik lol
lucid junco
You’re better off watching an organic chemistry tutor video. He has tons of videos on finding this stuff
topaz sinewBOT
Available help channel!
neon iron
hi i need help
topaz sinewBOT
hi i need help
versed cairn
cross multiply and simplify
neon iron
should i ignore the b?
thorny flameBOT
JustToPro
neon iron
ahh ic
wait lemme try solve it
you can cross multiply if one of numbers have the letter thing right?
versed cairn
yeah
neon iron
sorry i literally know no techincal terms 😭
versed cairn
yeah
topaz sinewBOT
topaz sinewBOT
Available help channel!
frail patrol
I have this problem that I am unsure of how to approach.
Prove that {(1-x),(1+x)} is a base for P_1(ℂ)
Any help appriciated. I am generally familliar with bases etc. But this question confuses me.
opal vault
Never had instances of proving something was a base?
frail patrol
nope, this is the first. I've done "prove subspace" but i am confused what to do here I understand that (1-x) and (1+x) would be the two vectors of the vector room that contains all Complex numbers
but not sure where to start
opal vault
What does being linearly independent mean?
frail patrol
That they can't be a linear combination of each other, i.e. not paralell in this case
frail patrol
In the complex plane? Probabaly not...
well not... that i can see, but should I use the proof that there is no a, so that (1-x)=a(1+x)
for any scalar a that is a member of Real Numbers
THat would solve the first part I guess....
frail patrol
I assume that means the vecctor space with one imaginary axis and one real axis
opal vault
No, really not
opal vault
The vector space of polynomials of degree less or equal to 1, with complex coefficients
You know, like iX + 2i + 1
or more generally, aX + b with a and b complex numbers
frail patrol
oh, right... yeah I'm with you now
opal vault
Exactly
First question solved, we have linear independence
Now generating (or spanning)
frail patrol
so is it enough to say that these two vecotrs constitues a base because the vector space is 2 dimensional (but how to prove this?) and that these are two non-paralell vectors in that space?
opal vault
Aye P1(C) is 2-dimensional
But that would require a basis
If you can name a basis as to why this true
frail patrol
lemme think...
opal vault
You have unconsciously used the fact that something else was a basis to show linear independence...
frail patrol
feels like I am looping here and not actually proving
frail patrol
That any vector in the space P_1 can be written as a linear combination of (1-x) and (1+x)
<@&286206848099549185>
finite quail
To prove that {(1-x),(1+x)} is a basis for P_1(ℂ), we need to show that the set is linearly independent and spans the vector space P_1(ℂ).
Linear independence means that there are no non-trivial linear combinations of the vectors that result in the zero vector. In other words, if a(1-x) + b(1+x) = 0, then a = b = 0. This can be seen by equating the coefficients of x and the constant terms:
a - b = 0 a + b = 0
Adding these equations gives 2a = 0, so a = 0. Subtracting them gives 2b = 0, so b = 0. Therefore, the set is linearly independent.
Spanning means that any vector in the vector space can be written as a linear combination of the vectors in the set. In this case, any polynomial of degree 1 or less in P_1(ℂ) can be written as a(1-x) + b(1+x) for some complex numbers a and b. For example, if we want to write 2x + 3 as a linear combination of (1-x) and (1+x), we can solve for a and b as follows:
a(1-x) + b(1+x) = 2x + 3 a - ax + b + bx = 2x + 3 (a + b) + (-a + b)x = 2x + 3
Equating the coefficients of x and the constant terms gives:
a + b = 3 -a + b = 2
Adding these equations gives 2b = 5, so b = 5/2. Subtracting them gives 2a = 1, so a = 1/2. Therefore, 2x + 3 = (1/2)(1-x) + (5/2)(1+x). This shows that the set spans P_1(ℂ).
Since the set is linearly independent and spans P_1(ℂ), it is a basis for P_1(ℂ).
reply
urban grove
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
full hazel
topaz sinewBOT
full hazel
don't understand some of these
so 10a
is f(x)-g(x)
i get that
this is inverse
but i don't know how to do the other ones
like what is (gof)(x)
neat surge
gof composition of 2 functions, (gof)(x) = g(f(x))
full hazel
gof composition of 2 functions, (gof)(x) = g(f(x))
what about 10b
just x^2+ 8 divided by x-5?
neat surge
yup
bitter hemlock
like what is (gof)(x)
by the way, it is read out loud g of f of x, so you can remember that circle kinda looks like the o of "of"
full hazel
ty
neat surge
(-1^2 +8)( 1/ -4)
-4?
bitter hemlock
but simplify it to: (x^2+8)(x-5)
full hazel
right right
neat surge
and (-1)^2, but yah correct
neat surge
mhm
topaz sinewBOT
topaz sinewBOT
Available help channel!
hollow plinth
topaz sinewBOT
hollow plinth
This question is asking me a few parts.
- How many cars has warren sold in a month.
- How many days has warren worked last month
I dont understand how to get the answer with the data provided
- 103 cars sold
- 21 days
Is this correct ?
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
neon iron
given 0 <= x, if for every epsilon greater than 0, x <= epsilon ====> x = 0
i did by contradiction i assumed x is not equal to 0
then x > 0,[because x != 0] , x <= epsilon, then we take epsilon to be x/2 and then x <= epsilon = x/2
but my question is isnt x/2 less than x and its given that epsilon is greater or equal to x?
neon iron
is it because of "for every epsilon" ?
robust zenith
is it because of "for every epsilon" ?
Yeah, that is the important part. Since you prove it by contradiction, you assume these two statements:
for every epsilon greater than 0, x <= epsilon
and
x > 0
It would be cleaner to prove it by using the contrapositive statement (and very similar).
To prove the implication p=>q, you can equivalently prove (not q) => (not p).
So you assume that x > 0. Then you need to prove the opposite of for every epsilon greater than 0, x <= epsilon, which would be
there exists an epsilon greater than 0, such that epsilon < x.
The last part, you have proven by choosing epsilon = x/2 > 0. It exists, and so you are done with the proof by contrapositive.
neon iron
how do you negate the original statement though
you start from the end to begining?
and negate the begining?
robust zenith
The original statement has the form of an implication p => q. You might know that this is the same as (not p) or q.
So the negation of an implication is (by DeMorgan's rules) p and (not q).
So to be specific, the negation of this statement:
for every epsilon greater than 0, x <= epsilon ====> x = 0
is equal to this statement:
(for every epsilon greater than 0, x <= epsilon) and (not x = 0)
neon iron
alright. thank you 👍 for me contradiction works better
robust zenith
np
neon iron
.close
olive stream
in terms of linear regression, what is the difference between a confidence and a prediction interval?
topaz sinewBOT
in terms of linear regression, what is the difference between a confidence and a...
olive stream
despite the $ +1 $ one has to add underneath the squareroot when calculating it
topaz sinewBOT
@olive stream Has your question been resolved?
olive stream
<@&286206848099549185>
topaz sinewBOT
@olive stream Has your question been resolved?
sweet shard
despite the $ +1 $ one has to add underneath the squareroot when calculating it
Show the two formulas you want explained
topaz sinewBOT
neat surge
99.4% chance 3 students score an A...?
how did you calculate this, it doesn't make sense
oh sorry
lemma check it
gosh i suck at probability
you mean 0.6?
yah i think that's correct
how did you do 11
94.15% looks good
if my math is right
topaz sinewBOT
@sweet remnant Has your question been resolved?
abstract wadi
It's an arithmetic progression.
narrow torrent
Linearity of the summation operator
gleaming thunder
Linearity of the summation operator
this is not an undergraduate student, avoid using vocabulary that is confusing much more than anything else
narrow torrent
Linearity is simple, it just means additivity and homogeneity of degree 1
To put it in simpler terms
gleaming thunder
you're trolling surely
narrow torrent
Not sure how much simpler it can get
gleaming thunder
actually explaining the thing
You know, like a HS teacher would/should
narrow torrent
When you do the big E to the thing it's the same thing as doing the big E to everything inside the thing
gleaming thunder
which this is not
gleaming thunder
$\sum_{r=1}^n (4r-6) = 4 \sum_{r=1}^n r - \sum_{r=1}^n 6$
thorny flameBOT
Bezier
neat surge
gleaming thunder
I shall now know to never interact positively with you ever again
Thank you for letting me know about you
narrow torrent
Lmao!
gleaming thunder
that's the point
gleaming thunder
**Bezier**
There's a formula you should know
gleaming thunder
It's an arithmetic progression.
because there's something you should notice
For which you may or may not use my remark
yeah
it depends a whole lot on the depth
and on your speed
can't answer that
best way to know is look at how long the national curriculum spends on the whole syllabus, what fraction of it this is, count how many hours that is, and have an idea of the ratio between the official hours and how many hours it takes you
something like that
it's easily 100h of work, depending on the depth and progression expected
but it's very hard to quantify
Could be 40
Could be 200
I just did all this stuff on khan academy some 4.5 years ago
time flies
gleaming thunder
I just did all this stuff on khan academy some 4.5 years ago
I'm not sure I'm the best person to answer that
but most of it seems pretty well ordered as is (column 1 then column 2)
Except maybe move vectors to before/after coordinate geometry
Unless it's vector functions, then after all the calculus stuff
nvm it's basic vector stuff
That goes hand in hand with coordinate geometry
the goal is to not spend 20 min on that
that's a simple question if you know your theory properly
Like 3 min if you're pretty competent
you were getting somewhere weren't you ?
well, find a and l
so that this formula can be used properly
well clearly that can only be achieved for a negative n
Are you sure about that ?
gleaming thunder
well clearly that can only be achieved for a negative n
Are you sure about that ...
turns out it also can't be achieved by a negative n
This expression is negative if n gets any kind of large, so it can't equal 720
try applying it better
I recommend you reread that bit of your lessons, and try to understand the idea/intuition
yeah no, largest term is 506, you get 128 of them
So that would sum to like, 30000
you don't try to learn math because you're bad at it
You try to learn math because you want to
though as a math major it's kind of because you must
But you must because you chose to
gleaming thunder
I recommend you reread that bit of your lessons, and try to understand the idea/...
go read that again, and do it by very small steps, making sure each one is correct
gleaming thunder
yeah no, largest term is 506, you get 128 of them
So that would sum to like, 300...
then you can also try and figure out how I managed to give the approximation of 30k (32k would be more accurate) using this formula
sequences and series is standard calc material
but this is child's play at that level
For instance, I see this and just go
||"ah yeah so this evaluates to a quadratic, then if they're nice I can spot a factorization, otherwise I just throw the quadratic formula at it and I'm done in under a minute, I just don't feel like writing it all out"||
gleaming thunder
go read that again, and do it by very small steps, making sure each one is corre...
see for yourself
it goes under the same name
It's much more advanced
you have no classes and lectures, only exercises ?
Bad method
don't "briefly look over" something you want to memorize long term
that's about as bad a method as it gets
I just used khan academy, but there are also many other ressources out there
I'm not very knowledgeable about them though
but KA is still very standard
topaz sinewBOT
topaz sinewBOT
Available help channel!
gentle ember
topaz sinewBOT
topaz sinewBOT
@gentle ember Has your question been resolved?
topaz sinewBOT
@gentle ember Has your question been resolved?
gentle ember
yall
noble laurel
<@&286206848099549185>
!15mins
topaz sinewBOT
<@&286206848099549185>
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.
noble laurel
the key word is once
gentle ember
my fault
wispy abyss
Uuuhh lemme look at it
gentle ember
Uuuhh lemme look at it
u got it?
gentle ember
any1 there
topaz sinewBOT
@gentle ember Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
Available help channel!
slow pasture
topaz sinewBOT
azure snow
r_1 and r_2 relate to P_1 and P_2
craggy haven
if p is (0, 0, 0) shouldn't r then just be 0?
$\vec{P_2P}$ is the vector from $P2$ to $P$
thorny flameBOT
ヘイリー
craggy haven
so then P2P would just be vector p - vector p2?
yeah
slow pasture
are they also taking absolute value?
wait
yea im dumb magnitude
ok cooool thanksss
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
winter drum
topaz sinewBOT
winter drum
is this correct
craggy haven
seems good to me, good choice of example for a.
may be helpful to ask where does your proof break down (if it does) if you remove the "nonempty" or "finite" conditions
oh that's just the first half
winter drum
ye
winter drum
oh that's just the first half
what about this one
i remembered my prof last sem doing something like this when we learnt countability
craggy haven
have fun 
that's an interesting one
craggy haven
yeah nice
topaz sinewBOT
craggy haven
rly clear explanations
topaz sinewBOT
Available help channel!
spring blaze
Not sure where i messed up
topaz sinewBOT
Not sure where i messed up
spring blaze
(forgot to add the negative, solved)
This is webassign, not sure (can't find) if there's +- button
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
quiet sorrel
do they cancel out? if so, why?
topaz sinewBOT
do they cancel out? if so, why?
ionic oar
yes they cancel out
thorny flameBOT
NEON
dense ginkgo
Sarika works twice as fast as Ajoy. If Sarika can complete the given task in 3 minutes, it will take___ to complete the task when both Sarika and Ajoy works together.
topaz sinewBOT
Sarika works twice as fast as Ajoy. If Sarika can complete the given task in 3 m...
dense ginkgo
can soemone help?
i have reached this far that sarika can complete the work in 3min and Ajoy in 1.5. How do i find it for both of them working together?
sour cliff
If both of them only have to do half I’m guessing just add half of 3 minutes and half of 1.5 minutes to get the full time
dense ginkgo
If both of them only have to do half I’m guessing just add half of 3 minutes and...
can you explain why?
ans is 2mins
sour cliff
that’s just my educated guess if we’re assuming they both do half of the task
but clearly that’s not the case
waxen flame
that's not correct
dense ginkgo
ig the answer 2mins ia lil weird
waxen flame
sarika and ajoy don't do equal amounts of work in the task
dense ginkgo
in 1min s can do - 1/3 and a can do - 2/3 so in 1 min they can togetehr finsi whys the asnwer 2mins?
waxen flame
in one minute, sarika completes 1/3 of the task and ajoy completes 1/6 of the task
waxen flame
yes
dense ginkgo
oh sorry
my calculations dumb
also
can you explain local maxima and lcoal minima to me
?
waxen flame
do you know the definitions?
dense ginkgo
not really (im an 8th grader) i just know all the maximas amnd minimas who are not the golbal are the locals
correct?
waxen flame
do you know what a maximum is?
dense ginkgo
yea a point on a graph is called maxima when it is above its neighbouring points
waxen flame
a global maximum is when it's above everything else
note that all global maxima are local maxima
dense ginkgo
oooo ty understood
also can i help me with oen mroe sum?
46247^281 fidn the units digit
i know that it has fluctuation power which will rotate between 7 9 3 1
then we divide 281 by 4
after that im lost
waxen flame
so if you know it goes 7, 9, 3, 1, then don't you know it repeats every 4 multiplications?
topaz sinewBOT
@dense ginkgo Has your question been resolved?
fresh lance
Hello
novel coral
Do u know integration
fresh lance
Do u know integration
Yeah
fresh lance
ohhhh
novel coral
are u getting the answer now
fresh lance
im trying to put it in a calculator
novel coral
Ok
novel coral
Umm
fresh lance
I don't know what I did wrong
novel coral
Mine is coming -42.9
novel coral
What is the actual answer
fresh lance
Idk it's on edfinity
novel coral
Popped the values in the calculator
wheat grove
!status
topaz sinewBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
burnt badger
When you have the variable in multiple denominators, the general operating procedure is to make a common denominator between all terms
Then you will be able to say the numerator on the left equals the numerator on the right
The product of those two denominators would be the common denominator
What you multiply by depends on each term
For example the first one is "missing" (x-3) but it has (x+1)
So the first term you'd multiply just by (x-3)/(x-3)
You need only multiply by what each term is "missing"
Keep in mind that it may be possible to arrive at extraneous solutions through algebra; these would be values that cause division by zero in the original equation
So when you arrive at the solutions you have to check to make sure they dont cause division by zero
If such a solution appears, you exclude it (this is an extraneous solution)
The common denominator to target in your problem is
(x + 1) * (x - 3)
To make that common denominator you multiply the first term by
(x - 3)/(x - 3)
That would yield
3*(x -3) / [common denominator]
Then the second term you would multiply by
(x + 1)/(x + 1)
That would yield
2 * (x + 1) / [common denominator]
Now that you have a common denominator on the left, we can add those fractions together
Overall you'd get
[ 3(x-3) + 2(x+1) ] / [(x-3)(x+1)]
So 1 you also want to rewrite with the same denominator
It's missing both the (x - 3) and (x + 1)
So we multiply both of them to top and bottom
You'd get
[(x -3)(x+1)] / [(x-3)(x+1)]
On the right side
Does that make sense so far?
At this point
Because the denominator on left and right are the same
You can conclude the numerators must be equal
So you can say
3(x-3) + 2(x+1) = (x-3)(x+1)
And you can solve as an ordinary Quadratic equation
Just keep in mind
If you get either x = 3 or x = -1
These solutions would cause division by zero in the original expression
So you cannot accept them as solutions they would be "extraneous solutions" and must be excluded as answers to the problem
So in similar problems always double check your answers to make sure they dont cause division by zero
topaz sinewBOT
topaz sinewBOT
Available help channel!
toxic aspen
Determine the equation for the tangent and the normal to the kurve:
y = cos(2x) in the point where x=pi/6
topaz sinewBOT
Determine the equation for the tangent and the normal to the kurve:
y = cos(2x) ...
toxic aspen
Any idea where i went wrong?
The answer differs from mine
at least the m value
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
jagged hatch
Hello i had to show that the set of continuous function M from [0,1] -> R with the sup metric is not compact.
I wanted to know if my reasonning is correct.
so i defined a function h from M -> R by h(f) = max (f) on [0,1]
I showed that h is continuous, and h (M) = R
Thus if M was compact, R would be compact, which is not the case and thus M is not compact
topaz sinewBOT
Hello i had to show that the set of continuous function M from [0,1] -> R with ...
@jagged hatch Has your question been resolved?
topaz sinewBOT
@jagged hatch Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
Available help channel!
spiral phoenix
Hello! Does anyone know a way to solve this integral. I tried using parity but the function is odd, not even so it doesn't work. Thanks!
topaz sinewBOT
Hello! Does anyone know a way to solve this integral. I tried using parity but t...
spiral phoenix
Here is the parity relation
knotty ledge
well for any odd function the integral from -a to a is 0
shadow vessel
ya
topaz sinewBOT
@spiral phoenix Has your question been resolved?
spiral phoenix
Wasn't it for an even function?
If f(-x)=f(x) then yeah, but not for an odd function
balmy roost
topaz sinewBOT
topaz sinewBOT
Available help channel!
dense nimbus
can someone explain me how to solve this ? my first instinct was 'it's obviously 1' but it's e. why ?
topaz sinewBOT
can someone explain me how to solve this ? my first instinct was '*it's obviousl...
@dense nimbus Has your question been resolved?
dense nimbus
i thought 1 / +inf = 0, 1 + 0 = 1, and 1 ^ +inf = 1, but it don't seem to be the correct way to solve limits
shell shard
i thought `1 / +inf = 0`, `1 + 0 = 1`, and `1 ^ +inf = 1`, but it don't seem to ...
yeah you can't just plug in infinity like this
topaz sinewBOT
@dense nimbus Has your question been resolved?
dense nimbus
yeah you can't just plug in infinity like this
what's the correct way ?
shell shard
what's the correct way ?
Well in this case there isn't really a way without having some alternative definition of e that you can apply
You can define e as that limit you posted
topaz sinewBOT
@dense nimbus Has your question been resolved?
waxen locust
I'm trying to make sense of this matrix multiplication
topaz sinewBOT
I'm trying to make sense of this matrix multiplication
waxen locust
the only way i get it to make sense, is if the defined (row) vector is represented as a column vector
you see it as V->0 = (1 0 0 0)
right?
but why is it written like that?
A would be the transformation vector
no
A is defined as column vector
not V->0
as far as i can see
oh actually yeah
A "and" current state
assuming V->0 is current state then yeah
that's right
but still is it common to use that notation for any vector?
no but you were right
yeah i get it
but then i assume that e.g. (1 2 3 4) is typically actually
(1
2
3
i guess?
as a notation for column vector
gotcha
helpful
thanks
.close
topaz sinewBOT
waxen locust
@sage siren why delete?
topaz sinewBOT
Available help channel!
toxic stirrup
how would i do this? im not sure where to start
topaz sinewBOT
how would i do this? im not sure where to start
restive inlet
try first finding the total sum of the numbers that'll be on the vertices
toxic stirrup
try first finding the total sum of the numbers that'll be on the vertices
that would be 78
toxic stirrup
note that each edge is connected to two vertices
so it would be double that?
,calc 2*78
thorny flameBOT
Result:
156
here is what i think the proof is: 156/8=19.5, which means that each sum is a decimal, but that isnt possible because we only have whole number values
restive inlet
yes
topaz sinewBOT
topaz sinewBOT
Available help channel!
inland minnow
Hey guys, I need help with this:
Jack sorts eggs into different sizes. For this purpose he has a number of isosceles triangles with an apex angle of 80° and with varying side lengths.
a) How long must the sides of such a triangle be so that an egg with a diameter of 45 mm can just slip through. It can be assumed that the organic butts on Jack's hens are completely circular!
inland minnow
and it's also given that a triangle's angle sum is 180° so we can say 180-80 = 100 → 100/2 = 50, so the two other angles is 50 each
The circle in the triangle is the egg. Now I have to find the side lengths
topaz sinewBOT
@inland minnow Has your question been resolved?
inland minnow
<@&286206848099549185>
keen valley
The circle in the triangle is the egg. Now I have to find the side lengths
try looking at the radius and how it can interact with the sides of the triangle
inland minnow
I know, but that is the problem I need help with
keen valley
I know, but that is the problem I need help with
can you make the radius perpendicular to the sides
inland minnow
inland minnow
can you make the radius perpendicular to the sides
shown in this photo
keen valley
shown in this photo
alright do you know trig
keen valley
soh stands for Sine = opposite over hypot
cah is cosine = adjacent over hypot
and toa is tangent = opposite over adjacent
ill draw it out
X represents measure of the angle
And you choose opposite and adj based on which angle you're using
Opposite will always be the side opposite the angle, and adjacent will always be the side adjacent. (Hypot. Doesn't change)
inland minnow
thanks, I'll try calculating
topaz sinewBOT
@inland minnow Has your question been resolved?
inland minnow
Opposite will always be the side opposite the angle, and adjacent will always be...
how do i calculate the side lengths from only three angles
keen valley
how do i calculate the side lengths from only three angles
ok so we have the tiny triangle we created with angles of 40, 90 and 50 correct?
inland minnow
yes
keen valley
in that triangle we also have a leg of 22.5 cm bc of the radius right?
inland minnow
yes
keen valley
if we find the hypot of that triangle what can we do with it
inland minnow
ok but how do I find that one then?
keen valley
so we have all angles and one leg, we are finding the hypot do you want to use sine or cosine
inland minnow
I'll do with sine
keen valley
what will the substitutions be for sinx=o/h
inland minnow
I don't know, what you mean?
keen valley
im using o/h as opposite over hypot
inland minnow
yes
inland minnow
ohh, I'm so sorry, now I understand
outer cloak
How do i divie this shape into 4 equal and similar pieces?
topaz sinewBOT
How do i divie this shape into 4 equal and similar pieces?
outer cloak
It contains 24 squares so 6 squares each piece
But idk how to make the form similar
.close
topaz sinewBOT
keen valley
.
So take the number and add it to 22.5 to get the full length of the line splitting the triangle and lastly use trig agn using half the isosceles triangle and the full length u just found to get the hypot (one of the 2 equal sides on the whole triangle) and the bottom which is half the actual bottom so multiply that by 2
And you're done
inland minnow
So take the number and add it to 22.5 to get the full length of the line splitti...
i don't know if I did it correctly but I got the hypot to be 35.003? Should I add that to 22.5?
keen valley
i don't know if I did it correctly but I got the hypot to be 35.003? Should I ad...
What did you input to get 35
topaz sinewBOT
Available help channel!
inland minnow
(I use maple) (don't really know if that's how I should've used your formula)
inland minnow
What did you input to get 35
.
inland minnow
thanks,
inland minnow
Yeah add that to 22.5
one more thing...
what does trig agn stand for
keen valley
Trig is short for trigonometry
Remember that's only the height of the isosceles triangle, u have to do 2 more eqs for it to find one of the legs that are equal and other u find is half the base. Just multiply that by 2 and u have your sides
Gl man
inland minnow
thank you for the help, I appreciate it man
inland minnow
thats fine, thanks
topaz sinewBOT
@inland minnow Has your question been resolved?
cyan elm
topaz sinewBOT
cyan elm
I got:
a. C(1)=1, C(2)=2, C(3)=4
b. C(n)=C(n-1)+C(n-2)+...+C(1)
but i'm pretty sure it's wrong, could someone help me out?
topaz sinewBOT
@cyan elm Has your question been resolved?
grand bough
topaz sinewBOT
grand bough
For this problem im aware there is 1 root, but im confused on the difference between the wording
For exactly and at least
Like what differentiates the two?
restive inlet
exactly one means only one and definitely no more than that
at least means there could potentially be more
grand bough
Yes, but in an exam situation how would i know if its an atleast or an exact
Is it based on the brackets?
Im guessing for this one it would be 1 exact since it has the closed interval bracket
molten vine
What if the function goes to 0 on (1,2)
grand bough
At least?
restive inlet
consider if there's a way for you to introduce more roots without conflicting with the given info
note that atm, you're just given distinct points and the condition of continuity
grand bough
consider if there's a way for you to introduce more roots without conflicting wi...
sorry im not too sure what that supposed solution is
restive inlet
it'd help you visualise if you were to plot these points
grand bough
Ok ill try that
restive inlet
and consider what ivt states
note that it states "at least one" instead of "exactly one"
grand bough
restive inlet
try and make crazy stuff happen in between
points don't need to be connected smoothly
grand bough
Sorry, im not sure what u mean 😭
restive inlet
going just horizontally isn't the only way to get from B→C above
grand bough
I’m sorry but im still a but confused, are you saying there could be an additional potential point?
restive inlet
no
i'm saying you don't have to go efficiently between points
and that you can make pretty much anything you want happen in between (while still satisifying properties of a function/continuity)
grand bough
Right but how does that differentiate when its exact
grand bough
Like what?
restive inlet
given equation
info about derivatives/increasing/decreasing
here, you're given nothing concerning that
topaz sinewBOT
topaz sinewBOT
Available help channel!
iron widget
this is a question in my book, it doesnt tell me the answer but i think its D) 5, the way i've come to that conclusion is that ive rearranged them in order, then found the lcm to make them all the same denominator and picked 5 because 5x/30 is the middle, so D) "5". however i do believe this is not correct and im using the wrong way to find the answer
topaz sinewBOT
this is a question in my book, it doesnt tell me the answer but i think its D) 5...
gray storm
I would first calculate the value of x and then calculate the median
iron widget
I would first calculate the value of x and then calculate the median
but how? shouldnt i have more stuff to find the average?
gray storm
Like adding them isn't that hard and there's a reason mean is given in the question
iron widget
Like adding them isn't that hard and there's a reason mean is given in the quest...
ill try to add them then 1 sec
thorny flameBOT
iron widget
x is 30
i got 5x/3
but then i just move /3 so it becomes 5x = 3 then x = 3/5
or is that wrong
i dont see how u got x = 30
gray storm
Mean is sum/number of elements
iron widget
Mean is sum/number of elements
i know that but im tryna find x and im not getting 30
mean is given in the question but i cant seem to figure out why
ie not sure which step id use it in
gray storm
(5x/3)/5=10
iron widget
(5x/3)/5=10
i think i finally got the answer
oh forgot to write median is the middle number so 5
is it right?
topaz sinewBOT
@iron widget Has your question been resolved?
topaz sinewBOT
@iron widget Has your question been resolved?
minor pollen
So I'm guessing I just post my question here and it'll turn into a channel?
I'm finding the amount of work it will take to pump water out of a tank, I just want to know where I'm wrong at. Also a couple of smaller questions needing clearing up.
topaz sinewBOT
@minor pollen Has your question been resolved?
inland oak
am i going crazy or isnt this wrong???
topaz sinewBOT
am i going crazy or isnt this wrong???
sweet shard
am i going crazy or isnt this wrong???
It's not wrong
inland oak
they start with x^2+10x-3y=13 then I Assume that they do -3y-13=-x^2-10x then they multiply by negative 1 but then its supposed to be 3y+13?=x^2+10x
but they have 3y-13 still
sweet shard
No
inland oak
wait let me post the original question
sweet shard
They just add 25 to both sides
molten raven
they start with x^2+10x-3y=13 then I Assume that they do -3y-13=-x^2-10x then th...
If that’s part of the original question then yes, you are correct
inland oak
molten raven
And it’s not part of the original question. It’s -13, not 13
inland oak
💀
sweet shard
They just added 3y to both sides
inland oak
alright I was tweaking for no reason then
I didnt see the -13 😭
alright thanks yall, I need some more coffee
.close
real basin
would someone mind helping me with tghis one? it seems my current proof is flawed but im unsure the correct way to go about solving it.
my current logic for it is to suppose n is an even integer. this means n=2j for some j in Z. n=4k is the same as n=2(2k). k is an integer so 2k is basically any integer in Z which proves n=4k is even. similarly, n=4k+2 is equal to n=2(2k+1) where 2k+1 is also a valid int. both n values fit the definition of even so if n is even then it is also equal to n=4k or n=4k+2 for some int k
topaz sinewBOT
would someone mind helping me with tghis one? it seems my current proof is flawe...
real basin
i closed the other one
pseudo sonnet
contrapositive is probably easier for something like this
pseudo bear
For your current proof, why are 2k and 2k + 1 exhaustive?
I mean they're both valid forms of integers, but do they include all integers when put together?
real basin
contrapositive is probably easier for something like this
so i should prove that if n != 4k and n!= 4k+2 then n is odd?
real basin
I mean they're both valid forms of integers, but do they include all integers wh...
well no but dont they fall into the even integer category?? idk i dont think i fully get it
pseudo bear
Well, you're saying that 2(2k) and 2(2k + 1) are both even numbers for any integer k.
But that doesn't exclude a third form like 2(something), that aren't included in either of those, which would also be even.
For example, 2(3k) and 2(3k + 1) are both even.
But then there's 2(3k + 2) which is also even, but which isn't included in the first two.
real basin
so is the issue that while n encompasses ALL even integers, 2k and 2k+1 dont?
pseudo bear
I'm not sure what you mean.
Oh, I think I see the issue.
You're proving that 4k and 4k + 2 are both even.
But that's not what it's asking you to prove.
real basin
well yeah but if n is an even integer and those two are also even, isnt it a true statement to say n is equal to those two?
pseudo bear
Sorry, can you use less pronouns? I don't know what "those two" refer to.
pseudo bear
OK, so let's do this.
There's 6k and 6k + 2.
Those are both even.
But 4 isn't in either one of them.
So, just because they're both even and 4 is an even number, that doesn't mean that 4 is in one of them.
real basin
ah
well in that case im not really sure how to go about doing the proof. maybe by starting w the contrapositive like the other user mentioned previously
pseudo bear
Well, there are a few ways.
You can say that 2k and 2k + 1 are the even and odd integers, which combine to give all integers.
You can use induction to prove that if you have 2(2k) now, the next even number will be of the form 2(2k + 1). And then, if you have 2(2k + 1) now, the next even number will be of the form 2(2k).
You can then do that for the negative numbers.
Then you prove that 2(2(0)) is an even number.
real basin
we havent really learned induction
real basin
You can say that 2k and 2k + 1 are the even and odd integers, which combine to g...
but in this case theyre 4k and 4k+2 respectively so theyre both even no?
pseudo bear
Well, the form of even integers is 2j, right?
real basin
yeah\
pseudo bear
And j needs to be able to be any integer, right?
real basin
ohhh so its 2 * every odd integer and 2 times every even integer
pseudo bear
Right.
real basin
meaning its every even integer
ah
i see
so could my proof simply be:
if n is an even integer then n = 4k or n = 4k + 2 . Through being an even int, n=2j for some j in Z. n=4k and n=4k+2 also respectively translate to n=2(2k) and n=2(2k+1) for various values of k. Given that 2k+1 and 2k are the definitions for both even and odd integers, they would encompass all even integers. Because n is even, n would be equal to 2(2k) and 2(2k+1)?
idk phrasing it is always the hard part
pseudo bear
That's a good first draft.
real basin
how might you improve it?
pseudo bear
2j with j as any integer is the form of all even integers. 2k and 2k + 1 are the even and odd integers respectively, and so 2k and 2k + 1 put together give all integers. So, 2(2k) and 2(2k + 1) allow us to multiply 2 by any integer j. So, all even integers are of either the form 2(2k) or 2(2k + 1), which expand to 4k and 4k + 2.
Something like that.
real basin
yeah that is smoother than mine 😭
pseudo bear
It's like writing nonmath papers. Unless you're in a test, you write a rough draft, then you make revisions until it looks decent.
You can also read other people's proofs to see what makes them understandable or hard to understand.
real basin
yeah but sometimes its hard to find problems similar enough to the point they like help yk?
thank you though
pseudo bear
You're welcome.
real basin
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
inland oak
51
inland oak
So I was just wondering but if you put the eigenvectors in a different order then you get a different equation so that for example the textbook provides this equation but i had it so x^2/12+y^2/4=1. is my answer still correct?
also since its in a different order then for the Q matrix, we would have a different rotated coordinate system no?
heres the full answer, i have my sketch flipped around
would the first eigen vector be the x axis and the second eigen vector be the y axis?
topaz sinewBOT
@inland oak Has your question been resolved?
split cloak
Do you know how to solve equations?
icy sky
split cloak
Ig 0
topaz sinewBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
split cloak
Well if it's an expression then it's not possible to simplify
lusty cedar
can anyone help me out?? i feel like im supposed to use iterative approach and i feel like my calculations are right but ig theres an error
topaz sinewBOT
can anyone help me out?? i feel like im supposed to use iterative approach and i...
lusty cedar
i feel like it might be related to the force acting on the ball by the air but i've got no idea how to calculate that
topaz sinewBOT
@lusty cedar Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
Available help channel!
maiden wave
topaz sinewBOT
maiden wave
whats voltage at A --- B
i get -10v, but answer is 30v somehow
30 would only make sense if 10v was flipped or current flowing in other direction no ?
teacher made a mistake then, i can't possibly wrong
craggy haven
you're probably going to have to show work
maiden wave
you're probably going to have to show work
g
craggy haven
seems weird that the rest of the circuit would be irrelevant here
but i guess that makes sense?
maiden wave
seems weird that the rest of the circuit would be irrelevant here
it does to me, but either teacher is wrong (unprobable) or me
craggy haven
circuitlab really doesn't like this circuit
maiden wave
circuitlab really doesn't like this circuit
neither do I
what happens when current flows inside the + of a battery ?
craggy haven
irl? probably recharges the battery
here? i guess it flows out the other end but at a lower voltage??
like i see your logic and i agree that it looks like someone messed up and added 10+20 instead of doing 10-20
topaz sinewBOT
@maiden wave Has your question been resolved?
topaz sinewBOT
@maiden wave Has your question been resolved?
topaz sinewBOT
@maiden wave Has your question been resolved?
topaz sinewBOT
@maiden wave Has your question been resolved?
waxen flame
seems weird that the rest of the circuit would be irrelevant here
it's irrelevant because the current source tells you the current through the 10 ohm resistor, so the voltages are basically fixed, unless the circuit wants to have the equivalent of two voltage sources connected in parallel
as for why it's 30 volts, you know that the voltage across the 10 ohm resistor is 20 V (where the top is more positive / higher potential than the bottom), so adding that to the 10 V voltage source gives you 30, and then subtracting the 40 V (note the orientation) and adding back in the current across the 5 ohm resistor gives you 0
@maiden wave in case you want to come back
and as for why your answer of -10 V is wrong, you have a sign error in your KVL
I guess another easier way to look at it is the 40V minus the 2A * 5 ohm
elder terrace
topaz sinewBOT