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#help-38
eternal dawn
guys how do i multiply 1/2(15)^2(2π/3)
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guys how do i multiply 1/2(15)^2(2π/3)
eternal dawn
its for finding the arc length
sharp herald
!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
uh i dont know where to begin
with multiplying
the radian was 15 inches
and theta was 120 degrees
so i converted that into radian measure
and i got 2π/3 radian
then i plugged it into the formula for the area of a sector of a circle
which was like A=1/2(r)^2(θ)
so now its 1/2(15)^2(2π/3)
but idk how to multiply
alpine saffron
So you have $\frac{1}{2}\cdot\frac{15^2}{1}\cdot\frac{2\pi}{3}$
solid kilnBOT
otheol
eternal dawn
arc length
maiden zinc
which was like A=1/2(r)^2(θ)
.
maiden zinc
whats the correct one
eternal dawn
s = rθ
maiden zinc
ye
maiden zinc
ye
alpine saffron
Indeed
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serene timber
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serene timber
i have a slight feeling this is incorrect
what i was thinking is x^3 - 7 = 1 , x^3=8, x =2
eager comet
no that looks right to me
serene timber
sweet thank you
eager comet
weird question
clever trellis
the fact that ure supposed to add it up feels odd to me
serene timber
the fact that ure supposed to add it up feels odd to me
this is what tripped me up..
eager comet
it just looks like a bait but it's just of the interaction between inverse functions?
i dunno
serene timber
it just looks like a bait but it's just of the interaction between inverse funct...
Yeah lol
i have another question thats kinda oddly formatted as well
lemme type up my answer(s):
$x=\frac{\ln(\arcsin(0.3)+2\pi n)-1}{2}$
solid kilnBOT
j
serene timber
$x=\frac{\ln(\pi - \arcsin(0.3)+2\pi n)-1}{2}$
solid kilnBOT
j
serene timber
These were my two answers
Im running off a few hours of sleep and i feel like this doesnt match with the options though 😭
Unless im blindly missing it or made a slight mistake
eager comet
make it a square root
1/2 ln( ) via power rule
is that it, im also running at no sleep x-x
eager comet
yeah that looks like the two square root ones on the multiple choice
serene timber
okok tysm for ur help
eager comet
👍
somber merlin
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somber merlin
i don’t understand factorials
i checked the solution numerator is (2n-1)(2n-2)(2n-3)…. i see that in formula
but the denominator is (2n+1)(2n)(2n-1)(2n)(2n-2)…. i don’t understand why we do the first 2n+1 and multiply 2n
silent oyster
somber merlin
.close
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manic jackal
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manic jackal
all of the terms in the right side are congruent modulo p to 1
and the sum gives us 1 + 1 + 1 + 1 + ... p-1 times
so the sum in the left side is congruent to p-1 which leads us to the congruence modulo p by just simplifying the modulo
dull temple
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wraith hinge
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bold ivy
I need yall's help real quick
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I need yall's help real quick
bold ivy
so I was solving for a question it's about the area of a circle
the radius is 2
area = ?
my answer is 19.71
turns out my answer was wrong
the correct answer is 12.56637
I keep on getting the wrong answer how ?
<@&286206848099549185>
grizzled musk
hey, i did the calculation and the answer i got was 12.57
the formula for circle is pi x radius squared
taking pi as 22/7, we get 22/7 x 2^2
22/7 x 4
22 x 4= 88
88/7
dividing 88 by 7 will give you 12.57
which is the answer in google too
grizzled musk
the formula says radius squared, so its supposed to be 3.14 x 4
bold ivy
what did i do wrong
grizzled musk
3.14 x 2 = 6.28
3.14 is pi, and 2 is the radius, right?
grizzled musk
so the area formula is pi x radius squared
like pi x r^2
so you take 3.14, and then the radius 2
and u square the radius
so it becomes 2^2, which is 4
then multiply 3.14 x 4
should give you 12.56
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finite locust
Let I = [a, b] ⊂ R be an interval with a < b. Show that the mapping (...) is continuous, where ‖-‖ denotes the supremum norm
I don't understand how I can obtain continuity here, since an integral outputs just a number.
finite locust
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kind raven
Let I = [a, b] ⊂ R be an interval with a < b. Show that the mapping (...) is co...
topologically, a mapping is continuous if the preimage of an open set is open
so you have to prove that set of all functions in C0 that map to an open interval in R is open in C0
finite locust
ok i try that ty
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exotic gorge
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south latch
Solve the first equation in quadratic form and plug your solutions into the second
exotic gorge
Solve the first equation in quadratic form and plug your solutions into the seco...
rootss are unreal tho
im getting like -root3
south latch
That's ok
Well, let's see
x + 1/x = sqrt3
--> x^2 + 1 = (sqrt3)x
--> x^2 - sqrt(3)x + 1 = 0
$x = \frac{\sqrt{3} \pm \sqrt{3 - 4\cdot 1 \cdot (1)}}{2(1)}$
That's real
*those are
south latch
$x = \frac{\sqrt{3} \pm i}{2}$
south latch
It's still going to be alright because 100 is a multiple of 4
Write those solutions in Euler form
exotic gorge
we dont have euler form
south latch
$|z| = \sqrt{3/4 + 1/4} = 1$
solid kilnBOT
Melvin Eugene Punymier
south latch
(That's just the sqrt of the sum of the squares of A and B)
We can get the angle by using definitions of sine or cosine
exotic gorge
u talking bout radians
south latch
$\sin{(\theta)} = \frac{1/2}{1}$
solid kilnBOT
Melvin Eugene Punymier
south latch
That's just sin(theta) = 1/2, which is 30 degrees, or pi/6 radians
Oh... and this is the math I did for the "plus" case
So we get
$z = 1\cdot e^{i\pi/6}$
solid kilnBOT
Melvin Eugene Punymier
south latch
(We don't need the leading 1, the modulus "r", obviously)
The modulus for the subtraction case will be the same, since we are squaring the negative anyway in that formula
sin(theta) = -1/2 --> theta = 330 degrees or -30 degrees, or -pi/6 radians
(shocking!)
So the other solution was
$z = e^{-i\pi/6}$
solid kilnBOT
Melvin Eugene Punymier
south latch
Ok, now we can feed these solutions to the second problem
${(e^{i\pi/6})}^{100} + {(e^{i\pi/6})}^{-100}$
solid kilnBOT
Melvin Eugene Punymier
south latch
How did you cube it?
I think line 1 to line 2 is incorrect, or at least doesn't follow
Do you want me to continue with this or do you want to try a different method
@exotic gorge
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cosmic meadow
Use x=cos(m)+isin(m)
And 1/x=cos(m)-isin(m)
Find m and replace in the second equation
@exotic gorge
exotic gorge
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shell basalt
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shell basalt
does this mean that they could have 1 or more in between them
i still dont know how to solve it either way tho xD
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round mango
exactly one between them
means any of the other 5
can go in between A and B
consider 'A_B' as a one object, where the __ can be occupied by any of the 5 people
shell basalt
so ONLY 1 in between them
round mango
yes
shell basalt
they cant be seated on the outside'
round mango
you mean A on one edge and B on the other, no
shell basalt
ok
shell basalt
consider 'A_B' as a one object, where the __ can be occupied by any of the 5 peo...
wdym by this
oh
ok
i see
shell basalt
@round mango
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mild isle
Hello I don't understand these manipulation steps I have already seen the complex numbers but for the 2 steps that I have arrowed I don't know what procedure we use
rose sail
I can’t really help but just wondering what level of maths is this?
mild isle
1st year of bachelor
tepid rock
I can’t really help but just wondering what level of maths is this?
It's technically physics.
AC
rose sail
Alright then Ty
mental wind
Hello I don't understand these manipulation steps I have already seen the comple...
isnt the firt arrow just distrubiting and exp()*exp() = exp(+)
mild isle
so i sould not post it here ?
dull pilot
Is this electrical stuff?
tepid rock
so i sould not post it here ?
You're fine.
tepid rock
Is this electrical stuff?
Yes.
mental wind
Hello I don't understand these manipulation steps I have already seen the comple...
btw is j sqrt(-1)
i cant tell if its electronics or hypercomplex
oh its electronics
dull pilot
btw is j sqrt(-1)
yeah lmao
mental wind
Hello I don't understand these manipulation steps I have already seen the comple...
e^ix = isin x + cos x
dull pilot
engineering moment
mild isle
isnt the firt arrow just distrubiting and exp()*exp() = exp(+)
o yes my bad
mental wind
and if you take the re its just cos
dull pilot
because i is current
kind raven
Hello I don't understand these manipulation steps I have already seen the comple...
the second is taking the real part
tepid rock
like i don't get th exp^(iwt) is equale to cos(wt)
it's not, the real part of it is.
kind raven
real part of $e^(jωt)$ is $cos(ωt$
tepid rock
real part of $e^(jωt)$ is $cos(ωt$
^{}
mental wind
like i don't get th exp^(iwt) is equale to cos(wt)
e^ix is cis which is i*sin x + cos x
mental wind
e^ix is cis which is i*sin x + cos x
becouse complex numbers funny
tepid rock
and we can juste take it like that
No, but you already hace $\mathfrak{R}$ which suggests you are concerned with the real part.
solid kilnBOT
! What the hell am I doing here?
mild isle
No, but you already hace $\mathfrak{R}$ which suggests you are concerned with th...
you would have resources on the complex treating the subject well for electronics because my course is very poor on this subject
kind raven
real part of $e^{j\omega t}$ is $cos(\omega t)$
solid kilnBOT
mzdunek
mental wind
e^ipi+1=0
kind raven
euler's formula is magic
tepid rock
I had never seen that before the strange R
That's for "real part"
kind raven
have you learned calculus before?
mental wind
I had never seen that before the strange R
fancy r = take real part
fancy I = take imaginary part
mild isle
That's for "real part"
yep but i mean the complexe in generale
mental wind
have you learned calculus before?
to who this question was directed to
kind raven
sorry, I meant the OP
mental wind
anyways i think here is resolved
mild isle
have you learned calculus before?
the base but not realy the compex
mental wind
ill be going
mild isle
that why i'm asking some resources
kind raven
taking the real part of e^ix is basic calculus/complex numbers
mental wind
the base but not realy the compex
only thing you need is e^ix = isinx + cosx and thats basicly it
complex anal has alot more if you want to discorver
kind raven
yeah and that's from Taylor's theorem
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wraith hinge
<[american,cuteinductors]circuitikz>
[\ctikzset{bipoles/thickness=1}
\ctikzset{switch arrows/color=red}
\ctikzset{switches/scale = 2}
\tikzset{
wire/.style={line width=1pt}
}
]
\textbf{Question:} For the circuit given below, derive an expression for $v_C(t)$ when $t>0$
\e{center}{
\e{circuitikz}{
\draw[wire] (0,0) to [isource, l = $\vb{3\,A}$] (0,4) -- (2,4);
\draw[wire] (0,0) -- (2,0) to[R=$\vb*{10\,\Omega}$, *-*] (2,4) to [ospst = {$\vb*{t=0}$}] (6,4) to[cC = $\vb{4\,F}$, *-*, v = $\vb*{v_C(t)}$] (6,0) -- (2,0);
\draw[wire] (6,4) to [L=$\vb{1\,H}$, -*, i>_=$\vb*{i_L(t)}$] (10,4) to [R = $\vb*{5\,\Omega}$, -*] (10,0) -- (6,0);
\draw[wire] (12,0) to[isource, l_= $\vb*{4\theta(t)}$] (12,4) -- (10,4);
\draw[wire] (10,0) -- (12,0);
}
}
Where $\theta(t)$ is the heaviside function.
\vs{5 mm}
\textbf{My attempt:} I managed to calculate the initial conditions to be $v_C(0) = 10 \, \t V$ and $i_L(0) = 2 \, \t A$. But my confusion lies in the circuit configuration for $t>0$. Which one of the following will it be:
\begin{figure}
\begin{minipage}[t]{0.45\textwidth}
\centering
\scalebox{0.5}{
\e{circuitikz}{
\draw[wire] (0,0) to [isource, l = $\vb{3\,A}$] (0,4) -- (2,4);
\draw[wire] (0,0) -- (2,0) to[R=$\vb*{10\,\Omega}$, *-*] (2,4);
\draw [wire] (6,4) to[cC = $\vb{4\,F}$, *-*, v = $\vb*{v_C(t)}$] (6,0) -- (2,0);
\draw[wire] (6,4) to [L=$\vb{1\,H}$, -*, i>_=$\vb*{i_L(t)}$] (10,4) to [R = $\vb*{5\,\Omega}$, -*] (10,0) -- (6,0);
\draw[wire] (12,0) to[isource, l_= $\vb*{4\theta(t)}$] (12,4) -- (10,4);
\draw[wire] (10,0) -- (12,0);
}
}
\caption{First Circuit}
\label{fig:first}
\end{minipage}
\hfill
\begin{minipage}[t]{0.45\textwidth}
\centering
\scalebox{0.5}{
\e{circuitikz}{
\draw[wire](6,4) to[cC = $\vb{4\,F}$, *-*, v = $\vb*{v_C(t)}$] (6,0);
\draw[wire] (6,4) to [L=$\vb{1\,H}$, -*, i>_=$\vb*{i_L(t)}$] (10,4) to [R = $\vb*{5\,\Omega}$, -*] (10,0) -- (6,0);
\draw[wire] (12,0) to[isource, l_= $\vb*{4\theta(t)}$] (12,4) -- (10,4);
\draw[wire] (10,0) -- (12,0);
}
}
\caption{Second Circuit}
\end{minipage}
\end{figure}
I am not so sure if it actually matters or not, but I would think so? I asked a few people about this and I am getting conflicting answers lol
shrewd vessel
I can't help but I'm impressed, I didn't know one can draw a circuit with latex
dull temple
surely the first
wraith hinge
My TA somehow is telling me its the second
dull temple
i mean your ta probably knows more than we do
wraith hinge
i mean your ta probably knows more than we do
well, asking some of my other TAs they are saying it is the first
so uh
asking for some confirmation
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tough iron
Anyone familiar with the Z-transform? I think my prof made a mistake but i cannot search up on google because I don't know how to translate the terminology well
austere cedar
tough iron
So for a system that is causal, the region of convergence is the outside of a circle whose radius is the modulus of the farthest pole
e.g. if it has a pole in 1, the ROC is |z| > 1
If a system is anticausal, the region of convergence is the inside of a circle whose radius is the modulus of the closest pole
e.g. if it has a pole in 2, the ROC is |z| < 2
So if a system is anticausal, my prof drew a ring to represent the ROC
But isn't it everything BUT the ring?
The causal part is the blue region, outside the blue circle, and the anticausal part is the yellow region, inside the yellow circle
My prof however highlighted the middle ring
which makes really 0 sense to me
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tough iron
<@&286206848099549185>
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tall viper
so every point that s inside the circumference of radius 1 belongs to that expression
however because its |z|<1 it should be a discontinuous line and not continious because a point that is exactly in the circumference wouldn t belong cause its <1 and not (smaller or equal) to 1
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jolly loom
can someone help me solve this?? i have 4 of my 5 tries wrong 😭
vernal warren
have u tried smthing?
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abstract charm
Shouldn’t it be 0/0 because any real number over infinity is 0?
abstract charm
ik the question probably is lame af i am not the brightest in math (or anything kinda 😭)
For context this was the original question
hallow kite
when plugging in infinitny at first it goes to infinity / infinity
so you can use l'hopitals on (ln(6x))^2 and (ln(2x))^2
and your limit becomes (2ln(6x)/x) / (2ln(2x)/x)
which simplifies to 2ln(6x) / 2ln(2x) = ln(6x) / ln(2x)
that still goes to infinity so you can do l'hopitals again on ln(6x) and ln(2x) and your limit becomes (1/x) / (1/x) which simplifies to 1
a better way to think about it is this if you don't want to use l'hopitals
the limit of (ln(6x) / ln(2x))^2 will just be the square of the limit of ln(6x) / ln(2x) so you can evaluate that first and square the result
then ln(6x) = ln(2x * 3) = ln(2x) + ln3 by log rules
so that limit becomes (ln(2x) + ln3) / ln(2x) = ln(2x) / ln(2x) + ln3 / ln(2x) = 1 + ln3 / ln(2x)
and when you let x tend to infinity that second term vanishes and you just get 1
which lets you conclude that ln(ax) / ln(bx) always tends to 1 as x tends to infinity
abstract charm
Ohhh ok ok i think i got it, i was thinking 1/x is 0(x being infinity) so i thought that 1/x / 1/x whould just be 0/0. Now thinking of it, 1/infinity approaches 0 at the same rate on both sides so it makes sense that it’ll be equal to 1
Thank you :)
how do i close this now?
Nvm found it, @hallow kite thank you again :D
.close
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clever trellis
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clever trellis
so the graph u see the x and the y in tbe curly braces
given is a line
which intersects with S
they want the coordinates of S
now what I did was
plug in the x and y into my line and solved for T
but ive got three solutions
which is correct
but idk which solution of T would be the intersect S (it intersects w itself in S), the line isnt graphed here
the answer is t = -1 or t = 3 but how do I know?
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plain junco
slender shard
Consider the coefficient that determines the vertical stretch.
plain junco
Consider the coefficient that determines the vertical stretch.
what does this mean
slender shard
$f(x) = a\cdot (x+1)(x-1)(x-3)^3$
plain junco
im not sure how to find the leading coefficient
solid kilnBOT
Kookiemon
slender shard
You are given a point not on the x-axis. Use that to solve for a.
plain junco
0, 4.5?
slender shard
Yes.
slender shard
yw
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worthy forum
Hello. I need help with the following proof:
Use complete induction to show that one obtains the derivative of the Wronskian determinant by differentiating the last row of the corresponding fundamental matrix.
Oirignal: Zeigen Sie mit Hilfe von vollst¨andiger Induktion, dass man die Ableitung der Wronski-Determinante erhält, in dem man die letzte Zeile der entsprechenden Fundamentalmatrix ableitet.
worthy forum
I have no idea how to do that 😦
would this be correct for the start?
Maybe this question is too hard idk
<@&286206848099549185>
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carmine quartz
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knotty quest
divide 'x' on both sides
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eternal sky
Hey could someone please help me with this?
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eternal sky
210=180+30
So I just have to apply (180+30)
Which becomes sin30 degrees or do I just say 30degrees?
Like 2cos(x-25) =2 +sin210
=cos(x-25)=1+sin30
OR…
=cos(x-25)=1+sin15
?
Please let me know.
hallow cliff
Please let me know.
Neither
hallow cliff
Sin(180+30)=-sin(30)
eternal sky
Sin(180+30)=-sin(30)
Okay I know this.
hallow cliff
So you want to solve 2cos(x-25°)=2-sin(30°)
Can you take it from here? (Sin(30°)=1/2)
eternal sky
So you want to solve 2cos(x-25°)=2-sin(30°)
Yes I want to find the general formula of this question.
eternal sky
Can you take it from here? (Sin(30°)=1/2)
Okay I’ll go do it now then I’ll send you my answer too see if it’s correct or wrong.
Give me 5 minutes.
hallow cliff
Im sorry i have to go rn, maybe one of the helpers can help
eternal sky
Im sorry i have to go rn, maybe one of the helpers can help
Alright bye, yeah someone should help me.
runic dew
Alright bye, yeah someone should help me.
You have not performed the simplification
eternal sky
I’m currently stuck now. I’ve got my reference angle but now I must put them in their respective quadrants.
runic dew
you are on right track
The solution to cos(theta) = d
theta = 360*n +/- cos^-1(d)
Instead theta you have x -25 degrees
So you want make a substitution
Let theta = x-25
From there you apply the theorem
And at the end make x the subject
eternal sky
you are on right track
Happy to hear this.
eternal sky
From there you apply the theorem
I’ve never heard of this approach before. All I know is that right now I must figure out the quadrants from my reference angle.
I have another question as well.
How do I figure out what k is? Like the degrees.
runic dew
k?
eternal sky
Like sometimes is 180 degrees and sometimes it’s 360 degrees.
runic dew
360 degrees is the period of sin and cos
the period of tan is 180 degrees
Without the exact context I cannot help
eternal sky
k?
You know the k is an integer of blah blah etc.
I’ll send you a picture quickly.
What I’m talking about.
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weary comet
Did i do something wrong? Cuz i cant solve this
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cosmic meadow
Third line is incorrect
cosmic meadow
Did i do something wrong? Cuz i cant solve this
-1-3 is not 2
cosmic meadow
You can avoid this mistakes by writing out all steps
So third step is missing equality property
If you write like e^x-1-3=3-3-3e^(-x) u will realize faster if you have a misreading
weary comet
👍
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main narwhal
im stuck on how to get x.
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main narwhal
<@&286206848099549185>
raw vine
can u write the question more readable
raw vine
u can't find x in here bc when you multiply 24x with 1/6 it becomes 4x and bc there is 4x in the other side they cancel each other and you end up with 9>=-2
main narwhal
oh so theres no sulution?
raw vine
yes
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wraith hinge
@vernal warren is the lim always 0? So I can plug it in h always?
tardy hemlock
wraith hinge
Thank you bro
vernal warren
its the definition of derivative D:
vernal warren
<@691353193384509443> is the lim always 0? So I can plug it in h always?
also if u plug it in , at the very first step u get something like this
$$\frac{something something}{0} $$ which is undefined so thats why u gotta simplify first
solid kilnBOT
JustToPro
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runic sphinx
Guyz help me out with this logical question...
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amber wharf
runic sphinx
solemn schooner
uhhh wdym by that
runic sphinx
uhhh wdym by that
Means I got the answer
solemn schooner
aight nice
runic sphinx
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strange willow
How did this become e^5?
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How did this become e^5?
cosmic meadow
Use power properties
main sigil
Use power properties
hmm which ones?
I would personally choose substitution u = x/5 here
whoops, now its correct
cosmic meadow
hmm which ones?
The ones from the log properties
You can use ln to solve
F=that limit
Ln(F) = ln of the limit
Put the ln inside, etc
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valid ledge
If we have a fraction (3e -1)/(9x - 4a), and we need to substitute conditions for which the lower part of the fraction will not equal zero, then we can expand (9x - 4a) into (3√x - 2√a )(3√x + 2√a). And now it turns out that 3√x is not equal to 2√a and -2√a. Is not it? And now, when we raise everything to a power, it turns out that in the fraction (3e -1)/(9x - 4a) the conditions for the lower part of the fraction are:
9x is not equal to 4a
9x is not equal to -4a
Is there an error in my proposal?
austere cedar
The problem comes from squaring each condition
I don't follow why that would work
9x - 4a = 0
9x = 4a
valid ledge
The problem comes from squaring each condition
Why can’t we
I was wrong, the correct conditions would be 9x does not equal 4a and 9x ≠ (-2i√a)². is not it?
So we get 9x ≠ 4a and 9x ≠ -4a
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full dock
For part a) one solution states that if I/Imax Vs cos^2(x) is graphed, malus’ law can be verified if it has a gradient of 1, why is this the case
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trail ingot
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stray citrus
I don’t really understand change of base and I’m stuck on how to start
stray citrus
can you elaborate on how that would help me find the next step
I dont think I understand the connection
austere cedar
Use change of base on both. Choose the same base for each
stray citrus
so make both loga for example
my friend did something like this
and I kind of understand it
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cwatson
sweet hare
it can be anything. I'd do log base "e", which is just the natural log
but it shouldn't matter
sweet hare
how did you get b = a^(x^2)?
sweet hare
I guess that could work, but it might be simpler not to do that yet
work on the second equation
cosmic meadow
Aren’t you allowed to use log_a(b)=1/log_b(a)?
maiden zinc
oh i wrote in exponteital form first
then found a sub for b
and then just plugged it in
stray citrus
oh wait lemme try that
wait wha
would it be possible for you to write out what you did
maiden zinc
its kinda confusing
stray citrus
is it over for me 😔
cosmic meadow
Dont u like your friends solution or what
stray citrus
it just seems like I wouldnt get full marks if I preformed just that on the exam
stray citrus
theres an example of a similar question where substitution was used when there were a and b variables
cosmic meadow
Math should make your life easier not harder. But this you have to ask to your teacher. For me, doing what ur friend did is the best
Well, need a bit more of steps showing but its good
maiden zinc
stray citrus
how did you manage the 6?
maiden zinc
no apple pencil
stray citrus
what is happening in the second line
stray citrus
ah I see
stray citrus
Im a visual learner so I need to write the whole thing out and look at it
maiden zinc
not too out of line
maiden zinc
uh just to cancel out a
because its base a on the left
for the exponential
so in order to cancel out that a in order to isolate x
heres an easier visual of wha ti did
stray citrus
I understand that part where you do same base same argument to make it equal to 1
Im having trouble just understanding the log_a part
stray citrus
sure
maiden zinc
if i take log base a
of both sides
im just left with u=1
idk i would honestly follow your friends work
bc their answer is much easier to follow and understand
stray citrus
I think I will ask my teacher tmrw for clarification
thanks for the help though
much appreciated
maiden zinc
np
stray citrus
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plush ether
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desert stream
hey ive been having a lot of trouble doing this could someone help me figure it out
desert stream
I thought you did it by dividing the diameter by 2 then squaring what you got. after that you plug it into the formula π x r^2 x h
which you would then divide by 2
because its half of a cylander
is this wrong?
<@&286206848099549185>
slender shard
I thought you did it by dividing the diameter by 2 then squaring what you got. a...
What answer did you get?
$A_{\text{sector}} = \frac{r^2}{2} \cdot {radian}$
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Kookiemon
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small torrent
is this wrong?
thats right
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formal meteor
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formal meteor
how is it not E
fathom ivy
because either 1 or 3 of A B C are true
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lapis hazel
Why is the function x^2/(1 + x^4) not bijective?
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Why is the function x^2/(1 + x^4) not bijective?
lapis hazel
I tried f(x1) = f(x2) substituted functions and then I am getting x1 = x2.
frail yarrow
Well both the numerator and denominator are positive... So
lapis hazel
But if you take 2 and 1/2 you get the same answer.
frail yarrow
I tried f(x1) = f(x2) substituted functions and then I am getting x1 = x2.
I'm not sure you have the right definition of bijective
lapis hazel
I'm not sure you have the right definition of bijective
Wait calm down bro.
frail yarrow
Sorry
lapis hazel
That's only for injectivity.
lapis hazel
No it's not.
Take 2 and 1/2.
If you input them you get the same answer.
It's not injective.
But when I use the definition, I am getting it as injective.
frail yarrow
Why is the function x^2/(1 + x^4) not bijective?
So you have your answer?
lapis hazel
So you have your answer?
I have my answer but I am not understanding it?
whole coral
But when I use the definition, I am getting it as injective.
And how are you getting the injectivity by the definition? You’re likely doing something illegal?
lapis hazel
I checked online but I didn't get it why my method ain't working.
lapis hazel
And how are you getting the injectivity by the definition? You’re likely doing s...
If f(x1) = f(x2), then try to prove x1 = x2.
I did it.
But it seems not to be the case.
frail yarrow
Probably making assumptions about the square roots
lapis hazel
Doesn't matter it is an even function.
Take 2 and - 2 you get same.
Oh wait.
Eh.
I got it I think.
x1^2 = x2^2 so now how do we go here?
whole coral
(And even functions are automatically not injective, immediately by their definition)
lapis hazel
-x1 = x2 is possible?
Ok but if that's the case then how do we get 2 and 1/2 having the same answer.
whole coral
-x1 = x2 is possible?
Can you also show the steps before the point here?
lapis hazel
whole coral
Dividing by zero
whole coral
Ok but if that's the case then how do we get 2 and 1/2 having the same answer.
Choose these and you get that factor as zero - you can’t cancel factors unless you verify they’re nonzero
lapis hazel
x1^2 - x2^2 = 0
whole coral
Squaring and multiplying them gets you 1, then subtracting 1 turns that to zero, so you’ve lost solutions at that step
lapis hazel
Squaring and multiplying them gets you 1, then subtracting 1 turns that to zero,...
Squaring what?
I mean in the end you will get x2 = -x1 or vice versa.
It's not one-one.
It probably only shows that it is not one-one doesn't say the property about the elements.
Explains why 2 and 1/2 work.
I think my answer is solved.
Alright.
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whole coral
Squaring what?
.I was saying that x1 = 2, x2 = 1/2 satisfy x1^2 x2^2 - 1 = 0
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sullen galleon
can someone help me with this question? :)
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can someone help me with this question? :)
sullen galleon
I tried separating it into 3 shapes and finding each angle but that didn't turn out well for me
I don't think I knew what I was doing tho..
narrow prawn
The sum of internal angles of a hexagon is 720
Find EDC then use this
Do you know internal angle of an n sided polygon is (n-2)×180° ?
sullen galleon
oh 720º
do I use the fact tha vertically opposite angles are equal or smth?
so D is also 144º
this is what I did so far
narrow prawn
so D is also 144º
No it's not
sullen galleon
then how do I find that little angle next to the 144º?
blissful ridge
the parallel lines are important!
narrow prawn
Does it click something?
narrow prawn
💀 because it is
narrow prawn
is this what u mean?
sullen galleon
Does it click something?
just the '180-92' part doesn't make much sense
narrow prawn
just the '180-92' part doesn't make much sense
Its 42
sullen galleon
but why did u do that?
blissful ridge
drawing the lines and interpreting angles off of it can make it seem like angles different from what actually are
narrow prawn
Because lines are parallel
blissful ridge
try to make sure you know what the angles are for certain using supplementary angles
narrow prawn
Do you know parallel lines equal angles with intersecting line?
sullen galleon
uhh idk what that means
sullen galleon
oh C angles
blissful ridge
consider what the angle EAB will equal, and the use that along with the idea that quadrilateral angles sum to 360
narrow prawn
consider what the angle EAB will equal, and the use that along with the idea tha...
Bro can you handle here i gotta go
sullen galleon
consider what the angle EAB will equal, and the use that along with the idea tha...
would it be equal to 42º?
blissful ridge
similar yes
sullen galleon
since BC and AD are parallel
I thought it's BC and ED that are parallel?
or is it cuz it's extended?
blissful ridge
yes you're right, im extending it in my head
i should call point "A" something else
it is the extended ED and BC that are parallel
sullen galleon
u can stick with AD..
oh
AD is point A
I only knew it when it's three letters and the letter in the middle is the point sorry
blissful ridge
its okay!
once you know the angle for EAD you can solve for angle EDC
and from there you just need find the angle on the inside where E is
then once you know E, you can remember that since that is 360 degrees, the angle on the outside will be 360-inside
blissful ridge
yes, edc is not 144
blissful ridge
its not 36 since the top line is not parallel with the bottom line
blissful ridge
its not neccesarily a triangle
remove the line cutting ABCD in half
itll be a 4 sided shape
but you can tell that the angle with measure 36 degrees is that since the angle on the right is 144
sullen galleon
the 4 sided shape adds up to 360º right?
blissful ridge
yes!
sullen galleon
but you can tell that the angle with measure 36 degrees is that since the angle ...
oh so u did 180-144 to get that
blissful ridge
yes! correct
sullen galleon
is this good?
I subtracted 30 from 180 to give 150
then I did the opposite angles theorem thingy
correct me if i'm wrong- i'm not very confident in this topic
blissful ridge
yes that looks good at first glance
sullen galleon
the answer should be 110º tho ;-;
sullen galleon
size of angle DEF
blissful ridge
oh! okay
let me look closer
okay
in fhis case
i would recalculate the angle using
720-(all the itnerior angles)
to find the inside "e" angle
and the do 360 minus that "e" angle
you should get 110
blissful ridge
yes, because that 30 is not neccesarily true
the way its drawn it would actually be equal to 70
though you dont need to find it
sullen galleon
720-(all the itnerior angles)
I got 250..
sullen galleon
E right?
blissful ridge
subtracting that from 360
gets you 110
the inside angle is 250
and the exterior is 110
adding to 360!
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distant abyss
Suppose a, b and c are real numbers. If a=b, a>0 and c>1 then ac>b
distant abyss
We can use the theorem: suppose a, b and c are real numbers. If a=b and a>c then b>c.
sterile musk
Have you tried anything yet?
distant abyss
Have you tried anything yet?
ive just been toying with it around
but i wasnt able to do anything
i just know that with the graeter than defintion, 0+x = a and 1+x = c
so x=a (by additive identity)
sterile musk
I suppose you are supposed to do this with a limited number of axioms? What exactly do we know.
Since obvious is c > 1, c > b/a => ac > b, but judging from what your saying that argument uses things you are not allowed to use.
distant abyss
We can use the theorem: suppose a, b and c are real numbers. If a=b and a>c then...
we could use this theorem, if that helps
distant abyss
Since obvious is c > 1, c > b/a => ac > b, but judging from what your saying tha...
yeah i dont think we could do that b/a thing
oh waiot
if a=b, then hmm yeah b/a = 1
jaunty ether
abdul jakul salsalani 😭😭😭
sterile musk
I may have accidentally spoiled it there in that case, I am sorry
I though there would be restrictions on what you could do.
distant abyss
well, the existence of a multiplicative inverse is available
i think all the regular axioms are
sterile musk
Yeah, well then thats it, since a>0.
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stray citrus
Is cube root of 1/8 positive negative 1/2 or just positive 1/2?
shrewd ridge
if you want a number as a result, it's just positive 1/2
positive negative 1/2 is not a number
stray citrus
I was just wondering cause
Sqr root gives you positive negative values
So does the same apply to cube roots
shrewd ridge
the same applies
stray citrus
What’s the third ?
shrewd ridge
positive and negative and positive negative is 3
stray citrus
Oh what
stray citrus
Why not
shrewd ridge
so yeah, cube root is different
stray citrus
Does this apply
shrewd ridge
you get 1 certain answer either way if it's a cube root
stray citrus
Yea but I need all answers
shrewd ridge
1 answer
shrewd ridge
if it was negative, there would be one answer −1/2
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sudden drum
!help
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sudden drum
hi
h
how do you know the correct way
to manipulate equations
this could of easily been -5i = -21
burnt mulch
this could of easily been -5i = -21
Can you show the steps to arrive at this?
sudden drum
the steps dont matter
im just asking for step 9/11
it says i + 9 = 4i - 12
and solving for i you get 3i = 21
sow hat they did was they subtracted i to both sides and added 12 to both sides
worldly wing
the steps dont matter
the steps matter because the equation you gave is wrong.
burnt mulch
the steps dont matter
Well clearly something went wrong to get this
^ I’m asking for the steps to see what exactly went wrong
sudden drum
the equation i gave isnt wrong
its a screesnshot of khan acadwemy solution
so it cannot be wrong
worldly wing
this could of easily been -5i = -21
this equation is wrong
sudden drum
yes i under
i understand
so what they did to solve for i is they got 3i = 21
this one is correct
worldly wing
yes
sudden drum
so what they basically did is they subtracted i to boths ides and added 12 to both sides
but why cant you subtract 4i to both sides and subtract 9 to both sides
that also isolates i
which gives you -5i = -21
so it obviously matters which way you do manipulate the equation
so how do you know which way is the correct way to manipualate the equation
worldly wing
which gives you -5i = -21
no indeed it doesnt
burnt mulch
$i-4i=-12-9 \longrightarrow -3i=-21$ tbh
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Civil Service Pigeon
worldly wing
so it obviously matters which way you do manipulate the equation
and it does not matter