to it gave all possible ones but I just had my signs wrong in my answer
#help-10
steel escarp
timid silo
hello, would the answer be 2/3
obtuse pebbleBOT
hello, would the answer be 2/3
timid silo
i did d/dx F(x) = 2x then int 0 1 of 2x^2
but this seems weird, is ther not a better way to do it than to go from the pdf
smoky vigil
i would note the part where it only works if the support is non-negative
since its 0 to 1 here, support is nonnegative
timid silo
i see
i havent learned the changing integration shits but
@smoky vigil can you explain what it means to integrate a CDF
cuz ik pdf -> cdf by integration
but 1 - cdf -> E(x) by another?
how does that make sense
smoky vigil
well in the second line note they're integrating a function of t with respect to x, so antiderivative is just xf(t)
also there is a more general conception of this with n-th moments if you've learned those
n-moment is just E(X^n)
timid silo
well in the second line note they're integrating a function of t with respect to...
that feels kinda weird but ig the math is right so ill just try to internalize it lol
timid silo
n-moment is just E(X^n)
i just barely studeid that lemme see idk if i can grasp this
smoky vigil
timid silo
do we not have to prove lim x-> infinity x(1-F(x)) = 0 on the second line
smoky vigil
well, for cdf, it's always 1 beyond its support
and 0 below its support
this makes sense if you think about it in terms of an integral of the pdf
timid silo
well, for cdf, it's always 1 beyond its support
ah ok i see
is it like as long as the support is finite then it should work?
smoky vigil
well it'llw ork even if support is infinite
timid silo
o
smoky vigil
because limit as F(x) approaches infinity should be 1
if f(x) is a pdf
becausee total area under f(x) is 1
timid silo
ok i dont know what this really has to do with n moments but i understand the lbue rectangle and the sentence under it but not the graph
timid silo
ok i dont know what this really has to do with n moments but i understand the lb...
oh wait i think i got what this ha to do with moment function 💀
@smoky vigil thanks i think i kind of got it after looking at teh graph a bit more, E(x) is just the total gray area??
smoky vigil
E(X) is total grey area if support is purely positive yes
timid silo
if support includes negative numbers do u do area > 0 - area < 0
smoky vigil
area above-area below
area below only occurs in negatives though
area below is just the normal integral though
timid silo
ok so still you're adding, but just the top and bottom function are differnt
timid silo
like you add these two areas?
smoky vigil
integral F(X) is grey area for x<0, we subtract this off
smoky vigil
iron mason
I need help
obtuse pebbleBOT
I need help
tardy epoch
,rotate
warm shaleBOT
obtuse pebbleBOT
@iron mason Has your question been resolved?
glossy lintel
45 degrees
iron mason
Please show me how to solve it
spark merlin
Do you know trigonometry?
I'll draw a diagram to help.
Double check my working, but there's a lot we can learn about this situation from the only knowing the diameter (19m) and the perpendicular distance from the chord (in orange) to the circle (4m). It means the opposite side of the triangle from our angle of interest is 15m long (19-4). We know the radius of the circle is half the diameter, so in red, we have 19/2. This makes another right triangle. We know its hypotenuse is red, we know that one side in grey is the radius minus the distance to the chord (19/2 - 4). From the Pythogorean theorem , we can get the bottom side of that triangle (pink is 2sqrt(15). That's the same as the adjacent side of the triangle with the mystery angle.
We have the opposite (15m) and the adjacent (2sqrt(15)m). From trigonometry, we know that the tangent of the angle is the same as its opposite over its adjacent, so the angle itself is the arctangent of the same ratio. That's this bit:
We can get an actual value in radians or degrees depending on your calculator by plugging in those values, but I think this is usually a good place to stop. The course or teacher may want you to go further, depending.
In General, the approach is to figure out at least two sides of the right triangle somehow or another, and use trig to get the angle back.
Does this make sense, @iron mason?
fiery ingot
Hello
fiery ingot
[ABSTRACT ALGEBRA] [PERMUTATION / CYCLE] [GROUP THEORY]
Question : ** Let n be an integer. How many fixed points on {1, . . . , n} a does permutation belonging to Sn have on average? Check it for n = 3 and n = 4 by explicit calculations**
I wrote the partitions for n = 4 and for each partition I wrote the products of cycles.
4 = 4 (0 fixed point) there is a 3! cycles product which gives this partition
4 = 3 + 1 (1 fixed point) there is a 2!0! cycles product which gives this partition
4 = 2 +2 (0 fixed point) there is a 1!1! cycles product which gives this partition
4 = 2 + 1 +1 (2 fixed point) there is a 1!0!0! cycles product which gives this partition
4 = 1 +1 + 1 +1 (4 fixed point) there is a 0!0!0!0! cycles product which gives this partition
But something is missing
In my teacher's correction in front of the parentheses it is written : 1 = ... , 4 = ... , 3 = .... , 6 = ..., 1 =
I would like to know how to determine its numbers and what they mean
If someone can explain it to me detail by detail, I have a lot of difficulty in mathematics
i'm talking about that
obtuse pebbleBOT
@fiery ingot Has your question been resolved?
obtuse pebbleBOT
@fiery ingot Has your question been resolved?
fallen inlet
How do I figure out what the graph of g(x) = (0.5)^x+3 - 4 is ?
obtuse pebbleBOT
How do I figure out what the graph of g(x) = (0.5)^x+3 - 4 is ?
fallen inlet
I tried it put in desmos but it’s blank
high lily
did you zoom out?
fallen inlet
Yes a lot
forest sinew
try clicking the 🏠 icon
high lily
pic of what it seeing please
fallen inlet
high lily
zoomed out tooo much
forest sinew
click home
high lily
also syntax issue
fallen inlet
also syntax issue
Idk what that is
past sand
Your 3 is a superscript for some reason
high lily
see that warning symbol
past sand
How do I figure out what the graph of g(x) = (0.5)^x+3 - 4 is ?
Just copy what you just wrote here and paste it back into Desmos...
forest sinew
forest sinew
you dont want a superscript
high lily
redo it,
fallen inlet
Just copy what you just wrote here and paste it back into Desmos...
I tried but it’s not doing the exponent thing
Idk what a superscript is
high lily
seems you want the + in super too
high lily
after typing that x, continue typing the +3 instead of dropping back down to the base line
past sand
after typing that x, continue typing the +3 instead of dropping back down to th...
It automatically drops
You have to go back into the exponent
high lily
put the cursor back on top if needed
fallen inlet
(0.5)^{x+3} - 4
I tried this and the wanrning says a piece wise expression must have at least one condition
high lily
use () instead of {}
fallen inlet
Ohhh that worked
past sand
Oh you literally typed the {}
fallen inlet
Yes
past sand
I meant it as "copy paste that"
fallen inlet
Ohh ok
Oh also guys one more question
For this problem
In my notes it says range is y > 0 but the answers have 9 or 3
So idk how to do it
@past sand sorry for ping
past sand
What are your notes
past sand
b^x-h or b^(x-h) ?
past sand
Yeah so b^(x-h)
past sand
For this problem
In my notes it says range is y > 0 but the answers have 9 or 3
That's not what you have here
fallen inlet
No??
Oh yeah
Wait you’re right
My other notes
My other notes for the correct function says range is y > k
It’s the second answer right
past sand
Yeah
fallen inlet
Ok thx!
obtuse pebbleBOT
@fallen inlet Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
proven citrus
i need help finding vertices of a plane intersecting a 1x1x1 cube
obtuse pebbleBOT
i need help finding vertices of a plane intersecting a 1x1x1 cube
proven citrus
ideally I want a general way for each of these 4 situations (num sides = 3, 4, 5, 6)
i doubt theres a way for that tho
if someone can help me with one of these I can do the rest 😄
ty
obtuse pebbleBOT
@proven citrus Has your question been resolved?
proven citrus
<@&286206848099549185>
ok i have a good start
i can find the coordinates individually for each case (3, 4, 5, 6)
if anyone wants to help me lump em all together into a general equation
that would be aweomse
ok upon further consideration I suspect its impossible
but im still open to suggestions if anyone has any ideas
obtuse pebbleBOT
@proven citrus Has your question been resolved?
proven citrus
<@&286206848099549185>
obtuse pebbleBOT
@proven citrus Has your question been resolved?
obtuse pebbleBOT
@proven citrus Has your question been resolved?
proven citrus
.close
lunar vigil
Hi, can anyone please explain step deviation method?
obtuse pebbleBOT
Hi, can anyone please explain step deviation method?
lunar vigil
In statistics
obtuse pebbleBOT
@lunar vigil Has your question been resolved?
obtuse pebbleBOT
@lunar vigil Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
topaz prism
obtuse pebbleBOT
topaz prism
how to get yellow hightlight? why v1, Tv1, T^2v1... equal to v1, a1v2, ....
worn coyote
how to get yellow hightlight? why v1, Tv1, T^2v1... equal to v1, a1v2, ....
By definition, i-th column of A represents the coordinates of the image of the i-th basis vector: $Tv_i$. E.g. $Tv_1$ has coordinates listed in the first column of matrix A.
Note that the first column also denotes the coordinates of $a_1 v_2$, because coordinates of $v_2$ are $(0, 1, 0, ..., 0)$. From here it's easy to see that $T^2 v_1 = T a_1 v_2 = a_1 a_2 v_3$, because $T v_2$ has coordinates listed in the second column of A.
warm shaleBOT
EQUENOS
topaz prism
ok im reading. a few mins
topaz prism
By definition, i-th column of A represents the coordinates of the image of the i...
ok i got it. something like this:
$Tv_1 = a_1v_2, Tv_2 = a_2v_3, Tv_3 = a_3v_4$
So
$TTv_1 = Ta_1v_2 = a_1a_2v_3$
$TTTv_1 = Ta_1a_2v_3=a_1a_2a_3v_4$ ...
warm shaleBOT
yehuihe
worn coyote
ok i got it. something like this:
$Tv_1 = a_1v_2, Tv_2 = a_2v_3, Tv_3 = a_3v_4$
...
exactly
topaz prism
how to give you credits or points for discord? things like that? THank you so much
worn coyote
how to give you credits or points for discord? things like that? THank you so mu...
Idk if it's a thing here, I joined like yesterday
Anyways, you're welcome
obtuse pebbleBOT
@topaz prism Has your question been resolved?
sage dagger
I’m not sure how to begin this one
obtuse pebbleBOT
I’m not sure how to begin this one
warm canopy
Plug and chug
signal current
🗣️
sage dagger
Plug and chug
Uh I don’t think I understand, what am I plugging in?
warm canopy
You are given a solution to an equation, only one thing you could plug in here
high lily
given: $y = e^{kt}$ \
first find $\dv[2]{y}{t}$ and $\dv{y}{t}$
warm shaleBOT
ℝαμΩℕωⅤ
sage dagger
Oh alright
sage dagger
given: $y = e^{kt}$ \\
first find $\dv[2]{y}{t}$ and $\dv{y}{t}$
I got up to here but something is definitely wrong
high lily
why do you think something is wrong
sage dagger
Because the k quadratic has no real solutions I can’t factor it and you can’t solve e^kt = 0 because ln(0) just breaks the function
But I need a value of k
high lily
why do you think it has no real solutions
sage dagger
I can’t factor
high lily
just because something can't be factored doesn't mean it has no real solutions
just means it doesn't have rational solutions
royal basin
shhhhh ramonov didn't you know Q = R
high lily
value of the discriminant is what determines whether you have real solutions or not
sage dagger
high lily
-4ac isn't -4
sage dagger
Oh yeah
royal basin
sign errors are very sneaky
royal basin
Running on 3 hours of sleep is also very sneaky <:opencry:586078614865444865>
no, it's just bad
foggy prawn
Looking for help with Q8 part C
obtuse pebbleBOT
Looking for help with Q8 part C
light raft
maybe use the formula v dot u = |v||u|cos(theta)
foggy prawn
Sorry I don't know that formula can you break it down a bit for me
light raft
basically, the dot product of two vectors is equal to the product of the magnitude or length of the two vectors multiplied by cosine of the angle between the vectors
so take the dot product of AC and BD, and you can equate this to the length of AC * length of BD * cos(theta), where theta is the angle you need to find
foggy prawn
Okay so the dot product of AC is 2k and BD is 2k so it would be |2|.|2|?
light raft
wait, what did you get as the vector AC and the vector BD
foggy prawn
Sorry all my working out is in the 2nd photo
light raft
ok im not fully checking your work, ill assume your vectors are correct. AC = (0,0,2) and BD = (0,0,2), so AC dot BD = 4
so, 4 = |AC| * |BD| cos(theta)
the lengths you got are |AC| = 2, and |BD| = 2, so 4 = 4cos(theta)
now you just have to solve cos(theta) = 1
foggy prawn
So would that be cos^-1(1/2x2)
obtuse pebbleBOT
Available help channel!
violet rapids
obtuse pebbleBOT
violet rapids
Focusing on left endpoint
It’s overestimation
my question is
If the graph was f(x)=2(squarerootx+3)+2
Would it still be a overestimation
that would still be a overestimation but if the graph was like
lol
Like
basiclaly if the grpah was the other way around
would it still be overestimate
For LEFT end point
would it change ?
Nvm I figured it out
.close
hexed gull
why is the set which only contains the null-vector linearly dependent?
obtuse pebbleBOT
why is the set which only contains the null-vector linearly dependent?
spice citrus
maybe because it can be written as the linear combination of 0 vectors
fickle turret
why is the set which only contains the null-vector linearly dependent?
Because you can find a non-trivial linear combination of vectors such that they equal to 0. Just let the y before the 0 be anything that you want
obtuse pebbleBOT
twilit bay
xsqaure = 2 to the power x
obtuse pebbleBOT
xsqaure = 2 to the power x
royal basin
$x^2 = 2^x$
warm shaleBOT
Ann
ancient ledge
timid silo
take log2
timid silo
u cant achieve a solvable equation
hmmm
timid silo
at least i didnt
True, there isn’t a solavable equation
spark merlin
The problem with using log is that it'll impose a domain restriction that will lose the negative root. If you don't want to graph but you're cool with some analysis, you can set this up as $f(x) = x^2-2^x$, take the derivative with respect to x, $f'(x) = 2 x - 2^x log(2)$, and employ Newton's Method to hunt them down.
warm shaleBOT
Shenzao
twilit bay
Use Maclaurin’s series expansion
brother if i knew what that is i would
timid silo
brother if i knew what that is i would
warm shaleBOT
G͟e͟l͟l͟e͟r͟t
timid silo
you get an equation $x^2 = 2^x = e^xln(2)$
lemme try
tardy epoch
xsqaure = 2 to the power x
,w solve 2^x = x^2
warm shaleBOT
tardy epoch
You're just supposed to identify x=2 and 4 are the only solution by plugging in small numbers and checking.
twilit bay
-0.76?
tardy epoch
Yea you're not meant to find the negative solution
twilit bay
what 💀
spark merlin
It can be found, but you need calculus and some analysis to get there.
If you don't know Maclaurin's Series, going into the W Lambert function like Wolfram is recommending there is probably off the table for now.
olive cobalt
hi
olive cobalt
what it the general way to solve this type of questions
m = asinx + bcosx
as an example im trying to solve
4 = 6sinx - 5 cosx
and what is the best way to find just cosx or sinx (in case there is no need to find x)
solid cargo
4 = 6sinx - 5 cosx
so u want to bring them into one trigonometric ratio
like either everything in sin
or everything in cosine
or everything in tan
Thats what were aiming for.
Usually If u had 6sinx = 5cosx it wouldve been easy to make tanx by dividing both sides by cosx
But in ur question we also have a constant so we gotta try a different approach
4= 6sinx - 5cosx
5cosx = 6sinx - 4
Square both sides
25cos^2 x = (6sinx - 4)^2
25cos^2x = 36sin^2x -48sinx + 16
Use identity , cos^2x = 1-sin^2x
25-25sin^2x = 36sin^2x - 48sinx + 16
We have now brought the equation into one trig ratio Sine
By simplifying we see that its a quadratic in terms of sin U can easily solve it further by substitution now
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
wanton kraken
does this = 1?
wanton kraken
<@&286206848099549185>
wicked nymph
does this = 1?
no it is infinity
wanton kraken
no it is infinity
how come?
wanton kraken
numenator goes to infinity but Denominator is between -1 and +1
why infinity?
wicked nymph
why infinity?
maybe i’m wrong but it cant be 1
stuck bough
help, i tried to find common factors but still cant
stuck bough
sorry
jagged falcon
.close
serene nymph
.close
stuck bough
.close
worldly bolt
How would I put a into my calculator? I can put an equals sign to do =1
obtuse pebbleBOT
How would I put a into my calculator? I can put an equals sign to do =1
cyan sinew
why put it into a calculator? lol
search about the general forms of ellipse, hyperbola, parabola and circles
obtuse pebbleBOT
worldly bolt
.reopen
obtuse pebbleBOT
✅
robust raven
no
$\frac{\left( x-x_{0} \right)^{2}}{a^{2}}+\frac{\left( y-y_{0} \right)^{2}}{b^{2}}=1\text{ }\text{ is ellipse}\\\frac{\left( x-x_{0} \right)^{2}}{a^{2}}-\frac{\left( y-y_{0} \right)^{2}}{b^{2}}=1\text{ }\text{ is hyperbola}\\\left( x-x_{0} \right)^{2}+\left( y-y_{0} \right)^{2}=r^{2}\text{ }\text{ is circle}$
warm shaleBOT
Joanna Angel
worldly bolt
Oh hyperbola has a -
robust raven
yes )
worldly bolt
Ok 👍
robust raven
very subtle diffeernce
obtuse pebbleBOT
robust raven
yw)
obtuse pebbleBOT
Available help channel!
modern sierra
coudl someone please explain to me how to find the area of the shaded region with provided z score? doi use calculator?
obtuse pebbleBOT
coudl someone please explain to me how to find the area of the shaded region wit...
worn coyote
coudl someone please explain to me how to find the area of the shaded region wit...
There's no simple formula for areas like that. Generally you should use a calculator for areas under the gaussian
The answer is $\frac{1}{\sqrt{2 \pi}} \int_{-0.83}^\infty e^{-\frac{t^2}{2}} dt$
modern sierra
i'm sorry im just not quite sure what to do with the calculator for this i missed a class n im lost now
i have a ti 84
so what would i plug in is basically what im asking
worn coyote
Depends on which calculator you're using
warm shaleBOT
EQUENOS
worn coyote
It's 0.7967...
modern sierra
.close
real pulsar
I need help regarding if a specific series shown in the picture converges or diverges.
obtuse pebbleBOT
I need help regarding if a specific series shown in the picture converges or div...
real pulsar
We can just use quotient test (its called by us in germany), root test, dirichlet, leibniz, majorant & minorant and cauchy (i think atleast)
I tried already quotient and root, but its not doable by hand, cause there i get on the wrong track and i couldnt find a good majorant ( from wolfram alpha i do know it converges)
fickle turret
Kennst du den P-Series test?
fossil crag
use comparison with $\sum_{n\geq 1} \frac{1}{n^\alpha}$
warm shaleBOT
rafilou2003
fossil crag
find a good alpha
fossil crag
I need help regarding if a specific series shown in the picture converges or div...
maybe consider multiplying the numerator by a nice quantity
real pulsar
Kennst du den P-Series test?
Dürfen wir nicht.
fickle turret
**rafilou2003**
So you are not allowed to use this comparison?
real pulsar
maybe consider multiplying the numerator by a nice quantity
difficult
real pulsar
So you are not allowed to use this comparison?
aah, is there another name how its called ? hard time comparing english and german
fossil crag
aah, is there another name how its called ? hard time comparing english and germ...
Riemann sum maybe
real pulsar
Ah you mean integral probably, right?
If so, we cant use integral.
fickle turret
aah, is there another name how its called ? hard time comparing english and germ...
This result is also called P-Series test. Are you allowed to use it?
real pulsar
Nope, tbh didnt heard of it.
Ah its part of the integral test, so i cant use it.
nvm i think we can use it
We stated, that if p is bigger than 1 it converges
serene dawn
You can use root theorem to prove P-series
serene dawn
We stated, that if p is bigger than 1 it converges
Nice
real pulsar
but didnt call it p test, just had it at the beginning of series
1 thing i thought about, but isnt the best solution in my eyes is, that for n gets really big sqrt(n+1)/n and 1/sqrt(n) both converge to zero, therefore the series should converge to zero. But hmm, not the best i think
fossil crag
ok
serene dawn
In that case multiply the top and bottom by sqrt(n + 1) + sqrt(n)
And then the denominator will be n(sqrt(n + 1) + sqrt(n))
Remove the 1 to get n(sqrt(n) + sqrt(n)) = n(2sqrt(n)) = 2n^1.5
But its (1/n^p)^(1/n)
fossil crag
1 thing i thought about, but isnt the best solution in my eyes is, that for n ge...
that won't work
real pulsar
In that case multiply the top and bottom by sqrt(n + 1) + sqrt(n)
And then the ...
gonna try it
real pulsar
In that case multiply the top and bottom by sqrt(n + 1) + sqrt(n)
And then the ...
can i just easily remove the 1 ?
fickle turret
But its (1/n^p)^(1/n)
Still the limit is 1?
serene dawn
can i just easily remove the 1 ?
It makes the denominator smaller making the entire term greater so yes
real pulsar
It makes the denominator smaller making the entire term greater so yes
True 🤔
fickle turret
Didn't see a polynomial where root test makes sense. Just wanted to ask because I was very confused 😅
real pulsar
But the problem is that i have $\frac{n+1-\sqrt{n+1} \sqrt{n} -n}{2n\sqrt{n}}$
warm shaleBOT
Nitrolack
warm shaleBOT
Nitrolack
serene dawn
nsqrt(n) = n^1.5
Thus if the series of 1/n^p converges if p > 1 then if p = 1.5 it converges
real pulsar
Thank you so damm much, ty 😄
Math student ?
serene dawn
Nope, autodidact
real pulsar
Not bad 😄
serene dawn
Wikipedia is my school XD
real pulsar
Another 0.5 points in the homework xD
Idk why i even make so much stress for half a point lol
/close
obtuse pebbleBOT
Available help channel!
forest mirage
can someone help me with where i went wrong here?
obtuse pebbleBOT
can someone help me with where i went wrong here?
@forest mirage Has your question been resolved?
worn coyote
can someone help me with where i went wrong here?
What was the task and what did you do?
forest mirage
What was the task and what did you do?
the integral is the question and i substituted x=a sec (theta), a is 16
eventutally through simplifying I got to the integral of (16than(theta))/x with respect to theta
tan instead of than that was typo
so i pulled 16/x out of the integral and integrated tan(theta) to my final answer which is 16/x - ln|(cos(theta))| + C
O man
was i supposed to solve for theta to write it in terms of x?
so if i solve for theta, x=16(sec(theta), I would get 1/16 sec^-1(x) = theta?
and I just plug that in for final answer, so
16/x - ln|cos((1/16)sec^-1(x))|+C ?
.close
dark idol
obtuse pebbleBOT
dark idol
This right?
timid silo
does 0 solve the initial equation?
ebon yoke
no, you are not taking into account the area of acceptable values
pseudo raft
how did you get x^2 - 4x?
it suppose to be like this:
x^2 -4x + 2
you can also check by urself if u got a right answer or no
for example as i can see u got x = 4 as an answer right?
we can plug in x = 4 in sqrt(2x - 1) + 1 = x
-> sqrt(8-1) + 1 = 4
-> sqrt(7) + 1 = 4
sqrt(7) + 1 not equal to 4 so x = 4 not a right answer
scarlet gale
Yeah, if you're unsure whether you got a right answer, check it like that.
obtuse pebbleBOT
@dark idol Has your question been resolved?
glossy lintel
if i have my class intervals like this,
50-60
61-70
71-80
would i need to convert them to decimals first & then figure out the class marks?
obtuse pebbleBOT
if i have my class intervals like this,
50-60
61-70
71-80
would i need to conve...
fathom flicker
Can you provide more context
What do you mean by class intervals and class marks
I assume you're trying to figure out your grade in a class right?
fathom flicker
What?
obtuse pebbleBOT
@glossy lintel Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
honest flicker
obtuse pebbleBOT
somber hare
the fraction will be undefined when the denominator is = 0
azure anchor
(4y-6)/(y^2-3y)
you can simplify that further
honest flicker
how
honest flicker
so
unreal musk
factor out y from the denominator ()
(They say "in expanded form" though?)
azure anchor
(They say "in expanded form" though?)
for the sake of finding zeros of the denominator though... way easier to look at the factors.
unreal musk
for the sake of finding zeros of the denominator though... way easier to look at...
Sure - though of course the question comes in two parts, the factoring helps for the second part(!)
honest flicker
anyways
So is it simplified furthest fr
and the domain restrictions areee
B
C
I think that's it
unreal musk
(As a side note, it's worth bearing in mind that if you cancel factors out, be careful to keep note that those "will be part of what makes the original expression undefined" - in this case you don't really lose anything, but in some cases you might (e.g. x/x simplifying to 1, but undefined when x=0))
honest flicker
plz teach antiderivatives
spark merlin
You've really been practicing rational functions today from the looks of it. It's good to see practice, but make sure that each time you come back, you're providing more and more of what you've attempted.
gentle sigil
Any takers?
unreal musk
Any takers?
!occupied
obtuse pebbleBOT
Any takers?
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
gentle sigil
Ok
unreal musk
plz teach antiderivatives
And maybe 
mind you I'm not great at teaching 
I'm better with like examples and stuff 
honest flicker
look i find this
unreal musk
Oooh cool 
scarlet gale
I've seen that one recently.
unreal musk
That's like noting that the integral represents the signed area under the curve and all
honest flicker
idk how do
honest flicker
I've seen that one recently.
yes I stole it from a help channel I think
scarlet gale
You get the equations of the three line segments at the top. You get their antiderivatives, including C. You solve for C in each one. Then, you have f(x).
unreal musk
idk how do
Also 6 + 1 = 7 
honest flicker
wat
scarlet gale
Well, you can divide 24 and 4 by 6.
honest flicker
how
scarlet gale
Well, what's 24/4?
honest flicker
oh
scarlet gale
Oh, sorry, 24/6.
honest flicker
4x+2k/3
honest flicker
Idk doesn't matter
scarlet gale
Oh, it doesn't ask like last question?
honest flicker
No
scarlet gale
Oh, OK.
unreal musk
Well think about it anyway 
honest flicker
x≠-k
unreal musk
(As a side note, it's worth bearing in mind that if you cancel factors out, be c...
It's worth doing so, as per the comment i said before here 
scarlet gale
Right.
honest flicker
look i find this
OK LETS DO THIS THINGY
Maybe
so likee
between 0 and 2
ummmm
the area is 4 right
Fr
honest flicker
wat
scarlet gale
look i find this
This one?
unreal musk
the area is 4 right
The area, sure, but remember what the integral represents...
honest flicker
yes
honest flicker
The area, sure, but remember what the integral represents...
Idek what an integral is
scarlet gale
Oh, then you can't really do that problem.
unreal musk
look i find this
honest flicker
Oh, then you can't really do that problem.
Ruh roh
unreal musk
Tl;dr those
honest flicker
isn't it just area fr
unreal musk
There's a key word missing from there...
scarlet gale
Yes, it's the area under the curve of f'(x) from x = 0 to x = 2.
I guess you could break it into a rectangle and triangle.
Never mind, it's just a triangle.
unreal musk
(Signed by whether it's under or below the x axis)
honest flicker
Idk if below the x axis matters
scarlet gale
It does. The area under the x axis is negative area. The area above is positive area.
honest flicker
ruh roh
scarlet gale
That's why the area here is negative because it's all below the x axis between x = 0 and x = 2.
honest flicker
I THOUGHT U CANT HAVE A NEGATIVE AREA
scarlet gale
It's more like they're both positive areas, but the part below the x axis subtracts and the part above adds.
It's trying to tell the part above the x axis - the part below.
That's because the idea is to get the area above the x axis, and the area below cancels it out.
honest flicker
wat
scarlet gale
Well, it's sort of like a game.
honest flicker
I will win
scarlet gale
If you get area above the x axis, you get points.
If you get area below the x axis, you lose points.
It adds together all those points and that's the total score.
honest flicker
umm doesn't it like go up forever like in that positive area idk
scarlet gale
What do you mean?
honest flicker
IDK
scarlet gale
No, you color in the x axis.
Then, you see that the function being graphed is below the x axis in that region.
So, you color in the part between the x axis and the graph.
From x = 2 to x = 4, you color in the triangle between the graph and the x axis.
From x = 4 to x = 6, you color in the triangle between the graph and the x axis.
honest flicker
so is the area -4
scarlet gale
Yes.
scarlet gale
Yeah, it's easy with straight lines.
honest flicker
Does this look right so far fr
honest flicker
Integrals become useful once the functions get harder.
too easy
honest flicker
Does this look right so far fr
Idk about the domain restrictions
unreal musk
Idk about the domain restrictions
This one, you're kind of lucky - which real numbers, if any, make the original denominator zero)
scarlet gale
Yes, that looks fine.
scarlet gale
I think it's Discord, I kept lagging.
Well, there are up to four zeroes in the bottom.
spark merlin
Unrelated to the topic of the channel, I'm seeing discord outages cropping up here and there, so hang tight! I'm sure they're working on it.
scarlet gale
You can say u = z^3 and then figure out what u values produce 0.
honest flicker
guys I got it right
scarlet gale
Yeah, there are no real roots of the denominator.
scarlet gale
It means you find the value of a function at some x value.
But you don't do it the normal way.
Instead, you look at what the graph looks like really close to that x value.
You figure out what y value the graph is heading towards from both sides of the x value.
And whatever value it's heading towards is the limit, even if the actual y value is different.
Like if you had y = x^2 except y = 100 at x = 3, the limit at x = 3 would be 9 because you ignore what it is at the actual point and you see that all the rest of the points nearby narrow in on y = 9.
long fossil
isnt that answer vertex form ? ignore the answer i spammed random stuff to get to see the answer
obtuse pebbleBOT
isnt that answer vertex form ? ignore the answer i spammed random stuff to get t...
forest sinew
isnt that answer vertex form ? ignore the answer i spammed random stuff to get t...
yea
forest sinew
seems like it
high lily
certain places use "standard form" to describe vertex from
ripe shard
how do i intergrate (cos x)^4 (sin x)^2
obtuse pebbleBOT
how do i intergrate (cos x)^4 (sin x)^2
scarlet gale
Do you know how to integrate cos^n(x)?
ripe shard
doesnt the method change depending on n
like i wold do somehting different for cos^3(x) than cos^4(x)
scarlet gale
Well, you can use the Pythagorean identity to get cos^4(x) and cos^6(x).
ripe shard
oh
is there an easer way so i don thaeve to deal with thos ehigh powers
theya re long to integrate
scarlet gale
Oh, I'm not sure.
obtuse pebbleBOT
@ripe shard Has your question been resolved?
obtuse pebbleBOT
ripe shard
.reopen
obtuse pebbleBOT
✅
sour sun
ripe shard
thats waht id di
i split cos^4 to cos^2cos^2
then with the sin^2
i get (1/2 sin2x)^2
obtuse pebbleBOT
@ripe shard Has your question been resolved?
chrome basin
Anyone cna help me graph iit im not really good with graphings things with 1/2 and 1/3 factor
obtuse pebbleBOT
Anyone cna help me graph iit im not really good with graphings things with 1/2 ...
leaden ginkgo
scale each side down by a factor of 1/3
chrome basin
Yea i know it says that but i dont know how to cause i just learned this today in class but we had a short period so im not really sure that much
leaden ginkgo
if you had to scale up by a factor of 2, what would you do?
fallen inlet
Hi for
F(x) = 9^1/2x
X is -2
Would it be 9^1.5 ?
In my solution it says 9^-1 = 1/9
fallen inlet
Why
unreal musk
$F(x) = 9^{\frac12 x}$ - do you mean this?
warm shaleBOT
@unreal musk
warm shaleBOT
@atomic umbra
atomic umbra
Hi for
F(x) = 9^1/2x
X is -2
Would it be 9^1.5 ?
In my solution it says 9^-1...
Would it be 9^1.5 ?
no because -2/2 is not 1.5
unreal musk
beat me to it
Ambiguous notation there needs to be an emote for that (and for "show work" too )
fallen inlet
$F(x) = 9^{\frac12 x}$ - do you mean this?
Yes
atomic umbra
,tex $$f(-2)$$ $$= 9^{ \frac{-2}{2}}$$ $$= 9^{-1}$$ $$= \frac{1}{ 9^{1}}$$ $$= \frac{1}{9}$$
warm shaleBOT
@atomic umbra
atomic umbra
Isn’t it like 1/2 - 2
no
fallen inlet
Oh then idk
atomic umbra
this problem is the reason i prefer x/2 and not (1/2)x
,tex $$\frac{x}{2} = \frac{1}{2}x$$
warm shaleBOT
@atomic umbra
fallen inlet
I don’t really get x/2 for me I wonder what is the x
Is the x always 1/2 in that type of fraction ?
atomic umbra
I don’t really get x/2 for me I wonder what is the x
x can be any nomber
fallen inlet
So how do I find out then
atomic umbra
So how do I find out then
when you are given a value for the variable x, multiply it by any numbers touching the x variable
in this case you were given x = -2
yes
1/2 = 0.5
0.5 * 2 = 1
but you forgot the negative
no
atomic umbra
first you do the division, then the multiplication
fallen inlet
Oh ok
atomic umbra
this problem is the reason i prefer x/2 and not (1/2)x
_ _
fallen inlet
Wait division by what
atomic umbra
?
atomic umbra
because your taking the value of 1/2, x times
atomic umbra
Ok if it’s x/2 but x is 0.5
I did 0.5 divide 2 = 4 now what
no, 0.5/2 = 0.25
fallen inlet
Ok thx I got it
atomic umbra
bro i thought it was dia who needed help
fathom pier
This question throws me off because I believe by "vertical angle theorem" JMG and KMH are congruent but then it follows by saying the shit about AAS and how thats how you find JMG and KMH being congruent and not through "vertical angle theorm"
obtuse pebbleBOT
This question throws me off because I believe by "vertical angle theorem" JMG an...
subtle sinew
This question throws me off because I believe by "vertical angle theorem" JMG an...
What are you confused about?
The problem asks to prove that JMG and KMH are congruent
The vertical angle theorem just states that if there are two opposite vertical angles, then they are congruent
fathom pier
and the two opposite vertical angles are JMG and KMH right?
subtle sinew
Yes
fathom pier
Its the fact that after that it says "JMG and KMH are conguent by AAS" making me doubt they're congreunt by vertical angle theorem
subtle sinew
Vertical angle theorem only proves that two opposite vertical angles are congruent
It does not tell you overall that the triangles are congruent
You have to use other given info to prove that
And determine if it's SSS, ASA, etc
fathom pier
Are MJG and MKH vertical angels? I don't think so. but maybe I just don't understand vertical angles
fathom pier
okay thank you, I understand what you're saying, I don't I explained what was confusing me quiet well.
subtle sinew
And as mentioned, vertical angles are opposite
Like this
So you asked if MJG and MKH are vertical angles, using that, are they?
fathom pier
Nerp
subtle sinew
Correct, they are not vertical angles
fathom pier
okay thank you
obtuse pebbleBOT
@fathom pier Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
oblique kelp
I don't know how to manipulate the equation 🤔
obtuse pebbleBOT
https://media.discordapp.net/attachments/1049809139481727076/1181977517968588950...
oblique kelp
(context: hard practice question in final grade, first semester, of Vietnam)
obtuse pebbleBOT
https://media.discordapp.net/attachments/1049809139481727076/1181977517968588950...
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
brazen gorge
factor 4x^2-4x+1
oblique kelp
(2x - 1)²
brazen gorge
mhm
oblique kelp
no clue how to proceed yet
the 4x² + 1 outside is suspicious, but I don't feel like it's gonna help much
brazen gorge
now that i thought about, i don't know either
oblique kelp
:p
brazen gorge
farthest i got was $2\log_7(2x-1) - \log_7(2x) + 4x^2 + 1 = 6x$
cyan sinew
firstly the question seems a bit off to me because there's no clear definition upon which root will be considered as x1 and which one as x2. If you have roots as 1 and 2, then x1 + 3x2 could be 1 + 2*3 and also 2 + 1*3, and both are different
that's incorrect, it'll be -log(7)2x
brazen gorge
oops
warm shaleBOT
artemetra
brazen gorge
you are right
oblique kelp
firstly the question seems a bit off to me because there's no clear definition u...
that was the original question already 🤔
cyan sinew
I never said it wasn't. I just said it seems off to me, unless I am missing something
oblique kelp
ye
oh wait, I sincerely apologize 😭
I cut off the part where x_1 was supposed to not be greater than x_2 in the original paper
it was not the original question
cyan sinew
ok
obtuse pebbleBOT
@oblique kelp Has your question been resolved?
obtuse pebbleBOT
@oblique kelp Has your question been resolved?
oblique kelp
https://media.discordapp.net/attachments/1049809139481727076/1181977517968588950...
<@&286206848099549185>
I will check how this role works.
question is here, and I do not know what to do with the (first) equation.
meager swift
https://media.discordapp.net/attachments/1049809139481727076/1181977517968588950...
Rewrite it as $\log_7\left(\frac{4x^2 - 4x + 1}{2x}\right) + 4x^2 - 4x + 1 = 2x$
warm shaleBOT
edwardborn
meager swift
Do you see anything peculiar?
oblique kelp
...so it was important after all!
that 4x^2 - 4x + 1 chunk could appear outside the logarithm!
wait.
why is 2x suspiciously outside there as well-
meager swift
Yes very sus
meager swift
Truth is unraveling
oblique kelp
wait
am I supposed to manipulate log7(a / b) = b - a now?
log7(a) + a = log7(b) + b is what I can do-
wait?
meager swift
Let the man think drugs
oblique kelp
(I'm not "the man", given my identity lol)
meager swift
*person
meager swift
gl
oblique kelp
thx
oblique kelp
so I have log7(a) + log7(7^a) = log7(b) + log7(7^b)
log7(a * 7^a) = log7(b * 7^b)
a/b = 7^b/7^a (...?)
I'm a little less confident now 💀
meager swift
If you were to desperately find just one solution without thinking too much about formalism
What would you do?
oblique kelp
I would feel completely clueless unless I had a calculator
(also known as plugging some numbers™️)
meager swift
Yeah forgot that you could do that stuff these days
oblique kelp
what were you hinting at, anyway
meager swift
log7(a) + a = log7(b) + b is what I can do-
wait?
Let's say that you had a function f(x) = lg7x + x how would lhf and rhs of this equation look like
And could you state just one condition in order for this equation to be true
oblique kelp
I would absolutely not be able to imagine either side 💀
ye, sorry
please clarify further
meager swift
Addict can take over. I gtg sorry
oblique kelp
aw, okay
devout yarrow
Hi, I might be putting you on the wrong track, but based on what I see, you have the same unknown in the base and the exponent, maybe u could try lambert W function
take my advice lightly
i also cant solve this question
oblique kelp
what is "lambert W function" 💀
devout yarrow
oh
nvm
then there must be some other way to solve it
since u havent been taught this
meager swift
yeah if it is what i think it is then that's probably not the right way to solve this
Would be correct tho if it was a numerics course
meager swift
log7(a) + a = log7(b) + b is what I can do-
wait?
Study this equation
Just looking over it quickly can you state one case where this is true
oblique kelp
...a = b?
meager swift
hard to disagree with that
oblique kelp
making x equal to (3 + sqrt(5))/4 or (3 - sqrt(5))/4 🤔🤔
devout yarrow
if a = b (btw not a good choice of unknowns as they are used in a different context in the qn) then we have 4x^2-4x+1=2x
meager swift
That's two real solutions isnt it?
oblique kelp
two real solutions indeed
devout yarrow
making x equal to (3 + sqrt(5))/4 or (3 - sqrt(5))/4 🤔🤔
how did u get that
by the quadratic equation?
oblique kelp
by solving a = b, ye
devout yarrow
like 4x^2-6x+1=0
oblique kelp
ye
I still want a better way to analyze log7(a) + a = log7(b) + b
meager swift
ye
I still want a better way to analyze log7(a) + a = log7(b) + b
You would have to analyze the function f(x) = log7(x) + x
In this case f(x) is something called injective meaning that f(a) = f(b) is true if and only if a = b
This is due to f(x) monotonically increasing
devout yarrow
yes
meager swift
This is probably not something that's is expected of you to figure out yet so if the question ask you to find two real roots then there probably only are two real roots
oblique kelp
use a graphing calculator
no idea yet-
devout yarrow
no idea yet-
have u solved it?
oblique kelp
not quite, because I still do not have an idea what you meant
the second equation's left-hand side is (6+sqrt(5))/2, which is equal to 1/4(12+2sqrt(5)), making the sum equal to 17 and resolving the question
however, I do not feel satisfied
a * 7^a = b * 7^b my beloved
oblique kelp
You would have to analyze the function f(x) = log7(x) + x
so ye, how am I supposed to resolve this step?
I have to analyze it to finalize that a = b and end the question once and for all
f(x) = log7(x * 7^x) will not be defined for non-positive reals (of x * 7^x), indeed
but I cannot say why it will strictly not decrease
wait!
the derivative!!
f'(x) = 1/(x ln 7) + 1
devout yarrow
f(x) = log7(x * 7^x) will not be defined for non-positive reals (of x * 7^x), in...
x is strictly increasing, and 7^x is strictly increasing, and it is clear that their product will also strictly increase when x is positive
however, when x is negative, x*7^x is negative too and thus its logarithm will not have a real solution
and as the log is strictly incresing, this entire expression is strictly increasing
oblique kelp
thank you 👍
oblique kelp
f'(x) = 1/(x ln 7) + 1
x cannot be non-positive or the entire log will be undefined
this will only be positive when x is positive
f(x) is definitely strictly increasing
oblique kelp
https://media.discordapp.net/attachments/1049809139481727076/1181977517968588950...
I can now say with confidence that the question is completely solved.
given x_1 < x_2, a + b = 17.
.close
obtuse pebbleBOT
devout yarrow
x cannot be non-positive or the entire log will be undefined
this will only be p...
not undefined
oblique kelp
.reopen
obtuse pebbleBOT
✅
oblique kelp
I clarify that I can only work with real numbers rn
devout yarrow
srsly
oblique kelp
worth learning a bit, and then it's closing time lol
devout yarrow
the solution is complex
devout yarrow
if its 0 its truly undefined
devout yarrow
as in complex number...?
ya
oblique kelp
oke
devout yarrow
close
glossy lintel
if i have my class intervals like this,
50-60
61-70
71-80
would i need to convert them to decimals first & then figure out the class marks?
obtuse pebbleBOT
if i have my class intervals like this,
50-60
61-70
71-80
would i need to conve...
glossy lintel
woke up
obtuse pebbleBOT
@glossy lintel Has your question been resolved?
timid silo
obtuse pebbleBOT
severe reef
Show your work?
timid silo
I don’t have any
severe reef
Alright what do you think we can do to isolate x
severe reef
Let's first try simplifying the radical with 18
Can you rewrite √18
As something simpler
past sand
Let's first try simplifying the radical with 18
You don't need to
timid silo
I hate surds
timid silo
Now do you see how we can cancel out a 3 pretty easily
Oh
root 3 divided by root 3
nothing