could you elaborate?
#help-42
dawn canopy
you'll find further ideas on proving in solving mathematical problems by terry tao
dawn canopy
could you elaborate?
like, a =c, b=c, a=b, so a=c
earnest heath
like, a =c, b=c, a=b, so a=c
no i know what an intermediate step is, im asking what is that step here
dawn canopy
imagine if yo can prove a simple version
dawn canopy
no i know what an intermediate step is, im asking what is that step here
link the question
earnest heath
this is pretty clear
potent lotusBOT
lakshya
earnest heath
earnest heath
using this
dawn canopy
i assume there is a typo since in the second part ur talking about ratios whereas it is dr cosine
earnest heath
no it is not
for l1, l2 , l3 to be direction cosines
you would first need to prove sum of their squares is 1
which we dont know yet
(however, that's also true, i also want to prove that)
dawn canopy
direction cosines are l1, l2, l3...
earnest heath
direction cosines are l1, l2, l3...
what?
dawn canopy
at least that's what you wrote in the first half 
earnest heath
given that l_1, m_1, n_1 and so on are direction cosines, does not imply that l_1 , l_2 , l_3 would also be direction cosines ( by which i mean sum of their squares is equal to 1) however generally any 3 numbers could be direction RATIOS
dawn canopy
that's the flaw of your reasoning here, when you already wrote them as cosines they can't change.
Other than that l,m,n are used to denote dr cosines
a,b,c are ratios
they dividethe cosines
@earnest heath reflecting back on this... you should look up the dot product relation between the two
and then setup equations
if ur problem is solved close it
earnest heath
i think u dont know what direction cosines and ratios are but i dont care i got it
.close
calm coralBOT
unique jackal
rustic coyote
Hello...
calm coralBOT
Available help channel!
zealous mulch
Probably a really basic question, since it's purely one variable calculus based, but I just can't seem to wrap my head around it:
Why is this function's domain not empty? It supposedly maps reals to reals, however, no matter which value of x you choose , you'll end up with an improper integral
abstract wave
Probably a really basic question, since it's purely one variable calculus based,...
for every $x \in \mathbb R , e^x > 0$
potent lotusBOT
Horsi135
abstract wave
so $t>0$ and $ln(t)$ is defined
potent lotusBOT
Horsi135
zealous mulch
so $t>0$ and $ln(t)$ is defined
the lower bound, however, is always 0
zinc plover
graph sin(lnx)
you see that the area for all postive real values is defined
e^x is always postive
zealous mulch
so the logarithm wouldnt be defined
zinc plover
what
abstract wave
the sin function sets it to be between -1 and 1
zinc plover
so
zealous mulch
so for any value of x you input, 0 will always be there, and the logarithm isn´t defined for it
zinc plover
it doesnt work like that
int 0 to inf sinx/x = pi/2
notice how if you put 0 , function becomes indeterminatwe
so does it mean the integral is undefined ?
zealous mulch
so does it mean the integral is undefined ?
alright, guess i get it
though it still feels kinda strange
zinc plover
you can also evaluate the integral its not hard
abstract wave
because when x -> 0 the limit is not infinity or negative infinity
zealous mulch
because when x -> 0 the limit is not infinity or negative infinity
that same integral with just ln(x) also produces a curve
and it does diverge there
well, thanks to the both of you, guess ill just be more careful from here on
.close
calm coralBOT
calm coralBOT
Available help channel!
raven crest
Can someone please help me on this question:
calm coralBOT
Can someone please help me on this question:
sand sky
!show
calm coralBOT
Show your work, and if possible, explain where you are stuck.
raven crest
Well I know that at least two of the digits HAVE to be even
sand sky
Well I know that at least two of the digits HAVE to be even
Yeah and the least one must be even
sand sky
Well I know that at least two of the digits HAVE to be even
But two odds one even works too right ?
raven crest
yeah
raven crest
numbers that are 1 more than a multiple of 111 will be one possible case
hollow totem
223 is even moment
sand sky
numbers that are 1 more than a multiple of 111 will be one possible case
You can't do it like this
raven crest
oh i thought you could split it up into casework
sand sky
223 is even moment
?
hollow totem
you can but not like that
sand sky
What does moment mean here ?
hollow totem
you might want to ask yourself how many possibilities are there when the first two numbers are the same
hollow totem
What does moment mean here ?
it's skibidi rizz notation
raven crest
lol wth
raven crest
you might want to ask yourself how many possibilities are there when the first t...
112, 114, 116, 118, 110, etc
sand sky
Start with fixing the units and tens digits
raven crest
so there are 5*9=45 total possibilities for that?
sand sky
Units and 10s digits can be equal in
00,22,44,66,88 that's 5 ways
And we can fill the hundreds place with , 1,2,3,4,5,6,7,8,9
raven crest
Units and 10s digits can be equal in
00,22,44,66,88 that's 5 ways
there's also 45 total possibilities for this too
sand sky
So now lets consider the units digit and hundreds are equal
It can happen 2_2,4_4,6_6,8_8
raven crest
45 possibilities for that too
sand sky
there's also 45 total possibilities for this too
No
raven crest
oh wait i forgot 0 doesn't count
sand sky
You ignored cases where all three are the same !
raven crest
i meant 9*4=36 total possibilities
sand sky
i meant 9*4=36 total possibilities
?
sand sky
Units and 10s digits can be equal in
00,22,44,66,88 that's 5 ways
When it's 00, we can fill in 9 ways, when it's 22,44,66,88 we can in 9-1 = 8 ways
So 8*4+9
raven crest
how is it only 8 ways
sand sky
how is it only 8 ways
We exclude 222,444,666,888
raven crest
no i was talking about the other case
raven crest
hundreds and 10 th is equal !
41 ways
sand sky
When we choose 11,33,55,77,99 units can be in 5 ways (0,2,4,6,8)
But when we choose 22,44,66,88 units can be in 4 ways
raven crest
so 41 ways
potent lotusBOT
Result:
118
copper notch
calm coralBOT
pure kayak
x is a scalar so T^-1 x T = xT^-1 T=xE_n
calm coralBOT
calm coralBOT
Available help channel!
mental charm
how to do the circled question?
calm coralBOT
how to do the circled question?
sick lark
do exactly what you have done in 19
mental charm
do exactly what you have done in 19
so
(x-3-2i)(x-2+root5)?
inner zealot
Complex roots always have a conjugate pair.
stray tundra
even if the coefficients of the poly are complex?
mental charm
so (x-3+2i) is also one?
sick lark
Ye
you can multiply then after that u can rewrtie the equation in more simple way
or simpler way
calm coralBOT
remote kite
not the right place
drowsy spruce
Huh
remote kite
Your finding out what x is?
drowsy spruce
Your finding out what x is?
Yy
remote kite
yy?
drowsy spruce
Ye*
ancient grotto
I cant calculate sin^-1(3/2)
because...it doesn't exist, in the real world at least.
remote kite
I cant read your hand writing
drowsy spruce
because...it doesn't exist, in the real world at least.
But i did all right?
ancient grotto
also, $\tan^{-1}(x)$ doesn't represent $\frac{1}{\tan(x)}$
potent lotusBOT
;(
remote kite
also, $\tan^{-1}(x)$ doesn't represent $\frac{1}{\tan(x)}$
yipee
ancient grotto
But i did all right?
no, your interpretation was wrong.
ancient grotto
$\tan^{-1}(x)=\arctan(x)$
potent lotusBOT
;(
drowsy spruce
remote kite
Is there even a solution?
ancient grotto
which is, the inverse tangent of x.
remote kite
I can't work it out
drowsy spruce
Tan^-1
ancient grotto
i.e., for $y=\tan(x)$, we have $x=\tan^{-1}(y)$
potent lotusBOT
;(
drowsy spruce
I can't work it out
In book says solution: 30° and 150°
ancient grotto
its supposed to be represented as $(\tan(x))^{-1}$.
potent lotusBOT
;(
ancient grotto
lets start from scratch. $\cos(x)\cdot\tan^{-1}(x)=\frac32$.
potent lotusBOT
;(
remote kite
Whats the question
ancient grotto
yeah, fix the notation.
drowsy spruce
cos(x)*cotan(c) = 3/2
That
ancient grotto
please.
ancient grotto
anyways, we have $\cos(x)\cdot\cot(x)=\cos(x)\cdot\frac{\cos(x)}{\sin(x)}=\frac32$.
potent lotusBOT
;(
ancient grotto
Like this?
well, im scratching whatever i said, since you stated that tg^(-1) isn't inverse tangent in this case.
drowsy spruce
TAN IS SIN/COS?
ancient grotto
yes.
drowsy spruce
Ohhhh
ancient grotto
you know what, why don't we just have a review session of trig somewhere?
drowsy spruce
Type shi-, let me try to solve it
drowsy spruce
you know what, why don't we just have a review session of trig somewhere?
I did
I just forgot either it’s cos/sen
calm coralBOT
Available help channel!
calm coralBOT
why did the channel suddenly close?
drowsy spruce
why did the channel suddenly close?
I haw no idea
ancient grotto
anyways.
drowsy spruce
Ok
ancient grotto
continue solving
drowsy spruce
Um
glass heart
.
ancient grotto
check in with me and ping once you're done
ancient grotto
$\frac{\cos^2(x)}{\sin(x)}=\frac32$
potent lotusBOT
;(
ancient grotto
recall the pythagorean identity
ancient grotto
1-sin(x) = 3/2?
not necessarily
drowsy spruce
Why
leaden thunder
1-sin(x) = 3/2?
How did you get here
potent lotusBOT
;(
ancient grotto
there's no simplifciation from here
drowsy spruce
Isn’t sin^2(x) = sin(x)*sin(x)?
ancient grotto
and?
drowsy spruce
since the multiplication isn't going through the entire numerator.
Oh
In that case
ancient grotto
if you're saying "i want to cancel that sin(x) on the bottom", you get $\frac{\sin(x)(\csc(x)-\sin(x))}{\sin(x)}$
potent lotusBOT
;(
drowsy spruce
1-sin^2(x)= 3/2sin(x)
ancient grotto
yes
drowsy spruce
Okkkkkkk
ancient grotto
now ler u=sin(x); its just a polynomial now.
drowsy spruce
Should i get rid of(/2) beforehand?
ancient grotto
.close
calm coralBOT
ancient grotto
THX <@1245133657690214403>
👍
calm coralBOT
Available help channel!
raven wedge
How's it going, my linear algebra class is currently touching on the topic of creating our own 3x3 system of equations that imitate these forms of planes and I was really stumped on finding the method to creating these. i've tried to use the desmos3d graphing calculator but my planes aren't exact. does anyone have any methods or ideas to help me with this? really appreciate it <3
clever ruin
You know the planes can make these possible intersections, YOU DO NOT NEED TO PLOT THEM! instead think about how in a) they do not meet at a single point but any two planes meet at a straight line, how are those straight lines related?
In b) two of the planes are parallel, so you can identify when we have this as look at the planes and see two are parallel
in c) same idea
the final one is where they all meet at one point (d which is not here)
raven wedge
I understand that c they don't meet and so in that case for C each z can be one variable and it will create that
clever ruin
in which case the determinant of the matrix is non-zero
raven wedge
right? since each plane there is differing based on the z axis at least graphically
clever ruin
In c) the 3 linear equations will be parallel planes
raven wedge
right right. if you had z=3 z=5 z=6 wouldnt those be parallel since they would never touch
clever ruin
ie. $x+y+z=2, 2x+2y+2z=10, -x-y-z=3$ would be an example
potent lotusBOT
Max
clever ruin
right right. if you had z=3 z=5 z=6 wouldnt those be parallel since they would n...
yea
raven wedge
**Max**
wait so would this for for A?
how do you go about knowing that relationship to use other variables
looking at those though wouldnt each plane be parallel
clever ruin
Im just showing an example that would fit c) we know it would fit c because if we look at the left side (the part with the variables) the planes are parallel
raven wedge
ahhh okay okay
i gotcha that makes sense
so with that example, if we made the middle plane which was x+y+2 inverted horizontally it would create A?
b* not a
e.g. -x-y+z=2
i think that makes sense for B and C. i feel like the process for A is different though since i'm really unsure how one plane can be at the bottom to the angle the two other planes to meet on the same line
clever ruin
For a) Find how the pairs of planes intersect, you'll see they are parallel lines
For b) you will have two parallel planes
For c) you will have three parallel planes
raven wedge
ohhhh
okay okay
i get b and c
just for a, you have two perpendicular lines with one bottom level plane then?
clever ruin
look at how the planes intersect
raven wedge
the top two planes would have to be perpendicular to intersect
where then you would just have a lower plane that intersects on the line with those other two
right?
calm coralBOT
@raven wedge Has your question been resolved?
jagged finch
Help
swift laurel
treat that entire part as being between the 60 isotherm and an unseen 70 isotherm
jagged finch
treat that entire part as being between the 60 isotherm and an unseen 70 isother...
So i color under it yellow and at 71 i color it as orange?
swift laurel
something like that
jagged finch
Should i color harder to make the color more color?
swift laurel
if you want to
jagged finch
jagged finch
if you want to
Is that good?
barren urchin
Is the yellow warmer?
jagged finch
Yeah
jagged finch
10
barren urchin
What class
jagged finch
Science
barren urchin
Like physical science? Or environmental?
jagged finch
We dont have specific science classes in grade 10 at my school
jagged finch
What should say for it
barren urchin
cuz thry seem dependent on the other words
An isobar connects points of equal atmospheric pressure
Isotherm connect temperature
And isoline connects points of equal value for something (like temperature or atmospheric pressure)
Do you understand?
calm coralBOT
@jagged finch Has your question been resolved?
jagged finch
Do you understand?
I rewrote it
barren urchin
Perfect
barren urchin
The bottom picture?
jagged finch
yeah
barren urchin
I have no idea bro
jagged finch
oh
barren urchin
Ima be real with you, i looked up the definitions lol
jagged finch
oh
jagged finch
oh
barren urchin
I cant help with the map
But if you can do thr map, then the other questions should be pretty simple
jagged finch
ok
barren urchin
Cuz the new ones you wrote are correct
calm coralBOT
calm coralBOT
Available help channel!
remote mural
calm coralBOT
remote mural
Inorder to write this statement using logical notations
Can i use the COnvergence defination
potent lotusBOT
Axe
remote mural
yeah like for all symbol,there exists symbol
keen flower
these?
keen flower
$\forall \epsilon > 0$ there are infinitely many $n$...
potent lotusBOT
Axe
remote mural
problem is using notation to write the infinitly many n thingy
flat gorge
$\forall \epsilon > 0 (\exists N) (\forall n > N), ||a_n - 0|| < \epsilon$
remote mural
but this is used for
potent lotusBOT
Arya
remote mural
remote mural
one small thing
both the statements are similar right
"all but finitely many" and "infinitely many"
keen flower
the two statements you posted?
remote mural
yeah
keen flower
they are not equivalent
because it can hold for even n for example
then it holds for infinitely many (the evens)
and it also fails for infinitely many (the odds)
drifting seal
all but finitely many implies there are infinitely many but infinitely many doesn’t say anything about there being finitely many that don’t satisfy it
calm coralBOT
calm coralBOT
Available help channel!
shy mantle
is this possible to do?
calm coralBOT
is this possible to do?
vagrant oak
is that the only point of intersection?
shy mantle
no..
exotic cosmos
so that's a comma?
shy mantle
is that the only point of intersection?
yeah
vagrant oak
if it intersects at a single point, then they must be tangent
so you can compare their values and derivatives
2 unknowns 2 equations
shy mantle
so you can compare their values and derivatives
ok
vagrant oak
not e but sqrt of 5
oh, that makes way more sense
shy mantle
how do i compare the values
vagrant oak
how do i compare the values
you need f(10) = 5
that gives you one equation
f'(10) = g'(10) gives you another one, if we take g(x) = (sqrt(5))^(x-8)
shy mantle
f'(10) = g'(10) gives you another one, if we take g(x) = (sqrt(5))^(x-8)
what do i do from here
vagrant oak
f and g have to intersect at (10, 5)
which means that both f(10) and g(10) must be 5
shy mantle
yeah
vagrant oak
the equation for f(x) is -a(x-h)^2 + 25
shy mantle
yeah
vagrant oak
so f(10) = -a(10-h)^2 + 25 = 5
shy mantle
ah ok
vagrant oak
similarly, you can do f'(10) = g'(10)
vagrant oak
ok so i take the derivative now
Yeah, probably
vagrant oak
isnt the derivative 0?
why?
shy mantle
because its equal to 5
vagrant oak
because its equal to 5
It's equal to 5 only at x = 10
shy mantle
yeah
vagrant oak
x^2 = 1 at x = 1, does that mean the derivative of x^2 is 0?
shy mantle
no 2x
vagrant oak
Yeah, we have to take the derivative of the function and only after that plug in the given x
shy mantle
ah
shy mantle
Yeah, we have to take the derivative of the function and only after that plug in...
is this correct?
sorry its flipped
vagrant oak
,rccw
potent lotusBOT
vagrant oak
not quite
first compute g'(x)
what's the derivative of $\left(\sqrt{5}\right)^{x-8}$
potent lotusBOT
MæthIsAlwaysRight
vagrant oak
(x-8)×(sqrt5) ?
nope
it's exponential function
it's somewhat like e^x
$e^{\ln\left(\sqrt{5}\right)\left(x-8\right)}$
potent lotusBOT
MæthIsAlwaysRight
vagrant oak
it's same as this function
vagrant oak
$\sqrt{5} = e^{\ln\left(\sqrt{5}\right)}$
potent lotusBOT
MæthIsAlwaysRight
vagrant oak
and so it's the same as $\left(e^{\ln\left(\sqrt{5}\right)}\right)^{\left(x-8\right)}$
potent lotusBOT
MæthIsAlwaysRight
shy mantle
oh
vagrant oak
in general, derivative of a^x (where a is constant) is ln(a) * a^x
so e.g. derivative e^x is ln(e) * e^x = 1 * e^x = e^x
shy mantle
is f' right
vagrant oak
is f' right
yep
vagrant oak
now i put in 10?
yeah, sure
shy mantle
okok
shy mantle
**MæthIsAlwaysRight**
wait its not this😭
vagrant oak
in general, derivative of a^x (where a is constant) is ln(a) * a^x
Do you know this rule?
calm coralBOT
calm coralBOT
Available help channel!
sick escarp
Hello!
sick escarp
I had a Question regarding the concept of the FTC and Net Change theorems:
What is the difference between the two?
ancient grotto
What is the difference between the two?
one is a theorem that leads to the corollary on the right
(sorry i cannot spell corollary for the life of me)
sick escarp
And also how would you guys solve for the integral of
sick escarp
one is a theorem that leads to the corollary on the right
so it's an application of the first?
ancient grotto
so it's an application of the first?
in essence, yes
sick escarp
So they are interchangable?
ancient grotto
And also how would you guys solve for the integral of
theres a lot of options here
ancient grotto
So they are interchangable?
not necessarily
(this is my answer when im not 100% sure)
sick escarp
So the definite integral of a function is also always equal to the net change of the function over the interval.
ancient grotto
yes
sick escarp
And also how would you guys solve for the integral of
And of this?
ancient grotto
And of this?
break the fraction down
sick escarp
turn it into x^-2?
ancient grotto
$\int_1^4\frac{x}{x^2}-\frac{4}{x^2}dx$
potent lotusBOT
;(
ancient grotto
and then use your regular properties
sick escarp
Because you don't have any rules to differentiate division, so it would end up as
1/x - 4/x^2
ancient grotto
Because you don't have any rules to differentiate division, so it would end up a...
yeah
you can use power rule then
sick escarp
The first term integrates as ln|x| the second would be (2x^-1)
ancient grotto
do you know the integral of 1/x
sick escarp
do you know the integral of 1/x
ln |x|
ancient grotto
The first term integrates as ln|x| the second would be (2x^-1)
yep
so now just do $\ln(x)-\frac{2}{x}\bigg\vert_1^4$!
potent lotusBOT
;(
sick escarp
Okay, thanks so much! I think I got it now. Whenever you have a product or quotient you essentially just distribute if u-sub is not applicable?
Or in cases where usub doesn't deal with the term being multiplied or divided?
ancient grotto
Okay, thanks so much! I think I got it now. Whenever you have a product or quoti...
yes
calm coralBOT
calm coralBOT
Available help channel!
eternal shard
,w gcd(2x^4+5x^3+8x^2+6x+3,x^4+2x^3+x^2-1)
calm coralBOT
,w gcd(2x^4+5x^3+8x^2+6x+3,x^4+2x^3+x^2-1)
potent lotusBOT
eternal shard
Hi, can somebody tell me where I went wrong
The context is to find - if possible - a solution to the equation
ancient thistle
,w quotient and remainder (2x^4+5x^3+8x^2+6x+3)/(x^4+2x^3+x^2-1)
potent lotusBOT
ancient thistle
,w quotient and remainder (x^4 + 2x^3 + x^2 - 1)/(x^3 + 6x^2 + 6x + 5)
potent lotusBOT
ancient thistle
,w quotient and remainder (x^3 + 6x^2 + 6x + 5)/(x^2 + x + 1)
potent lotusBOT
ancient thistle
there isnt one?
eternal shard
oh i just realized it's the same but i had a factor 19
and so since the gcd ain't 1 there are no solutions
ok thanks for checking lol didnt know wolfram could do that
.solved
final verge
whr do i begin for this
calm coralBOT
whr do i begin for this
fathom solstice
start combining the resistors to get it to one resistor and find the current
final verge
but theres like 3 voltage source i cant tell which is series or parallel
12 10 6 in series?
fathom solstice
there is one voltage source
final verge
there is one voltage source
like this
fathom solstice
it doesnt actually matter
fathom solstice
voltages are the same at any point where there are no resistors
final verge
1/(25+5) + 1/30 +1/10 =1/R?
fathom solstice
any line*
final verge
those are parallel right
final verge
den i would find total current first?
fathom solstice
yes, it would be very useful to find the current through the circuit
but you dont need to do that if you instead used voltage division
final verge
i got current = 0.5 A
fathom solstice
yes, it would be very useful to find the current through the circuit
current through the voltage source*
final verge
so how do i split back into v1 and v2
fathom solstice
go back to the original circuit knowing that current through the voltage source is 0.5A and calculate voltages at other spots using voltage drops
final verge
uhhhh how
fathom solstice
pick some spot to be 0V or ground
i would suggest the bottom left corner
then use ohms law and current division to figure out the voltage drops or gains from that point
final verge
can i do like this
since i foudn that the voltage for the combined parallel resistance is 3V
fathom solstice
i think i get what youre saying, so yes
calm coralBOT
calm coralBOT
Available help channel!
viral pecan
Hi, can anyone help me with that?
calm coralBOT
Hi, can anyone help me with that?
viral pecan
calm coralBOT
@viral pecan Has your question been resolved?
mortal oyster
what do we need to show to proof that a function is differentiable
mortal oyster
if a function is continuous at x = a, and its derivative is also continuous at x = a, is that a sufficient condition
mortal oyster
$\lim_{x \to a^-} f'(x) = \lim_{x \to a^+} f'(x) = f'(a)$ not required?
potent lotusBOT
SirGareth
mortal oyster
i was thinking of smt like |x|
keen flower
that is a sufficient condition
because if the derivative is continuous at x=a, it exists at x=a
mortal oyster
if a function is continuous at x = a, and its derivative is also continuous at x...
you mean this?
keen flower
yeah
keen flower
um
they got that h''(x) isn't differentiable and said that it was a contradiction
but the assumption was that h'(x) is differentiable so i don't get it
mortal oyster
yea i was thinking it looked a little wrong
ah wait
they're asking about differentiability of h' not h
.close
calm coralBOT
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strange crown
if I wanted to get rid of the radical in the denominator, this is perfectly valid right?
ancient grotto
if I wanted to get rid of the radical in the denominator, this is perfectly vali...
wdym
silver mauve
yea
flat gorge
if I wanted to get rid of the radical in the denominator, this is perfectly vali...
that is correct
silver mauve
$\frac{1}{\sqrt{x}}=\frac{\sqrt{x}}{x}$
potent lotusBOT
haygiya
ancient grotto
last line, root c in demon
demon!
strange crown
oh woops auto correct
ancient grotto
yes good
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radiant dragon
what is the z transform of (2^k)*1[k+2] ?
calm coralBOT
what is the z transform of (2^k)*1[k+2] ?
@radiant dragon Has your question been resolved?
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@radiant dragon Has your question been resolved?
pallid halo
what is the z transform of (2^k)*1[k+2] ?
show your definition of z transform, and explain the notation 1[k+2]
radiant dragon
show your definition of z transform, and explain the notation 1[k+2]
1[k+2] is a unit signal that means 1 for k > -2
this is the definition of it
pallid halo
what does k=0- mean in this context?
radiant dragon
what does k=0- mean in this context?
a bunch of signal propieties shit related to ROC
pallid halo
but k is an integer, does the sum start at 0 or not?
radiant dragon
yeah it starts at 0
pallid halo
the 1[k+2] doesn't seem to do anything in that case
since it's 1 for all k > -2, hence for all k >= 0
radiant dragon
the 1[k+2] doesn't seem to do anything in that case
its only there so the instructor feels good about himself 🤡
pallid halo
so you just need to calculate $\sum_{k=0}^\infty 2^k z^{-k}$
potent lotusBOT
Bungo
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gusty lance
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gusty lance
how do you do part b?
I got 2^10 = 1024 for the first part
if we leave one question blank
its essentially a 9 question true false test
so wouldn't that be 2^9
and if we follow that logic, 2 unansswered is 2^8
etc
do we just add all those together
keen flower
you have the option to leave each question blank
gusty lance
yeah
keen flower
that's 3 options
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civic delta
hi guys
so basically im getting the IVT (intermediate value theorem)
And lets say i got 15 pounds from getting the point horizontally.... is it valid if i try to get the x value that way too? Like by drawing a point vertically?
or no?
ancient grotto
hi guys
so basically im getting the IVT (intermediate value theorem)
And lets ...
give an example, and context.
civic delta
well im trying to solve this, the IVT is already given in the question
Let’s say a baby boy weighs 7 pounds at birth, and then 20 pounds when he is 1 year old (12 months). At some point, he must have weighed 15 pounds, for example, or any number of pounds between 7 and 20 pounds, since human weight is continuous. In this case, the baby’s age is the x -value, and the baby’s weight is the y-value, with x∈(0, 12). In other words, for a weight to get from some number to another, it must have hit all the numbers in between.
and thenn
i drew this
honestly we havent discussed ivt yet but i need to learn it for my assignment 😭
civic delta
give an example, and context.
heyyy is this okay? orrr
ancient grotto
heyyy is this okay? orrr
yeah, it works.
but, do you know the 3 conditions of IVT?
civic delta
yeah, it works.
okayy from these values do yk which one ill use to get limit of constant 6?
civic delta
but, do you know the 3 conditions of IVT?
uhh i can pull up a yt video that i just watched with it 😭
but its basically just staying within the interval?
civic delta
okayy from these values do yk which one ill use to get limit of constant 6?
i basically want to construct tabular approach with this
and graphical
but idk if im doing it right
ancient grotto
but its basically just staying within the interval?
no.
here are the three conditions for a function $f$: $f$ must be continuous on $[a,b]$, $f(b)\neq f(a)$, and $a<c<b$, therefore, by IVT, we have that $f(a)<f(c)<f(b)$ for some $c\in[a,b]$
potent lotusBOT
;(
ancient grotto
that’s the essential statement of IVT; i might have a few technical errors here, though
feel free to correct me if i do, if any helper comes along
civic delta
i seee i seee thank youuu
civic delta
but idk if im doing it right
is it okay to ask if this is right?
if i were to put a table about it?
and if thats the table ill use to get the limit*
ancient grotto
and if thats the table ill use to get the limit*
yeah, sure.
so long as it satisfies the 3 conditions.
civic delta
so long as it satisfies the 3 conditions.
thank you so muchh, ill try getting the limits noww
civic delta
have a good day/night/whatever time it is for you!
you too!! thank you and bless uuuu
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civic delta
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civic delta
heyy @ancient grotto sorry i still have one last question 😭
so basically im supposed to construct a word problem (Context above)
and then so since im making my own, i want to make something like
Compute lim (where constant would either be 12 and infinity)
For the function f(x) can i just write anything or do i have to be careful about it?
ancient grotto
heyy <@1245133657690214403> sorry i still have one last question 😭
so basicall...
civic delta
<:_catdespair:1296546203592298537>
UHH 😭
ancient grotto
heyy <@1245133657690214403> sorry i still have one last question 😭
so basicall...
just write whatever works and make sure it follows continuity, otherwise let hell break loose
civic delta
just write whatever works and make sure it follows continuity, otherwise let hel...
okay lemme see what i can doo 😔
civic delta
just write whatever works and make sure it follows continuity, otherwise let hel...
can i copy these questions and just change the constant? would that be fine?
ancient grotto
can i copy these questions and just change the constant? would that be fine?
ht...
you do you
this is your assignment not mine
civic delta
this is your assignment not mine
okayy thank youu
calm coralBOT
@civic delta Has your question been resolved?
marble lake
hi, i'm taking calculus and i have a couple questions asking about approximation. i'm a little confused on what approximation is and what an example of that would even be
marble lake
if i need to supply the function and all that i will but i guess i'm more concerned about what approximations are and how to evaluate/calculate those
swift laurel
can you provide the original problem?
marble lake
sure,
here is the function
wait
and i got that through all this (questions 4 and 5 were like 38.9 and then 39.6)
i am wrong
marble lake
yea
LOL
it was
267.6
for the height
at H(3)
would that be the peak distance?
swift laurel
but that's the height at 3 seconds. how do you know it isn't getting higher?
marble lake
hmm i dont. would i find that through graphing calculator only?
swift laurel
what kind of function is the height function?
actually can you show what the questions immediately before this one are?
swift laurel
ok so a "good approximation" means rounded to a few decimal places here
marble lake
what kind of function is the height function?
quadratic? is that what you mean?
swift laurel
yes, it is a quadratic
marble lake
ok so a "good approximation" means rounded to a few decimal places here
yea my calculator just gives back 267.6
no more decimals
swift laurel
so if you had a quadratic that opens downward like the one on the right, where would the maximum value be?
marble lake
vertex point
swift laurel
yes
marble lake
ohh so do i put in the efunction in my calculator
and then use max and then that would be my peak?
we are allowed graphing calculators for these problems
also*
swift laurel
i'm not sure if that would be allowed, but if it is then that would work
marble lake
i'm not sure if that would be allowed, but if it is then that would work
if i were to solve it without a graphing calculator what would i do?
swift laurel
do you have a method of finding the vertex of a parabola?
swift laurel
that is the formula, yes
marble lake
okay ill do that
one sec
okay sorry about the wait i found that the vertex is at 292.6
or y=292.6
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cyan mango
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cyan mango
need help with e) please
nova surge
need help with e) please
I think the answers above also need to be looked at, should we go from the top? 
clear delta
what are the terms of that pledge you signed?
nova surge
only homework
It says "You may get help but the work must be your own" so I think its all good
nova surge
but im stuck with e
But the answers for the above questions don't look correct to me either
strange crown
Given the way logs work, is this valid?
calm coralBOT
https://media.discordapp.net/attachments/1018769084252422177/1331127710826631219...
@strange crown Has your question been resolved?
keen flower
yes
river helm
https://media.discordapp.net/attachments/1018769084252422177/1331127710826631219...
Yes
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viscid path
Can anyone help to spot the mistake?
calm coralBOT
Can anyone help to spot the mistake?
tribal copper
middle expression expanding, think you wrote 20 instead of 20x
,w collect like terms 6(x+2)(x+4)-5(x+1)(x+4)+8(x+1)(x+2)
potent lotusBOT
viscid path
middle expression expanding, think you wrote 20 instead of 20x
Oh
@tribal copper Tysm bro
calm coralBOT
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wintry veldt
Combinatorics
Find the no. of possible combination of variables
problem 1
x+y+z=6 x,y,z are whole number greater than or equal to 1
I create 6 sticks , then I have to fill up 5 spaces with 2 stars
the answer is (5*4)or(5C1x4C1) ie 20. but I cannot use 5C2
problem 2
x+y+z+a=12 x,y,z,a are whole number greater than or equal to 1
use same concept of markers the answer is 11C3. but not 11x10x9.
I CANNOT UNDERSTAND THE DIFFERENCE
note:the answer 20 for first problem and 165 for second problem are strictly correct
wintry veldt
huh
warm warren
<@&268886789983436800>
exotic cosmos
Combinatorics
Find the no. of possible combination of variables
problem 1
x+y+z...
i mean from stars and bars the first one is clearly 5C2
wdym u can't use 5C2?
wintry veldt
help
exotic cosmos
wintry veldt
bro it's written 20 in the book
exotic cosmos
:V
wintry veldt
just run the code if you're unsure
idk how to run
exotic cosmos
wintry veldt
flat gorge
Combinatorics
Find the no. of possible combination of variables
problem 1
x+y+z...
for the second problem, 11C3 is indeed the answer, and you get that by using Stars and Bars
exotic cosmos
and then proceeds to do that by 5P2
it's 5C2 lol
also you can always trust code
wintry veldt
ok
flat gorge
11C3 is answer for part b. That's correct. For part a) answer should be 5C2, and book made error
exotic cosmos
wdym generate code?
wintry veldt
how did u generate this
exotic cosmos
by running my code in an ide
wintry veldt
by running my code in an ide
I have to manually write code or there is website where I don't have to code to generate outcomes
exotic cosmos
it's easy to manually write code for things like this
but i would guess you can use
github copilot and such
calm coralBOT
exotic cosmos
the error happens here
they're treating the asterisks as distinct
so they count smth like this twice
the other one being when the two asterisks are swapped
but as you know those give you the exact same thing twice
@wintry veldt
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icy mulch
Find all curves in the xy-plane for which the normal at each point (x,y) intersects the x-axis at (x + 1, 0)
- differential equations
icy mulch
Can anyone give hints? I just know that some part of the equation should be -dx/dy since the normal is the negative reciprocal of the tangent
And i think the initial conditions are when x = x + 1 , y = 0
And there’s just sumn like this
Idk how to put it together
calm coralBOT
@icy mulch Has your question been resolved?
calm coralBOT
@icy mulch Has your question been resolved?
loud fiber
Can anyone give hints? I just know that some part of the equation should be -dx/...
Give me the original question
icy mulch
Find all curves in the xy-plane for which the normal at each point (x,y) interse...
.
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merry yoke
hi yall i have some questions bout elastic collisions
calm coralBOT
hi yall i have some questions bout elastic collisions
merry yoke
and non elastic
cause i have this question "if a ball were to be bounced on the ground, would it return to its original height? assume an elastic collision"
but it can be elastic even if it didnt return to its original height? right??
cause that just means within the system...
zealous glade
but it can be elastic even if it didnt return to its original height? right??
elastic?
merry yoke
ye
zealous glade
perfectly elastic yes
zealous glade
theres a diff bw elastic and perfectly elastic
just write it like
if its perfectly elastic yes, if not - no.
i would do that
merry yoke
ok but even if it was perfectly elastic couldnt it not bounce to the original height
merry yoke
but why
zealous glade
like its conserved
merry yoke
but its no loss of kinetic energy through the entire system
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marsh blade
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crystal forge
so what would be the momentum of the ball at the moment it is thrown, just from the car moving?
crystal forge
while the car is moving, the ball has the same velocity \ momentum as the car because the person holding it is moving with the car right?
crystal forge
i mean while you are inside the car and the car is moving lets say to the right, you are also moving to the right, arent you? and any objects you are holding
marsh blade
true
if we say perpendicular
why would the ball be thrown at an angle
isnt perpendicular 90 degres
crystal forge
yeah but from the perspective of the person throwing the ball the ball isnt moving relative to them, so from their perspective they dont see that motion toward the right
crystal forge
so think of it like this, lets say the person throwing the ball throws it perpendicular, from their point of view the ball just appears to move down right? but the car also continues to move to the right
marsh blade
ok
crystal forge
but to an observer standing on the sidewalk they can see that motion to the right as well so they see the ball both moving toward them and moving to the right
marsh blade
is called frame reference
crystal forge
think about someone jumping off their skateboard to do a trick, just because they jumped off doesn't mean they suddenly stop moving forward, they have momentum forward as well so when they land back down on their board they are at the same place even though they have both moved forward at that time and when they are jumping they are "jumping straight up"
marsh blade
i think i get it
crystal forge
or in a western movie, people jumping all over from train car to train car durring a robbery scene, the train is moving forward 60 miles an hour or whatever, how come it doesnt move from under them a great amount while they are in the air for lets say 2 seconds to jump? well because they are also moving at 60 miles an hour while they are jumping, they are moving with the train while also moving maybe a little faster from running on top of the train at the same time so they can jump from car to car
marsh blade
thanks i get it
crystal forge
so the first one is a graph of velocity? and it's just a line?
then the acceleration is constant throughout, acceleration would just be the slope of that line (a constant negative acceleration)
marsh blade
no they are different graphs
i am just asking about the concept
like the + acceleration and - velocty
i am trying to learn to interpret these graphs
crystal forge
so yeah a good way to think of acceleration is the slope of the velocity graph
the velocity in the first just is constantly getting smaller and smaller (and well then moving in the negative direction which we also consider smaller)
in the 2nd graph just because the acceleration is positive doesnt mean the velocity is too, we'd have to know the "initial velocity" the object starts with, maybe it starts with a very negative velocity and then positive acceleration is just making it slightly less negative
marsh blade
ok so the acceleration graph doesnt tell us the velocity
crystal forge
no, it just tells us how its changing
marsh blade
returning to this question, if there was air resistance, it would have been A?
crystal forge
yes
marsh blade
air resistance causes the ball to slow down so it will bend, am i correct
crystal forge
because the air resistance would resist the ball moving to the right (i.e. accelerate it to the left)
but the shape might also depend on how fast you throw the ball
lets assume the car is moving faster than you throw it i guess
if you shot the ball out of a cannon then the air resistance would be more pronounced in the other direction actually
then it might look more like C :p
marsh blade
then it might look more like C :p
is this correct
also how do i know when a person "opens a parachute"
crystal forge
so the left most note is correct, becuase yeah the velocity is increasing so the acceleration must be positive
after that on the right and top most, what does that say? A_0 acceleration or ?
marsh blade
no