[f^-1(y)]' = 1
#help-23
patent flame
supple shore
what are you doing ? no it's not working like this
patent flame
how confident are you that im wrong (genuine question)
because if you havent been taught the lambert w function
and you arent evaluating for a single point
supple shore
it's just absurd, y is not equal to x + e^x
patent flame
i wouldnt necessarily believe so. think of a straight line equation. we write y = f(x) = mx+b, its common to use y as the output and x as the input
so taking the inverse of the ouput just gives us the input - which in this case is x
supple shore
So if you are correct we have f^-1 = x right we know that fof^-1 (x) = x right ? but fof^-1 = x+e^x = x so e^x = 0 ?
patent flame
no, f(f^-1(x))=x by definition
supple shore
yes it's what I said basically just watch
we know that fof^-1 (x), it's this here
can someone else help
patent flame
you can @ helpers if you want
supple shore
yes maybe after a short time, don't want to bother them
halcyon carbon
Don’t see a way you can do this without knowing lambert W
Maybe you can post again when you have a picture of the question
supple shore
there is no need of a picture I say all that I know, all the question is here there is no more, my teacher gives me this as an exercise and I don't know about lambert w function
halcyon carbon
I see. Good luck
supple shore
ty
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patent flame
which bit of q41
what is 0.75 in terms of a fraction
yes, so we have ln(0.75) = ln(3/4). do you see any properties of ln that can simplify this
or get us closer to our answer
great
yeah
nw
apply similar procedures for the other parts
flat frigateBOT
Jeremy
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slim lantern
Hello there. I need help clearing this question. It should not be hard for you but since I'm just a middle school student, I wanna know how to solve this:
safe radishBOT
Hello there. I need help clearing this question. It should not be hard for you b...
slim lantern
icy lance
bit of a throwback not sure if i remember this right but oh well
let x be that number
10000x=9715.151515...
100x=97.1515...
10000x-100x=9715-97=9900x
9900x=9618
x=9618/9900
then just try to simplify it
icy lance
the aim is to try and subtract away the recurring bit
shadow glade
dots on top of the digits represent repeating decimals nowadays?
icy lance
ah yeah, i forgot about that one, cant remember when it changed
tepid walrus
!status
safe radishBOT
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
wide cloud
Is this correct?
safe radishBOT
Is this correct?
icy lance
seems so
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fathom goblet
I keep getting this wrong, what point am I getting wrong?
safe radishBOT
I keep getting this wrong, what point am I getting wrong?
fathom goblet
Options are:
- Saddle Point
- Relative Max
- Relative Min
- Not a Critical Point
You can see the ones I picked in the image above
At least one of them is incorrect
^ bigger image of counter map
tag me if you reply
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fathom goblet
<@&286206848099549185>
plucky elk
Can also try asking in #multivariable-calculus
fathom goblet
Can also try asking in <#496784996510466057>
thanks, I might try that instead
.close
tranquil heron
The answer is 1802 but what is the solution to arrive at that number??
torpid fable
The last line implies he was born between 1801 and 1851. Then line before that makes it very easy to guess and check
gritty glacier
between 1801 and 1851 find all the multiples of 17 and brute force it
tranquil heron
between 1801 and 1851 find all the multiples of 17 and brute force it
Whats a quicker way to find the multiples
gritty glacier
well 1801 is 1001 greater than 1700 so you can start by multiplying by 106 likeso
harsh parcel
The multiple of 31 are 31 62 93
So he couldnt have died on 31
Nor on 62 because then no multiples of 17 to be born on
So its 93
So your choices are 17 or 34
Now check where 3 digit are same
gritty glacier
no
19th century pal
so we cant consider those first numbers
its about year not age
untold sky
none of those numbers are divisible by 31
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tranquil heron
well 1801 is 1001 greater than 1700 so you can start by multiplying by 106 likes...
Wait why 106?
gritty glacier
so it is approximately close to 1800
it may not be exact but it would suffice for a start
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magic tusk
Could someone help me understand domain and ranges?
safe radishBOT
Could someone help me understand domain and ranges?
magic tusk
or is there a website that could help me understand
i dont have anything specific right now that I don't understand
its pretty broad
my understanding of domain and ranges is little to none at the moment
(i didnt pay attention in class 👍)
magic tusk
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magic tusk
i am confused
pulsar pecan
so h(n)= -2(n+6)-1
!nosols
safe radishBOT
so h(n)= -2(n+6)-1
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
lean otter
!shtup
magic tusk
.close
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somber heath
in the trapezoid ABCD, with the bases AB > CD, we note M,N the means of AD, respectively BC. The bisectors of angles A and B intersect MN in E and F, respectively. It shows that EF= AB+CD/2 - AD+BC/2
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in the trapezoid ABCD, with the bases AB > CD, we note M,N the means of AD, resp...
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somber heath
<@&286206848099549185>
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thorny condor
math proves the existence of a higher being
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@somber heath Has your question been resolved?
somber heath
math proves the existence of a higher being
what
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somber heath
<@&286206848099549185>
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lean otter
math proves the existence of a higher being
wtf you on?
patent kindle
he is on a different plane of understanding than the rest of us
somber heath
<@&286206848099549185>
main merlin
The case where they intersect above MN is easily provable
somber heath
The case where they intersect above MN is easily provable
Can you elaborate?
It really frustrates me
It looks easy but it aint
If you can, try not to use sin and cos, they're not included in this chapter
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stoic saddle
Can you elaborate?
If the angle bisectors intersect above the line MN, then you can prove that Δ MFA is isoceles(∠MAE=∠MFA bc of alternate angles), hence MF = AM = AD/2 and similarly that EN = CB/2. Since FE = (AB+CD)/2 - (MF + EN), we can susbtitute our results and get that FE = (AB+CD)/2 - (AD+BC)/2
In the case when the angle bisectors intersect below MN, the formula is actually not true
but its conjugate is
Following is the proof for when the angle bisectors intersect below MN (your diagram):
∠EAB = ∠MEA (alternate angles)
Therefore triangle AME is isoceles (base angles are same)
Therefore AM = ME
or ME = AD/2 (AM + MD = AD but AM = MD)
or MN - EN = AD/2 (i)
Similarly MN - MF = BC/2 (ii)
Adding eqs (i) and (ii) together:
2MN - (EN + MF) = (AD+BC)/2
or 2MN - ((MN-FE-MF) + MF) = (AD+BC)/2 (EN = MN-FE-MF)
or 2MN - (MN-FE) = (AD+BC)/2
or MN + FE = (AD+BC)/2
or (AB+CD)/2 + FE = (AD+BC)/2 (MN = (AB+CD)/2)
or FE =(AD+BC)/2 - (AB+CD)/2
Hence there are two seperate equations for FE depending on wether they intersect above or below MN
sorry if my proof is very sloppy
somber heath
I'll try and write it down when I have time.
so i can understand it
safe radishBOT
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somber heath
or FE =(AD+BC)/2 - (AB+CD)/2
This is here
Ive still been trying for the past days
I gotta prove that FE = (AB+CD)/2 - (AD+BC)/2
On which we've proved the inverted.
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somber heath
<@848592586134519841>
they're busy probab;y
lean otter
<@&286206848099549185>
lean otter
or FE =(AD+BC)/2 - (AB+CD)/2
@somber heath bro it is proved here.
somber heath
<@848592586134519841> bro it is proved here.
somber heath
.close
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reef grail
Can someone help me understand maximal and minimal elements
safe radishBOT
Can someone help me understand maximal and minimal elements
reef grail
e.g, does this set contain maximal and minimal elements, if so what are they
on the subset relation btw
final halo
for small examples like this you might want to draw whats called a "hasse diagram" like this
solar hazel
for this one i think you could also just look at it and know, if you understand what maximal and minimal elements are
reef grail
for this one i think you could also just look at it and know, if you understand ...
I dont really understand what they are tbh
I've asked chatGPT about it and it talks about whether there exists a set strictly greater than all the other elements
for this example would that mean the maximal element would be {a, b, c}?
solar hazel
the maximal element is not the right term until you have determined there is only one (which you don't even need to do here)
reef grail
ok
solar hazel
I've asked chatGPT about it and it talks about whether there exists a set strict...
also no this is incorrect
reef grail
I feel as though chatGPT's explanation here is quite vague
solar hazel
there is no point in using chatgpt if you don't understand the definitions n stuff and can't verify what it's saying
reef grail
there is no point in using chatgpt if you don't understand the definitions n stu...
true
solar hazel
let $X$ be your set. an element $A\in X$ is maximal if it is not ``smaller" than any other set in $X$. I.e. for every $B\in X$ with $B\neq A$, it is not the case that $A\subseteq B$.
flat frigateBOT
layla
solar hazel
you can just look through the elements in X and see if any satisfy that
is {b} contained in any other set in X? yes (e.g. {a,b,c}), so it's not maximal
is {c} contained in any other set in X? yes, so it's not maximal
is {a,b} contained in any other set in X? yes, so it's not maximal
is {a,c} contained in any other set in X? yes, so it's not maximal
is {a,b,c} contained in any other set in X? no, so it's maximal
reef grail
for the last line do you mean it is maximal?
solar hazel
yes sorry
reef grail
cool
I think I understand now thank you very much
and for minimal elements
would it be that for every element that isn't itself, it is a subset of another set?
solar hazel
what
reef grail
what
would the list of minimal elements only contain elements which are subsets of other sets
solar hazel
in this case yea but not in general and that's not the definition
if we put {e,f,g} in this set, it would be minimal
but it's not a subset of anything else in X
it would also be maximal
reef grail
ah
reef grail
**layla**
please could I have the formal definition of minimal elements like you did here
solar hazel
let $X$ be your set. an element $A\in X$ is minimal if it is not ``larger" than any other set in $X$. I.e. for every $B\in X$ with $B\neq A$, it is not the case that $B\subseteq A$.
flat frigateBOT
layla
reef grail
perfect, thank you very much
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crimson matrix
lean otter
ok sorry
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vale hollow
I first found p by taking the sqrt(0^2 + 0^2 + 12^2) = 12
I then used z = pcosφ to solve for φ
but that equation gives cosφ = 1
So is φ 0 or 2pi ....?
not too sure, any help would be appreciated
stoic dune
Note that φ is between 0 and π
vale hollow
ohh yeah
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cold zealot
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cold zealot
first answer 8.8 cm 1 dp
second answer 66.4 degrees 1 dp
can someone just confirm these answers for me please
final halo
people are much more likely to check your working rather than do the question themselves just to check if you're right
so try showing your work
cold zealot
This is my working
<@&286206848099549185> please can i get some help I have a test tomorrow I really need to know if im right
cold zealot
ye
dusky crag
Wouldn't it be half of AC? which is 9.4÷2
dusky crag
Np
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plucky elk
!show
safe radishBOT
Show your work, and if possible, explain where you are stuck.
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fair pecan
hello
fair pecan
i thought cubic functions with a positive leading coefficient would always look like: goes bottom left to top right. However, this is not the case. Why?
fleet condor
i thought cubic functions with a positive leading coefficient would always look ...
try zooming out :)
(it is the case)
fair pecan
it just goes down foreverrrr
fleet condor
it just goes down foreverrrr
it does not in fact do that
fleet condor
the large negative co-efficient on the x^2 term is "stronger" than the x^3 for a while
fair pecan
oh, i never thought of it as that way
ill make sure to note that down
wiat thats so big brain
thank u
fleet condor
vale hollow
Anyone know multivariable calc and can help?
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vale hollow
any <@&286206848099549185> know multivariable calc and can help?
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lilac cradle
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hazy elbow
are you aware of the formula for perpedicular length from a point to a line
at the point of intersection of the tangent and circle, radius drawn from centre to that point would be perpendicular to it
hazy elbow
show your work
hazy elbow
lilac cradle
What is this
desert juniper
Okay, first off, your drawing is kind of bad. You got a grid, use it for much better accuracy.
Also, you're not drawing the circle tangent to the line.
Gimme a sec to post a better graph:
lilac cradle
Okay
desert juniper
now, the green line is your original line, the red circle is (obviously) the circle, P is the center of the circle, and the orange line is perpendicular to the green line
your distance asked for is from P, center of circle, to the interesection of the green and orange lines. Let's call that Q
You know that PQ is the radius of the circle
you also know that if the green line is tangent to the circle, the radius to the tangency point is perpendicular to said tangent line
good so far?
lilac cradle
Yes
desert juniper
okay. To obtain the orange line, you know that it's perpendicular to the green (original) line, and that it goes through P, the center of the circle. Do you know how to do that?
desert juniper
Okay. After having both lines, you can obtain Q, the intersection point.
After having Q, you can obtain the distance from P to Q.
Do you know how to do that?
desert juniper
The equation of the radius is y=-1/2x-3
i'm not obtaining that. That line does not go through P.
lilac cradle
Why not
Because it’s perpendicular to the tangent
And also goes through the centre
desert juniper
because if y=-3, and x=2:
-3=-(1/2)*2-3
-3=-1-3
-3=-4
(also, this is kind of cheating, but you can see in the graph that the y-intercept of the orange line is not at y=-3)
desert juniper
so now you can obtain Q, and thus PQ
lilac cradle
I got x =-3.2
And y =-0.4
Nvm
I got the answer
Thank you for helping
there’s another question I’m struggling with
desert juniper
it's a variation of the same question
with the equation given like that, you got the center of the circle and the radius
specifically, (2,1), and sqrt(d)
if you know the center of the circle, and the tangent line, you can get the distance same as the previous exercise
if the radius of the circle is equal to that, the line is tangent
if the radius is larger, the line is secant
if the radius is smaller, the circle is not large enough to meet the line
lilac cradle
Secant meaning
I can’t seem to get the right answer for this
<@&286206848099549185>
atomic flame
hi
lilac cradle
plz help
atomic flame
lilac cradle
😭😭😭😭😭
atomic flame
inland tangle
wow nostalgia
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pastel minnow
hello
peak smelt
safe radishBOT
what is the answer
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
pastel minnow
i know i mean what should i do
limber lion
what is the answer
have you attempted to do it?
what did you do?
can you send it here
pastel minnow
5>2x
pastel minnow
then
limber lion
and the second one?
safe radishBOT
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@pastel minnow Has your question been resolved?
pastel minnow
no(
limber lion
thank you
your welcome,
dont close this channel yet, try to read the method, solve it, and just ask if you have any doubts
dont forget to ping/tag me or @ helpers
to just notify us
pastel minnow
okay
lean otter
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lean otter
Hello I have to proof this with general induction and I know how to do those but I’m confused about the left term
It goes x to the power of n minus two and then the next even number but eventually it becomes a fraction?
I wanted to know why
In my first step I have to proof that this is true for n=1 but I don’t know how to do that since I can’t think of a way to show the whole term
Maybe x to the power of n minus 2 and 1 decided by x to the power of n minus two and then combine all those somehow?but I’m not sure
peak estuary
well if eg n=7 then the exponents would be 7,5,3,1,-1,-3,-5,-7
and remember that eg x^-5=1/x^5
for n=1 its just x+1/x
lean otter
Aaaaah so x to the power of -2 is the same as 1 devided by x to the power of 2?
I started doing it for 1 .do the x^-5 and 1/x^-5 add to 0?
If everyone cancelled eachother out only x^1 and 1/x would stay right?
safe radishBOT
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lean otter
hmm? it stops as soon as you hit -n
What do you mean it Stopps?
This is how I tried to proof n=1 is it wrong.?
peak estuary
yes the sum of those things is not zero
for n=1 your sum just has the terms x and 1/x
no other terms
lean otter
for n=1 your sum just has the terms x and 1/x
But why?
lean otter
This shows infinite more x^n-6 etc
It’s always a bigger even number isn’t it ?
Somwhy would it just be x and 1/x?
peak estuary
this ... notation is not supposed to be taken that literally
the exponents start at n, go down in steps by 2 until they reach -n
thats what that notation means
lean otter
thats what that notation means
Okay thanks
lean otter
thats what that notation means
So this is just n=1?
How can I proof that it’s bigger than 2?
peak estuary
well you can do the same as the very last step in your previous attempt
using that sqrt(x) exists
lean otter
using that sqrt(x) exists
lean otter
well you can do the same as the very last step in your previous attempt
Last time x was squared this time it’s not so i don’t know what to do after this
peak estuary
x = (sqrt(x))^2
peak estuary
you have number^2+1/number^2-2
just like you had it before
your original proof also more or less works, you just need to argue why you can square the inequality (you cant in general) and you messed up one of the lines
lean otter
lean otter
you have number^2+1/number^2-2
Like this?
I really am having a very hard time understanding what you’re saying can you please say why I need to do certain stuff?
I don’t feel like I’m learning
peak estuary
$x+\frac1x-2=(\sqrt x)^2 + \frac{1}{(\sqrt x)^2}-2 = \left(\sqrt x-\frac{1}{\sqrt x}\right)^2$
flat frigateBOT
Denascite
lean otter
.close
jovial scroll
safe radishBOT
jovial scroll
this is a physics question but i am not getting any help in the physics channel, but it's quite simple
am i getting the friction force and normal force correctly as per this illustration?
friction force up = weight of car (in the opposite direction) down
i believe weight of car down should be (90 - 10) degrees times weight force
the question is: am i calculating this right
.close
waxen moon
Would x = 4 be an inflection point and not x = 5?
safe radishBOT
Would x = 4 be an inflection point and not x = 5?
waxen moon
Pls turn reply pings on
fleet condor
Pls turn reply pings on
x=5 is an inflection point and x=4 is not
wait
oh inflection point not critical point
x=4 is probably an inflection point, at x=5 the slope goes from decreasing to increasing, so it is as well
loud crag
both
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lean otter
What is x that satisfies the equation? (Translation)
safe radishBOT
What is x that satisfies the equation? (Translation)
lean otter
I have only come here
Idk what to do anymore
İn mu equation
X is negative number
İ obviusly did something wrong
neat kiln
Hard to understand
lean otter
I m doing it true
Like the way i do is it true should i do it that way
Or should i find a new way?
Ok bro👍
.close
frigid pewter
Do you know how to show that a subset of Rn is a subspace?
In that case do you know what a subspace is?
It's a set of vectors of your whole space (R3 for you) where the sum of any two vectors set is also in the set, and scalar multiples of vectors in the set are also in the set
Try showing that if you take any two arbitrary vectors in H, then their sum is in H
placid totem
frigid pewter
You're seeing whether sums of vectors in H are in H. This doesn't have to do with dot products
yep
There will be the tiniest bit of algebra, and you'll see that the sum is an element of H
Nope, you want b and c to be arbitrary.
When we say "arbitrary" we mean "not particular values"
This is an arbitrary element of H. That's good. But you're testing if sums of arbitrary elements are in H; you need another arbitrary element of H.
(You can also save typing by writing u,v instead of your vectors)
Remember, if you are writing an arbitrary vector in H, you don't get to pick the coefficients. If you choose 0, you're setting both scalars to 0
You've shown that a particular linear combination of elements of H is in H. There might be another one that isn't, and you're trying to rule out that possibility. You can't get there by choosing some particular vectors
Yes, that is exactly the problem you're trying to solve.
The first step will be something like "suppose w_1 and w_2 are in H". Then you'll write out w_1+w_2, expand them, and see that it is in H
The video will almost definitely do that
The process is exactly the same for any vector space, including R^n
frigid pewter
The first step will be something like "suppose w_1 and w_2 are in H". Then you'l...
I have to go, but try showing this for the simpler case where H is a subset of R2 where x=y. If you can show that sums of vectors of H are in H, and you address the scalar multiplication requirement, you'll have shown H is a subspace
The video you linked probably does this, and so will your course textbook if you have one
And lectures
safe radishBOT
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pliant shadow
Hi, so I just started studying about Mandelbrot sets for an investigation, and I kinda understand the whole Im(x) and Re(x) aspects of it but I don't understand the...
- mathematical criteria for which an orbit becomes stable
- why they're even orbits in the first place
This is the video I was watching - https://www.youtube.com/watch?v=FFftmWSzgmk
safe radishBOT
Hi, so I just started studying about Mandelbrot sets for an investigation, and I...
@pliant shadow Has your question been resolved?
pliant shadow
<@&286206848099549185>
fallow wren
Hi, so I just started studying about Mandelbrot sets for an investigation, and I...
the mandelbrot set is the set of points c for which the sequence defined recursively with z_1=c and z_{n+1}=z_n²+c is bounded
pliant shadow
So is the orbit supposed to be a set of points that recurse till infinity?
pliant shadow
depends what you mean by recurse till infinity
like, you put a value in a function
put the result in the same function again
like f(f(f(f(x)))) n stuff
pliant shadow
wait is that the right meaning for that
i dont get the difference between a stable and unstable orbit tho, like i can interpret this as a spectrum of stableness
fallow wren
whats interesting about the ones with the mandelbrot set is that the "magnitude" of the number resulting from doing that arbitrarily many times is never greater than some value
pliant shadow
i dont get the difference between a stable and unstable orbit tho, like i can in...
which gets exponentially greater as i move the point away from the origin
fallow wren
i dont get the difference between a stable and unstable orbit tho, like i can in...
ok so in this case what youd mean by unstable is unbounded
pliant shadow
ok so in this case what youd mean by unstable is unbounded
yes yes
fallow wren
which gets exponentially greater as i move the point away from the origin
not exponential!! z²+c is a polynomjal
pliant shadow
not exponential!! z²+c is a polynomjal
oh yea my bad, polynomial
fallow wren
very clearly will get big
arbitrarily big
but if you start eg at -1
the sequence looks like
(-1)²+-1 = 0, 0²+(-1)=-1, 0, -1, etc
which is clearly bounded by 1
pliant shadow
yeahhhh i noticed
on the number line its pretty stable when x < 1
so if i take this lil orbit, its basically a set of points you get from a recursive function right?
fallow wren
in fact you can prove that if |z|<1/2 z is always in the mandelbrot set and if |z|>2 z is never in jt
it*
fallow wren
so if i take this lil orbit, its basically a set of points you get from a recurs...
p much
still not a big fan of the word orbit but yeah
pliant shadow
still not a big fan of the word orbit but yeah
what would you call it then?
oh ye
spiral
fallow wren
a sequence
pliant shadow
oh ok ok
does the stable sequence still technically have infinity points in it tho?
fallow wren
infinity points?
pliant shadow
like, you recurse infinity times and get infinity points
or, at least, sufficient times to get sufficient points for the sequence's structure
pliant shadow
i think there's a calculus aspect behind how the distance between the points increase as i move further away from the origin
fallow wren
i think there's a calculus aspect behind how the distance between the points inc...
afaik its not much to do with calculus because jts all discrete
fallow wren
or, at least, sufficient times to get sufficient points for the sequence's struc...
but this is a meaningless statement
pliant shadow
i just dont get why it is considered unstable beyond the unit circle
pliant shadow
afaik its not much to do with calculus because jts all discrete
oh ye alr
pliant shadow
but this is a meaningless statement
mbmb
fallow wren
i just dont get why it is considered unstable beyond the unit circle
if you take -2, thats outside the unit circle but is bounded so idrk what you mean
maybe theres some properties of the mandelbrot set im unaware of
pliant shadow
if you take -2, thats outside the unit circle but is bounded so idrk what you me...
well in the video i watched they said the sequence becomes unstable beyond the unit circle
fallow wren
in that case idk how they define stable
pliant shadow
in that case idk how they define stable
thats what i also wanted to know lol
fallow wren
because that doesnt sound right and wikipedia doesnt mention the word stable
pliant shadow
oki
fallow wren
might watch the vid later so i actually know what theyre on about
for now tho igtg bye
cedar lily
How is dy/dx defined for non-functional relationships between y and x?
cedar lily
Like for y^2 = x, I could differentiate that using various rules, but the definition of the derivative doesn't seems to work
safe radishBOT
@cedar lily Has your question been resolved?
deep vine
safe radishBOT
plucky elk
$\sin(x) + \cos(x) = \sqrt(2) \sin(x+pi/4)$
flat frigateBOT
riemann
plucky elk
something like that
deep vine
is this a rule?
halcyon carbon
its like harmonic form or smth you get this from using sum formula for Rsin(a+b)
flat frigateBOT
riemann
plucky elk
first line with theta = pi/4
deep vine
I hate my life fuck this question
halcyon carbon
honestly you can just say sinx + cosx is between -2 and 2
hm actually no
dont do that
safe radishBOT
Available help channel!
shut basin
is there like a place I can find restrictive domains in terms of radians
shut basin
like arccsc, arccot, arcsec
a lot of sources I find are not like, in terms of the unit circle
drowsy karma
when you talk about inverses to trig functions, then you do not talk about thier domaisn expressed in terms of radians
shut basin
when you talk about inverses to trig functions, then you do not talk about thier...
really?
that's really, really, really sucky because the answers for the homework are expressed in terms of radians
drowsy karma
ofc, please read the definution of thier inverses
shut basin
okay I'll try my best thank you
flat frigateBOT
Joanna Angel
drowsy karma
then you get that:
drowsy karma
$y=arcsinx\text{ for }|x|\leqslant 1$
flat frigateBOT
Joanna Angel
shut basin
can the 1 represent anything on the unit circle
drowsy karma
can you see both formuals fo royu ?
drowsy karma
$sin\frac{\pi}{2}=1$
flat frigateBOT
Joanna Angel
shut basin
yes I understand this
shut basin
oh shoot
drowsy karma
arcsine wors in opposite way
shut basin
so, coodinate input radian output?
drowsy karma
$arcsin1=\frac{\pi}{2}$
flat frigateBOT
Joanna Angel
shut basin
basically, sin of what is equal to pi/2, that's how I've been phrasing it
shut basin
you're right, that's true, that's the hard part
so I can only express restrictive domain in terms of, idk what you'd even call it man
the 1 here
coordinate?
sin 1 is the y value
can't express in degrees or radians?
drowsy karma
the otger exampel i show you
$arcsin\frac{1}{2}=\frac{\pi}{6}<=>sin\frac{\pi}6{}=\frac{1}2{}$
flat frigateBOT
Joanna Angel
flat frigateBOT
Joanna Angel
shut basin
so that range is 90 degrees to 0 degrees?
drowsy karma
must be onto and one to one
x belogns to domains, and y belogns to range
let me write it
shut basin
x domain y to range, that makes sense, it's a possible 1, -1, or 0
sort of
so since sin is less than or equal to 1, that means that it's less than or equal to sin 1?
drowsy karma
$\text{Let }f\text{ be a bijective mapping, means a bijection, then if }f(x)=sinx\text{ for }|x|\leqslant \frac{\pi}{2}\text{ then }|y|\leqslant 1$
flat frigateBOT
Joanna Angel
drowsy karma
so , ven on yoru table, you have ut it here, you can see that range is expressed in radians
but not domain
and you must add
you tlak ab arc functions
not ab trig fucntions
if you want to talk ab trig fucbtions then you must say: domain is expresed in radians
junior smelt
$arcsin\frac{1}{2}=\frac{\pi}{6}<=>sin\frac{\pi}6{}=\frac{1}2{}$
($\iff$ as a tip btw)
flat frigateBOT
@junior smelt
shut basin
I think I got it now
drowsy karma
<@788085606483361802>
it is also possibe, though very rarely, that
you can take trig fucntions on the other intervaks where they are bijecitons
but it happens rare
then you get, th eother branches of arc fucntions
but your table refers to normal = classical itnervals
drowsy karma
($\iff$ as a tip btw)
thx for the tip )
shut basin
.close
safe radishBOT
How can i solve for theta
halcyon carbon
Is theta meant to be complex
slow sluice
Its supposed to be an angle between two vectors
slow sluice
halcyon carbon
|v| = sqrt(12) and |w| = sqrt(2)
halcyon carbon
slow sluice
.close
dull salmon
how would i do question 2?
patent musk
safe radishBOT
patent musk
am i right with B here?
lost patrol
!show
safe radishBOT
Show your work, and if possible, explain where you are stuck.
icy lance
why ask then if youre certain
lean thorn
i mean it obviously is less than
the key here is to show so that you can confirm it instead of inferring it.
so what would be the steps for each probability?
patent musk
.close
wise schooner
safe radishBOT
wise schooner
Where did I go wrong?
I think I found the mistake, is it cause
(sqrt(x+8))^2 != x+8
?
wise schooner
YOU ALGEBRA'D A BIT WRONG HERE
it should be 2rootx+8 * du right?
sinful zodiac
it should be 2rootx+8 * du right?
YEP
wise schooner
WHY ALWAYS THE CAPS THO
sinful zodiac
I FORGET
wise schooner
ALRIGHT TY
wise schooner
I FORGET
QUESTION, IF IM INTEGRATING SAY XROOT(X+8) WITH RESPECT TO U, WHAT WOULD THAT BE?
icy lance
whats even going on
icy lance
QUESTION, IF IM INTEGRATING SAY XROOT(X+8) WITH RESPECT TO U, WHAT WOULD THAT BE...
whats u
icy lance
whats wrong
wise schooner
icy lance
again, what is u
wise schooner
how do you integrate x with respect to u tho?
icy lance
np
wise schooner
.close
safe radishBOT
safe radishBOT
Available help channel!
sharp light
viral vault
<@&286206848099549185> 20. Length of the fence of a trapezium shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC. ^can someone help me with this please?
.
sharp light
its ok
rose hamlet
thanks friend
viral vault
I have another method
Area of the trapezium is 12×15(40+48)=12×15×88=15×44=660m2
and I got a different pic than yours
safe radishBOT
@sharp light Has your question been resolved?
sharp light
<@&268886789983436800> this is my help channel!
wild cape
@viral vault this channel is occupied. see #❓how-to-get-help
sharp light
<@&286206848099549185> i still need help
plucky elk
<@&286206848099549185> i still need help
Did you take the log of both sides
safe radishBOT
safe radishBOT
Available help channel!
fallen thunder
Hi, i got the answer to this question but now that i think about it
fallen thunder
This question is a bit wrong right?
How can a circle be "inscribed" inside a rectangle? Unless the rectangle is a square
Doesn't inscribed mean that the circle should touch all edges of the rectangle?
simple oak
safe radishBOT
@fallen thunder Has your question been resolved?
safe radishBOT
@fallen thunder Has your question been resolved?
eternal steppe
can anyone help me with remainder theorem
safe radishBOT
can anyone help me with remainder theorem
frigid spruce
!da2a
safe radishBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
thin bridge
what are the exact intructions of the question
whole badger
Just insert -6 in place of p in the polynomial dividend
whole badger
what are the exact intructions of the question
To find the remainder most probs
thin bridge
probs not good enough
whole badger
can anyone help me with remainder theorem
.
thin bridge
yeh, and the question may be asking for something else entirely
which could've been misinterpreted
(happens quite often)
whole badger
yeh, and the question may be asking for something else entirely
Well the question can ask for two things in this case
One find the quotient
and second find the remainder
thin bridge
and we should wait for a clear response from the op to know which
eternal steppe
and we should wait for a clear response from the op to know which
hello?
whole badger
how though
The question is asking for the remainder right?
eternal steppe
The question is asking for the remainder right?
yeah and the result
thin bridge
wdym and the result
whole badger
i was peeing
Too much information💀
whole badger
wdym and the result
Quotient
thin bridge
so they want both the quotient and the remainder?
eternal steppe
so they want both the quotient and the remainder?
yep
thin bridge
ok, then you should approach this with polynomial long division or synthetic division
eternal steppe
ok, then you should approach this with polynomial long division or synthetic div...
wait there's other than long division?
thin bridge
have you done either of those yet?
eternal steppe
have you done long division with numbers?
no
thin bridge
e.g. stuff like
$$7)\overline{123}$$
flat frigateBOT
ℝαμΩℕωⅤ
eternal steppe
is it like this?
thin bridge
where instead of working with powers of 10
eternal steppe
eternal steppe
question is it like this?
thin bridge
that's how you'd set it up, but
the line at the top should be longer
eternal steppe
oh how do i start with it?
thin bridge
like that but
the line at the top should be longer
fossil shell
@thin bridge what's so special about 180*pi / (180 + pi) ?
thin bridge
$\text{divisor})\overline{\text{dividend}}$
flat frigateBOT
ℝαμΩℕωⅤ
eternal steppe
aight
thin bridge
with that horizontal line sufficient long to cover the whole dividend
eternal steppe
should i write it?
eternal steppe
like this?
thin bridge
with that horizontal line sufficient long to cover the whole dividend
eternal steppe
thin bridge
issue i mentioned is still there
eternal steppe
sorry
thin bridge
eternal steppe
so how do i start?
thin bridge
how many times does p go into p^4
thin bridge
yes
eternal steppe
put it on top?
thin bridge
yes
eternal steppe
nice
what next
oh wait can i send you a pic
i already answered it
idk if it's right or not
hello?
thin bridge
send it
thin bridge
5-6 isn't 1
thin bridge
yes, its -1
eternal steppe
sorry for the chat mb
thin bridge
thus 5p^3 - 6p^3 will be -p^3
eternal steppe
5p^3 - 6p^3 isn't p^3
that's only the error?
thin bridge
yeh, and restart your work from there
