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fierce current
Water in a canal, 30 dm wide and 12 dm deep is flowing with a velocity of 10km/hr. How much area will it irrigate in 30 minutes, if 8 cm of standing water is required for irrigation?
final saddleBOT
Water in a canal, 30 dm wide and 12 dm deep is flowing with a velocity of 10km/h...
fierce current
<@&286206848099549185>
midnight ginkgo
- Show your work
- Wait 15 minutes before pinging helpers
fierce current
1. Show your work
2. Wait 15 minutes before pinging helpers
ok
sorry
i want help with the entire question
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heady anchor
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manic herald
so did this person get the period wrong
yes
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wet solstice
Wrong vector function notation? On the second line, do you add the C to both the "i" unit vector and the "j" unit vector?
final saddleBOT
Wrong vector function notation? On the second line, do you add the C to both the...
tranquil pine
Wrong vector function notation? On the second line, do you add the C to both the...
Really lacking a lot of context here, but if it is $\vec{C}$ then yes
soft zealotBOT
♡A(lex)♡
tranquil pine
As in the vector integration constant
wet solstice
My bad, the C is the center of the circle
Is the "C vector" just a positon vector to the point C?
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mild coral
Find the gradient of the scalar field $w=(\vec{a}\cross\vec{b})\cdot \vec{r}$ if $\vec{a}=(2,3,6)$ and $\vec{b}=(-1,4,0)$ and $\vec{r}$ is the radius vector of the point $M(x,y,z)$.
final saddleBOT
Find the gradient of the scalar field $w=(\vec{a}\cross\vec{b})\cdot \vec{r}$ if...
soft zealotBOT
Legija
mild coral
okay so here I found the cross product a x b
got a x b = -24i -6j + 11k
now since r is the radius vector of the point M(x,y,z) what is r equal to?
r^2 = x^2+y^2+z^2 ?
r = sqrt(x^2+y^2+z^2) is that correct?
final saddleBOT
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mild coral
actually i think thats just
$\vec{r} = x\cdot \vec{i} + y\cdot\vec{j} + z\cdot\vec{k}$
soft zealotBOT
Legija
mild coral
so
$w = (\vec{a}\cross\vec{b})\cdot\vec{r} = (-24,-6,11) \cdot (x,y,z) = (-24x,-6y,11z)$
soft zealotBOT
Legija
mild coral
and then wouldnt the gradient of w be like
$\nabla w = \pdv{w}{x}\vec{i}+\pdv{w}{y}\vec{j}+\pdv{w}{z}\vec{k} = -24\vec{i} - 6\vec{j} + 11\vec{k}$
soft zealotBOT
Legija
mild coral
is that right?
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@mild coral Has your question been resolved?
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@mild coral Has your question been resolved?
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wooden veldt
.close
tranquil pine
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primal ivy
You have 2 tests.
Test 1 is 20% of your total
Test 2 is 80% of your total
You get 25/100 (25%) on your first test.
How much do you need to score on Test 2 for you to pass?
(Passing is getting 50%)
primal ivy
The simplest of math, but im mindfucked
supple mantle
Okay
So you got 25% of the initial 20%
Which means you got 1/4(20%) = 5%
Oops
Oops
Oops
Gave too much
@primal ivy
Where did you get?
In this question so far?
supple mantle
Which means you got 1/4(20%) = 5%
Do you understand this part?
primal ivy
Yes
supple mantle
Alright
If we need to pass at exactly 50%
And we got 5% in the first exam
What's the remaining percentage we need to have in the second exam?
primal ivy
Would say 55, but i know thats incorrect
Its probably really simple maths tbf
But i actually
dont know
💀
supple mantle
First exam + second exam = 50% right?
supple mantle
So (25% of 20%) + (x of 80%) = 50%??
primal ivy
62.5?
supple mantle
So (25% of 20%) + (x of 80%) = 50%??
No I meant that this equation is what you meant
primal ivy
Yes
supple mantle
Hmm
How long did you stay awake for today?
And be honest please. We can do this later if you stayed up for too long.
Your well-being is more important than this question
primal ivy
How long did you stay awake for today?
Too long, have an exam tomorrow
But i think 62.5 is the correct answer
supple mantle
How many hours till your exam?
supple mantle
But i think 62.5 is the correct answer
As in 62.5% of 80%?
primal ivy
How many hours till your exam?
20 hours from now, still got some things to study
primal ivy
As in 62.5% of 80%?
Yes
supple mantle
20 hours from now, still got some things to study
tranquil pine
salut a toi j'aimerais juste savoir si tu pouvais niquer ta mère stp merci
après tous va bien niquer ta maman
supple mantle
salut a toi j'aimerais juste savoir si tu pouvais niquer ta mère stp merci
Veuillez utiliser un autre canal
!help
final saddleBOT
Please read #❓how-to-get-help
primal ivy
You ignored the (25% of 20%)
Ah i see, its (around) 56.3% then
56.3% of 80% is 0.45
- the 0.05 from the other test
= 0.5
supple mantle
Yepp
primal ivy
And what calculation did you do to get 56.3?
i just plugged in random numbers untill ~0.45
supple mantle
primal ivy
supple mantle
Hopefully you master this concept xd
primal ivy
.close
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reef river
I am having problems translating/formalizing sentences into logic expressions/gates. ( L1 is Hungarian, sorry for bad translation)
- "Those and only those are doing mathematics, who do music and sports"
- "There is someone who likes doing cardgames but not fishing"
"All ppl who likes soccer does fishing, or atleast doesnt like cardgames"
"It is true that who doesnt do fishing likes soccer or it is true who does fishing dont like soccer" - "Every A consequently B"
"There is a B that is C"
final saddleBOT
I am having problems translating/formalizing sentences into logic expressions/ga...
@reef river Has your question been resolved?
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tranquil pine
So got more of a conceptual question in my mind, suppose you have some vector space V, and that vector space is isomorphic to its dual. Does that mean that every linear subset of V is also isomorphic to its dual?
dry light
LOL
mellow cedar
vital crag
bot only makes errors against active people
tranquil pine
Discrimination 
low hawk
tranquil pine
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fair ginkgo
how can i find the height corresponding to a travelled circular distance?
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pallid egret
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final tangle
is this the original question?
spring stone
Use the pythagorean theorem to find last side of the smaller triangle
final tangle
and original diagram
spring stone
And find the length of the side using the fact that the triangles are similar
pallid egret
Use the pythagorean theorem to find last side of the smaller triangle
Yes but how does that find the length of the lake
final tangle
as is, it's insufficient info
pallid egret
How would I find the length
spring stone
Similar triangles
spring stone
29/2 i think
spring stone
First we find the length of the unknown side of the smaller side
pallid egret
I got square root of 52
spring stone
I got square root of 52
Then use the fact that the triangles are similar and establish a proportion
The right answer should be 13
final tangle
how are you getting both sqrt(52) and 9
pallid egret
how are you getting both sqrt(52) and 9
no sqrt of 52 for the hypothenuse
and I guessed the answer to the wholke thing was 9
final tangle
is this the original diagram?
pallid egret
Yes
spring stone
Looks like an Sat question
final tangle
were you told any additional stuff?
pallid egret
No
final tangle
specifically whether that angle at the bottom was supposed to be a right angle?
pallid egret
specifically whether that angle at the bottom was supposed to be a right angle?
well it can't?
spring stone
Im Just assuming It is
final tangle
what can't
spring stone
The problem wouldn't make sense otherwise
final tangle
the "bottom"...
pallid egret
it is
final tangle
were you explicitly told that?
pallid egret
yes
final tangle
ok.
final tangle
applying similar triangles or
geometric mean for a right triangle will get you a nice value for the length of the lake
final tangle
which gets you the ||9|| you had earlier, (no guessing required)
pallid egret
I was right
spring stone
Oh i forgot to subtract 4
final saddleBOT
pallid egret
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fierce orchid
Use similar triangles
pallid egret
how
fierce orchid
What have you tried?
pallid egret
I honestly didn't have a clue
I wasn't there when we learned this
so i was hoping someone can teach me
fierce orchid
Do you know what similar triangles are?
pallid egret
like two trianges that arent the same size but are a proportion?
pallid egret
mhm
fierce orchid
So try finding those lengths
pallid egret
yeah but i didnt know how
tranquil pine
Well
pallid egret
Can anyone help?
final saddleBOT
@pallid egret Has your question been resolved?
hearty zephyr
similar triangles have equal ratios of their sides. So, for example XE/YE = AE/DE
pallid egret
so XE is 17?
hearty zephyr
🤷 show your work
ebon tiger
So for my math problem in my class I’m given this 2nd degree function : f(x) = a(x-1)² + k
and these 2 points : (0,5) and (18,581)
and what I need to find is how many times the function touches the x axis
But, I have no idea how to do it. I feel like I’m missing a value or something, because i can’t think of a formula that could help me find one of the missing parameters
All I’ve found so far is that a > 0 and that k < 5, but now I’m stuck and I don’t know what to do next. I know I just need to find the value of k but idk how.
final saddleBOT
So for my math problem in my class I’m given this 2nd degree function : f(x) = a...
hearty zephyr
make a system of equations, plug in both your points for x and y and you'll have two equations with the two unknowns a and k
hushed sonnet
Surely filling in both values might help?
(0, 5) gives 5 = a+k
and
(18, 581) gives 581 = a(17)^2+k
You can rewrite the first one as k = 5-a
Which gives 581=a(17)^2+5-a
Solve for a which gives a. Hope you can figure it out afterwards?
random chasm
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random chasm
im not sure how to prove this identity
modest birch
do 10^ to both sides, and you might see easier identities to prove
sick rock
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sick rock
Only thing ive noticed is that in the first row its adding by 5
And last row its adding by 6
celest crane
I don't think there is any right or wrong answer as long as you have a valid reason for the number you choose.
sick rock
Nah this test has specific answers
celest crane
Well, assuming linear growth for both series, you found the method for 34,39,44. What might a reasonable assumption be for the 7,?,15?
sick rock
Well I would probably choose 11
Because that would create some type of pattern
Because 7,11,15
celest crane
That would be my choice as well.
nimble frost
how is the margin of error 4%?
final saddleBOT
how is the margin of error 4%?
nimble frost
(stats)
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glossy phoenix
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glossy phoenix
i managed to take the derivative on both sides
and find f(x) = x^(3/2)
not too sure how to find the value of a
tulip coyote
Why not substitute f back into the integral and work it out directly?
glossy phoenix
oh i can do that
pseudo knot
not too sure how to find the value of a
Put f(x) back in the original equation
glossy phoenix
and just integrate as i would normally?
pseudo knot
Yesh
hybrid heath
do ".close" when done, por favor
final saddleBOT
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stiff nymph
Hi ho do i find h in 8
final saddleBOT
Hi ho do i find h in 8
final tangle
as the question describes
have you made any attempt in determining the shaded area?
onyx sand
final saddleBOT
onyx sand
just wanted to ask if this means the statement is a tautology or not
since for all P being true, Q is true
but like not every instance of the truth table is true (if that makes sense)
hearty zephyr
tautology means it's always true
onyx sand
so this would not be a tautology
since just for example
p doesnt always imply q
actually not sure
so this is
because
if P is true
Q is true
tranquil pine
Shouldn't be a tautology yes
tranquil pine
finish your truth table first and you will see why
onyx sand
right i know I will have some falses
OH
i see
so even in the instances where P is true
Q isnt always true
therefore it isnt
hearty zephyr
hearty zephyr
yes
tranquil pine
Oop
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marsh mural
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stuck owl
What would be the shortest way of proving the trivial fact that if you have an interval [a,b] and functions f,g with f(a)=g(a) that if the derivative of f is strictly greater than that of g that f(b) >= g(b)?
Pretty much just a proof for the fact that faster growing functions grow more over the same interval. Can't use integrals so I cant just integrate and set the f(a), etc...
final saddleBOT
What would be the shortest way of proving the trivial fact that if you have an i...
stuck owl
I also wonder if the above is true for f(b) > g(b). If its possible to have a strictly greater derivative but the end values still align
probably not if the derivative is strictly greater everywhere
desert mantle
mean value theorem
stuck owl
mean value theorem
something like this?:
f'(c) = (f(b) - f(a)) / (b - a)
g'(c) = (g(b) - g(a)) / (b - a)
Since f(a) = g(a) and f'(x) > g'(x) for all x in [a, b], it follows that f'(c) > g'(c) and therefore:
(f(b) - f(a)) / (b - a) > (g(b) - g(a)) / (b - a)
f(b) - f(a) > g(b) - g(a)
f(b) > g(b).
nevermind it makes sense that "it follows that f'(c) > g'(c)" is true
that should be enough right? I just need to add a short sentence for why "it follows that f'(c) > g'(c)" is true
.close
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desert mantle
I mean you don't want to show f'(c) > g'(c). you want to show f(c) > g(c) if anything
stuck owl
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stuck owl
I mean you don't want to show f'(c) > g'(c). you want to show f(c) > g(c) if any...
Why? If f'(c) > g'(c) then doesnt the thing I want: f(b) > g(b) follow from that?
and f'(c) > g'(c) is true because we are given that f'(x) > g'(x) for all x in the interval [a,b], which includes the point c by the mean value theorem
desert mantle
you don't know that the point c is the same for the functions f and g
stuck owl
hmm right
desert mantle
what's the thing that most of the time happens in proofs before applying the mean value theorem or intermediate value theorem
stuck owl
I don't know this is the first proof I've seen with it
desert mantle
first step is very often to define a help function
stuck owl
first step is very often to define a help function
Given the assumption that f'(x) > g'(x) for all x in [a, b], we know that for any two points x1, x2 in the interval the ratio of the change in f(x) to the change in x will be greater than the ratio of the change in g(x) to the change in x.
Given a fixed x1 in (a,b) and an x2 approaching x1 from the left, we have
f(x2) - f(x1) > g(x2) - g(x1) (after multiplying by the change in x on both sides)
Given x2 approaching x1 from the right, we have the same inequality
f(x2) - f(x1) > g(x2) - g(x1)
Since the inequality holds for any x2 approaching x1 from the left or right:
f(x1) > g(x1)
is this something that works
and then i follow from the above that f(b) > g(b)? But it seems problematic because you cant approach x1 = b from the right
so it doesnt feel like it works
desert mantle
it's unprecise with the "ratio of the change in f(x) to the change in x"
stuck owl
i wanted to use the derivative limit definition and show it for both sides
so isnt it equal to the derivatve definition
desert mantle
lets define the function h(x)=f(x)-g(x). lets assume that h(b) < 0
what does that give us
what is h(a)
stuck owl
distance between the two functions at each x?
just a difference between both functions at given x
oh nvm i misunderstood the question
desert mantle
so h(a)=0 and h(b)<0
now mean value theorem
the assumption h(b)<0 is equivalent to f(b)<g(b)
stuck owl
is this proof by contradiction?
desert mantle
yes
flat flame
the scale is 1:25 million, if the distance between Toronto and Montreal is 2.1cm on a map, what is the approx. distance between these cites
final saddleBOT
the scale is 1:25 million, if the distance between Toronto and Montreal is 2.1cm...
flat flame
2 : 50 million
I think the 0.1 is 100 000 ?
could someone let me know?
I’m not exactly sure if I’m right
trim jolt
Linear algebra: A linear transformation L on R^3 with a basis B = {(1,0,0);(1,1,0);(1,1,1)}is given by the matrix
\begin{pmatrix}
1 & 0 & 5 \
0 & 2 & 2 \
1 & -2 & 0 \
\end{pmatrix}
determine the function rule of the transformation.
While trying to understand/disecting the question i stumbled upon the question of wether L(v) has to be in terms of the standard basis or not
final saddleBOT
Linear algebra: A linear transformation L on R^3 with a basis B = {(1,0,0);(1,1,...
soft zealotBOT
نعمان
Compile Error! Click the 
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(You may edit your message to recompile.)
trim jolt
I gues my question is, does L(v) have to be a function of v and output well L(v) itself (aka the coordinates of L(v) in terms of the standard basis) or the coordinates of L(v) in terms of the basis B
I dont understand how it is a set of functions, could you explain?
ocean lintel
Misinterpreted the notations a bit
trim jolt
Oh okey, mustve been my messy LaTeX
ocean lintel
No. It's just that I'm used to L(E) as being the set of linear applications on E, so I thought "v is a weird name for a vector space, but I've seen worse, why not"
trim jolt
Ah haha, its a linear transformation on R^3
Anyway, i think L(v) is supposed to be specified in terms of the standard basis. But im not clear on how to progress
ocean lintel
What's "the function rule" of the transformation ?
trim jolt
I know L(v) = basis row vector x transform matrix x coordinates of vector for a general linear map
ocean lintel
L(v) = Av where A is L's matrix in the basis in which v is expressed
trim jolt
Doesnt that specify the coordinates of L(v) in terms of the non standard basis. So in other words Co(L(v))= Av
While Lv = B Av with B being a matrix with in every column a basisvectors of W in terms of the standard basis
ocean lintel
To go from a vector represented in B to a vector represented in S (standard basis) yes
ocean lintel
What's "the function rule" of the transformation ?
The thing is I'm not really sure what the question is asking for, so it's kind of hard to help
trim jolt
What's "the function rule" of the transformation ?
Ohh i misinterpreted this as a guiding question. Im not sure what the english word is, in dutch its called "functievoorschrift". For example sin: R --> R is given by x --> sin(x)
We call sin(x) the function rule
or x --> x^2
The rule with which the function can be specified in terms of the variable
ocean lintel
wtf are you dutch with an arabic username lol
trim jolt
Or perhaps im a dutch speaking person who's not ethnically dutch haha
ocean lintel
I guessed so, anyways
They should have specified that they want it in the standard basis
trim jolt
So the funtion rule specifies the function's value in terms of the variable. Meaning L(v) should specify the vector L(v) and not its coordinate vector in B. And since vectors in R^3 are always specified in terms of the standard basis i should do a change of basis
ocean lintel
Imo this question lacks critical information to remove ambiguity. Although there isn't much else that would make sense as a question
trim jolt
They should have specified that they want it in the standard basis
yeah i feel like that too but ig its an exercise in what a vector in R^3 truly means, or being able to seperate the coordinates of a vector in R^n with the vector itself
Anyway, If i find Co(L(v)) with Ax, i should figure out L(v) and x in terms of the standard basis for a function rule but idk how to do that
ocean lintel
So you want L's matrix in the standard basis ?
trim jolt
Thats the thing im not sure what i want haha
I need a function rule that specifies the image L(v) of a vector as a function of a vector v
ocean lintel
Which they give you
trim jolt
Bot L(v) and v have to be specified in terms of the standard basis as thats what a vector in R^n is
ocean lintel
That's why it would make sense to think they want it in the standard basis
ocean lintel
Bot L(v) and v have to be specified in terms of the standard basis as thats what...
They don't
trim jolt
What do you mean they don't
ocean lintel
I can define L as being the diagonal matrix with entries 1,1,2 in the basis B. That defines L just fine
trim jolt
Yes you can define L, but L(v) is a vector in R^3 not a map on R^3. And ive been thought (actually assumed bcs my professor didnt answer my question) that a vector in R^3 is specified in terms of the standard basis
ocean lintel
Doesn't have to
trim jolt
Otherwise a vector v = (3,2,5) could mean any vector in the plane while in terms of the standard basis its always (3,2,5) and a change of basis changes its coordinate vector but not the vector itself
ocean lintel
But conventionally yes
trim jolt
Doesn't have to
But then how do i specify a vector in R^3
trim jolt
By its 3 coordinates in a given basis
Arent you then specifying its coordinate vector?
This way a vector does not exist seperatly from a given basis
but it does
ocean lintel
An element of R^3, by definition, is a triplet of numbers. A vector of R^3 is directly its coordinate vector in the standard basis
trim jolt
An element of R^3, by definition, is a triplet of numbers. A vector of R^3 is di...
So if i change the basis on R^3 the vector would still be its coordinate vector in the standard basis but its coordinate vector would be its coordinates in terms of the new basis
Isnt that consistent with what im saying
trim jolt
Haha sorry, i get caught up in the details sometimes
but no time for that when my exam is in 3 days lmaoo
Anyway, so i CAN figure out L(v) in terms of the basis B in function of v in terms of the basis B
But i need to figure out L(v) in terms of the standard basis in function of v in terms of the standard basis
Im not sure how i can do that
ocean lintel
Change of basis, it's all there is
Option 1) change of basis matrix. Computers love it, humans find it computationally heavy
Option 2) doing the same thing "by hand", weirdly makes it more manageable because you have a feel for what you're doing
trim jolt
Oh okey
But how do i know the equality holds
I know Co(L(v) = Ax but idk if L(v) = Av
ocean lintel
What's Co ?
trim jolt
Coordinate map, Co(L(v)) being the coordinates of L(v) in terms of B
ocean lintel
Should specify the basis there then
Anyways
You can just figure out the image of each standard basis vector by L and use that to find L's standard matrix
supple dove
Does anyone know what it’s 1a instead of 4a here
final saddleBOT
Does anyone know what it’s 1a instead of 4a here
supple dove
if it passes through the point (2,1) then shouldn’t it be
(2^2)a + (2)b + c = 1 => 4a + 2b + c = 1
versed crater
Is there a part above that you’re cutting out
supple dove
no
versed crater
Questions don’t usually start with the word since
supple dove
it’s just getting the other points
in the same way
u can see in the system of equations below
versed crater
Well I have no idea what the set up here is…
supple dove
here is my previous work which I got incorrect because I put a 4 instead of a 1
I’m extremely confused
Is there a mistake in my work?
none of these points are collinear
I’ve confirmed that
versed crater
I’m very confused
I start with the same ones you did and I get the right answer
So you did the Gaussian elim wrong
But idk about the 4 and 1
Don’t know why it says 4 instead of 1
supple dove
I start with the same ones you did and I get the right answer
can you show me your augmented matrix ?
supple dove
oh
versed crater
But idk about this
supple dove
istg I plugged in the solution it got from doing that
versed crater
I get 2/3x² -3x + 13/3 and that has all 3 points
supple dove
and it got all three correct
supple dove
😔whatever I’ll just correct my elimination
wasted so much time trying to figure out what that was
.close
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supple dove
I feel like it was just a typo then
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eager stirrup
should i use induction?
final saddleBOT
should i use induction?
rustic musk
That looksl ike an argument for which you would try induction
modern crypt
final saddleBOT
modern crypt
got to $\frac{16x^2y^3+24x^3y^2-6x^3}{2xy}$
soft zealotBOT
Zyme><SOL
tulip coyote
Do they give you an explicit aim as to what you should get this as?
modern crypt
simplify
but like
this is the answer
assuming they just cancelled out an x?
bit odd
tulip coyote
Yea just cancel it down here!
tulip coyote
Yep cancel out 2x because common factor
final saddleBOT
@modern crypt Has your question been resolved?
narrow arch
consider the polynomial function g(x) = 3x^4 + 8x^3 - 41x^2 - 138x - 72 with known factor of (3x + 2) and (x-4) write down g(x) as a linear factor
final saddleBOT
consider the polynomial function g(x) = 3x^4 + 8x^3 - 41x^2 - 138x - 72 with kno...
narrow arch
I’ve been out of school for a bit so I’m not sure how I’m suppose to do this
If you could walk me through this warm up question I could try doing one by myself
ember pawn
this function g(x) will have four factors (since its highest power of x is 4)
if we know (3x+2) and (x-4), we know we will have two others of the form (x-a) and (x-b)
since then all the x terms will multiply to give the 3x^4 that we have, so there is no coefficient on the other x's
(3x+2)(x-4)(x-a)(x-b)=g(x)
multiply it out and we get:
(3x^2-10x-8)(x^2-(a+b)x+ab)=g(x)
and multiply out again
in the end i have this
$3x^4-(10+3a+3b)x^3+(3ab+10a+10b-8)x^2+(8a+8b-10ab)x-8ab=g(x)$
soft zealotBOT
spicygreenpeppers
ember pawn
since our function lines up, we just solve for a and b by comparing with the coefficients of our g(x) from the start
unless i've gone wrong with the algebra, that should lead to a solution, but if not you can understand my method
narrow arch
So this would be the whole answer? Seems a lot different then what the reference notes had gotten on a similar question
ember pawn
they've done the same thing as me, just with box multiplication
i can show you that method if you'd like
narrow arch
Yeah but the answers seems a lot more complicated then what you’ve gotten
Please do it’s a lot easier for me
ember pawn
there's no voice channels here ;-;
narrow arch
Yh I just noticed lmao we could do it in dms if you’d like
ember pawn
sure
narrow arch
Alright
scenic bay
Hello. Does anyone mind explaining how question 269 = 1/5? I am not getting that answer 🫤
final saddleBOT
Hello. Does anyone mind explaining how question 269 = 1/5? I am not getting that...
worldly vale
show your work
rustic musk
Do you know the formula for the derivative of the inverse of f
I got to the answer of 1/5
So did you get f^-1 (0)
scenic bay
@worldly vale I wrote my work by hand. And that's what I did, but I think I got the wrong inverse function @rustic musk . Do you mind showing me how you got the inverse of f?
rustic musk
I didn't figure out the inverse function, I just found f^-1 (0)
Do you know the real value of x that solves the equation x^3 + 2x + 3 = 0
scenic bay
Is it (y - 5)^1/2?
normal hill
I didn't figure out the inverse function, I just found f^-1 (0)
How did u do this without finding inverse?
tranquil pine
$f^{-1}(x)=y, f(y)=x$
rustic musk
Mortta, the derivative of f^-1 (x) is 1/f'(f^-1 (x))
soft zealotBOT
starlight
rustic musk
So we work out f^-1 (0) by figuring out f^-1 (0) (which is -1) and then finding f'(-1)
scenic bay
**starlight**
What did you do here @rustic musk? Lol. I did what you did - I solved f^-1 (0) - but I got the sqrt of -5. However, you can't take the square root of a negative number, no?
scenic bay
I don't think I've learned how to solve for cubic roots 🫤
rustic musk
You plug in random numbers
try 0, 1, -1, 2, -2
If it ain't one of those, your teacher's mean
scenic bay
Plug in random numbers for x?
rustic musk
Yes but there are rules to figure it out
I forgot the name of some of the theorems
Rational root theorem and Descartes theorem was it?
And it suggests to you numbers to try
The rational roots theorem tells you to try all these numbers that it describes (you can search it up if you didn't learn it), and if none of them work it has no rational roots
In which case your teacher is REAL mean
tranquil pine
bc we are trying find for $f^{-1}(0) $ if you set $f^{-1}(0)$ equal to a variable for example y, $f(y)=0$, so you would try to find the value of y, equating $x^3+2x+3$ to $0$
soft zealotBOT
starlight
scenic bay
@rustic musk I am going to research these theorems. Hopefully I can figure this out after reading about them.
rustic musk
Focus on rational root theorem
scenic bay
bc we are trying find for $f^{-1}(0) $ if you set $f^{-1}(0)$ equal to a variabl...
I am not sure how f(y) = 0 😔
scenic bay
Focus on rational root theorem
Will do. Thank you
scenic bay
bc we are trying find for $f^{-1}(0) $ if you set $f^{-1}(0)$ equal to a variabl...
Btw, how is it that you can just set some function equal to a variable? Or, rather, how do you know that setting a function equal to a variable will help you solve a problem like this?
rustic musk
You set it equal to a variable so you can manipulate it in a way where you can solve for it
Like you might see in a class you write log_3 (243) = x so that they could write 3^x = 243 which it is easier to see that x = 5
scenic bay
Ok. I see what you mean. How do I think like a mathematician, though? (i.e. set f^-1(0) equal to y to make it easier to solve.)
final saddleBOT
@scenic bay Has your question been resolved?
rustic musk
Well you want to find f^-1 (0). What is f^-1 (0)? It is the number y such that f(y) = 0. f(y) = y^3 + 2y + 3, so we look for a number y such taht y^3 + 2y + 3 = 0. It isn't really that much of a jump; it is simply using what f^-1 (0) means.
final saddleBOT
final saddleBOT
Available help channel!
shut fern
Hello, I have a problem in functional analysis. Suppose $E$ is a vector space over $\bR$ or $\bC$, and $p,q$ are norms over $E$. We denote $E'_p$ and $E'_q$ the topological dual spaces associated respectively to $(E, p)$ and $(E,q)$. Suppose that $E'_q \subset E'_p$. \\ I need to prove that the inclusion $Id : E'_q \to E'_p$ is continuous. I understood that it means there is some $k\ge 0$ such that $q\le kp$ and I thought I could prove that the graph of $Id$ is closed but I wasn't able to do it.
final saddleBOT
Hello, I have a problem in functional analysis. Suppose $E$ is a vector space ov...
soft zealotBOT
Silfer
final saddleBOT
@shut fern Has your question been resolved?
shut fern
No one likes functional analysis ? 😭
fallow wren
me
shut fern
😄
rapid torrent
fallow wren
sorry but is $E'_p=E'_q$ ..the only difference its the norm right?
soft zealotBOT
everg
soft zealotBOT
Silfer
shut fern
I meant the topological dual space so the functions in it are continuous relative to the norm associated
fallow wren
mmhh maybe i don t know very well this subject ...but the dual space its the same (you don t even have to have a norm to define it)..the only difference are the norm's that you put in it
shut fern
mmhh maybe i don t know very well this subject ...but the dual space its the sa...
I meant the topological dual space
It's not $E^*$
soft zealotBOT
Silfer
fallow wren
ah ok
shut fern
Some functions in $E^*$ are not continuous. In the topological dual, you only take the continuous ones. Namely :
$$E'_p = \mathcal{L} ((E,p), \mathbb{K})$$
soft zealotBOT
Silfer
fallow wren
ahh ok because linear don t implies continuity ..so its not E^*
shut fern
Yes. Except if your space is finite dimensional
fallow wren
yes because linear + bounded implies cont.. and finite dimens. implies B_1 compact
fallow wren
mhhh if i have $(f_n)\in E_q' \text{ with } q(f_n)\le 1$ then i can find a $\delta>0 s.t. q(f_n(v))<\varepsilon \forall n , v\in B(\delta)_q$
soft zealotBOT
everg
shut fern
Huh
I dont think so
I thought about using Banach-Steinhaus using this kind of "boundings" argument but you know that if f is in E'q then for all n, nf also is
final saddleBOT
@shut fern Has your question been resolved?
final saddleBOT
is this not four?
tranquil pine
Bruh its 2 obviously
fathom walrus
Bruh its 2 obviously
Why do u say so
fathom walrus
Yea so for 2cosx = 0, cosx = 0, thus x = pi/2 and 3pi/2 and for tanx - sqrt(3) = 0, tanx = sqrt(3) so x = pi/3 and 4pi/3
That’s what I was thinking as well
But this is what I got upon graphing
What’s going on?!?!?!
white rock
idk
fathom walrus
Wait a second
2sinx - 2sqrt(3) * cosx = 0 so sinx = sqrt(3) * cosx. Tanx = sqrt(3) and we know from there that x = pi/3 and 4pi/3
I was thinking abt that at the start but it still doesn’t explain 1 thing
fathom walrus
2sinx - 2sqrt(3) * cosx = 0 so sinx = sqrt(3) * cosx. Tanx = sqrt(3) and we know...
Do u understand how I got here
I distributed the 2cosx
white rock
yes
final saddleBOT
@white rock Has your question been resolved?
worthy sedge
could someone help me rationalize, (-5)^2 + (-3 sqrt(3))^2 = x^2
final saddleBOT
could someone help me rationalize, (-5)^2 + (-3 sqrt(3))^2 = x^2
What step are you on?
- I don't know where to begin
- I have begun but got stuck midway
- I got an answer but I'm told it's wrong
- I got an answer and would like my work checked
- I have a question about someone else's worked solution
- None of the above
worthy sedge
2
lunar umbra
could someone help me rationalize, (-5)^2 + (-3 sqrt(3))^2 = x^2
what do u have so far?
worthy sedge
i got 25 + 9sqrt(3) = x^2
but i think the 9sqrt(3) is wrong
worthy sedge
so then 9 * 3?
lunar umbra
yeah
worthy sedge
alright thanks
final saddleBOT
Available help channel!
mild flame
final saddleBOT
mild flame
any idea how to solve this?
frosty musk
lopital?
mild flame
damn lemme check if we studied that
i dont think i;ve heard that term b4
I think i understood how to do it
do i just evaluate it?
(made a mistake its correct now)
final saddleBOT
@mild flame Has your question been resolved?
mild flame
if i do it this way it gives me 0 and it should be -4/3 so idk if i did sum wrong or the lopital thing doesnt work
final saddleBOT
@mild flame Has your question been resolved?
minor kayak
Start by noticing that
$$(2x+7)\ln\left(\frac{3x-1}{3x+1}\right)=(2x+7)\ln\left(1-\frac{2}{3x+1}\right).$$
Then set $u=-\frac{2}{3x+1}$ so that $x=-\frac{u+2}{3u}$, and
$$(2x+7)\ln\left(1-\frac{2}{3x+1}\right)=\left(7-\frac{2(u+2)}{3u}\right)\ln\left(1+u\right).$$
Finally, as $u\to0$ as $x\to\infty$, and as
$$\lim_{u\to0}\frac{\ln(1+u)}{u}=1,$$
we get that
$$\lim_{x\to\infty}(2x+7)\ln\left(\frac{3x-1}{3x+1}\right)=\lim_{u\to0}\underbrace{\left(7u-\frac{2(u+2)}{3}\right)}{\to-\frac{4}{3}=}\underbrace{\frac{\ln\left(1+u\right)}{u}}{\to 1}=-\frac{4}{3}$$
This does the trick
Nothing too fancy
Wait
soft zealotBOT
Lorago
minor kayak
Had a typo, fixed it
mild flame
oh 😭
np
okay
woah
makes perfect sense i wouldn't never came with this idea tho
thanks a lot!
.close
slender cargo
final saddleBOT
slender cargo
is this right
topaz rune
Someone correct me if I am mistaken, isn’t there a log property where ifs a log to the same base u can cancel the log and proceed with the inside
final saddleBOT
@slender cargo Has your question been resolved?
fathom walrus
I’ll check it, 1 sec
From the first to second step, u did sqrt(4)=2, then what next?
O wait I see
ln(2/3)-ln6= ln(1/9)
=-ln9
Gottt it
How come u took away the negative root?
Here @slender cargo
Everything looks good except for that
U shoulda had 1 route where u did + and another where u did -
Ping me if u return
slender cargo
U shoulda had 1 route where u did + and another where u did -
sorry i was afk
slender cargo
How come u took away the negative root?
i took the negative because it was a length and it couldn’t be negative
fathom walrus
Right, but when both sides get e^, it’s no longer negative
slender cargo
if i kept the negative i would have gotten x≈0.58 and ln(num less than 1) is negative
fathom walrus
Ohhhhhh
Nice one
Yep everything looks good then
Well done too, the solution is super clear
lethal cliff
Hi I need help with this and I just joined this group so I’m Not sure if I’m doing this right 😅
final saddleBOT
Hi I need help with this and I just joined this group so I’m Not sure if I’m doi...
cloud zephyr
Which one?
lethal cliff
1st
cloud zephyr
What answer did you get ?
lethal cliff
The thing is I don’t know how to solve it
cloud zephyr
Oh so you haven’t tried anything
Okay so
Do you know how to multiply monomials?
In general?
lethal cliff
No 😭
cloud zephyr
Do you mind if I give you links to some videos?
That you can watch for better clarification than via text?
lethal cliff
Do you mind if I give you links to some videos?
Nope! I don’t mind!
lethal cliff
That you can watch for better clarification than via text?
Okay
lethal cliff
Okay thank you!
Sorry for wasting your time my cousin can help me, now that his not busy ty for helping me a bit
cloud zephyr
Okay, close the channel if you are done
lethal cliff
.close
tranquil pine
I’m trying to figure out the multiplicity of (2,0) but I don’t what step I would take first to do so
final saddleBOT
I’m trying to figure out the multiplicity of (2,0) but I don’t what step I would...
grim badger
• Show your work, and if possible, explain where you are stuck.```
rancid idol
missing a lot of context
tired walrus
@tranquil pine show the full problem
tranquil pine
Here it is: (x+7)^(x-2)(x+8)
Is it possible to find the multiplicity of just an x-intercept
final saddleBOT
@tranquil pine Has your question been resolved?
rain compass
i don't know if showing it is tough or not but you could try something simple like z = 1. then |z-i| = |1-i| = sqrt2
|iz*-1| = |i-1| = sqrt2
|z-1| = |1-1| = 0
and |z| - 1 = |1| - 1 = 0
final saddleBOT
@flat cape Has your question been resolved?
final saddleBOT
flat cape
i don't know if showing it is tough or not but you could try something simple li...
thank you @rain compass !
jovial nova
Can someone explain to me why we did that first step?
final saddleBOT
Can someone explain to me why we did that first step?
jovial nova
Like what exactly would make me think to do that
hollow iron
intuition and experience? im not sure lol
jovial nova
Ah so there is no reason?
wet wren
Help me with the ones I screwed up on
final saddleBOT
Help me with the ones I screwed up on
wet wren
.close
astral path
When doing trig for complex numbers, are you required to simplify when the problem asks for the trigonometric form?
final saddleBOT
When doing trig for complex numbers, are you required to simplify when the probl...
astral path
or just write the trigonometric from ( z = r(cosx + isinx) )
proud glacier
I have a question regarding shells method of volume of integration:
final saddleBOT
I have a question regarding shells method of volume of integration:
proud glacier
Why is the outer radius 4-y and not y-4?
is this because we are working in quadrant 1 (of the cartesian plane), and hence going by convention of "larger - smaller" values
final saddleBOT
@proud glacier Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
final saddleBOT
modern crypt
tranquil pine
I want to learn taylor series... Where do i start? I know limits, ints, derivatives which I see most people consider "calculus 1", so what would be like the prereqs of "calculus 2" i should learn before taylor series?
final saddleBOT
I want to learn taylor series... Where do i start? I know limits, ints, derivati...
tranquil pine
Like I know theres different types of series, but which ones should I learn first?
tranquil pine
I dont know what is considered the entirety of calc 1
is it just limits derivs and integrals?
silk saddle
khanacademy probably has it
tranquil pine
and I thought taylor series was a more difficult series
silk saddle
ehh
I can't really speak to it because my knowledge of taylor series is from real analysis
tranquil pine
I can't really speak to it because my knowledge of taylor series is from real an...
when would I see partial derivatives?
tranquil pine
so calc 1->calc 2-> (...) -> multi
vast nest
I'm quite lost as to what to do here. I'm assuming I'm setting up my scalar incorrectly, but as to how, I'm a bit lost. I feel confident that my |u| is in fact equal to sqrt(34) and that I can just simply take off the negatives, but I'm lost as to what to do after that. Any leads on that would be much appreciated.
This is Calc 3 btw.
final saddleBOT
I'm quite lost as to what to do here. I'm assuming I'm setting up my scalar inco...
grim badger
Gonna be honest, I don't recall calc 3, sorry. If you just wait, someone who doesn't will come and help you
ebon walrus
final saddleBOT
ebon walrus
how to solve it using intermediate value theorem
digital steeple
that is all you know about f(x)?
ebon walrus
yup
ebon walrus
assume f(x) = x^3 - x
what then
digital steeple
my f(x) fulfil all your conditions and is not from the form f(c) = 1 - 2c^2. So we have a counterexample.
ebon walrus
my f(x) fulfil all your conditions and is not from the form f(c) = 1 - 2c^2. So ...
that's what I am thinking
digital steeple
that's what I am thinking
that is why i ask for additional conditions.
ebon walrus
that is why i ask for additional conditions.
no additional condition
tulip coyote
my f(x) fulfil all your conditions and is not from the form f(c) = 1 - 2c^2. So ...
They're saying there exists a point c such that it holds, not that it's of that form for all choices of c
ebon walrus
g(0) is -1, g(1) is 1
yes I know how to continue from there
ebon walrus
g(0) is -1, g(1) is 1
please tell why they assumed g(x) that way
$g(x)=f(x) + x^2-1$ why ?
soft zealotBOT
Garuda
tulip coyote
Because of the above of what I said - your aim is to find a point c between 0 and 1 such that f(c) = 1 - 2c^2
digital steeple
They're saying there exists a point c such that it holds, not that it's of that ...
ok, than i misread something. sorry
tulip coyote
So ideally you want a point c such that f(c) - (1 - 2c^2) = 0
ebon walrus
what is the application of this idea
tulip coyote
Which naturally leads to considering the function they made
tulip coyote
ok, than i misread something. sorry
It happens 
ebon walrus
like what is that we can say after it seeing it that way @tulip coyote
beyond this question
like how can this idea be used in future problem
of consider another idea
safe ibex
tulip coyote
Not sure I'm getting your question, but I'm about to go to bed
grim badger
g left parenthesis x right parenthesis equal sign f left parenthesis x right parenthesis plus x to the power of two minus one
There you go
That equation words
ebon walrus
g left parenthesis x right parenthesis equal sign f left parenthesis x right par...
do you know how to solve it or do you want to joke around.
finite spire
He knows how to, but that's what you asked
grim badger
I don't even know the context. I just saw that you said write that equation in words
ebon walrus
I don't even know the context. I just saw that you said write that equation in w...
please see the context
finite spire
Anyways, your question is with regards to a function that is continuous in a given interval, right
ebon walrus
He knows how to, but that's what you asked
yup
finite spire
The value of the function at x=0 and x=1 is given to be 0. It now is asking you to prove that at some point x=c, f(x) has the value 1-2c^2
ebon walrus
yes
finite spire
Yup, so what have you tried
ebon walrus
I will give you some statements just tell whether they are true or not
question is saying that there exist some x=c such that f(x) will have value of the format 1-2c^2 @finite spire
finite spire
Yes
soft zealotBOT
finite spire
Well
They want you to find some x=c such that f(x)=1-2c^2 right
So, what you do in that case is take that and assume a new function and apply ivt on that
ebon walrus
where c is belongs to (0,1)
ebon walrus
So, what you do in that case is take that and assume a new function and apply iv...
I think I get it now and it is quite clear from the graph if f(0) = 0 and f(1)=0
then f(x) must pass through 1-2x^2 atleast once in interval (0,1)
ebon walrus
When did you get that f(x) was equal to 1-2x^2
we cannot draw any function f(x) such that it is not equal to 1-2x^2 in value at some C where c belongs to (0,1)
following the given condition in the question
that function must pass through f(0)=0 and f(1) =0
finite spire
So how does that say that f(x) = 1-2x^2
ebon walrus
at some point c in interval (0,1)
finite spire
At some point yeah
So, if you're maybe doing an answer using graphical representation, you could go ahead
but, thats not the way you'd solve it algebraically
ebon walrus
So, if you're maybe doing an answer using graphical representation, you could go...
I know that
but it does not make sense algebraically why you are doing that
ebon walrus
ok
ebon walrus
yup
finite spire
So
It's saying
There's some value c
For which this function becomes equal to 1-2c^2
Just at that point
And that very point c, lies in the open interval (0, 1)
ebon walrus
ok
ebon walrus
but if you don't know the nature of 1-2c^2 you cannot comment any thing
ebon walrus
For which this function becomes equal to 1-2c^2
this is what we have to prove