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#help-38
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viral kernel
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limpid dawn
I get the denominator but not the numerator
when there are real roots you use one letter without x
when there are no real roots
then you use Ax + B in the numerator (a linear function)
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@viral kernel Has your question been resolved?
solar notch
I'm confused mainly on error bounds, K, and midpoint rule to approximate the integral to be more specific, I have a couple of question revolving around these topics
solar notch
an example question would be using midpoint rule to approximate the integral from -1 to 1 of e^(-x^2) dx What is the smallest integer n
for which the Error Bounds theorem guarantees that Mn is within 10^-12.
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solar notch
i understand that the integral from -1 to 1 of e^(-x^2) dx isn't a elementary integral thus making it impossible to integrate
for the K value I'm confused on how to exact determine the maximum and minmum in situations like the one listed
open fulcrum
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vernal wraith
I'm getting 0.438 and 0.171 as answers.
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@open fulcrum Has your question been resolved?
sacred sapphire
putting 0.391 doesnt work either
are you sure you're calculating it correctly
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lean hazel
Hello, I was able to get the answer, however, I got confused in pi/2 on the left minus pi/2. Could someone explain why the value I got from inverse tanx approaches pi/2 on the left?
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Hello, I was able to get the answer, however, I got confused in pi/2 on the left...
@lean hazel Has your question been resolved?
lean hazel
yessir
ivory talon
Lezgo
Ok look the the left
x approaches positive infinity
And positive infinity can be written as 1/0, no?
lean hazel
yepp
ivory talon
So now its tan-1(1/0)
And tan is sin/cos
So now its sin-1/cos-1
And what angle could there be for its sine to be 1 and cos to be 0?
Look at the unit circle
Low quality sorry lmao
lean hazel
pi/2 right?
lean hazel
oh yeah, I was able to understand that but why should it approach from the left instead of right? Could it be because when we write pi it's counterclockwise?
ivory talon
Because cos(x) when approaching from the right equals a negative value which does not satisfy the +inf from the limit
It would be -1/0 or -inf
cos(x) is negative from pi/2 to 3pi/2
ivory talon
No problem
lean hazel
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neon mural
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neon mural
The mid segment theorem should be applied
I forgot how to do this question even though I solved it yesterday
So I just need a brief explaination that's all
vernal wraith
$\frac{4x+3}{4x+3+5x-2} = \frac{4x+3}{9x+1} = \frac{1}{2}$
solid kilnBOT
Solomaniac
vernal wraith
@neon mural
frail heron
yeah, itβs 46
neon mural
<@1188145024316227666>
No
frail heron
Heβs done the progress for you
vernal wraith
@frail heron wait
neon mural
yeah, itβs 46
Pls explain
frail heron
You just need to add up
vernal wraith
Let us hear what he has to say
frail heron
Sure XD
neon mural
The midsegment theorem states that Segment MN should be half the size of segment XZ
frail heron
Iβll leave for other questions
vernal wraith
The midsegment theorem states that Segment MN should be half the size of segment...
Yes it does.
neon mural
So 1/2 x (2x+1)?
vernal wraith
Iβll leave for other questions
You are needed for far more important battles,my brother.
vernal wraith
So 1/2 x (2x+1)?
What's this ?
vernal wraith
And do we know the length of XZ ?
neon mural
We dont
vernal wraith
Can u solve for me?
I have solved for you !!
vernal wraith
We dont
Good. It seems you haven't understood the midsegment theorem. The midsegment theorem is just a special case of Triangular Similarity. Understand that triangle YMN and YXZ are similar by the All Angle Similarity. This means the ratio of YM/YX = YN/YZ = MN/XZ.
Use the first two from the three sided equality to find x
vernal wraith
No issues. Happy learning.π
neon mural
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robust coral
Hello, I have this map :
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Hello, I have this map :
robust coral
And I computed before the Tangent linear map :
Now I want to compute the linear map at x = (1,0) and determine to which tangent space to SU(2) it does belong to.
Idk if I'm right but for me in x = (1,0) the tangent linear map is just the first term of the equation before (second term 0). But it seems to easy...
scarlet escarp
consider asking in #diff-geo-diff-top
robust coral
Ok thanks
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void glen
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tidal forge
I suggest using product to sum formula
void glen
I suggest using product to sum formula
There's a formula for this series that's easier
I need help with that
void glen
Need a proper solution to this
tidal forge
There's a formula for this series that's easier
if u know that formula, then why u ask?
wraith hinge
the idea is to write cos (16pi/33) as cos (pi/2 - pi/33) = sin(pi/33)
then absorb the sin(pi/33) with the first cos(pi/33) and a factor of 2
to write it as sin(2pi/33)
ill let u continue from here
void glen
to write it as sin(2pi/33)
Oh makes sense
void glen
if u know that formula, then why u ask?
I wanted to know i didn't knew
tidal forge
I wanted to know i didn't knew
oh
void glen
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dapper basin
A pair of dice is rolled, what is the probability where first number is odd and second number is sum.
I dont understand the wordings at all, can someone hel
dapper basin
I got 1.5 but probabilities shouldn't extend to 1 so now I'm confused
wraith hinge
can you show, how you arrived at that answer
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verbal nebula
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verbal nebula
Came across this for mobius transformations, my only concern was that given the quadratic $cz^2-(d-a)z-b=0$ given by the transformation, the second and third dot pointed statements are contradictory
solid kilnBOT
jstn.
verbal nebula
since if c=0 and a=d, then b must equal 0 by the quadratic
but then again in the original fraction definition of M(z) b does not necessarily have to be 0
or does it??
scarlet escarp
im confused
they say to use the quadratic if c=/=0
ah i see what you're saying
consider M(z) = z. then supposing c = 0
az + b = dz
if b = 0, then every point satisfies this equation granted a = d
if b =/= 0 then no points satisfy this equation granted a = d
so if b =/= 0, there are no fixed points. by assuming the quadratic has a solution, you are forcing b = 0
@verbal nebula
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verbal nebula
so if b =/= 0, there are no fixed points. by assuming the quadratic has a soluti...
ohhh that is what I was missing. rearranging the equation into a quadratic essentially forced it to have a solution
thanks loads for the help
have a good one
primal axle
primal axle
<@&286206848099549185>
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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
simple haven
Also, what level is this problem?
primal axle
Also, what level is this problem?
Adv
primal axle
I've solved it brother
simple haven
Cool
dapper basin
In rolling 2 dice, what is the probability of an odd sum or even sum
dapper basin
by the word "or" you'd have to do the odd sum and even sum separately right
primal axle
yes
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hallow wadi
Can someone help me understand why, when rotating using quaternions, you also have to multiply with the inverse of q. See f(p)=qpq-1
stoic iron
The 3blue1brown video on quaternions probably sheds light on this very well
hallow wadi
Already watched that video but it doesn't give a clear answer of why you have to multiply by the inverse of q
<@&286206848099549185>
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hallow wadi
<@&286206848099549185>
simple haven
What would you consider to be a "clear answer" in this situation?
@hallow wadi just to be clear, you watched the quaterion video on 3d rotations, and then used the website https://eater.net/quaternions ?
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hallow wadi
<@669994216507703326> just to be clear, you watched the quaterion video on 3d ro...
Yes I watched the video's but I still don't really understand.
simple haven
@hallow wadi did you watch all 7 interactive videos on that page?
played with the controls and listened to the audio and you still don't really grasp the concept?
because if so, I don't know if anyone can do any better than that.
note, If you did, and you're still having trouble, that's OK, this is weird stuff
but I just wanted to make sure you actually did go through that website, rather than just passively watching the 2 youtube videos on the topic
hallow wadi
I watched but the concept is still a little vague to me. So by rotating let's say 45 degrees the sphere also gets bigger. And to cancel that you have to multiply by the inverse so the sphere stays the same size. But it also rotates another 45 degrees right?
Why does the sphere get bigger tho, I really don't understand that.
I can visualize what's happening but I don't understand the math.
simple haven
I'm not sure what you mean by "I don't understand the math." You understand geometrically what's happening, and presumably you understand mechanically how the multiplication of quaternions work. It sounds like you're uncomfortable with the idea.
@hallow wadi
The structure of qpq^-1 is very common in other areas of math, but it's likely the first time you've encountered it here
you see it in, for instance, linear algebra and in group theory
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unique plinth
hey for this is the solution
{1 β 2x^2 + 3x^3, 1 β 2x +3x^2 β x^3, 1 β 8x + 4x^2, x^3}
or
{1 β 2x^2 + 3x^3, 1 β 2x +3x^2 β x^3, 1 β 8x + 4x^2, 1}
and what is the correct approach to go about solving it?
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hey for this is the solution
{1 β 2x^2 + 3x^3, 1 β 2x +3x^2 β x^3, 1 β 8x + 4x^...
zinc ginkgo
Unclear either 1 or x^3 are linearly independent from the given 3 vectors. Try Gram Schmidt?
Or write a general vector and set the dot product to all 3 to zero to get coefficients
unique plinth
Or write a general vector and set the dot product to all 3 to zero to get coeffi...
can wolfram check linear independance
,wolfram linear independance {1 β 2x^2 + 3x^3, 1 β 2x +3x^2 β x^3, 1 β 8x + 4x^2, x^3}
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unique plinth
wtf
knotty locust
When you arrive here you will find a man who can tell you if the vectors are linearly independent
unique plinth
Unclear either 1 or x^3 are linearly independent from the given 3 vectors. Try G...
apparently both are linearly independent?
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zinc ginkgo
apparently both are linearly independent?
,w rref{{1, 0, -2, 3}, {1, -2, 3, -1}, {1, -8, 4, 0}, {0, 0, 0, 1}}
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zinc ginkgo
,w rref{{1, 0, -2, 3}, {1, -2, 3, -1}, {1, -8, 4, 0}, {1, 0, 0, 0}}
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zinc ginkgo
<:wat:524691995390902273>
did i type something wrong. or is {1, 0, 0, 0} not the right vector for the polynomial 1
zinc ginkgo
1 is the loneliest number
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unique plinth
so what is the answer?
,w rref{{1, 0, -2, 3}, {1, -2, 3, -1}, {1, -8, 4, 0}, {0, 1, 0, 0}}
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unique plinth
,w rref{{1, 0, -2, 3}, {1, -2, 3, -1}, {1, -8, 4, 0}, {0, 0, 1, 0}}
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unique plinth
,w rref{{1, 0, -2, 3}, {1, -2, 3, -1}, {1, -8, 4, 0}, {0, 0, 2, 1}}
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simple haven
It's true for all sets of 4 vectors which span the space
,w rref{{1, 1, 1, 0}, {0, -2, -8, 0}, {-2, 3, 4, 2}, {-3, 7, 9, 4}}
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simple haven
@unique plinth this is a counter example
unique plinth
,w rref{{1, 1, 1, 0}, {0, -2, -8, 0}, {-2, 3, 4, 2}, {-3, 7, 9, 4}}
wait what this doesnt even include the polynomials in the question
this is the original q
simple haven
@unique plinth it wasn't supposed to be anything except an example of a matrix with a rref that wasn't the identity.
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strong lintel
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left oriole
this looks fine, what's the concern?
strong lintel
this is the book answer
left oriole
ohh, i see
nimble stone
you set f=0 rather than its derivative
strong lintel
you set f=0 rather than its derivative
so f(0)?
strong lintel
can you show me
strong lintel
Yes that's what the question asks
it confused me at first yeh
,w differentiate \2x-e^3x
that is not what i asked bruh lmao
strong lintel
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manic briar
if i plug in n=12, i get x^12/15!
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if i plug in n=12, i get x^12/15!
manic briar
so how do i figure out f^12(0)
kindred pier
so how do i figure out f^12(0)
Do you know the general formula for the Maclaurin series?
manic briar
(f^n(0) (x)^n)/n!
kindred pier
if i plug in n=12, i get x^12/15!
And what is the 12th term for the Maclaurin series for f given here?
kindred pier
You need to use this
tepid hamlet
which is the term in that given maclaurin series that corresponds with f^(12)?
manic briar
And what is the 12th term for the Maclaurin series for f given here?
f^12(0) x^12/15! ? im confused sorry
tepid hamlet
in this series:
1/3! = f(0)
x/4! = f'(0)x / 1!
x^2/5! = f''(0)x^2/2!
...
each term corresponds to a term in the general formula you are giving
does that make sense?
tepid hamlet
be careful though, the 1st term is just f(0), the 2nd is first derivative, the 3rd is 2nd derivative etc. so you would be making an off by 1 error, the 13th term is the one that will atually have the 12th derivative
but yes in essence, replace what you had on the left with the 13th term
does that make sense?
actualy sorry you're right, the first term is n = 0, so never mind all i just said π¬
manic briar
oh
tepid hamlet
n = 12 will give you 13th term as needed
tepid hamlet
so i should set x^12/15! to f^12(0)x^12/12!
so yes to this
tepid hamlet
cause that's the term in the given series that corresponds to the f^(12) term not sure how else to explain it sorry if im doing a poor job
manic briar
would i set another series equal to x^12/12! if the series had a different equation
tepid hamlet
you would set whatever equation of the series youre given to the f^(12)(0)x^12/12! thats the general equation for maclaurin
youre literally just matching up the given series with the general equation term by term
well the 12th derivative only shows up in a single term
so you focus on that one
manic briar
okay, that makes a lot of sense
kindred pier
okay, that makes a lot of sense
@tepid hamlet with the genius teaching aides
manic briar
so its 1/15x14x13?
kindred pier
fun fact, you can just find the standard form of the function and calculate the 12th derivative that way
But that would be idiotic. Don't do that
kindred pier
!status
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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
i don't know where to begin
blissful bison
i don't know where to begin
you need to know: the theorem on the uniqueness of the expansion of a function into a power series and the formula for the radius of convergence of a power series
have you ever heard about it ?
UniquenessofPowerSeriesRepresentations :
and radius formulaes:
and that is all, you need to solve your problem
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manic briar
and that is all, you need to solve your problem
so.. should i use the ratio test?
blissful bison
so.. should i use the ratio test?
depends on you, but first you have to find c_n, the general, term
use the first photo
to establish c_n
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bright patio
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bright patio
I'm extremely confused on scale factors
vernal wraith
Ratio of AB/FJ
tepid hamlet
basically these figures are similar (one is like a scaled up\down version of the other) so there's a correspondence between for example the sides i colored red
how many times longer is the one on the left compared to the right one (AB vs JF as solomaniac said)?
bright patio
3:2?
tepid hamlet
right, 18/12 simplifies to 3/2 so the answer for the scale is 3/2
bright patio
But then the entire shape scale factor confuses me
tepid hamlet
the nice thing with similar polygons is that the ratio will be the same for ALL SIDES
bright patio
And then how do I use that information to find the values of the variables?
tepid hamlet
so since the ratio will be the same in ALL pairs of corresponding sides, like where you take 1 from the big polygon and 1 from the small, you can just use that to set up simple equations like this using that ratio
so for example with x:
$\frac{18}{12} = \frac{15}{x}$
bright patio
Oh
solid kilnBOT
Soosh
tepid hamlet
ratio of those 18 and 12 sides is the same as the 15 to x
and then just solve for x
bright patio
So 10?
tepid hamlet
ya exactly
tepid hamlet
try it with y now
tepid hamlet
what was the equation you wrote?
bright patio
18/12 = 8/y
tepid hamlet
so on the left we are keeping the figure on the left in the top of the fraction, stay consistent on the right, y should also be in the top of the fraction
x was on the bottom before because it was for the figure on the right, but this time y is for the figure on the left
so it should be 18/12 = y/8
see how both the lengths of the big figure is on top and the lengths of the small one on the bottom?
or both small on top and big ones on bottom, doesnt matter as long as they are consistent
tepid hamlet
so it should be 18/12 = y/8
simplify this, solve for y
bright patio
12?
tepid hamlet
yes
bright patio
O
tepid hamlet
ok now try z and pay attention to what we talked about
tepid hamlet
yep, good
tepid hamlet
that's all it is, it's really a very simple concept like youre just streching out the figure by some amount
bright patio
They need to correspond?
Or else I won't get a solid answer
Or I mean
A whole number answer
tepid hamlet
i mean you won't necessarily get a whole number answer, that just happened to be the case for this particular figure
bright patio
Ik
Oops
I mean ok
Tysm for showing me how to do this
It was overwhelmingly confusing
tepid hamlet
don't overthink it though, it isn't anything weird going on, it's just that literally you are stretching out the figure on the left by some amount, (happens to be 1.5 times in this case) and all the lengths of each side gets multiplied by 1.5
or sorry er divided in this case, i was thinking going from right one to left one
bright patio
I might open another help channel in a moment because there is another related problem I am confused on
But you really helped me with the scale factors
It makes so much more sense now
Ty
tepid hamlet
It makes so much more sense now
!done
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It makes so much more sense now
If you are done with this channel, please mark your problem as solved by typing .close
knotty locust
!done
See, if there is no Animal it gets ignored
surely if there was some buff squirrel
this would've been closed
@scarlet escarp
bright patio
.close
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wraith hinge
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wraith hinge
i got mass of water = 50-2t
F(t) = mass of water * g
dx/dt = 2m/s so dx = 2dt
and we get the W = integral from 0 to 25 of g(50-2t)2dt
is this right
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brazen spruce
how was the 156 degree angle figured out in the example
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how was the 156 degree angle figured out in the example
@brazen spruce Has your question been resolved?
brazen spruce
<@&286206848099549185>
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@brazen spruce Has your question been resolved?
frail heron
@brazen spruce has your question been resolved?
brazen spruce
<@343214362636320779> has your question been resolved?
no
frail heron
Ok
frail heron
Sure, let me solve the problem first
brazen spruce
Sure, let me solve the problem first
well, assuming the angle 156degrees is correct we can just use the cosine law to solve the sides....but i want to know how they got 156 in the first place
@frail heron still there?
brazen spruce
i have solution, its just an example in the course material by the way. i just dont know how they got that one angle in question
frail heron
Sorry, I canβt solve it since Iβm not familiar with bearings
Maybe next helper could help
Take care
prime badger
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oak schooner
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oak schooner
How to continue from here?
marsh forum
what;s the question. Is it $\lim_{x\rightarrow\infty}\left(\frac{\left(\left(\ln\left(9\right)+\ln\left(x\right)\right)\right)}{\ln\left(4\right)+\ln\left(x\right)}\right)^{\ ^{ln(x)}}$
oak schooner
Yes 9 and 4
wanton rune
also the exponent is ln(x)
solid kilnBOT
Why am. I here
marsh forum
looks like it's in the $1^{\infty}$ form to me
solid kilnBOT
Why am. I here
oak schooner
Yea itβs Euler limit
wanton rune
i'm not sure how you went from 1st step to 2nd step
marsh forum
Yea itβs Euler limit
then use the formula for this form
oak schooner
I try I bring the equation to the form of 1 + 1/f(x) )^f(x)
marsh forum
why? There's a standard way to solve such limits
oak schooner
How? π
marsh forum
let $\lim_{x\rightarrow a}f\left(x\right)^{g\left(x\right)}=1^{\infty}$
solid kilnBOT
Why am. I here
solid kilnBOT
Why am. I here
nova spire
I try I bring the equation to the form of 1 + 1/f(x) )^f(x)
let y = ln(4) + ln(x), try to remove every instance of x to make y appear instead
oak schooner
marsh forum
I'd probably use L'hopital's rule from here
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oak schooner
I suppose not to used it in this exe
nova spire
or write even better ln(x) = ln(4x) - ln(4)
trim urchin
Hello guys ! I struggle to understand some notations, can someone help me with it pls ?
trim urchin
They say it's the taylor formula but I don't understand the squiggly lines right to the equal sign, nor the flipped triangle
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wraith hinge
For the cone [
z = \3{x^2+y^2},\q 0\le z\le 1
]
you can find the parameterisation [
\6{\vj r}{r,\theta}=\9{r\6\cos\theta}\vc*\imath +\9{r\6\sin\theta}\vc*\jmath+r\vc*k
]
but how can i figure out if this parameterisation is one-to-one on its domain?
solid kilnBOT
simple haven
Well, you seem to have the pretty standard polar mapping of x = r cos ΞΈ, y = r sin ΞΈ, which you're certainly aware is not 1-to-1 for unrestricted values of ΞΈ
wraith hinge
Well, you seem to have the pretty standard polar mapping of x = r cos ΞΈ, y = r s...
my book says it is one-to-one in the interior of the domain though
but not on the boundary
which i dont quite understaned to be fair
simple haven
Are they using 0 β€ ΞΈ β€ 2Ο as the domain?
So you have repetition on the boundary?
wraith hinge
can u explain? i really dont understand
simple haven
Ok there's two cases of repeated points here
Case 1. x = r cos 0, and x = r cos 2Ο
Because both 0 and 2Ο are in the domain of ΞΈ we have a repetition on the boundary
wraith hinge
ah
simple haven
Case 2, x = 0 cos ΞΈ, and x = 0 cos Ο for ΞΈ β Ο
Because r = 0 is on the boundary, and that's also a bit of a problematic point to deal with in polar coordinates.
wraith hinge
how would r = 0 look like exactly in this case?
i mean you just will get 0? is the issue that there are several possible values of theta that map to 0 in this case
simple haven
Yes
Essentially on your rectangle, if you have ΞΈ = 0 on the left edge, ΞΈ = 2Ο on the right edge, r = 0 on the bottom edge, and r = 1 on the top, then you have the left edge repeating the right edge, and the bottom edge repeating a single point
wraith hinge
ah yeah fair enough
i understand now
just an additional question
my wondering is that for more complex cases like this one, how can u verify the one-to-oneness of the interior region
such as this
Like obviously i can find contradictions on the boundary from our condition
but idk how to conclude for certain that the parameterisation is one-to-one in the interior
simple haven
You would just need to show that the functions used are invertable. In the case of spherical coordinates, you can just algebraically invert them by solving for r, ΞΈ, Ο in terms of x, y, z.
And verifying that the domain of the inverse functions are valid.
wraith hinge
And verifying that the domain of the inverse functions are valid.
oh can we do that now as a little exercise for me to make sense of this
wraith hinge
alright
simple haven
So x = r cos t, y = r sin t
Consider the value x^2 + y^2 = r^2(cos^2 t + sin^2 t)
r = Β±β(x^2 + y^2)
(We take r to be positive)
Consider y/x = r sin t / r cos t = tan t
So arctan(y/x) = t
However, the codomain of arctan is smaller than the range of t, so we must introduce a little bit more robust method of inverting y/x = tan(t)
t = atan2(y, x)
For spherical coordinates, you'll get that the polar angle is arccos and the azimuthal angle is atan2 again.
Iirc
wraith hinge
oh wow this seems a bit abstract
simple haven
Atan2 is just arctan with some extra tests to put the result in the right quadrant if x is negative, and handle infinities when x = 0
I'm just being bullied by texbot
Halp
wraith hinge
ill look into this later thanks!
thanks a bunch
oh but one last question i suppose if u dont mind
hmmm
ok nevermind
thanks1
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hexed lantern
hello
hexed lantern
yo lets say a functions domain and range were something, and they want you to plot f(2) which lets say isn't inside that domain and range. Would it be possible to plot it in some way?
like making is a uncolored circle so it's not included etc etc
Grade 11 math btw
cause if I were to draw a line within the domain and range, and also include points outside the domain and range but not make them included would it even count?, and would they still be part of one main function?
Weird question, so weird prompts sorry lmao
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zinc ginkgo
do you have an actual example of functions
hexed lantern
(xer/1<x<7) and we have to see what f(-2) would be
hexed lantern
do you have an actual example of functions
also its supposed to be < and equal to dk hwo to do that
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dry laurel
what do I do
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what do I do
gritty harness
Use different trigo ratios, do you know them
brazen forge
yeah use trigs definitions
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exotic raven
what do I do
Trig ratios
SOH CAH TOA
sine = opposite/hypotenouse
cosine = adjacent/hypotenouse
tangent = opposite/adjacent
Number 1 would be
cos(theta) = adjacent/hypotenouse
So,
Theta = 37Β°
Adjacent = 11
Hypotnouse = x
So,
cos(37) = 11/x
Solve for x
Then use your calculator.
11/cos37 = x
Use your calculator and
Get your answer.
Try solving the rest and remember to use the trig ratios
chilly raven
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vagrant prism
how did you find the partial fractions?
chilly raven
how did you find the partial fractions?
I just knew x^2-81 is (x-9)(x+9)
vagrant prism
yes
vagrant prism
yes, but
vagrant prism
okay
so
the way i was taught was this:\
let's say $\frac{1}{x^2-81} = \frac{A}{x-9}+\frac{B}{x+9}$
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artemetra
vagrant prism
you get $\frac{A(x+9)+B(x-9)}{x^2-81} = \frac{1}{x^2-81}$
solid kilnBOT
artemetra
vagrant prism
so $A(x+9)+B(x-9)=1$
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artemetra
vagrant prism
what you now do is first substitute x=9, so x-9 vanishes and solve for A
then the same thing but with x=-9, so x+9 vanishes and solve for B
and those will be your values
vagrant prism
yep
chilly raven
suspicious
vagrant prism
yeah lol
but those are your values
now you can separate them integrate the usual way
chilly raven
so really a coefficient was added
will this always be the case in partial fraction decomposition for 2nd degree denominators?
vagrant prism
yes, and a minus inbetween
vagrant prism
will this always be the case in partial fraction decomposition for 2nd degree de...
no
vagrant prism
why 18
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chilly raven
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chilly raven
@vagrant prism off topic but I have a question if you are willing
vagrant prism
yes
chilly raven
when practicing math questions, I notice that I tend to get stuck on different cases of similar problems (like harder cases of partial fractions will give me a headache I am sure). Do you think it's worthwhile not to practice a lot of questions, but rather as varied of questions as possible?
in other words, depth or breadth
?
vagrant prism
both, always
why? depth gives you intuition
you get the 'feel' for some problems
why breadth? well you didn't stop on times table did you
jk jk
but yeah breadth is important cuz you might not be presented with something obvious and doing a little digging is always good
chilly raven
I see, should I start first with breadth then depth?
get a high level overview then do deep in each
vagrant prism
high level
vagrant prism
you get the 'feel' for some problems
it honestly depends on this
some topics are easy and i just jump straight into breadth
some topics are a little more unintuitive/confusing, that's when you gotta do depth and really make sure you understand what you are doing
(ironically) there's no formula to it
chilly raven
(ironically) there's no formula to it
the higher level maths I go into the less formulaic it seems
vagrant prism
sorta
vagrant prism
well, thanks for the advice, now off the solving more problems π
have fun!
vagrant prism
well, thanks for the advice, now off the solving more problems π
should i close this?
chilly raven
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gray compass
hi how would I prove this having trouble with this question
gray compass
Ik it obviously minimizes the costs but how would I start this proof
viscid flower
are you sure 
say c_i are all equal
and theres only 2 beaches
one has p_1 = 0.75 and the other p_2 = 0.25
oh, ascending 
viscid flower
trying to think if we can just use the definition
but i guess what you want is
you want the partial expected value to be strictly decreasing?
gray compass
yes
gray compass
how would I use a conditional here
viscid flower
idk im trying to think of the easiest way to formulate the sum
is it enough to show that r is decreasing
no, increasing
gray compass
mmm idk just showing that r is increasing just tells you ur PEV is decreasing but is that enough to tell you the strategy is optimal? idk
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past spoke
.
is there a function that subtracts all the prime numbers from the given imput x
for example x=18 ( from 0 to 18 there are 7 prime numbers (2,3,5,7,9,11,13,17) )
18-7= 11
is that even possible?
vagrant marsh
its increibly difficult to get the count of primes up to a certain number
marble wharf
past spoke
see <https://en.wikipedia.org/wiki/Prime-counting_function>
alr i will but i doubt there would be the direct answer
verbal cloak
how would I go about sketching x^2+y+1=0 by hand
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how would I go about sketching x^2+y+1=0 by hand
verbal cloak
i know y = -1 but the x answers would be imaginary
also i know it is a cylinder because 2 var.
zinc ginkgo
(0)^2-1 = y
where did this equation come from
verbal cloak
yeah
ik but it doesnt have any real x ints
i assume i would use that as my trace
or should i just plug arbitrary values
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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.
verbal cloak
number 5
I get it looks like this.
but if i didnt how would i know what values to plug in to get the trace of y = -x^2-1
zinc ginkgo
https://www.cuemath.com/geometry/parabola/
learn how to plot a parabola first
that'll be the trace in the z=0 plane
then since x^2 + y + 1 = 0 has no z variable, it's the same shape for all z=k planes
verbal cloak
yeah i understand that
i just felt like pugging in i.e x = 1 wouldnt be the best way to go
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verbal cloak
ty!
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frank merlin
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queen widget
queen widget
Whatβs the resistance of R.
delicate bobcat
Is the 0.35A current in the branch with 20 Ohm?
queen widget
Yes, the 0.35A comes out of the 20ohm resistor
short kiln
Calculate equivalent resistance in terms of R
Get current through 11 ohm resistor by V/R_eq
Apply junction rule where parallel begins
Solve for R
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uneven parcel
explain d
delicate bobcat
power rule
brazen forge
remember how power rule looks
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lament stone
i just have a quick question abt sin, cos, and tan. does the opposite and adjacent stay the same every single time?
brazen forge
i just have a quick question abt sin, cos, and tan. does the opposite and adjace...
the opposite is always opposite to the angle of trig you're using hence the name
you're welcome
lament stone
the opposite is always opposite to the angle of trig you're using hence the name
what if the angle is like 90?
brazen forge
then you use unit cricle definition
and not right triangle definition
so there is no "opposite" "adjacent"
lament stone
Ohh
orchid wagon
what if the angle is like 90?
then the angle you choose happens to be the angle directly to the hypotenuse
lament stone
then the angle you choose happens to be the angle directly to the hypotenuse
ohh
so for example
the opposite of 0 would. Be 15?
orchid wagon
so there is no "opposite" "adjacent"
the theorem still applies
the opposite happens to be the hypotenuse, which equates to 1 for sin
brazen forge
the theorem still applies
im too tired to check properly but you just use x and y i think
orchid wagon
there is no adjacent, so adjacent is 0
lament stone
the opposite of 0 would. Be 15?
like sin0 would be 15/x?
brazen forge
its just terminology
lament stone
there is no adjacent, so adjacent is 0
wait if the question is asking for the primary trigonometric ratios, they mean all of them right?
oh nvm wait it says in the question
my bad
orchid wagon
wait if the question is asking for the primary trigonometric ratios, they mean a...
yes
sin cos tan
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lament stone
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lament stone
@orchid wagon so sorry for the tag but if i get like 15/17 for sin0, do i solve for what 15/17 equals or is that not necessary
orchid wagon
youd get theta = arcsin15/17
lament stone
youd get theta = arcsin15/17
idk what those are
orchid wagon
think of them as reverse trig
say, sin(x) = a
therefore a =arcsin(x)
or also notated sin^-1(x)
lament stone
is it ok if i just solve for it tho cuz i donβt think my teacher expects that just yet
orchid wagon
therefore a =arcsin(x)
this is very big oversimplification here, but ill prioritize your grasp on what inverse trig are first
orchid wagon
is it ok if i just solve for it tho cuz i donβt think my teacher expects that ju...
if you have a calc and you are allowed to use it, go ahead
lament stone
okk
orchid wagon
else, leave it as arcsin(15/17)
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haughty root
hi
haughty root
i dont have paper is it needed
haughty root
for the problem
brazen forge
you have a problem you want to solve rigth? just write the problem here or post a photo of it
haughty root
Y=mx+b
brazen forge
and whats the question?
brazen forge
so you want to find m right?
haughty root
yes
brazen forge
there are many options depending what information you get in specifing questioon
haughty root
y=mx+b solve for m
sorry if im making this difficult i literally have no idea about anything relating to the problem
brazen forge
is it for school?
brazen forge
do you know what a function is?
haughty root
no
brazen forge
do you know what a cartesian plane is?
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copper garnet
Hi, I-donβt understand the concept behind when the meaning of the probability of the 5th question when the probability becomes a variable like (1+x)/6, thank you
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Hi, I-donβt understand the concept behind when the meaning of the probability of...
copper garnet
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copper garnet
<@&286206848099549185>
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fair jewel
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fair jewel
yo go away
elfin yew
my fault
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astral fiber
Simplifying and expressing answer in positive indices
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Simplifying and expressing answer in positive indices
astral fiber
My working out, the answer is the last image
well the textbook answer not my working out answer
It's out of order so the 3rd image is the first one, the 1st image is the second one and the 2nd image is the last one where my wrong answer shows up
gaunt echo
fiery goblet
textbook answer is correct
your working is incorrect
you have b^-6 in the numerator and b^2 in the denominator
what does that work out to?
fiery goblet
whereβd b^(-2) go? second fractionβs denominator
astral fiber
whereβd b^(-2) go? second fractionβs denominator
I did b^4 X b^2 which is b^6
astral fiber
whereβd b^(-2) go? second fractionβs denominator
I accidentally made it positive after flipping it here #help-38 message
fiery goblet
yup
astral fiber
yup
so what do I do next
I forgot the 4 but just pretend it's there
Only got here because I knew the textbook answer
This probably isn't the way you are meant to find the answer
astral fiber
.reopen
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astral fiber
I still need proper explanation and working out rather then what I did which was brute forcing it
<@&286206848099549185> ?
green lichen
qs ?
astral fiber
qs ?
could you explain the working out I should've done #help-38 message (unless that was somehow the correct way)
I'm sure there was a more reasonable way
astral fiber
Can you write the question properly and send ?
It's all the way up here #help-38 message
green lichen
ok then give me 5 mins I will send the picture with full answers
astral fiber
ok then give me 5 mins I will send the picture with full answers
that's alright
astral fiber
<@947819101223526400>
yep I'm just going through it right now
green lichen
ok
zinc ginkgo
astral fiber
Could you explain the 3b^+2+2?
green lichen
answer was right just the explanation was required
green lichen
Could you explain the 3b^+2+2?
when b^-2 moves to numerator it becomes positive (+2) we already have a b^(+2) in numerator so we add them as b(+2+2) = b^(4)
astral fiber
wait no your answer was 9a^2 over 4b^8? The textbook here said #help-38 message 27 over 4b^8
you forgot to square the 3 in the second fraction because the 3 was inside the brackets
green lichen
wait no your answer was 9a^2 over 4b^8? The textbook here said https://discord.c...
yeah sorry it happens my bad
astral fiber
yeah sorry it happens my bad
this is where I got stuck at
27b^-6
b^2
green lichen
,rotate
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green lichen
rotate and send
astral fiber
Alright
green lichen
b^(-2)+b^(2)
astral fiber
b^(-2)+b^(2)
? which part are you mentioning
green lichen
last cancelling
astral fiber
last cancelling
so the final fraction would be 27 over 4 or am I doing something wrong
Because it would turn into b^0 which is just 1
And 1 is irrelevant
green lichen
we have b^-6 also right ?
astral fiber
we have b^-6 also right ?
yeah it's b^-6 and b^2 as the last 2 and the rest are numbers
green lichen
yeah
astral fiber
yeah
Since it's between the numerator and the denominator would be division or division as in subtraction because of index laws
green lichen
Can you explain properly ?
astral fiber
Can you explain properly ?
so 27b^-6 is at the top
b^2 is at the bottom
Do I do b^-6 Γ· b^2 (proper division) that makes it b^-3
Or do I do b^2 Γ· b^-6 (as in subtraction so b^2--6) that makes it b^8
green lichen
so 27b^-6 is at the top
b^2 is at the bottom
Do I do b^-6 Γ· b^2 (proper divis...
index laws
Anyway both means the same
astral fiber
index laws
and that makes it 27 over 4b^8 which is the right answer according to the textbook
I think I'm satisfied with the answer
how do I close this
.close
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fringe prism
i need help
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wraith hinge
fringe prism
what
rough goblet
!occupied
fringe prism
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rough goblet
for the LAST TIME rizzgod
orchid wagon
please tell me where can i ask
read the bot meesage
wraith hinge
where
rough goblet
@fringe prism sorry for clogging up your channel
rough goblet
do i go new one or just wait
whatever u wanna do
rough goblet
@fringe prism do .close here
fringe prism
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gritty gyro
prove: (simple)
tan2x(2cosx - secx) = 2sinx.
solve tan2x(2cosx - secx) = (-sqrt3)/2secx
vernal wraith
prove: (simple)
tan2x(2cosx - secx) = 2sinx.
solve tan2x(2cosx - secx) = (-sqrt...
Which one is your doubt ?
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terse shore
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