sturdy mango
i tried doing l'h rule for the limit as n->inf but got stuck w 2^xln2 / 1 = infinity n if i keep doing L'h itll never simplify to regular numerator how do i like properly evaluate the limit
#help-28
spice orchid
you cant do lhoptial again bc the new limit is not in the form inf/inf or 0/0, infact the first application of LH is telling you the limit is infinity
elfin stream
,rcw
glossy valveBOT
elfin stream
Question: can I change the encircled sum sign to an integral sign? If yes, how?
limpid moat
to study convergeness?
fast peak
no. why should that work
elfin stream
Well to be exact can I use the definition of a Riemann sum here to convert the sums into integral?
@fast peak
If yes how would I find the integrand
fast peak
for a riemann sum you would want something like sum f(x) dx. that dx is not there and the f is currently an awful sum term
also most of the sums are just from 1 to 1, aka zero, anyway
elfin stream
Hmm could I turn the inner sum to an integral? But isn't that missing dx too
elfin stream
also most of the sums are just from 1 to 1, aka zero, anyway
Well thats if z approaches infinity no? For a finitely large z and N, the sums will not all be 0, will they?
trail barn
what are you trying to do
fast peak
floor(N/b^big number) is 1
I said most sums, not all
which one are you sending to infty first, N or z
elfin stream
which one are you sending to infty first, N or z
That matters? Also what if I don't send them to infinity
trail barn
yes it does
elfin stream
What if I send N and z to very large numbers, but infinity
elfin stream
floor(N/b^big number) is 1
Ah right
trail barn
yes it does
the stupid example to show it does is that the limit of x/y as both approach 0 is 0 if you do x first, and doesn't exist if you do y first
elfin stream
the stupid example to show it does is that the limit of x/y as both approach 0 i...
Hmm makes sense. Well I would like to see how this turns out in either case
fast peak
I mean in your case you would have to send z to infty first
elfin stream
I mean in your case you would have to send z to infty first
If I don't..?
fast peak
and then basically the thing inside lim N->infty will be the same thing anyway, but will look even worse than before. I doubt you can get any nice closed type formula
well then you need to justify why you can just switch them
elfin stream
I mean in your case you would have to send z to infty first
And if thats the case, how do I proceed?
elfin stream
and then basically the thing inside lim N->infty will be the same thing anyway, ...
I don't need a formula, I am looking for a finite approximation on my own
fast peak
lets talk some intuition first
why should this approach do anything useful
the integral you get will most likely be absolutely horrendous
elfin stream
the integral you get will most likely be absolutely horrendous
I still want to try
I am free anyways
elfin stream
why should this approach do anything useful
It doesn't matter; I am just trying crap.
@fast peak atleast give me a idea
fast peak
I have no idea how to salvage that
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glad helm
how do i proof that the red circled divides 6?
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how do i proof that the red circled divides 6?
glad helm
how do i proof that the red circled divides 6?
using mathematical induction
onyx glen
how do i proof that the red circled divides 6?
do you mean "is divisible by 6"
glad helm
i skiped the part checking for n=1
glad helm
do you mean "is divisible by 6"
yeah
onyx glen
also are you required to check it with induction
cant you just say 3n(n+1) is 3 times an even number
rough surge
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junior monolith
Bro just use the function in place of f(x) to show it's equivalent
minor crater
both of your functions are quadratic (degree 2), which means they can be defined uniquely by 2+1 = 3 points, that you already have.
you can also substitute those values (-2, -1, and 5) into both f(x) and g(x) and you'll get that a=r, b=s, c=t
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tepid elk
if i had an inverse matrix
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if i had an inverse matrix
tepid elk
and i wanted to turn it back into its standard form
say A^-1 => A
what would i have to do
worn matrix
,,
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civic nexus
Yall whats
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Yall whats
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Yall whats
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6. I have completed the problem and don't need help anymore. Thank you.
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1
rocky vale
it's all multiplication, which cancels over the division bar
cancel everything you can, and then what's left?
@civic nexus
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left bane
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left bane
Stages I, II, III of a pattern of cubes are shown below. Notice that Stage I has 1 cube, Stage II has 4 cubes, and Stage III has 10 cubes. How many cubes will there be in Stage IX of this pattern
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cedar pumice
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left bane
.close
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obtuse orbit
hello
wind heart
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wind heart
I'm having quite a bit of trouble with limit comparison tests and can't seem to get the hang of it
This is one of the few problems im struggling with
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paper beacon
Quick question, why is m undefined? Shouldn't it be zero since the denominator (x) is given and we are looking for a numerator (y)?
azure grove
for vertical lines the slope is not defined
azure grove
yes
paper beacon
thank you
azure grove
b = 5.5
paper beacon
.close
proper sonnet
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proper sonnet
Can someone help me with this integration
glossy valveBOT
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@proper sonnet Has your question been resolved?
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@proper sonnet Has your question been resolved?
lyric sluice
I think I figured this out but IDRK the accuracy of this,
could someone check me on this?
lyric sluice
^ i forgot to write down + Tp(comb) max at the end of the top equation
red blade
I think I figured this out but IDRK the accuracy of this,
could someone check me...
hmm
I'm not too familiar with this
what's the equation again
lyric sluice
the equation for max clock frequency is 1/T_c
T_c is the critical path delay
which is the longest path through the circuit
so i think that's how you do it??? i tried re-reading my lecture but i couldnt find anything on it :\
red blade
T_c is the critical path delay
so the minimum delay would be 9 ns + 6 ns + 2 ns
right
17 ns
red blade
i would believe so 😵💫
calculate the clock frequency with 17 ns
lyric sluice
but since it's asking for the max i think it would be the longest time
red blade
but since it's asking for the max i think it would be the longest time
just try it out
lyric sluice
that would be 1/17 * 1,000,000/1
wait-
for MHz
which is not an answer choice
red blade
that would be 1/17 * 1,000,000/1
I think you should be fine
red blade
ill just stick with htis
yeah sounds good
red blade
is it a command?
no
lofty rover
Need help with the gradient
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Need help with the gradient
lofty rover
on question e
onyx glen
do you know how to find the gradient of a line in general?
lofty rover
yea
jovial stirrup
nmadougie moment
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onyx glen
nmadougie moment
do you have anything constructive to contribute?
jovial stirrup
just a little bit of shenanigans AnnGhost
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old ember
I’d like to show that for every positive rational point on the unit circle, (p1/p2, q1/q2), there is an associated primitive Pythagorean triple, i.e. one that cannot be divided through by anything. I let m be lcm(p2,q2), so there exists k and l such that p1/p2 = kp1/m and q1/q2 = lq1/m.
We know that the point is on the unit circle so we get that (kp1, lq1, m) or equivalently (mp1/p2, mq1/q2, m) is a Pythagorean triple.
How do I show that this is primitive?
onyx glen
do you maybe want to assume p1/p2 and q1/q2 are in lowest terms as well
old ember
yeah sorry, I am also assuming that
onyx glen
you want to show gcd(kp_1, lq_1, m) = 1
old ember
yep
onyx glen
actually wait
you dont like
need to construct it explicitly do you
you can just say $(p_1 q_2, p_2 q_1, p_2q_2)$ is a pythagorean triple (without concern for primitivity) and then divide THAT out by its GCD
glossy valveBOT
AnnGhost
old ember
yeah that's possible, but I've been told that the triple I'm referencing is primitive, so I wanted to explicitly show this
onyx glen
oh augh
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@old ember Has your question been resolved?
paper monolith
#help-28 If a, b, and c are consecutive integers such that a < b < c, which of the following must be true?
A) b is even
B) c is odd
C) a + b + c is even
D) b – a is odd
E) b + c is even
wide sundial
<#903486480985489478> If a, b, and c are consecutive integers such that a < b < ...
what have you tried
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6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
@paper monolith
fathom lotus
New guy I think
onyx glen
Answer was solved in https://discord.com/channels/268882317391429632/90343033232...
it is against server rules to give out answers
not to mention that that answer was wrong lmao
merry thicket
Rip
onyx glen
don't spam.
motivational it may be, but you're still flooding all the help channels with it.
torn jolt
jst continue
fathom lotus
One sentence in every damn channel
torn jolt
motivational it may be, but you're still flooding all the help channels with it.
It's not gonna do anything
fathom lotus
How do you even
torn jolt
neither postive or negative
torn jolt
it is an obstruction.
you know just us talking about it is an "obstruction"
but regardless you are right
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jagged pulsar
<@&268886789983436800> can we ban this person for posting their questions in every channel
calm nacelle
Stop posting your questions in random help channels, please see #❓how-to-get-help this channel is now occupied since you didn't reply to the bot message
jagged pulsar
<@&286206848099549185>
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torn jolt
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noble pine
!status
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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
1
torn jolt
ok so first what is an upper bound
torn jolt
ok so first what is an upper bound
the higher bound
what part is confusing you
49.35
7.65
LB
49.25
7.55
i dont know what to do after
onyx glen
@torn jolt its gonna be really hard and inconvenient for people to help you with 3 different questions all at once.
torn jolt
49.35
7.65
good
torn jolt
<@456226577798135808> its gonna be really hard and inconvenient for people to he...
1 by 1
torn jolt
i dont know what to do after
what you are suposssed to so is subrtact 7.65 from 49.25
41.6
wait nvm
straight up what is 49.3-7.6
41.7
and what is upper bound of that
49.35
7.65
no of 41.7
torn jolt
next
it says this
so calculate the lower bound also
41.65?
believe so
ok lets skip for now
next one?
torn jolt
and same with 17
16.5
now add them
28
yep
in total that is the least they can way
correct
do you understand how we came to that answer and why
torn jolt
do you understand how we came to that answer and why
a bit
what dont you understand
i can do it
if it was the same question
ok do you want to move on?
torn jolt
ok do you want to move on?
yea
ok what do they mean when they say rounded to 1 significant figure
to the 1st decimal
yes
what do you think you do next
i dont know
so from 70-ish they remove 20-ish
50
now what is the upper bound
50
yes i think so
torn jolt
yes i think so
says it wrong
did you ever learn how to calculate upper and lower bound
torn jolt
did you ever learn how to calculate upper and lower bound
no
that might not be helping you with this
question changed
cause i got it wrong
interesting
were you ever taught how to calculate upper and lower bounds?
torn jolt
were you ever taught how to calculate upper and lower bounds?
no
then why are being assigned this stuff about it
cause my teacher just sets random stuff he can find
same here im supposed to be doing my math hw no idea what is going on
torn jolt
cause my teacher just sets random stuff he can find
have you asked any classmates/
torn jolt
new school?
no in year 10 we mix with other side of year i only know like 2 of them and i dont speak to them
Initial volume of water: 70 litres (rounded to 1 significant figure)
Volume removed: 30 litres (rounded to 1 significant figure)
Upper bound = Initial volume - Volume removed
Upper bound = 75 litres - 35 litres
Upper bound = 40 litres
So, the upper bound for the volume of water left in the fish tank is 40 litres.
says its wrong for me
though
idk then
sparxmaths
on bottom
there is this person im talking to that might be able to help
it was 50
i did it
good job
.close
compact leaf
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compact leaf
I have found the point of intersection
I have a good idea that first find the whole area then substract the triangle area
But having confusion at integration how to select the limit and function
spiral vigil
I have a good idea that first find the whole area then substract the triangle ar...
that's a good plan
spiral vigil
But having confusion at integration how to select the limit and function
integral of top function minus bottom function
compact leaf
I'm getting 9/4
spiral vigil
did you fix the parentheses like i suggested?
spiral vigil
,w int[0,9] √x - (x-3)/2
glossy valveBOT
spiral vigil
oh you took x/2 and integrated it to x²/2 by mistake
compact leaf
I rechecked
Yes my mistake
I got 11.25
So now time to substrate the triangle
.close
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plain depot
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plain depot
Hiii guys i have a question
if you have this function
can we say that if x ∈ ] -∞ , 1 ] f(x) is defined by ( x^3 - 3x^2 + 2x ) / (1 - x) ?
or this is wrong because 1 is not part of the domain of f?
terse fractal
depends on the continuity of it
plain depot
so instead we should write x ∈ ] -∞ , 1 [
terse fractal
so instead we should write x ∈ (-∞ , 1 ]
glossy valveBOT
USS-Enterprise
plain depot
its the first time i am seeing this notation
tawdry seal
some people use ]a,b[ instead of (a,b)
terse fractal
some people use ]a,b[ instead of (a,b)
() for no inclusive [] for inclusive simple
tawdry seal
yea thats what i use
neon basin
some people use ]a,b[ instead of (a,b)
Looks horrible though
tawdry seal
true
terse fractal
yea thats what i use
which grade
tawdry seal
which grade
12th
tawdry seal
nice
plain depot
So for example if you have a polynomial you would say that the domain of a polynomial is R of course , but if you would like to express that as an interval you would express that as ( - ∞ , ∞ ) ?
tawdry seal
can we say that if x ∈ ] -∞ , 1 ] f(x) is defined by ( x^3 - 3x^2 + 2x ) / (1 - ...
1 is indeed in the domain of f
and f is defined as ( x^3 - 3x^2 + 2x ) / (1 - x) for x=1
neon basin
So for example if you have a polynomial you would say that the domain of a polyn...
Yeah, haven't seen of $x \in ]-\infty, \infty[$
glossy valveBOT
USS-Enterprise
terse fractal
1 is indeed in the domain of f
simple factorization
plain depot
oh ok its the first time i am seeing this , here in Portugal we use ] -∞ , ∞ [
neon basin
Fascinating
plain depot
Yeah, haven't seen of $x \in ]-\infty, \infty[$
Exacly
neon basin
I'd say () is more universal
tawdry seal
wait no, 1 isnt in the domain
since you have to do division by zero
which breaks things
neon basin
So normal brackets for non inclusive or open and square brackets for inclusive or closed
tawdry seal
the image is incorrect
terse fractal
x!=1
tawdry seal
oh ok its the first time i am seeing this , here in Portugal we use ] -∞ , ∞ [
whichever feels comfortable u can use it
neon basin
whichever feels comfortable u can use it
Yep
tawdry seal
i'd say the expression written in the image is incorrect and x<1 should be the condition for f(x)=( x^3 - 3x^2 + 2x ) / (1 - x)
terse fractal
(-infi,infi)-{1}
tawdry seal
and not <=
terse fractal
and not <=
yeah
but
its same thing
cause its still less than 1
so valid question
tawdry seal
simple factorization
by factoring in, we only calcluate the limit as x->1 but never the value of f(1) since f(1) does not exist
terse fractal
by factoring in, we only calcluate the limit as x->1 but never the value of f(1)...
are nhi bro,>= and > are same unless there is a condition for equality
like 0>=x , where x=-1
plain depot
So for example saying ∀ x: (-infi , 1 ] f(x) is defined by ( x^3 − 3x^2 + 2x ) / (1 - x ) is wrong rihgt ?
since x cant be 1
tawdry seal
So for example saying ∀ x: (-infi , 1 ] f(x) is defined by ( x^3 − 3x^2 + 2x ) ...
i'd say the expression written in the image is incorrect, since the less than or equal to sign implies x is in the domain of f, which it isnt since it would involve division by zero which isnt possible
where'd u get the image from?
terse fractal
So for example saying ∀ x: (-infi , 1 ] f(x) is defined by ( x^3 − 3x^2 + 2x ) ...
(-infi,1)
plain depot
I am doing Mathematical analisis in college ( my english is not that good sorry for that )
terse fractal
it means 1's not included
plain depot
Because the f(x) for x = 1 is not defined
tawdry seal
yeah, 1 shouldnt be included in the domain of f
terse fractal
Because the f(x) for x = 1 is not defined
exactly
u can also write (-infi,infi)-{1}
tawdry seal
or even R-{1}
terse fractal
or even R-{1}
which coaching?
plain depot
The question is very simple its asking to study the function about her continuity and her differenciability , if i was in highschool i would instantly write f(x) is continous in all of her domain , because the first expression its a racional expression and its continous in all of her Domain and the the other one is an exponencial which is also continous in all of her domain , but here i ma trying to be more formal thats why i am asking
terse fractal
not kota tho
more better 😂
terse fractal
The question is very simple its asking to study the function about her continuit...
u r correct just take care of brackets
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toxic marlin
Assume that when human resource managers are randomly selected, 57% say job applicants should follow up within two weeks. If 7 human resource managers are randomly selected, find the probability that exactly 2 of them say job applicants should follow up within two weeks.
So I have identified n = 7, p = .57, x = 2
so after doing n!/(n-x)!x! I get 10.5
Then 10.5 * .57^2 * .43^5 = 0.5015119.....
The formula used was (n/X)⋅p^X⋅(1−p)^n−X
The answer is supposed to be .1003 so what am I doing wrong?
Sorry if this is confusing, but I am confused myself haha
toxic marlin
now if I input n = 7, p = .57, x = 2 into binomialpdf on my ti84 I get .1003 but I need to learn how to do it by hand
<@&286206848099549185>
any help would be greatly apprecited 🙂
kindred grove
so after doing n!/(n-x)!x! I get 10.5
that's weird
this only gets you integers normally
@toxic marlin
kindred grove
,w 7!
glossy valveBOT
kindred grove
yes
toxic marlin
🤦♂️
let me re work it now
ok so n!/(n-x)!x! = 21
YES
I got .1003
Thanks so much @kindred grove
.close
devout spear
how do I factor x^3 + 6x^2 +11x + 6
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how do I factor x^3 + 6x^2 +11x + 6
devout spear
like (x^3 + 6x^2 +11x + 6) /-1 ?
spice orchid
divide by the corresonding factor
devout spear
but what if x is like 189 surely I wouldnt need to check this many numbers XD
torn jolt
you should probably know about rational root theorem instead of haphazardly plugging in numbers and hoping for the best
devout spear
you should probably know about rational root theorem instead of haphazardly plug...
whats that
oh kk so like ik if you plug -1 for x it equals 0
okay that makes sense so how do I proceed
torn jolt
whats that
wise thistle
yo
wise thistle
they’re asking us for an expression that describes the total amount of trees for x trees planted
i have no idea how to go on anout this
minor crater
notice that in year 2, the side length is 2, and in year 3, the side length is 3
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ripe valley
is this really an inflection point? shouldn't it be a switch in signs
spice orchid
its the sign of the derivative, either side of -2 the derivative is always negative so the function is decreasing either side
ripe valley
its the sign of the derivative, either side of -2 the derivative is always negat...
so no inflection point right?
spice orchid
yes an inflection point
the function is decreasing before and after -2
so its not a min or max
ripe valley
ah thank you
i thought inflection point was only when - became +
for example
.close
ripe valley
how did they isolate y?
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how did they isolate y?
queen crater
$2\sqrt{2}y - \frac{2}{\sqrt{2}} = y - \frac{1}{\sqrt{2}\sqrt{2}}$
glossy valveBOT
Nel
queen crater
Just dividing by 2*sqrt(2)
green sentinel
No, first you add 2/sqrt(2) to both sides.
queen crater
2/sqrt(2) divided by 2*sqrt(2) gives 2/(2sqrt(2)sqrt(2)) gives 1/(sqrt(2)sqrt(2))
ripe valley
could you maybe show me the algebra? written out so i understand better
im really confused
green sentinel
No, first you add 2/sqrt(2) to both sides.
$2\sqrt{2}y - \frac{2}{\sqrt{2}} + \frac{2}{\sqrt{2}} = 0 + \frac{2}{\sqrt{2}}$
glossy valveBOT
Narynbek
green sentinel
what do you get?
queen crater
$2\sqrt{2}y - \frac{2}{\sqrt{2}} = \frac{2\sqrt{2}y}{2\sqrt{2}} - \frac{\frac{2}{\sqrt{2}}}{2\sqrt{2}} = y - \frac{2}{\sqrt{2}2\sqrt{2}}$
glossy valveBOT
Nel
ripe valley
are these both the same method
green sentinel
I think yours is generally more difficult to understand)
queen crater
$2\sqrt{2}y - \frac{2}{\sqrt{2}} = 2\sqrt{2}\sqrt{2}y - \frac{2\sqrt{2}}{\sqrt{2}} = 4y - 2$
queen crater
Well you still have the = 0 on the right side
Sorry I meant to write 4y-2 at the end
glossy valveBOT
Nel
queen crater
$4y - 2 = 0 \implies 4y = 2 \implies y = \frac{2}{4}$
glossy valveBOT
Nel
lone hinge
can someone give me a yt video/practice problems for this lesson in college algebra i need to prepare for the graded part
lone hinge
(i cant view the lesson yet its for next week)
gritty rose
Khan academy has this
lone hinge
Khan academy has this
do you mind sending the link?
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grizzled sigil
How do I solve for x with -5cos(x) = 0? I’m looking for inflection points, and that’s the second derivative
spiral vigil
you can divide both sides by -5
torn jolt
well, do you know what the roots of cos(x) are?
grizzled sigil
I’m not sure what you mean, but it’s in the interval [0,2pi] if that helps. I struggle solving for x with trig functions
limpid moat
do you know derivative but not zeros of cosine ?
grizzled sigil
Yes
limpid moat
wow
grizzled sigil
-5cos(x) is the 2nd derivative
limpid moat
yes
queen crater
What's cos(pi/2)?
grizzled sigil
0
queen crater
So if x = pi/2, is -5cos(x) = 0 true?
queen crater
Why not?
grizzled sigil
3pi/2
Let me send a picture because when I put these points into my homework problem, it says it’s wrong
queen crater
That would be because y is not 0
It's supposed to be f(x), not f''(x)
Granted it's a bit odd to ask for both x and y
grizzled sigil
So do I plug in pi/2 and 3pi/2 into f(x) or f’’(x)?
grizzled sigil
I’m still having issues getting the answer. I plug pi/2 into f(x), and I’ve tried rounding multiple ways, but I’m just not getting the y value right
queen crater
You don't need to round, just plug it into x + 5 cos x and simplify
queen crater
No, not with a calculator
grizzled sigil
Really? Im not sure how then
queen crater
Wdym? If f(x) = x + 5cos(x), then what is f(pi/2)?
queen crater
You're welcome
grizzled sigil
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blazing wasp
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blazing wasp
OHH
glossy valveBOT
glacial pasture
pi/2
blazing wasp
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subtle elm
An infinite pattern of tiles looks like this:
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An infinite pattern of tiles looks like this:
subtle elm
What is the ratio between the areas of the two colors (dark blue divided by light blue)?
these are the options:
A. 0.925
B. 1
C. 1.329
D. 1.414
i dont even have an idea how to solve this...
<@&286206848099549185>
quartz gale
I think that you can take a circle and a light blue “square” that is just to the right of the circle and calculate the ratio only for those two
Because this pattern can be defined only with this form (circle + “square”)
rapid rain
Actually half circle
quartz gale
Why ?
rapid rain
The motif is 2 dark blue 'ellipses' and 1 light blue 'square'
quartz gale
The circle would work though no ?
rapid rain
This is the smallest motif that can be repeated without overusing squares or ellipses
quartz gale
Yeah okay
rapid rain
Taking one whole circle as the motif (so 4 ellipses) creates overlap
subtle elm
i dont really uunderstand
quartz gale
Taking one whole circle as the motif (so 4 ellipses) creates overlap
No but yours is the smallest motif so it’s better
quartz gale
i dont really uunderstand
He did the same thing I did, wich is find a motif that you can use to create the whole pattern
With two elipses and one light square you can recreate the whole thing
So now you juste have two find the ratio in that motif
subtle elm
how would i find the ratio
like i understood that 2 elsipses and 1 light square can make the whole pattern
but i dont understand how that helps to find the ratio
quartz gale
Do you get that if you find the ratio in that motif, it will be the same as the ratio in the whole pattern ?
quartz gale
It will be 2 * (Area of one ellipse) / (Area of the light square)
So now you’re down to find those two different area
quartz gale
It will be 2 * (Area of one ellipse) / (Area of the light square)
That’s the ratio between the area of dark blue and light blue
subtle elm
how can i express both the areas of the eklipse and the light square
i cant find any way
like maybe tge area of one elipse is x and the area of light square is y
so 2x/y is the proport
but i cant define x with y or y with x
i dont have any info
somehow i gotta get to a number
i dont understand how tho
quartz gale
I actually don’t know the answer to that question sorry
subtle elm
<@&286206848099549185>
quartz gale
The only way I can think of is double integration but do you know that ?
subtle elm
nope
ig i dont have an answer 
i gtg but thanks for ur time
<@&286206848099549185>
if anyone know how to solve this pls dm me
tawny nest
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tawny nest
idk what im doing wrong here either i checked on calculator and it said it was right
got it
fathom lotus
Is your interval correct?
hardy pivot
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hardy pivot
where does 3/5 come from
im pretty sure the foci are +-c
which should be
c^2 = a^2 + b^2
but im getting anything but 3/5
spiral vigil
well finding y-intercepts for any curve is pretty straightforward
just set x to 0 and then solve for y
so $25y^2 - 4x^2 = 9$ becomes $25y^2 - 4\cdot\blue0^2 = 9$
glossy valveBOT
Haylsune Miku
torn jolt
Analyze the graph and answer.
a) What are the amplitudes of the trigonometric functions like?
Both have a value of 3.
b) How much do the periods of the trigonometric functions differ?
Both have a period of π.
torn jolt
Are my answers correct?
quartz tulip
Looks about right buddy
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eternal juniper
wait so y=a(x-h)^2+k is vertex form
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wait so y=a(x-h)^2+k is vertex form
naive bison
How do I do this problem?
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How do I do this problem?
nova topaz
We know when complex numbers are multiplied, their angles are added and their magnitudes are multiplied
naive bison
yeah
nova topaz
We know the magnitude of z=cis(289) is 1
so all we need to do is rotate it by 289* 5 times
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naive bison
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hushed plume
sin^3 x)/(cos x) + (cos^3 x)/(sin x) - 2sin x * cos x = 2 can you help me prove this?
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sin^3 x)/(cos x) + (cos^3 x)/(sin x) - 2sin x * cos x = 2 can you help me prove ...
naive bison
sin^3 x)/(cos x) + (cos^3 x)/(sin x) - 2sin x * cos x = 2 can you help me prove ...
can you simplify the (sin^3 x)/(cos x) + (cos^3 x)/(sin x)
hushed plume
yeah its (sin^2x-cos^2x)^2/sinxcosx
naive bison
tbh, I'm learning this rn so I'm not the fastest yet
naive bison
yeah its (sin^2x-cos^2x)^2/sinxcosx
how did you get the (sin^2x-cos^2x)^2 part
and where did you get the minus
hushed plume
if you connect 2sinxcosx to the fraction you get sin^4x-2sin^2xcos^2x+cos^4x
fast marlin
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@fast marlin Has your question been resolved?
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@fast marlin Has your question been resolved?
fathom lotus
Yeah? @fast marlin
fast marlin
Yeah? <@869395681683587133>
?
fathom lotus
What is your question
fast marlin
21
fathom lotus
y = mx + b
fast marlin
How does the tsngent line for a linear equation have a slope
fast marlin
A non zero slope
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crystal cobalt
Dumb question but what's the maximum value of P(A n B)?
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Dumb question but what's the maximum value of P(A n B)?
torn jolt
1?
you can have two equal sets that are both the universal set and equal to each other
crystal cobalt
Oh yeah if both the venn diagrams are on each other
crystal cobalt
you can have two equal sets that are both the universal set and equal to each ot...
right right
okay what if like
I give you P(A) = 0.9
P(B) = 0.4 maybe
what's the maximum value of P(A n B) then?
0.9?
torn jolt
well if B is entirely contained in A then the maximum would be 0.4 I'd assume, and if it wasn't then it would be less
someone fact check me tho in case I'm speaking voodoo
crystal cobalt
well if B is entirely contained in A then the maximum would be 0.4 I'd assume, a...
i thought that way too but i remember doing a question and they actually said it could be <= 0.9
well the question used a different value (not 0.9) but yeah generally that was the principle
torn jolt
oop fixed
actually I feel like I'm speaking bs 
I'll delete
I'll let someone deal with this lol
crystal cobalt
actually I feel like I'm speaking bs <:cheeto:1074397590805823582> I'll delete
No i think you might be right yeah
glossy valveBOT
hiii
crystal cobalt
I think
torn jolt
why min tho they aren't like changing are they
oh wait I think I just understood what that notation is implying
crystal cobalt
The "mutual area" can't be more than the entire probability of A or B right? 😭
torn jolt
yeah fair enough
crystal cobalt
Okay so i think the site
torn jolt
😅
torn jolt
glossy valveBOT
crystal cobalt
,,\mbb{P} (A \cup B) \geq \operatorname{max} {\mbb{P}(A), \mbb{P}(B)}
glossy valveBOT
hiii
crystal cobalt
also join the $\le$ gang and abandon $\leq$
crystal cobalt
**hiii**
maybe that's what they meant?
Honestly idk what's going on lmao
But this makes sense ig?
torn jolt
I think just use Ur intuition
😅
I mean unlikely
don't see how an intersection can be bigger than the set itself
torn jolt
crystal cobalt
But yeah okay thanks~
torn jolt
nw good luck
crystal cobalt
nw good luck
also do you know the name for like describing
the "probability of a universal set"
surely that's not the right way to describe it
but i guess you get the idea
crystal cobalt
it's just 1 right? probability of everything
but i wanted to read something on stackexchange regarding it
torn jolt
the axioms of probability are:
\env{itemize}{
\ii Axiom 1: For any event $A, \map P A \ge 0$.
\ii Axiom 2: Probability of the sample space $S$ is $\map P S = 1$.
\ii Axiom 3: If $A_1, A_2, A_3, \dots$ are disjoint events, then $\map P{A_1\cup A_2 \cup \dots} =\map P{A_1} +\map P{A_2} + \map P{A_3} + \dots$
}
glossy valveBOT
crystal cobalt
Okay axiom 2 it is
torn jolt
It'd be 2
crystal cobalt
Indeed okay nice
U got this off wiki right?
Was it just probability?
Or what was the page
torn jolt
U got this off wiki right?
no I just made it myself 
idk where I got it from
I forgor
those are the probability axioms tho
crystal cobalt
no I just made it myself <:cryingLaughing:583069559955914752>
oh LOL okay thanks for writing it out then
okay i think that's about it
thanks again
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torn jolt
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compact leaf
$range of arccos{(x^2+1)/(x^2+2)}$
glossy valveBOT
arjun the learner
compact leaf
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astral wyvern
how do i graph the exponential function?
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how do i graph the exponential function?
stiff summit
you can put values of x into it, and then evaluate the function at those points
astral wyvern
this one has a k value
stiff summit
like x = 0 and x = 1
shadow lava
mb ill put it in another channel
stiff summit
mb ill put it in another channel
yep this one is taken
astral wyvern
like x = 0 and x = 1
so just plug in 0 and 1 into the function?
but how am i gonna get the ordered pairs? since thats just one value
stiff summit
so just plug in 0 and 1 into the function?
and then find f(0) and f(1)
shadow lava
yep this one is taken
yea i was writing the mathjax and i i said id write it then copy but sent on accident lol
stiff summit
but how am i gonna get the ordered pairs? since thats just one value
the ordered pairs are (0, f(0)) and (1, f(1))
astral wyvern
because this is what my teacher did and i dont get it
astral wyvern
the ordered pairs are (0, f(0)) and (1, f(1))
what about for the other ordered pair?
since i have to connect 2 points
stiff summit
an ordered pair is just a pair of two numbers, like (a,b)
stiff summit
Well, you can evaluate it at x = 2
That will give you a third ordered pair
And you can evaluate it at x = 3, x = 2.5, x = 2.1, and so on
stiff summit
i just plugged in 0 and i got 1021
so you could try other values that give a smaller y value
astral wyvern
so you could try other values that give a smaller y value
but thatd take forever
since id have to plug in multiple different values
and hope that its a proper one
which cant work in a test :(
stiff summit
since id have to plug in multiple different values
you could try a bigger value
astral wyvern
thatd make bigger numbers
its overall inefficient
unfortunately, i cant just plug random values and hope it works
stiff summit
thatd make bigger numbers
no, it wouldn’t
stiff summit
thatd make bigger numbers
consider x = 4
stiff summit
but is that for the x value or y value in the ordered pair?
you put in x = 4, you get out f(x) = 1
y = f(x) = 1
so the ordered pair is (x,y) = (x, f(x)) = (4, 1)
astral wyvern
ok
astral wyvern
so the ordered pair is (x,y) = (x, f(x)) = (4, 1)
thanks. so what about the other ordered pair? since i have to have 2 points to graph it
stiff summit
thanks. so what about the other ordered pair? since i have to have 2 points to g...
Another x value
This time you could do x = 5 or x = 9
since none of those are out of the given graph paper
astral wyvern
i tried both, then put it in desmos but it wasnt correct unfortunately
since there was no point like that on the graph
stiff summit
What did you do for both
astral wyvern
also, both gave me the same answer for some reason
stiff summit
Can you show your work
astral wyvern
i put the plugging in the calculator
stiff summit
since there was no point like that on the graph
By definition, the graph is the line that you get by joining up all the points that look like (x, f(x))
astral wyvern
since i inputted 5, then the ordered pair should be (5,-2.996)
lemme look to see if that point is there
stiff summit
since i inputted 5, then the ordered pair should be (5,-2.996)
I got -2
Maybe it might be a problem with the parens?
astral wyvern
maybe
because (5,-2) was a point on the graph
ill try again
ok i got it
how can I know what values to input?
for the function
also, i inputted 9 and got 2
but on the graph, the y value for 9 is -2.996
this is really confusing
wait, nevermind
it was a parens issue
both are correct
astral wyvern
how can I know what values to input?
but back to this
my main problem is finding the correct values
stiff summit
these are correct ordered pairs, they are on the graph
astral wyvern
Yes, I found that out
Im just wondering how we find the correct x values to input
since you know that i should input 5 and 9
stiff summit
If you input enough x values, you will eventually get a smooth curve
astral wyvern
hopefully i get better at this with more practice
ill try one last one
ill try to solve it first
i put in -3 and got 2
yet theres no point that says that on the graph
stiff summit
i put in -3 and got 2
Check your arithmetic again
It might be faster to do it in your head
astral wyvern
it keeps being incorrect
i have no idea why
can i just distribute the 4?
wait
i had the wrong 'a' value in there
now its correct
f(-3) = 0
(-3,0)
stiff summit
i had the wrong 'a' value in there
what is a
stiff summit
are you not calculating $$ 2 \bigl(\frac13\bigr)^{4(-3+3)} - 2 $$ in your head
glossy valveBOT
rysrobrgldvoelroep>vneae=u
stiff summit
also, f(5) = -2
ordered pair: (5,-2)
you left out some decimal places
astral wyvern
**rysrobrgldvoelroep>vneae=u**
i put it in the calculator, but i can try calculating it in my head
2/3(0) - 2
= -2
astral wyvern
you left out some decimal places
oh
but desmos also said that point was correct
its on the horizontal asymptote according to it
i get the general idea now
all thats left is more and more practice, and i'll get good
thank you so much, man
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compact leaf
$$n^{n^{n^n}} $$
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$$n^{n^{n^n}} $$
glossy valveBOT
arjun the learner
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