i got x^2 - 16
#help-13
brittle field
vagrant elbow
yeah
livid hound
i got x^2 - 16
not quite done, even assuming you mean y=x^2-16
that does not accurately represent the given graph
brittle field
oh
vagrant elbow
yeah wait
livid hound
y = (x-4)(x+4)
only gives a function with the intercepts -4 and 4
ignoring everything else
brittle field
whats that dy/dx?
vagrant elbow
oh boy
livid hound
genearlly you would need to account for a scaling factor
y = a(x-4)(x+4)
which can be determined by substituting in another point on the parabola
in this case the y-intercept (0,-4) would be the most convenient
derivatives unnecessary
vagrant elbow
yeah mb
but if you only need the intervals in which the function is positive
you don't need the equation
brittle field
is it going to be (infinity, -4), (4,infinity) ?
i feel like my answer needs to look like that
cedar kilnBOT
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bold quiver
Which equation, factorized, vertex form, or standard?
brittle field
actually im looking for a solution set when the function is greater than 0
bold quiver
So when the parabola has two real roots? Since the discriminant is greater than zero
brittle field
are roots the parts where the parabola touches the x axis?
bold quiver
Yes
Those are called the roots
The x intercepts
If there are two, the discriminant is greater than zero
brittle field
how is that written in interval form?
bold quiver
Interval notation for domain and range you mean?
Is that what you are trying to write
brittle field
interval notation when the function is greater than 0
brittle field
ya
brittle field
.close
final gorge
2x+y=p-1
2x1+y1=1
can we somehow find out what is x1 congruent to mod p
gaunt hamlet
!15m
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final gorge
2k+c=p-1 and you have to find what is k congruent to mod p
thats the problem
p is prime
cedar kilnBOT
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sick sparrow
- The resultant force of two forces of magnitude P and 2P is √3P. Find the angle between the two forces. Find the angle between the resultant force and the first force
sick sparrow
from R^2=P^2+Q^2+2PQCOSteta
sick sparrow
what is alpha
final gorge
angle between p and 2p
cedar kilnBOT
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crimson sedge
Please help
I need to calculate the Fourier transform of the function f(x)=sin(2 pi 10 x)
The Fourier transform is f(x) = int(-inf; inf) g(x)*e^(-i2piwx) dx
When i trying to calculate primitive function i get stuck, because i cannot calculate primitive function of product of functions
cedar kilnBOT
Please help
I need to calculate the Fourier transform of the function f(x)=sin(2...
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crimson sedge
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desert lichen
hello, can some one help to find this integral?
cedar kilnBOT
hello, can some one help to find this integral?
desert lichen
i have already tried the method of uncertain coefficients and Ostrogradsky 's method
so, I realized that I need to somehow decompose this into the product of multipliers in order to continue using the method of indefinite coefficients, do you have any ideas?
dark mantle
Guys?
celest maple
oh hell naw
desert lichen
hah
celest maple
the hand writing is like hard for me so
sry
it’s gonna take me a long time to process it
desert lichen
i can write carefully
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formal nest
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white delta
hi i need help with algebra : what is an obvious endomorphism in R2 that got exactly 2 invariant subspaces
crimson delta
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radiant mason
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radiant mason
number 4 and 6 ;-;
for number 4 i put it into tvm solver
but like
idk if im supposed to multiply 15 by 4 or 12
nvm not 12
i mean 1
dull oxide
,rccw
wraith daggerBOT
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warm glacier
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warm glacier
How can I solve this limit without L hopitals rule?
latent bloom
Using the list of growing functions
You can say that because e^{6x} grows to infinity a lot faster than x does, the limit goes to infinity
Wait
Ok you can use numerical method
Like approximately reach the limit from left and from right
With 0.001 positive and negative
@warm glacier
thorny shadow
What about splitting it up so you get
6e^(6x) / x - 6 / x
Both terms will be undefined if evaluated on their own
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lusty marlin
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digital cliff
a is 9x9x8. the first digit cannot be 0 so there are 9 options (1-9), the second digit cannot be the same as the first but can be 0 so still 9 options the last digit cannot be the same as either of the first so 8 options
lusty marlin
how did u cut it down to 8 mate
digital cliff
there are 10 numbers from 0-9, we have used 2 already so there are 8 possible digits left
lusty marlin
we have used 0, what is the other digit
cedar kilnBOT
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quaint leaf
Hello, I am attempting to find a conversion formula (or factor) for animation interpolation dependent on the amount of time between keyframes of an animation
I have 3 data points which are spaced out from each other (25 frame distance in t = 0.833333, 50 frame distance in t = 1.66667, 100 frame distance in t = 3.33333)
t = the amount of time between frames
in₁ = the interpolation value we are trying to make the conversion factor/formula for
-25 frame distance
when t = 0.833333
in₁ = 2.32711
-50 frame distance
when t = 1.66667
in₁ = 4.65421
-100 frame distance
when t = 3.33333
in₁ = 9.30842
cedar kilnBOT
Hello, I am attempting to find a conversion formula (or factor) for animation in...
@quaint leaf Has your question been resolved?
quaint leaf
the functions t/2.79091 = x and (its inverse) t = 0.36 * x appears to approximately fit this, is there a constant value near these values?
2.7182 is eulers number, but that is not as good of a fit as I think I need it to be
quaint leaf
guess the question is, what is a content value near 2.79253
cedar kilnBOT
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quaint leaf
<@&286206848099549185> 👀
lethal jackal
Hello, I am attempting to find a conversion formula (or factor) for animation in...
are you saying that in_1 should vary linearly with t and asking how to determine the best fitting linear model for it?
quaint leaf
are you saying that in_1 should vary linearly with t and asking how to determine...
yes
lethal jackal
if you want to calculate it by hand, you can use the linear least squares formula lol
quaint leaf
the functions t/2.79091 = x and (its inverse) t = 0.36 * x appears to approximat...
@lethal jackal that is pretty much how I got these
but its not an exact fit
lethal jackal
well you have rounding errors in your data
so I wouldn't expect it to be exactly fitting
lethal jackal
2.792526 to 2.792532 would be a closer estimate of the coefficient
quaint leaf
unless someone had a better idea
lethal jackal
one of those is good up to like 6 decimal places yeah?
if you're expecting more than that, then you'll probably need non-rounded data
quaint leaf
3 decimal places in comparing it to the data set
lethal jackal
in_1 = 2.792526t seems almost exactly correct
the difference is very low
like 0.000009
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crimson sedge
Q: express log2 (x+2) + log2 (x-5) - log4 9 as single log
Idk what's next. can someone help pls
toxic moat
convert all to same base first
crimson sedge
U can multiply them
you mean the (x+2)
Yep
Log base 2 9 is 2 log base 2 3
U can cancel out the 2s
then it can be written as log((x+2)(x-9))/3
Like that
alr
:]
thank you, teacher
nah I’m not teacher
far from it
Np tho
wht do you mean you taught me just now
u can google for the rules of logarithms
crimson sedge
u can google for the rules of logarithms
okay
runic garnet
<@&268886789983436800>
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misty otter
ye 8% and 10% is per annum
dim tiger
A block of aluminum occupies a volume of 25.0 mL and weighs 55.3 g. What is its density?
wild oracle
Duplicate question? @dim tiger
wild oracle
dim tiger
ohh, sorry
south tundra
Just divide mass by volume, no?
sonic stag
cedar kilnBOT
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crimson sedge
i don’t know how to solve but if we compare DY and XY, since DY is 4 cm and it’s that long then i think, by intuition that XY would be like a quarter of 4cm so XY is 1 cm, and if we duplicate it a bit and make it the length of BY I think BY is around 4-5cm but that’s just my opinion by looking at it
wild oracle
Yeah 12 seems right
for labelling purposes
You can show that triangles DEY and AEX are congruent (ASA), and from there you can establish that AX = 4
Since AXYZ is a square, XY = 4, so EY = 2
Then you can find DE, using the pythagorean theorem, and use congruent triangles to find AE
DE + AE equal to the side of the large square, and use AB and AE to find EB using pythagorean theorem
EB + EY should get you the answer
cedar kilnBOT
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crimson sedge
Can you find numbers (x, y, z) that satisfy the equation 2x(z-x)-y(2x+y)+z(2y-z)=2022?
crimson sedge
i got this on my olympiad, and i didnt get it correct, can anyone tell me what it is
wait nvm
.close
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crimson sedge
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crimson sedge
I found that b was 3
and so
1 = A*b^0.5
is
1 = A*3^0.5
but when I do
1/3^0.5 i get the wrong result for A
(answer model says B = 3 is the right answer)
cerulean sail
(answer model says B = 3 is the right answer)
The result for A is?
crimson sedge
yeah
crimson sedge
yes 😭
vagrant elbow
Hmm
vagrant elbow
-_-
crimson sedge
(1/3)^1/2
vagrant elbow
:P
cerulean sail
bro nvm i am so dumb
I mean, you got the right answer, soooo 😂
cedar kilnBOT
crimson sedge
ty ty
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tender meadow
How do I use mental math to solve for 20/.25
cedar kilnBOT
How do I use mental math to solve for 20/.25
tender meadow
Also .5 x 5280
coral imp
How do I use mental math to solve for 20/.25
20/.25
livid hound
think with fractions
livid hound
It becomes 20•100/25
a bit excessive
coral imp
Not wrong tho-
tender meadow
can you explain it in a different way?
livid hound
consider
$$\frac{20}{0.25} = \frac{20}{1/4}$$
and that $4\cdot0.25 = 4\cdot \frac14 = 1$
wraith daggerBOT
ℝamonov
livid hound
and multiply the numerator and denominator by 4
as for
.5 x 5280
note that 0.5 = 1/2
the expression is the same as dividing 5280 by 2
tender meadow
so you're multiplying the denominator of 1/4 which is 4 by .25 if I'm making sense
livid hound
no
tender meadow
where did you get the 4?
coral imp
0.25=1/4
tender meadow
okay I get .25=1/4
livid hound
denominator of 20/(1/4)
multiply the numerator and denominator by 4
$$\frac{20}{1/4} = \frac{20\times 4}{\frac14 \times 4}$$
wraith daggerBOT
ℝamonov
tender meadow
how did you get 4? I know it's a dumb question
coral imp
He's multiplying both numerator and denominator by 4
livid hound
performing such an action will simplify your fraction
tender meadow
ah okay
livid hound
i mean you could also apply
$$\frac{a}{b/c} = \frac{ac}{b}$$
which is more or less the same thing
wraith daggerBOT
ℝamonov
coral imp
Yep
tender meadow
oh thank you so much now what about solving for 5280x.5 using mental math?
5280x1/2=
merry heath
is it okay to use fractions to represent probability?
cedar kilnBOT
is it okay to use fractions to represent probability?
flint plinth
sure, as long as they're between 0 and 1... why wouldn't it be OK?
earnest socket
irrational probabilities?
merry heath
is fractions the same thing as proportions?
tropic oxide
no
merry heath
alright let's just say that the question is
there are two people, one is black and one is white. Find the probability that the chosen person is white
can all these 3 be accepted as answers?
cedar kilnBOT
merry heath
.reopen
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merry heath
what form is 1/2?
tropic oxide
it's a fraction...
merry heath
0.5 is proportion?
tropic oxide
as far as forms go, i personally would say that 0.5 is a decimal, 1/2 is a fraction, 50% is a percentage
if your teacher disagrees on terminology then i guess you should follow your teacher
cedar kilnBOT
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modest lava
Hi
modest lava
How can I interpret graphs of differential equations?
I don't know so I couldn't match the graphs
cedar kilnBOT
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severe pasture
How can I interpret graphs of differential equations?
solve the differential equations
and then if x is an exponential function then it should be 3 and if its a polynomial it should be 4
and so on
cedar kilnBOT
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cerulean sail
Hint for a: rewrite that as x”=-4x. Which functions, when you differentiate them twice, are the negative of their originals?
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simple shale
Is sinx = x - 2pi/3 solvable?
cedar kilnBOT
Is sinx = x - 2pi/3 solvable?
crimson sedge
Is sinx = x - 2pi/3 solvable?
it is solvable
simple shale
it is solvable
how do I get into x?
livid hound
graphing or use methods of approximation
simple shale
graphing or use methods of approximation
that kinda counters "solvable"
livid hound
there's no nice solution
gray quest
Hello, can I get someone to help me in this problem? I am not sure of my answer
gray quest
I used this formula but I am not sure about my answer and if whether the answer is negative or positive
My answer is 0.85N
cedar kilnBOT
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bright apex
It is known that in a convex quadrilateral 𝐴𝐵𝐶𝐷
A
B
C
D
, the angles 𝐴𝐵𝐷
A
B
D
and 𝐵𝐷𝐶
B
D
C
are equal to 50∘
50
∘
, and the angles 𝐵𝐶𝐴
B
C
A
and 𝐶𝐴𝐷
C
A
D
are 40∘
40
degrees. It is known that the angle 𝐴
A
is less than the angle 𝐵
B
, 𝐴𝐵=𝐵𝐶
A
B
B
C
.
Determine what each angle is equal to.
cedar kilnBOT
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@bright apex Has your question been resolved?
crimson sedge
A large tank initially holds 500 liters of gasoline. At 8 hours, the refilling of the petrol tank begins with an inlet flow of
crimson sedge
where Q is expressed in liters per hour and where t is the number of hours elapsed since the start of the
filling.
When faced with that question
I was asked to find the amount of liters at 14 hours
I did the integral
from 8 to 14
with this function
but I got 100 liters more then what I was supposed to get
scarlet garnet
from 8 to 14
why from 8 to 14
the task At 8 hours, the refilling of the petrol tank begins with an inlet flow of says that t=0 is actually already 8 hours in
crimson sedge
because " At 8 hours, the refilling of the petrol tank begins"
scarlet garnet
yes but
crimson sedge
ok
scarlet garnet
the tasks says that the function describes the filling at 8 hours
so I think its from 0 to 14-8
scarlet garnet
I believe so, yes
scarlet garnet
alright
crimson sedge
thanks
scarlet garnet
remember to read carefully, a bad way to lose points is doing it right but reading the question wrong 🙂
crimson sedge
.close
atomic granite
How come
lim as k>inf (5^k/2^k) = inf/inf which is indeterminate form
However
lim as k>inf (5/2)^k = inf
Even though they're equivalent?
jaunty shore
You are correct that the two expressions you have given are equivalent. However, when you take the limit of an expression, the way you write the expression can affect the result you get.
In the first expression, you have the limit of the quotient of two expressions: 5^k/2^k. This is an indeterminate form, because when k becomes very large, both 5^k and 2^k become very large, and it is not clear whether the quotient will approach a finite value or become infinite.
In the second expression, you have the limit of the expression (5/2)^k, which is the kth power of the quotient of 5 and 2. In this case, when k becomes very large, the quotient of 5 and 2 becomes very small, so the entire expression approaches 0.
In general, when taking the limit of an expression, it is best to write the expression in a way that makes it clear what the limit will be. In this case, the second expression makes it clear that the limit is 0, while the first expression is indeterminate.
atomic granite
In the second expression, you have the limit of the expression (5/2)^k, which is...
lim k>inf (5/2)^k isn't the limit infinity not 0?
jaunty shore
When you take the limit of the expression (5/2)^k as k approaches infinity, the result is infinity, not 0. This is because when k becomes very large, the quotient of 5 and 2 becomes very small, so the entire expression becomes very large.
However, this is not the same as the first expression you gave, which is the limit of the quotient of two expressions: 5^k/2^k. In this case, when k becomes very large, both 5^k and 2^k become very large, and it is not clear whether the quotient will approach a finite value or become infinite. This is why the first expression is an indeterminate form.
In general, when taking the limit of an expression, it is best to write the expression in a way that makes it clear what the limit will be. In this case, the second expression makes it clear that the limit is infinity, while the first expression is indeterminate.
atomic granite
Was this a mistake here then? Did you mean "the second expression makes it clear that the limit is infinity"?
atomic granite
In the second expression, you have the limit of the expression (5/2)^k, which is...
^
jaunty shore
Yes, you are correct. In the previous response, I mistakenly said that the second expression had a limit of 0, when in fact it has a limit of infinity. My mistake was due to a misunderstanding of the two expressions you gave.
To clarify, the first expression you gave is the limit of the quotient of two expressions: 5^k/2^k. This is an indeterminate form, because when k becomes very large, both 5^k and 2^k become very large, and it is not clear whether the quotient will approach a finite value or become infinite.
In contrast, the second expression you gave is the limit of the expression (5/2)^k, which is the kth power of the quotient of 5 and 2. In this case, when k becomes very large, the quotient of 5 and 2 becomes very small, so the entire expression becomes very large, and the limit is infinity.
sry
atomic granite
Yes, I see, thank you for the clear explanation. It is impressive how fast you respond and explain, to the point it was unclear whether you were a bot or a real person responding hahaha, ty!
sand wind
cedar kilnBOT
austere mortar
Graph it
sand wind
the rigorous definition of oscillatory discontinuity, is that, lim of f might not exist at that c but around delta neighbourhood of that c f is bounded
sand wind
now can I use this definition to just assert that at 1 f is bounded between some delta>1 nbd of 1?
sand wind
I didn’t see the rational and irrational
yeah lol
its not infinite discontinuity neither removable (or is it?)
crimson sedge
any open neighbourhood around 1 contains both rationals and irrationals
sand wind
yes
i understand that it a discontinuity of the second kind, where nor LHS neither RHS limit exist
from this how can I know which type of discontinuity it is
also this question, what does it mean by oscillation of f?
calm sierra
also this question, what does it mean by oscillation of f?
the book probably defined this before, try finding it
cedar kilnBOT
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sand wind
@calm sierra is this okay?
this is the first time im learning about oscillation of a function
calm sierra
not sure, do you have a pic of the def in the book?
sand wind
i dont know where it is in the book... this is the first time im learning about it, so i googled it
quartz seal
Show that in an equilateral triangle with side a, Area = 34a2 applies
sand wind
area 34a2?
quartz seal
yah
sand wind
you mean (root3 /4 )a^2
quartz seal
no i mean 34a^2
sand wind
this
crimson sedge
can someone explain to me what each of the numbers in the equation do in the graph?
unborn sonnet
cedar kilnBOT
violet night
@crimson sedge
https://www.desmos.com/calculator play around with this to learn graphing transformations
crimson sedge
ok thanks
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static jasper
e I have a number of Ip coins, twice as many 2p coins, three times as many 5p coins and four times as many 10p coins.
Altogether I have £6.00.
How many of each coin do I have?
bitter reef
say you have x 1p coins
then you have twice as many (2x) 2p coins
three times as many (3x) 5p coins
fout times as many (4x) 10p coins
these will be worth £6.00 = 600p in total
bitter reef
so it's 2x + 3x +4x = 600
no because you're missing 1p coins here and you're forgetting that the coins are worth different amounts
you have 2 * 2x = 4x from 2p coins
static jasper
3 * 3x from 5p coins
static jasper
oh yea
bitter reef
so if you had 9 of the 5p coins it'd be worth 9 * 5 = 45
static jasper
so that's 15x
bitter reef
yeah
bitter reef
yeah
bitter reef
yeah all of it adds up to 600
bitter reef
x + 4x + 15x + 40x = 600
bitter reef
solve for x
bitter reef
yup
bitter reef
no no
static jasper
10 5ps
bitter reef
he had 2x of 2p s
bitter reef
yup
static jasper
and then 10 1ps?
bitter reef
mhm
bitter reef
yup
static jasper
ok thanks man
your a legend
it's my younger brothers homework and I got a wee bit stuck so
thanks bro
cedar kilnBOT
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marsh pond
cedar kilnBOT
marsh pond
Are these the same? If so what is being done to make it so?
Just changing base?
And combing logarithm with exponent?
floral forge
$\log_37=\frac{\ln 7}{\ln 3}$
wraith daggerBOT
Duh Hello
floral forge
And combing logarithm with exponent?
yeah
marsh pond
Interesting..
Argument goes in the attic, base goes in the basement
Numerator and denominator helpful thing to remember it by
floral forge
i just remember that the base i lower down so it goes in the bottom lol
modern compass
alternatively, the definition of logarithm gives log_3(7) = x if and only if 3^x = 7, then take the ln of both sides.
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wraith obsidian
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tropic oxide
,rccw
cedar kilnBOT
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tropic oxide
that would've been a bot command to rotate your image 90° counterclockwise
bc as-is it's a neckbreaker
wraith obsidian
oh why didnt it work
,rccw
yk how to do it
ive been doin it for hrs
and am going insane
karmic crater
hi
karmic crater
can anyone explain following statement please?
Two functions that agree except for one point (or even finitely many points) will clearly give the same result when integrated against e^-2pist
what means to integrate against? and why the will give the same result?
cedar kilnBOT
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karmic crater
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cosmic marten
I'm trying to find the Maclaurin series for $\ln(1-x^2)$ of degree 3. I strated by letting $g(t)= \ln(1+t)$. This gives me the following derivatives, $g'(t) = \frac{1}{1+t}$,$g''(t) = -\frac{1}{(1+t)^2}$,$g'''(t) = \frac{1}{(1+t)^3}$, which results in
$p_3(t) = g'(0)t-\frac{g''(0)t^2}{2} +\frac{g''(0)t^3}{6} = t-\frac{t^2}{2}+ \frac{t^3}{3}$, now letting $t = -x^2$ gives $p_3(x) = -x^2+\frac{x^4}{2}-\frac{x^6}{3}$
wraith daggerBOT
Chippotle Maths
cosmic marten
However the correct answer is -x^2
cedar kilnBOT
@cosmic marten Has your question been resolved?
dire geode
However the correct answer is -x^2
degree means the power on x, not the number of terms
what you have is degree 6 or 7
cosmic marten
Oh, that is a horrible missunderstanding
In this case is degree denoted as n+1? So degree of 3 is actually a seocnd degree?
And degree 1 is just a constant?
Otherwise, I am not sure why the answer is -x^2 since its degree is 2
Solved it
thank you, Riemann.
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limber ether
cedar kilnBOT
lime bluff
gravity ball
limber ether
?
cedar kilnBOT
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tulip pond
can anyone help me with this one question please
cedar kilnBOT
can anyone help me with this one question please
tulip pond
i have tried for 20 mins
and i suck at geometry i know this is rather easy but im a beginner :/
it asks about a
<@&286206848099549185>
guys please
<@&286206848099549185>
pls
no one is awake :/
cedar kilnBOT
@tulip pond Has your question been resolved?
limber snow
f(x) = 7-sqrt(2x)
cedar kilnBOT
f(x) = 7-sqrt(2x)
limber snow
has no local max and no local min right
I tried setting to 0
and dint get anything
runic garnet
What did u set to 0
limber snow
why not the whole derivative doe
runic garnet
To find critical points, we set the numerator = 0 and denominator = 0 and solve
runic garnet
If the solutions are in our interval, we have found critical points
limber snow
for the abs max and min
theres none right
or acc since we got the local max
(0, 7)
that can be our abs max too right
runic garnet
Are u given an interval or no
runic garnet
Ok so (0,7) is our abs max
limber snow
mhm so if Im not given an interval
I can also lsit
the local max
as my abs max
wait local max is the max inna given interval right
and abs max is the overall max
runic garnet
Np
limber snow
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cedar kilnBOT
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agile turret
I am doing practice can someone explain to me the correct way of writing this out and solveing it for an example just a bit confused thank you so much
bold lotus
I am doing practice can someone explain to me the correct way of writing this ou...
which question
cedar kilnBOT
@agile turret Has your question been resolved?
cedar kilnBOT
@agile turret Has your question been resolved?
chrome turret
I am trying to convert radians to degrees if anyone could help
obsidian coral
Use the idea of 180 degrees = pi radians
chrome turret
What would the answer then be here ( if this is right) since I get pi = 24 degrees
obsidian coral
If 180 degrees = pi radians, then 1 degree = pi/180 radian
Or 1 radian = 180/pi degree
If you wanted to convert that to degrees, would you multiply by pi/180 or 180/pi?
obsidian coral
Yes
latent bloom
Ok radians means that you have the pi up
When you convert radians to degrees, you want to remove the pi, so you multiply it by pi down
And make sure your that the 180 is above the pi
chrome turret
Ohh so instead of dividing by by 15 I divide by pi ?
latent bloom
Yep
And multiply the result by 180
To convert it to degrees
You could also divide by 2π and multiply by 360
Works too
What's your answer now? :)
latent bloom
Oo you got it right
chrome turret
do i just write it as that then?
latent bloom
Does the headline tell you to keep it in between 0 and 360?
chrome turret
no it only says to round to the hundredths place so i dont think so
latent bloom
warm glacier
cedar kilnBOT
warm glacier
could someone tell me where i went wrong
I'm trying to simplify tan(arccos(x))
the answer is suppose to be sqrt(1-x^2)/x
zealous compass
draw a triangle
rotund hinge
zealous compass
if you want the easy way you can just draw a triangle 🤣
cedar kilnBOT
@warm glacier Has your question been resolved?
neat viper
cedar kilnBOT
cedar kilnBOT
@neat viper Has your question been resolved?
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balmy jewel
cedar kilnBOT
balmy jewel
how is this solved
how would I know if 1/n is greater than or equal to n!/n^n to setup an inequality
zealous compass
write out the expansion
balmy jewel
hmm k will try
uh
n * (n - 1)!/(n * n^(n - 1))?
n cancel so (n - 1)!/n^(n - 1)
hmm
zealous compass
have you realised that $\frac{1}{n}$ is in that mess
wraith daggerBOT
ed
balmy jewel
yeah I see it
zealous compass
wait im stupid is the question asking whether the sum of $a_n$ converges or whether $a_n$ converges
wraith daggerBOT
ed
zealous compass
i assume the sum right
balmy jewel
yes it is asking if the sequence converges or diverges
zealous compass
ok ok
flint plinth
it turns out that the series also converges, for similar reasons, but for that you need to do slightly more work (like compare with 1/n^2)
balmy jewel
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fierce parcel
cedar kilnBOT
plucky summit
cedar kilnBOT
plucky summit
how should i start on this?
buoyant latch
Have you tried just bruteforcing it
buoyant latch
I don’t have paper with me but id start by just brute forcing and see where that leads me
plucky summit
i know its a chain rule
buoyant latch
So, chain rule, derivative of the outside times the derivative of the inside
plucky summit
like x becomes a 1
buoyant latch
Try that and see where you get
plucky summit
my teacher's work is this
i see why that's a product rule now
one more question though
dy/dx
we multiply x's by that?
or y's
buoyant latch
d/dx x = 1
plucky summit
oh wait...
buoyant latch
d/dx y = dy/dx
plucky summit
y moves into numerator?
buoyant latch
Well kinda
plucky summit
y/1
buoyant latch
When you have y = 3x²
And I tell you what to find dy/dx
You take d/dx of both sides
Left becomes dy/dx and right is your answer
buoyant latch
It’s d/dx (x) * y + x * d/dx (y) right?
So this just turns into 1 * y + x * dy/dx
plucky summit
oh oky
buoyant latch
Which is what your answer sheet says
plucky summit
because derivative of y is dy/dx
buoyant latch
because derivative of y is dy/dx
With respect to x yes
plucky summit
y' -> dy/dx
buoyant latch
Yep
plucky summit
okayokay
buoyant latch
Different notation same meaning
buoyant latch
Yep
buoyant latch
Yep
tired inlet
hey
tired inlet
can anyone help me out with this?
I formed two equations with it: K=3D
and K-4 = 5D - 4
tired inlet
(k-4) = (5D - 4) ?
buoyant latch
and K-4 = 5D - 4
This represents Kevin’s age 4 years ago is equal to 5 times daniel’s current age - 4 years
tired inlet
yes
buoyant latch
You want it to represent Kevin’s age 4 years ago is equal to 5 times daniel’s age 4 years ago
tired inlet
correct
buoyant latch
Do you see the difference
First one you multiplied by 5 then went back 4 years
The second one you go back 4 years then multiply by 5
tired inlet
.close
boreal thunder
help is the right answer
cedar kilnBOT
help is the right answer
boreal thunder
everything about my answer seems right
but desmos says it's not :/
pic with intercepts
the blue line is y = 1/2x
buoyant latch
You need to look at more than just the leading x term
boreal thunder
hwat
buoyant latch
boreal thunder
well where do i look
buoyant latch
,w expand ((x+3)(x-2)^3)
boreal thunder
what the
wraith daggerBOT
buoyant latch
,w expand 2(x+2)^2(x-3)
wraith daggerBOT
boreal thunder
so...
buoyant latch
,w long division ((x+3)(x-2)^3)/(2(x+2)^2(x-3))
wraith daggerBOT
boreal thunder
yeah thats what i thought too
but i havent learned any end behavior with x - 2
how do u get that mathematically
buoyant latch
Do you know polynomial long division
To turn 2x³ to x⁴ you multiply by x/2, but this also creates x/2 * 2x² = x³ , we want the 3 degree term to be -3x³ , if we multiply the first term by -2, -2 * 2x² = -4x³
The x³ and -4x³ combine to be -3x³
It’s quite difficult to explain what polynomial division is doing lol
boreal thunder
yeah ik what long division is
but what i was taught
was that if degree > 1, the end behavior would be y = lc * x^(degree)
and also that is totally opposite of the question's graph
which is why im wondering if the graph is wrong or my answer is wrong
buoyant latch
Did you draw those lines?
boreal thunder
To turn 2x³ to x⁴ you multiply by x/2, but this also creates x/2 * 2x² = x³ , we...
i did this btw idk why and idk what this accomplishes
buoyant latch
i did this btw idk why and idk what this accomplishes
See the top
That’s your oblique asymptote
boreal thunder
i see but what about the remainder
what happens with that
or does anything happen with that
buoyant latch
Because your entire equation is equal to top part * left side + 1/remainder
As x tends to +- inf
That 1/remainder disappears to 0
Representing that the difference between the curve and the asymptote is going to 0
boreal thunder
Because your entire equation is equal to top part * left side + 1/remainder
i thought it was remainder/left side
boreal thunder
Representing that the difference between the curve and the asymptote is going to...
so there's a difference but it's too small to do anything right
buoyant latch
i thought it was remainder/left side
Oh yeah sorry
Point is that the degree of x is greater on the bottom
So it tends to 0
And x goes to +- inf
boreal thunder
so there's a difference but it's too small to do anything right
so this right
either way that equation different to what this graph has here
buoyant latch
so this right
As x tends to +- inf yes
boreal thunder
either way that equation different to what this graph has here
so im wondering if the graph in this picture is wrong or if im wrong
buoyant latch
That means either the graph or the eq is wrong
buoyant latch
Did you make the equation?
boreal thunder
yeah
the question asks to find the oblique asymptote
so i made the equation for the graph
and got y = 1/2x as the oblique asymptote
which was actually just y = 1/2x - 2
buoyant latch
That means your equation was wrong
boreal thunder
That means your equation was wrong
so what would the equation be
cus otherwise i have no clue
buoyant latch
Hmm I’m very rusty on equation making
cedar kilnBOT
@boreal thunder Has your question been resolved?
boreal thunder
Hmm I’m very rusty on equation making
it's ok
i'll find out tmr anyways
thanks anyways
.close
cedar kilnBOT
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crimson sedge
Hello guys
cedar kilnBOT
Hello guys
crimson sedge
Now i honestly forgot what parallel lines are
toxic moat
1 is opp 2
then para lines has that
property thing
so 2 = 3
if the lines r para
crimson sedge
But what does complementary mean
tropic oxide
complementary angles are angles whose sum is 90°. i think you might be interested in supplementary angles (ones that sum to 180°) instead
crimson sedge
Hm okay
crimson sedge
complementary angles are angles whose sum is 90°. i think you might be intereste...
Why would it be supplementary though?
They both go opposite ways
tropic oxide
don't know who "they" are
but if any pair of angles here was complementary, they would add up to a right angle. and i fail to see any right angles.
crimson sedge
What is a supplementary angle
Oh ok nvm
But how am i supposed to figure out how lines a and b are parallel
pliant valley
U know how 1 and 2 are equal cuz of vertically opposite angles
crimson sedge
Yea
pliant valley
And 2 and 3 are corresponding angles
If they are equal then lines are parallel
So if 1 and 3 are equal, corresponding angles are equal so lines are parallel
crimson sedge
So the answer is B?
pliant valley
Yes
crimson sedge
Unless there is more steps?
pliant valley
But do u understand why
crimson sedge
I'm trying to
cedar kilnBOT
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tiny dome
hello, i couldn't calculate the second part of this problem. can anyone help?
tropic oxide
presumably $\Lambda$ is meant to be a diagonal matrix, which means that $e^{\Lambda t}$ can be calculated by just taking the exponential of each of its diagonal entries
wraith daggerBOT
Ann
tiny dome
presumably $\Lambda$ is meant to be a diagonal matrix, which means that $e^{\Lam...
i don't think i understand :(( can you break it down a little more?
cerulean sail
i don't think i understand :(( can you break it down a little more?
Find the eigenvalues and eigenvectors of that A?
Then from there, you know how to write it as they said