wait so im finding the value of x in -2x?
#help-38
wraith hinge
No, i just meant the power rule still applies when finding the derivative of -2x
the derivative of -2x is -2
because the derivative of x is x^0, making it -2*1
sour dagger
i see i understand
but how would that work for 1? in x^3-2x+1=0
would it just equal 1 since 1^1-1 = 1?
wraith hinge
No because 1 is a constant
there's no variable to relate to
the rate of change for a constant, is... 0
because there is no rate of change
sour dagger
ok so f(x) prime would be. 3x^2 - 2 right?
wraith hinge
Yes
sour dagger
nice thank you very much for the help
wraith hinge
No problem 🙂 good luck!
wraith hinge
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wraith hinge
I need help solving this
long basin
find f(x+a) first
wraith hinge
find f(x+a) first
a is -3 i suppose
long basin
f(x+a) is not (x+a)^2
wraith hinge
f(x+a) is not (x+a)^2
o
wraith hinge
find f(x+a) first
how would i find that?
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wraith hinge
Replace x with x+a
but why would i do that?
wraith hinge
which **literally** means to replace x with x + a
ahhh i see
wraith hinge
because you need to find f(x+a)
long basin
Wel you fully expanded it out
I was hoping for something like x^2 + 2(a+2)x + (a+2)^2
Because then that'll just imply that:
2(a+2) = -6
(a+2)^2 = 9
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wraith hinge
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fast crown
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fast crown
I got two values for a
-5 and 5
But apparently there’s only supposed to be one
For part b
frozen plover
But apparently there’s only supposed to be one
It says a is a positive real number
So only 5
frozen plover
Yeah what's the matter with part b
frozen plover
,w differentiate x^2y^3 + e^(2y) = 5
solid kilnBOT
frozen plover
Yeah alright
fast crown
Yeah then I set it equal to 0
fast crown
What why
fast crown
Is that the only way to verify
frozen plover
You could plot it in desmos and have a look for yourself
But this is generally enough to rule out y being 0
fast crown
So then how can I use the information that x=0 that there’s only one s.p
frozen plover
There's only one value of x for which the derivative is 0
Which means there's only one stationary point
If there were two real values, then there would be 2, and so on
fast crown
Thank you, I will take note of that
frozen plover
Stationary points occur when the slope of the tangent at a point on the graph is 0
And there's only one point here right so
¯_(ツ)_/¯
frozen plover
You're meant to solve the differential equation
fast crown
I umm I flipped dp/dt and flipped the rhs too then integrated with dt 💀, is this mathematically wrong? I’m guessing it is
frozen plover
No it's fine
fast crown
dP
frozen plover
Wait
solid kilnBOT
fast crown
Oops
frozen plover
Yeah that's fine
Part a told you about partial fractions
You're meant to use that result here
fast crown
Yeah that's fine
Is it correct so far?
frozen plover
,w integrate 100/(p(5-p))
It's correct just remove the + C and plug in the limits
You have an initial condition
fast crown
This is different from what I wrote
frozen plover
It's the same you just multiplied the 100 in
solid kilnBOT
fast crown
Yeah, I got 5/5
solid kilnBOT
frozen plover
Your partial fractions is right
I think you messed up the integration
$\int \frac{1}{5P} \dd P = \frac 15 \ln P$
solid kilnBOT
NEONPerseus
frozen plover
The other one is alright
No wait you're missing a minus sign
:P
In the partial fractions
fast crown
**NEONPerseus**
I think I’ve been integrating wrong this entire time
I thought, for example, if I had to integrate 1/2x it would be 2ln2x +c
fast crown
no wonder, anytime I integrate one over a linear equation it’s always wrong
frozen plover
I'll take your leave now, hopefully someone else will come now
fast crown
Thank you
frozen plover
no wonder, anytime I integrate one over a linear equation it’s always wrong
Dont worry about itz you'll get it
That was quick Riemann
fast crown
Dont worry about itz you'll get it
My exam’s in three days lol
frozen plover
frozen plover
My exam’s in three days lol
But you got it now, in less than a minute
zinc ginkgo
I thought, for example, if I had to integrate 1/2x it would be 2ln2x +c
another way to see this is to use log rules
$\log(2x) = \log(2) + \log(x)$ now differentiate both sides
solid kilnBOT
riemann
zinc ginkgo
I thought, for example, if I had to integrate 1/2x it would be 2ln2x +c
or also just factor out the 1/2 from the integrand
fast crown
or also just factor out the 1/2 from the integrand
How would I integrate the second fraction? Like what are the steps
1/5(5-P)
I take out a common factor of 1/5 so 1/5 x 1/5-P
Then I get -1/5ln(5-P)
But say i had to integrate 1/5-2P
What would the integral be
zinc ginkgo
$\frac{1}{5-2p} =\frac{1}{2} \cdot \frac{1}{5/2-p}$
solid kilnBOT
riemann
zinc ginkgo
then you've factored out the 1/2 and can do the same thing
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fast crown
I’m going to lose my mind, what have I done wrong? Is my approach incorrect?
fast crown
then you've factored out the 1/2 and can do the same thing
My value for the constant is different, is there something wrong with my approach because it’s not the same as the marking scheme
Ignore dx
I meant dP
This is what I did before hand
zinc ginkgo
My value for the constant is different, is there something wrong with my approac...
their C is on the t integral, yours is on the P integral
they have t + c = f(p). you have t = f(p) + c, so of course it's gonna have opposite signs
zinc ginkgo
Next one
what you really care about is P(t)
Write that for both your approach and theirs and compare
fast crown
Yeah, the thing is I don’t really understand how to get P(t) the mark scheme just shows the answer after that
zinc ginkgo
it's a lot of algebra manipulation
zinc ginkgo
Yeah, the thing is I don’t really understand how to get P(t) the mark scheme jus...
start at equation 8.4.2
https://math.libretexts.org/Courses/Monroe_Community_College/MTH_211_Calculus_II/Chapter_8%3A_Introduction_to_Differential_Equations/8.4%3A_The_Logistic_Equation
fast crown
start at equation 8.4.2
https://math.libretexts.org/Courses/Monroe_Community_Co...
Thank you, I got the right answer 😭🙏
That example question is basically the same as the exam question
How did you find it
zinc ginkgo
Google?
fast crown
i guess i knew that this is called the "logistic equation"
Ah, ok
fast crown
Google?
I got a) i) -6 and a) ii) -4 but my value of the first term was very wrong. I used Un=a + (n-1)d. Was I meant to use a different formula?
simple haven
How is a first term being -5 wrong?
fast crown
How is a first term being -5 wrong?
The answer is 115
-5 isn’t the first term its the 21st
simple haven
oh, that makes sense, sorry.
fast crown
It’s ok but I don’t know how to get 115
simple haven
Un = a + (n-1)d, so -5 = a + (20)(-6), solve for a.
simple haven
You're welcome
fast crown
Also
simple haven
Use the geometric series formula: Hint: 1 + r + r^2 + r^3 + ... = (1 + r^n)/(1-r), what happens as n goes to infinity?
fast crown
Ummmm no clue
simple haven
if r < 1 then r^n goes to zero
fast crown
Value decreases?
simple haven
1/10 -> 1/100 -> 1/1000 -> and so on
so eventually you wind up with 1/(1-r)
which is the limit as n goes to infinite for a geometric series.
simple haven
well, if 1/(1 - r) = 64/3
You got two different possible ratios. If one of them is less than 1 and satisfies that equation, then the proposition is true, otherwise it is false.
simple haven
from (c) "Find the two possible values of y and the corresponding common ratios"
"r" is the "common ratio", and you'll have two values of y and two values of r.
"one of the values of y" blah blah "has a sum to infinity" means that for that value of "y" the value of "r" is less than 1.
if we actually perform this infinite sum (using the geometric series formula) does this sum equal 64/3
n.b. that the geometric series formula I posted is a simplified one assumes that the series begins at 1. If it begins at a different value, (let's call it a), then the series becomes a + ar + ar^2 + ... = a (1 + r + r^2 + ...) = a/(1-r)
Does this help @fast crown ?
fast crown
Kind of…
fast crown
from (c) "Find the two possible values of y and the corresponding common ratios"
This is what the mark scheme says, i’m so confused
Like I understand what you said but I don’t know how to apply it to part d ii)
simple haven
So they calculated a and found that it was inconsistent with y.
(but it would have been consistent if there were a different value of y)
fast crown
So they calculated a and found that it was inconsistent with y.
Oh but it doesn’t say y-1 is the first term…
Or does it maybe I’m missing something
simple haven
So if a = 32, then ar = -16, ar^2 = 8, and ar^3 = -4
but y-1 is 4. We can clearly see that 4 will not appear in this sequence
(instead a would need to be -32, or 16, or -8, or 64, or something)
solemn mantle
why does the demand shift down here?
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why does the demand shift down here?
simple haven
The (fallacious) idea here is that if you have more money you would consume fewer foods that are store brand (to save money) and instead consume more foods that are brand name.
Economics examples are sometimes irrational, just like economics itself.
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solemn mantle
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simple haven
The demand curve of what? The same store foods graph?
simple haven
oh dang, they were talking about Y-12 near ORNL
So the idea is that if Y-12 hires 200 more workers, people in Y-12 make generally good wages and generally move into the Oak Ridge area to take the job, so it results in an influx of people to the area with disposable income, and this results in an increase in the demand of fast food
so therefore the demand curve of burger king woppers will increase, I guess?
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mortal breach
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mortal breach
How is it done? wouldn't the omega have power of 4 and 8?
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pearl elbow
Hi so I'm at 10° grade The article(i believe it's said that way?) I'm giving is about the modular equation the left equation is right but the right one isn't idk why, the result is supposed to be 3 can plz someone help me? Thx
pearl elbow
Here's the fuction (the one in blue ink)
And the exercise says : calculate f(x)=2
Maybe i should use the | 1 - X | let me try
Hmmm no
The result gave x=-1 not what i wanted
Btw "se" means "if"
<@&286206848099549185>
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old veldt
The result gave x=-1 not what i wanted
Its not -1
It's 1
You forgot the absolute value --> | |
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pearl elbow
It's 1
But then what am i doing wrong, the results are supposed to be {-5/2 ; 3} i already got the -5/2 how can i get to the 3?
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brave wadi
What would tan 45 be finding? It seems I should use tan 13 to find the length of line ** PR**
bright tulip
You could use cosine of B to find pr tho
brave wadi
Angle β would be 90-45 deg right?
brave wadi
Actually nvm, I was using the wrong trig ratio
bright tulip
You could also use Sine of 45 to find PR
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supple copper
Literally read #❓how-to-get-help
It will be fine just read and follow the instructions there
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rare cradle
For b, am I meant to simply substitute for x and y in the x,y vector or is there a different way to do this because when I tried substituting I wasn't getting the right answer
twilit meteor
did you remember to include the 2/5?
rare cradle
Yes I included it
twilit meteor
hm
well, maybe sub x → (18x/5 - 4y/5) and y → (-4x/5 + 12y/5) in the circle's equation and see what happens?
rare cradle
Ohhh okay ima try that
twilit meteor
if that doesn't work i got nothing
i can tell you how to do the area thing, but that's easy enough that you probably don't need me
rare cradle
Yea I get the area thing
It looks kind of similar when I substituted what you said I'm going to recheck
I'm not sure what I did wrong but it's like reversed
I did it
I made the (x,y) vector the subject then substituted into the circle equation
Thanks for your help
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empty dawn
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crude blaze
what
empty dawn
I think I figured it out finally
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woven breach
Hey, i need to find a polynome with real coefficients where this is true:
woven breach
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woven breach
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patent crow
have you considered differentiating both sides? @woven breach
from there you get a simple ode
woven breach
patent crow
excellent
put all terms on the same side, divide e^x (because it cannot be 0)
you get
[p''-p'-p=0]
solid kilnBOT
Scythe
patent crow
that works too
it equals 0 either way
but convention dictates you leave the highest order term positive
and alone, ideally
woven breach
ahh you just changed the signs i see
patent crow
do you know how to solve this ode?
woven breach
im thinking but not really
patent crow
right right uh
now that I think about it this is impractical
since this is a simple linear homogenous ode, the answer is in the form p1=e^r1x and p2=e^r2x, (two solutions bc order 2 ode)
but those are exponential solutions
r1 and r2 are (1±sqrt(5))/2 if you're curious, you use the coefficients of the ode p''-p'-p=0 to get r^2-r-1=0 to find the roots by plugging in p=e^rx and differentiating
patent crow
plus since this is out of your expertise it wouldn't appear to be the right way to solve this
this is a standard calc problem yes?
woven breach
this is analysis 2 and we havent really gone through de's
i think analysis is calculus in the us?
patent crow
perhaps
woven breach
the lectures were about riemann integrals
woven breach
but i study physics and but my mathematics courses i take are the same courses the mathematicians take so maybe they went through de's in a seperate course
i find that unlikely though
patent crow
gonna be honest not sure how you can find a polynomial other than p(x)=0 where this is true
tabular integration perhaps?
woven breach
the actual task i had was different, that was just were i got stuck
maybe my approach was wrong, i can send the actual exercise
patent crow
write
[p(x)=\sum_{n=0}^{∞}a_nx^n]
solid kilnBOT
Scythe
patent crow
find a general integral for p''(x)e^x, then solve for =p(x) for the coefficients?
woven breach
patent crow
that's the only way I can think of for this part, though idr riemann integral
woven breach
Let p(x) be a polynomial with real coefficients. Prove that there exists another polynomial q(x) with real coefficients where this is true
patent crow
hmm
so basically you're proving there are two valid polynomials where this works? given p(x) is one find at least one other?
patent crow
why did you say c=0?
woven breach
uhm
wait ill send how i got to that equation i sent before
if this was true, i could say -p'(x) = q(x)
And the equation at the top would be satisfied
woven breach
Yeah
patent crow
differentiate, you get p'e^x+pe^x=qe^x, p'+p=q
polynomials are continuously differentiable
go back to this,
[p(x)=\sum_{n=0}^{∞}a_nx^n]
solid kilnBOT
Scythe
patent crow
therefore
[p'(x)=\sum_{n=0}^{∞}a_{n+1}(n)x^n]
solid kilnBOT
Scythe
patent crow
therefore
[q(x)=\sum_{n=0}^{∞}((n)a_{n+1}+a_n)x^n]
solid kilnBOT
Scythe
woven breach
Wait so what do i differentiate
patent crow
the whole equation, the original one
woven breach
this?
patent crow
yup
woven breach
differentiate, you get p'e^x+pe^x=qe^x, p'+p=q
how do you get this though
woven breach
The left side just removes the integral
patent crow
p(x)e^x=q'e^x+qe^x
woven breach
ah yeah
patent crow
whooops
woven breach
that seems right
patent crow
divide out e^x, you get p=q'+q
that's actual math though
still have to set up the series I think, imo
but I like series, sometimes
d'you know how to do that or?
solid kilnBOT
Scythe
patent crow
and
[q=\sum_{n=0}^{∞}b_nx^n]
[q'=\sum_{n=0}^{∞}(n)b_{n+1}x^n]
solid kilnBOT
Scythe
woven breach
divide out e^x, you get p=q'+q
wait cant i just guess a polynomial where this might work
patent crow
for instance let a_n = 0 for n>5 and 2n otherwise, you get the polynomial p=0+2x+4x^2+6x^3+8x^4+10x^5, as an example. in reality there can be any order
patent crow
wait cant i just guess a polynomial where this might work
not so sure, since p can be any real polynomial
patent crow
yup that satisfies the equation
woven breach
if i integrate p(x)e^xdx i should get q(x)e^x
patent crow
Let p(x) be a polynomial with real coefficients. Prove that there exists another...
but you are proving for any p(x) polynomial with real coefficients
otherwise we would say p=q=0 and be done with it
woven breach
I mean they cant be equal so that wouldnt work
patent crow
true enough ig
woven breach
but you are proving for **any** p(x) polynomial with real coefficients
but now that you say it
im not sure if its for any p or if i just need to find one
patent crow
Let p(x) be a polynomial with real coefficients. Prove that there exists another polynomial q(x) with real coefficients where this is true
generally real, not there exists
that's for all real polynomials p(x)
also it works btw
if you wanted to check without suffering through integrating
so look
you understand the above series formulas for a polynomial, right?
woven breach
yes
patent crow
excellent
so we just plug these into p=q'+q
we get
[\sum_{n=0}^{∞}a_nx^n=\sum_{n=0}^{∞}b_nx^n+\sum_{n=0}^{∞}(n)b_{n+1}x^n]
solid kilnBOT
Scythe
solid kilnBOT
Scythe
patent crow
with me so far?
woven breach
yeah
patent crow
now, at every power of x
the coefficients have to equal 0 independently
there is no a for which ax^4 + some bx^3=0 for all x
coefficients have to cancel out on the same power level
so
[a_n=b_n+nb_{n+1}, n≥0]
solid kilnBOT
Scythe
patent crow
we are given a_n, the polynomial p, remember
woven breach
yes
patent crow
so basically we need to prove that for a real sequence of a_n, n≥0, that there is some sequence of b_n for which this is true
patent crow
ask away
woven breach
**Scythe**
shouldnt it be x^(n-1) for q'
patent crow
nope
notice how it's b_n+1
instead of doing starting from n=1 (since constant is gone) of b_n*x^(n-1)
I did starting from n=0 of b_n+1 of x^n
which is the same series
woven breach
ohhhh
patent crow
we need to match the x^n in each one or it won't merge right
woven breach
yeah makes sense
solid kilnBOT
Scythe
patent crow
I confess I'm not quite sure where to go from here, since we need to solve b_n in terms of a_n
hmmm so if the highest power of p is A at power x^N, then a_N=A, b_N=A too, b_(N-1)=A_(N-1)-NA?
ugh is this a proof of induction to just prove it exists?
let n > 0, assume real b_n implies real b_n+1
therefore
b_n+1=(b_n-a_n)/n
therefore, b_n+1 is real
therefore, for real a_n, then real b_n exists for all n≥0```yup
and since a_n is real, and previous b_n is real, then b_n+1 is real
marvelous
patent crow
yup! I think so
woven breach
damn thanks a lot for helping me
patent crow
I just hope I got it right
I probably grossly overcomplicated things
but at least it works :'D
do you understand how the proof by induction works?
patent crow
and the idea that we're just proving it exists, rather than a specific q(x)?
hmm that could be helpful
it will cause me pain to read the simple answer I bet it will be though
ah, to hurt or not to hurt
woven breach
i will be honest its 4:30 am in germany and my brain is fried
so we
differentiated the equation
put in series for the polynomials
simplified
patent crow
mhm
woven breach
**Scythe**
and saw that our polynomial has to satisfy this
This we proved by induction
just that it exists
And were finished
rough harbor
pls help <@&268886789983436800> <@&286206848099549185>
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lethal anvil
!15m
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lethal anvil
also don't ping the mods unless you need a mod related issue
rough harbor
ok sry i didn't know
lethal anvil
np
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scarlet escarp
pls help <@&268886789983436800> <@&286206848099549185>
is this multiple choice
spring otter
f(x) = 1/x , x belongs to (0,1) is not uniform continuous. But f(x) =1/x , x belongs to (a,1), a>0 is Uniform continuous. What is difference between these functions
digital bison
1/x has a vertical asymptote at 0. So it increases very rapidly over very small intervals.
for x > 1, it changes very slowly over even very large intervals.
kindred pier
you can bound the latter
spring otter
you can bound the latter
thnx..now i got it
spring otter
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coral abyss
I'm supposed to make this in Python. I specifically don't understand how I know something is 'accurate to 10 decimal places when compared against exponentiation'
coral abyss
I'm supposed to make this in Python. I specifically don't understand how I know...
But even if it isn't right, how do I go about solving this?
potent bone
well the terms beyond some point are going to be divided by huge factorials so they'll be less than 10^-10
potent bone
...isn't $\texttt{c ** (1/r)}$ just $\sqrt[r]{c}$ \
kind of a weird thing to use when that's what you're trying to approximate
solid kilnBOT
bee
umbral lily
Someone teach how the ans of (c) Is -3/2y~ ?
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Someone teach how the ans of (c) Is -3/2y~ ?
shell barn
Why don't we try solving for x and y first?
What are x and y, in terms of their horizontal and vertical components?
umbral lily
What are x and y, in terms of their horizontal and vertical components?
huh? U mean x = 6 units, y = 2√2 units ?
shell barn
Well those are the distances
We want the individual components
So a horizontal component, then a vertical component for both x and y
umbral lily
We want the individual components
dont understand sry
shell barn
Would it make sense if I told you that y = (-2,-2)
umbral lily
what is that stand for ?
shell barn
If not then I think you need to read up on what a vector is
How about this:
To get from U to V, you go how many units left and how many units down?
umbral lily
ohh i get it is smtg like translation isnt it ?
shell barn
Yes
umbral lily
okay... then whats next ?
shell barn
So now does it make sense to you to say y = (-2,-2)
umbral lily
yes
shell barn
Great, now find x
umbral lily
for A to B is ( 3,3)
so i need to do is the similar triangle compare as AB and UV ?
right ?
shell barn
That would also work yeah
But let's do this
If we know that y=(-2,-2)
Then will some multiple of y be (3,3)?
I want you to find a number c such that c × (-2,-2) = (3,3)
umbral lily
(3,3) divide by (-2,-2) ?
shell barn
Well not quite
When we multiply vectors by numbers we have to multiply their components
So we get:
(-2c,-2c) = (3,3)
Which gives us the system
-2c = 3
-2c = 3
Notice how we have the same equation twice
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harsh wave
could u guys help me
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could u guys help me
harsh wave
let x be a real number in the interval[0, pi/2]
such that sinx cos x =1/2
shows that sin x= cos x
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ripe valley
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harsh wave
okay
brave shell
Yup
harsh wave
cos x= 1
harsh wave
pi/4
harsh wave
pi/4
harsh wave
waiiit
harsh wave
2sin x cos x=sin pi/4
harsh wave
nah x=pi/4
harsh wave
Should I explain a bit clear
yep
harsh wave
2 sinx = 2 cos x
harsh wave
the question is shows that sinx = cos x
harsh wave
yep
brave shell
Sinxcosx=1/2
Multiply with 2 on both sides
harsh wave
2sin x cos x= 1
harsh wave
sin 2x?
brave shell
Umm sin2x=what
harsh wave
1
brave shell
Sin2x formula I mean
harsh wave
2sin x cos x = sin 2x
brave shell
Yeahhh
harsh wave
and 2 sin x cos x=1
brave shell
Sin2x=1
harsh wave
so sin 2x =1
brave shell
2x=?
harsh wave
pi /2
harsh wave
pi /4
harsh wave
cos pi/4= sin pi/4
harsh wave
wait
brave shell
Yup
harsh wave
values of what?
brave shell
Values of cos pi/4and sin pi/4
harsh wave
pi /4 +2kpi ; -pi/4 + 2kpi ?
harsh wave
aaah its square root 2/2
brave shell
Ok what is cos 45°?
harsh wave
square root 22
brave shell
Check the calculator or Google
harsh wave
yea
harsh wave
yes ur right
harsh wave
yeesss
harsh wave
ofc i appreciate you
harsh wave
yees ofc
tame solstice
@harsh wave type .close if ur problem is solved
harsh wave
tyysm
brave shell
Welcome
harsh wave
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shrewd ridge
it's just algebra there's like no exotic insight
stark lantern
hello i have a question about this question, would my drawing be right? (sorry for the bad drawing)
stark lantern
like are the values placed in the right place?
trim lichen
yes
languid bluff
I'm having a hard time understanding the proof for the domination number of helm graph. It's given that Y(Hn)=n, and proved it like this
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I'm having a hard time understanding the proof for the domination number of helm...
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<@&286206848099549185>
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wraith hinge
how to draw vector diagram for this
proper shard
use some vector multiplication
so you've got a vector pointing east with a magnitude of 400Km/h
and you've got a vector pointing north-east at 50km/h
calculate the resultant vector
wraith hinge
I just need a vector diagram @proper shard
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proper shard
draw one in ms paint
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rough torrent
Can anyone help me with this
quick narwhal
Can anyone help me with this
Pythagorean theorem
zinc ginkgo
,rotate
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zinc ginkgo
Well you know the base of the right triangle
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inland orbit
You mean the blank bit at the bottom? lol
Oh, you posted question 6 though
What was the original problem for number 5?
Ahh okay
you factored out 4
but you still used a=4
I think you meant a=1
In the polynomial 4x^2 + 300x - 9000, yes
not in x^2 + 75x - 2250
You can treat that as a new quadratic basically, because if x^2 + 75x - 2250 is equal to 0, then of course 4 times that polynomial is also equal to 0
no need to apologize 👍
Looks like the answer key has rounded a bit
It's not 23 exactly
but should be pretty close
Happens to everyone lol
no problem 👍
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modern karma
Hey! I need to convolute these functions using the graphic method. I solved a nearly identical exercise early but x1(t) was possible. I'm not sure how to approach this bc they don't overlap when I add them. I'd appreciate any help, thanks!
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Hey! I need to convolute these functions using the graphic method. I solved a ne...
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weak orchid
How did they do this part?
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How did they do this part?
weak orchid
delicate bobcat
u mean how does the hint work?
wraith hinge
How did they do this part?
separate it, $\frac{5n}{n}-\frac{1}{n}$
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physicsIsThicc
true coral
take points A, and A' which are symmetrical by line l, given any point B on l does A'B=AB?
dusty hound
by definition of the mediatrix yes
true coral
so considering M the point of symmetry triangles A'MB and AMB are the same?
they arent ho
so silly
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unreal tendon
I have a doubt
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I have a doubt
native ocean
,rotate acw
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Show your work, and if possible, explain where you are stuck.
unreal tendon
,rotate acw
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unreal tendon
Question 12, 13
If you are doing please tell I will wait
And send me the answer in written form
sweet hare
"do these several exercises for me"
no
show what you've tried, where you're stuck, what you don't understand, etc.
unreal tendon
I had stuck in all these questions
I hadn't send you the whole exercise
These were the questions which i was stucked
This is ntse based and extra questions
There are 40 more questions in this exercise
SO YEAH
These were the questions I was struggling
So kindly tell
<@&286206848099549185>
unreal tendon
.
unreal tendon
.
pastel robin
do you know how exponents work
for question 12 first, can you tell me what 5^x is?
what is 5^x equal to
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weak orchid
...
unreal tendon
what is 5^x equal to
What?
I guess it's 3
Because then it would be 125
But i need formulae
Forgot those questions
I have just 2 new questions
Please help me with these 2 questions only
final coyote
for 9) how can you write p(x) in terms of c and d?
unreal tendon
Good Greif
But it's an open door question
It cannot be wrong
<@&286206848099549185>
final coyote
for 9) how can you write p(x) in terms of c and d?
i will help you, can you answer this?
final coyote
no.c and d are zeros from p(x), so p(x) = (x-c)(x-d)
final coyote
expand this and compare with the given formula
final coyote
(x-c)(x-d)=x^2+(c+d)x+cd
final coyote
i a not doiing the job for you, i will help you to find the answer yourself. so you have to do something your own. compare the last formula with the given formula
can you say something about a?
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earnest breach
How do you approach this problem?
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How do you approach this problem?
sturdy leaf
you can split up an integral
so that you get one from 0 to 4 and one from 4 to 6
then you can sub in the f(x) into these integrals
wraith hinge
someone how the fuck do i do these
sturdy leaf
@wraith hinge #❓how-to-get-help
wraith hinge
How do you approach this problem?
you tryna build a rocket ship or som?
earnest breach
you tryna build a rocket ship or som?
what?
wraith hinge
<@456226577798135808> <#488120190538743810>
there isnt a channel for me
do i need to create one
somehow
or
sturdy leaf
under #❓how-to-get-help there is #1021175428326633542 and under that, there are channels that you can claim for yourself
one of these
earnest breach
so that you get one from 0 to 4 and one from 4 to 6
when you split up the intergral, what does that mean? Like the upper and lower bounds are going to be different from what I started with? With your example, it would be
sturdy leaf
think of it like you are calculating an area
we are pretty much splitting the area in two
earnest breach
I see
visually, I see what you mean
I'm still a bit unsure how to deal with the problem though
sturdy leaf
$\int\limits_a^c=\int\limits_a^b+\int\limits_b^c$
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~Martin
sturdy leaf
now let's say we are going from 0 to 4
earnest breach
mhmm
earnest breach
right
would that be [4] - [4] ?
Or would I not need to do that part of the definiate integral
solid kilnBOT
~Martin
sturdy leaf
this is not 4-4
sturdy leaf
yes 👍
sturdy leaf
F(b)-F(a)
earnest breach
Those are the two sets that I've been following
sturdy leaf
where F is the antiderivative of f
sturdy leaf
👍
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cursive musk
@earnest breach why not
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frank sable
how do I do c?
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how do I do c?
boreal dome
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hazy ridge
Is this solution correct?
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Is this solution correct?
harsh berry
to..?
hazy ridge
What?
hazy ridge
So what is correct answer?
marble wharf
next you have to factor out the x on the right side
hazy ridge
How to factor the x?
marble wharf
so on the right side you have 1*x + sqrt(2)*x
can you rewrite that as (something+something)*x ?
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hazy ridge
So is something like this
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weak thunder
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dusty hound
Try to apply the binomial theorem
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weak thunder
Try to apply the binomial theorem
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weak thunder
thank
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cosmic gate
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cosmic gate
Im having some trouble with part d of this question
here is my working out
the solutions say the angle should be 109.5 degrees
high hearth
ok
to get the angle u want the angle between XD and XF
XD is (-1/2 a, 1/2 a, 1/2 a)
XF is (1/2 a, -1/2 a, 1/2 a)
then you use the dot product
seems like what you did is XD and FX not XD and XF
high hearth
np
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stiff scarab
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stiff scarab
i am a bit curious
what would the proof for showing the triangles are congruent be?
<@&286206848099549185>
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tame solstice
@stiff scarab i don't really think u should form the two traingles to make them congreunt since one of them isn't right angled
tame solstice
oh so the angle CED = 90 degrres?
stiff scarab
yes