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#help-27
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manic sandal
what formula am i to use for b?
devout snowBOT
what formula am i to use for b?
scarlet sequoia
what formula am i to use for b?
so you if you have 'a' and 'd' u can use any formula for the sum of ap
manic sandal
however once i apply this, i get a polynomial which if i work out leads to the incorrect answer
or ig it just doesnt match with the answers list
scarlet sequoia
what's your 'a' and 'd'?
scarlet sequoia
so
manic sandal
the value for b is the supposed correct answer
scarlet sequoia
$$S_{n}=\frac{(2 \cdot 5 + (n-1)4)n}{2}=\frac{(10+4n-4)n}{2}=\frac{(6+4n)n}{2}=$$
$$=(3+2n)n=2555$$
woven radishBOT
Modus
scarlet sequoia
you got this?
manic sandal
okay so
manic sandal
is this that formula
scarlet sequoia
yes
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restive river
What does it mean when k times the unit digit and deleting the unit digit again?
supple knot
yes because it's one giant word salad
lime linden
what is this formula called?
devout snowBOT
what is this formula called?
neon folio
What formula?
supple knot
Not enough context
stone stump
density transformation formula or something?
lime linden
im dealing with jacobian matrix
the |J(x1, x2)|^-1 is the inverse determinant of a jacobian matrix
idk what the use of this is though
stone stump
iirc that's how you transform the density of a random variable
or something similar to this anyway
did you really find that formula without any other kind of context?
lime linden
iirc that's how you transform the density of a random variable
transform to what?
stone stump
something like X=(X_1, X_2), then you set Y=g(X) or something and then the density of Y can be computed using that formula and the density of X
something like that
oh well thank you we apparently have context
supple knot
oh well thank you we apparently have context
supple knot
Probably just change of variables
lime linden
wdym
supple knot
It doesn't have an official name because it's so simple
Change of variable is descriptive enough
lime linden
Probably just change of variables
whats the point in change of variables?
supple knot
Have you taken multivariate calculus?
lime linden
Have you taken multivariate calculus?
does it have to do with regions?
supple knot
You can just say no
lime linden
ok no
supple knot
Calculating probabilities or distribution functions with more than one dependent variable is sometimes hard in traditional Cartesian coordinates like x, y, z. So the Jacobian let's you evaluate them in other coordinates, say polar or spherical or cylindrical.
https://youtu.be/eho8xH3E6mE
e.g. multivariate gaussian in polar coordinates
lime linden
you need anything in calc 3 for prob just double integrals, pd, and multivariate gaussian distributions
which is hwta i will go over now
whats the point of that vid?
supple knot
just an example of multivariate distribution
lime linden
when will i ever need to use that formula?
supple knot
how do i know
wooden veldt
when will i ever need to use that formula?
probably next week
lime linden
i mean in what situation willn i use it
so the joint density function of a multivariable function, is just its jacobian matrix right?
supple knot
what 2 formulas are you thinking of and why do you care
lime linden
for changing variables formula
there is a g1 and g2
if you want to change the formulas of those respective equations
it would be 2 instead of 1
supple knot
what change? it's given to you
lime linden
the formula im talking about in 7.1
fy1, y2
im saying
if we want to use it
we would end up with 2 formulas
since there is functions g1 and g2
supple knot
7.1 is one formula. what other formula do you think there should be?
lime linden
if we want to change the variables of g1 and g2
wont there be 2 seperate formulas for each
lime linden
idk what else will i do with the formula?
lime linden
for which equation?
lime linden
yes
supple knot
the solution's given, what don't you understand about it?
supple knot
solution to what?
lime linden
the determinant of the jacobian matrix right?
lime linden
yes
so by finding the determinant of the jacobian matrix, i am finding the change of variables through that?
nvm ill just take a break
this is confusing
that formula
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vernal apex
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vernal apex
I keep on getting this wrong
I put 0.95 for percentile, df1 = 3, df2 = 8
so qf(0.95,3,8)
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vernal apex
<@&286206848099549185>
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hot steeple
does qf test both sides
vernal apex
does qf test both sides
Not sure
hot steeple
I looked it up a bit
Qf gives the chance that a random number is below or equal to a given percentile
vernal apex
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inland jolt
,w 2*sqrt(2)≥3-1/(2)
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,w 2*sqrt(2)≥3-1/(2)
woven radishBOT
inland jolt
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tardy brook
I read from some paper that if n=pq where p and q are distinct primes lambda(n)=lcm(p-1,q-1) then gcd(lambda(n),n)=1
devout snowBOT
I read from some paper that if n=pq where p and q are distinct primes lambda(n)=...
tardy brook
can anyone have a proof or explain why that is true
also lambda(x) is carmichael's function of x
frail basin
i don’t think it’s true, for example p=3 q=7
tardy brook
yea I think of it after I ask the question
at page 226 second paragraph fifth line it says like that
I will close it now
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twilit cobalt
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twilit cobalt
anyone have a clue on how to do c)
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@twilit cobalt Has your question been resolved?
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@twilit cobalt Has your question been resolved?
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keen urchin
Having an issue with this Taylor series, have no Idea what's wrong with it
keen urchin
wooden wraith
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mild summit
I dont understand how they concluded that the primitive of sin^4t*cost is sin^5t/5
devout snowBOT
I dont understand how they concluded that the primitive of sin^4t*cost is sin^5t...
neon aspen
I dont understand how they concluded that the primitive of sin^4t*cost is sin^5t...
let u = sint
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long rampart
if you increase your travel speed by x% why does your travel time not reduce by x%?
devout snowBOT
if you increase your travel speed by x% why does your travel time not reduce by ...
loud root
because they're not proportional:
$$speed=\frac{distance}{time}$$
if you reduce the speed by x%, the time is going to increase by $\frac{1}{x}%$
woven radishBOT
Andrea276
long rampart
Oh awesome thank you! I haven't mathed in a while and I have a placement exam as a non-traditional student. I was so confused why I couldn't get the same answer with x=k/y for an inverse relationship as just increasing both numbers by the percentage of the whole if that makes sense.
Sorry if it is a stupid question! I appreciate the insight!
loud root
Don't worry, it wasn't a stupid question, it's not obvious
scarlet badger
Hi.
We're throwing 2 dies one after another. D_1 has 2/7 probability for "4", D_2 has 2/7 probability for "3". All other probabilities are normal ("1/7").
Is it correct to say that the probability space is (D_1 x D_2) U (D_2 x D_1)?
Is the probability function correct, if I say:
Pr(d_1, d_2) = {
2/7 * 2/7 if d_1 = 4 AND d_2 = 3
2/7 * (5 * 1/7) if d_1 = 4 AND d_2 != 3
(5 * 1/7) * 2/7 if d_1 != 4 AND d_2 = 3
(5 * 1/7) * (5 * 1/7) if d_1 != 4 AND d_2 != 3
?
devout snowBOT
Hi.
We're throwing 2 dies one after another. D_1 has 2/7 probability for "4", D_...
scarlet badger
I've changed the Pr now
if we add up all 4 cases we'll land at 49/49
which correctly equals 1
but should there also be a Pr(d_2, d_1) with basically the same cases? This would account for that we start with dice_2 instead of dice_1
or does the order of arguments not matter in a Pr-function (like if it would matter, one would write the cases down)?
devout snowBOT
@scarlet badger Has your question been resolved?
scarlet badger
To reduce the question: Do I have to account for the order in defining a) probability space? b) probability function?
(D1 x D2) U (D2 x D1) true or false?
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wheat cave
Hi.
We're throwing 2 dies one after another. D_1 has 2/7 probability for "4", D_...
Naturally I would only define prob space D1 x D2
And i do define D1 as the first dice rolled whenever he's dice A or dice B
scarlet badger
Hello @wheat cave
wheat cave
Hello @scarlet badger
scarlet badger
why would D1xD2 suffice? Is order not important in probability spaces?
scarlet badger
I was thinking of D1 = {1_a, 2_a, ..., 6_a}
wheat cave
I mean
wheat cave
If i was doing it, my prob space would be [[1;6]]x[[1;6]]
scarlet badger
I'll do like that aswell then
while we're at it, can I ask you another question?
If I draw 5 of 52 poker cards at once, and want exactly 2 A's, exactly 2 J's or exactly 2 Q's
is the correct calculation 5C2 * 3 * 2/52 * 1/51
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restive river
what does a 4 component vector look like
devout snowBOT
what does a 4 component vector look like
lethal copper
what does a 4 component vector look like
I dont know what you mean i just theres bist another value
lethal copper
You cant visualize it often its the time i think
lethal copper
In what context
restive river
idk
lethal copper
Where have you seen it
woven radishBOT
lethal copper
Thats 2 dimensional x is 7 y is 3
reef pilot
@analog trellis
devout snowBOT
<@234339303944224768>
reef pilot
it closed
analog trellis
Yes. It is the chain rule.
I might as well include the first part before this too since it's small for completeness.
reef pilot
i see
analog trellis
I'd set
F(x, y, z) = f(x, y, z) - 6 = 0 then differentiate with respect to y to obtain
f_2 + f_3 ∂z/∂y = 0, etc. (f_y + f_z ∂z/∂y = 0.)
Where f_2 is the derivative of f with respect to the second variable in the bracket, here it's y.
We just need to acknowledge here that z is considered the dependent variable and x, y are to be considered the independent variables.
It might not always be the most useful for the problem you have but there's a really nice memory technique for more complicated problems with more than one equation.
reef pilot
It might not always be the most useful for the problem you have but there's a re...
like if x and y were dependent on other variables?
analog trellis
Like here.
Obviously, the memory rule won't be clear to you but you might not even want to worry about this stuff for your current studies.
The numerator and denominator are both different jacobians which can be computed and are easy to set up with the knowledge of the text. It saves you having to set up everything each time.
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vale valve
How do I determine the number of solutions to the equation -5 = x +3x^2
without solving it?
proud perch
Move all the terms to one side
vale valve
Move all the terms to one side
Okay, then what?
proud perch
find the discriminant
vale valve
Do I need to find the roots?
bold prism
How do I determine the number of solutions to the equation -5 = x +3x^2
without...
will always be 2, now real solutions could be 0,1,2 for that you'd need to find the discriminant as mentioned before
proud perch
will always be 2, now real solutions could be 0,1,2 for that you'd need to find ...
Not always
Double roots
bold prism
ah yes
vale valve
will always be 2, now real solutions could be 0,1,2 for that you'd need to find ...
I just need to figure out the number, not what the actual solutions are
proud perch
But only the real solutions?
vale valve
how do I figure out the # of solutions without solving it?
vale valve
But only the real solutions?
It's not specified
proud perch
Then yeah just take the discriminant
vale valve
So, 2?
bold prism
have you been taught complex solutions?
vale valve
Not that I remember
bold prism
yeah then its only real solutions
pseudo basin
have you been taught the discriminant
vale valve
yes
pseudo basin
this problem is a dead ringer for it
pseudo basin
putting your equation in standard form yields:
3x^2 + x + 5 = 0
loud root
Am I supposed to look for roots?
It asks you to find the number of solutions without solving it, so no, you can't do that
pseudo basin
you are supposed to calculate the discriminant
loud root
You have to use the discriminant as Ann suggested
vale valve
Okay I'll do that
pseudo basin
and infer the solution count from the sign thereof
loud root
How did you find that?
vale valve
b^2-4ac
loud root
3x²+x+5=0
This is your equation, right?
vale valve
well that's the standard form, yeah
loud root
What's b?
vale valve
1?
loud root
If the discriminant is less than 0, the equation has no real solutions, if it's 0 the equation has one real solution and if it's greater than 0 the equation has 2 solutions
vale valve
oh so roots
loud root
roots means real solutions
vale valve
oh
Tysm @loud root, @bold prism and @pseudo basin , appreciate it lots
(unrelated) I have not slept in 2 nights and I'm going to try my hardest to sleep tonight thank you once again
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silk plank
Hi everyone
devout snowBOT
Hi everyone
silk plank
Hi everyone
It's given that "x" more than "y" and "z" more than "t" which one of these options is true
x>y
z>t
potent nebula
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silk plank
Hi everyone
<@&286206848099549185> could you help please
timber pebble
<@&286206848099549185> could you help please
what is the prompt?
which one are you looking at
its not really clear what youre tasked to do here
but i can be stupid sometimes so maybe its just not obvious to me 
can you clarify?
timber pebble
alright
silk plank
Could u explain please
silk plank
do you have gut feeling about any of them?
D i guess, but i am not confident
timber pebble
so i would start like this
write down what you know, and what youre curious about
oops i accidentally a letter
here we go
@silk plank
the hope is that you start with one side of the inequality, and through clever substitution, you end up at the other side
and the inequality points in the correct direction
the work is logical; you need to make sure that when you make a substitution, the inequality is actually supposed to point one way or another afterwards
I am saying that if we replace 7t with 7z, we will have a larger quantity
because t < z, so it follows that 7t < 7z
make sense?
timber pebble
lets think it through
silk plank
And D
timber pebble
you start with x < y
silk plank
Yes
timber pebble
multiply by 13
still true
13x < 13y
what happens when you multiply by a negative
silk plank
Swap the inequality sign
timber pebble
yea
so -13x > -13y
another way of thinking of it is
if you substitute y for x
you are removing a larger amount than before
so you cannot say its bigger
do you see?
silk plank
you start with x < y
From where did u got
timber pebble
oh
silk plank
That x less than y
silk plank
Thank u a lot
silk plank
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wary halo
the 3 question?
devout snowBOT
the 3 question?
brazen star
factor out (2x^3 - x^2 - x)
or just divide by (2x^3 - x^2 - x)
either way works
@wary halo you there?
wary halo
yes
wary halo
(x-2)-(2-x)=0 ?
opaque haven
you cant really divide by that term
factoring is the only option
if the term is equal to 0, which it very well could be, dividing by it is undefined
so youre gonna have to factor
lilac pulsar
hello can someone please help me with this question? i don't know what its asking or even where to start
devout snowBOT
hello can someone please help me with this question? i don't know what its askin...
lilac pulsar
hello
where would i start??
i have the answers by the way i just dont know how to get there
plush light
Well, for the first one you could probably draw a graph monitoring the amount of drugs in the bloodstream.
Every 6 hours one serving of drugs are added to the bloodstream while the previous one is decreased by 0.625
$\left(a+\left(a+\left(a+\left(a\cdot0.375\right)\cdot0.375\right)\cdot0.375\right)\cdot0.375\right)$
woven radishBOT
dabbingpotato
plush light
This would be the first day I think
plush light
a would be x in this situation
a is the amount of drug registered every time the user takes it
lilac pulsar
**dabbingpotato**
so do i expand this
plush light
So for example if I got 2 mg of drug in my bloodstream every shot
lilac pulsar
yes
plush light
so do i expand this
i believe you could simplify it to the answer for question a
To solve part B, it would be x(1 + 0.375 + 0.375^2 ---- + 0.375^39)
$x(1+0.375+0.375^2 - + 0.375^39) = 8$
woven radishBOT
dabbingpotato
lilac pulsar
So for example if I got 2 mg of drug in my bloodstream every shot
can u continue explaining this
i still dont understand what u did for a
plush light
ok
say if I got 2mg every shot, every 6 hours there would be 0.375 of the drug left
right?
lilac pulsar
yes
plush light
so it would be 2*0.375
now say you got the it agian
you would add 2 mg to the amount you already have
so it would be 2+(2*0.375)
lilac pulsar
so it would be 2*0.375
why isnt it just this x2
plush light
what is x
plush light
after 6 hours its 2*0.375
lilac pulsar
yes so 12 hours is just double that?
lilac pulsar
ohh so ur taking like 2 + 2*0.375 and multiply that whole thing by 0.375 yes?
plush light
x(1+0.375) this is second time your putting it in
plush light
ohh so ur taking like 2 + 2*0.375 and multiply that whole thing by 0.375 yes?
yep
x(1+0.375+0.375^2) this is after putting it in 3 times
x(1+0.375+0.375^2+0.375^3) after putting it in 4 times
lilac pulsar
so does x represent the dose in blood after 6 hours
plush light
x represents how much you put in each time
lilac pulsar
x(1) this is when you first put it in
but in this case if x was like 2mg then wouldnt it just be 2 x 1
plush light
yep, if you just put it in
after 6 hours you put it in again, how much should be in your blood stream now?
plush light
$x(1 + 0.375 + 0.375^2)$
woven radishBOT
dabbingpotato
plush light
Basically, the 1 represents the new batch of drugs coming into your bloodstream when you get the shot, the 0.375 represents the amount of drugs from the previous shot still remaining in your bloodstream, and the 0.375^2 represents the amount of drugs still left in you bloodstream from your first shot
Do you see how this equation works now?
plush light
its a bit challenging
lilac pulsar
yes so i think u should come back in 3 minutes because thats when i will get stuck 
nvm i got the answer i just dont know if i did it the right way
ook i solved c
thx a lot for ur help
empty flame
hello
empty flame
i want to prove that abs(sum of the first n numbers) is less than or equal to the sum of absolute value of the first n numbers
what i did is that i used the formula of adding the first n numbers which is n(n+1)/2
the first one will be abs(n(n+1))/2
my problem is with the second one
midnight dirge
its triangle inequality applied n-1 times
pastel pasture
the first one will be abs(n(n+1))/2
are n naturals
I don't think n is limited to naturals
empty flame
no its not limited to naturals
empty flame
its triangle inequality applied n-1 times
i dont think that it is but let me send you a screenshot of the question
here n(n+1)/2 isnt true ?
bc the summation isnt just of natural numbers
half vessel
you can prove it by induction and triangle inequality
midnight dirge
triangle inequality
|a+b| <= |a| + |b|
so applied n-1 times its
|a1 + a2 + ... + an| <= |a1| + |a2 + ... + an|
<= |a1| + |a2| + |a3 + ... + an|
<= |a1| + |a2| + |a3| + ... + |an|
expand the summation and u get that
half vessel
here n(n+1)/2 isnt true ?
yes it's not true
midnight dirge
here n(n+1)/2 isnt true ?
i mean it is true, but thats not how u go about solving/showing this inequality
empty flame
how can i express the second summation in terms of this formula
half vessel
yes it's not true
oh i meant it's not true for any other series
main scarab
The name is such a clickbait
I thought this channel was asking calculus 😢😠😠
empty flame
The name is such a clickbait
I thought this channel was asking calculus 😢😠😠
i am learning summation bc ill need it for integration which i am learning now
so its not a clickbait XD
midnight dirge
how can i express the second summation in terms of this formula
the second summation is just |a1| + |a2| + |a3| + ... + |an|
midnight dirge
triangle inequality
|a+b| <= |a| + |b|
so applied n-1 times its
|a1 + a2 + ... +...
oh sorry, all = here should be <=
empty flame
triangle inequality
|a+b| <= |a| + |b|
so applied n-1 times its
|a1 + a2 + ... +...
how will i get these results
midnight dirge
the starting triangle inequality? |a+b| <= |a| + |b|?
empty flame
i mean the first sum is abs(a1+a2+...+an-1+an)
midnight dirge
yes
empty flame
and the second is abs(a1) + abs(a2) + ...+abs(an-1) + abs(an)
midnight dirge
why so
empty flame
i can say that the first one is abs(n(n+1))/2 but i cant find a similar formula for the second one if i can then it will be solved
half vessel
Suppose $|a_1+...+a_n|\leq |a_1|+...+|a_n|$. For n+1 terms, by triangle inequality, $|a_{n+1}+a_1+...+a_n|\leq |a_{n+1}|+|a_1+...+a_n|\leq |a_{n+1}|+|a_1|+...+|a_n|$
woven radishBOT
JellyShark
half vessel
yeah that's right
empty flame
i have a question
proof by induction is to show that the statement is true for 1 and suppose that its true for k then show that it is true for k+1 according to the assumption which will prove that the statement is true for all n ??
midnight dirge
um its morelike
define a proposition Pn
show that it is true for P1
assume Pk is true
show that P(k+1) is true when Pk is true
as P1 is true and Pk implies Pk+1, Pn is true for all n in N+
empty flame
as P1 is true and Pk implies Pk+1, Pn is true for all n in N+
why not in R
midnight dirge
because we generally start from 1 and we do it in increments of 1, so all natural numbers
empty flame
pictures of what
midnight dirge
if u want to show something in R then u have to use a different method
empty flame
this guy means something bad if i am right ?
midnight dirge
show that P(k+1) is true when Pk is true
if u want it show it for Z (aka negative numbers as well ) then u can do induction as earlier, but also show that Pk imples Pk-1
empty flame
Maybe picture of this
this looks nice
empty flame
Maybe picture of this
but are all the letters here variables ?
or some are constants ??
empty flame
if u want it show it for Z (aka negative numbers as well ) then u can do inducti...
oh ok
but if u prove that its true for pk+1 and pk-1 then its true for all numbers bc you didnt put a condition that k belongs to N
midnight dirge
well
ur initial statement is P1 is true
or P0 whichever u show first
u cant possibly show all R is true as there are infinitely many numbers in R from 0 to 1 for instance
not by using induction anyway
empty flame
yea but you showed that its true for some constant k
midnight dirge
not that i know of anyway
yea but thats essentially saying for our base case so in the original statement
empty flame
where k is a number you dont specify where k lies
empty flame
yea but can P1 be a real number
midnight dirge
something like P1.5 is not true unless u first show it is true
empty flame
P is the statement so it can be that the statement will result in a real number after changing its variable by 1
midnight dirge
if u modify induction u might be able to do it but i dont think ive seen it
like instead of Pk implies Pk+1 u would have something like Pk implies Pk+delta where delta>0 or similar?
but ive never seen it used that way
or if u can even do that
in the case of Pk implies Pk+1, if u have P1 as true, u can get P2 as true, but u cant get P1.1 or P2.1 as true
u can show P1.1 is true and that will imply P2.1 is true as well but then there will be another real number eg 1.11, 1.111, 1.1111
and u have to show them one by one which u cant do to my knowledge
empty flame
but if you prove it for a rational number then cant u generalize that to all rational numbers like you do to natural numbers ?
midnight dirge
nope
its because the difference between each natural number is 1 so it works
but the difference between each real number can be infinitely small
empty flame
ok but i guess that if you show that its true for P2.1 for example then it should work for P2.2 and P2.3 and so on bc the difference is 0.1 between them ?
empty flame
hmm
midnight dirge
like instead of Pk implies Pk+1 u would have something like Pk implies Pk+delta ...
i mean thats why i said this
but generally ive mainly seen it in natural numbers as its used to show a certain property of a series so n will always be a natural number
restive river
devout snowBOT
restive river
Is this correct?
Since 1/2 in the k value
And the reciprocal would be 2?
It's fine I'll just put that as the answer
.close
restive river
devout snowBOT
<:bleak:877093280905592842>
grim agate
Get some relation for ratio of roots of equation in terms of sum and product of roots
Let l m be roots of first equation and n o be roots of second equation
So we have $\frac l m = \frac n o$
woven radishBOT
grim agate
And $\frac m l = \frac o n$
woven radishBOT
grim agate
Add them so you’ll have a relationship to compare
$\frac m l + \frac lm = \frac n o + \frac o n$
woven radishBOT
grim agate
Hmm?
grim agate
Did you try to proceed from here and solve this?
restive river
i dont think i would be able to solve by comparing
grim agate
$\frac {m^2 + l^2 } {ml} = \frac {n^2+o^2}{on}$
woven radishBOT
grim agate
$\frac {(m+l)^2 -2ml } {ml} = \frac {(n+o)^2-2no}{on}$
woven radishBOT
restive river
oh wait
grim agate
Now plug sum of roots and product of roots
grim agate
grim agate
terms cancel out as always
Wym?
grim agate
Hmm?
restive river
and same happened for this one
restive river
nu
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naive estuary
It's a bit tricky for me because of the 11 in the parentheses...so basically i have a bit of trouble starting it off
devout snowBOT
It's a bit tricky for me because of the 11 in the parentheses...so basically i h...
main gull
It's a bit tricky for me because of the 11 in the parentheses...so basically i h...
Distribute
Using the concept of $a(b + c) = ab + ac$
woven radishBOT
dldh06
woven radishBOT
jswatj
naive estuary
Oh, what i meant was subtract 2 from the 2 in 5h+2
main gull
use the concept he mentioned on $2(11-h)$
Way to gender assume... jk
main gull
Quick question what do you mean by "$" just want to make sure
It's the method to do the latex
Aka the math font text thing
Like 1/2 looks fine but $\frac{1}{2}$
woven radishBOT
dldh06
naive estuary
Oh
restive river
Way to gender assume... jk
apologies
devout snowBOT
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finite shoal
Hey guys im about to be a sophmore and some of the stuff they have on this packet I’ve never seen before so I need some help thanks!
devout snowBOT
Hey guys im about to be a sophmore and some of the stuff they have on this packe...
finite shoal
^47
I honestly don’t get what they tryna make me do so idk what they mean
Then this one is the last thanks!
Oops forgot about 27
midnight dirge
..ask one question at a time
finite shoal
Mb bro bro
midnight dirge
do u know what are piecewise functions
finite shoal
No
midnight dirge
this is an example
so depending on the value of x, the function will be a bit different
so they want u to give a function in this form to fit the graph given
midnight dirge
um ignore one side of the v first and try to find a function that fits that
midnight dirge
um ignore one side of the v first and try to find a function that fits that
such tht u get a line
finite shoal
I see on one half its -2 the other half is +2 slope
midnight dirge
mhm yes and what equation would say the one with a 2 gradient slope take one?
midnight dirge
yes
finite shoal
Can I write 2x
I see one is on the thing -1/2x so I’m guessing I can write the slope as one
midnight dirge
wait sry, what do u mean by that?
finite shoal
So on the example
It says
-1/2x
That’s the slope of a line there
So can I write plus or minus 2x
midnight dirge
wait did u move on to another Q?
finite shoal
No
Im still on the piecewise function
I just don’t know how to write the function I
Like idk how to write this as this type of function
midnight dirge
howd u get the -1/2x though
midnight dirge
oh..
um
that was just an example of a random piecewise function i got by searching it
to kinda visualise what it is
finite shoal
Sorry if im kinda slow I’ve never heard of this stuff befo
midnight dirge
not exactly related to urs especially not the numbers, maybe except by coincidence
yea anyway
um
so whats the point that the v is at
the bottom point
finite shoal
1,-4
midnight dirge
Sorry if im kinda slow I’ve never heard of this stuff befo
nah u are good u managed to get the slopes
midnight dirge
1,-4
ok good
then so what is the equation of a line that passes through 1,-4 with gradient of 2
midnight dirge
yep
finite shoal
Ok and the other one is y=-2x-2?
midnight dirge
then we want to write it in this form
so in this case the line is split into 2 parts, when x<=1 and when x>1
finite shoal
Yes
midnight dirge
and when its <=1 u use the equation u just calculated for the approriate line
midnight dirge
in this case, yep
midnight dirge
write it in this form, so u write the curvy thing, then u write
-2x-2 , x<1
2x-6 , x>=1
finite shoal
Ok is that it?
midnight dirge
yep
finite shoal
Alright can you help me on the next one?
midnight dirge
yea sure
finite shoal
47
Im guessing it’s saying the volleyball can be either 26.5 or 25.5
And its ok
I just don’t know how to write that basically
midnight dirge
they said absolute value inequality
|26 - x|<=0.5
this essentially means that x cannot differ from 26 by more than 0.5
finite shoal
Yes
midnight dirge
i had no idea what absolute value inequality was but i googled it haha
finite shoal
Yea dude these teachers
Makin me rmr stuff from like
2 years ago
And half this stuff I’ve never seen
midnight dirge
lol idt ive seen that term till now
finite shoal
Do you know what this question is asking
19,20,21
It gives x and y
And then it says to find y when x=3 which is weird
midnight dirge
they say x and y vary directly
this means that when 1 increases the other increases as well
aka if u draw a graph theyve a slope of 1
midnight dirge
oh crap
yes
im wrong u are right
haha
yea it instead means
if u draw a graph it passes through 0
oops
midnight dirge
i think u let the number of small windmills be x and the other be y
then u make an equation where the total energy made from them is 180
then make a graph
midnight dirge
yea
but u shld also write a statement on which u let be x and y as it isnt stated in the question
so write a little statement on that
finite shoal
Yea
midnight dirge
and i guess u should then shade the region that is greater than 180
midnight dirge
27?
finite shoal
Ya
midnight dirge
so try to graph the function
it will be similar to the piecewise function we got first
midnight dirge
um when the part in the absolute value is positive and when it is negative
midnight dirge
D= a-1.50?
um small d, then yes u graph that for one region
finite shoal
And then +1.50
finite shoal
Ok i graphed it
So since it’s asking me for the values where it’s more than 1.50?
Becuase that’s the difference
finite shoal
It’s a v
midnight dirge
its asking for when d=0.25
midnight dirge
not really
it could be them making less money as well
its more like a being the prediction
finite shoal
So what values will d be .25?
midnight dirge
wait i mean 1.5 is the prediction
a=1.75 or 1.25
so the prediction is 1.5
a is the actual value
if a is more than 1.5, itll lead to some difference, same when a is less than 1.5
d is like how much is this difference i guess
midnight dirge
wait no
i already told u the answer
its just a = 1.75 and 1.25
but u should also probably draw that on th graph
so draw a line where d=0.25
midnight dirge
np
finite shoal
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sinful creek
devout snowBOT
sinful creek
Did I mess up by multiplying my num. by just sqrt5 ??
exotic stump
i'm not exactly sure what you did for step 1
sinful creek
ohhhh
restive river
so you multiply by (sqrt5 + 2) over itself
restive river
and that gets your answer
exotic stump
try not to give answers directly
restive river
try not to give answers directly
yea good point, my b.
can you see why if you multiply the bottom and top by sqrt5 as you did why it would be incorrect though?
sinful creek
yes indeed, and how would I know when to take a conjugate of anything?
restive river
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sinful creek
thanks for all the help guys :))
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drowsy trout
Hi, can anybody explain a theorem to me, i mean why it is true?
devout snowBOT
Hi, can anybody explain a theorem to me, i mean why it is true?
drowsy trout
Why would the max gradient be L
max norm*
Thanks in advance!
nvm im dumb i think i got it after washing my face
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lunar raft
I'm confusedbon why points C and R are congruent
devout snowBOT
I'm confusedbon why points C and R are congruent
wicked turtle
,rotate
woven radishBOT
wicked turtle
the markings indicate that the angle at C equals the angle at R, and the two sides that join at C have the same length as the two sides that join at R
lunar raft
The markings?
wicked turtle
the dark shaded "cone" at each angle
and the single and double ticks on the line segments
moreover the problem statement itself says "with congruent angles and sides marked"
lunar raft
Are T and A congruent?
wicked turtle
and says outright that angle C = angle R
wicked turtle
Are T and A congruent?
well, consider side-angle-side
wicked turtle
what theorems do you know that allow you to conclude that two triangles are congruent?
lunar raft
Pythagoras
wicked turtle
well this isn't a right triangle so that won't help here
lunar raft
I dont get the 3 letter thing
wicked turtle
surely your teacher stated what SAS says when he/she mentioned it?
wicked turtle
,rotate
woven radishBOT
lunar raft
Nvm
lunar raft
Yes
wicked turtle
should surely be covered in there
red osprey
How would you approach #2?
devout snowBOT
How would you approach #2?
topaz axle
how did you do #1?
red osprey
how did you do #1?
Im not sure if its right, but what I did was take the weight of cells and divided by the weight of a single cell to get the # of cells
it also says on the bottom of the page, that (a) and (b) are not consistent
devout snowBOT
@red osprey Has your question been resolved?
devout snowBOT
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inner oyster
devout snowBOT
inner oyster
<@&286206848099549185>
devout snowBOT
@inner oyster Has your question been resolved?
still pulsar
need a walkthrough?
inner oyster
yes
still pulsar
Gimme 5 mins, I'm on switching bus
inner oyster
aright its fine
still pulsar
aright its fine
first draw a lime from O to the intersection of x and 2x
find that hyp, and note that is the radius
then you can also observe that the angle that makes up the arc of the shaded region is 90 degrees from the triangle you just drew (also draw one on the other side)
this means the arc length is exactly <insert fraction> of the circle's circumference (use 2 pi r)
Solve for x, using the fact that the radius = the hyp, and the add the perimeters of the shaded area together
still pulsar
what does yhat simplify to
inner oyster
3
still pulsar
$3 \pi$
woven radishBOT
Rαιη
inner oyster
idk how to solve for x
still pulsar
ok, you have the "triangles" drawn right?
inner oyster
ye
still pulsar
What is the length (base) and height of the triangle?
inner oyster
6x6
still pulsar
not quite
inner oyster
x+x/2?
still pulsar
inner oyster
yah
inner oyster
pythagorean theorem?
still pulsar
$a^2+b^2=c^2$
woven radishBOT
Rαιη
inner oyster
ya
inner oyster
6
still pulsar
no
inner oyster
x^2+x^2=6